id	sid	tid	token	lemma	pos
ejpam-2648	1	1	european	european	PROPN
ejpam-2648	1	2	journal	journal	PROPN
ejpam-2648	1	3	of	of	ADP
ejpam-2648	1	4	pure	pure	ADJ
ejpam-2648	1	5	and	and	CCONJ
ejpam-2648	1	6	applied	apply	VERB
ejpam-2648	1	7	mathematics	mathematic	NOUN
ejpam-2648	1	8	vol	vol	NOUN
ejpam-2648	1	9	.	.	PROPN
ejpam-2648	2	1	10	10	NUM
ejpam-2648	2	2	,	,	PUNCT
ejpam-2648	2	3	no	no	INTJ
ejpam-2648	2	4	.	.	NOUN
ejpam-2648	2	5	4	4	NUM
ejpam-2648	2	6	,	,	PUNCT
ejpam-2648	2	7	2017	2017	NUM
ejpam-2648	2	8	,	,	PUNCT
ejpam-2648	2	9	749	749	NUM
ejpam-2648	2	10	-	-	SYM
ejpam-2648	2	11	762	762	NUM
ejpam-2648	2	12	issn	issn	PROPN
ejpam-2648	2	13	1307	1307	NUM
ejpam-2648	2	14	-	-	SYM
ejpam-2648	2	15	5543	5543	NUM
ejpam-2648	2	16	–	–	PUNCT
ejpam-2648	3	1	www.ejpam.com	www.ejpam.com	X
ejpam-2648	3	2	published	publish	VERB
ejpam-2648	3	3	by	by	ADP
ejpam-2648	3	4	new	new	PROPN
ejpam-2648	3	5	york	york	PROPN
ejpam-2648	3	6	business	business	PROPN
ejpam-2648	3	7	global	global	PROPN
ejpam-2648	3	8	hasse	hasse	PROPN
ejpam-2648	3	9	-	-	PUNCT
ejpam-2648	3	10	schmidt	schmidt	NOUN
ejpam-2648	3	11	derivations	derivation	NOUN
ejpam-2648	3	12	on	on	ADP
ejpam-2648	3	13	banach	banach	NOUN
ejpam-2648	3	14	-	-	PUNCT
ejpam-2648	3	15	jordan	jordan	NOUN
ejpam-2648	3	16	pairs	pair	NOUN
ejpam-2648	3	17	hassan	hassan	PROPN
ejpam-2648	3	18	marhnine1	marhnine1	PROPN
ejpam-2648	3	19	,	,	PUNCT
ejpam-2648	3	20	chafika	chafika	PROPN
ejpam-2648	3	21	zarhouti1,∗	zarhouti1,∗	NOUN
ejpam-2648	3	22	1	1	NUM
ejpam-2648	3	23	av	av	PROPN
ejpam-2648	3	24	.	.	PUNCT
ejpam-2648	4	1	my	my	PRON
ejpam-2648	4	2	abdelaziz	abdelaziz	ADJ
ejpam-2648	4	3	,	,	PUNCT
ejpam-2648	4	4	souani	souani	NOUN
ejpam-2648	4	5	,	,	PUNCT
ejpam-2648	4	6	b.p	b.p	PROPN
ejpam-2648	4	7	.	.	PROPN
ejpam-2648	4	8	3117	3117	NUM
ejpam-2648	4	9	tangier	tangy	ADJ
ejpam-2648	4	10	90000	90000	NUM
ejpam-2648	4	11	,	,	PUNCT
ejpam-2648	4	12	morocco	morocco	PROPN
ejpam-2648	4	13	abstract	abstract	NOUN
ejpam-2648	4	14	.	.	PUNCT
ejpam-2648	5	1	the	the	DET
ejpam-2648	5	2	aim	aim	NOUN
ejpam-2648	5	3	of	of	ADP
ejpam-2648	5	4	this	this	DET
ejpam-2648	5	5	paper	paper	NOUN
ejpam-2648	5	6	consists	consist	VERB
ejpam-2648	5	7	in	in	ADP
ejpam-2648	5	8	establishing	establish	VERB
ejpam-2648	5	9	the	the	DET
ejpam-2648	5	10	automatic	automatic	ADJ
ejpam-2648	5	11	continuity	continuity	NOUN
ejpam-2648	5	12	of	of	ADP
ejpam-2648	5	13	hasseschmidt	hasseschmidt	ADJ
ejpam-2648	5	14	derivations	derivation	NOUN
ejpam-2648	5	15	on	on	ADP
ejpam-2648	5	16	banach	banach	NOUN
ejpam-2648	5	17	-	-	PUNCT
ejpam-2648	5	18	jordan	jordan	NOUN
ejpam-2648	5	19	pairs	pair	NOUN
ejpam-2648	5	20	and	and	CCONJ
ejpam-2648	5	21	banach	banach	NOUN
ejpam-2648	5	22	-	-	PUNCT
ejpam-2648	5	23	jordan	jordan	PROPN
ejpam-2648	5	24	algebras	algebras	PROPN
ejpam-2648	5	25	satisfying	satisfy	VERB
ejpam-2648	5	26	some	some	DET
ejpam-2648	5	27	algebraic	algebraic	ADJ
ejpam-2648	5	28	conditions	condition	NOUN
ejpam-2648	5	29	.	.	PUNCT
ejpam-2648	6	1	namely	namely	ADV
ejpam-2648	6	2	,	,	PUNCT
ejpam-2648	6	3	higher	high	ADJ
ejpam-2648	6	4	derivations	derivation	NOUN
ejpam-2648	6	5	on	on	ADP
ejpam-2648	6	6	semiprimitive	semiprimitive	ADJ
ejpam-2648	6	7	banach	banach	NOUN
ejpam-2648	6	8	-	-	PUNCT
ejpam-2648	6	9	jordan	jordan	NOUN
ejpam-2648	6	10	pairs	pair	NOUN
ejpam-2648	6	11	and	and	CCONJ
ejpam-2648	6	12	semiprimitive	semiprimitive	ADJ
ejpam-2648	6	13	banach	banach	NOUN
ejpam-2648	6	14	-	-	PUNCT
ejpam-2648	6	15	jordan	jordan	PROPN
ejpam-2648	6	16	algebras	algebras	PROPN
ejpam-2648	6	17	are	be	AUX
ejpam-2648	6	18	continuous	continuous	ADJ
ejpam-2648	6	19	.	.	PUNCT
ejpam-2648	7	1	2010	2010	NUM
ejpam-2648	7	2	mathematics	mathematic	NOUN
ejpam-2648	7	3	subject	subject	NOUN
ejpam-2648	7	4	classifications	classification	NOUN
ejpam-2648	7	5	:	:	PUNCT
ejpam-2648	7	6	17c65	17c65	NUM
ejpam-2648	7	7	,	,	PUNCT
ejpam-2648	7	8	46h40	46h40	NUM
ejpam-2648	7	9	,	,	PUNCT
ejpam-2648	7	10	46h70	46h70	X
ejpam-2648	7	11	key	key	ADJ
ejpam-2648	7	12	words	word	NOUN
ejpam-2648	7	13	and	and	CCONJ
ejpam-2648	7	14	phrases	phrase	NOUN
ejpam-2648	7	15	:	:	PUNCT
ejpam-2648	7	16	derivation	derivation	NOUN
ejpam-2648	7	17	,	,	PUNCT
ejpam-2648	7	18	higher	high	ADJ
ejpam-2648	7	19	derivation	derivation	NOUN
ejpam-2648	7	20	,	,	PUNCT
ejpam-2648	7	21	automatic	automatic	ADJ
ejpam-2648	7	22	continuity	continuity	NOUN
ejpam-2648	7	23	,	,	PUNCT
ejpam-2648	7	24	banach	banach	NOUN
ejpam-2648	7	25	-	-	PUNCT
ejpam-2648	7	26	jordan	jordan	NOUN
ejpam-2648	7	27	pairs	pair	NOUN
ejpam-2648	7	28	,	,	PUNCT
ejpam-2648	7	29	banach	banach	NOUN
ejpam-2648	7	30	-	-	PUNCT
ejpam-2648	7	31	jordan	jordan	PROPN
ejpam-2648	7	32	algebras	algebras	PROPN
ejpam-2648	8	1	1	1	X
ejpam-2648	8	2	.	.	PUNCT
ejpam-2648	8	3	introduction	introduction	NOUN
ejpam-2648	8	4	higher	high	ADJ
ejpam-2648	8	5	derivations	derivation	NOUN
ejpam-2648	8	6	were	be	AUX
ejpam-2648	8	7	introduced	introduce	VERB
ejpam-2648	8	8	first	first	ADV
ejpam-2648	8	9	by	by	ADP
ejpam-2648	8	10	hasse	hasse	NOUN
ejpam-2648	8	11	and	and	CCONJ
ejpam-2648	8	12	schmidt	schmidt	PROPN
ejpam-2648	9	1	[	[	X
ejpam-2648	9	2	12	12	NUM
ejpam-2648	9	3	]	]	X
ejpam-2648	9	4	,	,	PUNCT
ejpam-2648	9	5	that	that	PRON
ejpam-2648	9	6	’s	’	VERB
ejpam-2648	9	7	why	why	SCONJ
ejpam-2648	9	8	algebraist	algebraist	NOUN
ejpam-2648	9	9	sometimes	sometimes	ADV
ejpam-2648	9	10	call	call	VERB
ejpam-2648	9	11	them	they	PRON
ejpam-2648	9	12	hasse	hasse	ADJ
ejpam-2648	9	13	-	-	PUNCT
ejpam-2648	9	14	schmidt	schmidt	NOUN
ejpam-2648	9	15	derivations	derivation	NOUN
ejpam-2648	9	16	.	.	PUNCT
ejpam-2648	10	1	for	for	ADP
ejpam-2648	10	2	further	further	ADJ
ejpam-2648	10	3	algebraic	algebraic	ADJ
ejpam-2648	10	4	properties	property	NOUN
ejpam-2648	10	5	about	about	ADP
ejpam-2648	10	6	these	these	DET
ejpam-2648	10	7	operators	operator	NOUN
ejpam-2648	10	8	,	,	PUNCT
ejpam-2648	10	9	the	the	DET
ejpam-2648	10	10	reader	reader	NOUN
ejpam-2648	10	11	is	be	AUX
ejpam-2648	10	12	referred	refer	VERB
ejpam-2648	10	13	to	to	ADP
ejpam-2648	10	14	[	[	PROPN
ejpam-2648	10	15	5,7,11,17,27,28	5,7,11,17,27,28	X
ejpam-2648	10	16	]	]	PUNCT
ejpam-2648	10	17	where	where	SCONJ
ejpam-2648	10	18	they	they	PRON
ejpam-2648	10	19	are	be	AUX
ejpam-2648	10	20	studied	study	VERB
ejpam-2648	10	21	in	in	ADP
ejpam-2648	10	22	other	other	ADJ
ejpam-2648	10	23	context	context	NOUN
ejpam-2648	10	24	.	.	PUNCT
ejpam-2648	11	1	higher	high	ADJ
ejpam-2648	11	2	derivations	derivation	NOUN
ejpam-2648	11	3	are	be	AUX
ejpam-2648	11	4	used	use	VERB
ejpam-2648	11	5	in	in	ADP
ejpam-2648	11	6	[	[	X
ejpam-2648	11	7	30	30	NUM
ejpam-2648	11	8	]	]	PUNCT
ejpam-2648	11	9	to	to	PART
ejpam-2648	11	10	study	study	VERB
ejpam-2648	11	11	generic	generic	ADJ
ejpam-2648	11	12	solving	solving	NOUN
ejpam-2648	11	13	of	of	ADP
ejpam-2648	11	14	higher	high	ADJ
ejpam-2648	11	15	differential	differential	ADJ
ejpam-2648	11	16	equations	equation	NOUN
ejpam-2648	11	17	.	.	PUNCT
ejpam-2648	12	1	loy	loy	PROPN
ejpam-2648	12	2	proved	prove	VERB
ejpam-2648	12	3	in	in	ADP
ejpam-2648	12	4	[	[	X
ejpam-2648	12	5	22	22	NUM
ejpam-2648	12	6	]	]	PUNCT
ejpam-2648	12	7	that	that	SCONJ
ejpam-2648	12	8	if	if	SCONJ
ejpam-2648	12	9	a	a	PRON
ejpam-2648	12	10	is	be	AUX
ejpam-2648	12	11	an	an	DET
ejpam-2648	12	12	(	(	PUNCT
ejpam-2648	12	13	f	f	X
ejpam-2648	12	14	)	)	PUNCT
ejpam-2648	12	15	-algebra	-algebra	NOUN
ejpam-2648	12	16	which	which	PRON
ejpam-2648	12	17	is	be	AUX
ejpam-2648	12	18	a	a	DET
ejpam-2648	12	19	subalgebra	subalgebra	NOUN
ejpam-2648	12	20	of	of	ADP
ejpam-2648	12	21	a	a	DET
ejpam-2648	12	22	banach	banach	NOUN
ejpam-2648	12	23	algebra	algebra	NOUN
ejpam-2648	12	24	b	b	PROPN
ejpam-2648	12	25	of	of	ADP
ejpam-2648	12	26	power	power	NOUN
ejpam-2648	12	27	series	series	NOUN
ejpam-2648	12	28	,	,	PUNCT
ejpam-2648	12	29	then	then	ADV
ejpam-2648	12	30	every	every	DET
ejpam-2648	12	31	higher	high	ADJ
ejpam-2648	12	32	derivation	derivation	NOUN
ejpam-2648	12	33	{	{	PUNCT
ejpam-2648	12	34	dn	dn	NOUN
ejpam-2648	12	35	}	}	PUNCT
ejpam-2648	12	36	:	:	PUNCT
ejpam-2648	12	37	a	a	DET
ejpam-2648	12	38	−→	−→	NOUN
ejpam-2648	12	39	b	b	NOUN
ejpam-2648	12	40	(	(	PUNCT
ejpam-2648	12	41	n	n	NOUN
ejpam-2648	12	42	=	=	SYM
ejpam-2648	12	43	0	0	NUM
ejpam-2648	12	44	,	,	PUNCT
ejpam-2648	12	45	1	1	NUM
ejpam-2648	12	46	,	,	PUNCT
ejpam-2648	12	47	2	2	NUM
ejpam-2648	12	48	,	,	PUNCT
ejpam-2648	12	49	...	...	PUNCT
ejpam-2648	12	50	)	)	PUNCT
ejpam-2648	12	51	is	be	AUX
ejpam-2648	12	52	automatically	automatically	ADV
ejpam-2648	12	53	continuous	continuous	ADJ
ejpam-2648	12	54	.	.	PUNCT
ejpam-2648	13	1	jewell	jewell	PROPN
ejpam-2648	13	2	showed	show	VERB
ejpam-2648	13	3	in	in	ADP
ejpam-2648	13	4	[	[	X
ejpam-2648	13	5	15	15	NUM
ejpam-2648	13	6	]	]	PUNCT
ejpam-2648	13	7	that	that	SCONJ
ejpam-2648	13	8	any	any	DET
ejpam-2648	13	9	higher	high	ADJ
ejpam-2648	13	10	derivation	derivation	NOUN
ejpam-2648	13	11	from	from	ADP
ejpam-2648	13	12	a	a	DET
ejpam-2648	13	13	banach	banach	NOUN
ejpam-2648	13	14	algebra	algebra	NOUN
ejpam-2648	13	15	into	into	ADP
ejpam-2648	13	16	a	a	DET
ejpam-2648	13	17	semisimple	semisimple	NOUN
ejpam-2648	13	18	banach	banach	NOUN
ejpam-2648	13	19	algebra	algebra	NOUN
ejpam-2648	13	20	is	be	AUX
ejpam-2648	13	21	continuous	continuous	ADJ
ejpam-2648	13	22	provided	provide	VERB
ejpam-2648	13	23	ker(d0	ker(d0	PROPN
ejpam-2648	13	24	)	)	PUNCT
ejpam-2648	13	25	⊆	⊆	NUM
ejpam-2648	13	26	ker(dn	ker(dn	X
ejpam-2648	13	27	)	)	PUNCT
ejpam-2648	13	28	,	,	PUNCT
ejpam-2648	13	29	for	for	ADP
ejpam-2648	13	30	all	all	DET
ejpam-2648	13	31	n	n	PRON
ejpam-2648	13	32	≥	≥	NOUN
ejpam-2648	13	33	1	1	NUM
ejpam-2648	13	34	.	.	PUNCT
ejpam-2648	14	1	s.	s.	PROPN
ejpam-2648	14	2	hejazian	hejazian	PROPN
ejpam-2648	14	3	and	and	CCONJ
ejpam-2648	14	4	t.l	t.l	PROPN
ejpam-2648	14	5	.	.	PROPN
ejpam-2648	14	6	shatery	shatery	PROPN
ejpam-2648	14	7	show	show	NOUN
ejpam-2648	14	8	in	in	ADP
ejpam-2648	14	9	[	[	X
ejpam-2648	14	10	13	13	NUM
ejpam-2648	14	11	]	]	PUNCT
ejpam-2648	14	12	that	that	SCONJ
ejpam-2648	14	13	every	every	DET
ejpam-2648	14	14	higher	high	ADJ
ejpam-2648	14	15	derivation	derivation	NOUN
ejpam-2648	14	16	{	{	PUNCT
ejpam-2648	14	17	dn	dn	NOUN
ejpam-2648	14	18	}	}	PUNCT
ejpam-2648	14	19	from	from	ADP
ejpam-2648	14	20	a	a	DET
ejpam-2648	14	21	jb∗−algebra	jb∗−algebra	NOUN
ejpam-2648	14	22	a	a	PRON
ejpam-2648	14	23	into	into	ADP
ejpam-2648	14	24	a	a	DET
ejpam-2648	14	25	jb∗−algebra	jb∗−algebra	PROPN
ejpam-2648	14	26	b	b	NOUN
ejpam-2648	14	27	is	be	AUX
ejpam-2648	14	28	continuous	continuous	ADJ
ejpam-2648	14	29	provided	provide	VERB
ejpam-2648	14	30	that	that	SCONJ
ejpam-2648	14	31	d0	d0	NOUN
ejpam-2648	14	32	is	be	AUX
ejpam-2648	14	33	a	a	DET
ejpam-2648	14	34	*	*	X
ejpam-2648	14	35	-homomorphism	-homomorphism	NOUN
ejpam-2648	14	36	.	.	PUNCT
ejpam-2648	15	1	they	they	PRON
ejpam-2648	15	2	also	also	ADV
ejpam-2648	15	3	prove	prove	VERB
ejpam-2648	15	4	that	that	SCONJ
ejpam-2648	15	5	every	every	DET
ejpam-2648	15	6	higher	high	ADJ
ejpam-2648	15	7	derivation	derivation	NOUN
ejpam-2648	15	8	from	from	ADP
ejpam-2648	15	9	a	a	DET
ejpam-2648	15	10	commutative	commutative	ADJ
ejpam-2648	15	11	c∗−algebra	c∗−algebra	NOUN
ejpam-2648	15	12	or	or	CCONJ
ejpam-2648	15	13	from	from	ADP
ejpam-2648	15	14	a	a	DET
ejpam-2648	15	15	c∗−algebra	c∗−algebra	PROPN
ejpam-2648	15	16	which	which	PRON
ejpam-2648	15	17	has	have	VERB
ejpam-2648	15	18	minimal	minimal	ADJ
ejpam-2648	15	19	idempotents	idempotent	NOUN
ejpam-2648	15	20	and	and	CCONJ
ejpam-2648	15	21	is	be	AUX
ejpam-2648	15	22	the	the	DET
ejpam-2648	15	23	closure	closure	NOUN
ejpam-2648	15	24	of	of	ADP
ejpam-2648	15	25	its	its	PRON
ejpam-2648	15	26	socle	socle	NOUN
ejpam-2648	15	27	is	be	AUX
ejpam-2648	15	28	continuous	continuous	ADJ
ejpam-2648	15	29	.	.	PUNCT
ejpam-2648	16	1	m.	m.	NOUN
ejpam-2648	16	2	mirzavaziri	mirzavaziri	PROPN
ejpam-2648	16	3	gives	give	VERB
ejpam-2648	16	4	in	in	ADP
ejpam-2648	16	5	[	[	X
ejpam-2648	16	6	24	24	NUM
ejpam-2648	16	7	]	]	PUNCT
ejpam-2648	16	8	a	a	DET
ejpam-2648	16	9	characterization	characterization	NOUN
ejpam-2648	16	10	of	of	ADP
ejpam-2648	16	11	higher	high	ADJ
ejpam-2648	16	12	derivations	derivation	NOUN
ejpam-2648	16	13	on	on	ADP
ejpam-2648	16	14	algebras	algebra	NOUN
ejpam-2648	16	15	.	.	PUNCT
ejpam-2648	17	1	in	in	ADP
ejpam-2648	17	2	this	this	DET
ejpam-2648	17	3	paper	paper	NOUN
ejpam-2648	17	4	,	,	PUNCT
ejpam-2648	17	5	we	we	PRON
ejpam-2648	17	6	deal	deal	VERB
ejpam-2648	17	7	with	with	ADP
ejpam-2648	17	8	higher	high	ADJ
ejpam-2648	17	9	derivations	derivation	NOUN
ejpam-2648	17	10	on	on	ADP
ejpam-2648	17	11	banach	banach	NOUN
ejpam-2648	17	12	-	-	PUNCT
ejpam-2648	17	13	jordan	jordan	NOUN
ejpam-2648	17	14	pairs	pair	NOUN
ejpam-2648	17	15	.	.	PUNCT
ejpam-2648	18	1	we	we	PRON
ejpam-2648	18	2	intend	intend	VERB
ejpam-2648	18	3	to	to	PART
ejpam-2648	18	4	settle	settle	VERB
ejpam-2648	18	5	the	the	DET
ejpam-2648	18	6	automatic	automatic	ADJ
ejpam-2648	18	7	continuity	continuity	NOUN
ejpam-2648	18	8	of	of	ADP
ejpam-2648	18	9	these	these	DET
ejpam-2648	18	10	operators	operator	NOUN
ejpam-2648	18	11	provided	provide	VERB
ejpam-2648	18	12	that	that	SCONJ
ejpam-2648	18	13	some	some	DET
ejpam-2648	18	14	algebraic	algebraic	ADJ
ejpam-2648	18	15	conditions	condition	NOUN
ejpam-2648	18	16	are	be	AUX
ejpam-2648	18	17	satisfied	satisfied	ADJ
ejpam-2648	18	18	.	.	PUNCT
ejpam-2648	19	1	our	our	PRON
ejpam-2648	19	2	approach	approach	NOUN
ejpam-2648	19	3	to	to	ADP
ejpam-2648	19	4	this	this	DET
ejpam-2648	19	5	result	result	NOUN
ejpam-2648	19	6	consists	consist	VERB
ejpam-2648	19	7	in	in	ADP
ejpam-2648	19	8	intensive	intensive	ADJ
ejpam-2648	19	9	use	use	NOUN
ejpam-2648	19	10	of	of	ADP
ejpam-2648	19	11	local	local	ADJ
ejpam-2648	19	12	algebras	algebras	PROPN
ejpam-2648	19	13	theory	theory	NOUN
ejpam-2648	19	14	frequently	frequently	ADV
ejpam-2648	19	15	used	use	VERB
ejpam-2648	19	16	by	by	ADP
ejpam-2648	19	17	authors	author	NOUN
ejpam-2648	19	18	in	in	ADP
ejpam-2648	19	19	jordan	jordan	PROPN
ejpam-2648	19	20	structures	structure	NOUN
ejpam-2648	19	21	.	.	PUNCT
ejpam-2648	20	1	let	let	VERB
ejpam-2648	20	2	us	we	PRON
ejpam-2648	20	3	note	note	VERB
ejpam-2648	20	4	that	that	SCONJ
ejpam-2648	20	5	jordan	jordan	PROPN
ejpam-2648	20	6	pairs	pair	NOUN
ejpam-2648	20	7	are	be	AUX
ejpam-2648	20	8	a	a	DET
ejpam-2648	20	9	natural	natural	ADJ
ejpam-2648	20	10	∗corresponding	∗corresponde	VERB
ejpam-2648	20	11	author	author	NOUN
ejpam-2648	20	12	.	.	PUNCT
ejpam-2648	21	1	email	email	NOUN
ejpam-2648	21	2	addresses	address	NOUN
ejpam-2648	21	3	:	:	PUNCT
ejpam-2648	21	4	radimarhn@hotmail.com	radimarhn@hotmail.com	X
ejpam-2648	21	5	(	(	PUNCT
ejpam-2648	21	6	h.	h.	PROPN
ejpam-2648	21	7	marhnine	marhnine	PROPN
ejpam-2648	21	8	)	)	PUNCT
ejpam-2648	21	9	,	,	PUNCT
ejpam-2648	21	10	chafikazar@hotmail.com	chafikazar@hotmail.com	X
ejpam-2648	21	11	(	(	PUNCT
ejpam-2648	21	12	c.	c.	PROPN
ejpam-2648	21	13	zarhouti	zarhouti	PROPN
ejpam-2648	21	14	)	)	PUNCT
ejpam-2648	21	15	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2648	22	1	749	749	NUM
ejpam-2648	22	2	c	c	X
ejpam-2648	22	3	©	©	PROPN
ejpam-2648	22	4	2017	2017	NUM
ejpam-2648	22	5	ejpam	ejpam	NOUN
ejpam-2648	22	6	all	all	DET
ejpam-2648	22	7	rights	right	NOUN
ejpam-2648	22	8	reserved	reserve	VERB
ejpam-2648	22	9	.	.	PUNCT
ejpam-2648	23	1	h.	h.	PROPN
ejpam-2648	23	2	marhnine	marhnine	PROPN
ejpam-2648	23	3	,	,	PUNCT
ejpam-2648	23	4	c.	c.	PROPN
ejpam-2648	23	5	zarhouti	zarhouti	PROPN
ejpam-2648	23	6	/	/	SYM
ejpam-2648	23	7	eur	eur	PROPN
ejpam-2648	23	8	.	.	PUNCT
ejpam-2648	24	1	j.	j.	PROPN
ejpam-2648	24	2	pure	pure	PROPN
ejpam-2648	24	3	appl	appl	PROPN
ejpam-2648	24	4	.	.	PROPN
ejpam-2648	24	5	math	math	PROPN
ejpam-2648	24	6	,	,	PUNCT
ejpam-2648	24	7	10	10	NUM
ejpam-2648	24	8	(	(	PUNCT
ejpam-2648	24	9	4	4	NUM
ejpam-2648	24	10	)	)	PUNCT
ejpam-2648	24	11	(	(	PUNCT
ejpam-2648	24	12	2017	2017	NUM
ejpam-2648	24	13	)	)	PUNCT
ejpam-2648	24	14	,	,	PUNCT
ejpam-2648	24	15	749	749	NUM
ejpam-2648	24	16	-	-	SYM
ejpam-2648	24	17	762	762	NUM
ejpam-2648	24	18	750	750	NUM
ejpam-2648	24	19	extension	extension	NOUN
ejpam-2648	24	20	of	of	ADP
ejpam-2648	24	21	jordan	jordan	PROPN
ejpam-2648	24	22	algebras	algebras	PROPN
ejpam-2648	24	23	and	and	CCONJ
ejpam-2648	24	24	arise	arise	VERB
ejpam-2648	24	25	as	as	ADV
ejpam-2648	24	26	well	well	ADV
ejpam-2648	24	27	in	in	ADP
ejpam-2648	24	28	a	a	DET
ejpam-2648	24	29	natural	natural	ADJ
ejpam-2648	24	30	way	way	NOUN
ejpam-2648	24	31	in	in	ADP
ejpam-2648	24	32	the	the	DET
ejpam-2648	24	33	geometry	geometry	NOUN
ejpam-2648	24	34	of	of	ADP
ejpam-2648	24	35	bounded	bounded	ADJ
ejpam-2648	24	36	symmetric	symmetric	ADJ
ejpam-2648	24	37	domains	domain	NOUN
ejpam-2648	24	38	.	.	PUNCT
ejpam-2648	25	1	loos	loo	NOUN
ejpam-2648	25	2	proved	prove	VERB
ejpam-2648	25	3	in	in	ADP
ejpam-2648	25	4	[	[	X
ejpam-2648	25	5	21	21	NUM
ejpam-2648	25	6	]	]	X
ejpam-2648	25	7	a	a	DET
ejpam-2648	25	8	strong	strong	ADJ
ejpam-2648	25	9	dependence	dependence	NOUN
ejpam-2648	25	10	between	between	ADP
ejpam-2648	25	11	homogeneous	homogeneous	ADJ
ejpam-2648	25	12	circled	circle	VERB
ejpam-2648	25	13	domains	domain	NOUN
ejpam-2648	25	14	,	,	PUNCT
ejpam-2648	25	15	in	in	ADP
ejpam-2648	25	16	finite	finite	ADJ
ejpam-2648	25	17	complex	complex	ADJ
ejpam-2648	25	18	vector	vector	NOUN
ejpam-2648	25	19	spaces	space	NOUN
ejpam-2648	25	20	,	,	PUNCT
ejpam-2648	25	21	and	and	CCONJ
ejpam-2648	25	22	jordan	jordan	PROPN
ejpam-2648	25	23	pairs	pair	NOUN
ejpam-2648	25	24	.	.	PUNCT
ejpam-2648	26	1	2	2	X
ejpam-2648	26	2	.	.	NUM
ejpam-2648	26	3	preliminaries	preliminary	NOUN
ejpam-2648	26	4	in	in	ADP
ejpam-2648	26	5	this	this	DET
ejpam-2648	26	6	paper	paper	NOUN
ejpam-2648	26	7	we	we	PRON
ejpam-2648	26	8	shall	shall	AUX
ejpam-2648	26	9	deal	deal	VERB
ejpam-2648	26	10	with	with	ADP
ejpam-2648	26	11	jordan	jordan	PROPN
ejpam-2648	26	12	pairs	pairs	PROPN
ejpam-2648	26	13	and	and	CCONJ
ejpam-2648	26	14	jordan	jordan	PROPN
ejpam-2648	26	15	algebras	algebras	PROPN
ejpam-2648	26	16	over	over	ADP
ejpam-2648	26	17	a	a	DET
ejpam-2648	26	18	commutative	commutative	ADJ
ejpam-2648	26	19	ring	ring	NOUN
ejpam-2648	26	20	of	of	ADP
ejpam-2648	26	21	scalars	scalars	PROPN
ejpam-2648	26	22	r	r	NOUN
ejpam-2648	26	23	of	of	ADP
ejpam-2648	26	24	characteristic	characteristic	ADJ
ejpam-2648	26	25	not	not	PART
ejpam-2648	26	26	two	two	NUM
ejpam-2648	26	27	.	.	PUNCT
ejpam-2648	27	1	the	the	DET
ejpam-2648	27	2	reader	reader	NOUN
ejpam-2648	27	3	is	be	AUX
ejpam-2648	27	4	referred	refer	VERB
ejpam-2648	27	5	to	to	ADP
ejpam-2648	27	6	[	[	X
ejpam-2648	27	7	18	18	NUM
ejpam-2648	27	8	]	]	PUNCT
ejpam-2648	27	9	for	for	ADP
ejpam-2648	27	10	further	further	ADJ
ejpam-2648	27	11	details	detail	NOUN
ejpam-2648	27	12	.	.	PUNCT
ejpam-2648	28	1	however	however	ADV
ejpam-2648	28	2	,	,	PUNCT
ejpam-2648	28	3	we	we	PRON
ejpam-2648	28	4	shall	shall	AUX
ejpam-2648	28	5	record	record	VERB
ejpam-2648	28	6	in	in	ADP
ejpam-2648	28	7	this	this	DET
ejpam-2648	28	8	section	section	NOUN
ejpam-2648	28	9	some	some	DET
ejpam-2648	28	10	notations	notation	NOUN
ejpam-2648	28	11	and	and	CCONJ
ejpam-2648	28	12	results	result	NOUN
ejpam-2648	28	13	.	.	PUNCT
ejpam-2648	29	1	a	a	DET
ejpam-2648	29	2	jordan	jordan	PROPN
ejpam-2648	29	3	pair	pair	PROPN
ejpam-2648	29	4	over	over	ADP
ejpam-2648	29	5	a	a	DET
ejpam-2648	29	6	commutative	commutative	ADJ
ejpam-2648	29	7	ring	ring	NOUN
ejpam-2648	29	8	r	r	NOUN
ejpam-2648	29	9	of	of	ADP
ejpam-2648	29	10	characteristic	characteristic	ADJ
ejpam-2648	29	11	not	not	PART
ejpam-2648	29	12	two	two	NUM
ejpam-2648	29	13	is	be	AUX
ejpam-2648	29	14	a	a	DET
ejpam-2648	29	15	pair	pair	NOUN
ejpam-2648	29	16	of	of	ADP
ejpam-2648	29	17	rmodules	rmodule	NOUN
ejpam-2648	29	18	p	p	X
ejpam-2648	29	19	=	=	X
ejpam-2648	29	20	(	(	PUNCT
ejpam-2648	29	21	p+	p+	NOUN
ejpam-2648	29	22	,	,	PUNCT
ejpam-2648	29	23	p−	p−	NOUN
ejpam-2648	29	24	)	)	PUNCT
ejpam-2648	29	25	endowed	endow	VERB
ejpam-2648	29	26	with	with	ADP
ejpam-2648	29	27	a	a	DET
ejpam-2648	29	28	couple	couple	NOUN
ejpam-2648	29	29	(	(	PUNCT
ejpam-2648	29	30	q+	q+	NOUN
ejpam-2648	29	31	,	,	PUNCT
ejpam-2648	29	32	q−	q−	PROPN
ejpam-2648	29	33	)	)	PUNCT
ejpam-2648	29	34	of	of	ADP
ejpam-2648	29	35	quadratic	quadratic	ADJ
ejpam-2648	29	36	operators	operator	NOUN
ejpam-2648	29	37	qσ	qσ	PROPN
ejpam-2648	29	38	:	:	PUNCT
ejpam-2648	29	39	p	p	NOUN
ejpam-2648	29	40	σ	σ	NUM
ejpam-2648	29	41	−→	−→	ADJ
ejpam-2648	29	42	homr(p−σ	homr(p−σ	PROPN
ejpam-2648	29	43	,	,	PUNCT
ejpam-2648	29	44	p	p	PROPN
ejpam-2648	29	45	σ	σ	PROPN
ejpam-2648	29	46	)	)	PUNCT
ejpam-2648	29	47	such	such	ADJ
ejpam-2648	29	48	that	that	SCONJ
ejpam-2648	29	49	the	the	DET
ejpam-2648	29	50	following	follow	VERB
ejpam-2648	29	51	identities	identity	NOUN
ejpam-2648	29	52	hold	hold	VERB
ejpam-2648	29	53	for	for	ADP
ejpam-2648	29	54	all	all	DET
ejpam-2648	29	55	(	(	PUNCT
ejpam-2648	29	56	x	x	NOUN
ejpam-2648	29	57	,	,	PUNCT
ejpam-2648	29	58	y	y	NOUN
ejpam-2648	29	59	)	)	PUNCT
ejpam-2648	29	60	∈	∈	PROPN
ejpam-2648	29	61	p	p	PROPN
ejpam-2648	29	62	σ	σ	PROPN
ejpam-2648	29	63	×	×	PROPN
ejpam-2648	29	64	p−σ	p−σ	PROPN
ejpam-2648	29	65	(	(	PUNCT
ejpam-2648	29	66	σ	σ	PROPN
ejpam-2648	29	67	=	=	SYM
ejpam-2648	29	68	±	±	PROPN
ejpam-2648	29	69	)	)	PUNCT
ejpam-2648	29	70	v	v	ADP
ejpam-2648	29	71	σ	σ	PROPN
ejpam-2648	29	72	(	(	PUNCT
ejpam-2648	29	73	x	x	X
ejpam-2648	29	74	,	,	PUNCT
ejpam-2648	29	75	y)q	y)q	NOUN
ejpam-2648	29	76	σ	σ	NOUN
ejpam-2648	29	77	x	x	PUNCT
ejpam-2648	29	78	=	=	NOUN
ejpam-2648	29	79	qσxv	qσxv	ADJ
ejpam-2648	29	80	−σ	−σ	NOUN
ejpam-2648	29	81	(	(	PUNCT
ejpam-2648	29	82	y	y	NOUN
ejpam-2648	29	83	,	,	PUNCT
ejpam-2648	29	84	x	x	NOUN
ejpam-2648	29	85	)	)	PUNCT
ejpam-2648	29	86	,	,	PUNCT
ejpam-2648	29	87	v	v	ADP
ejpam-2648	29	88	σ	σ	PROPN
ejpam-2648	29	89	(	(	PUNCT
ejpam-2648	29	90	qσxy	qσxy	PROPN
ejpam-2648	29	91	,	,	PUNCT
ejpam-2648	29	92	x	x	X
ejpam-2648	29	93	)	)	PUNCT
ejpam-2648	29	94	=	=	SYM
ejpam-2648	29	95	v	v	PROPN
ejpam-2648	29	96	σ	σ	X
ejpam-2648	29	97	(	(	PUNCT
ejpam-2648	29	98	x	x	X
ejpam-2648	29	99	,	,	PUNCT
ejpam-2648	29	100	q−σ	q−σ	X
ejpam-2648	29	101	y	y	NOUN
ejpam-2648	29	102	x	x	PROPN
ejpam-2648	29	103	)	)	PUNCT
ejpam-2648	29	104	,	,	PUNCT
ejpam-2648	29	105	where	where	SCONJ
ejpam-2648	29	106	v	v	ADP
ejpam-2648	29	107	σ	σ	X
ejpam-2648	29	108	(	(	PUNCT
ejpam-2648	29	109	x	x	X
ejpam-2648	29	110	,	,	PUNCT
ejpam-2648	29	111	y)z	y)z	X
ejpam-2648	29	112	=	=	PUNCT
ejpam-2648	29	113	qσ(x	qσ(x	PROPN
ejpam-2648	29	114	,	,	PUNCT
ejpam-2648	29	115	z)y	z)y	NOUN
ejpam-2648	29	116	=	=	SYM
ejpam-2648	29	117	{	{	PUNCT
ejpam-2648	29	118	x	x	NOUN
ejpam-2648	29	119	,	,	PUNCT
ejpam-2648	29	120	y	y	PROPN
ejpam-2648	29	121	,	,	PUNCT
ejpam-2648	29	122	z}σ	z}σ	PROPN
ejpam-2648	29	123	,	,	PUNCT
ejpam-2648	29	124	qσ(x	qσ(x	NOUN
ejpam-2648	29	125	,	,	PUNCT
ejpam-2648	29	126	z	z	NOUN
ejpam-2648	29	127	)	)	PUNCT
ejpam-2648	29	128	=	=	SYM
ejpam-2648	30	1	qσx+z	qσx+z	NUM
ejpam-2648	30	2	−qσx	−qσx	NUM
ejpam-2648	30	3	−qσz	−qσz	NOUN
ejpam-2648	30	4	and	and	CCONJ
ejpam-2648	30	5	{	{	PUNCT
ejpam-2648	30	6	x	x	NOUN
ejpam-2648	30	7	,	,	PUNCT
ejpam-2648	30	8	y	y	PROPN
ejpam-2648	30	9	,	,	PUNCT
ejpam-2648	30	10	x}σ	x}σ	PROPN
ejpam-2648	30	11	=	=	SYM
ejpam-2648	30	12	2qσxy	2qσxy	NUM
ejpam-2648	30	13	.	.	PUNCT
ejpam-2648	31	1	an	an	DET
ejpam-2648	31	2	example	example	NOUN
ejpam-2648	31	3	of	of	ADP
ejpam-2648	31	4	jordan	jordan	PROPN
ejpam-2648	31	5	pairs	pair	NOUN
ejpam-2648	31	6	over	over	ADP
ejpam-2648	31	7	a	a	DET
ejpam-2648	31	8	field	field	NOUN
ejpam-2648	31	9	k	k	PRON
ejpam-2648	31	10	is	be	AUX
ejpam-2648	31	11	given	give	VERB
ejpam-2648	31	12	by	by	ADP
ejpam-2648	31	13	taking	take	VERB
ejpam-2648	31	14	p	p	NOUN
ejpam-2648	31	15	=	=	PUNCT
ejpam-2648	31	16	a(m	a(m	NOUN
ejpam-2648	31	17	,	,	PUNCT
ejpam-2648	31	18	r,ϕ)j	r,ϕ)j	ADV
ejpam-2648	31	19	,	,	PUNCT
ejpam-2648	31	20	where	where	SCONJ
ejpam-2648	31	21	m	m	VERB
ejpam-2648	31	22	=	=	SYM
ejpam-2648	31	23	(	(	PUNCT
ejpam-2648	31	24	m+,m−	m+,m−	X
ejpam-2648	31	25	)	)	PUNCT
ejpam-2648	31	26	is	be	AUX
ejpam-2648	31	27	a	a	DET
ejpam-2648	31	28	pair	pair	NOUN
ejpam-2648	31	29	of	of	ADP
ejpam-2648	31	30	r	r	NOUN
ejpam-2648	31	31	-	-	PUNCT
ejpam-2648	31	32	vector	vector	NOUN
ejpam-2648	31	33	spaces	space	NOUN
ejpam-2648	31	34	such	such	ADJ
ejpam-2648	31	35	that	that	DET
ejpam-2648	31	36	m+	m+	NOUN
ejpam-2648	31	37	is	be	AUX
ejpam-2648	31	38	a	a	DET
ejpam-2648	31	39	left	left	ADJ
ejpam-2648	31	40	r	r	NOUN
ejpam-2648	31	41	-	-	PUNCT
ejpam-2648	31	42	module	module	NOUN
ejpam-2648	31	43	and	and	CCONJ
ejpam-2648	31	44	m−	m−	PROPN
ejpam-2648	31	45	is	be	AUX
ejpam-2648	31	46	a	a	DET
ejpam-2648	31	47	right	right	ADJ
ejpam-2648	31	48	r	r	NOUN
ejpam-2648	31	49	-	-	PUNCT
ejpam-2648	31	50	module	module	NOUN
ejpam-2648	31	51	over	over	ADP
ejpam-2648	31	52	an	an	DET
ejpam-2648	31	53	associative	associative	ADJ
ejpam-2648	31	54	k	k	NOUN
ejpam-2648	31	55	-	-	NOUN
ejpam-2648	31	56	algebra	algebra	NOUN
ejpam-2648	31	57	r	r	NOUN
ejpam-2648	31	58	and	and	CCONJ
ejpam-2648	31	59	ϕ	ϕ	NOUN
ejpam-2648	31	60	:	:	PUNCT
ejpam-2648	31	61	m+×m−	m+×m−	VERB
ejpam-2648	31	62	−→	−→	NOUN
ejpam-2648	31	63	r	r	NOUN
ejpam-2648	31	64	is	be	AUX
ejpam-2648	31	65	an	an	DET
ejpam-2648	31	66	r	r	NOUN
ejpam-2648	31	67	-	-	PUNCT
ejpam-2648	31	68	bilinear	bilinear	ADJ
ejpam-2648	31	69	form	form	NOUN
ejpam-2648	31	70	in	in	ADP
ejpam-2648	31	71	the	the	DET
ejpam-2648	31	72	sense	sense	NOUN
ejpam-2648	31	73	that	that	SCONJ
ejpam-2648	31	74	ϕ(ax	ϕ(ax	PROPN
ejpam-2648	31	75	,	,	PUNCT
ejpam-2648	31	76	yb	yb	PROPN
ejpam-2648	31	77	)	)	PUNCT
ejpam-2648	31	78	=	=	PUNCT
ejpam-2648	31	79	aϕ(x	aϕ(x	PROPN
ejpam-2648	31	80	,	,	PUNCT
ejpam-2648	31	81	y)b	y)b	NOUN
ejpam-2648	31	82	.	.	PUNCT
ejpam-2648	32	1	the	the	DET
ejpam-2648	32	2	product	product	NOUN
ejpam-2648	32	3	of	of	ADP
ejpam-2648	32	4	p	p	NOUN
ejpam-2648	32	5	=	=	PUNCT
ejpam-2648	32	6	a(m	a(m	NOUN
ejpam-2648	32	7	,	,	PUNCT
ejpam-2648	32	8	r,ϕ)j	r,ϕ)j	ADV
ejpam-2648	32	9	is	be	AUX
ejpam-2648	32	10	defined	define	VERB
ejpam-2648	32	11	by	by	ADP
ejpam-2648	32	12	:	:	PUNCT
ejpam-2648	32	13	qxy	qxy	PROPN
ejpam-2648	32	14	=	=	SYM
ejpam-2648	32	15	ϕ(x	ϕ(x	PROPN
ejpam-2648	32	16	,	,	PUNCT
ejpam-2648	32	17	y)x	y)x	NOUN
ejpam-2648	32	18	and	and	CCONJ
ejpam-2648	32	19	qyx	qyx	NOUN
ejpam-2648	32	20	=	=	SYM
ejpam-2648	32	21	yϕ(x	yϕ(x	X
ejpam-2648	32	22	,	,	PUNCT
ejpam-2648	32	23	y	y	PROPN
ejpam-2648	32	24	)	)	PUNCT
ejpam-2648	32	25	∀(x	∀(x	PROPN
ejpam-2648	32	26	,	,	PUNCT
ejpam-2648	32	27	y	y	NOUN
ejpam-2648	32	28	)	)	PUNCT
ejpam-2648	32	29	∈m+	∈m+	PROPN
ejpam-2648	32	30	×m−.	×m−.	DET
ejpam-2648	32	31	a	a	DET
ejpam-2648	32	32	jordan	jordan	PROPN
ejpam-2648	32	33	pair	pair	PROPN
ejpam-2648	32	34	p	p	X
ejpam-2648	32	35	=	=	X
ejpam-2648	32	36	(	(	PUNCT
ejpam-2648	32	37	p+	p+	NOUN
ejpam-2648	32	38	,	,	PUNCT
ejpam-2648	32	39	p−	p−	PROPN
ejpam-2648	32	40	)	)	PUNCT
ejpam-2648	32	41	is	be	AUX
ejpam-2648	32	42	said	say	VERB
ejpam-2648	32	43	to	to	PART
ejpam-2648	32	44	be	be	AUX
ejpam-2648	32	45	normed	norme	VERB
ejpam-2648	32	46	(	(	PUNCT
ejpam-2648	32	47	banach	banach	NOUN
ejpam-2648	32	48	)	)	PUNCT
ejpam-2648	32	49	provided	provide	VERB
ejpam-2648	32	50	the	the	DET
ejpam-2648	32	51	vector	vector	NOUN
ejpam-2648	32	52	spaces	space	NOUN
ejpam-2648	32	53	p+	p+	ADJ
ejpam-2648	32	54	and	and	CCONJ
ejpam-2648	32	55	p−	p−	NOUN
ejpam-2648	32	56	are	be	AUX
ejpam-2648	32	57	endowed	endow	VERB
ejpam-2648	32	58	with	with	ADP
ejpam-2648	32	59	norms	norm	NOUN
ejpam-2648	32	60	(	(	PUNCT
ejpam-2648	32	61	complete	complete	ADJ
ejpam-2648	32	62	)	)	PUNCT
ejpam-2648	32	63	,	,	PUNCT
ejpam-2648	32	64	both	both	PRON
ejpam-2648	32	65	denoted	denote	VERB
ejpam-2648	32	66	by	by	ADP
ejpam-2648	32	67	‖.‖	‖.‖	NOUN
ejpam-2648	32	68	,	,	PUNCT
ejpam-2648	32	69	making	make	VERB
ejpam-2648	32	70	continuous	continuous	ADJ
ejpam-2648	32	71	the	the	DET
ejpam-2648	32	72	triple	triple	ADJ
ejpam-2648	32	73	products	product	NOUN
ejpam-2648	32	74	{	{	PUNCT
ejpam-2648	32	75	x	x	NOUN
ejpam-2648	32	76	,	,	PUNCT
ejpam-2648	32	77	y	y	PROPN
ejpam-2648	32	78	,	,	PUNCT
ejpam-2648	32	79	z}σ	z}σ	PROPN
ejpam-2648	32	80	of	of	ADP
ejpam-2648	32	81	p	p	PRON
ejpam-2648	32	82	,	,	PUNCT
ejpam-2648	32	83	merely	merely	ADV
ejpam-2648	32	84	denoted	denote	VERB
ejpam-2648	32	85	{	{	PUNCT
ejpam-2648	32	86	x	x	NOUN
ejpam-2648	32	87	,	,	PUNCT
ejpam-2648	32	88	y	y	PROPN
ejpam-2648	32	89	,	,	PUNCT
ejpam-2648	32	90	z	z	NOUN
ejpam-2648	32	91	}	}	PUNCT
ejpam-2648	32	92	.	.	PUNCT
ejpam-2648	33	1	a	a	DET
ejpam-2648	33	2	typical	typical	ADJ
ejpam-2648	33	3	example	example	NOUN
ejpam-2648	33	4	of	of	ADP
ejpam-2648	33	5	banach	banach	NOUN
ejpam-2648	33	6	-	-	PUNCT
ejpam-2648	33	7	jordan	jordan	NOUN
ejpam-2648	33	8	pairs	pair	NOUN
ejpam-2648	33	9	is	be	AUX
ejpam-2648	33	10	given	give	VERB
ejpam-2648	33	11	by	by	ADP
ejpam-2648	33	12	taking	take	VERB
ejpam-2648	33	13	p+	p+	NOUN
ejpam-2648	33	14	=	=	SYM
ejpam-2648	33	15	bl(x	bl(x	X
ejpam-2648	33	16	,	,	PUNCT
ejpam-2648	33	17	y	y	PROPN
ejpam-2648	33	18	)	)	PUNCT
ejpam-2648	33	19	,	,	PUNCT
ejpam-2648	33	20	p−	p−	NOUN
ejpam-2648	33	21	=	=	SYM
ejpam-2648	33	22	bl(y	bl(y	X
ejpam-2648	33	23	,	,	PUNCT
ejpam-2648	33	24	x	x	PROPN
ejpam-2648	33	25	)	)	PUNCT
ejpam-2648	33	26	,	,	PUNCT
ejpam-2648	33	27	the	the	DET
ejpam-2648	33	28	pair	pair	NOUN
ejpam-2648	33	29	of	of	ADP
ejpam-2648	33	30	linear	linear	PROPN
ejpam-2648	33	31	bounded	bounded	PROPN
ejpam-2648	33	32	operators	operator	NOUN
ejpam-2648	33	33	between	between	ADP
ejpam-2648	33	34	real	real	ADJ
ejpam-2648	33	35	or	or	CCONJ
ejpam-2648	33	36	complex	complex	ADJ
ejpam-2648	33	37	banach	banach	NOUN
ejpam-2648	33	38	spaces	space	VERB
ejpam-2648	33	39	x	x	PUNCT
ejpam-2648	33	40	and	and	CCONJ
ejpam-2648	33	41	y	y	PROPN
ejpam-2648	33	42	with	with	ADP
ejpam-2648	33	43	the	the	DET
ejpam-2648	33	44	multiplication	multiplication	NOUN
ejpam-2648	33	45	quv	quv	PROPN
ejpam-2648	33	46	=	=	PUNCT
ejpam-2648	33	47	uvu	uvu	PROPN
ejpam-2648	33	48	.	.	PUNCT
ejpam-2648	34	1	such	such	ADJ
ejpam-2648	34	2	pair	pair	NOUN
ejpam-2648	34	3	is	be	AUX
ejpam-2648	34	4	frequently	frequently	ADV
ejpam-2648	34	5	denoted	denote	VERB
ejpam-2648	34	6	by	by	ADP
ejpam-2648	34	7	b(x	b(x	PROPN
ejpam-2648	34	8	,	,	PUNCT
ejpam-2648	34	9	y	y	PROPN
ejpam-2648	34	10	)	)	PUNCT
ejpam-2648	34	11	.	.	PUNCT
ejpam-2648	35	1	a	a	DET
ejpam-2648	35	2	(	(	PUNCT
ejpam-2648	35	3	linear	linear	PROPN
ejpam-2648	35	4	)	)	PUNCT
ejpam-2648	35	5	jordan	jordan	PROPN
ejpam-2648	35	6	algebra	algebra	PROPN
ejpam-2648	35	7	is	be	AUX
ejpam-2648	35	8	a	a	DET
ejpam-2648	35	9	vector	vector	NOUN
ejpam-2648	35	10	space	space	NOUN
ejpam-2648	35	11	j	j	PROPN
ejpam-2648	35	12	endowed	endow	VERB
ejpam-2648	35	13	with	with	ADP
ejpam-2648	35	14	a	a	DET
ejpam-2648	35	15	binary	binary	ADJ
ejpam-2648	35	16	product	product	NOUN
ejpam-2648	35	17	(	(	PUNCT
ejpam-2648	35	18	a	a	PRON
ejpam-2648	35	19	,	,	PUNCT
ejpam-2648	35	20	b	b	NOUN
ejpam-2648	35	21	)	)	PUNCT
ejpam-2648	35	22	7−→	7−→	NOUN
ejpam-2648	35	23	ab	ab	NOUN
ejpam-2648	35	24	satisfying	satisfy	VERB
ejpam-2648	35	25	the	the	DET
ejpam-2648	35	26	identities	identity	NOUN
ejpam-2648	35	27	:	:	PUNCT
ejpam-2648	35	28	ab	ab	PROPN
ejpam-2648	35	29	=	=	SYM
ejpam-2648	35	30	ba	ba	PROPN
ejpam-2648	35	31	,	,	PUNCT
ejpam-2648	35	32	and	and	CCONJ
ejpam-2648	35	33	a2(ba	a2(ba	PROPN
ejpam-2648	35	34	)	)	PUNCT
ejpam-2648	35	35	=	=	SYM
ejpam-2648	35	36	(	(	PUNCT
ejpam-2648	36	1	a2b)a	a2b)a	X
ejpam-2648	36	2	.	.	PUNCT
ejpam-2648	37	1	if	if	SCONJ
ejpam-2648	37	2	a	a	DET
ejpam-2648	37	3	complete	complete	ADJ
ejpam-2648	37	4	norm	norm	NOUN
ejpam-2648	37	5	is	be	AUX
ejpam-2648	37	6	defined	define	VERB
ejpam-2648	37	7	on	on	ADP
ejpam-2648	37	8	j	j	PROPN
ejpam-2648	37	9	and	and	CCONJ
ejpam-2648	37	10	makes	make	VERB
ejpam-2648	37	11	continuous	continuous	ADJ
ejpam-2648	37	12	its	its	PRON
ejpam-2648	37	13	product	product	NOUN
ejpam-2648	37	14	ab	ab	PROPN
ejpam-2648	37	15	,	,	PUNCT
ejpam-2648	37	16	j	j	PROPN
ejpam-2648	37	17	is	be	AUX
ejpam-2648	37	18	said	say	VERB
ejpam-2648	37	19	to	to	PART
ejpam-2648	37	20	be	be	AUX
ejpam-2648	37	21	a	a	DET
ejpam-2648	37	22	banach	banach	NOUN
ejpam-2648	37	23	-	-	PUNCT
ejpam-2648	37	24	jordan	jordan	NOUN
ejpam-2648	37	25	algebra	algebra	PROPN
ejpam-2648	37	26	.	.	PUNCT
ejpam-2648	38	1	jordan	jordan	PROPN
ejpam-2648	38	2	pairs	pair	NOUN
ejpam-2648	38	3	are	be	AUX
ejpam-2648	38	4	known	know	VERB
ejpam-2648	38	5	by	by	ADP
ejpam-2648	38	6	their	their	PRON
ejpam-2648	38	7	intimate	intimate	ADJ
ejpam-2648	38	8	relationship	relationship	NOUN
ejpam-2648	38	9	with	with	ADP
ejpam-2648	38	10	jordan	jordan	PROPN
ejpam-2648	38	11	algebras	algebras	PROPN
ejpam-2648	38	12	.	.	PUNCT
ejpam-2648	39	1	indeed	indeed	ADV
ejpam-2648	39	2	,	,	PUNCT
ejpam-2648	39	3	any	any	DET
ejpam-2648	39	4	associative	associative	ADJ
ejpam-2648	39	5	,	,	PUNCT
ejpam-2648	39	6	alternative	alternative	NOUN
ejpam-2648	39	7	or	or	CCONJ
ejpam-2648	39	8	jordan	jordan	PROPN
ejpam-2648	39	9	algebra	algebra	PROPN
ejpam-2648	39	10	a	a	DET
ejpam-2648	39	11	gives	give	VERB
ejpam-2648	39	12	rise	rise	NOUN
ejpam-2648	39	13	to	to	ADP
ejpam-2648	39	14	a	a	DET
ejpam-2648	39	15	jordan	jordan	PROPN
ejpam-2648	39	16	pair	pair	PROPN
ejpam-2648	39	17	(	(	PUNCT
ejpam-2648	39	18	a	a	DET
ejpam-2648	39	19	,	,	PUNCT
ejpam-2648	39	20	a	a	NOUN
ejpam-2648	39	21	)	)	PUNCT
ejpam-2648	39	22	with	with	ADP
ejpam-2648	39	23	a	a	DET
ejpam-2648	39	24	quadratic	quadratic	ADJ
ejpam-2648	39	25	multiplication	multiplication	NOUN
ejpam-2648	39	26	xyx	xyx	PROPN
ejpam-2648	39	27	or	or	CCONJ
ejpam-2648	39	28	uxy	uxy	PROPN
ejpam-2648	39	29	,	,	PUNCT
ejpam-2648	39	30	with	with	ADP
ejpam-2648	39	31	u	u	NOUN
ejpam-2648	39	32	denoting	denote	VERB
ejpam-2648	39	33	the	the	DET
ejpam-2648	39	34	usual	usual	ADJ
ejpam-2648	39	35	u	u	NOUN
ejpam-2648	39	36	-operator	-operator	NOUN
ejpam-2648	39	37	of	of	ADP
ejpam-2648	39	38	a	a	DET
ejpam-2648	39	39	jordan	jordan	PROPN
ejpam-2648	39	40	algebra	algebra	PROPN
ejpam-2648	39	41	defined	define	VERB
ejpam-2648	39	42	by	by	ADP
ejpam-2648	39	43	uxy	uxy	PROPN
ejpam-2648	39	44	=	=	SYM
ejpam-2648	39	45	2x(xy)−	2x(xy)−	NUM
ejpam-2648	39	46	x2y	x2y	PROPN
ejpam-2648	39	47	.	.	PUNCT
ejpam-2648	40	1	in	in	ADP
ejpam-2648	40	2	the	the	DET
ejpam-2648	40	3	opposite	opposite	ADJ
ejpam-2648	40	4	direction	direction	NOUN
ejpam-2648	40	5	,	,	PUNCT
ejpam-2648	40	6	given	give	VERB
ejpam-2648	40	7	a	a	DET
ejpam-2648	40	8	jordan	jordan	PROPN
ejpam-2648	40	9	pair	pair	PROPN
ejpam-2648	40	10	v	v	NOUN
ejpam-2648	40	11	=	=	PUNCT
ejpam-2648	40	12	(	(	PUNCT
ejpam-2648	40	13	v	v	ADP
ejpam-2648	40	14	+	+	NOUN
ejpam-2648	40	15	,	,	PUNCT
ejpam-2648	40	16	v	v	ADP
ejpam-2648	40	17	−	−	NOUN
ejpam-2648	40	18	)	)	PUNCT
ejpam-2648	40	19	and	and	CCONJ
ejpam-2648	40	20	an	an	DET
ejpam-2648	40	21	element	element	NOUN
ejpam-2648	40	22	u	u	PROPN
ejpam-2648	40	23	∈	∈	PROPN
ejpam-2648	40	24	v	v	ADP
ejpam-2648	40	25	−σ	−σ	NOUN
ejpam-2648	40	26	,	,	PUNCT
ejpam-2648	40	27	the	the	DET
ejpam-2648	40	28	vector	vector	NOUN
ejpam-2648	40	29	space	space	NOUN
ejpam-2648	40	30	v	v	PROPN
ejpam-2648	40	31	σ	σ	PROPN
ejpam-2648	40	32	gives	give	VERB
ejpam-2648	40	33	rise	rise	NOUN
ejpam-2648	40	34	to	to	ADP
ejpam-2648	40	35	a	a	DET
ejpam-2648	40	36	jordan	jordan	PROPN
ejpam-2648	40	37	algebra	algebra	PROPN
ejpam-2648	40	38	by	by	ADP
ejpam-2648	40	39	defining	define	VERB
ejpam-2648	40	40	the	the	DET
ejpam-2648	40	41	u	u	PROPN
ejpam-2648	40	42	-operator	-operator	PROPN
ejpam-2648	40	43	ua	ua	PROPN
ejpam-2648	40	44	=	=	PROPN
ejpam-2648	40	45	u	u	PROPN
ejpam-2648	40	46	(	(	PUNCT
ejpam-2648	40	47	u	u	NOUN
ejpam-2648	40	48	)	)	PUNCT
ejpam-2648	40	49	a	a	DET
ejpam-2648	40	50	=	=	X
ejpam-2648	40	51	qaqu	qaqu	NOUN
ejpam-2648	40	52	,	,	PUNCT
ejpam-2648	40	53	and	and	CCONJ
ejpam-2648	40	54	the	the	DET
ejpam-2648	40	55	square	square	ADJ
ejpam-2648	40	56	a(2,u	a(2,u	NOUN
ejpam-2648	40	57	)	)	PUNCT
ejpam-2648	41	1	=	=	SYM
ejpam-2648	41	2	qau	qau	NOUN
ejpam-2648	41	3	.	.	PUNCT
ejpam-2648	42	1	this	this	DET
ejpam-2648	42	2	jordan	jordan	PROPN
ejpam-2648	42	3	algebra	algebra	PROPN
ejpam-2648	42	4	,	,	PUNCT
ejpam-2648	42	5	denoted	denote	VERB
ejpam-2648	42	6	by	by	ADP
ejpam-2648	42	7	v	v	NOUN
ejpam-2648	42	8	σ(u	σ(u	NOUN
ejpam-2648	42	9	)	)	PUNCT
ejpam-2648	42	10	,	,	PUNCT
ejpam-2648	42	11	is	be	AUX
ejpam-2648	42	12	called	call	VERB
ejpam-2648	42	13	the	the	DET
ejpam-2648	42	14	u	u	NOUN
ejpam-2648	42	15	-	-	NOUN
ejpam-2648	42	16	homotope	homotope	NOUN
ejpam-2648	42	17	of	of	ADP
ejpam-2648	42	18	v	v	NOUN
ejpam-2648	42	19	at	at	ADP
ejpam-2648	42	20	u.	u.	PROPN
ejpam-2648	42	21	if	if	SCONJ
ejpam-2648	42	22	v	v	NOUN
ejpam-2648	42	23	is	be	AUX
ejpam-2648	42	24	a	a	DET
ejpam-2648	42	25	linear	linear	ADJ
ejpam-2648	42	26	jordan	jordan	PROPN
ejpam-2648	42	27	pair	pair	PROPN
ejpam-2648	42	28	,	,	PUNCT
ejpam-2648	42	29	we	we	PRON
ejpam-2648	42	30	just	just	ADV
ejpam-2648	42	31	need	need	VERB
ejpam-2648	42	32	to	to	PART
ejpam-2648	42	33	define	define	VERB
ejpam-2648	42	34	the	the	DET
ejpam-2648	42	35	linear	linear	ADJ
ejpam-2648	42	36	product	product	NOUN
ejpam-2648	42	37	in	in	ADP
ejpam-2648	42	38	v	v	NOUN
ejpam-2648	42	39	σ(u	σ(u	NOUN
ejpam-2648	42	40	)	)	PUNCT
ejpam-2648	42	41	as	as	SCONJ
ejpam-2648	42	42	follows	follow	VERB
ejpam-2648	42	43	:	:	PUNCT
ejpam-2648	42	44	a.b	a.b	PROPN
ejpam-2648	42	45	=	=	SYM
ejpam-2648	42	46	1	1	NUM
ejpam-2648	42	47	2	2	NUM
ejpam-2648	42	48	{	{	PUNCT
ejpam-2648	42	49	a	a	PRON
ejpam-2648	42	50	,	,	PUNCT
ejpam-2648	42	51	u	u	NOUN
ejpam-2648	42	52	,	,	PUNCT
ejpam-2648	42	53	b	b	NOUN
ejpam-2648	42	54	}	}	PUNCT
ejpam-2648	42	55	.	.	PUNCT
ejpam-2648	43	1	h.	h.	PROPN
ejpam-2648	43	2	marhnine	marhnine	PROPN
ejpam-2648	43	3	,	,	PUNCT
ejpam-2648	43	4	c.	c.	PROPN
ejpam-2648	43	5	zarhouti	zarhouti	PROPN
ejpam-2648	43	6	/	/	SYM
ejpam-2648	43	7	eur	eur	PROPN
ejpam-2648	43	8	.	.	PUNCT
ejpam-2648	44	1	j.	j.	PROPN
ejpam-2648	44	2	pure	pure	PROPN
ejpam-2648	44	3	appl	appl	PROPN
ejpam-2648	44	4	.	.	PROPN
ejpam-2648	44	5	math	math	PROPN
ejpam-2648	44	6	,	,	PUNCT
ejpam-2648	44	7	10	10	NUM
ejpam-2648	44	8	(	(	PUNCT
ejpam-2648	44	9	4	4	NUM
ejpam-2648	44	10	)	)	PUNCT
ejpam-2648	44	11	(	(	PUNCT
ejpam-2648	44	12	2017	2017	NUM
ejpam-2648	44	13	)	)	PUNCT
ejpam-2648	44	14	,	,	PUNCT
ejpam-2648	44	15	749	749	NUM
ejpam-2648	44	16	-	-	SYM
ejpam-2648	44	17	762	762	NUM
ejpam-2648	44	18	751	751	NUM
ejpam-2648	44	19	local	local	ADJ
ejpam-2648	44	20	algebras	algebra	NOUN
ejpam-2648	44	21	of	of	ADP
ejpam-2648	44	22	a	a	DET
ejpam-2648	44	23	jordan	jordan	PROPN
ejpam-2648	44	24	pair	pair	PROPN
ejpam-2648	44	25	.	.	PUNCT
ejpam-2648	45	1	let	let	VERB
ejpam-2648	45	2	v	v	PART
ejpam-2648	45	3	be	be	AUX
ejpam-2648	45	4	a	a	DET
ejpam-2648	45	5	jordan	jordan	PROPN
ejpam-2648	45	6	pair	pair	NOUN
ejpam-2648	45	7	and	and	CCONJ
ejpam-2648	45	8	0	0	NUM
ejpam-2648	45	9	6=	6=	NUM
ejpam-2648	45	10	u	u	PROPN
ejpam-2648	45	11	∈	∈	PROPN
ejpam-2648	45	12	v	v	NOUN
ejpam-2648	45	13	−σ	−σ	NOUN
ejpam-2648	45	14	.	.	PUNCT
ejpam-2648	46	1	by	by	ADP
ejpam-2648	46	2	[	[	X
ejpam-2648	46	3	18	18	NUM
ejpam-2648	46	4	,	,	PUNCT
ejpam-2648	46	5	4.19	4.19	NUM
ejpam-2648	46	6	]	]	PUNCT
ejpam-2648	46	7	the	the	DET
ejpam-2648	46	8	set	set	NOUN
ejpam-2648	46	9	ker(u	ker(u	PROPN
ejpam-2648	46	10	)	)	PUNCT
ejpam-2648	46	11	whose	whose	DET
ejpam-2648	46	12	elements	element	NOUN
ejpam-2648	46	13	are	be	AUX
ejpam-2648	46	14	those	those	DET
ejpam-2648	46	15	x	x	PUNCT
ejpam-2648	46	16	∈	∈	PROPN
ejpam-2648	46	17	v	v	ADP
ejpam-2648	46	18	σ	σ	PRON
ejpam-2648	46	19	such	such	ADJ
ejpam-2648	46	20	that	that	DET
ejpam-2648	46	21	qux	qux	NOUN
ejpam-2648	46	22	=	=	PUNCT
ejpam-2648	46	23	quqxu	quqxu	VERB
ejpam-2648	46	24	=	=	SYM
ejpam-2648	46	25	0	0	NUM
ejpam-2648	46	26	,	,	PUNCT
ejpam-2648	46	27	turns	turn	VERB
ejpam-2648	46	28	out	out	ADP
ejpam-2648	46	29	to	to	PART
ejpam-2648	46	30	be	be	AUX
ejpam-2648	46	31	an	an	DET
ejpam-2648	46	32	ideal	ideal	NOUN
ejpam-2648	46	33	of	of	ADP
ejpam-2648	46	34	v	v	NOUN
ejpam-2648	46	35	σ(u	σ(u	NOUN
ejpam-2648	46	36	)	)	PUNCT
ejpam-2648	46	37	and	and	CCONJ
ejpam-2648	46	38	the	the	DET
ejpam-2648	46	39	quotient	quotient	NOUN
ejpam-2648	46	40	v	v	NOUN
ejpam-2648	46	41	σ(u)/	σ(u)/	ADJ
ejpam-2648	46	42	ker(u	ker(u	PROPN
ejpam-2648	46	43	)	)	PUNCT
ejpam-2648	46	44	is	be	AUX
ejpam-2648	46	45	a	a	DET
ejpam-2648	46	46	jordan	jordan	PROPN
ejpam-2648	46	47	algebra	algebra	PROPN
ejpam-2648	46	48	called	call	VERB
ejpam-2648	46	49	the	the	DET
ejpam-2648	46	50	local	local	ADJ
ejpam-2648	46	51	algebra	algebra	NOUN
ejpam-2648	46	52	of	of	ADP
ejpam-2648	46	53	v	v	NOUN
ejpam-2648	46	54	at	at	ADP
ejpam-2648	46	55	u	u	NOUN
ejpam-2648	46	56	which	which	PRON
ejpam-2648	46	57	we	we	PRON
ejpam-2648	46	58	denote	denote	VERB
ejpam-2648	46	59	by	by	ADP
ejpam-2648	46	60	vu	vu	X
ejpam-2648	46	61	.	.	PUNCT
ejpam-2648	47	1	as	as	SCONJ
ejpam-2648	47	2	pointed	point	VERB
ejpam-2648	47	3	out	out	ADP
ejpam-2648	47	4	in	in	ADP
ejpam-2648	47	5	[	[	X
ejpam-2648	47	6	9	9	NUM
ejpam-2648	47	7	,	,	PUNCT
ejpam-2648	47	8	1.2.4(ii	1.2.4(ii	NUM
ejpam-2648	47	9	)	)	PUNCT
ejpam-2648	47	10	]	]	PUNCT
ejpam-2648	48	1	the	the	DET
ejpam-2648	48	2	condition	condition	NOUN
ejpam-2648	48	3	quqxu	quqxu	VERB
ejpam-2648	48	4	=	=	SYM
ejpam-2648	48	5	0	0	NUM
ejpam-2648	48	6	is	be	AUX
ejpam-2648	48	7	superfluous	superfluous	ADJ
ejpam-2648	48	8	if	if	SCONJ
ejpam-2648	48	9	v	v	NOUN
ejpam-2648	48	10	is	be	AUX
ejpam-2648	48	11	linear	linear	ADJ
ejpam-2648	48	12	or	or	CCONJ
ejpam-2648	48	13	nondegenerate	nondegenerate	VERB
ejpam-2648	48	14	:	:	PUNCT
ejpam-2648	48	15	qx	qx	PROPN
ejpam-2648	48	16	=	=	SYM
ejpam-2648	48	17	0	0	NUM
ejpam-2648	48	18	implies	imply	VERB
ejpam-2648	48	19	x	x	PUNCT
ejpam-2648	48	20	=	=	SYM
ejpam-2648	48	21	0	0	X
ejpam-2648	48	22	.	.	PUNCT
ejpam-2648	49	1	if	if	SCONJ
ejpam-2648	49	2	v	v	NOUN
ejpam-2648	49	3	is	be	AUX
ejpam-2648	49	4	a	a	DET
ejpam-2648	49	5	normed	normed	ADJ
ejpam-2648	49	6	jordan	jordan	PROPN
ejpam-2648	49	7	pair	pair	PROPN
ejpam-2648	49	8	,	,	PUNCT
ejpam-2648	49	9	then	then	ADV
ejpam-2648	49	10	v	v	ADP
ejpam-2648	49	11	σ(u	σ(u	NOUN
ejpam-2648	49	12	)	)	PUNCT
ejpam-2648	49	13	is	be	AUX
ejpam-2648	49	14	a	a	DET
ejpam-2648	49	15	normed	normed	ADJ
ejpam-2648	49	16	jordan	jordan	PROPN
ejpam-2648	49	17	algebra	algebra	PROPN
ejpam-2648	49	18	for	for	ADP
ejpam-2648	49	19	the	the	DET
ejpam-2648	49	20	norm	norm	NOUN
ejpam-2648	49	21	|x|	|x|	PROPN
ejpam-2648	49	22	=	=	NOUN
ejpam-2648	49	23	‖x‖σ	‖x‖σ	ADJ
ejpam-2648	49	24	‖u‖−σ	‖u‖−σ	PUNCT
ejpam-2648	49	25	.	.	PUNCT
ejpam-2648	50	1	moreover	moreover	ADV
ejpam-2648	50	2	,	,	PUNCT
ejpam-2648	50	3	by	by	ADP
ejpam-2648	50	4	[	[	PUNCT
ejpam-2648	50	5	23	23	NUM
ejpam-2648	50	6	,	,	PUNCT
ejpam-2648	50	7	§	§	PROPN
ejpam-2648	50	8	ii	ii	NOUN
ejpam-2648	50	9	.	.	PUNCT
ejpam-2648	50	10	lemma	lemma	PROPN
ejpam-2648	50	11	3.1	3.1	NUM
ejpam-2648	50	12	]	]	PUNCT
ejpam-2648	50	13	,	,	PUNCT
ejpam-2648	50	14	the	the	DET
ejpam-2648	50	15	local	local	ADJ
ejpam-2648	50	16	algebra	algebra	NOUN
ejpam-2648	50	17	vu	vu	NOUN
ejpam-2648	50	18	is	be	AUX
ejpam-2648	50	19	also	also	ADV
ejpam-2648	50	20	normed	norme	VERB
ejpam-2648	50	21	for	for	ADP
ejpam-2648	50	22	the	the	DET
ejpam-2648	50	23	quotient	quotient	NOUN
ejpam-2648	50	24	norm	norm	NOUN
ejpam-2648	50	25	‖x+	‖x+	PROPN
ejpam-2648	50	26	ker(u)‖	ker(u)‖	PUNCT
ejpam-2648	51	1	=	=	SYM
ejpam-2648	51	2	inf	inf	ADJ
ejpam-2648	51	3	z∈ker(u	z∈ker(u	NOUN
ejpam-2648	51	4	)	)	PUNCT
ejpam-2648	51	5	|x+	|x+	PROPN
ejpam-2648	51	6	z|	z|	PRON
ejpam-2648	51	7	which	which	PRON
ejpam-2648	51	8	is	be	AUX
ejpam-2648	51	9	complete	complete	ADJ
ejpam-2648	51	10	if	if	SCONJ
ejpam-2648	51	11	so	so	ADV
ejpam-2648	51	12	are	be	AUX
ejpam-2648	51	13	the	the	DET
ejpam-2648	51	14	norms	norm	NOUN
ejpam-2648	51	15	of	of	ADP
ejpam-2648	51	16	v.	v.	ADP
ejpam-2648	51	17	socle	socle	NOUN
ejpam-2648	51	18	and	and	CCONJ
ejpam-2648	51	19	capacity	capacity	NOUN
ejpam-2648	51	20	.	.	PUNCT
ejpam-2648	52	1	for	for	ADP
ejpam-2648	52	2	a	a	DET
ejpam-2648	52	3	nondegenerate	nondegenerate	PROPN
ejpam-2648	52	4	jordan	jordan	PROPN
ejpam-2648	52	5	pair	pair	PROPN
ejpam-2648	52	6	v	v	ADP
ejpam-2648	52	7	,	,	PUNCT
ejpam-2648	52	8	its	its	PRON
ejpam-2648	52	9	socle	socle	NOUN
ejpam-2648	52	10	,	,	PUNCT
ejpam-2648	52	11	denoted	denote	VERB
ejpam-2648	52	12	by	by	ADP
ejpam-2648	52	13	soc(v	soc(v	PROPN
ejpam-2648	52	14	)	)	PUNCT
ejpam-2648	52	15	,	,	PUNCT
ejpam-2648	52	16	is	be	AUX
ejpam-2648	52	17	the	the	DET
ejpam-2648	52	18	ideal	ideal	ADJ
ejpam-2648	52	19	soc(v	soc(v	PROPN
ejpam-2648	52	20	)	)	PUNCT
ejpam-2648	52	21	=(	=(	NOUN
ejpam-2648	52	22	soc(v	soc(v	PRON
ejpam-2648	52	23	+	+	NOUN
ejpam-2648	52	24	)	)	PUNCT
ejpam-2648	52	25	,	,	PUNCT
ejpam-2648	52	26	soc(v	soc(v	DET
ejpam-2648	52	27	−	−	NOUN
ejpam-2648	52	28	)	)	PUNCT
ejpam-2648	52	29	)	)	PUNCT
ejpam-2648	52	30	,	,	PUNCT
ejpam-2648	52	31	where	where	SCONJ
ejpam-2648	52	32	soc(v	soc(v	PROPN
ejpam-2648	52	33	σ	σ	NOUN
ejpam-2648	52	34	)	)	PUNCT
ejpam-2648	52	35	denotes	denote	VERB
ejpam-2648	52	36	the	the	DET
ejpam-2648	52	37	sum	sum	NOUN
ejpam-2648	52	38	of	of	ADP
ejpam-2648	52	39	all	all	DET
ejpam-2648	52	40	minimal	minimal	ADJ
ejpam-2648	52	41	inner	inner	ADJ
ejpam-2648	52	42	ideals	ideal	NOUN
ejpam-2648	52	43	of	of	ADP
ejpam-2648	52	44	v	v	NOUN
ejpam-2648	52	45	±.	±.	NOUN
ejpam-2648	52	46	(	(	PUNCT
ejpam-2648	52	47	2.1	2.1	NUM
ejpam-2648	52	48	)	)	PUNCT
ejpam-2648	52	49	let	let	VERB
ejpam-2648	52	50	v	v	PART
ejpam-2648	52	51	be	be	AUX
ejpam-2648	52	52	a	a	DET
ejpam-2648	52	53	nondegenerate	nondegenerate	ADJ
ejpam-2648	52	54	jordan	jordan	PROPN
ejpam-2648	52	55	pair	pair	PROPN
ejpam-2648	52	56	and	and	CCONJ
ejpam-2648	52	57	u	u	NOUN
ejpam-2648	52	58	∈	∈	PROPN
ejpam-2648	52	59	v	v	NUM
ejpam-2648	52	60	σ	σ	PROPN
ejpam-2648	52	61	.	.	PUNCT
ejpam-2648	53	1	then	then	ADV
ejpam-2648	53	2	u	u	PROPN
ejpam-2648	53	3	∈	∈	PROPN
ejpam-2648	53	4	soc(v	soc(v	PROPN
ejpam-2648	53	5	σ	σ	PROPN
ejpam-2648	53	6	)	)	PUNCT
ejpam-2648	53	7	if	if	SCONJ
ejpam-2648	53	8	and	and	CCONJ
ejpam-2648	53	9	only	only	ADV
ejpam-2648	53	10	if	if	SCONJ
ejpam-2648	53	11	vu	vu	PROPN
ejpam-2648	53	12	has	have	VERB
ejpam-2648	53	13	finite	finite	ADJ
ejpam-2648	53	14	capacity	capacity	NOUN
ejpam-2648	53	15	[	[	X
ejpam-2648	53	16	25	25	NUM
ejpam-2648	53	17	,	,	PUNCT
ejpam-2648	53	18	0.7(b	0.7(b	NUM
ejpam-2648	53	19	)	)	PUNCT
ejpam-2648	53	20	]	]	PUNCT
ejpam-2648	53	21	.	.	PUNCT
ejpam-2648	54	1	a	a	DET
ejpam-2648	54	2	nondegenerate	nondegenerate	PROPN
ejpam-2648	54	3	jordan	jordan	PROPN
ejpam-2648	54	4	pair	pair	PROPN
ejpam-2648	54	5	v	v	PROPN
ejpam-2648	54	6	has	have	VERB
ejpam-2648	54	7	a	a	DET
ejpam-2648	54	8	finite	finite	ADJ
ejpam-2648	54	9	capacity	capacity	NOUN
ejpam-2648	54	10	if	if	SCONJ
ejpam-2648	54	11	it	it	PRON
ejpam-2648	54	12	contains	contain	VERB
ejpam-2648	54	13	an	an	DET
ejpam-2648	54	14	orthogonal	orthogonal	ADJ
ejpam-2648	54	15	system	system	NOUN
ejpam-2648	54	16	{	{	PUNCT
ejpam-2648	54	17	e1	e1	PROPN
ejpam-2648	54	18	,	,	PUNCT
ejpam-2648	54	19	...	...	PUNCT
ejpam-2648	54	20	,	,	PUNCT
ejpam-2648	54	21	en	en	ADP
ejpam-2648	54	22	}	}	PUNCT
ejpam-2648	54	23	of	of	ADP
ejpam-2648	54	24	division	division	NOUN
ejpam-2648	54	25	idempotents	idempotent	NOUN
ejpam-2648	54	26	(	(	PUNCT
ejpam-2648	54	27	v2(ei	v2(ei	PROPN
ejpam-2648	54	28	)	)	PUNCT
ejpam-2648	54	29	is	be	AUX
ejpam-2648	54	30	a	a	DET
ejpam-2648	54	31	division	division	NOUN
ejpam-2648	54	32	jordan	jordan	PROPN
ejpam-2648	54	33	pair	pair	PROPN
ejpam-2648	54	34	)	)	PUNCT
ejpam-2648	54	35	such	such	ADJ
ejpam-2648	54	36	that	that	PRON
ejpam-2648	54	37	∩ni=1v0(ei	∩ni=1v0(ei	PROPN
ejpam-2648	54	38	)	)	PUNCT
ejpam-2648	54	39	=	=	SYM
ejpam-2648	54	40	0	0	NUM
ejpam-2648	54	41	,	,	PUNCT
ejpam-2648	54	42	equivalently	equivalently	ADV
ejpam-2648	54	43	the	the	DET
ejpam-2648	54	44	lengths	length	NOUN
ejpam-2648	54	45	of	of	ADP
ejpam-2648	54	46	its	its	PRON
ejpam-2648	54	47	chains	chain	NOUN
ejpam-2648	54	48	of	of	ADP
ejpam-2648	54	49	principal	principal	ADJ
ejpam-2648	54	50	inner	inner	ADJ
ejpam-2648	54	51	ideals	ideal	NOUN
ejpam-2648	54	52	are	be	AUX
ejpam-2648	54	53	bounded	bound	VERB
ejpam-2648	54	54	primitive	primitive	ADJ
ejpam-2648	54	55	jordan	jordan	PROPN
ejpam-2648	54	56	pairs	pair	NOUN
ejpam-2648	54	57	and	and	CCONJ
ejpam-2648	54	58	jacobson	jacobson	PROPN
ejpam-2648	54	59	radical	radical	PROPN
ejpam-2648	54	60	.	.	PUNCT
ejpam-2648	55	1	a	a	DET
ejpam-2648	55	2	jordan	jordan	PROPN
ejpam-2648	55	3	pair	pair	PROPN
ejpam-2648	55	4	v	v	NOUN
ejpam-2648	55	5	=	=	PUNCT
ejpam-2648	55	6	(	(	PUNCT
ejpam-2648	55	7	v	v	ADP
ejpam-2648	55	8	+	+	NOUN
ejpam-2648	55	9	,	,	PUNCT
ejpam-2648	55	10	v	v	ADP
ejpam-2648	55	11	−	−	NOUN
ejpam-2648	55	12	)	)	PUNCT
ejpam-2648	55	13	is	be	AUX
ejpam-2648	55	14	said	say	VERB
ejpam-2648	55	15	to	to	PART
ejpam-2648	55	16	be	be	AUX
ejpam-2648	55	17	primitive	primitive	ADJ
ejpam-2648	55	18	at	at	ADP
ejpam-2648	55	19	b	b	PROPN
ejpam-2648	55	20	∈	∈	PROPN
ejpam-2648	55	21	v	v	ADP
ejpam-2648	55	22	−σ	−σ	NOUN
ejpam-2648	55	23	if	if	SCONJ
ejpam-2648	55	24	there	there	PRON
ejpam-2648	55	25	exists	exist	VERB
ejpam-2648	55	26	a	a	DET
ejpam-2648	55	27	proper	proper	ADJ
ejpam-2648	55	28	inner	inner	ADJ
ejpam-2648	55	29	ideal	ideal	NOUN
ejpam-2648	55	30	k	k	PROPN
ejpam-2648	55	31	of	of	ADP
ejpam-2648	55	32	v	v	NOUN
ejpam-2648	55	33	σ	σ	NUM
ejpam-2648	55	34	such	such	ADJ
ejpam-2648	55	35	that	that	SCONJ
ejpam-2648	55	36	:	:	PUNCT
ejpam-2648	55	37	i	i	PRON
ejpam-2648	55	38	)	)	PUNCT
ejpam-2648	56	1	k	k	X
ejpam-2648	56	2	is	be	AUX
ejpam-2648	56	3	a	a	DET
ejpam-2648	56	4	c	c	NOUN
ejpam-2648	56	5	-	-	PUNCT
ejpam-2648	56	6	modular	modular	ADJ
ejpam-2648	56	7	inner	inner	ADJ
ejpam-2648	56	8	ideal	ideal	NOUN
ejpam-2648	56	9	of	of	ADP
ejpam-2648	56	10	the	the	DET
ejpam-2648	56	11	homotope	homotope	NOUN
ejpam-2648	56	12	v	v	ADP
ejpam-2648	56	13	σ(b	σ(b	PROPN
ejpam-2648	56	14	)	)	PUNCT
ejpam-2648	56	15	for	for	ADP
ejpam-2648	56	16	some	some	DET
ejpam-2648	56	17	c	c	PROPN
ejpam-2648	56	18	∈	∈	PROPN
ejpam-2648	56	19	v	v	ADP
ejpam-2648	56	20	σ	σ	PROPN
ejpam-2648	56	21	,	,	PUNCT
ejpam-2648	56	22	ii	ii	NOUN
ejpam-2648	56	23	)	)	PUNCT
ejpam-2648	56	24	k	k	NOUN
ejpam-2648	56	25	complements	complement	VERB
ejpam-2648	56	26	the	the	DET
ejpam-2648	56	27	(	(	PUNCT
ejpam-2648	56	28	σ)-parts	σ)-part	NOUN
ejpam-2648	56	29	of	of	ADP
ejpam-2648	56	30	nonzero	nonzero	PROPN
ejpam-2648	56	31	ideals	ideal	NOUN
ejpam-2648	56	32	:	:	PUNCT
ejpam-2648	56	33	iσ	iσ	VERB
ejpam-2648	56	34	+	+	PROPN
ejpam-2648	56	35	k	k	X
ejpam-2648	56	36	=	=	X
ejpam-2648	56	37	v	v	PROPN
ejpam-2648	56	38	σ	σ	NOUN
ejpam-2648	56	39	for	for	ADP
ejpam-2648	56	40	any	any	DET
ejpam-2648	56	41	nonzero	nonzero	NOUN
ejpam-2648	56	42	ideal	ideal	NOUN
ejpam-2648	57	1	i	i	PRON
ejpam-2648	57	2	=	=	SYM
ejpam-2648	57	3	(	(	PUNCT
ejpam-2648	57	4	i+	i+	PROPN
ejpam-2648	57	5	,	,	PUNCT
ejpam-2648	57	6	i−	i−	PROPN
ejpam-2648	57	7	)	)	PUNCT
ejpam-2648	57	8	of	of	ADP
ejpam-2648	57	9	v.	v.	PROPN
ejpam-2648	57	10	.	.	PUNCT
ejpam-2648	58	1	anquela	anquela	PROPN
ejpam-2648	58	2	and	and	CCONJ
ejpam-2648	58	3	cortés	corté	NOUN
ejpam-2648	58	4	proved	prove	VERB
ejpam-2648	58	5	in	in	ADP
ejpam-2648	58	6	[	[	X
ejpam-2648	58	7	1	1	NUM
ejpam-2648	58	8	]	]	PUNCT
ejpam-2648	58	9	and	and	CCONJ
ejpam-2648	58	10	[	[	X
ejpam-2648	58	11	2	2	X
ejpam-2648	58	12	]	]	X
ejpam-2648	58	13	the	the	DET
ejpam-2648	58	14	following	following	ADJ
ejpam-2648	58	15	results	result	NOUN
ejpam-2648	58	16	:	:	PUNCT
ejpam-2648	58	17	(	(	PUNCT
ejpam-2648	58	18	2.2	2.2	NUM
ejpam-2648	58	19	)	)	PUNCT
ejpam-2648	58	20	v	v	NOUN
ejpam-2648	58	21	is	be	AUX
ejpam-2648	58	22	primitive	primitive	ADJ
ejpam-2648	58	23	at	at	ADP
ejpam-2648	58	24	b	b	PROPN
ejpam-2648	58	25	∈	∈	PROPN
ejpam-2648	58	26	v	v	ADP
ejpam-2648	58	27	−σ	−σ	NOUN
ejpam-2648	58	28	if	if	SCONJ
ejpam-2648	58	29	and	and	CCONJ
ejpam-2648	58	30	only	only	ADV
ejpam-2648	58	31	if	if	SCONJ
ejpam-2648	58	32	vb	vb	NOUN
ejpam-2648	58	33	is	be	AUX
ejpam-2648	58	34	a	a	DET
ejpam-2648	58	35	primitive	primitive	ADJ
ejpam-2648	58	36	jordan	jordan	PROPN
ejpam-2648	58	37	algebra	algebra	PROPN
ejpam-2648	58	38	and	and	CCONJ
ejpam-2648	58	39	v	v	NOUN
ejpam-2648	58	40	is	be	AUX
ejpam-2648	58	41	strongly	strongly	ADV
ejpam-2648	58	42	prime	prime	ADJ
ejpam-2648	58	43	.	.	PUNCT
ejpam-2648	59	1	(	(	PUNCT
ejpam-2648	59	2	2.3	2.3	NUM
ejpam-2648	59	3	)	)	PUNCT
ejpam-2648	59	4	if	if	SCONJ
ejpam-2648	59	5	v	v	NOUN
ejpam-2648	59	6	is	be	AUX
ejpam-2648	59	7	primitive	primitive	ADJ
ejpam-2648	59	8	at	at	ADP
ejpam-2648	59	9	some	some	DET
ejpam-2648	59	10	0	0	NUM
ejpam-2648	59	11	6=	6=	ADP
ejpam-2648	59	12	b0	b0	ADP
ejpam-2648	59	13	∈	∈	PROPN
ejpam-2648	59	14	v	v	ADP
ejpam-2648	59	15	−σ	−σ	NOUN
ejpam-2648	59	16	then	then	ADV
ejpam-2648	59	17	so	so	ADV
ejpam-2648	59	18	is	be	AUX
ejpam-2648	59	19	v	v	NOUN
ejpam-2648	59	20	at	at	ADP
ejpam-2648	59	21	every	every	DET
ejpam-2648	59	22	element	element	NOUN
ejpam-2648	59	23	0	0	NUM
ejpam-2648	60	1	6=	6=	PUNCT
ejpam-2648	60	2	b	b	PROPN
ejpam-2648	60	3	∈	∈	PROPN
ejpam-2648	60	4	v	v	ADP
ejpam-2648	60	5	±.	±.	NOUN
ejpam-2648	60	6	further	further	ADJ
ejpam-2648	60	7	results	result	NOUN
ejpam-2648	60	8	on	on	ADP
ejpam-2648	60	9	primitive	primitive	ADJ
ejpam-2648	60	10	jordan	jordan	PROPN
ejpam-2648	60	11	pairs	pair	NOUN
ejpam-2648	60	12	can	can	AUX
ejpam-2648	60	13	be	be	AUX
ejpam-2648	60	14	found	find	VERB
ejpam-2648	60	15	in	in	ADP
ejpam-2648	60	16	[	[	X
ejpam-2648	60	17	1	1	NUM
ejpam-2648	60	18	]	]	PUNCT
ejpam-2648	60	19	,	,	PUNCT
ejpam-2648	61	1	[	[	X
ejpam-2648	61	2	2	2	NUM
ejpam-2648	61	3	]	]	PUNCT
ejpam-2648	61	4	and	and	CCONJ
ejpam-2648	61	5	[	[	X
ejpam-2648	61	6	3	3	NUM
ejpam-2648	61	7	]	]	PUNCT
ejpam-2648	61	8	.	.	PUNCT
ejpam-2648	62	1	following	follow	VERB
ejpam-2648	62	2	[	[	X
ejpam-2648	62	3	18	18	NUM
ejpam-2648	62	4	]	]	PUNCT
ejpam-2648	62	5	,	,	PUNCT
ejpam-2648	62	6	the	the	DET
ejpam-2648	62	7	jacobson	jacobson	PROPN
ejpam-2648	62	8	radical	radical	PROPN
ejpam-2648	62	9	of	of	ADP
ejpam-2648	62	10	a	a	DET
ejpam-2648	62	11	jordan	jordan	PROPN
ejpam-2648	62	12	pair	pair	PROPN
ejpam-2648	62	13	v	v	NOUN
ejpam-2648	62	14	is	be	AUX
ejpam-2648	62	15	defined	define	VERB
ejpam-2648	62	16	as	as	ADP
ejpam-2648	62	17	the	the	DET
ejpam-2648	62	18	the	the	DET
ejpam-2648	62	19	ideal	ideal	ADJ
ejpam-2648	62	20	rad(v	rad(v	NOUN
ejpam-2648	62	21	)	)	PUNCT
ejpam-2648	63	1	=	=	SYM
ejpam-2648	63	2	(	(	PUNCT
ejpam-2648	63	3	rad(v	rad(v	NOUN
ejpam-2648	63	4	+	+	NOUN
ejpam-2648	63	5	)	)	PUNCT
ejpam-2648	63	6	,	,	PUNCT
ejpam-2648	63	7	rad(v	rad(v	NOUN
ejpam-2648	63	8	−	−	NOUN
ejpam-2648	63	9	)	)	PUNCT
ejpam-2648	63	10	)	)	PUNCT
ejpam-2648	63	11	,	,	PUNCT
ejpam-2648	63	12	where	where	SCONJ
ejpam-2648	63	13	rad(v	rad(v	NOUN
ejpam-2648	63	14	σ	σ	NOUN
ejpam-2648	63	15	)	)	PUNCT
ejpam-2648	63	16	is	be	AUX
ejpam-2648	63	17	the	the	DET
ejpam-2648	63	18	set	set	NOUN
ejpam-2648	63	19	of	of	ADP
ejpam-2648	63	20	properly	properly	ADV
ejpam-2648	63	21	quasi	quasi	ADJ
ejpam-2648	63	22	-	-	ADJ
ejpam-2648	63	23	invertible	invertible	ADJ
ejpam-2648	63	24	elements	element	NOUN
ejpam-2648	63	25	of	of	ADP
ejpam-2648	63	26	v	v	NOUN
ejpam-2648	63	27	σ	σ	NOUN
ejpam-2648	63	28	,	,	PUNCT
ejpam-2648	63	29	that	that	ADV
ejpam-2648	63	30	is	is	ADV
ejpam-2648	63	31	,	,	PUNCT
ejpam-2648	63	32	those	those	DET
ejpam-2648	63	33	elements	element	NOUN
ejpam-2648	63	34	which	which	PRON
ejpam-2648	63	35	are	be	AUX
ejpam-2648	63	36	quasi	quasi	ADJ
ejpam-2648	63	37	-	-	ADJ
ejpam-2648	63	38	invertible	invertible	ADJ
ejpam-2648	63	39	in	in	ADP
ejpam-2648	63	40	every	every	DET
ejpam-2648	63	41	homotope	homotope	NOUN
ejpam-2648	63	42	v	v	ADP
ejpam-2648	63	43	σ(u	σ(u	NOUN
ejpam-2648	63	44	)	)	PUNCT
ejpam-2648	63	45	.	.	PUNCT
ejpam-2648	64	1	a	a	DET
ejpam-2648	64	2	jordan	jordan	PROPN
ejpam-2648	64	3	pair	pair	PROPN
ejpam-2648	64	4	is	be	AUX
ejpam-2648	64	5	said	say	VERB
ejpam-2648	64	6	to	to	PART
ejpam-2648	64	7	be	be	AUX
ejpam-2648	64	8	semiprimitive	semiprimitive	ADJ
ejpam-2648	64	9	is	be	AUX
ejpam-2648	64	10	rad(v	rad(v	NOUN
ejpam-2648	64	11	)	)	PUNCT
ejpam-2648	64	12	=	=	SYM
ejpam-2648	65	1	0	0	X
ejpam-2648	65	2	.	.	PUNCT
ejpam-2648	66	1	as	as	ADP
ejpam-2648	66	2	in	in	ADP
ejpam-2648	66	3	the	the	DET
ejpam-2648	66	4	case	case	NOUN
ejpam-2648	66	5	of	of	ADP
ejpam-2648	66	6	associative	associative	ADJ
ejpam-2648	66	7	algebras	algebra	NOUN
ejpam-2648	66	8	,	,	PUNCT
ejpam-2648	66	9	an	an	DET
ejpam-2648	66	10	ideal	ideal	ADJ
ejpam-2648	66	11	p	p	NOUN
ejpam-2648	66	12	of	of	ADP
ejpam-2648	66	13	a	a	DET
ejpam-2648	66	14	jordan	jordan	PROPN
ejpam-2648	66	15	system	system	NOUN
ejpam-2648	66	16	(	(	PUNCT
ejpam-2648	66	17	algebra	algebra	NOUN
ejpam-2648	66	18	or	or	CCONJ
ejpam-2648	66	19	pair	pair	NOUN
ejpam-2648	66	20	)	)	PUNCT
ejpam-2648	66	21	v	v	NOUN
ejpam-2648	66	22	is	be	AUX
ejpam-2648	66	23	called	call	VERB
ejpam-2648	66	24	primitive	primitive	ADJ
ejpam-2648	66	25	if	if	SCONJ
ejpam-2648	66	26	the	the	DET
ejpam-2648	66	27	factor	factor	NOUN
ejpam-2648	66	28	system	system	NOUN
ejpam-2648	66	29	(	(	PUNCT
ejpam-2648	66	30	algebra	algebra	NOUN
ejpam-2648	66	31	or	or	CCONJ
ejpam-2648	66	32	pair	pair	NOUN
ejpam-2648	66	33	)	)	PUNCT
ejpam-2648	66	34	v	v	NOUN
ejpam-2648	66	35	/	/	SYM
ejpam-2648	66	36	p	p	NOUN
ejpam-2648	66	37	is	be	AUX
ejpam-2648	66	38	primitive	primitive	ADJ
ejpam-2648	66	39	.	.	PUNCT
ejpam-2648	67	1	moreover	moreover	ADV
ejpam-2648	67	2	,	,	PUNCT
ejpam-2648	67	3	it	it	PRON
ejpam-2648	67	4	follows	follow	VERB
ejpam-2648	67	5	from	from	ADP
ejpam-2648	67	6	[	[	X
ejpam-2648	67	7	14	14	NUM
ejpam-2648	67	8	,	,	PUNCT
ejpam-2648	67	9	a.4.8	a.4.8	ADP
ejpam-2648	67	10	]	]	PUNCT
ejpam-2648	67	11	,	,	PUNCT
ejpam-2648	67	12	or	or	CCONJ
ejpam-2648	67	13	either	either	CCONJ
ejpam-2648	67	14	[	[	X
ejpam-2648	67	15	31	31	NUM
ejpam-2648	67	16	]	]	PUNCT
ejpam-2648	67	17	.	.	PUNCT
ejpam-2648	68	1	(	(	PUNCT
ejpam-2648	68	2	2.4	2.4	NUM
ejpam-2648	68	3	)	)	PUNCT
ejpam-2648	68	4	the	the	DET
ejpam-2648	68	5	jacobson	jacobson	PROPN
ejpam-2648	68	6	radical	radical	PROPN
ejpam-2648	68	7	of	of	ADP
ejpam-2648	68	8	a	a	DET
ejpam-2648	68	9	jordan	jordan	PROPN
ejpam-2648	68	10	pair	pair	PROPN
ejpam-2648	68	11	is	be	AUX
ejpam-2648	68	12	the	the	DET
ejpam-2648	68	13	intersection	intersection	NOUN
ejpam-2648	68	14	of	of	ADP
ejpam-2648	68	15	all	all	DET
ejpam-2648	68	16	its	its	PRON
ejpam-2648	68	17	primitive	primitive	ADJ
ejpam-2648	68	18	ideals	ideal	NOUN
ejpam-2648	68	19	.	.	PUNCT
ejpam-2648	69	1	3	3	X
ejpam-2648	69	2	.	.	X
ejpam-2648	69	3	technical	technical	ADJ
ejpam-2648	69	4	results	result	NOUN
ejpam-2648	69	5	recall	recall	VERB
ejpam-2648	69	6	that	that	SCONJ
ejpam-2648	69	7	we	we	PRON
ejpam-2648	69	8	can	can	AUX
ejpam-2648	69	9	measure	measure	VERB
ejpam-2648	69	10	the	the	DET
ejpam-2648	69	11	continuity	continuity	NOUN
ejpam-2648	69	12	of	of	ADP
ejpam-2648	69	13	a	a	DET
ejpam-2648	69	14	linear	linear	ADJ
ejpam-2648	69	15	operator	operator	NOUN
ejpam-2648	69	16	acting	act	VERB
ejpam-2648	69	17	between	between	ADP
ejpam-2648	69	18	two	two	NUM
ejpam-2648	69	19	normed	normed	ADJ
ejpam-2648	69	20	spaces	space	NOUN
ejpam-2648	69	21	by	by	ADP
ejpam-2648	69	22	considering	consider	VERB
ejpam-2648	69	23	its	its	PRON
ejpam-2648	69	24	so	so	ADV
ejpam-2648	69	25	called	call	VERB
ejpam-2648	69	26	separating	separate	VERB
ejpam-2648	69	27	subspace	subspace	NOUN
ejpam-2648	69	28	.	.	PUNCT
ejpam-2648	70	1	indeed	indeed	ADV
ejpam-2648	70	2	,	,	PUNCT
ejpam-2648	70	3	if	if	SCONJ
ejpam-2648	70	4	t	t	PROPN
ejpam-2648	70	5	is	be	AUX
ejpam-2648	70	6	a	a	DET
ejpam-2648	70	7	linear	linear	PROPN
ejpam-2648	70	8	h.	h.	PROPN
ejpam-2648	70	9	marhnine	marhnine	PROPN
ejpam-2648	70	10	,	,	PUNCT
ejpam-2648	70	11	c.	c.	PROPN
ejpam-2648	70	12	zarhouti	zarhouti	PROPN
ejpam-2648	70	13	/	/	SYM
ejpam-2648	70	14	eur	eur	PROPN
ejpam-2648	70	15	.	.	PUNCT
ejpam-2648	71	1	j.	j.	PROPN
ejpam-2648	71	2	pure	pure	PROPN
ejpam-2648	71	3	appl	appl	PROPN
ejpam-2648	71	4	.	.	PROPN
ejpam-2648	71	5	math	math	PROPN
ejpam-2648	71	6	,	,	PUNCT
ejpam-2648	71	7	10	10	NUM
ejpam-2648	71	8	(	(	PUNCT
ejpam-2648	71	9	4	4	NUM
ejpam-2648	71	10	)	)	PUNCT
ejpam-2648	71	11	(	(	PUNCT
ejpam-2648	71	12	2017	2017	NUM
ejpam-2648	71	13	)	)	PUNCT
ejpam-2648	71	14	,	,	PUNCT
ejpam-2648	71	15	749	749	NUM
ejpam-2648	71	16	-	-	SYM
ejpam-2648	71	17	762	762	NUM
ejpam-2648	71	18	752	752	NUM
ejpam-2648	71	19	operator	operator	NOUN
ejpam-2648	71	20	defined	define	VERB
ejpam-2648	71	21	between	between	ADP
ejpam-2648	71	22	two	two	NUM
ejpam-2648	71	23	real	real	ADJ
ejpam-2648	71	24	or	or	CCONJ
ejpam-2648	71	25	complex	complex	ADJ
ejpam-2648	71	26	normed	normed	ADJ
ejpam-2648	71	27	vector	vector	NOUN
ejpam-2648	71	28	spaces	space	NOUN
ejpam-2648	71	29	x	x	PUNCT
ejpam-2648	71	30	and	and	CCONJ
ejpam-2648	71	31	y	y	PROPN
ejpam-2648	71	32	,	,	PUNCT
ejpam-2648	71	33	then	then	ADV
ejpam-2648	71	34	its	its	PRON
ejpam-2648	71	35	separating	separate	VERB
ejpam-2648	71	36	subspace	subspace	NOUN
ejpam-2648	71	37	s(t	s(t	PROPN
ejpam-2648	71	38	)	)	PUNCT
ejpam-2648	71	39	is	be	AUX
ejpam-2648	71	40	defined	define	VERB
ejpam-2648	71	41	by	by	ADP
ejpam-2648	71	42	:	:	PUNCT
ejpam-2648	71	43	s(t	s(t	PROPN
ejpam-2648	71	44	)	)	PUNCT
ejpam-2648	72	1	=	=	PRON
ejpam-2648	72	2	{	{	PUNCT
ejpam-2648	72	3	y	y	PROPN
ejpam-2648	72	4	∈	∈	PROPN
ejpam-2648	72	5	y	y	PROPN
ejpam-2648	72	6	:	:	PUNCT
ejpam-2648	72	7	∃{xn}n	∃{xn}n	VERB
ejpam-2648	72	8	⊂	⊂	X
ejpam-2648	72	9	x	x	PUNCT
ejpam-2648	72	10	such	such	ADJ
ejpam-2648	72	11	that	that	DET
ejpam-2648	72	12	limxn	limxn	ADV
ejpam-2648	72	13	=	=	SYM
ejpam-2648	72	14	0	0	NUM
ejpam-2648	72	15	and	and	CCONJ
ejpam-2648	72	16	limt	limt	NOUN
ejpam-2648	72	17	(	(	PUNCT
ejpam-2648	72	18	xn	xn	X
ejpam-2648	72	19	)	)	PUNCT
ejpam-2648	72	20	=	=	SYM
ejpam-2648	73	1	y	y	PROPN
ejpam-2648	73	2	}	}	PUNCT
ejpam-2648	73	3	.	.	PUNCT
ejpam-2648	74	1	it	it	PRON
ejpam-2648	74	2	is	be	AUX
ejpam-2648	74	3	easily	easily	ADV
ejpam-2648	74	4	seen	see	VERB
ejpam-2648	74	5	that	that	SCONJ
ejpam-2648	74	6	the	the	DET
ejpam-2648	74	7	separating	separate	VERB
ejpam-2648	74	8	subspace	subspace	NOUN
ejpam-2648	74	9	of	of	ADP
ejpam-2648	74	10	t	t	PROPN
ejpam-2648	74	11	is	be	AUX
ejpam-2648	74	12	a	a	DET
ejpam-2648	74	13	closed	closed	ADJ
ejpam-2648	74	14	subspace	subspace	NOUN
ejpam-2648	74	15	of	of	ADP
ejpam-2648	74	16	y.	y.	PROPN
ejpam-2648	74	17	moreover	moreover	ADV
ejpam-2648	74	18	,	,	PUNCT
ejpam-2648	74	19	by	by	ADP
ejpam-2648	74	20	the	the	DET
ejpam-2648	74	21	closed	closed	ADJ
ejpam-2648	74	22	graph	graph	NOUN
ejpam-2648	74	23	theorem	theorem	VERB
ejpam-2648	74	24	,	,	PUNCT
ejpam-2648	74	25	if	if	SCONJ
ejpam-2648	74	26	both	both	DET
ejpam-2648	74	27	x	x	X
ejpam-2648	74	28	and	and	CCONJ
ejpam-2648	74	29	y	y	PROPN
ejpam-2648	74	30	are	be	AUX
ejpam-2648	74	31	banach	banach	ADV
ejpam-2648	74	32	spaces	space	NOUN
ejpam-2648	74	33	,	,	PUNCT
ejpam-2648	74	34	then	then	ADV
ejpam-2648	74	35	t	t	PROPN
ejpam-2648	74	36	is	be	AUX
ejpam-2648	74	37	continuous	continuous	ADJ
ejpam-2648	74	38	if	if	SCONJ
ejpam-2648	74	39	and	and	CCONJ
ejpam-2648	74	40	only	only	ADV
ejpam-2648	74	41	if	if	SCONJ
ejpam-2648	74	42	s(t	s(t	PROPN
ejpam-2648	74	43	)	)	PUNCT
ejpam-2648	75	1	=	=	PUNCT
ejpam-2648	75	2	0	0	X
ejpam-2648	75	3	.	.	PUNCT
ejpam-2648	76	1	let	let	VERB
ejpam-2648	76	2	v	v	NOUN
ejpam-2648	76	3	and	and	CCONJ
ejpam-2648	76	4	w	w	NOUN
ejpam-2648	76	5	be	be	AUX
ejpam-2648	76	6	two	two	NUM
ejpam-2648	76	7	jordan	jordan	PROPN
ejpam-2648	76	8	pairs	pair	NOUN
ejpam-2648	76	9	.	.	PUNCT
ejpam-2648	77	1	by	by	ADP
ejpam-2648	77	2	a	a	DET
ejpam-2648	77	3	higher	high	ADJ
ejpam-2648	77	4	derivation	derivation	NOUN
ejpam-2648	77	5	of	of	ADP
ejpam-2648	77	6	rank	rank	NOUN
ejpam-2648	77	7	k	k	PROPN
ejpam-2648	77	8	(	(	PUNCT
ejpam-2648	77	9	k	k	PROPN
ejpam-2648	77	10	may	may	AUX
ejpam-2648	77	11	be	be	AUX
ejpam-2648	77	12	infinite	infinite	ADJ
ejpam-2648	77	13	)	)	PUNCT
ejpam-2648	77	14	,	,	PUNCT
ejpam-2648	77	15	we	we	PRON
ejpam-2648	77	16	mean	mean	VERB
ejpam-2648	77	17	a	a	DET
ejpam-2648	77	18	family	family	NOUN
ejpam-2648	77	19	of	of	ADP
ejpam-2648	77	20	linear	linear	ADJ
ejpam-2648	77	21	mappings	mapping	NOUN
ejpam-2648	77	22	{	{	PUNCT
ejpam-2648	77	23	ϕn	ϕn	NOUN
ejpam-2648	77	24	=	=	SYM
ejpam-2648	77	25	(	(	PUNCT
ejpam-2648	77	26	ϕ+	ϕ+	NOUN
ejpam-2648	77	27	n	n	PROPN
ejpam-2648	77	28	,	,	PUNCT
ejpam-2648	77	29	ϕ	ϕ	NOUN
ejpam-2648	77	30	−	−	PROPN
ejpam-2648	77	31	n	n	NOUN
ejpam-2648	77	32	)	)	PUNCT
ejpam-2648	77	33	}	}	PUNCT
ejpam-2648	77	34	kn=1	kn=1	PROPN
ejpam-2648	77	35	from	from	ADP
ejpam-2648	77	36	v	v	NUM
ejpam-2648	77	37	into	into	ADP
ejpam-2648	77	38	w	w	ADP
ejpam-2648	77	39	such	such	ADJ
ejpam-2648	77	40	that	that	DET
ejpam-2648	77	41	ϕσn	ϕσn	PROPN
ejpam-2648	77	42	{	{	PUNCT
ejpam-2648	77	43	x	x	PROPN
ejpam-2648	77	44	,	,	PUNCT
ejpam-2648	77	45	y	y	PROPN
ejpam-2648	77	46	,	,	PUNCT
ejpam-2648	77	47	z	z	NOUN
ejpam-2648	77	48	}	}	PUNCT
ejpam-2648	77	49	=	=	SYM
ejpam-2648	77	50	∑	∑	PUNCT
ejpam-2648	77	51	i+j+h	i+j+h	ADJ
ejpam-2648	77	52	=	=	SYM
ejpam-2648	77	53	n	n	NOUN
ejpam-2648	77	54	{	{	PUNCT
ejpam-2648	77	55	ϕσi	ϕσi	NOUN
ejpam-2648	77	56	x	x	NOUN
ejpam-2648	77	57	,	,	PUNCT
ejpam-2648	77	58	ϕ	ϕ	PROPN
ejpam-2648	77	59	−σ	−σ	PROPN
ejpam-2648	77	60	j	j	PROPN
ejpam-2648	77	61	y	y	PROPN
ejpam-2648	77	62	,	,	PUNCT
ejpam-2648	77	63	ϕσhz	ϕσhz	PROPN
ejpam-2648	77	64	}	}	PUNCT
ejpam-2648	77	65	,	,	PUNCT
ejpam-2648	77	66	(	(	PUNCT
ejpam-2648	77	67	x	x	X
ejpam-2648	77	68	,	,	PUNCT
ejpam-2648	77	69	z	z	PROPN
ejpam-2648	77	70	∈	∈	PROPN
ejpam-2648	77	71	v	v	PROPN
ejpam-2648	77	72	σ	σ	PROPN
ejpam-2648	77	73	,	,	PUNCT
ejpam-2648	77	74	y	y	PROPN
ejpam-2648	77	75	∈	∈	PROPN
ejpam-2648	77	76	v	v	ADP
ejpam-2648	77	77	−σ	−σ	NOUN
ejpam-2648	77	78	,	,	PUNCT
ejpam-2648	77	79	n	n	PROPN
ejpam-2648	77	80	=	=	SYM
ejpam-2648	77	81	0	0	NUM
ejpam-2648	77	82	,	,	PUNCT
ejpam-2648	77	83	1	1	NUM
ejpam-2648	77	84	,	,	PUNCT
ejpam-2648	77	85	2	2	NUM
ejpam-2648	77	86	,	,	PUNCT
ejpam-2648	77	87	...	...	PUNCT
ejpam-2648	77	88	,	,	PUNCT
ejpam-2648	77	89	k	k	PROPN
ejpam-2648	77	90	)	)	PUNCT
ejpam-2648	77	91	,	,	PUNCT
ejpam-2648	77	92	where	where	SCONJ
ejpam-2648	77	93	ϕσ0	ϕσ0	PROPN
ejpam-2648	77	94	=	=	SYM
ejpam-2648	77	95	idv	idv	PROPN
ejpam-2648	77	96	σ	σ	PROPN
ejpam-2648	77	97	(	(	PUNCT
ejpam-2648	77	98	σ	σ	PROPN
ejpam-2648	77	99	=	=	SYM
ejpam-2648	77	100	±	±	PROPN
ejpam-2648	77	101	)	)	PUNCT
ejpam-2648	77	102	.	.	PUNCT
ejpam-2648	78	1	let	let	VERB
ejpam-2648	78	2	d	d	NOUN
ejpam-2648	78	3	=	=	SYM
ejpam-2648	78	4	(	(	PUNCT
ejpam-2648	78	5	d+	d+	X
ejpam-2648	78	6	,	,	PUNCT
ejpam-2648	78	7	d−	d−	PROPN
ejpam-2648	78	8	)	)	PUNCT
ejpam-2648	78	9	be	be	AUX
ejpam-2648	78	10	a	a	DET
ejpam-2648	78	11	derivation	derivation	NOUN
ejpam-2648	78	12	from	from	ADP
ejpam-2648	78	13	v	v	NOUN
ejpam-2648	78	14	into	into	ADP
ejpam-2648	78	15	w	w	PROPN
ejpam-2648	78	16	,	,	PUNCT
ejpam-2648	78	17	that	that	PRON
ejpam-2648	78	18	is	be	AUX
ejpam-2648	78	19	a	a	DET
ejpam-2648	78	20	pair	pair	NOUN
ejpam-2648	78	21	of	of	ADP
ejpam-2648	78	22	linear	linear	PROPN
ejpam-2648	78	23	operators	operator	NOUN
ejpam-2648	78	24	dσ	dσ	VERB
ejpam-2648	78	25	:	:	PUNCT
ejpam-2648	78	26	v	v	X
ejpam-2648	78	27	σ	σ	NUM
ejpam-2648	78	28	−→	−→	NOUN
ejpam-2648	78	29	v	v	ADP
ejpam-2648	78	30	σ	σ	NOUN
ejpam-2648	78	31	satisfying	satisfy	VERB
ejpam-2648	78	32	dσ	dσ	PROPN
ejpam-2648	78	33	{	{	PUNCT
ejpam-2648	78	34	x	x	PROPN
ejpam-2648	78	35	,	,	PUNCT
ejpam-2648	78	36	y	y	PROPN
ejpam-2648	78	37	,	,	PUNCT
ejpam-2648	78	38	z	z	NOUN
ejpam-2648	78	39	}	}	PUNCT
ejpam-2648	78	40	=	=	SYM
ejpam-2648	78	41	{	{	PUNCT
ejpam-2648	78	42	dσx	dσx	NOUN
ejpam-2648	78	43	,	,	PUNCT
ejpam-2648	78	44	y	y	PROPN
ejpam-2648	78	45	,	,	PUNCT
ejpam-2648	78	46	z}+	z}+	NUM
ejpam-2648	78	47	{	{	PUNCT
ejpam-2648	78	48	x	x	NOUN
ejpam-2648	78	49	,	,	PUNCT
ejpam-2648	78	50	d−σy	d−σy	NOUN
ejpam-2648	78	51	,	,	PUNCT
ejpam-2648	78	52	z}+	z}+	NUM
ejpam-2648	78	53	{	{	PUNCT
ejpam-2648	78	54	x	x	NOUN
ejpam-2648	78	55	,	,	PUNCT
ejpam-2648	78	56	y	y	PROPN
ejpam-2648	78	57	,	,	PUNCT
ejpam-2648	78	58	dσz	dσz	NOUN
ejpam-2648	78	59	}	}	PUNCT
ejpam-2648	78	60	,	,	PUNCT
ejpam-2648	78	61	for	for	ADP
ejpam-2648	78	62	all	all	DET
ejpam-2648	78	63	(	(	PUNCT
ejpam-2648	78	64	x	x	NOUN
ejpam-2648	78	65	,	,	PUNCT
ejpam-2648	78	66	z	z	PROPN
ejpam-2648	78	67	∈	∈	PROPN
ejpam-2648	78	68	v	v	PROPN
ejpam-2648	78	69	σ	σ	PROPN
ejpam-2648	78	70	,	,	PUNCT
ejpam-2648	78	71	y	y	PROPN
ejpam-2648	78	72	∈	∈	PROPN
ejpam-2648	78	73	v	v	ADP
ejpam-2648	78	74	−σ	−σ	NOUN
ejpam-2648	78	75	.	.	PUNCT
ejpam-2648	79	1	any	any	DET
ejpam-2648	79	2	derivation	derivation	NOUN
ejpam-2648	79	3	d	d	NOUN
ejpam-2648	79	4	=	=	SYM
ejpam-2648	79	5	(	(	PUNCT
ejpam-2648	79	6	d+	d+	X
ejpam-2648	79	7	,	,	PUNCT
ejpam-2648	79	8	d−	d−	PROPN
ejpam-2648	79	9	)	)	PUNCT
ejpam-2648	79	10	from	from	ADP
ejpam-2648	79	11	v	v	NOUN
ejpam-2648	79	12	into	into	ADP
ejpam-2648	79	13	w	w	PROPN
ejpam-2648	79	14	gives	give	VERB
ejpam-2648	79	15	rise	rise	NOUN
ejpam-2648	79	16	to	to	ADP
ejpam-2648	79	17	a	a	DET
ejpam-2648	79	18	standard	standard	ADJ
ejpam-2648	79	19	example	example	NOUN
ejpam-2648	79	20	of	of	ADP
ejpam-2648	79	21	higher	high	ADJ
ejpam-2648	79	22	derivations	derivation	NOUN
ejpam-2648	79	23	{	{	PUNCT
ejpam-2648	79	24	ϕn	ϕn	NOUN
ejpam-2648	79	25	=	=	SYM
ejpam-2648	79	26	(	(	PUNCT
ejpam-2648	79	27	ϕ+	ϕ+	NOUN
ejpam-2648	79	28	n	n	PROPN
ejpam-2648	79	29	,	,	PUNCT
ejpam-2648	79	30	ϕ	ϕ	NOUN
ejpam-2648	79	31	−	−	PROPN
ejpam-2648	79	32	n	n	NOUN
ejpam-2648	79	33	)	)	PUNCT
ejpam-2648	79	34	}	}	PUNCT
ejpam-2648	79	35	n≥0	n≥0	NOUN
ejpam-2648	79	36	from	from	ADP
ejpam-2648	79	37	v	v	NOUN
ejpam-2648	79	38	into	into	ADP
ejpam-2648	79	39	w	w	NOUN
ejpam-2648	79	40	by	by	ADP
ejpam-2648	79	41	setting	set	VERB
ejpam-2648	79	42	ϕ+	ϕ+	ADP
ejpam-2648	79	43	n	n	NOUN
ejpam-2648	79	44	=	=	SYM
ejpam-2648	79	45	1	1	NUM
ejpam-2648	79	46	n	n	NOUN
ejpam-2648	79	47	!	!	PUNCT
ejpam-2648	80	1	dn	dn	PROPN
ejpam-2648	81	1	+	+	ADV
ejpam-2648	81	2	,	,	PUNCT
ejpam-2648	81	3	and	and	CCONJ
ejpam-2648	81	4	ϕ−n	ϕ−n	NOUN
ejpam-2648	81	5	=	=	SYM
ejpam-2648	81	6	1	1	NUM
ejpam-2648	81	7	n	n	NOUN
ejpam-2648	81	8	!	!	PUNCT
ejpam-2648	82	1	dn	dn	NOUN
ejpam-2648	82	2	−.	−.	ADV
ejpam-2648	82	3	remark	remark	VERB
ejpam-2648	82	4	1	1	NUM
ejpam-2648	82	5	.	.	PUNCT
ejpam-2648	83	1	i	i	PRON
ejpam-2648	83	2	)	)	PUNCT
ejpam-2648	84	1	it	it	PRON
ejpam-2648	84	2	follows	follow	VERB
ejpam-2648	84	3	from	from	ADP
ejpam-2648	84	4	the	the	DET
ejpam-2648	84	5	last	last	ADJ
ejpam-2648	84	6	definitions	definition	NOUN
ejpam-2648	84	7	that	that	PRON
ejpam-2648	84	8	ϕ1	ϕ1	VERB
ejpam-2648	84	9	=	=	SYM
ejpam-2648	84	10	(	(	PUNCT
ejpam-2648	84	11	ϕ+	ϕ+	ADP
ejpam-2648	84	12	1	1	NUM
ejpam-2648	84	13	,	,	PUNCT
ejpam-2648	84	14	ϕ	ϕ	NOUN
ejpam-2648	84	15	−	−	PROPN
ejpam-2648	84	16	1	1	NUM
ejpam-2648	84	17	)	)	PUNCT
ejpam-2648	84	18	is	be	AUX
ejpam-2648	84	19	a	a	DET
ejpam-2648	84	20	derivation	derivation	NOUN
ejpam-2648	84	21	.	.	PUNCT
ejpam-2648	85	1	ii	ii	X
ejpam-2648	85	2	)	)	PUNCT
ejpam-2648	85	3	in	in	ADP
ejpam-2648	85	4	order	order	NOUN
ejpam-2648	85	5	to	to	PART
ejpam-2648	85	6	simplify	simplify	VERB
ejpam-2648	85	7	notations	notation	NOUN
ejpam-2648	85	8	,	,	PUNCT
ejpam-2648	85	9	the	the	DET
ejpam-2648	85	10	index	index	NOUN
ejpam-2648	85	11	σ	σ	NOUN
ejpam-2648	85	12	=	=	SYM
ejpam-2648	85	13	±	±	NOUN
ejpam-2648	85	14	in	in	ADP
ejpam-2648	85	15	expressions	expression	NOUN
ejpam-2648	85	16	like	like	ADP
ejpam-2648	85	17	d±i	d±i	PROPN
ejpam-2648	85	18	(	(	PUNCT
ejpam-2648	85	19	x	x	NOUN
ejpam-2648	85	20	)	)	PUNCT
ejpam-2648	85	21	,	,	PUNCT
ejpam-2648	85	22	ϕ±i	ϕ±i	PROPN
ejpam-2648	85	23	(	(	PUNCT
ejpam-2648	85	24	x	x	NOUN
ejpam-2648	85	25	)	)	PUNCT
ejpam-2648	85	26	,	,	PUNCT
ejpam-2648	85	27	...	...	PUNCT
ejpam-2648	85	28	will	will	AUX
ejpam-2648	85	29	be	be	AUX
ejpam-2648	85	30	sometimes	sometimes	ADV
ejpam-2648	85	31	suppressed	suppress	VERB
ejpam-2648	85	32	if	if	SCONJ
ejpam-2648	85	33	there	there	PRON
ejpam-2648	85	34	is	be	VERB
ejpam-2648	85	35	no	no	DET
ejpam-2648	85	36	confusion	confusion	NOUN
ejpam-2648	85	37	.	.	PUNCT
ejpam-2648	86	1	lemma	lemma	PROPN
ejpam-2648	86	2	1	1	X
ejpam-2648	86	3	.	.	PUNCT
ejpam-2648	87	1	let	let	VERB
ejpam-2648	87	2	v	v	PART
ejpam-2648	87	3	be	be	AUX
ejpam-2648	87	4	a	a	DET
ejpam-2648	87	5	normed	normed	ADJ
ejpam-2648	87	6	jordan	jordan	PROPN
ejpam-2648	87	7	pair	pair	PROPN
ejpam-2648	87	8	and	and	CCONJ
ejpam-2648	87	9	let	let	VERB
ejpam-2648	87	10	k	k	PROPN
ejpam-2648	87	11	≥	≥	NUM
ejpam-2648	87	12	2	2	NUM
ejpam-2648	87	13	be	be	AUX
ejpam-2648	87	14	a	a	DET
ejpam-2648	87	15	fixed	fix	VERB
ejpam-2648	87	16	positive	positive	ADJ
ejpam-2648	87	17	integer	integer	NOUN
ejpam-2648	87	18	.	.	PUNCT
ejpam-2648	88	1	if	if	SCONJ
ejpam-2648	88	2	ϕn	ϕn	PRON
ejpam-2648	88	3	=	=	PUNCT
ejpam-2648	88	4	(	(	PUNCT
ejpam-2648	88	5	ϕ+	ϕ+	NOUN
ejpam-2648	88	6	n	n	PROPN
ejpam-2648	88	7	,	,	PUNCT
ejpam-2648	88	8	ϕ	ϕ	NOUN
ejpam-2648	88	9	−	−	PROPN
ejpam-2648	88	10	n	n	NOUN
ejpam-2648	88	11	)	)	PUNCT
ejpam-2648	88	12	}	}	PUNCT
ejpam-2648	88	13	is	be	AUX
ejpam-2648	88	14	a	a	DET
ejpam-2648	88	15	higher	high	ADJ
ejpam-2648	88	16	derivation	derivation	NOUN
ejpam-2648	88	17	on	on	ADP
ejpam-2648	88	18	v	v	ADP
ejpam-2648	88	19	such	such	ADJ
ejpam-2648	88	20	that	that	DET
ejpam-2648	88	21	ϕσi	ϕσi	PROPN
ejpam-2648	88	22	is	be	AUX
ejpam-2648	88	23	continuous	continuous	ADJ
ejpam-2648	88	24	for	for	ADP
ejpam-2648	88	25	every	every	DET
ejpam-2648	88	26	i	i	PROPN
ejpam-2648	88	27	∈	∈	PROPN
ejpam-2648	88	28	{	{	PUNCT
ejpam-2648	88	29	0	0	NUM
ejpam-2648	88	30	,	,	PUNCT
ejpam-2648	88	31	1	1	NUM
ejpam-2648	88	32	,	,	PUNCT
ejpam-2648	88	33	...	...	PUNCT
ejpam-2648	88	34	,	,	PUNCT
ejpam-2648	88	35	k	k	PROPN
ejpam-2648	89	1	−	−	PROPN
ejpam-2648	89	2	1	1	NUM
ejpam-2648	89	3	}	}	PUNCT
ejpam-2648	89	4	(	(	PUNCT
ejpam-2648	89	5	σ	σ	X
ejpam-2648	89	6	=	=	PUNCT
ejpam-2648	89	7	+	+	ADJ
ejpam-2648	89	8	,	,	PUNCT
ejpam-2648	89	9	−	−	PROPN
ejpam-2648	89	10	)	)	PUNCT
ejpam-2648	89	11	,	,	PUNCT
ejpam-2648	89	12	then	then	ADV
ejpam-2648	89	13	the	the	DET
ejpam-2648	89	14	separating	separate	VERB
ejpam-2648	89	15	subspace	subspace	NOUN
ejpam-2648	89	16	s(ϕk	s(ϕk	NOUN
ejpam-2648	89	17	)	)	PUNCT
ejpam-2648	89	18	=	=	SYM
ejpam-2648	89	19	(	(	PUNCT
ejpam-2648	89	20	s(ϕ+	s(ϕ+	PROPN
ejpam-2648	89	21	k	k	X
ejpam-2648	89	22	)	)	PUNCT
ejpam-2648	89	23	,	,	PUNCT
ejpam-2648	89	24	s(ϕ−k	s(ϕ−k	PROPN
ejpam-2648	89	25	)	)	PUNCT
ejpam-2648	89	26	)	)	PUNCT
ejpam-2648	90	1	of	of	ADP
ejpam-2648	90	2	ϕk	ϕk	ADV
ejpam-2648	90	3	is	be	AUX
ejpam-2648	90	4	a	a	DET
ejpam-2648	90	5	closed	closed	ADJ
ejpam-2648	90	6	ideal	ideal	NOUN
ejpam-2648	90	7	of	of	ADP
ejpam-2648	90	8	v.	v.	ADP
ejpam-2648	90	9	proof	proof	NOUN
ejpam-2648	90	10	.	.	PUNCT
ejpam-2648	91	1	since	since	SCONJ
ejpam-2648	91	2	the	the	DET
ejpam-2648	91	3	characteristic	characteristic	NOUN
ejpam-2648	91	4	of	of	ADP
ejpam-2648	91	5	the	the	DET
ejpam-2648	91	6	ground	ground	NOUN
ejpam-2648	91	7	field	field	NOUN
ejpam-2648	91	8	is	be	AUX
ejpam-2648	91	9	zero	zero	NUM
ejpam-2648	91	10	,	,	PUNCT
ejpam-2648	91	11	it	it	PRON
ejpam-2648	91	12	suffices	suffice	VERB
ejpam-2648	91	13	to	to	PART
ejpam-2648	91	14	prove	prove	VERB
ejpam-2648	91	15	that	that	DET
ejpam-2648	91	16	s(ϕn	s(ϕn	NOUN
ejpam-2648	91	17	)	)	PUNCT
ejpam-2648	91	18	is	be	AUX
ejpam-2648	91	19	an	an	DET
ejpam-2648	91	20	outer	outer	ADJ
ejpam-2648	91	21	ideal	ideal	NOUN
ejpam-2648	91	22	of	of	ADP
ejpam-2648	91	23	v.	v.	CCONJ
ejpam-2648	91	24	that	that	PRON
ejpam-2648	91	25	is	be	AUX
ejpam-2648	91	26	qv	qv	INTJ
ejpam-2648	91	27	−σs(ϕσk	−σs(ϕσk	PROPN
ejpam-2648	91	28	)	)	PUNCT
ejpam-2648	92	1	⊂	⊂	PROPN
ejpam-2648	92	2	s(ϕσk	s(ϕσk	PROPN
ejpam-2648	92	3	)	)	PUNCT
ejpam-2648	92	4	and	and	CCONJ
ejpam-2648	92	5	{	{	PUNCT
ejpam-2648	92	6	s(ϕσk	s(ϕσk	PROPN
ejpam-2648	92	7	)	)	PUNCT
ejpam-2648	92	8	,	,	PUNCT
ejpam-2648	92	9	v	v	NOUN
ejpam-2648	92	10	−σ	−σ	NOUN
ejpam-2648	92	11	,	,	PUNCT
ejpam-2648	92	12	v	v	NOUN
ejpam-2648	92	13	σ	σ	PROPN
ejpam-2648	92	14	}	}	PUNCT
ejpam-2648	92	15	⊂	⊂	PROPN
ejpam-2648	92	16	s(ϕσk	s(ϕσk	PROPN
ejpam-2648	92	17	)	)	PUNCT
ejpam-2648	92	18	.	.	PUNCT
ejpam-2648	93	1	let	let	VERB
ejpam-2648	93	2	s	s	PRON
ejpam-2648	93	3	be	be	AUX
ejpam-2648	93	4	an	an	DET
ejpam-2648	93	5	element	element	NOUN
ejpam-2648	93	6	of	of	ADP
ejpam-2648	93	7	s(ϕσk	s(ϕσk	PROPN
ejpam-2648	93	8	)	)	PUNCT
ejpam-2648	93	9	and	and	CCONJ
ejpam-2648	93	10	a	a	PRON
ejpam-2648	93	11	be	be	AUX
ejpam-2648	93	12	an	an	DET
ejpam-2648	93	13	arbitrary	arbitrary	ADJ
ejpam-2648	93	14	element	element	NOUN
ejpam-2648	93	15	of	of	ADP
ejpam-2648	93	16	v	v	NUM
ejpam-2648	93	17	−σ	−σ	NOUN
ejpam-2648	93	18	.	.	PUNCT
ejpam-2648	94	1	then	then	ADV
ejpam-2648	94	2	there	there	PRON
ejpam-2648	94	3	exist	exist	VERB
ejpam-2648	94	4	a	a	DET
ejpam-2648	94	5	sequence	sequence	NOUN
ejpam-2648	94	6	{	{	PUNCT
ejpam-2648	94	7	xn}n	xn}n	PROPN
ejpam-2648	94	8	⊂	⊂	PROPN
ejpam-2648	94	9	v	v	ADP
ejpam-2648	94	10	σ	σ	PROPN
ejpam-2648	94	11	such	such	ADJ
ejpam-2648	94	12	that	that	DET
ejpam-2648	94	13	limxn	limxn	ADV
ejpam-2648	94	14	=	=	SYM
ejpam-2648	94	15	0	0	NUM
ejpam-2648	94	16	and	and	CCONJ
ejpam-2648	94	17	limϕσk(xn	limϕσk(xn	PROPN
ejpam-2648	94	18	)	)	PUNCT
ejpam-2648	94	19	=	=	VERB
ejpam-2648	94	20	s.	s.	PROPN
ejpam-2648	94	21	consider	consider	VERB
ejpam-2648	94	22	the	the	DET
ejpam-2648	94	23	sequence	sequence	NOUN
ejpam-2648	94	24	{	{	PUNCT
ejpam-2648	94	25	qaxn	qaxn	NOUN
ejpam-2648	94	26	}	}	PUNCT
ejpam-2648	94	27	.	.	PUNCT
ejpam-2648	95	1	by	by	ADP
ejpam-2648	95	2	continuity	continuity	NOUN
ejpam-2648	95	3	of	of	ADP
ejpam-2648	95	4	the	the	DET
ejpam-2648	95	5	operator	operator	NOUN
ejpam-2648	95	6	qa	qa	NOUN
ejpam-2648	95	7	,	,	PUNCT
ejpam-2648	95	8	we	we	PRON
ejpam-2648	95	9	get	get	VERB
ejpam-2648	95	10	limqaxn	limqaxn	ADJ
ejpam-2648	96	1	=	=	PUNCT
ejpam-2648	96	2	qa	qa	X
ejpam-2648	96	3	limxn	limxn	ADV
ejpam-2648	96	4	=	=	NOUN
ejpam-2648	96	5	0	0	X
ejpam-2648	96	6	.	.	PUNCT
ejpam-2648	97	1	moreover	moreover	ADV
ejpam-2648	97	2	,	,	PUNCT
ejpam-2648	97	3	using	use	VERB
ejpam-2648	97	4	the	the	DET
ejpam-2648	97	5	continuity	continuity	NOUN
ejpam-2648	97	6	of	of	ADP
ejpam-2648	97	7	the	the	DET
ejpam-2648	97	8	triple	triple	ADJ
ejpam-2648	97	9	product	product	NOUN
ejpam-2648	97	10	of	of	ADP
ejpam-2648	97	11	v	v	NOUN
ejpam-2648	97	12	and	and	CCONJ
ejpam-2648	97	13	that	that	PRON
ejpam-2648	97	14	of	of	ADP
ejpam-2648	97	15	ϕσj	ϕσj	INTJ
ejpam-2648	97	16	such	such	ADJ
ejpam-2648	97	17	that	that	SCONJ
ejpam-2648	97	18	0	0	NUM
ejpam-2648	97	19	≤	≤	NUM
ejpam-2648	97	20	j	j	PROPN
ejpam-2648	97	21	≤	≤	PROPN
ejpam-2648	97	22	k−1	k−1	PROPN
ejpam-2648	97	23	,	,	PUNCT
ejpam-2648	97	24	we	we	PRON
ejpam-2648	97	25	see	see	VERB
ejpam-2648	97	26	h.	h.	PROPN
ejpam-2648	97	27	marhnine	marhnine	PROPN
ejpam-2648	97	28	,	,	PUNCT
ejpam-2648	97	29	c.	c.	PROPN
ejpam-2648	97	30	zarhouti	zarhouti	PROPN
ejpam-2648	97	31	/	/	SYM
ejpam-2648	97	32	eur	eur	PROPN
ejpam-2648	97	33	.	.	PUNCT
ejpam-2648	98	1	j.	j.	PROPN
ejpam-2648	98	2	pure	pure	PROPN
ejpam-2648	98	3	appl	appl	PROPN
ejpam-2648	98	4	.	.	PROPN
ejpam-2648	98	5	math	math	PROPN
ejpam-2648	98	6	,	,	PUNCT
ejpam-2648	98	7	10	10	NUM
ejpam-2648	98	8	(	(	PUNCT
ejpam-2648	98	9	4	4	NUM
ejpam-2648	98	10	)	)	PUNCT
ejpam-2648	98	11	(	(	PUNCT
ejpam-2648	98	12	2017	2017	NUM
ejpam-2648	98	13	)	)	PUNCT
ejpam-2648	98	14	,	,	PUNCT
ejpam-2648	98	15	749	749	NUM
ejpam-2648	98	16	-	-	SYM
ejpam-2648	98	17	762	762	NUM
ejpam-2648	98	18	753	753	NUM
ejpam-2648	98	19	that	that	SCONJ
ejpam-2648	98	20	the	the	DET
ejpam-2648	98	21	terms	term	NOUN
ejpam-2648	98	22	{	{	PUNCT
ejpam-2648	98	23	ϕσi	ϕσi	NOUN
ejpam-2648	98	24	a	a	NOUN
ejpam-2648	98	25	,	,	PUNCT
ejpam-2648	98	26	ϕ	ϕ	PROPN
ejpam-2648	98	27	−σ	−σ	PROPN
ejpam-2648	98	28	j	j	PROPN
ejpam-2648	98	29	xn	xn	PROPN
ejpam-2648	98	30	,	,	PUNCT
ejpam-2648	98	31	ϕ	ϕ	PROPN
ejpam-2648	98	32	σ	σ	X
ejpam-2648	98	33	ha	ha	INTJ
ejpam-2648	98	34	}	}	PUNCT
ejpam-2648	98	35	converge	converge	VERB
ejpam-2648	98	36	to	to	ADP
ejpam-2648	98	37	zero	zero	NUM
ejpam-2648	98	38	when	when	SCONJ
ejpam-2648	98	39	n	n	PRON
ejpam-2648	98	40	tends	tend	VERB
ejpam-2648	98	41	to	to	ADP
ejpam-2648	98	42	∞	∞	PROPN
ejpam-2648	98	43	and	and	CCONJ
ejpam-2648	98	44	consequently	consequently	ADV
ejpam-2648	98	45	we	we	PRON
ejpam-2648	98	46	have	have	AUX
ejpam-2648	98	47	limϕσkqaxn	limϕσkqaxn	VERB
ejpam-2648	98	48	=	=	SYM
ejpam-2648	98	49	1	1	NUM
ejpam-2648	98	50	2	2	NUM
ejpam-2648	98	51	limϕσk	limϕσk	NOUN
ejpam-2648	98	52	{	{	PUNCT
ejpam-2648	98	53	a	a	PROPN
ejpam-2648	98	54	,	,	PUNCT
ejpam-2648	98	55	xn	xn	PROPN
ejpam-2648	98	56	,	,	PUNCT
ejpam-2648	98	57	a	a	PRON
ejpam-2648	98	58	}	}	PUNCT
ejpam-2648	98	59	=	=	SYM
ejpam-2648	98	60	1	1	NUM
ejpam-2648	98	61	2	2	NUM
ejpam-2648	98	62	lim	lim	PROPN
ejpam-2648	98	63	∑	∑	PROPN
ejpam-2648	98	64	i+j+h	i+j+h	PROPN
ejpam-2648	98	65	=	=	SYM
ejpam-2648	98	66	k	k	X
ejpam-2648	98	67	{	{	PUNCT
ejpam-2648	98	68	ϕσi	ϕσi	PROPN
ejpam-2648	98	69	a	a	NOUN
ejpam-2648	98	70	,	,	PUNCT
ejpam-2648	98	71	ϕ	ϕ	PROPN
ejpam-2648	98	72	−σ	−σ	PROPN
ejpam-2648	99	1	j	j	PROPN
ejpam-2648	99	2	xn	xn	PROPN
ejpam-2648	99	3	,	,	PUNCT
ejpam-2648	99	4	ϕ	ϕ	PROPN
ejpam-2648	99	5	σ	σ	X
ejpam-2648	99	6	ha	ha	INTJ
ejpam-2648	99	7	}	}	PUNCT
ejpam-2648	99	8	=	=	SYM
ejpam-2648	99	9	1	1	NUM
ejpam-2648	99	10	2	2	NUM
ejpam-2648	99	11	{	{	PUNCT
ejpam-2648	99	12	a	a	PRON
ejpam-2648	99	13	,	,	PUNCT
ejpam-2648	99	14	limϕ−σk	limϕ−σk	NOUN
ejpam-2648	99	15	xn	xn	PROPN
ejpam-2648	99	16	,	,	PUNCT
ejpam-2648	99	17	a	a	DET
ejpam-2648	99	18	}	}	PUNCT
ejpam-2648	99	19	=	=	SYM
ejpam-2648	99	20	1	1	NUM
ejpam-2648	99	21	2	2	NUM
ejpam-2648	99	22	{	{	PUNCT
ejpam-2648	99	23	a	a	DET
ejpam-2648	99	24	,	,	PUNCT
ejpam-2648	99	25	s	s	PROPN
ejpam-2648	99	26	,	,	PUNCT
ejpam-2648	99	27	a	a	DET
ejpam-2648	99	28	}	}	PUNCT
ejpam-2648	99	29	=	=	SYM
ejpam-2648	99	30	qas	qas	PROPN
ejpam-2648	99	31	,	,	PUNCT
ejpam-2648	99	32	which	which	PRON
ejpam-2648	99	33	establishes	establish	VERB
ejpam-2648	99	34	qv	qv	NOUN
ejpam-2648	99	35	−σs(ϕσk	−σs(ϕσk	PROPN
ejpam-2648	99	36	)	)	PUNCT
ejpam-2648	99	37	⊂	⊂	PROPN
ejpam-2648	99	38	s(ϕσk	s(ϕσk	PROPN
ejpam-2648	99	39	)	)	PUNCT
ejpam-2648	99	40	.	.	PUNCT
ejpam-2648	100	1	on	on	ADP
ejpam-2648	100	2	the	the	DET
ejpam-2648	100	3	other	other	ADJ
ejpam-2648	100	4	hand	hand	NOUN
ejpam-2648	100	5	,	,	PUNCT
ejpam-2648	100	6	for	for	ADP
ejpam-2648	100	7	arbitrary	arbitrary	ADJ
ejpam-2648	100	8	pair	pair	NOUN
ejpam-2648	100	9	(	(	PUNCT
ejpam-2648	100	10	u	u	NOUN
ejpam-2648	100	11	,	,	PUNCT
ejpam-2648	100	12	v	v	NOUN
ejpam-2648	100	13	)	)	PUNCT
ejpam-2648	100	14	of	of	ADP
ejpam-2648	100	15	elements	element	NOUN
ejpam-2648	100	16	in	in	ADP
ejpam-2648	100	17	v	v	NUM
ejpam-2648	100	18	−σ	−σ	NOUN
ejpam-2648	100	19	×	×	PROPN
ejpam-2648	100	20	v	v	PROPN
ejpam-2648	100	21	σ	σ	PROPN
ejpam-2648	100	22	,	,	PUNCT
ejpam-2648	100	23	the	the	DET
ejpam-2648	100	24	sequence	sequence	NOUN
ejpam-2648	100	25	{	{	PUNCT
ejpam-2648	100	26	xn	xn	PROPN
ejpam-2648	100	27	,	,	PUNCT
ejpam-2648	100	28	u	u	NOUN
ejpam-2648	100	29	,	,	PUNCT
ejpam-2648	100	30	v	v	NOUN
ejpam-2648	100	31	}	}	PUNCT
ejpam-2648	100	32	converges	converge	VERB
ejpam-2648	100	33	to	to	ADP
ejpam-2648	100	34	0	0	NUM
ejpam-2648	100	35	.	.	PUNCT
ejpam-2648	101	1	using	use	VERB
ejpam-2648	101	2	again	again	ADV
ejpam-2648	101	3	the	the	DET
ejpam-2648	101	4	continuity	continuity	NOUN
ejpam-2648	101	5	of	of	ADP
ejpam-2648	101	6	the	the	DET
ejpam-2648	101	7	triple	triple	ADJ
ejpam-2648	101	8	product	product	NOUN
ejpam-2648	101	9	of	of	ADP
ejpam-2648	101	10	v	v	NOUN
ejpam-2648	101	11	as	as	ADV
ejpam-2648	101	12	well	well	ADV
ejpam-2648	101	13	as	as	ADP
ejpam-2648	101	14	that	that	PRON
ejpam-2648	101	15	of	of	ADP
ejpam-2648	101	16	ϕσi	ϕσi	NOUN
ejpam-2648	101	17	such	such	ADJ
ejpam-2648	101	18	that	that	SCONJ
ejpam-2648	101	19	0	0	NUM
ejpam-2648	101	20	≤	≤	NUM
ejpam-2648	101	21	i	i	PROPN
ejpam-2648	101	22	≤	≤	PROPN
ejpam-2648	101	23	k−	k−	PROPN
ejpam-2648	101	24	1	1	NUM
ejpam-2648	101	25	and	and	CCONJ
ejpam-2648	101	26	i+	i+	NOUN
ejpam-2648	101	27	j	j	NOUN
ejpam-2648	101	28	+	+	NUM
ejpam-2648	101	29	h	h	NOUN
ejpam-2648	101	30	=	=	SYM
ejpam-2648	101	31	k	k	NOUN
ejpam-2648	101	32	,	,	PUNCT
ejpam-2648	101	33	we	we	PRON
ejpam-2648	101	34	see	see	VERB
ejpam-2648	101	35	that	that	SCONJ
ejpam-2648	101	36	,	,	PUNCT
ejpam-2648	101	37	for	for	ADP
ejpam-2648	101	38	arbitrary	arbitrary	ADJ
ejpam-2648	101	39	pair	pair	NOUN
ejpam-2648	101	40	(	(	PUNCT
ejpam-2648	101	41	u	u	NOUN
ejpam-2648	101	42	,	,	PUNCT
ejpam-2648	101	43	v	v	NOUN
ejpam-2648	101	44	)	)	PUNCT
ejpam-2648	101	45	of	of	ADP
ejpam-2648	101	46	elements	element	NOUN
ejpam-2648	101	47	in	in	ADP
ejpam-2648	101	48	v	v	NUM
ejpam-2648	101	49	−σ×v	−σ×v	NUM
ejpam-2648	101	50	σ	σ	NOUN
ejpam-2648	101	51	,	,	PUNCT
ejpam-2648	101	52	the	the	DET
ejpam-2648	101	53	terms	term	NOUN
ejpam-2648	101	54	{	{	PUNCT
ejpam-2648	101	55	ϕσi	ϕσi	NOUN
ejpam-2648	101	56	xn	xn	PROPN
ejpam-2648	101	57	,	,	PUNCT
ejpam-2648	101	58	ϕ	ϕ	PROPN
ejpam-2648	101	59	σ	σ	PROPN
ejpam-2648	101	60	j	j	PROPN
ejpam-2648	101	61	u	u	PROPN
ejpam-2648	101	62	,	,	PUNCT
ejpam-2648	101	63	ϕ	ϕ	PROPN
ejpam-2648	101	64	σ	σ	PROPN
ejpam-2648	101	65	hv	hv	PROPN
ejpam-2648	101	66	}	}	PUNCT
ejpam-2648	101	67	converge	converge	VERB
ejpam-2648	101	68	to	to	ADP
ejpam-2648	101	69	zero	zero	NUM
ejpam-2648	101	70	when	when	SCONJ
ejpam-2648	101	71	n	n	PRON
ejpam-2648	101	72	tends	tend	VERB
ejpam-2648	101	73	to	to	ADP
ejpam-2648	101	74	∞.	∞.	PROPN
ejpam-2648	101	75	consequently	consequently	ADV
ejpam-2648	101	76	,	,	PUNCT
ejpam-2648	101	77	we	we	PRON
ejpam-2648	101	78	do	do	AUX
ejpam-2648	101	79	have	have	VERB
ejpam-2648	101	80	limϕσk({xn	limϕσk({xn	NOUN
ejpam-2648	101	81	,	,	PUNCT
ejpam-2648	101	82	u	u	NOUN
ejpam-2648	101	83	,	,	PUNCT
ejpam-2648	101	84	v	v	NOUN
ejpam-2648	101	85	}	}	PUNCT
ejpam-2648	101	86	)	)	PUNCT
ejpam-2648	102	1	=	=	SYM
ejpam-2648	102	2	lim	lim	PROPN
ejpam-2648	102	3	∑	∑	PROPN
ejpam-2648	102	4	i+j+h	i+j+h	PROPN
ejpam-2648	102	5	=	=	SYM
ejpam-2648	102	6	k	k	X
ejpam-2648	102	7	{	{	PUNCT
ejpam-2648	102	8	ϕσi	ϕσi	PROPN
ejpam-2648	102	9	(	(	PUNCT
ejpam-2648	102	10	xn	xn	PROPN
ejpam-2648	102	11	)	)	PUNCT
ejpam-2648	102	12	,	,	PUNCT
ejpam-2648	102	13	ϕ−σj	ϕ−σj	X
ejpam-2648	102	14	(	(	PUNCT
ejpam-2648	102	15	u	u	NOUN
ejpam-2648	102	16	)	)	PUNCT
ejpam-2648	102	17	,	,	PUNCT
ejpam-2648	102	18	ϕσh(v	ϕσh(v	NOUN
ejpam-2648	102	19	)	)	PUNCT
ejpam-2648	102	20	}	}	PUNCT
ejpam-2648	102	21	=	=	PUNCT
ejpam-2648	102	22	∑	∑	PUNCT
ejpam-2648	102	23	i+j+h	i+j+h	PROPN
ejpam-2648	102	24	=	=	SYM
ejpam-2648	102	25	k	k	X
ejpam-2648	102	26	{	{	PUNCT
ejpam-2648	102	27	limϕσi	limϕσi	NOUN
ejpam-2648	102	28	(	(	PUNCT
ejpam-2648	102	29	xn	xn	PROPN
ejpam-2648	102	30	)	)	PUNCT
ejpam-2648	102	31	,	,	PUNCT
ejpam-2648	102	32	ϕ−σj	ϕ−σj	X
ejpam-2648	102	33	(	(	PUNCT
ejpam-2648	102	34	u	u	NOUN
ejpam-2648	102	35	)	)	PUNCT
ejpam-2648	102	36	,	,	PUNCT
ejpam-2648	102	37	ϕσh(v	ϕσh(v	NOUN
ejpam-2648	102	38	)	)	PUNCT
ejpam-2648	102	39	}	}	PUNCT
ejpam-2648	102	40	=	=	SYM
ejpam-2648	102	41	{	{	PUNCT
ejpam-2648	102	42	limϕσk(xn	limϕσk(xn	PROPN
ejpam-2648	102	43	)	)	PUNCT
ejpam-2648	102	44	,	,	PUNCT
ejpam-2648	102	45	u	u	NOUN
ejpam-2648	102	46	,	,	PUNCT
ejpam-2648	102	47	v	v	NOUN
ejpam-2648	102	48	}	}	PUNCT
ejpam-2648	102	49	=	=	PUNCT
ejpam-2648	102	50	{	{	PUNCT
ejpam-2648	102	51	s	s	PROPN
ejpam-2648	102	52	,	,	PUNCT
ejpam-2648	102	53	u	u	NOUN
ejpam-2648	102	54	,	,	PUNCT
ejpam-2648	102	55	v	v	NOUN
ejpam-2648	102	56	}	}	PUNCT
ejpam-2648	102	57	,	,	PUNCT
ejpam-2648	102	58	which	which	PRON
ejpam-2648	102	59	establishes	establish	VERB
ejpam-2648	102	60	{	{	PUNCT
ejpam-2648	102	61	s(ϕσk	s(ϕσk	PROPN
ejpam-2648	102	62	)	)	PUNCT
ejpam-2648	102	63	,	,	PUNCT
ejpam-2648	102	64	v	v	NOUN
ejpam-2648	102	65	−σ	−σ	NOUN
ejpam-2648	102	66	,	,	PUNCT
ejpam-2648	102	67	v	v	NOUN
ejpam-2648	102	68	σ	σ	PROPN
ejpam-2648	102	69	}	}	PUNCT
ejpam-2648	102	70	⊂	⊂	PROPN
ejpam-2648	102	71	s(ϕσk	s(ϕσk	PROPN
ejpam-2648	102	72	)	)	PUNCT
ejpam-2648	102	73	as	as	SCONJ
ejpam-2648	102	74	required	require	VERB
ejpam-2648	102	75	.	.	PUNCT
ejpam-2648	103	1	finally	finally	ADV
ejpam-2648	103	2	,	,	PUNCT
ejpam-2648	103	3	s(ϕk	s(ϕk	NOUN
ejpam-2648	103	4	)	)	PUNCT
ejpam-2648	103	5	is	be	AUX
ejpam-2648	103	6	an	an	DET
ejpam-2648	103	7	ideal	ideal	NOUN
ejpam-2648	103	8	of	of	ADP
ejpam-2648	103	9	v	v	NUM
ejpam-2648	103	10	which	which	PRON
ejpam-2648	103	11	is	be	AUX
ejpam-2648	103	12	closed	close	VERB
ejpam-2648	103	13	since	since	SCONJ
ejpam-2648	103	14	the	the	DET
ejpam-2648	103	15	separating	separate	VERB
ejpam-2648	103	16	subspace	subspace	NOUN
ejpam-2648	103	17	of	of	ADP
ejpam-2648	103	18	any	any	DET
ejpam-2648	103	19	linear	linear	ADJ
ejpam-2648	103	20	operator	operator	NOUN
ejpam-2648	103	21	is	be	AUX
ejpam-2648	103	22	closed	close	VERB
ejpam-2648	103	23	as	as	SCONJ
ejpam-2648	103	24	it	it	PRON
ejpam-2648	103	25	is	be	AUX
ejpam-2648	103	26	pointed	point	VERB
ejpam-2648	103	27	out	out	ADP
ejpam-2648	103	28	.	.	PUNCT
ejpam-2648	104	1	remark	remark	PROPN
ejpam-2648	104	2	2	2	NUM
ejpam-2648	104	3	.	.	PUNCT
ejpam-2648	105	1	let	let	AUX
ejpam-2648	105	2	{	{	PUNCT
ejpam-2648	105	3	dn	dn	VERB
ejpam-2648	105	4	=	=	SYM
ejpam-2648	105	5	(	(	PUNCT
ejpam-2648	105	6	d+	d+	X
ejpam-2648	105	7	n	n	X
ejpam-2648	105	8	,	,	PUNCT
ejpam-2648	105	9	d	d	PROPN
ejpam-2648	105	10	−	−	PROPN
ejpam-2648	105	11	n	n	X
ejpam-2648	105	12	)	)	PUNCT
ejpam-2648	105	13	}	}	PUNCT
ejpam-2648	105	14	be	be	AUX
ejpam-2648	105	15	a	a	DET
ejpam-2648	105	16	higher	high	ADJ
ejpam-2648	105	17	derivation	derivation	NOUN
ejpam-2648	105	18	on	on	ADP
ejpam-2648	105	19	a	a	DET
ejpam-2648	105	20	normed	normed	ADJ
ejpam-2648	105	21	jordan	jordan	PROPN
ejpam-2648	105	22	pair	pair	PROPN
ejpam-2648	105	23	v	v	NOUN
ejpam-2648	105	24	=	=	PUNCT
ejpam-2648	105	25	(	(	PUNCT
ejpam-2648	105	26	v	v	ADP
ejpam-2648	105	27	+	+	NOUN
ejpam-2648	105	28	,	,	PUNCT
ejpam-2648	105	29	v	v	ADP
ejpam-2648	105	30	−	−	NOUN
ejpam-2648	105	31	)	)	PUNCT
ejpam-2648	105	32	and	and	CCONJ
ejpam-2648	105	33	let	let	VERB
ejpam-2648	105	34	b	b	X
ejpam-2648	105	35	be	be	AUX
ejpam-2648	105	36	a	a	DET
ejpam-2648	105	37	nonzero	nonzero	NOUN
ejpam-2648	105	38	element	element	NOUN
ejpam-2648	105	39	in	in	ADP
ejpam-2648	105	40	v	v	NUM
ejpam-2648	105	41	−σ	−σ	NOUN
ejpam-2648	105	42	.	.	PUNCT
ejpam-2648	106	1	let	let	VERB
ejpam-2648	106	2	us	we	PRON
ejpam-2648	106	3	note	note	VERB
ejpam-2648	106	4	that	that	SCONJ
ejpam-2648	106	5	{	{	PUNCT
ejpam-2648	106	6	dσ	dσ	NOUN
ejpam-2648	106	7	n	n	CCONJ
ejpam-2648	106	8	}	}	PUNCT
ejpam-2648	106	9	is	be	AUX
ejpam-2648	106	10	not	not	PART
ejpam-2648	106	11	a	a	DET
ejpam-2648	106	12	higher	high	ADJ
ejpam-2648	106	13	derivation	derivation	NOUN
ejpam-2648	106	14	on	on	ADP
ejpam-2648	106	15	the	the	DET
ejpam-2648	106	16	jordan	jordan	PROPN
ejpam-2648	106	17	algebra	algebra	PROPN
ejpam-2648	106	18	v	v	ADP
ejpam-2648	106	19	σ(b	σ(b	PROPN
ejpam-2648	106	20	)	)	PUNCT
ejpam-2648	107	1	even	even	ADV
ejpam-2648	107	2	if	if	SCONJ
ejpam-2648	107	3	dσ	dσ	PROPN
ejpam-2648	107	4	n	n	ADV
ejpam-2648	107	5	vanishes	vanish	VERB
ejpam-2648	107	6	at	at	ADP
ejpam-2648	107	7	b	b	NOUN
ejpam-2648	107	8	for	for	ADP
ejpam-2648	107	9	all	all	DET
ejpam-2648	107	10	positive	positive	ADJ
ejpam-2648	107	11	integers	integer	NOUN
ejpam-2648	107	12	n.	n.	VERB
ejpam-2648	107	13	however	however	ADV
ejpam-2648	107	14	,	,	PUNCT
ejpam-2648	107	15	the	the	DET
ejpam-2648	107	16	behavior	behavior	NOUN
ejpam-2648	107	17	of	of	ADP
ejpam-2648	107	18	dσ	dσ	PROPN
ejpam-2648	107	19	n	n	PROPN
ejpam-2648	107	20	towards	towards	ADP
ejpam-2648	107	21	v	v	PROPN
ejpam-2648	107	22	σ(b	σ(b	PROPN
ejpam-2648	107	23	)	)	PUNCT
ejpam-2648	108	1	conserves	conserve	VERB
ejpam-2648	108	2	nice	nice	ADJ
ejpam-2648	108	3	properties	property	NOUN
ejpam-2648	108	4	as	as	SCONJ
ejpam-2648	108	5	it	it	PRON
ejpam-2648	108	6	is	be	AUX
ejpam-2648	108	7	clarified	clarify	VERB
ejpam-2648	108	8	in	in	ADP
ejpam-2648	108	9	the	the	DET
ejpam-2648	108	10	following	following	NOUN
ejpam-2648	108	11	.	.	PUNCT
ejpam-2648	109	1	lemma	lemma	PROPN
ejpam-2648	109	2	2	2	X
ejpam-2648	109	3	.	.	PUNCT
ejpam-2648	110	1	let	let	VERB
ejpam-2648	110	2	v	v	VERB
ejpam-2648	110	3	=	=	SYM
ejpam-2648	110	4	(	(	PUNCT
ejpam-2648	110	5	v	v	ADP
ejpam-2648	110	6	+	+	NOUN
ejpam-2648	110	7	,	,	PUNCT
ejpam-2648	110	8	v	v	ADP
ejpam-2648	110	9	−	−	NOUN
ejpam-2648	110	10	)	)	PUNCT
ejpam-2648	110	11	be	be	AUX
ejpam-2648	110	12	a	a	DET
ejpam-2648	110	13	normed	normed	ADJ
ejpam-2648	110	14	jordan	jordan	PROPN
ejpam-2648	110	15	pair	pair	PROPN
ejpam-2648	110	16	and	and	CCONJ
ejpam-2648	110	17	let	let	VERB
ejpam-2648	110	18	b	b	X
ejpam-2648	110	19	be	be	AUX
ejpam-2648	110	20	a	a	DET
ejpam-2648	110	21	nonzero	nonzero	NOUN
ejpam-2648	110	22	element	element	NOUN
ejpam-2648	110	23	in	in	ADP
ejpam-2648	110	24	v	v	NUM
ejpam-2648	110	25	−σ	−σ	NOUN
ejpam-2648	110	26	.	.	PUNCT
ejpam-2648	111	1	if	if	SCONJ
ejpam-2648	111	2	{	{	PUNCT
ejpam-2648	111	3	dn	dn	NOUN
ejpam-2648	111	4	=	=	SYM
ejpam-2648	111	5	(	(	PUNCT
ejpam-2648	111	6	d+	d+	X
ejpam-2648	111	7	n	n	X
ejpam-2648	111	8	,	,	PUNCT
ejpam-2648	111	9	d	d	PROPN
ejpam-2648	111	10	−	−	PROPN
ejpam-2648	111	11	n	n	NOUN
ejpam-2648	111	12	)	)	PUNCT
ejpam-2648	111	13	}	}	PUNCT
ejpam-2648	111	14	n≥0	n≥0	NOUN
ejpam-2648	111	15	is	be	AUX
ejpam-2648	111	16	a	a	DET
ejpam-2648	111	17	higher	high	ADJ
ejpam-2648	111	18	derivation	derivation	NOUN
ejpam-2648	111	19	on	on	ADP
ejpam-2648	111	20	v	v	ADP
ejpam-2648	111	21	such	such	ADJ
ejpam-2648	111	22	that	that	SCONJ
ejpam-2648	111	23	dσ	dσ	PROPN
ejpam-2648	111	24	i	i	PRON
ejpam-2648	111	25	is	be	AUX
ejpam-2648	111	26	continuous	continuous	ADJ
ejpam-2648	111	27	for	for	ADP
ejpam-2648	111	28	every	every	DET
ejpam-2648	111	29	i	i	PROPN
ejpam-2648	111	30	∈	∈	PROPN
ejpam-2648	111	31	{	{	PUNCT
ejpam-2648	111	32	0	0	NUM
ejpam-2648	111	33	,	,	PUNCT
ejpam-2648	111	34	1	1	NUM
ejpam-2648	111	35	,	,	PUNCT
ejpam-2648	111	36	...	...	PUNCT
ejpam-2648	111	37	,	,	PUNCT
ejpam-2648	111	38	k	k	PROPN
ejpam-2648	112	1	−	−	PROPN
ejpam-2648	112	2	1	1	NUM
ejpam-2648	112	3	}	}	PUNCT
ejpam-2648	112	4	where	where	SCONJ
ejpam-2648	112	5	k	k	PROPN
ejpam-2648	112	6	is	be	AUX
ejpam-2648	112	7	a	a	DET
ejpam-2648	112	8	fixed	fix	VERB
ejpam-2648	112	9	positive	positive	ADJ
ejpam-2648	112	10	integer	integer	NOUN
ejpam-2648	112	11	greater	great	ADJ
ejpam-2648	112	12	than	than	ADP
ejpam-2648	112	13	2	2	NUM
ejpam-2648	112	14	.	.	PUNCT
ejpam-2648	112	15	then	then	ADV
ejpam-2648	112	16	for	for	ADP
ejpam-2648	112	17	every	every	DET
ejpam-2648	112	18	t	t	NOUN
ejpam-2648	112	19	in	in	ADP
ejpam-2648	112	20	the	the	DET
ejpam-2648	112	21	multiplication	multiplication	NOUN
ejpam-2648	112	22	algebra	algebra	NOUN
ejpam-2648	112	23	m(v	m(v	PROPN
ejpam-2648	112	24	σ(b	σ(b	PROPN
ejpam-2648	112	25	)	)	PUNCT
ejpam-2648	112	26	)	)	PUNCT
ejpam-2648	112	27	of	of	ADP
ejpam-2648	112	28	the	the	DET
ejpam-2648	112	29	jordan	jordan	PROPN
ejpam-2648	112	30	algebra	algebra	PROPN
ejpam-2648	112	31	v	v	ADP
ejpam-2648	112	32	σ(b	σ(b	PROPN
ejpam-2648	112	33	)	)	PUNCT
ejpam-2648	112	34	,	,	PUNCT
ejpam-2648	112	35	the	the	DET
ejpam-2648	112	36	linear	linear	ADJ
ejpam-2648	112	37	operator	operator	NOUN
ejpam-2648	112	38	[	[	X
ejpam-2648	112	39	dσ	dσ	PROPN
ejpam-2648	112	40	k	k	PROPN
ejpam-2648	112	41	,	,	PUNCT
ejpam-2648	112	42	t	t	PROPN
ejpam-2648	112	43	]	]	PUNCT
ejpam-2648	112	44	is	be	AUX
ejpam-2648	112	45	continuous	continuous	ADJ
ejpam-2648	112	46	.	.	PUNCT
ejpam-2648	113	1	proof	proof	NOUN
ejpam-2648	113	2	.	.	PUNCT
ejpam-2648	114	1	consider	consider	VERB
ejpam-2648	114	2	the	the	DET
ejpam-2648	114	3	set	set	NOUN
ejpam-2648	114	4	b	b	PROPN
ejpam-2648	114	5	=	=	PRON
ejpam-2648	114	6	{	{	PUNCT
ejpam-2648	114	7	t	t	PROPN
ejpam-2648	114	8	∈m(v	∈m(v	PROPN
ejpam-2648	114	9	σ(b	σ(b	PROPN
ejpam-2648	114	10	)	)	PUNCT
ejpam-2648	114	11	)	)	PUNCT
ejpam-2648	114	12	:	:	PUNCT
ejpam-2648	115	1	[	[	X
ejpam-2648	115	2	dσ	dσ	PROPN
ejpam-2648	115	3	k	k	PROPN
ejpam-2648	115	4	,	,	PUNCT
ejpam-2648	115	5	t	t	PROPN
ejpam-2648	115	6	]	]	PUNCT
ejpam-2648	115	7	is	be	AUX
ejpam-2648	115	8	continuous	continuous	ADJ
ejpam-2648	115	9	}	}	PUNCT
ejpam-2648	115	10	.	.	PUNCT
ejpam-2648	116	1	h.	h.	PROPN
ejpam-2648	116	2	marhnine	marhnine	PROPN
ejpam-2648	116	3	,	,	PUNCT
ejpam-2648	116	4	c.	c.	PROPN
ejpam-2648	116	5	zarhouti	zarhouti	PROPN
ejpam-2648	116	6	/	/	SYM
ejpam-2648	116	7	eur	eur	PROPN
ejpam-2648	116	8	.	.	PUNCT
ejpam-2648	117	1	j.	j.	PROPN
ejpam-2648	117	2	pure	pure	PROPN
ejpam-2648	117	3	appl	appl	PROPN
ejpam-2648	117	4	.	.	PROPN
ejpam-2648	117	5	math	math	PROPN
ejpam-2648	117	6	,	,	PUNCT
ejpam-2648	117	7	10	10	NUM
ejpam-2648	117	8	(	(	PUNCT
ejpam-2648	117	9	4	4	NUM
ejpam-2648	117	10	)	)	PUNCT
ejpam-2648	117	11	(	(	PUNCT
ejpam-2648	117	12	2017	2017	NUM
ejpam-2648	117	13	)	)	PUNCT
ejpam-2648	117	14	,	,	PUNCT
ejpam-2648	117	15	749	749	NUM
ejpam-2648	117	16	-	-	SYM
ejpam-2648	117	17	762	762	NUM
ejpam-2648	117	18	754	754	NUM
ejpam-2648	117	19	it	it	PRON
ejpam-2648	117	20	is	be	AUX
ejpam-2648	117	21	clear	clear	ADJ
ejpam-2648	117	22	that	that	SCONJ
ejpam-2648	117	23	b	b	NOUN
ejpam-2648	117	24	is	be	AUX
ejpam-2648	117	25	a	a	DET
ejpam-2648	117	26	subspace	subspace	NOUN
ejpam-2648	117	27	of	of	ADP
ejpam-2648	117	28	m(v	m(v	PROPN
ejpam-2648	117	29	σ(b	σ(b	PROPN
ejpam-2648	117	30	)	)	PUNCT
ejpam-2648	117	31	)	)	PUNCT
ejpam-2648	117	32	.	.	PUNCT
ejpam-2648	118	1	moreover	moreover	ADV
ejpam-2648	118	2	,	,	PUNCT
ejpam-2648	118	3	a	a	DET
ejpam-2648	118	4	simple	simple	ADJ
ejpam-2648	118	5	computation	computation	NOUN
ejpam-2648	118	6	shows	show	VERB
ejpam-2648	118	7	that	that	SCONJ
ejpam-2648	118	8	the	the	DET
ejpam-2648	118	9	formula	formula	NOUN
ejpam-2648	118	10	t	t	NOUN
ejpam-2648	119	1	[	[	X
ejpam-2648	119	2	dσ	dσ	PROPN
ejpam-2648	119	3	k	k	PROPN
ejpam-2648	119	4	,	,	PUNCT
ejpam-2648	119	5	s	s	X
ejpam-2648	119	6	]	]	PUNCT
ejpam-2648	119	7	+	+	CCONJ
ejpam-2648	120	1	[	[	X
ejpam-2648	120	2	dσ	dσ	X
ejpam-2648	120	3	k	k	PROPN
ejpam-2648	120	4	,	,	PUNCT
ejpam-2648	120	5	t	t	X
ejpam-2648	120	6	]	]	X
ejpam-2648	120	7	s	s	X
ejpam-2648	120	8	=	=	X
ejpam-2648	121	1	[	[	X
ejpam-2648	121	2	dσ	dσ	PROPN
ejpam-2648	121	3	k	k	PROPN
ejpam-2648	121	4	,	,	PUNCT
ejpam-2648	121	5	ts	ts	PROPN
ejpam-2648	121	6	]	]	PUNCT
ejpam-2648	121	7	holds	hold	VERB
ejpam-2648	121	8	for	for	ADP
ejpam-2648	121	9	all	all	DET
ejpam-2648	121	10	t	t	PROPN
ejpam-2648	121	11	,	,	PUNCT
ejpam-2648	121	12	s	s	VERB
ejpam-2648	121	13	in	in	ADP
ejpam-2648	121	14	m(v	m(v	PROPN
ejpam-2648	121	15	σ(b	σ(b	PROPN
ejpam-2648	121	16	)	)	PUNCT
ejpam-2648	121	17	)	)	PUNCT
ejpam-2648	121	18	.	.	PUNCT
ejpam-2648	122	1	this	this	PRON
ejpam-2648	122	2	proves	prove	VERB
ejpam-2648	122	3	that	that	SCONJ
ejpam-2648	122	4	b	b	NOUN
ejpam-2648	122	5	is	be	AUX
ejpam-2648	122	6	a	a	DET
ejpam-2648	122	7	subalgebra	subalgebra	NOUN
ejpam-2648	122	8	of	of	ADP
ejpam-2648	122	9	m(v	m(v	PROPN
ejpam-2648	122	10	σ(b	σ(b	PROPN
ejpam-2648	122	11	)	)	PUNCT
ejpam-2648	122	12	)	)	PUNCT
ejpam-2648	122	13	.	.	PUNCT
ejpam-2648	123	1	on	on	ADP
ejpam-2648	123	2	the	the	DET
ejpam-2648	123	3	other	other	ADJ
ejpam-2648	123	4	hand	hand	NOUN
ejpam-2648	123	5	,	,	PUNCT
ejpam-2648	123	6	for	for	ADP
ejpam-2648	123	7	all	all	DET
ejpam-2648	123	8	a	a	DET
ejpam-2648	123	9	∈	∈	NOUN
ejpam-2648	123	10	v	v	ADP
ejpam-2648	123	11	σ(b	σ(b	PROPN
ejpam-2648	123	12	)	)	PUNCT
ejpam-2648	123	13	,	,	PUNCT
ejpam-2648	123	14	the	the	DET
ejpam-2648	123	15	left	left	ADJ
ejpam-2648	123	16	multiplication	multiplication	NOUN
ejpam-2648	123	17	la	la	X
ejpam-2648	123	18	lies	lie	NOUN
ejpam-2648	123	19	in	in	ADP
ejpam-2648	123	20	b.	b.	PROPN
ejpam-2648	123	21	indeed	indeed	ADV
ejpam-2648	123	22	,	,	PUNCT
ejpam-2648	123	23	since	since	SCONJ
ejpam-2648	123	24	la	la	X
ejpam-2648	123	25	=	=	SYM
ejpam-2648	123	26	1	1	NUM
ejpam-2648	123	27	2v(a	2v(a	NUM
ejpam-2648	123	28	,	,	PUNCT
ejpam-2648	123	29	b	b	NOUN
ejpam-2648	123	30	)	)	PUNCT
ejpam-2648	123	31	,	,	PUNCT
ejpam-2648	123	32	for	for	ADP
ejpam-2648	123	33	all	all	DET
ejpam-2648	123	34	x	x	SYM
ejpam-2648	123	35	∈	∈	PROPN
ejpam-2648	123	36	v	v	NOUN
ejpam-2648	123	37	σ	σ	NOUN
ejpam-2648	123	38	we	we	PRON
ejpam-2648	123	39	have	have	VERB
ejpam-2648	123	40	[	[	X
ejpam-2648	123	41	dσ	dσ	PROPN
ejpam-2648	123	42	k	k	PROPN
ejpam-2648	123	43	,	,	PUNCT
ejpam-2648	123	44	la]x	la]x	PROPN
ejpam-2648	123	45	=	=	SYM
ejpam-2648	124	1	dσ	dσ	PROPN
ejpam-2648	124	2	klax−	klax−	PROPN
ejpam-2648	124	3	ladσ	ladσ	PROPN
ejpam-2648	124	4	kx	kx	PROPN
ejpam-2648	125	1	=	=	NOUN
ejpam-2648	125	2	1	1	NUM
ejpam-2648	125	3	2	2	NUM
ejpam-2648	125	4	(	(	PUNCT
ejpam-2648	125	5	dσ	dσ	PROPN
ejpam-2648	125	6	k	k	PROPN
ejpam-2648	125	7	{	{	PUNCT
ejpam-2648	125	8	a	a	PROPN
ejpam-2648	125	9	,	,	PUNCT
ejpam-2648	125	10	b	b	NOUN
ejpam-2648	125	11	,	,	PUNCT
ejpam-2648	125	12	x	x	NOUN
ejpam-2648	125	13	}	}	PUNCT
ejpam-2648	125	14	−	−	PROPN
ejpam-2648	125	15	{	{	PUNCT
ejpam-2648	125	16	a	a	PROPN
ejpam-2648	125	17	,	,	PUNCT
ejpam-2648	125	18	b	b	NOUN
ejpam-2648	125	19	,	,	PUNCT
ejpam-2648	125	20	dσ	dσ	PROPN
ejpam-2648	125	21	kx	kx	PROPN
ejpam-2648	125	22	}	}	PUNCT
ejpam-2648	125	23	)	)	PUNCT
ejpam-2648	125	24	=	=	SYM
ejpam-2648	125	25	1	1	NUM
ejpam-2648	125	26	2	2	NUM
ejpam-2648	125	27	(	(	PUNCT
ejpam-2648	125	28	∑	∑	ADV
ejpam-2648	125	29	i+j+h	i+j+h	ADJ
ejpam-2648	125	30	=	=	SYM
ejpam-2648	125	31	k	k	X
ejpam-2648	125	32	{	{	PUNCT
ejpam-2648	125	33	dσ	dσ	PROPN
ejpam-2648	125	34	i	i	PRON
ejpam-2648	125	35	a	a	PRON
ejpam-2648	125	36	,	,	PUNCT
ejpam-2648	125	37	d	d	PROPN
ejpam-2648	125	38	−σ	−σ	NOUN
ejpam-2648	126	1	j	j	PROPN
ejpam-2648	126	2	b	b	PROPN
ejpam-2648	126	3	,	,	PUNCT
ejpam-2648	126	4	dσ	dσ	PROPN
ejpam-2648	126	5	hx	hx	PROPN
ejpam-2648	126	6	}	}	PUNCT
ejpam-2648	126	7	−	−	PROPN
ejpam-2648	126	8	{	{	PUNCT
ejpam-2648	126	9	a	a	PROPN
ejpam-2648	126	10	,	,	PUNCT
ejpam-2648	126	11	b	b	NOUN
ejpam-2648	126	12	,	,	PUNCT
ejpam-2648	126	13	dσ	dσ	PROPN
ejpam-2648	126	14	kx	kx	PROPN
ejpam-2648	126	15	}	}	PUNCT
ejpam-2648	126	16	)	)	PUNCT
ejpam-2648	126	17	=	=	SYM
ejpam-2648	126	18	1	1	NUM
ejpam-2648	126	19	2	2	NUM
ejpam-2648	126	20	(	(	PUNCT
ejpam-2648	126	21	∑	∑	ADV
ejpam-2648	126	22	i+j+h	i+j+h	ADJ
ejpam-2648	126	23	=	=	PROPN
ejpam-2648	126	24	k	k	PROPN
ejpam-2648	126	25	h≤k−1	h≤k−1	PROPN
ejpam-2648	126	26	{	{	PUNCT
ejpam-2648	126	27	dσ	dσ	PROPN
ejpam-2648	126	28	i	i	PRON
ejpam-2648	126	29	a	a	PRON
ejpam-2648	126	30	,	,	PUNCT
ejpam-2648	126	31	d	d	PROPN
ejpam-2648	126	32	−σ	−σ	NOUN
ejpam-2648	126	33	j	j	PROPN
ejpam-2648	126	34	b	b	PROPN
ejpam-2648	126	35	,	,	PUNCT
ejpam-2648	126	36	dσ	dσ	PROPN
ejpam-2648	126	37	hx	hx	PROPN
ejpam-2648	126	38	}	}	PUNCT
ejpam-2648	126	39	)	)	PUNCT
ejpam-2648	126	40	.	.	PUNCT
ejpam-2648	127	1	this	this	PRON
ejpam-2648	127	2	shows	show	VERB
ejpam-2648	127	3	that	that	SCONJ
ejpam-2648	128	1	[	[	X
ejpam-2648	128	2	dσ	dσ	PROPN
ejpam-2648	128	3	k	k	PROPN
ejpam-2648	128	4	,	,	PUNCT
ejpam-2648	128	5	la	la	PROPN
ejpam-2648	128	6	]	]	PUNCT
ejpam-2648	128	7	=	=	SYM
ejpam-2648	128	8	1	1	NUM
ejpam-2648	128	9	2	2	NUM
ejpam-2648	128	10	(	(	PUNCT
ejpam-2648	128	11	∑	∑	ADV
ejpam-2648	128	12	i+j+h	i+j+h	ADJ
ejpam-2648	128	13	=	=	SYM
ejpam-2648	128	14	k	k	NOUN
ejpam-2648	128	15	1≤h≤k−1	1≤h≤k−1	NUM
ejpam-2648	128	16	v(dσi	v(dσi	NOUN
ejpam-2648	128	17	a	a	PRON
ejpam-2648	128	18	,	,	PUNCT
ejpam-2648	128	19	d	d	PROPN
ejpam-2648	128	20	−σ	−σ	PROPN
ejpam-2648	128	21	j	j	PROPN
ejpam-2648	128	22	b)d	b)d	PROPN
ejpam-2648	128	23	σ	σ	PROPN
ejpam-2648	128	24	h	h	PROPN
ejpam-2648	128	25	+	+	CCONJ
ejpam-2648	128	26	∑	∑	PUNCT
ejpam-2648	128	27	i+j	i+j	NUM
ejpam-2648	128	28	=	=	PROPN
ejpam-2648	128	29	k	k	X
ejpam-2648	128	30	v(dσi	v(dσi	VERB
ejpam-2648	128	31	a	a	X
ejpam-2648	128	32	,	,	PUNCT
ejpam-2648	128	33	d	d	PROPN
ejpam-2648	128	34	−σ	−σ	NOUN
ejpam-2648	128	35	j	j	PROPN
ejpam-2648	128	36	b	b	PROPN
ejpam-2648	128	37	)	)	PUNCT
ejpam-2648	128	38	)	)	PUNCT
ejpam-2648	128	39	,	,	PUNCT
ejpam-2648	128	40	which	which	PRON
ejpam-2648	128	41	shows	show	VERB
ejpam-2648	128	42	that	that	SCONJ
ejpam-2648	128	43	the	the	DET
ejpam-2648	128	44	operator	operator	NOUN
ejpam-2648	128	45	[	[	X
ejpam-2648	128	46	dσ	dσ	PROPN
ejpam-2648	128	47	k	k	PROPN
ejpam-2648	128	48	,	,	PUNCT
ejpam-2648	128	49	la	la	PROPN
ejpam-2648	128	50	]	]	PUNCT
ejpam-2648	128	51	is	be	AUX
ejpam-2648	128	52	continuous	continuous	ADJ
ejpam-2648	128	53	since	since	SCONJ
ejpam-2648	128	54	so	so	ADV
ejpam-2648	128	55	are	be	AUX
ejpam-2648	128	56	v(dσi	v(dσi	ADJ
ejpam-2648	128	57	a	a	PRON
ejpam-2648	128	58	,	,	PUNCT
ejpam-2648	128	59	d	d	PROPN
ejpam-2648	128	60	−σ	−σ	NOUN
ejpam-2648	128	61	j	j	PROPN
ejpam-2648	128	62	b	b	PROPN
ejpam-2648	128	63	)	)	PUNCT
ejpam-2648	128	64	and	and	CCONJ
ejpam-2648	128	65	dσ	dσ	PROPN
ejpam-2648	128	66	h	h	PROPN
ejpam-2648	128	67	for	for	ADP
ejpam-2648	128	68	all	all	DET
ejpam-2648	128	69	h	h	NOUN
ejpam-2648	128	70	∈	∈	NOUN
ejpam-2648	128	71	{	{	PUNCT
ejpam-2648	128	72	1	1	NUM
ejpam-2648	128	73	,	,	PUNCT
ejpam-2648	128	74	...	...	PUNCT
ejpam-2648	128	75	,	,	PUNCT
ejpam-2648	128	76	k	k	PROPN
ejpam-2648	128	77	−	−	PROPN
ejpam-2648	128	78	1	1	NUM
ejpam-2648	128	79	}	}	PUNCT
ejpam-2648	128	80	.	.	PUNCT
ejpam-2648	129	1	finally	finally	ADV
ejpam-2648	129	2	,	,	PUNCT
ejpam-2648	129	3	since	since	SCONJ
ejpam-2648	129	4	m(v	m(v	PROPN
ejpam-2648	129	5	σ(b	σ(b	PROPN
ejpam-2648	129	6	)	)	PUNCT
ejpam-2648	129	7	)	)	PUNCT
ejpam-2648	129	8	is	be	AUX
ejpam-2648	129	9	generated	generate	VERB
ejpam-2648	129	10	by	by	ADP
ejpam-2648	129	11	all	all	DET
ejpam-2648	129	12	left	leave	VERB
ejpam-2648	129	13	multiplications	multiplication	NOUN
ejpam-2648	129	14	la	la	X
ejpam-2648	129	15	,	,	PUNCT
ejpam-2648	129	16	we	we	PRON
ejpam-2648	129	17	see	see	VERB
ejpam-2648	129	18	that	that	SCONJ
ejpam-2648	129	19	m(v	m(v	PROPN
ejpam-2648	129	20	σ(b	σ(b	PROPN
ejpam-2648	129	21	)	)	PUNCT
ejpam-2648	129	22	)	)	PUNCT
ejpam-2648	130	1	=	=	SYM
ejpam-2648	130	2	b.	b.	PROPN
ejpam-2648	130	3	the	the	DET
ejpam-2648	130	4	first	first	ADJ
ejpam-2648	130	5	automatic	automatic	ADJ
ejpam-2648	130	6	continuity	continuity	NOUN
ejpam-2648	130	7	result	result	NOUN
ejpam-2648	130	8	concerns	concern	VERB
ejpam-2648	130	9	higher	high	ADJ
ejpam-2648	130	10	derivations	derivation	NOUN
ejpam-2648	130	11	on	on	ADP
ejpam-2648	130	12	nondegenerate	nondegenerate	ADJ
ejpam-2648	130	13	banach	banach	NOUN
ejpam-2648	130	14	-	-	PUNCT
ejpam-2648	130	15	jordan	jordan	NOUN
ejpam-2648	130	16	pairs	pair	NOUN
ejpam-2648	130	17	with	with	ADP
ejpam-2648	130	18	nonzero	nonzero	PROPN
ejpam-2648	130	19	socle	socle	PROPN
ejpam-2648	130	20	.	.	PUNCT
ejpam-2648	131	1	theorem	theorem	NOUN
ejpam-2648	131	2	1	1	NUM
ejpam-2648	131	3	.	.	PUNCT
ejpam-2648	132	1	let	let	VERB
ejpam-2648	132	2	v	v	VERB
ejpam-2648	132	3	=	=	SYM
ejpam-2648	132	4	(	(	PUNCT
ejpam-2648	132	5	v	v	ADP
ejpam-2648	132	6	+	+	NOUN
ejpam-2648	132	7	,	,	PUNCT
ejpam-2648	132	8	v	v	ADP
ejpam-2648	132	9	−	−	NOUN
ejpam-2648	132	10	)	)	PUNCT
ejpam-2648	132	11	be	be	AUX
ejpam-2648	132	12	a	a	DET
ejpam-2648	132	13	nondegenerate	nondegenerate	ADJ
ejpam-2648	132	14	banach	banach	NOUN
ejpam-2648	132	15	-	-	PUNCT
ejpam-2648	132	16	jordan	jordan	NOUN
ejpam-2648	132	17	pair	pair	NOUN
ejpam-2648	132	18	with	with	ADP
ejpam-2648	132	19	nonzero	nonzero	PROPN
ejpam-2648	132	20	socle	socle	NOUN
ejpam-2648	132	21	.	.	PUNCT
ejpam-2648	133	1	if	if	SCONJ
ejpam-2648	133	2	dn	dn	NOUN
ejpam-2648	133	3	=	=	SYM
ejpam-2648	133	4	(	(	PUNCT
ejpam-2648	133	5	d+	d+	X
ejpam-2648	133	6	n	n	X
ejpam-2648	133	7	,	,	PUNCT
ejpam-2648	133	8	d	d	PROPN
ejpam-2648	133	9	−	−	PROPN
ejpam-2648	133	10	n	n	NOUN
ejpam-2648	133	11	)	)	PUNCT
ejpam-2648	133	12	}	}	PUNCT
ejpam-2648	133	13	n≥0	n≥0	NOUN
ejpam-2648	133	14	is	be	AUX
ejpam-2648	133	15	a	a	DET
ejpam-2648	133	16	higher	high	ADJ
ejpam-2648	133	17	derivation	derivation	NOUN
ejpam-2648	133	18	on	on	ADP
ejpam-2648	133	19	v	v	NUM
ejpam-2648	133	20	,	,	PUNCT
ejpam-2648	133	21	then	then	ADV
ejpam-2648	133	22	dσ	dσ	PROPN
ejpam-2648	133	23	k	k	PROPN
ejpam-2648	133	24	is	be	AUX
ejpam-2648	133	25	continuous	continuous	ADJ
ejpam-2648	133	26	for	for	ADP
ejpam-2648	133	27	every	every	DET
ejpam-2648	133	28	positive	positive	ADJ
ejpam-2648	133	29	integer	integer	NOUN
ejpam-2648	133	30	k.	k.	PROPN
ejpam-2648	133	31	proof	proof	PROPN
ejpam-2648	133	32	.	.	PUNCT
ejpam-2648	134	1	by	by	ADP
ejpam-2648	134	2	the	the	DET
ejpam-2648	134	3	closed	closed	ADJ
ejpam-2648	134	4	graph	graph	NOUN
ejpam-2648	134	5	theorem	theorem	VERB
ejpam-2648	134	6	,	,	PUNCT
ejpam-2648	134	7	it	it	PRON
ejpam-2648	134	8	suffices	suffice	VERB
ejpam-2648	134	9	to	to	PART
ejpam-2648	134	10	prove	prove	VERB
ejpam-2648	134	11	that	that	SCONJ
ejpam-2648	134	12	s(dσ	s(dσ	PROPN
ejpam-2648	134	13	k	k	PROPN
ejpam-2648	134	14	)	)	PUNCT
ejpam-2648	135	1	=	=	PUNCT
ejpam-2648	135	2	0	0	X
ejpam-2648	135	3	.	.	PUNCT
ejpam-2648	136	1	we	we	PRON
ejpam-2648	136	2	proceed	proceed	VERB
ejpam-2648	136	3	by	by	ADP
ejpam-2648	136	4	induction	induction	NOUN
ejpam-2648	136	5	on	on	ADP
ejpam-2648	136	6	k.	k.	PROPN
ejpam-2648	136	7	for	for	ADP
ejpam-2648	136	8	k	k	PROPN
ejpam-2648	136	9	=	=	SYM
ejpam-2648	136	10	0	0	PROPN
ejpam-2648	136	11	,	,	PUNCT
ejpam-2648	136	12	the	the	DET
ejpam-2648	136	13	identity	identity	NOUN
ejpam-2648	136	14	operator	operator	NOUN
ejpam-2648	136	15	dσ	dσ	VERB
ejpam-2648	136	16	0	0	PUNCT
ejpam-2648	137	1	=	=	SYM
ejpam-2648	138	1	idv	idv	PROPN
ejpam-2648	139	1	σ	σ	PROPN
ejpam-2648	139	2	is	be	AUX
ejpam-2648	139	3	obviously	obviously	ADV
ejpam-2648	139	4	continuous	continuous	ADJ
ejpam-2648	139	5	.	.	PUNCT
ejpam-2648	140	1	assume	assume	VERB
ejpam-2648	140	2	that	that	SCONJ
ejpam-2648	140	3	di	di	NOUN
ejpam-2648	140	4	is	be	AUX
ejpam-2648	140	5	continuous	continuous	ADJ
ejpam-2648	140	6	for	for	ADP
ejpam-2648	140	7	i	i	PROPN
ejpam-2648	140	8	=	=	NOUN
ejpam-2648	140	9	1	1	NUM
ejpam-2648	140	10	,	,	PUNCT
ejpam-2648	140	11	2	2	NUM
ejpam-2648	140	12	,	,	PUNCT
ejpam-2648	140	13	...	...	PUNCT
ejpam-2648	140	14	,	,	PUNCT
ejpam-2648	141	1	k	k	PROPN
ejpam-2648	142	1	−	−	PROPN
ejpam-2648	142	2	1	1	NUM
ejpam-2648	143	1	and	and	CCONJ
ejpam-2648	143	2	prove	prove	VERB
ejpam-2648	143	3	that	that	SCONJ
ejpam-2648	143	4	so	so	ADV
ejpam-2648	143	5	is	be	AUX
ejpam-2648	143	6	dk	dk	PROPN
ejpam-2648	143	7	.	.	PUNCT
ejpam-2648	144	1	in	in	ADP
ejpam-2648	144	2	virtue	virtue	NOUN
ejpam-2648	144	3	of	of	ADP
ejpam-2648	144	4	lemma	lemma	PROPN
ejpam-2648	144	5	1	1	NUM
ejpam-2648	144	6	,	,	PUNCT
ejpam-2648	144	7	it	it	PRON
ejpam-2648	144	8	is	be	AUX
ejpam-2648	144	9	known	know	VERB
ejpam-2648	144	10	that	that	SCONJ
ejpam-2648	144	11	s(dk	s(dk	PROPN
ejpam-2648	144	12	)	)	PUNCT
ejpam-2648	144	13	is	be	AUX
ejpam-2648	144	14	an	an	DET
ejpam-2648	144	15	ideal	ideal	NOUN
ejpam-2648	144	16	of	of	ADP
ejpam-2648	144	17	v	v	NOUN
ejpam-2648	144	18	.	.	PUNCT
ejpam-2648	145	1	we	we	PRON
ejpam-2648	145	2	claim	claim	VERB
ejpam-2648	145	3	that	that	SCONJ
ejpam-2648	145	4	soc(v	soc(v	DET
ejpam-2648	145	5	+	+	NOUN
ejpam-2648	145	6	)	)	PUNCT
ejpam-2648	145	7	∩	∩	NOUN
ejpam-2648	145	8	s(d+	s(d+	NUM
ejpam-2648	145	9	k	k	NOUN
ejpam-2648	145	10	)	)	PUNCT
ejpam-2648	146	1	=	=	SYM
ejpam-2648	146	2	0	0	X
ejpam-2648	146	3	.	.	X
ejpam-2648	146	4	assume	assume	VERB
ejpam-2648	146	5	that	that	SCONJ
ejpam-2648	146	6	this	this	PRON
ejpam-2648	146	7	is	be	AUX
ejpam-2648	146	8	not	not	PART
ejpam-2648	146	9	the	the	DET
ejpam-2648	146	10	case	case	NOUN
ejpam-2648	146	11	.	.	PUNCT
ejpam-2648	147	1	we	we	PRON
ejpam-2648	147	2	follow	follow	VERB
ejpam-2648	147	3	the	the	DET
ejpam-2648	147	4	pattern	pattern	NOUN
ejpam-2648	147	5	given	give	VERB
ejpam-2648	147	6	in	in	ADP
ejpam-2648	147	7	[	[	X
ejpam-2648	147	8	10	10	NUM
ejpam-2648	147	9	,	,	PUNCT
ejpam-2648	147	10	theorem	theorem	VERB
ejpam-2648	147	11	3.6	3.6	NUM
ejpam-2648	147	12	]	]	PUNCT
ejpam-2648	147	13	to	to	PART
ejpam-2648	147	14	look	look	VERB
ejpam-2648	147	15	for	for	ADP
ejpam-2648	147	16	a	a	DET
ejpam-2648	147	17	contradiction	contradiction	NOUN
ejpam-2648	147	18	.	.	PUNCT
ejpam-2648	148	1	by	by	ADP
ejpam-2648	148	2	[	[	X
ejpam-2648	148	3	10	10	NUM
ejpam-2648	148	4	,	,	PUNCT
ejpam-2648	148	5	lemma	lemma	PROPN
ejpam-2648	148	6	3.5	3.5	NUM
ejpam-2648	148	7	]	]	PUNCT
ejpam-2648	148	8	,	,	PUNCT
ejpam-2648	148	9	there	there	PRON
ejpam-2648	148	10	exists	exist	VERB
ejpam-2648	148	11	a	a	DET
ejpam-2648	148	12	nonzero	nonzero	NOUN
ejpam-2648	148	13	element	element	NOUN
ejpam-2648	148	14	r	r	NOUN
ejpam-2648	148	15	in	in	ADP
ejpam-2648	148	16	s(d+	s(d+	PROPN
ejpam-2648	148	17	k	k	X
ejpam-2648	148	18	)	)	PUNCT
ejpam-2648	148	19	∩	∩	X
ejpam-2648	148	20	soc(v	soc(v	DET
ejpam-2648	148	21	+	+	NOUN
ejpam-2648	148	22	)	)	PUNCT
ejpam-2648	148	23	such	such	ADJ
ejpam-2648	148	24	that	that	SCONJ
ejpam-2648	148	25	r	r	NOUN
ejpam-2648	148	26	is	be	AUX
ejpam-2648	148	27	reduced	reduce	VERB
ejpam-2648	148	28	:	:	PUNCT
ejpam-2648	148	29	qrv	qrv	VERB
ejpam-2648	148	30	−	−	PROPN
ejpam-2648	148	31	=	=	SYM
ejpam-2648	148	32	c.r	c.r	PROPN
ejpam-2648	148	33	.	.	PROPN
ejpam-2648	148	34	by	by	ADP
ejpam-2648	148	35	von	von	PROPN
ejpam-2648	148	36	neumann	neumann	PROPN
ejpam-2648	148	37	regularity	regularity	NOUN
ejpam-2648	148	38	of	of	ADP
ejpam-2648	148	39	soc(v	soc(v	NUM
ejpam-2648	148	40	)	)	PUNCT
ejpam-2648	148	41	,	,	PUNCT
ejpam-2648	148	42	there	there	PRON
ejpam-2648	148	43	exists	exist	VERB
ejpam-2648	148	44	a	a	DET
ejpam-2648	148	45	nonzero	nonzero	PROPN
ejpam-2648	148	46	element	element	NOUN
ejpam-2648	148	47	v	v	NOUN
ejpam-2648	148	48	in	in	ADP
ejpam-2648	148	49	v	v	NOUN
ejpam-2648	148	50	−	−	NOUN
ejpam-2648	148	51	such	such	ADJ
ejpam-2648	148	52	that	that	DET
ejpam-2648	148	53	r	r	NOUN
ejpam-2648	148	54	=	=	NOUN
ejpam-2648	148	55	qrv	qrv	NOUN
ejpam-2648	148	56	.	.	PUNCT
ejpam-2648	149	1	replace	replace	VERB
ejpam-2648	149	2	v	v	NOUN
ejpam-2648	149	3	by	by	ADP
ejpam-2648	149	4	u	u	NOUN
ejpam-2648	149	5	=	=	PROPN
ejpam-2648	149	6	qvr	qvr	PROPN
ejpam-2648	149	7	to	to	PART
ejpam-2648	149	8	see	see	VERB
ejpam-2648	149	9	that	that	PRON
ejpam-2648	149	10	,	,	PUNCT
ejpam-2648	149	11	using	use	VERB
ejpam-2648	149	12	jp3	jp3	PROPN
ejpam-2648	149	13	in	in	ADP
ejpam-2648	149	14	[	[	X
ejpam-2648	149	15	18	18	NUM
ejpam-2648	149	16	]	]	PUNCT
ejpam-2648	149	17	,	,	PUNCT
ejpam-2648	149	18	(	(	PUNCT
ejpam-2648	149	19	1	1	X
ejpam-2648	149	20	)	)	PUNCT
ejpam-2648	149	21	qru	qru	NOUN
ejpam-2648	149	22	=	=	SYM
ejpam-2648	149	23	qrqvr	qrqvr	NOUN
ejpam-2648	149	24	=	=	NOUN
ejpam-2648	149	25	qrqvqrv	qrqvqrv	NOUN
ejpam-2648	149	26	=	=	SYM
ejpam-2648	149	27	qqrvv	qqrvv	NOUN
ejpam-2648	149	28	=	=	SYM
ejpam-2648	149	29	qrv	qrv	VERB
ejpam-2648	149	30	=	=	PROPN
ejpam-2648	149	31	r.	r.	PROPN
ejpam-2648	149	32	h.	h.	PROPN
ejpam-2648	149	33	marhnine	marhnine	PROPN
ejpam-2648	149	34	,	,	PUNCT
ejpam-2648	149	35	c.	c.	PROPN
ejpam-2648	149	36	zarhouti	zarhouti	PROPN
ejpam-2648	149	37	/	/	SYM
ejpam-2648	149	38	eur	eur	PROPN
ejpam-2648	149	39	.	.	PUNCT
ejpam-2648	150	1	j.	j.	PROPN
ejpam-2648	150	2	pure	pure	PROPN
ejpam-2648	150	3	appl	appl	PROPN
ejpam-2648	150	4	.	.	PROPN
ejpam-2648	150	5	math	math	PROPN
ejpam-2648	150	6	,	,	PUNCT
ejpam-2648	150	7	10	10	NUM
ejpam-2648	150	8	(	(	PUNCT
ejpam-2648	150	9	4	4	NUM
ejpam-2648	150	10	)	)	PUNCT
ejpam-2648	150	11	(	(	PUNCT
ejpam-2648	150	12	2017	2017	NUM
ejpam-2648	150	13	)	)	PUNCT
ejpam-2648	150	14	,	,	PUNCT
ejpam-2648	150	15	749	749	NUM
ejpam-2648	150	16	-	-	SYM
ejpam-2648	150	17	762	762	NUM
ejpam-2648	150	18	755	755	NUM
ejpam-2648	150	19	by	by	ADP
ejpam-2648	150	20	idealness	idealness	NOUN
ejpam-2648	150	21	of	of	ADP
ejpam-2648	150	22	s(dk	s(dk	NOUN
ejpam-2648	150	23	)	)	PUNCT
ejpam-2648	150	24	,	,	PUNCT
ejpam-2648	150	25	u	u	NOUN
ejpam-2648	150	26	lies	lie	VERB
ejpam-2648	150	27	in	in	ADP
ejpam-2648	150	28	s(d−k	s(d−k	ADV
ejpam-2648	150	29	)	)	PUNCT
ejpam-2648	150	30	and	and	CCONJ
ejpam-2648	150	31	u	u	NOUN
ejpam-2648	150	32	is	be	AUX
ejpam-2648	150	33	nonzero	nonzero	NOUN
ejpam-2648	150	34	because	because	SCONJ
ejpam-2648	150	35	otherwise	otherwise	ADV
ejpam-2648	150	36	r	r	NOUN
ejpam-2648	150	37	=	=	SYM
ejpam-2648	150	38	0	0	NUM
ejpam-2648	150	39	,	,	PUNCT
ejpam-2648	150	40	which	which	PRON
ejpam-2648	150	41	is	be	AUX
ejpam-2648	150	42	a	a	DET
ejpam-2648	150	43	contradiction	contradiction	NOUN
ejpam-2648	150	44	.	.	PUNCT
ejpam-2648	151	1	hence	hence	ADV
ejpam-2648	151	2	,	,	PUNCT
ejpam-2648	151	3	there	there	PRON
ejpam-2648	151	4	exists	exist	VERB
ejpam-2648	151	5	a	a	DET
ejpam-2648	151	6	sequence	sequence	NOUN
ejpam-2648	151	7	{	{	PUNCT
ejpam-2648	151	8	xn	xn	NUM
ejpam-2648	151	9	}	}	PUNCT
ejpam-2648	151	10	in	in	ADP
ejpam-2648	151	11	v	v	NUM
ejpam-2648	151	12	−	−	NOUN
ejpam-2648	151	13	such	such	ADJ
ejpam-2648	151	14	that	that	DET
ejpam-2648	151	15	limxn	limxn	ADV
ejpam-2648	151	16	=	=	NOUN
ejpam-2648	151	17	0	0	NUM
ejpam-2648	151	18	and	and	CCONJ
ejpam-2648	151	19	limd−k	limd−k	ADJ
ejpam-2648	151	20	xn	xn	PROPN
ejpam-2648	151	21	=	=	PUNCT
ejpam-2648	152	1	u.	u.	NOUN
ejpam-2648	152	2	since	since	SCONJ
ejpam-2648	152	3	r	r	NOUN
ejpam-2648	152	4	is	be	AUX
ejpam-2648	152	5	reduced	reduce	VERB
ejpam-2648	152	6	,	,	PUNCT
ejpam-2648	152	7	we	we	PRON
ejpam-2648	152	8	have	have	AUX
ejpam-2648	152	9	qrv	qrv	VERB
ejpam-2648	152	10	−	−	PROPN
ejpam-2648	152	11	=	=	PUNCT
ejpam-2648	152	12	c.r	c.r	PROPN
ejpam-2648	152	13	and	and	CCONJ
ejpam-2648	152	14	consequently	consequently	ADV
ejpam-2648	152	15	,	,	PUNCT
ejpam-2648	152	16	for	for	ADP
ejpam-2648	152	17	every	every	DET
ejpam-2648	152	18	non	non	ADJ
ejpam-2648	152	19	negative	negative	ADJ
ejpam-2648	152	20	integer	integer	NOUN
ejpam-2648	152	21	n	n	CCONJ
ejpam-2648	152	22	,	,	PUNCT
ejpam-2648	152	23	there	there	PRON
ejpam-2648	152	24	exists	exist	VERB
ejpam-2648	152	25	a	a	DET
ejpam-2648	152	26	complex	complex	ADJ
ejpam-2648	152	27	number	number	NOUN
ejpam-2648	152	28	λn	λn	ADP
ejpam-2648	152	29	such	such	ADJ
ejpam-2648	152	30	qrxn	qrxn	NOUN
ejpam-2648	152	31	=	=	SYM
ejpam-2648	152	32	λnr	λnr	NOUN
ejpam-2648	152	33	.	.	PUNCT
ejpam-2648	153	1	now	now	ADV
ejpam-2648	153	2	the	the	DET
ejpam-2648	153	3	boundedness	boundedness	NOUN
ejpam-2648	153	4	of	of	ADP
ejpam-2648	153	5	the	the	DET
ejpam-2648	153	6	operator	operator	NOUN
ejpam-2648	153	7	qr	qr	PROPN
ejpam-2648	153	8	shows	show	VERB
ejpam-2648	153	9	that	that	DET
ejpam-2648	153	10	limqrxn	limqrxn	NOUN
ejpam-2648	153	11	=	=	PUNCT
ejpam-2648	153	12	qr	qr	NOUN
ejpam-2648	153	13	limxn	limxn	ADV
ejpam-2648	153	14	=	=	NOUN
ejpam-2648	153	15	0	0	X
ejpam-2648	153	16	.	.	PUNCT
ejpam-2648	154	1	this	this	PRON
ejpam-2648	154	2	makes	make	VERB
ejpam-2648	154	3	the	the	DET
ejpam-2648	154	4	sequence	sequence	NOUN
ejpam-2648	154	5	{	{	PUNCT
ejpam-2648	154	6	λn	λn	NOUN
ejpam-2648	154	7	}	}	PUNCT
ejpam-2648	154	8	converging	converge	VERB
ejpam-2648	154	9	to	to	ADP
ejpam-2648	154	10	zero	zero	NUM
ejpam-2648	154	11	in	in	ADP
ejpam-2648	154	12	the	the	DET
ejpam-2648	154	13	complex	complex	ADJ
ejpam-2648	154	14	field	field	NOUN
ejpam-2648	154	15	c.	c.	NOUN
ejpam-2648	154	16	it	it	PRON
ejpam-2648	154	17	follows	follow	VERB
ejpam-2648	154	18	that	that	SCONJ
ejpam-2648	154	19	(	(	PUNCT
ejpam-2648	154	20	2	2	X
ejpam-2648	154	21	)	)	PUNCT
ejpam-2648	155	1	limd+	limd+	X
ejpam-2648	155	2	k	k	X
ejpam-2648	155	3	(	(	PUNCT
ejpam-2648	155	4	qrxn	qrxn	NOUN
ejpam-2648	155	5	)	)	PUNCT
ejpam-2648	155	6	=	=	SYM
ejpam-2648	156	1	limd+	limd+	X
ejpam-2648	156	2	k	k	X
ejpam-2648	156	3	(	(	PUNCT
ejpam-2648	156	4	λnr	λnr	ADJ
ejpam-2648	156	5	)	)	PUNCT
ejpam-2648	156	6	=	=	SYM
ejpam-2648	156	7	limλnd	limλnd	NOUN
ejpam-2648	156	8	+	+	CCONJ
ejpam-2648	156	9	k	k	X
ejpam-2648	156	10	(	(	PUNCT
ejpam-2648	156	11	r	r	NOUN
ejpam-2648	156	12	)	)	PUNCT
ejpam-2648	156	13	=	=	NOUN
ejpam-2648	156	14	0	0	X
ejpam-2648	156	15	.	.	PUNCT
ejpam-2648	157	1	on	on	ADP
ejpam-2648	157	2	the	the	DET
ejpam-2648	157	3	other	other	ADJ
ejpam-2648	157	4	hand	hand	NOUN
ejpam-2648	157	5	,	,	PUNCT
ejpam-2648	157	6	by	by	ADP
ejpam-2648	157	7	making	make	VERB
ejpam-2648	157	8	use	use	NOUN
ejpam-2648	157	9	of	of	ADP
ejpam-2648	157	10	the	the	DET
ejpam-2648	157	11	triple	triple	ADJ
ejpam-2648	157	12	product	product	NOUN
ejpam-2648	157	13	of	of	ADP
ejpam-2648	157	14	v	v	NOUN
ejpam-2648	157	15	and	and	CCONJ
ejpam-2648	157	16	that	that	PRON
ejpam-2648	157	17	of	of	ADP
ejpam-2648	157	18	d−j	d−j	NOUN
ejpam-2648	157	19	,	,	PUNCT
ejpam-2648	157	20	such	such	ADJ
ejpam-2648	157	21	that	that	SCONJ
ejpam-2648	157	22	1	1	NUM
ejpam-2648	157	23	≤	≤	NUM
ejpam-2648	157	24	j	j	PROPN
ejpam-2648	157	25	≤	≤	PROPN
ejpam-2648	157	26	k−1	k−1	PROPN
ejpam-2648	157	27	,	,	PUNCT
ejpam-2648	157	28	we	we	PRON
ejpam-2648	157	29	see	see	VERB
ejpam-2648	157	30	that	that	SCONJ
ejpam-2648	157	31	all	all	DET
ejpam-2648	157	32	terms	term	NOUN
ejpam-2648	157	33	like	like	ADP
ejpam-2648	157	34	{	{	PUNCT
ejpam-2648	157	35	d+	d+	NOUN
ejpam-2648	157	36	i	i	PRON
ejpam-2648	157	37	r	r	VERB
ejpam-2648	157	38	,	,	PUNCT
ejpam-2648	157	39	d	d	PROPN
ejpam-2648	157	40	−	−	PROPN
ejpam-2648	157	41	j	j	PROPN
ejpam-2648	157	42	xn	xn	PROPN
ejpam-2648	157	43	,	,	PUNCT
ejpam-2648	158	1	d	d	PROPN
ejpam-2648	159	1	+	+	NUM
ejpam-2648	159	2	h	h	NOUN
ejpam-2648	159	3	r	r	NOUN
ejpam-2648	159	4	}	}	PUNCT
ejpam-2648	159	5	converge	converge	VERB
ejpam-2648	159	6	to	to	ADP
ejpam-2648	159	7	zero	zero	NUM
ejpam-2648	159	8	when	when	SCONJ
ejpam-2648	159	9	n	n	PRON
ejpam-2648	159	10	tends	tend	VERB
ejpam-2648	159	11	to	to	ADP
ejpam-2648	159	12	∞.	∞.	PROPN
ejpam-2648	159	13	that	that	PRON
ejpam-2648	159	14	is	be	AUX
ejpam-2648	159	15	lim{d+	lim{d+	ADJ
ejpam-2648	159	16	i	i	NOUN
ejpam-2648	159	17	r	r	NOUN
ejpam-2648	159	18	,	,	PUNCT
ejpam-2648	160	1	d	d	PROPN
ejpam-2648	160	2	−	−	PROPN
ejpam-2648	160	3	j	j	PROPN
ejpam-2648	160	4	xn	xn	PROPN
ejpam-2648	160	5	,	,	PUNCT
ejpam-2648	160	6	d	d	PROPN
ejpam-2648	160	7	+	+	NUM
ejpam-2648	161	1	h	h	NOUN
ejpam-2648	161	2	r	r	NOUN
ejpam-2648	161	3	}	}	PUNCT
ejpam-2648	161	4	=	=	SYM
ejpam-2648	161	5	{	{	PUNCT
ejpam-2648	161	6	d+	d+	PUNCT
ejpam-2648	161	7	i	i	NOUN
ejpam-2648	161	8	r	r	NOUN
ejpam-2648	161	9	,	,	PUNCT
ejpam-2648	161	10	limd−j	limd−j	NUM
ejpam-2648	161	11	xn	xn	NOUN
ejpam-2648	161	12	,	,	PUNCT
ejpam-2648	162	1	d	d	PROPN
ejpam-2648	162	2	+	+	NUM
ejpam-2648	162	3	h	h	NOUN
ejpam-2648	162	4	r	r	NOUN
ejpam-2648	162	5	}	}	PUNCT
ejpam-2648	162	6	=	=	SYM
ejpam-2648	162	7	{	{	PUNCT
ejpam-2648	162	8	d+	d+	PUNCT
ejpam-2648	162	9	i	i	PRON
ejpam-2648	162	10	r	r	VERB
ejpam-2648	162	11	,	,	PUNCT
ejpam-2648	162	12	d	d	PROPN
ejpam-2648	162	13	−	−	PROPN
ejpam-2648	162	14	j	j	PROPN
ejpam-2648	162	15	limxn	limxn	ADV
ejpam-2648	162	16	,	,	PUNCT
ejpam-2648	163	1	d	d	PROPN
ejpam-2648	164	1	+	+	NUM
ejpam-2648	164	2	h	h	NOUN
ejpam-2648	165	1	r	r	NOUN
ejpam-2648	165	2	}	}	PUNCT
ejpam-2648	165	3	=	=	SYM
ejpam-2648	165	4	0	0	X
ejpam-2648	165	5	.	.	PUNCT
ejpam-2648	166	1	it	it	PRON
ejpam-2648	166	2	follows	follow	VERB
ejpam-2648	166	3	that	that	SCONJ
ejpam-2648	166	4	,	,	PUNCT
ejpam-2648	166	5	taking	take	VERB
ejpam-2648	166	6	into	into	ADP
ejpam-2648	166	7	account	account	NOUN
ejpam-2648	166	8	(	(	PUNCT
ejpam-2648	166	9	1	1	NUM
ejpam-2648	166	10	)	)	PUNCT
ejpam-2648	166	11	,	,	PUNCT
ejpam-2648	166	12	limd+	limd+	X
ejpam-2648	166	13	k	k	X
ejpam-2648	166	14	(	(	PUNCT
ejpam-2648	166	15	qrxn	qrxn	NOUN
ejpam-2648	166	16	)	)	PUNCT
ejpam-2648	166	17	=	=	SYM
ejpam-2648	167	1	1	1	NUM
ejpam-2648	167	2	2	2	NUM
ejpam-2648	167	3	limd−k	limd−k	ADP
ejpam-2648	167	4	(	(	PUNCT
ejpam-2648	167	5	{	{	PUNCT
ejpam-2648	167	6	r	r	NOUN
ejpam-2648	167	7	,	,	PUNCT
ejpam-2648	167	8	xn	xn	PROPN
ejpam-2648	167	9	,	,	PUNCT
ejpam-2648	167	10	r	r	NOUN
ejpam-2648	167	11	}	}	PUNCT
ejpam-2648	167	12	)	)	PUNCT
ejpam-2648	167	13	=	=	SYM
ejpam-2648	167	14	1	1	NUM
ejpam-2648	167	15	2	2	NUM
ejpam-2648	167	16	lim	lim	PROPN
ejpam-2648	167	17	∑	∑	PROPN
ejpam-2648	167	18	i+j+h	i+j+h	PROPN
ejpam-2648	167	19	=	=	SYM
ejpam-2648	167	20	k	k	X
ejpam-2648	167	21	{	{	PUNCT
ejpam-2648	167	22	d+	d+	PUNCT
ejpam-2648	167	23	i	i	PRON
ejpam-2648	167	24	r	r	VERB
ejpam-2648	167	25	,	,	PUNCT
ejpam-2648	167	26	d	d	PROPN
ejpam-2648	167	27	−	−	PROPN
ejpam-2648	167	28	j	j	PROPN
ejpam-2648	167	29	xn	xn	PROPN
ejpam-2648	167	30	,	,	PUNCT
ejpam-2648	167	31	d	d	PROPN
ejpam-2648	168	1	+	+	NUM
ejpam-2648	168	2	h	h	NOUN
ejpam-2648	169	1	r	r	NOUN
ejpam-2648	169	2	}	}	PUNCT
ejpam-2648	169	3	=	=	SYM
ejpam-2648	169	4	1	1	NUM
ejpam-2648	169	5	2	2	NUM
ejpam-2648	169	6	{	{	PUNCT
ejpam-2648	169	7	r	r	NOUN
ejpam-2648	169	8	,	,	PUNCT
ejpam-2648	169	9	limd−k	limd−k	X
ejpam-2648	169	10	xn	xn	PROPN
ejpam-2648	169	11	,	,	PUNCT
ejpam-2648	169	12	r	r	NOUN
ejpam-2648	169	13	}	}	PUNCT
ejpam-2648	169	14	=	=	SYM
ejpam-2648	169	15	1	1	NUM
ejpam-2648	169	16	2	2	NUM
ejpam-2648	169	17	{	{	PUNCT
ejpam-2648	169	18	r	r	NOUN
ejpam-2648	169	19	,	,	PUNCT
ejpam-2648	169	20	u	u	NOUN
ejpam-2648	169	21	,	,	PUNCT
ejpam-2648	169	22	r	r	NOUN
ejpam-2648	169	23	}	}	PUNCT
ejpam-2648	169	24	=	=	PUNCT
ejpam-2648	169	25	qru	qru	NOUN
ejpam-2648	169	26	=	=	SYM
ejpam-2648	169	27	r	r	NOUN
ejpam-2648	169	28	,	,	PUNCT
ejpam-2648	169	29	which	which	PRON
ejpam-2648	169	30	contradicts	contradict	VERB
ejpam-2648	169	31	(	(	PUNCT
ejpam-2648	169	32	2	2	NUM
ejpam-2648	169	33	)	)	PUNCT
ejpam-2648	169	34	since	since	SCONJ
ejpam-2648	169	35	r	r	NOUN
ejpam-2648	169	36	is	be	AUX
ejpam-2648	169	37	nonzero	nonzero	NOUN
ejpam-2648	169	38	.	.	PUNCT
ejpam-2648	170	1	now	now	ADV
ejpam-2648	170	2	,	,	PUNCT
ejpam-2648	170	3	by	by	ADP
ejpam-2648	170	4	idealness	idealness	NOUN
ejpam-2648	170	5	of	of	ADP
ejpam-2648	170	6	s(dk	s(dk	NOUN
ejpam-2648	170	7	)	)	PUNCT
ejpam-2648	170	8	and	and	CCONJ
ejpam-2648	170	9	soc(v	soc(v	NUM
ejpam-2648	170	10	)	)	PUNCT
ejpam-2648	170	11	,	,	PUNCT
ejpam-2648	170	12	we	we	PRON
ejpam-2648	170	13	see	see	VERB
ejpam-2648	170	14	that	that	SCONJ
ejpam-2648	170	15	for	for	ADP
ejpam-2648	170	16	all	all	DET
ejpam-2648	170	17	s	s	PART
ejpam-2648	170	18	∈	∈	ADJ
ejpam-2648	170	19	soc(v	soc(v	DET
ejpam-2648	170	20	−	−	NOUN
ejpam-2648	170	21	)	)	PUNCT
ejpam-2648	170	22	qs(s(d+	qs(s(d+	PROPN
ejpam-2648	170	23	k	k	PROPN
ejpam-2648	170	24	)	)	PUNCT
ejpam-2648	170	25	)	)	PUNCT
ejpam-2648	171	1	⊂	⊂	PROPN
ejpam-2648	172	1	soc(v	soc(v	DET
ejpam-2648	172	2	−	−	NOUN
ejpam-2648	172	3	)	)	PUNCT
ejpam-2648	172	4	∩	∩	NOUN
ejpam-2648	172	5	s(d−k	s(d−k	ADV
ejpam-2648	172	6	)	)	PUNCT
ejpam-2648	173	1	=	=	SYM
ejpam-2648	173	2	0	0	X
ejpam-2648	173	3	.	.	PUNCT
ejpam-2648	174	1	this	this	PRON
ejpam-2648	174	2	shows	show	VERB
ejpam-2648	174	3	that	that	SCONJ
ejpam-2648	174	4	s(d+	s(d+	PROPN
ejpam-2648	174	5	k	k	X
ejpam-2648	174	6	)	)	PUNCT
ejpam-2648	174	7	⊆	⊆	NUM
ejpam-2648	174	8	ker(qs	ker(qs	NOUN
ejpam-2648	174	9	)	)	PUNCT
ejpam-2648	174	10	for	for	ADP
ejpam-2648	174	11	every	every	DET
ejpam-2648	174	12	s	s	NOUN
ejpam-2648	174	13	in	in	ADP
ejpam-2648	174	14	soc(v	soc(v	NUM
ejpam-2648	174	15	−	−	NOUN
ejpam-2648	174	16	)	)	PUNCT
ejpam-2648	174	17	,	,	PUNCT
ejpam-2648	174	18	that	that	PRON
ejpam-2648	174	19	is	be	AUX
ejpam-2648	174	20	s(d+	s(d+	ADJ
ejpam-2648	174	21	k	k	X
ejpam-2648	174	22	)	)	PUNCT
ejpam-2648	174	23	⊆	⊆	NUM
ejpam-2648	174	24	∩	∩	NOUN
ejpam-2648	174	25	s∈soc(v	s∈soc(v	ADP
ejpam-2648	174	26	−	−	NOUN
ejpam-2648	174	27	)	)	PUNCT
ejpam-2648	174	28	ker(qs	ker(qs	NOUN
ejpam-2648	174	29	)	)	PUNCT
ejpam-2648	174	30	.	.	PUNCT
ejpam-2648	175	1	but	but	CCONJ
ejpam-2648	175	2	in	in	ADP
ejpam-2648	175	3	virtue	virtue	NOUN
ejpam-2648	175	4	of	of	ADP
ejpam-2648	175	5	[	[	X
ejpam-2648	175	6	18	18	NUM
ejpam-2648	175	7	,	,	PUNCT
ejpam-2648	175	8	theorem	theorem	VERB
ejpam-2648	175	9	4.13	4.13	NUM
ejpam-2648	175	10	]	]	PUNCT
ejpam-2648	175	11	,	,	PUNCT
ejpam-2648	175	12	we	we	PRON
ejpam-2648	175	13	see	see	VERB
ejpam-2648	175	14	∩	∩	NOUN
ejpam-2648	175	15	s∈soc(v	s∈soc(v	ADP
ejpam-2648	175	16	−	−	NOUN
ejpam-2648	175	17	)	)	PUNCT
ejpam-2648	175	18	ker(qs	ker(qs	NOUN
ejpam-2648	175	19	)	)	PUNCT
ejpam-2648	175	20	⊆	⊆	NUM
ejpam-2648	175	21	rad(soc(v	rad(soc(v	NOUN
ejpam-2648	175	22	+	+	NOUN
ejpam-2648	175	23	)	)	PUNCT
ejpam-2648	175	24	)	)	PUNCT
ejpam-2648	175	25	and	and	CCONJ
ejpam-2648	175	26	rad(soc(v	rad(soc(v	PUNCT
ejpam-2648	175	27	+	+	NOUN
ejpam-2648	175	28	)	)	PUNCT
ejpam-2648	175	29	)	)	PUNCT
ejpam-2648	176	1	=	=	PUNCT
ejpam-2648	177	1	soc(v	soc(v	DET
ejpam-2648	177	2	+	+	NOUN
ejpam-2648	177	3	)	)	PUNCT
ejpam-2648	177	4	∩	∩	NOUN
ejpam-2648	177	5	rad(v	rad(v	NOUN
ejpam-2648	177	6	+	+	NOUN
ejpam-2648	177	7	)	)	PUNCT
ejpam-2648	177	8	.	.	PUNCT
ejpam-2648	178	1	but	but	CCONJ
ejpam-2648	178	2	,	,	PUNCT
ejpam-2648	178	3	the	the	DET
ejpam-2648	178	4	mccrimmon	mccrimmon	ADJ
ejpam-2648	178	5	radical	radical	ADJ
ejpam-2648	178	6	rad(v	rad(v	NOUN
ejpam-2648	178	7	)	)	PUNCT
ejpam-2648	178	8	is	be	AUX
ejpam-2648	178	9	reduced	reduce	VERB
ejpam-2648	178	10	to	to	ADP
ejpam-2648	178	11	zero	zero	NUM
ejpam-2648	178	12	by	by	ADP
ejpam-2648	178	13	nondegeneracy	nondegeneracy	NOUN
ejpam-2648	178	14	of	of	ADP
ejpam-2648	178	15	v	v	NOUN
ejpam-2648	178	16	.	.	PUNCT
ejpam-2648	179	1	this	this	PRON
ejpam-2648	179	2	proves	prove	VERB
ejpam-2648	179	3	that	that	SCONJ
ejpam-2648	179	4	s(d+	s(d+	VERB
ejpam-2648	179	5	k	k	X
ejpam-2648	179	6	)	)	PUNCT
ejpam-2648	180	1	=	=	SYM
ejpam-2648	180	2	0	0	PUNCT
ejpam-2648	181	1	and	and	CCONJ
ejpam-2648	181	2	,	,	PUNCT
ejpam-2648	181	3	by	by	ADP
ejpam-2648	181	4	the	the	DET
ejpam-2648	181	5	closed	closed	ADJ
ejpam-2648	181	6	graph	graph	NOUN
ejpam-2648	181	7	theorem	theorem	VERB
ejpam-2648	181	8	,	,	PUNCT
ejpam-2648	181	9	d+	d+	X
ejpam-2648	181	10	k	k	X
ejpam-2648	181	11	is	be	AUX
ejpam-2648	181	12	continuous	continuous	ADJ
ejpam-2648	181	13	.	.	PUNCT
ejpam-2648	182	1	by	by	ADP
ejpam-2648	182	2	the	the	DET
ejpam-2648	182	3	symmetry	symmetry	NOUN
ejpam-2648	182	4	of	of	ADP
ejpam-2648	182	5	the	the	DET
ejpam-2648	182	6	argument	argument	NOUN
ejpam-2648	182	7	we	we	PRON
ejpam-2648	182	8	see	see	VERB
ejpam-2648	182	9	that	that	SCONJ
ejpam-2648	182	10	d−k	d−k	PROPN
ejpam-2648	182	11	is	be	AUX
ejpam-2648	182	12	analogously	analogously	ADV
ejpam-2648	182	13	continuous	continuous	ADJ
ejpam-2648	182	14	.	.	PUNCT
ejpam-2648	183	1	as	as	ADP
ejpam-2648	183	2	a	a	DET
ejpam-2648	183	3	fundamental	fundamental	ADJ
ejpam-2648	183	4	example	example	NOUN
ejpam-2648	183	5	of	of	ADP
ejpam-2648	183	6	jordan	jordan	PROPN
ejpam-2648	183	7	pairs	pair	NOUN
ejpam-2648	183	8	having	have	VERB
ejpam-2648	183	9	nonzero	nonzero	PROPN
ejpam-2648	183	10	socle	socle	NOUN
ejpam-2648	183	11	,	,	PUNCT
ejpam-2648	183	12	b(x	b(x	NOUN
ejpam-2648	183	13	,	,	PUNCT
ejpam-2648	183	14	y	y	PROPN
ejpam-2648	183	15	)	)	PUNCT
ejpam-2648	183	16	the	the	DET
ejpam-2648	183	17	jordan	jordan	PROPN
ejpam-2648	183	18	pair	pair	PROPN
ejpam-2648	183	19	of	of	ADP
ejpam-2648	183	20	bounded	bounded	ADJ
ejpam-2648	183	21	linear	linear	PROPN
ejpam-2648	183	22	operators	operator	NOUN
ejpam-2648	183	23	between	between	ADP
ejpam-2648	183	24	two	two	NUM
ejpam-2648	183	25	banach	banach	NOUN
ejpam-2648	183	26	spaces	space	VERB
ejpam-2648	183	27	x	x	PUNCT
ejpam-2648	183	28	and	and	CCONJ
ejpam-2648	183	29	y	y	PROPN
ejpam-2648	183	30	.	.	PUNCT
ejpam-2648	184	1	so	so	ADV
ejpam-2648	184	2	we	we	PRON
ejpam-2648	184	3	have	have	VERB
ejpam-2648	184	4	the	the	DET
ejpam-2648	184	5	following	following	NOUN
ejpam-2648	184	6	.	.	PUNCT
ejpam-2648	185	1	h.	h.	PROPN
ejpam-2648	185	2	marhnine	marhnine	PROPN
ejpam-2648	185	3	,	,	PUNCT
ejpam-2648	185	4	c.	c.	PROPN
ejpam-2648	185	5	zarhouti	zarhouti	PROPN
ejpam-2648	185	6	/	/	SYM
ejpam-2648	185	7	eur	eur	PROPN
ejpam-2648	185	8	.	.	PUNCT
ejpam-2648	186	1	j.	j.	PROPN
ejpam-2648	186	2	pure	pure	PROPN
ejpam-2648	186	3	appl	appl	PROPN
ejpam-2648	186	4	.	.	PROPN
ejpam-2648	186	5	math	math	PROPN
ejpam-2648	186	6	,	,	PUNCT
ejpam-2648	186	7	10	10	NUM
ejpam-2648	186	8	(	(	PUNCT
ejpam-2648	186	9	4	4	NUM
ejpam-2648	186	10	)	)	PUNCT
ejpam-2648	186	11	(	(	PUNCT
ejpam-2648	186	12	2017	2017	NUM
ejpam-2648	186	13	)	)	PUNCT
ejpam-2648	186	14	,	,	PUNCT
ejpam-2648	186	15	749	749	NUM
ejpam-2648	186	16	-	-	SYM
ejpam-2648	186	17	762	762	NUM
ejpam-2648	186	18	756	756	NUM
ejpam-2648	186	19	corollary	corollary	ADJ
ejpam-2648	186	20	1	1	NUM
ejpam-2648	186	21	.	.	PUNCT
ejpam-2648	187	1	any	any	DET
ejpam-2648	187	2	higher	high	ADJ
ejpam-2648	187	3	derivation	derivation	NOUN
ejpam-2648	187	4	dn	dn	NOUN
ejpam-2648	187	5	=	=	SYM
ejpam-2648	187	6	(	(	PUNCT
ejpam-2648	187	7	d+	d+	X
ejpam-2648	187	8	n	n	X
ejpam-2648	187	9	,	,	PUNCT
ejpam-2648	187	10	d	d	PROPN
ejpam-2648	187	11	−	−	PROPN
ejpam-2648	187	12	n	n	CCONJ
ejpam-2648	187	13	)	)	PUNCT
ejpam-2648	187	14	on	on	ADP
ejpam-2648	187	15	the	the	DET
ejpam-2648	187	16	banach	banach	NOUN
ejpam-2648	187	17	-	-	PUNCT
ejpam-2648	187	18	jordan	jordan	PROPN
ejpam-2648	187	19	pair	pair	PROPN
ejpam-2648	187	20	b(x	b(x	PROPN
ejpam-2648	187	21	,	,	PUNCT
ejpam-2648	187	22	y	y	PROPN
ejpam-2648	187	23	)	)	PUNCT
ejpam-2648	187	24	consists	consist	VERB
ejpam-2648	187	25	of	of	ADP
ejpam-2648	187	26	continuous	continuous	ADJ
ejpam-2648	187	27	operators	operator	NOUN
ejpam-2648	187	28	.	.	PUNCT
ejpam-2648	188	1	proof	proof	NOUN
ejpam-2648	188	2	.	.	PUNCT
ejpam-2648	189	1	it	it	PRON
ejpam-2648	189	2	is	be	AUX
ejpam-2648	189	3	known	know	VERB
ejpam-2648	189	4	that	that	SCONJ
ejpam-2648	189	5	the	the	DET
ejpam-2648	189	6	banach	banach	NOUN
ejpam-2648	189	7	-	-	PUNCT
ejpam-2648	189	8	jordan	jordan	NOUN
ejpam-2648	189	9	pair	pair	PROPN
ejpam-2648	189	10	b(x	b(x	PROPN
ejpam-2648	189	11	,	,	PUNCT
ejpam-2648	189	12	y	y	PROPN
ejpam-2648	189	13	)	)	PUNCT
ejpam-2648	189	14	of	of	ADP
ejpam-2648	189	15	bounded	bounded	ADJ
ejpam-2648	189	16	linear	linear	PROPN
ejpam-2648	189	17	operators	operator	NOUN
ejpam-2648	189	18	between	between	ADP
ejpam-2648	189	19	two	two	NUM
ejpam-2648	189	20	banach	banach	NOUN
ejpam-2648	189	21	spaces	space	VERB
ejpam-2648	189	22	x	x	PUNCT
ejpam-2648	189	23	and	and	CCONJ
ejpam-2648	189	24	y	y	PROPN
ejpam-2648	189	25	is	be	AUX
ejpam-2648	189	26	nondegenerate	nondegenerate	ADJ
ejpam-2648	189	27	and	and	CCONJ
ejpam-2648	189	28	has	have	AUX
ejpam-2648	189	29	soc(b(x	soc(b(x	VERB
ejpam-2648	189	30	,	,	PUNCT
ejpam-2648	189	31	y	y	NOUN
ejpam-2648	189	32	)	)	PUNCT
ejpam-2648	189	33	)	)	PUNCT
ejpam-2648	190	1	=	=	SYM
ejpam-2648	190	2	(	(	PUNCT
ejpam-2648	190	3	fl(x	fl(x	PROPN
ejpam-2648	190	4	,	,	PUNCT
ejpam-2648	190	5	y),fl(y	y),fl(y	PROPN
ejpam-2648	190	6	,	,	PUNCT
ejpam-2648	190	7	x	x	PROPN
ejpam-2648	190	8	)	)	PUNCT
ejpam-2648	190	9	,	,	PUNCT
ejpam-2648	190	10	the	the	DET
ejpam-2648	190	11	banach	banach	NOUN
ejpam-2648	190	12	-	-	PUNCT
ejpam-2648	190	13	jordan	jordan	NOUN
ejpam-2648	190	14	pair	pair	NOUN
ejpam-2648	190	15	consisting	consist	VERB
ejpam-2648	190	16	in	in	ADP
ejpam-2648	190	17	bounded	bounded	ADJ
ejpam-2648	190	18	linear	linear	PROPN
ejpam-2648	190	19	operators	operator	NOUN
ejpam-2648	190	20	of	of	ADP
ejpam-2648	190	21	finite	finite	PROPN
ejpam-2648	190	22	rank	rank	PROPN
ejpam-2648	190	23	.	.	PUNCT
ejpam-2648	191	1	now	now	ADV
ejpam-2648	191	2	the	the	DET
ejpam-2648	191	3	continuity	continuity	NOUN
ejpam-2648	191	4	of	of	ADP
ejpam-2648	191	5	{	{	PUNCT
ejpam-2648	191	6	dn	dn	NOUN
ejpam-2648	191	7	=	=	SYM
ejpam-2648	191	8	(	(	PUNCT
ejpam-2648	191	9	d+	d+	X
ejpam-2648	191	10	n	n	X
ejpam-2648	191	11	,	,	PUNCT
ejpam-2648	191	12	d	d	PROPN
ejpam-2648	191	13	−	−	PROPN
ejpam-2648	191	14	n	n	X
ejpam-2648	191	15	)	)	PUNCT
ejpam-2648	191	16	}	}	PUNCT
ejpam-2648	191	17	follows	follow	VERB
ejpam-2648	191	18	immediately	immediately	ADV
ejpam-2648	191	19	from	from	ADP
ejpam-2648	191	20	theorem	theorem	ADJ
ejpam-2648	191	21	1	1	NUM
ejpam-2648	191	22	.	.	NOUN
ejpam-2648	191	23	4	4	NUM
ejpam-2648	191	24	.	.	X
ejpam-2648	191	25	main	main	ADJ
ejpam-2648	191	26	result	result	NOUN
ejpam-2648	191	27	before	before	ADP
ejpam-2648	191	28	going	go	VERB
ejpam-2648	191	29	on	on	ADP
ejpam-2648	191	30	the	the	DET
ejpam-2648	191	31	proof	proof	NOUN
ejpam-2648	191	32	the	the	DET
ejpam-2648	191	33	main	main	ADJ
ejpam-2648	191	34	theorem	theorem	NOUN
ejpam-2648	191	35	in	in	ADP
ejpam-2648	191	36	this	this	DET
ejpam-2648	191	37	paper	paper	NOUN
ejpam-2648	191	38	,	,	PUNCT
ejpam-2648	191	39	we	we	PRON
ejpam-2648	191	40	recall	recall	VERB
ejpam-2648	191	41	the	the	DET
ejpam-2648	191	42	following	follow	VERB
ejpam-2648	191	43	technical	technical	ADJ
ejpam-2648	191	44	results	result	NOUN
ejpam-2648	191	45	which	which	PRON
ejpam-2648	191	46	seem	seem	VERB
ejpam-2648	191	47	to	to	PART
ejpam-2648	191	48	be	be	AUX
ejpam-2648	191	49	useful	useful	ADJ
ejpam-2648	191	50	in	in	ADP
ejpam-2648	191	51	the	the	DET
ejpam-2648	191	52	sequel	sequel	NOUN
ejpam-2648	191	53	.	.	PUNCT
ejpam-2648	192	1	lemma	lemma	PROPN
ejpam-2648	192	2	3	3	X
ejpam-2648	192	3	.	.	PUNCT
ejpam-2648	193	1	[	[	X
ejpam-2648	193	2	29	29	NUM
ejpam-2648	193	3	]	]	PUNCT
ejpam-2648	193	4	.	.	PUNCT
ejpam-2648	194	1	let	let	VERB
ejpam-2648	194	2	x	x	PRON
ejpam-2648	194	3	be	be	AUX
ejpam-2648	194	4	a	a	DET
ejpam-2648	194	5	banach	banach	NOUN
ejpam-2648	194	6	space	space	NOUN
ejpam-2648	194	7	,	,	PUNCT
ejpam-2648	194	8	{	{	PUNCT
ejpam-2648	194	9	ti}i	ti}i	DET
ejpam-2648	194	10	a	a	DET
ejpam-2648	194	11	sequence	sequence	NOUN
ejpam-2648	194	12	of	of	ADP
ejpam-2648	194	13	continuous	continuous	ADJ
ejpam-2648	194	14	linear	linear	PROPN
ejpam-2648	194	15	operators	operator	NOUN
ejpam-2648	194	16	defined	define	VERB
ejpam-2648	194	17	on	on	ADP
ejpam-2648	194	18	x	x	PUNCT
ejpam-2648	194	19	and	and	CCONJ
ejpam-2648	194	20	let	let	VERB
ejpam-2648	194	21	{	{	PUNCT
ejpam-2648	194	22	ri}i	ri}i	PROPN
ejpam-2648	194	23	be	be	AUX
ejpam-2648	194	24	a	a	DET
ejpam-2648	194	25	sequence	sequence	NOUN
ejpam-2648	194	26	of	of	ADP
ejpam-2648	194	27	linear	linear	ADJ
ejpam-2648	194	28	continuous	continuous	ADJ
ejpam-2648	194	29	operators	operator	NOUN
ejpam-2648	194	30	whose	whose	DET
ejpam-2648	194	31	domain	domain	NOUN
ejpam-2648	194	32	is	be	AUX
ejpam-2648	194	33	x	x	PUNCT
ejpam-2648	194	34	but	but	CCONJ
ejpam-2648	194	35	which	which	PRON
ejpam-2648	194	36	may	may	AUX
ejpam-2648	194	37	map	map	VERB
ejpam-2648	194	38	into	into	ADP
ejpam-2648	194	39	other	other	ADJ
ejpam-2648	194	40	banach	banach	NOUN
ejpam-2648	194	41	spaces	space	NOUN
ejpam-2648	194	42	.	.	PUNCT
ejpam-2648	195	1	let	let	VERB
ejpam-2648	195	2	t	t	NOUN
ejpam-2648	195	3	be	be	AUX
ejpam-2648	195	4	a	a	DET
ejpam-2648	195	5	possibly	possibly	ADV
ejpam-2648	195	6	discontinuous	discontinuous	ADJ
ejpam-2648	195	7	map	map	NOUN
ejpam-2648	195	8	from	from	ADP
ejpam-2648	195	9	x	x	PRON
ejpam-2648	195	10	to	to	ADP
ejpam-2648	195	11	itself	itself	PRON
ejpam-2648	195	12	.	.	PUNCT
ejpam-2648	196	1	if	if	SCONJ
ejpam-2648	196	2	the	the	DET
ejpam-2648	196	3	operator	operator	NOUN
ejpam-2648	196	4	rntt1	rntt1	PROPN
ejpam-2648	196	5	...	...	PUNCT
ejpam-2648	196	6	tm	tm	PROPN
ejpam-2648	196	7	is	be	AUX
ejpam-2648	196	8	continuous	continuous	ADJ
ejpam-2648	196	9	for	for	ADP
ejpam-2648	196	10	m	m	NOUN
ejpam-2648	196	11	greater	great	ADJ
ejpam-2648	196	12	than	than	ADP
ejpam-2648	196	13	n	n	PRON
ejpam-2648	196	14	then	then	ADV
ejpam-2648	196	15	rntt1	rntt1	PROPN
ejpam-2648	196	16	...	...	PUNCT
ejpam-2648	197	1	tn	tn	PROPN
ejpam-2648	197	2	is	be	AUX
ejpam-2648	197	3	continuous	continuous	ADJ
ejpam-2648	197	4	when	when	SCONJ
ejpam-2648	197	5	n	n	PRON
ejpam-2648	197	6	is	be	AUX
ejpam-2648	197	7	sufficiently	sufficiently	ADV
ejpam-2648	197	8	large	large	ADJ
ejpam-2648	197	9	.	.	PUNCT
ejpam-2648	198	1	proposition	proposition	NOUN
ejpam-2648	198	2	1	1	NUM
ejpam-2648	198	3	.	.	PUNCT
ejpam-2648	199	1	[	[	X
ejpam-2648	199	2	10	10	NUM
ejpam-2648	199	3	]	]	PUNCT
ejpam-2648	199	4	.	.	PUNCT
ejpam-2648	200	1	let	let	VERB
ejpam-2648	200	2	j	j	PROPN
ejpam-2648	200	3	be	be	AUX
ejpam-2648	200	4	a	a	DET
ejpam-2648	200	5	banach	banach	NOUN
ejpam-2648	200	6	-	-	PUNCT
ejpam-2648	200	7	jordan	jordan	NOUN
ejpam-2648	200	8	algebra	algebra	PROPN
ejpam-2648	200	9	and	and	CCONJ
ejpam-2648	200	10	i	i	PRON
ejpam-2648	200	11	be	be	VERB
ejpam-2648	200	12	a	a	DET
ejpam-2648	200	13	primitive	primitive	ADJ
ejpam-2648	200	14	ideal	ideal	NOUN
ejpam-2648	200	15	of	of	ADP
ejpam-2648	200	16	j.	j.	PROPN
ejpam-2648	200	17	if	if	SCONJ
ejpam-2648	200	18	d	d	PROPN
ejpam-2648	200	19	is	be	AUX
ejpam-2648	200	20	a	a	DET
ejpam-2648	200	21	linear	linear	ADJ
ejpam-2648	200	22	operator	operator	NOUN
ejpam-2648	200	23	defined	define	VERB
ejpam-2648	200	24	on	on	ADP
ejpam-2648	200	25	j	j	PROPN
ejpam-2648	200	26	such	such	ADJ
ejpam-2648	200	27	that	that	SCONJ
ejpam-2648	200	28	[	[	X
ejpam-2648	200	29	d	d	X
ejpam-2648	200	30	,	,	PUNCT
ejpam-2648	200	31	t	t	PROPN
ejpam-2648	200	32	]	]	PUNCT
ejpam-2648	200	33	is	be	AUX
ejpam-2648	200	34	continuous	continuous	ADJ
ejpam-2648	200	35	for	for	ADP
ejpam-2648	200	36	all	all	DET
ejpam-2648	200	37	t	t	NOUN
ejpam-2648	200	38	in	in	ADP
ejpam-2648	200	39	m	m	PROPN
ejpam-2648	200	40	(	(	PUNCT
ejpam-2648	200	41	j	j	PROPN
ejpam-2648	200	42	)	)	PUNCT
ejpam-2648	200	43	,	,	PUNCT
ejpam-2648	200	44	then	then	ADV
ejpam-2648	200	45	the	the	DET
ejpam-2648	200	46	primitive	primitive	ADJ
ejpam-2648	200	47	jordan	jordan	PROPN
ejpam-2648	200	48	algebra	algebra	PROPN
ejpam-2648	200	49	(	(	PUNCT
ejpam-2648	200	50	s	s	X
ejpam-2648	200	51	(	(	PUNCT
ejpam-2648	200	52	d	d	NOUN
ejpam-2648	200	53	)	)	PUNCT
ejpam-2648	200	54	+	+	CCONJ
ejpam-2648	200	55	i	i	NOUN
ejpam-2648	200	56	)	)	PUNCT
ejpam-2648	200	57	/i	/i	PUNCT
ejpam-2648	200	58	has	have	VERB
ejpam-2648	200	59	finite	finite	ADJ
ejpam-2648	200	60	capacity	capacity	NOUN
ejpam-2648	200	61	.	.	PUNCT
ejpam-2648	201	1	lemma	lemma	PROPN
ejpam-2648	201	2	4	4	X
ejpam-2648	201	3	.	.	PUNCT
ejpam-2648	202	1	let	let	VERB
ejpam-2648	202	2	v	v	ADP
ejpam-2648	202	3	a	a	DET
ejpam-2648	202	4	nondegenerate	nondegenerate	ADJ
ejpam-2648	202	5	jordan	jordan	PROPN
ejpam-2648	202	6	pair	pair	PROPN
ejpam-2648	202	7	and	and	CCONJ
ejpam-2648	202	8	let	let	VERB
ejpam-2648	202	9	p1	p1	PROPN
ejpam-2648	202	10	,	,	PUNCT
ejpam-2648	202	11	...	...	PUNCT
ejpam-2648	202	12	,	,	PUNCT
ejpam-2648	202	13	pn	pn	PROPN
ejpam-2648	202	14	be	be	AUX
ejpam-2648	202	15	nonzero	nonzero	ADJ
ejpam-2648	202	16	ideals	ideal	NOUN
ejpam-2648	202	17	of	of	ADP
ejpam-2648	202	18	v.	v.	ADV
ejpam-2648	202	19	if	if	SCONJ
ejpam-2648	202	20	h	h	NOUN
ejpam-2648	202	21	is	be	AUX
ejpam-2648	202	22	an	an	DET
ejpam-2648	202	23	ideal	ideal	NOUN
ejpam-2648	202	24	of	of	ADP
ejpam-2648	202	25	v	v	NOUN
ejpam-2648	202	26	such	such	ADJ
ejpam-2648	202	27	that	that	SCONJ
ejpam-2648	202	28	h	h	NOUN
ejpam-2648	202	29	∩	∩	ADJ
ejpam-2648	202	30	p1	p1	NOUN
ejpam-2648	202	31	∩	∩	NOUN
ejpam-2648	202	32	...	...	PUNCT
ejpam-2648	202	33	∩	∩	PROPN
ejpam-2648	202	34	pn	pn	NOUN
ejpam-2648	202	35	=	=	SYM
ejpam-2648	202	36	0	0	PUNCT
ejpam-2648	202	37	then	then	ADV
ejpam-2648	202	38	.	.	PUNCT
ejpam-2648	203	1	h	h	NOUN
ejpam-2648	204	1	=	=	NOUN
ejpam-2648	204	2	0	0	X
ejpam-2648	204	3	.	.	PUNCT
ejpam-2648	205	1	proof	proof	NOUN
ejpam-2648	205	2	.	.	PUNCT
ejpam-2648	206	1	we	we	PRON
ejpam-2648	206	2	proceed	proceed	VERB
ejpam-2648	206	3	by	by	ADP
ejpam-2648	206	4	induction	induction	NOUN
ejpam-2648	206	5	.	.	PUNCT
ejpam-2648	207	1	for	for	ADP
ejpam-2648	207	2	n	n	NOUN
ejpam-2648	207	3	=	=	SYM
ejpam-2648	207	4	1	1	NUM
ejpam-2648	207	5	,	,	PUNCT
ejpam-2648	207	6	by	by	ADP
ejpam-2648	207	7	idealness	idealness	NOUN
ejpam-2648	207	8	of	of	ADP
ejpam-2648	207	9	h	h	NOUN
ejpam-2648	207	10	and	and	CCONJ
ejpam-2648	207	11	p1	p1	PROPN
ejpam-2648	207	12	,	,	PUNCT
ejpam-2648	207	13	we	we	PRON
ejpam-2648	207	14	have	have	VERB
ejpam-2648	207	15	,	,	PUNCT
ejpam-2648	207	16	for	for	ADP
ejpam-2648	207	17	all	all	DET
ejpam-2648	207	18	u	u	NOUN
ejpam-2648	207	19	∈	∈	PROPN
ejpam-2648	207	20	p	p	PROPN
ejpam-2648	207	21	σ1	σ1	PROPN
ejpam-2648	207	22	,	,	PUNCT
ejpam-2648	207	23	quh−σ	quh−σ	VERB
ejpam-2648	207	24	⊆	⊆	NUM
ejpam-2648	207	25	hσ	hσ	NOUN
ejpam-2648	207	26	∩	∩	PROPN
ejpam-2648	207	27	p	p	PROPN
ejpam-2648	207	28	σ1	σ1	PROPN
ejpam-2648	207	29	=	=	SYM
ejpam-2648	208	1	0	0	X
ejpam-2648	208	2	.	.	PUNCT
ejpam-2648	209	1	then	then	ADV
ejpam-2648	209	2	,	,	PUNCT
ejpam-2648	209	3	by	by	ADP
ejpam-2648	209	4	[	[	PUNCT
ejpam-2648	209	5	18	18	NUM
ejpam-2648	209	6	,	,	PUNCT
ejpam-2648	209	7	proposition	proposition	NOUN
ejpam-2648	209	8	4.19	4.19	NUM
ejpam-2648	209	9	]	]	PUNCT
ejpam-2648	209	10	together	together	ADV
ejpam-2648	209	11	with	with	ADP
ejpam-2648	209	12	[	[	PUNCT
ejpam-2648	209	13	18	18	NUM
ejpam-2648	209	14	,	,	PUNCT
ejpam-2648	209	15	theorem	theorem	VERB
ejpam-2648	209	16	4.13	4.13	NUM
ejpam-2648	209	17	]	]	PUNCT
ejpam-2648	209	18	h−σ	h−σ	PRON
ejpam-2648	209	19	⊆	⊆	NUM
ejpam-2648	209	20	∩u∈pσ1	∩u∈pσ1	ADJ
ejpam-2648	209	21	ker(u	ker(u	PROPN
ejpam-2648	209	22	)	)	PUNCT
ejpam-2648	210	1	⊂	⊂	PROPN
ejpam-2648	211	1	rad(p	rad(p	PROPN
ejpam-2648	211	2	σ1	σ1	PROPN
ejpam-2648	211	3	)	)	PUNCT
ejpam-2648	212	1	=	=	PUNCT
ejpam-2648	212	2	rad(v	rad(v	PROPN
ejpam-2648	212	3	σ	σ	NOUN
ejpam-2648	212	4	)	)	PUNCT
ejpam-2648	212	5	∩	∩	PROPN
ejpam-2648	212	6	p	p	PROPN
ejpam-2648	212	7	σ1	σ1	PROPN
ejpam-2648	212	8	,	,	PUNCT
ejpam-2648	212	9	and	and	CCONJ
ejpam-2648	212	10	hence	hence	ADV
ejpam-2648	212	11	hσ	hσ	NOUN
ejpam-2648	213	1	=	=	NOUN
ejpam-2648	213	2	0	0	NUM
ejpam-2648	213	3	by	by	ADP
ejpam-2648	213	4	nondegeneracy	nondegeneracy	NOUN
ejpam-2648	213	5	of	of	ADP
ejpam-2648	213	6	v	v	NOUN
ejpam-2648	213	7	:	:	PUNCT
ejpam-2648	213	8	rad(v	rad(v	NOUN
ejpam-2648	213	9	)	)	PUNCT
ejpam-2648	213	10	=	=	SYM
ejpam-2648	213	11	0	0	X
ejpam-2648	213	12	.	.	PUNCT
ejpam-2648	214	1	suppose	suppose	VERB
ejpam-2648	214	2	the	the	DET
ejpam-2648	214	3	statement	statement	NOUN
ejpam-2648	214	4	is	be	AUX
ejpam-2648	214	5	true	true	ADJ
ejpam-2648	214	6	for	for	ADP
ejpam-2648	214	7	some	some	DET
ejpam-2648	214	8	natural	natural	ADJ
ejpam-2648	214	9	integer	integer	NOUN
ejpam-2648	214	10	n	n	NOUN
ejpam-2648	214	11	and	and	CCONJ
ejpam-2648	214	12	let	let	VERB
ejpam-2648	214	13	p1	p1	PROPN
ejpam-2648	214	14	,	,	PUNCT
ejpam-2648	214	15	...	...	PUNCT
ejpam-2648	214	16	,	,	PUNCT
ejpam-2648	214	17	pn	pn	PROPN
ejpam-2648	214	18	,	,	PUNCT
ejpam-2648	214	19	pn+1	pn+1	VERB
ejpam-2648	214	20	be	be	AUX
ejpam-2648	214	21	nonzero	nonzero	ADJ
ejpam-2648	214	22	ideals	ideal	NOUN
ejpam-2648	214	23	of	of	ADP
ejpam-2648	214	24	v	v	NOUN
ejpam-2648	214	25	satisfying	satisfy	VERB
ejpam-2648	214	26	the	the	DET
ejpam-2648	214	27	condition	condition	NOUN
ejpam-2648	214	28	stated	state	VERB
ejpam-2648	214	29	in	in	ADP
ejpam-2648	214	30	the	the	DET
ejpam-2648	214	31	lemma	lemma	PROPN
ejpam-2648	214	32	.	.	PUNCT
ejpam-2648	215	1	then	then	ADV
ejpam-2648	215	2	the	the	DET
ejpam-2648	215	3	ideals	ideal	NOUN
ejpam-2648	215	4	p1	p1	NOUN
ejpam-2648	215	5	and	and	CCONJ
ejpam-2648	215	6	k	k	NOUN
ejpam-2648	215	7	=	=	PROPN
ejpam-2648	215	8	p2∩	p2∩	ADJ
ejpam-2648	215	9	...	...	PUNCT
ejpam-2648	215	10	∩pn+1∩h	∩pn+1∩h	PUNCT
ejpam-2648	215	11	also	also	ADV
ejpam-2648	215	12	satisfy	satisfy	VERB
ejpam-2648	215	13	the	the	DET
ejpam-2648	215	14	same	same	ADJ
ejpam-2648	215	15	condition	condition	NOUN
ejpam-2648	215	16	.	.	PUNCT
ejpam-2648	216	1	therefore	therefore	ADV
ejpam-2648	216	2	,	,	PUNCT
ejpam-2648	216	3	by	by	ADP
ejpam-2648	216	4	we	we	PRON
ejpam-2648	216	5	have	have	AUX
ejpam-2648	216	6	just	just	ADV
ejpam-2648	216	7	proved	prove	VERB
ejpam-2648	216	8	in	in	ADP
ejpam-2648	216	9	the	the	DET
ejpam-2648	216	10	case	case	NOUN
ejpam-2648	216	11	n	n	NOUN
ejpam-2648	216	12	=	=	SYM
ejpam-2648	216	13	1	1	NUM
ejpam-2648	216	14	,	,	PUNCT
ejpam-2648	216	15	k	k	NOUN
ejpam-2648	216	16	=	=	PUNCT
ejpam-2648	216	17	0	0	PUNCT
ejpam-2648	216	18	and	and	CCONJ
ejpam-2648	216	19	hence	hence	ADV
ejpam-2648	216	20	h	h	NOUN
ejpam-2648	217	1	=	=	NOUN
ejpam-2648	217	2	0	0	NUM
ejpam-2648	217	3	by	by	ADP
ejpam-2648	217	4	induction	induction	NOUN
ejpam-2648	217	5	.	.	PUNCT
ejpam-2648	218	1	given	give	VERB
ejpam-2648	218	2	a	a	DET
ejpam-2648	218	3	banach	banach	NOUN
ejpam-2648	218	4	space	space	NOUN
ejpam-2648	218	5	x	x	NOUN
ejpam-2648	218	6	,	,	PUNCT
ejpam-2648	218	7	we	we	PRON
ejpam-2648	218	8	denote	denote	VERB
ejpam-2648	218	9	by	by	ADP
ejpam-2648	218	10	cl(e	cl(e	NOUN
ejpam-2648	218	11	)	)	PUNCT
ejpam-2648	218	12	the	the	DET
ejpam-2648	218	13	closure	closure	NOUN
ejpam-2648	218	14	of	of	ADP
ejpam-2648	218	15	a	a	DET
ejpam-2648	218	16	subset	subset	NOUN
ejpam-2648	218	17	e	e	NOUN
ejpam-2648	218	18	of	of	ADP
ejpam-2648	218	19	x.	x.	NOUN
ejpam-2648	218	20	we	we	PRON
ejpam-2648	218	21	can	can	AUX
ejpam-2648	218	22	now	now	ADV
ejpam-2648	218	23	state	state	VERB
ejpam-2648	218	24	our	our	PRON
ejpam-2648	218	25	main	main	ADJ
ejpam-2648	218	26	result	result	NOUN
ejpam-2648	218	27	in	in	ADP
ejpam-2648	218	28	this	this	DET
ejpam-2648	218	29	paper	paper	NOUN
ejpam-2648	218	30	.	.	PUNCT
ejpam-2648	219	1	theorem	theorem	NOUN
ejpam-2648	219	2	2	2	NUM
ejpam-2648	219	3	.	.	PUNCT
ejpam-2648	220	1	let	let	AUX
ejpam-2648	220	2	{	{	PUNCT
ejpam-2648	220	3	dn	dn	VERB
ejpam-2648	220	4	=	=	SYM
ejpam-2648	220	5	(	(	PUNCT
ejpam-2648	220	6	d+	d+	X
ejpam-2648	220	7	n	n	X
ejpam-2648	220	8	,	,	PUNCT
ejpam-2648	220	9	d	d	PROPN
ejpam-2648	220	10	−	−	PROPN
ejpam-2648	220	11	n	n	X
ejpam-2648	220	12	)	)	PUNCT
ejpam-2648	220	13	}	}	PUNCT
ejpam-2648	220	14	be	be	AUX
ejpam-2648	220	15	a	a	DET
ejpam-2648	220	16	higher	high	ADJ
ejpam-2648	220	17	derivation	derivation	NOUN
ejpam-2648	220	18	on	on	ADP
ejpam-2648	220	19	a	a	DET
ejpam-2648	220	20	banach	banach	NOUN
ejpam-2648	220	21	-	-	PUNCT
ejpam-2648	220	22	jordan	jordan	NOUN
ejpam-2648	220	23	pair	pair	PROPN
ejpam-2648	220	24	v	v	NOUN
ejpam-2648	220	25	=	=	PUNCT
ejpam-2648	220	26	(	(	PUNCT
ejpam-2648	220	27	v	v	ADP
ejpam-2648	220	28	+	+	NOUN
ejpam-2648	220	29	,	,	PUNCT
ejpam-2648	220	30	v	v	ADP
ejpam-2648	220	31	−	−	NOUN
ejpam-2648	220	32	)	)	PUNCT
ejpam-2648	220	33	.	.	PUNCT
ejpam-2648	221	1	if	if	SCONJ
ejpam-2648	221	2	v	v	NOUN
ejpam-2648	221	3	is	be	AUX
ejpam-2648	221	4	semiprimitive	semiprimitive	ADJ
ejpam-2648	221	5	,	,	PUNCT
ejpam-2648	221	6	then	then	ADV
ejpam-2648	221	7	dσ	dσ	PROPN
ejpam-2648	221	8	k	k	PROPN
ejpam-2648	221	9	is	be	AUX
ejpam-2648	221	10	continuous	continuous	ADJ
ejpam-2648	221	11	for	for	ADP
ejpam-2648	221	12	every	every	DET
ejpam-2648	221	13	non	non	ADJ
ejpam-2648	221	14	negative	negative	ADJ
ejpam-2648	221	15	integer	integer	PROPN
ejpam-2648	221	16	k.	k.	PROPN
ejpam-2648	221	17	h.	h.	PROPN
ejpam-2648	221	18	marhnine	marhnine	PROPN
ejpam-2648	221	19	,	,	PUNCT
ejpam-2648	221	20	c.	c.	PROPN
ejpam-2648	221	21	zarhouti	zarhouti	PROPN
ejpam-2648	221	22	/	/	SYM
ejpam-2648	221	23	eur	eur	PROPN
ejpam-2648	221	24	.	.	PUNCT
ejpam-2648	222	1	j.	j.	PROPN
ejpam-2648	222	2	pure	pure	PROPN
ejpam-2648	222	3	appl	appl	PROPN
ejpam-2648	222	4	.	.	PROPN
ejpam-2648	222	5	math	math	PROPN
ejpam-2648	222	6	,	,	PUNCT
ejpam-2648	222	7	10	10	NUM
ejpam-2648	222	8	(	(	PUNCT
ejpam-2648	222	9	4	4	NUM
ejpam-2648	222	10	)	)	PUNCT
ejpam-2648	222	11	(	(	PUNCT
ejpam-2648	222	12	2017	2017	NUM
ejpam-2648	222	13	)	)	PUNCT
ejpam-2648	222	14	,	,	PUNCT
ejpam-2648	222	15	749	749	NUM
ejpam-2648	222	16	-	-	SYM
ejpam-2648	222	17	762	762	NUM
ejpam-2648	222	18	757	757	NUM
ejpam-2648	222	19	proof	proof	NOUN
ejpam-2648	222	20	.	.	PUNCT
ejpam-2648	223	1	we	we	PRON
ejpam-2648	223	2	proceed	proceed	VERB
ejpam-2648	223	3	by	by	ADP
ejpam-2648	223	4	induction	induction	NOUN
ejpam-2648	223	5	.	.	PUNCT
ejpam-2648	224	1	for	for	ADP
ejpam-2648	224	2	if	if	SCONJ
ejpam-2648	224	3	n	n	NOUN
ejpam-2648	224	4	=	=	SYM
ejpam-2648	224	5	0	0	NUM
ejpam-2648	224	6	,	,	PUNCT
ejpam-2648	224	7	dσ	dσ	AUX
ejpam-2648	224	8	0	0	X
ejpam-2648	224	9	=	=	SYM
ejpam-2648	224	10	idv	idv	PROPN
ejpam-2648	224	11	σ	σ	PROPN
ejpam-2648	224	12	is	be	AUX
ejpam-2648	224	13	trivially	trivially	ADV
ejpam-2648	224	14	continuous	continuous	ADJ
ejpam-2648	224	15	.	.	PUNCT
ejpam-2648	225	1	suppose	suppose	VERB
ejpam-2648	225	2	that	that	SCONJ
ejpam-2648	225	3	d1	d1	PROPN
ejpam-2648	225	4	,	,	PUNCT
ejpam-2648	225	5	...	...	PUNCT
ejpam-2648	225	6	,	,	PUNCT
ejpam-2648	225	7	dk	dk	PROPN
ejpam-2648	225	8	are	be	AUX
ejpam-2648	225	9	continuous	continuous	ADJ
ejpam-2648	225	10	and	and	CCONJ
ejpam-2648	225	11	show	show	VERB
ejpam-2648	225	12	that	that	SCONJ
ejpam-2648	225	13	this	this	PRON
ejpam-2648	225	14	is	be	AUX
ejpam-2648	225	15	also	also	ADV
ejpam-2648	225	16	the	the	DET
ejpam-2648	225	17	case	case	NOUN
ejpam-2648	225	18	for	for	ADP
ejpam-2648	225	19	dk+1	dk+1	NOUN
ejpam-2648	225	20	,	,	PUNCT
ejpam-2648	225	21	that	that	PRON
ejpam-2648	225	22	is	be	AUX
ejpam-2648	225	23	s(dk+1	s(dk+1	NOUN
ejpam-2648	225	24	)	)	PUNCT
ejpam-2648	225	25	=	=	SYM
ejpam-2648	225	26	0	0	X
ejpam-2648	225	27	.	.	PUNCT
ejpam-2648	225	28	suppose	suppose	VERB
ejpam-2648	225	29	that	that	SCONJ
ejpam-2648	225	30	dk+1	dk+1	NOUN
ejpam-2648	225	31	is	be	AUX
ejpam-2648	225	32	discontinuous	discontinuous	ADJ
ejpam-2648	225	33	.	.	PUNCT
ejpam-2648	226	1	then	then	ADV
ejpam-2648	226	2	,	,	PUNCT
ejpam-2648	226	3	there	there	PRON
ejpam-2648	226	4	exists	exist	VERB
ejpam-2648	226	5	a	a	DET
ejpam-2648	226	6	primitive	primitive	ADJ
ejpam-2648	226	7	ideal	ideal	NOUN
ejpam-2648	226	8	p	p	NOUN
ejpam-2648	226	9	such	such	ADJ
ejpam-2648	226	10	that	that	SCONJ
ejpam-2648	226	11	s(dk+1	s(dk+1	NOUN
ejpam-2648	226	12	)	)	PUNCT
ejpam-2648	226	13	is	be	AUX
ejpam-2648	226	14	not	not	PART
ejpam-2648	226	15	contained	contain	VERB
ejpam-2648	226	16	in	in	ADP
ejpam-2648	226	17	p	p	PROPN
ejpam-2648	226	18	.	.	PUNCT
ejpam-2648	227	1	as	as	ADP
ejpam-2648	227	2	a	a	DET
ejpam-2648	227	3	first	first	ADJ
ejpam-2648	227	4	step	step	NOUN
ejpam-2648	227	5	we	we	PRON
ejpam-2648	227	6	show	show	VERB
ejpam-2648	227	7	that	that	SCONJ
ejpam-2648	227	8	all	all	DET
ejpam-2648	227	9	primitive	primitive	ADJ
ejpam-2648	227	10	ideals	ideal	NOUN
ejpam-2648	227	11	contain	contain	VERB
ejpam-2648	227	12	s(dk+1	s(dk+1	NOUN
ejpam-2648	227	13	)	)	PUNCT
ejpam-2648	227	14	except	except	SCONJ
ejpam-2648	227	15	finitely	finitely	ADV
ejpam-2648	227	16	primitive	primitive	ADJ
ejpam-2648	227	17	ideals	ideal	NOUN
ejpam-2648	227	18	p1	p1	NOUN
ejpam-2648	227	19	,	,	PUNCT
ejpam-2648	227	20	...	...	PUNCT
ejpam-2648	227	21	,	,	PUNCT
ejpam-2648	227	22	pn	pn	NOUN
ejpam-2648	227	23	for	for	ADP
ejpam-2648	227	24	which	which	PRON
ejpam-2648	227	25	the	the	DET
ejpam-2648	227	26	quotient	quotient	NOUN
ejpam-2648	227	27	pairs	pair	NOUN
ejpam-2648	227	28	v	v	NOUN
ejpam-2648	227	29	/	/	SYM
ejpam-2648	227	30	pi	pi	NOUN
ejpam-2648	227	31	have	have	VERB
ejpam-2648	227	32	finite	finite	ADJ
ejpam-2648	227	33	capacity	capacity	NOUN
ejpam-2648	227	34	.	.	PUNCT
ejpam-2648	228	1	in	in	ADP
ejpam-2648	228	2	other	other	ADJ
ejpam-2648	228	3	words	word	NOUN
ejpam-2648	228	4	de	de	AUX
ejpam-2648	228	5	set	set	VERB
ejpam-2648	228	6	γ	γ	X
ejpam-2648	228	7	=	=	SYM
ejpam-2648	228	8	{	{	PUNCT
ejpam-2648	228	9	p	p	X
ejpam-2648	228	10	=	=	X
ejpam-2648	228	11	(	(	PUNCT
ejpam-2648	228	12	p+	p+	NOUN
ejpam-2648	228	13	,	,	PUNCT
ejpam-2648	228	14	p−	p−	NOUN
ejpam-2648	228	15	)	)	PUNCT
ejpam-2648	228	16	primitive	primitive	ADJ
ejpam-2648	228	17	ideal	ideal	NOUN
ejpam-2648	228	18	of	of	ADP
ejpam-2648	228	19	v	v	NOUN
ejpam-2648	228	20	:	:	PUNCT
ejpam-2648	228	21	s(dk+1	s(dk+1	NOUN
ejpam-2648	228	22	)	)	PUNCT
ejpam-2648	228	23	*	*	PUNCT
ejpam-2648	229	1	p	p	NOUN
ejpam-2648	229	2	}	}	PUNCT
ejpam-2648	229	3	is	be	AUX
ejpam-2648	229	4	finite	finite	ADJ
ejpam-2648	229	5	and	and	CCONJ
ejpam-2648	229	6	,	,	PUNCT
ejpam-2648	229	7	for	for	ADP
ejpam-2648	229	8	any	any	DET
ejpam-2648	229	9	p	p	PROPN
ejpam-2648	229	10	∈	∈	PROPN
ejpam-2648	229	11	γ	γ	NOUN
ejpam-2648	229	12	,	,	PUNCT
ejpam-2648	229	13	the	the	DET
ejpam-2648	229	14	quotient	quotient	NOUN
ejpam-2648	229	15	pair	pair	NOUN
ejpam-2648	229	16	v	v	ADP
ejpam-2648	229	17	/	/	SYM
ejpam-2648	229	18	p	p	NOUN
ejpam-2648	229	19	has	have	VERB
ejpam-2648	229	20	finite	finite	ADJ
ejpam-2648	229	21	capacity	capacity	NOUN
ejpam-2648	229	22	.	.	PUNCT
ejpam-2648	230	1	take	take	VERB
ejpam-2648	230	2	p	p	NOUN
ejpam-2648	230	3	=	=	X
ejpam-2648	230	4	(	(	PUNCT
ejpam-2648	230	5	p+	p+	NOUN
ejpam-2648	230	6	,	,	PUNCT
ejpam-2648	230	7	p−	p−	PROPN
ejpam-2648	230	8	)	)	PUNCT
ejpam-2648	230	9	in	in	ADP
ejpam-2648	230	10	γ	γ	PROPN
ejpam-2648	230	11	and	and	CCONJ
ejpam-2648	230	12	b	b	PROPN
ejpam-2648	230	13	∈	∈	PROPN
ejpam-2648	230	14	v	v	ADP
ejpam-2648	230	15	−	−	PROPN
ejpam-2648	231	1	such	such	ADJ
ejpam-2648	231	2	that	that	DET
ejpam-2648	231	3	b	b	NOUN
ejpam-2648	231	4	/∈	/∈	PUNCT
ejpam-2648	231	5	p−.	p−.	PROPN
ejpam-2648	231	6	since	since	SCONJ
ejpam-2648	231	7	p	p	PROPN
ejpam-2648	231	8	σ	σ	PROPN
ejpam-2648	231	9	is	be	AUX
ejpam-2648	231	10	closed	close	VERB
ejpam-2648	231	11	in	in	ADP
ejpam-2648	231	12	v	v	NOUN
ejpam-2648	231	13	σ	σ	NOUN
ejpam-2648	231	14	(	(	PUNCT
ejpam-2648	231	15	see	see	VERB
ejpam-2648	231	16	[	[	X
ejpam-2648	231	17	14	14	NUM
ejpam-2648	231	18	,	,	PUNCT
ejpam-2648	231	19	a.5.2	a.5.2	PROPN
ejpam-2648	231	20	]	]	X
ejpam-2648	231	21	)	)	PUNCT
ejpam-2648	231	22	,	,	PUNCT
ejpam-2648	231	23	v	v	X
ejpam-2648	231	24	/	/	SYM
ejpam-2648	231	25	p	p	PRON
ejpam-2648	231	26	is	be	AUX
ejpam-2648	231	27	a	a	DET
ejpam-2648	231	28	banach	banach	NOUN
ejpam-2648	231	29	-	-	PUNCT
ejpam-2648	231	30	jordan	jordan	NOUN
ejpam-2648	231	31	pair	pair	NOUN
ejpam-2648	231	32	and	and	CCONJ
ejpam-2648	231	33	hence	hence	ADV
ejpam-2648	231	34	by	by	ADP
ejpam-2648	231	35	(	(	PUNCT
ejpam-2648	231	36	2.2	2.2	NUM
ejpam-2648	231	37	)	)	PUNCT
ejpam-2648	231	38	(	(	PUNCT
ejpam-2648	231	39	v	v	NOUN
ejpam-2648	231	40	/	/	SYM
ejpam-2648	231	41	p	p	NOUN
ejpam-2648	231	42	)	)	PUNCT
ejpam-2648	231	43	b	b	NOUN
ejpam-2648	231	44	is	be	AUX
ejpam-2648	231	45	a	a	DET
ejpam-2648	231	46	primitive	primitive	ADJ
ejpam-2648	231	47	banachjordan	banachjordan	NOUN
ejpam-2648	231	48	algebra	algebra	NOUN
ejpam-2648	231	49	where	where	SCONJ
ejpam-2648	231	50	b	b	NOUN
ejpam-2648	231	51	=	=	SYM
ejpam-2648	231	52	b+p−	b+p−	PROPN
ejpam-2648	231	53	is	be	AUX
ejpam-2648	231	54	the	the	DET
ejpam-2648	231	55	image	image	NOUN
ejpam-2648	231	56	of	of	ADP
ejpam-2648	231	57	b	b	NOUN
ejpam-2648	231	58	under	under	ADP
ejpam-2648	231	59	the	the	DET
ejpam-2648	231	60	canonical	canonical	ADJ
ejpam-2648	231	61	projection	projection	NOUN
ejpam-2648	231	62	v	v	ADP
ejpam-2648	231	63	−	−	PROPN
ejpam-2648	231	64	7−→	7−→	PROPN
ejpam-2648	231	65	v	v	ADP
ejpam-2648	231	66	−/p−.	−/p−.	NOUN
ejpam-2648	231	67	the	the	DET
ejpam-2648	231	68	algebra	algebra	NOUN
ejpam-2648	231	69	(	(	PUNCT
ejpam-2648	231	70	v	v	NOUN
ejpam-2648	231	71	/	/	SYM
ejpam-2648	231	72	p	p	NOUN
ejpam-2648	231	73	)	)	PUNCT
ejpam-2648	231	74	b	b	PROPN
ejpam-2648	231	75	is	be	AUX
ejpam-2648	231	76	known	know	VERB
ejpam-2648	231	77	to	to	PART
ejpam-2648	231	78	be	be	AUX
ejpam-2648	231	79	isomorphic	isomorphic	ADJ
ejpam-2648	231	80	to	to	ADP
ejpam-2648	231	81	v	v	ADP
ejpam-2648	231	82	+	+	NOUN
ejpam-2648	231	83	(	(	PUNCT
ejpam-2648	231	84	b)/i	b)/i	NOUN
ejpam-2648	231	85	where	where	SCONJ
ejpam-2648	231	86	i	i	PRON
ejpam-2648	231	87	=	=	SYM
ejpam-2648	232	1	q−1	q−1	PROPN
ejpam-2648	232	2	b	b	X
ejpam-2648	232	3	(	(	PUNCT
ejpam-2648	232	4	p−	p−	NOUN
ejpam-2648	232	5	)	)	PUNCT
ejpam-2648	232	6	is	be	AUX
ejpam-2648	232	7	so	so	ADV
ejpam-2648	232	8	a	a	DET
ejpam-2648	232	9	primitive	primitive	ADJ
ejpam-2648	232	10	ideal	ideal	NOUN
ejpam-2648	232	11	of	of	ADP
ejpam-2648	232	12	the	the	DET
ejpam-2648	232	13	banach	banach	NOUN
ejpam-2648	232	14	-	-	PUNCT
ejpam-2648	232	15	jordan	jordan	PROPN
ejpam-2648	232	16	algebra	algebra	PROPN
ejpam-2648	232	17	v	v	ADP
ejpam-2648	232	18	+	+	PROPN
ejpam-2648	232	19	(	(	PUNCT
ejpam-2648	232	20	b	b	NOUN
ejpam-2648	232	21	)	)	PUNCT
ejpam-2648	232	22	.	.	PUNCT
ejpam-2648	233	1	moreover	moreover	ADV
ejpam-2648	233	2	,	,	PUNCT
ejpam-2648	233	3	by	by	ADP
ejpam-2648	233	4	lemma	lemma	PROPN
ejpam-2648	233	5	2	2	NUM
ejpam-2648	233	6	the	the	DET
ejpam-2648	233	7	linear	linear	ADJ
ejpam-2648	233	8	operator	operator	NOUN
ejpam-2648	233	9	dk+1	dk+1	NOUN
ejpam-2648	233	10	and	and	CCONJ
ejpam-2648	233	11	the	the	DET
ejpam-2648	233	12	ideal	ideal	NOUN
ejpam-2648	233	13	i	i	PRON
ejpam-2648	233	14	satisfy	satisfy	VERB
ejpam-2648	233	15	the	the	DET
ejpam-2648	233	16	conditions	condition	NOUN
ejpam-2648	233	17	required	require	VERB
ejpam-2648	233	18	in	in	ADP
ejpam-2648	233	19	proposition	proposition	NOUN
ejpam-2648	233	20	1	1	NUM
ejpam-2648	233	21	with	with	ADP
ejpam-2648	233	22	respect	respect	NOUN
ejpam-2648	233	23	to	to	ADP
ejpam-2648	233	24	the	the	DET
ejpam-2648	233	25	banach	banach	NOUN
ejpam-2648	233	26	-	-	PUNCT
ejpam-2648	233	27	jordan	jordan	PROPN
ejpam-2648	233	28	algebra	algebra	PROPN
ejpam-2648	233	29	v	v	ADP
ejpam-2648	233	30	+	+	PROPN
ejpam-2648	233	31	(	(	PUNCT
ejpam-2648	233	32	b	b	NOUN
ejpam-2648	233	33	)	)	PUNCT
ejpam-2648	233	34	.	.	PUNCT
ejpam-2648	234	1	therefore	therefore	ADV
ejpam-2648	234	2	,	,	PUNCT
ejpam-2648	234	3	(	(	PUNCT
ejpam-2648	234	4	s(dk+1)+i)/i	s(dk+1)+i)/i	PROPN
ejpam-2648	234	5	has	have	VERB
ejpam-2648	234	6	nonzero	nonzero	PROPN
ejpam-2648	234	7	finite	finite	ADJ
ejpam-2648	234	8	capacity	capacity	NOUN
ejpam-2648	234	9	.	.	PUNCT
ejpam-2648	235	1	this	this	PRON
ejpam-2648	235	2	implies	imply	VERB
ejpam-2648	235	3	that	that	SCONJ
ejpam-2648	235	4	(	(	PUNCT
ejpam-2648	235	5	v	v	NOUN
ejpam-2648	235	6	/	/	SYM
ejpam-2648	235	7	p	p	NOUN
ejpam-2648	235	8	)	)	PUNCT
ejpam-2648	235	9	b	b	PROPN
ejpam-2648	235	10	has	have	VERB
ejpam-2648	235	11	itself	itself	PRON
ejpam-2648	235	12	nonzero	nonzero	ADJ
ejpam-2648	235	13	finite	finite	ADJ
ejpam-2648	235	14	capacity	capacity	NOUN
ejpam-2648	235	15	[	[	X
ejpam-2648	235	16	26	26	NUM
ejpam-2648	235	17	,	,	PUNCT
ejpam-2648	235	18	theorem	theorem	VERB
ejpam-2648	235	19	18	18	NUM
ejpam-2648	235	20	]	]	PUNCT
ejpam-2648	235	21	.	.	PUNCT
ejpam-2648	236	1	thus	thus	ADV
ejpam-2648	236	2	by	by	ADP
ejpam-2648	236	3	(	(	PUNCT
ejpam-2648	236	4	2.1	2.1	NUM
ejpam-2648	236	5	)	)	PUNCT
ejpam-2648	236	6	,	,	PUNCT
ejpam-2648	236	7	soc(v	soc(v	PROPN
ejpam-2648	236	8	/	/	SYM
ejpam-2648	236	9	p	p	NOUN
ejpam-2648	236	10	)	)	PUNCT
ejpam-2648	237	1	=	=	SYM
ejpam-2648	237	2	v	v	NOUN
ejpam-2648	237	3	/	/	SYM
ejpam-2648	237	4	p	p	NOUN
ejpam-2648	237	5	and	and	CCONJ
ejpam-2648	237	6	hence	hence	ADV
ejpam-2648	237	7	,	,	PUNCT
ejpam-2648	237	8	by	by	ADP
ejpam-2648	237	9	completeness	completeness	NOUN
ejpam-2648	237	10	,	,	PUNCT
ejpam-2648	237	11	v	v	NOUN
ejpam-2648	237	12	/	/	SYM
ejpam-2648	237	13	p	p	NOUN
ejpam-2648	237	14	has	have	VERB
ejpam-2648	237	15	nonzero	nonzero	PROPN
ejpam-2648	237	16	finite	finite	ADJ
ejpam-2648	237	17	capacity	capacity	NOUN
ejpam-2648	237	18	.	.	PUNCT
ejpam-2648	238	1	suppose	suppose	VERB
ejpam-2648	238	2	that	that	SCONJ
ejpam-2648	238	3	the	the	DET
ejpam-2648	238	4	set	set	NOUN
ejpam-2648	238	5	γ	γ	NOUN
ejpam-2648	238	6	is	be	AUX
ejpam-2648	238	7	infinite	infinite	ADJ
ejpam-2648	238	8	,	,	PUNCT
ejpam-2648	238	9	then	then	ADV
ejpam-2648	238	10	we	we	PRON
ejpam-2648	238	11	can	can	AUX
ejpam-2648	238	12	take	take	VERB
ejpam-2648	238	13	an	an	DET
ejpam-2648	238	14	infinite	infinite	ADJ
ejpam-2648	238	15	sequence	sequence	NOUN
ejpam-2648	238	16	{	{	PUNCT
ejpam-2648	238	17	pn	pn	NOUN
ejpam-2648	238	18	}	}	PUNCT
ejpam-2648	238	19	of	of	ADP
ejpam-2648	238	20	distinct	distinct	ADJ
ejpam-2648	238	21	primitive	primitive	ADJ
ejpam-2648	238	22	ideals	ideal	NOUN
ejpam-2648	238	23	in	in	ADP
ejpam-2648	238	24	γ	γ	PROPN
ejpam-2648	238	25	.	.	PUNCT
ejpam-2648	239	1	by	by	SCONJ
ejpam-2648	239	2	we	we	PRON
ejpam-2648	239	3	have	have	AUX
ejpam-2648	239	4	just	just	ADV
ejpam-2648	239	5	proved	prove	VERB
ejpam-2648	239	6	,	,	PUNCT
ejpam-2648	239	7	v	v	X
ejpam-2648	239	8	/	/	SYM
ejpam-2648	239	9	pn	pn	PROPN
ejpam-2648	239	10	is	be	AUX
ejpam-2648	239	11	simple	simple	ADJ
ejpam-2648	239	12	with	with	ADP
ejpam-2648	239	13	finite	finite	ADJ
ejpam-2648	239	14	capacity	capacity	NOUN
ejpam-2648	239	15	and	and	CCONJ
ejpam-2648	239	16	hence	hence	ADV
ejpam-2648	239	17	has	have	AUX
ejpam-2648	239	18	finite	finite	PROPN
ejpam-2648	239	19	spectrum	spectrum	NOUN
ejpam-2648	239	20	(	(	PUNCT
ejpam-2648	239	21	see	see	VERB
ejpam-2648	239	22	[	[	X
ejpam-2648	239	23	19	19	NUM
ejpam-2648	239	24	,	,	PUNCT
ejpam-2648	239	25	theorem	theorem	VERB
ejpam-2648	239	26	1	1	NUM
ejpam-2648	239	27	]	]	PUNCT
ejpam-2648	239	28	and	and	CCONJ
ejpam-2648	239	29	[	[	X
ejpam-2648	239	30	20	20	NUM
ejpam-2648	239	31	,	,	PUNCT
ejpam-2648	239	32	theorem	theorem	VERB
ejpam-2648	239	33	3.8	3.8	NUM
ejpam-2648	239	34	]	]	PUNCT
ejpam-2648	239	35	)	)	PUNCT
ejpam-2648	239	36	.	.	PUNCT
ejpam-2648	240	1	by	by	ADP
ejpam-2648	240	2	a	a	DET
ejpam-2648	240	3	similar	similar	ADJ
ejpam-2648	240	4	process	process	NOUN
ejpam-2648	240	5	used	use	VERB
ejpam-2648	240	6	in	in	ADP
ejpam-2648	240	7	[	[	X
ejpam-2648	240	8	6	6	NUM
ejpam-2648	240	9	,	,	PUNCT
ejpam-2648	240	10	lemma	lemma	PROPN
ejpam-2648	240	11	2.8	2.8	NUM
ejpam-2648	240	12	]	]	PUNCT
ejpam-2648	240	13	,	,	PUNCT
ejpam-2648	240	14	we	we	PRON
ejpam-2648	240	15	show	show	VERB
ejpam-2648	240	16	the	the	DET
ejpam-2648	240	17	existence	existence	NOUN
ejpam-2648	240	18	of	of	ADP
ejpam-2648	240	19	an	an	DET
ejpam-2648	240	20	element	element	NOUN
ejpam-2648	240	21	b	b	NOUN
ejpam-2648	240	22	in	in	ADP
ejpam-2648	240	23	v	v	NUM
ejpam-2648	240	24	−	−	NOUN
ejpam-2648	240	25	and	and	CCONJ
ejpam-2648	240	26	a	a	DET
ejpam-2648	240	27	sequence	sequence	NOUN
ejpam-2648	240	28	{	{	PUNCT
ejpam-2648	240	29	an	an	NOUN
ejpam-2648	240	30	}	}	PUNCT
ejpam-2648	240	31	in	in	ADP
ejpam-2648	240	32	v	v	NOUN
ejpam-2648	240	33	+	+	NOUN
ejpam-2648	240	34	such	such	ADJ
ejpam-2648	240	35	that	that	DET
ejpam-2648	240	36	b	b	NOUN
ejpam-2648	240	37	/∈	/∈	PUNCT
ejpam-2648	240	38	∪np−n	∪np−n	NOUN
ejpam-2648	240	39	,	,	PUNCT
ejpam-2648	240	40	πm(an	πm(an	PROPN
ejpam-2648	240	41	)	)	PUNCT
ejpam-2648	240	42	is	be	AUX
ejpam-2648	240	43	invertible	invertible	ADJ
ejpam-2648	240	44	in	in	ADP
ejpam-2648	240	45	(	(	PUNCT
ejpam-2648	240	46	v	v	NOUN
ejpam-2648	240	47	/	/	SYM
ejpam-2648	240	48	pm)b	pm)b	PROPN
ejpam-2648	240	49	for	for	ADP
ejpam-2648	240	50	n	n	NOUN
ejpam-2648	240	51	<	<	X
ejpam-2648	240	52	m	m	NOUN
ejpam-2648	240	53	and	and	CCONJ
ejpam-2648	240	54	πm(an	πm(an	ADJ
ejpam-2648	240	55	)	)	PUNCT
ejpam-2648	241	1	=	=	SYM
ejpam-2648	241	2	0	0	NUM
ejpam-2648	242	1	for	for	ADP
ejpam-2648	242	2	m	m	PROPN
ejpam-2648	242	3	<	<	X
ejpam-2648	242	4	n	n	X
ejpam-2648	242	5	where	where	SCONJ
ejpam-2648	242	6	πm	πm	ADP
ejpam-2648	242	7	:	:	PUNCT
ejpam-2648	242	8	v	v	ADP
ejpam-2648	242	9	+	+	X
ejpam-2648	242	10	7−→	7−→	NOUN
ejpam-2648	242	11	v	v	ADP
ejpam-2648	242	12	+	+	NOUN
ejpam-2648	242	13	/p+	/p+	X
ejpam-2648	242	14	m	m	VERB
ejpam-2648	242	15	is	be	AUX
ejpam-2648	242	16	the	the	DET
ejpam-2648	242	17	natural	natural	ADJ
ejpam-2648	242	18	projection	projection	NOUN
ejpam-2648	242	19	.	.	PUNCT
ejpam-2648	243	1	indeed	indeed	ADV
ejpam-2648	243	2	,	,	PUNCT
ejpam-2648	243	3	take	take	VERB
ejpam-2648	243	4	b1	b1	NOUN
ejpam-2648	243	5	in	in	ADP
ejpam-2648	243	6	v	v	NOUN
ejpam-2648	243	7	−	−	NOUN
ejpam-2648	243	8	such	such	ADJ
ejpam-2648	243	9	that	that	DET
ejpam-2648	243	10	b1	b1	NOUN
ejpam-2648	243	11	/∈	/∈	PUNCT
ejpam-2648	244	1	p−1	p−1	PROPN
ejpam-2648	244	2	.	.	PUNCT
ejpam-2648	245	1	by	by	ADP
ejpam-2648	245	2	induction	induction	NOUN
ejpam-2648	245	3	we	we	PRON
ejpam-2648	245	4	can	can	AUX
ejpam-2648	245	5	construct	construct	VERB
ejpam-2648	245	6	the	the	DET
ejpam-2648	245	7	sequences	sequence	NOUN
ejpam-2648	245	8	{	{	PUNCT
ejpam-2648	245	9	bn	bn	ADP
ejpam-2648	245	10	}	}	PUNCT
ejpam-2648	245	11	in	in	ADP
ejpam-2648	245	12	v	v	NOUN
ejpam-2648	245	13	−	−	PROPN
ejpam-2648	245	14	and	and	CCONJ
ejpam-2648	245	15	{	{	PUNCT
ejpam-2648	245	16	λn	λn	NOUN
ejpam-2648	245	17	}	}	PUNCT
ejpam-2648	245	18	in	in	ADP
ejpam-2648	245	19	the	the	DET
ejpam-2648	245	20	complex	complex	ADJ
ejpam-2648	245	21	field	field	NOUN
ejpam-2648	245	22	such	such	ADJ
ejpam-2648	245	23	that	that	DET
ejpam-2648	245	24	λ1	λ1	PROPN
ejpam-2648	245	25	=	=	SYM
ejpam-2648	245	26	1	1	X
ejpam-2648	245	27	.	.	PUNCT
ejpam-2648	246	1	having	having	AUX
ejpam-2648	246	2	defined	define	VERB
ejpam-2648	246	3	b1	b1	NOUN
ejpam-2648	246	4	,	,	PUNCT
ejpam-2648	246	5	...	...	PUNCT
ejpam-2648	246	6	,	,	PUNCT
ejpam-2648	246	7	bn−1	bn−1	PROPN
ejpam-2648	246	8	and	and	CCONJ
ejpam-2648	246	9	λ1	λ1	ADJ
ejpam-2648	246	10	,	,	PUNCT
ejpam-2648	246	11	...	...	PUNCT
ejpam-2648	246	12	,	,	PUNCT
ejpam-2648	246	13	λn−1	λn−1	PROPN
ejpam-2648	246	14	,	,	PUNCT
ejpam-2648	246	15	we	we	PRON
ejpam-2648	246	16	take	take	VERB
ejpam-2648	246	17	bn	bn	INTJ
ejpam-2648	246	18	in	in	ADP
ejpam-2648	246	19	n−1	n−1	PROPN
ejpam-2648	246	20	∩	∩	NOUN
ejpam-2648	246	21	i=1	i=1	ADP
ejpam-2648	246	22	p−i	p−i	PROPN
ejpam-2648	246	23	with	with	ADP
ejpam-2648	246	24	‖bn‖	‖bn‖	NOUN
ejpam-2648	246	25	=	=	SYM
ejpam-2648	246	26	1	1	NUM
ejpam-2648	246	27	,	,	PUNCT
ejpam-2648	246	28	1	1	NUM
ejpam-2648	246	29	<	<	X
ejpam-2648	246	30	λn	λn	X
ejpam-2648	246	31	<	<	X
ejpam-2648	246	32	1	1	NUM
ejpam-2648	246	33	2n	2n	NUM
ejpam-2648	246	34	and	and	CCONJ
ejpam-2648	246	35	n∑	n∑	PROPN
ejpam-2648	246	36	i=1	i=1	PROPN
ejpam-2648	246	37	λibi	λibi	NOUN
ejpam-2648	246	38	/∈	/∈	PUNCT
ejpam-2648	247	1	p−n	p−n	NOUN
ejpam-2648	247	2	.	.	PUNCT
ejpam-2648	248	1	this	this	DET
ejpam-2648	248	2	last	last	ADJ
ejpam-2648	248	3	condition	condition	NOUN
ejpam-2648	248	4	is	be	AUX
ejpam-2648	248	5	satisfied	satisfied	ADJ
ejpam-2648	248	6	since	since	SCONJ
ejpam-2648	248	7	n−1	n−1	PROPN
ejpam-2648	248	8	∩	∩	NOUN
ejpam-2648	248	9	i=1	i=1	PRON
ejpam-2648	248	10	pi	pi	NOUN
ejpam-2648	248	11	is	be	AUX
ejpam-2648	248	12	not	not	PART
ejpam-2648	248	13	contained	contain	VERB
ejpam-2648	248	14	in	in	ADP
ejpam-2648	248	15	pn	pn	PROPN
ejpam-2648	248	16	.	.	PUNCT
ejpam-2648	249	1	since	since	SCONJ
ejpam-2648	249	2	the	the	DET
ejpam-2648	249	3	series	series	PROPN
ejpam-2648	249	4	n∑	n∑	PROPN
ejpam-2648	249	5	i=1	i=1	PROPN
ejpam-2648	249	6	λibi	λibi	NOUN
ejpam-2648	249	7	,	,	PUNCT
ejpam-2648	249	8	converges	converge	VERB
ejpam-2648	249	9	in	in	ADP
ejpam-2648	249	10	v	v	NOUN
ejpam-2648	249	11	−	−	NOUN
ejpam-2648	249	12	,	,	PUNCT
ejpam-2648	249	13	we	we	PRON
ejpam-2648	249	14	write	write	VERB
ejpam-2648	249	15	b	b	NOUN
ejpam-2648	250	1	=	=	SYM
ejpam-2648	250	2	∞∑	∞∑	NUM
ejpam-2648	250	3	i=1	i=1	PROPN
ejpam-2648	250	4	λibi	λibi	NOUN
ejpam-2648	250	5	.	.	PUNCT
ejpam-2648	251	1	we	we	PRON
ejpam-2648	251	2	see	see	VERB
ejpam-2648	251	3	that	that	DET
ejpam-2648	251	4	b	b	PROPN
ejpam-2648	251	5	=	=	SYM
ejpam-2648	251	6	n∑	n∑	NOUN
ejpam-2648	251	7	i=1	i=1	PROPN
ejpam-2648	251	8	λibi	λibi	NOUN
ejpam-2648	251	9	is	be	AUX
ejpam-2648	251	10	nonzero	nonzero	NOUN
ejpam-2648	251	11	in	in	ADP
ejpam-2648	251	12	v	v	NUM
ejpam-2648	251	13	−/p−n	−/p−n	NOUN
ejpam-2648	251	14	and	and	CCONJ
ejpam-2648	251	15	hence	hence	ADV
ejpam-2648	251	16	b	b	X
ejpam-2648	251	17	/∈	/∈	PUNCT
ejpam-2648	251	18	∪np−n	∪np−n	PROPN
ejpam-2648	251	19	.	.	PUNCT
ejpam-2648	252	1	now	now	ADV
ejpam-2648	252	2	take	take	VERB
ejpam-2648	252	3	u1	u1	NOUN
ejpam-2648	252	4	in	in	ADP
ejpam-2648	252	5	v	v	NOUN
ejpam-2648	252	6	+	+	ADP
ejpam-2648	252	7	such	such	ADJ
ejpam-2648	252	8	that	that	DET
ejpam-2648	252	9	u1	u1	NOUN
ejpam-2648	252	10	/∈	/∈	PUNCT
ejpam-2648	252	11	p+	p+	PROPN
ejpam-2648	252	12	1	1	NUM
ejpam-2648	252	13	.	.	PUNCT
ejpam-2648	253	1	we	we	PRON
ejpam-2648	253	2	proceed	proceed	VERB
ejpam-2648	253	3	by	by	ADP
ejpam-2648	253	4	choosing	choose	VERB
ejpam-2648	253	5	{	{	PUNCT
ejpam-2648	253	6	un	un	PROPN
ejpam-2648	253	7	}	}	PUNCT
ejpam-2648	253	8	in	in	ADP
ejpam-2648	253	9	v	v	NOUN
ejpam-2648	253	10	+	+	CCONJ
ejpam-2648	253	11	and	and	CCONJ
ejpam-2648	253	12	,	,	PUNCT
ejpam-2648	253	13	for	for	ADP
ejpam-2648	253	14	any	any	DET
ejpam-2648	253	15	natural	natural	ADJ
ejpam-2648	253	16	number	number	NOUN
ejpam-2648	253	17	k	k	NOUN
ejpam-2648	253	18	,	,	PUNCT
ejpam-2648	253	19	the	the	DET
ejpam-2648	253	20	scalars	scalar	NOUN
ejpam-2648	253	21	{	{	PUNCT
ejpam-2648	253	22	λkn	λkn	X
ejpam-2648	253	23	}	}	PUNCT
ejpam-2648	253	24	∞	∞	PROPN
ejpam-2648	253	25	n	n	CCONJ
ejpam-2648	253	26	=	=	SYM
ejpam-2648	253	27	k	k	X
ejpam-2648	253	28	such	such	ADJ
ejpam-2648	253	29	that	that	DET
ejpam-2648	253	30	λkk	λkk	NOUN
ejpam-2648	253	31	=	=	NOUN
ejpam-2648	253	32	1	1	X
ejpam-2648	253	33	.	.	PUNCT
ejpam-2648	253	34	having	having	AUX
ejpam-2648	253	35	selected	select	VERB
ejpam-2648	253	36	them	they	PRON
ejpam-2648	253	37	up	up	ADP
ejpam-2648	253	38	to	to	ADP
ejpam-2648	253	39	n	n	NOUN
ejpam-2648	253	40	−	−	PROPN
ejpam-2648	253	41	1	1	NUM
ejpam-2648	253	42	,	,	PUNCT
ejpam-2648	253	43	we	we	PRON
ejpam-2648	253	44	take	take	VERB
ejpam-2648	253	45	un	un	PROPN
ejpam-2648	253	46	and	and	CCONJ
ejpam-2648	253	47	λkn	λkn	ADP
ejpam-2648	253	48	such	such	ADJ
ejpam-2648	253	49	that	that	DET
ejpam-2648	253	50	un	un	PROPN
ejpam-2648	253	51	∈	∈	PROPN
ejpam-2648	253	52	n−1	n−1	PROPN
ejpam-2648	253	53	∩	∩	NOUN
ejpam-2648	254	1	i=1	i=1	PROPN
ejpam-2648	254	2	p+	p+	VERB
ejpam-2648	254	3	i	i	PRON
ejpam-2648	254	4	,	,	PUNCT
ejpam-2648	254	5	πn(un	πn(un	PROPN
ejpam-2648	254	6	)	)	PUNCT
ejpam-2648	254	7	is	be	AUX
ejpam-2648	254	8	the	the	DET
ejpam-2648	254	9	unit	unit	NOUN
ejpam-2648	254	10	of	of	ADP
ejpam-2648	254	11	the	the	DET
ejpam-2648	254	12	banach	banach	NOUN
ejpam-2648	254	13	-	-	PUNCT
ejpam-2648	254	14	jordan	jordan	PROPN
ejpam-2648	254	15	algebra	algebra	PROPN
ejpam-2648	254	16	(	(	PUNCT
ejpam-2648	254	17	v	v	NOUN
ejpam-2648	254	18	/	/	SYM
ejpam-2648	254	19	pm)b	pm)b	PROPN
ejpam-2648	254	20	,	,	PUNCT
ejpam-2648	254	21	0	0	PUNCT
ejpam-2648	254	22	<	<	X
ejpam-2648	254	23	λkn	λkn	X
ejpam-2648	254	24	<	<	X
ejpam-2648	254	25	1	1	NUM
ejpam-2648	254	26	2n‖un‖	2n‖un‖	NUM
ejpam-2648	254	27	and	and	CCONJ
ejpam-2648	254	28	πn	πn	INTJ
ejpam-2648	254	29	(	(	PUNCT
ejpam-2648	254	30	n∑	n∑	NOUN
ejpam-2648	254	31	i	i	PROPN
ejpam-2648	254	32	=	=	PROPN
ejpam-2648	254	33	k	k	PROPN
ejpam-2648	254	34	λki	λki	PROPN
ejpam-2648	254	35	ui	ui	PROPN
ejpam-2648	254	36	)	)	PUNCT
ejpam-2648	254	37	is	be	AUX
ejpam-2648	254	38	invertible	invertible	ADJ
ejpam-2648	254	39	.	.	PUNCT
ejpam-2648	255	1	if	if	SCONJ
ejpam-2648	255	2	we	we	PRON
ejpam-2648	255	3	take	take	VERB
ejpam-2648	255	4	an	an	DET
ejpam-2648	255	5	=	=	SYM
ejpam-2648	255	6	∞∑	∞∑	PROPN
ejpam-2648	255	7	i	i	NOUN
ejpam-2648	255	8	=	=	PROPN
ejpam-2648	255	9	n	n	NUM
ejpam-2648	255	10	λni	λni	PROPN
ejpam-2648	255	11	ui	ui	PROPN
ejpam-2648	255	12	,	,	PUNCT
ejpam-2648	255	13	then	then	ADV
ejpam-2648	255	14	we	we	PRON
ejpam-2648	255	15	will	will	AUX
ejpam-2648	255	16	have	have	AUX
ejpam-2648	255	17	πm(an	πm(an	NOUN
ejpam-2648	255	18	)	)	PUNCT
ejpam-2648	255	19	is	be	AUX
ejpam-2648	255	20	invertible	invertible	ADJ
ejpam-2648	255	21	in	in	ADP
ejpam-2648	255	22	(	(	PUNCT
ejpam-2648	255	23	v	v	NOUN
ejpam-2648	255	24	/	/	SYM
ejpam-2648	255	25	pm)b	pm)b	PROPN
ejpam-2648	255	26	for	for	ADP
ejpam-2648	255	27	m	m	PROPN
ejpam-2648	255	28	>	>	X
ejpam-2648	255	29	n	n	PROPN
ejpam-2648	255	30	and	and	CCONJ
ejpam-2648	255	31	πm(an	πm(an	ADJ
ejpam-2648	255	32	)	)	PUNCT
ejpam-2648	256	1	=	=	SYM
ejpam-2648	256	2	0	0	NUM
ejpam-2648	257	1	for	for	SCONJ
ejpam-2648	257	2	m	m	PROPN
ejpam-2648	257	3	<	<	X
ejpam-2648	257	4	n	n	PRON
ejpam-2648	257	5	as	as	SCONJ
ejpam-2648	257	6	required	require	VERB
ejpam-2648	257	7	.	.	PUNCT
ejpam-2648	258	1	now	now	ADV
ejpam-2648	258	2	consider	consider	VERB
ejpam-2648	258	3	an	an	DET
ejpam-2648	258	4	arbitrary	arbitrary	ADJ
ejpam-2648	258	5	x	x	NOUN
ejpam-2648	258	6	in	in	ADP
ejpam-2648	258	7	v	v	NOUN
ejpam-2648	258	8	+	+	CCONJ
ejpam-2648	258	9	and	and	CCONJ
ejpam-2648	258	10	positive	positive	ADJ
ejpam-2648	258	11	integers	integer	NOUN
ejpam-2648	258	12	m	m	VERB
ejpam-2648	258	13	,	,	PUNCT
ejpam-2648	258	14	n.	n.	NOUN
ejpam-2648	258	15	we	we	PRON
ejpam-2648	258	16	compute	compute	VERB
ejpam-2648	258	17	in	in	ADP
ejpam-2648	258	18	(	(	PUNCT
ejpam-2648	258	19	v	v	NOUN
ejpam-2648	258	20	/	/	SYM
ejpam-2648	258	21	pn)b	pn)b	PROPN
ejpam-2648	258	22	h.	h.	PROPN
ejpam-2648	258	23	marhnine	marhnine	PROPN
ejpam-2648	258	24	,	,	PUNCT
ejpam-2648	258	25	c.	c.	PROPN
ejpam-2648	258	26	zarhouti	zarhouti	PROPN
ejpam-2648	258	27	/	/	SYM
ejpam-2648	258	28	eur	eur	PROPN
ejpam-2648	258	29	.	.	PUNCT
ejpam-2648	259	1	j.	j.	PROPN
ejpam-2648	259	2	pure	pure	PROPN
ejpam-2648	259	3	appl	appl	PROPN
ejpam-2648	259	4	.	.	PROPN
ejpam-2648	259	5	math	math	PROPN
ejpam-2648	259	6	,	,	PUNCT
ejpam-2648	259	7	10	10	NUM
ejpam-2648	259	8	(	(	PUNCT
ejpam-2648	259	9	4	4	NUM
ejpam-2648	259	10	)	)	PUNCT
ejpam-2648	259	11	(	(	PUNCT
ejpam-2648	259	12	2017	2017	NUM
ejpam-2648	259	13	)	)	PUNCT
ejpam-2648	259	14	,	,	PUNCT
ejpam-2648	259	15	749	749	NUM
ejpam-2648	259	16	-	-	SYM
ejpam-2648	259	17	762	762	NUM
ejpam-2648	259	18	758	758	NUM
ejpam-2648	259	19	to	to	PART
ejpam-2648	259	20	have	have	VERB
ejpam-2648	259	21	πndk+1u	πndk+1u	NUM
ejpam-2648	259	22	(	(	PUNCT
ejpam-2648	259	23	b	b	X
ejpam-2648	259	24	)	)	PUNCT
ejpam-2648	259	25	a1	a1	NOUN
ejpam-2648	259	26	u	u	NOUN
ejpam-2648	259	27	(	(	PUNCT
ejpam-2648	259	28	b	b	NOUN
ejpam-2648	259	29	)	)	PUNCT
ejpam-2648	259	30	a2	a2	PROPN
ejpam-2648	259	31	...	...	PUNCT
ejpam-2648	260	1	u	u	NOUN
ejpam-2648	260	2	(	(	PUNCT
ejpam-2648	260	3	b	b	NOUN
ejpam-2648	260	4	)	)	PUNCT
ejpam-2648	260	5	am(x	am(x	PUNCT
ejpam-2648	260	6	)	)	PUNCT
ejpam-2648	260	7	=	=	SYM
ejpam-2648	260	8	1	1	NUM
ejpam-2648	260	9	4	4	NUM
ejpam-2648	260	10	πndk+1	πndk+1	NOUN
ejpam-2648	260	11	{	{	PUNCT
ejpam-2648	260	12	a1	a1	NOUN
ejpam-2648	260	13	,	,	PUNCT
ejpam-2648	260	14	{	{	PUNCT
ejpam-2648	260	15	b	b	X
ejpam-2648	260	16	,	,	PUNCT
ejpam-2648	260	17	u	u	NOUN
ejpam-2648	260	18	(	(	PUNCT
ejpam-2648	260	19	b	b	NOUN
ejpam-2648	260	20	)	)	PUNCT
ejpam-2648	260	21	a2	a2	PROPN
ejpam-2648	260	22	...	...	PUNCT
ejpam-2648	260	23	u	u	NOUN
ejpam-2648	260	24	(	(	PUNCT
ejpam-2648	260	25	b	b	NOUN
ejpam-2648	260	26	)	)	PUNCT
ejpam-2648	260	27	am(x	am(x	NOUN
ejpam-2648	260	28	)	)	PUNCT
ejpam-2648	260	29	,	,	PUNCT
ejpam-2648	260	30	b	b	X
ejpam-2648	260	31	}	}	PUNCT
ejpam-2648	260	32	,	,	PUNCT
ejpam-2648	260	33	a1	a1	NOUN
ejpam-2648	260	34	}	}	PUNCT
ejpam-2648	260	35	=	=	SYM
ejpam-2648	260	36	1	1	NUM
ejpam-2648	260	37	4	4	NUM
ejpam-2648	260	38	πn	πn	INTJ
ejpam-2648	260	39	∑	∑	PUNCT
ejpam-2648	260	40	i+j+h	i+j+h	ADJ
ejpam-2648	260	41	=	=	PRON
ejpam-2648	260	42	k+1	k+1	X
ejpam-2648	260	43	{	{	PUNCT
ejpam-2648	260	44	dia1	dia1	PROPN
ejpam-2648	260	45	,	,	PUNCT
ejpam-2648	260	46	dj	dj	X
ejpam-2648	260	47	{	{	PUNCT
ejpam-2648	260	48	b	b	NOUN
ejpam-2648	260	49	,	,	PUNCT
ejpam-2648	260	50	u	u	NOUN
ejpam-2648	260	51	(	(	PUNCT
ejpam-2648	260	52	b	b	NOUN
ejpam-2648	260	53	)	)	PUNCT
ejpam-2648	260	54	a2	a2	PROPN
ejpam-2648	260	55	...	...	PUNCT
ejpam-2648	260	56	u	u	NOUN
ejpam-2648	260	57	(	(	PUNCT
ejpam-2648	260	58	b	b	NOUN
ejpam-2648	260	59	)	)	PUNCT
ejpam-2648	260	60	am(x	am(x	NOUN
ejpam-2648	260	61	)	)	PUNCT
ejpam-2648	260	62	,	,	PUNCT
ejpam-2648	260	63	b	b	X
ejpam-2648	260	64	}	}	PUNCT
ejpam-2648	260	65	,	,	PUNCT
ejpam-2648	260	66	dha1	dha1	NOUN
ejpam-2648	260	67	}	}	PUNCT
ejpam-2648	260	68	=	=	SYM
ejpam-2648	260	69	1	1	NUM
ejpam-2648	260	70	4	4	NUM
ejpam-2648	260	71	πn	πn	INTJ
ejpam-2648	260	72	∑	∑	PUNCT
ejpam-2648	260	73	i+j+h	i+j+h	ADJ
ejpam-2648	260	74	=	=	PRON
ejpam-2648	260	75	k+1	k+1	X
ejpam-2648	260	76	j≤k	j≤k	X
ejpam-2648	260	77	{	{	PUNCT
ejpam-2648	260	78	dia1	dia1	PROPN
ejpam-2648	260	79	,	,	PUNCT
ejpam-2648	260	80	dj	dj	X
ejpam-2648	260	81	{	{	PUNCT
ejpam-2648	260	82	b	b	NOUN
ejpam-2648	260	83	,	,	PUNCT
ejpam-2648	260	84	u	u	NOUN
ejpam-2648	260	85	(	(	PUNCT
ejpam-2648	260	86	b	b	NOUN
ejpam-2648	260	87	)	)	PUNCT
ejpam-2648	260	88	a2	a2	PROPN
ejpam-2648	260	89	...	...	PUNCT
ejpam-2648	261	1	u	u	NOUN
ejpam-2648	261	2	(	(	PUNCT
ejpam-2648	261	3	b	b	NOUN
ejpam-2648	261	4	)	)	PUNCT
ejpam-2648	261	5	amx	amx	PROPN
ejpam-2648	261	6	,	,	PUNCT
ejpam-2648	261	7	b	b	NOUN
ejpam-2648	261	8	}	}	PUNCT
ejpam-2648	261	9	,	,	PUNCT
ejpam-2648	261	10	dha1	dha1	NOUN
ejpam-2648	261	11	}	}	PUNCT
ejpam-2648	261	12	+	+	CCONJ
ejpam-2648	261	13	1	1	NUM
ejpam-2648	261	14	4	4	NUM
ejpam-2648	261	15	πn	πn	INTJ
ejpam-2648	261	16	{	{	PUNCT
ejpam-2648	261	17	a1	a1	PROPN
ejpam-2648	261	18	,	,	PUNCT
ejpam-2648	261	19	dk+1	dk+1	X
ejpam-2648	261	20	{	{	PUNCT
ejpam-2648	261	21	b	b	NOUN
ejpam-2648	261	22	,	,	PUNCT
ejpam-2648	261	23	u	u	NOUN
ejpam-2648	261	24	(	(	PUNCT
ejpam-2648	261	25	b	b	NOUN
ejpam-2648	261	26	)	)	PUNCT
ejpam-2648	261	27	a2	a2	PROPN
ejpam-2648	261	28	...	...	PUNCT
ejpam-2648	261	29	u	u	NOUN
ejpam-2648	261	30	(	(	PUNCT
ejpam-2648	261	31	b	b	NOUN
ejpam-2648	261	32	)	)	PUNCT
ejpam-2648	261	33	amx	amx	PROPN
ejpam-2648	261	34	,	,	PUNCT
ejpam-2648	261	35	b	b	NOUN
ejpam-2648	261	36	}	}	PUNCT
ejpam-2648	261	37	,	,	PUNCT
ejpam-2648	261	38	a1	a1	NOUN
ejpam-2648	261	39	}	}	PUNCT
ejpam-2648	261	40	=	=	SYM
ejpam-2648	261	41	ϕ(x	ϕ(x	NOUN
ejpam-2648	261	42	)	)	PUNCT
ejpam-2648	262	1	+	+	CCONJ
ejpam-2648	262	2	1	1	NUM
ejpam-2648	262	3	2	2	NUM
ejpam-2648	262	4	πnqa1	πnqa1	NOUN
ejpam-2648	262	5	(	(	PUNCT
ejpam-2648	262	6	∑	∑	ADV
ejpam-2648	262	7	i+j+h	i+j+h	ADJ
ejpam-2648	262	8	=	=	PRON
ejpam-2648	262	9	k+1	k+1	X
ejpam-2648	262	10	{	{	PUNCT
ejpam-2648	262	11	dib	dib	PROPN
ejpam-2648	262	12	,	,	PUNCT
ejpam-2648	262	13	dju	dju	PROPN
ejpam-2648	262	14	(	(	PUNCT
ejpam-2648	262	15	b	b	NOUN
ejpam-2648	262	16	)	)	PUNCT
ejpam-2648	262	17	a2	a2	PROPN
ejpam-2648	262	18	...	...	PUNCT
ejpam-2648	262	19	u	u	NOUN
ejpam-2648	262	20	(	(	PUNCT
ejpam-2648	262	21	b	b	NOUN
ejpam-2648	262	22	)	)	PUNCT
ejpam-2648	262	23	amx	amx	PROPN
ejpam-2648	262	24	,	,	PUNCT
ejpam-2648	262	25	dhb	dhb	NOUN
ejpam-2648	262	26	}	}	PUNCT
ejpam-2648	262	27	)	)	PUNCT
ejpam-2648	263	1	=	=	SYM
ejpam-2648	263	2	ϕ(x	ϕ(x	X
ejpam-2648	263	3	)	)	PUNCT
ejpam-2648	264	1	+	+	CCONJ
ejpam-2648	264	2	1	1	NUM
ejpam-2648	264	3	2	2	NUM
ejpam-2648	264	4	πnqa1	πnqa1	NOUN
ejpam-2648	264	5	(	(	PUNCT
ejpam-2648	264	6	∑	∑	ADV
ejpam-2648	264	7	i+j+h	i+j+h	ADJ
ejpam-2648	264	8	=	=	PRON
ejpam-2648	264	9	k+1	k+1	X
ejpam-2648	264	10	j≤k	j≤k	X
ejpam-2648	264	11	{	{	PUNCT
ejpam-2648	264	12	dib	dib	PROPN
ejpam-2648	264	13	,	,	PUNCT
ejpam-2648	264	14	dju	dju	PROPN
ejpam-2648	264	15	(	(	PUNCT
ejpam-2648	264	16	b	b	NOUN
ejpam-2648	264	17	)	)	PUNCT
ejpam-2648	264	18	a2	a2	PROPN
ejpam-2648	264	19	...	...	PUNCT
ejpam-2648	264	20	u	u	NOUN
ejpam-2648	264	21	(	(	PUNCT
ejpam-2648	264	22	b	b	NOUN
ejpam-2648	264	23	)	)	PUNCT
ejpam-2648	264	24	amx	amx	PROPN
ejpam-2648	264	25	,	,	PUNCT
ejpam-2648	264	26	dhb	dhb	PROPN
ejpam-2648	264	27	}	}	PUNCT
ejpam-2648	264	28	)	)	PUNCT
ejpam-2648	265	1	+	+	ADJ
ejpam-2648	265	2	πnqa1qbdk+1u	πnqa1qbdk+1u	NOUN
ejpam-2648	265	3	(	(	PUNCT
ejpam-2648	265	4	b	b	NOUN
ejpam-2648	265	5	)	)	PUNCT
ejpam-2648	265	6	a2	a2	PROPN
ejpam-2648	265	7	...	...	PUNCT
ejpam-2648	265	8	u	u	NOUN
ejpam-2648	265	9	(	(	PUNCT
ejpam-2648	265	10	b	b	NOUN
ejpam-2648	265	11	)	)	PUNCT
ejpam-2648	265	12	amx	amx	NOUN
ejpam-2648	265	13	=	=	SYM
ejpam-2648	265	14	ψ1(x	ψ1(x	PROPN
ejpam-2648	265	15	)	)	PUNCT
ejpam-2648	265	16	+	+	CCONJ
ejpam-2648	265	17	πnu	πnu	ADJ
ejpam-2648	265	18	(	(	PUNCT
ejpam-2648	265	19	b	b	NOUN
ejpam-2648	265	20	)	)	PUNCT
ejpam-2648	265	21	a1	a1	NOUN
ejpam-2648	265	22	dk+1u	dk+1u	NOUN
ejpam-2648	265	23	(	(	PUNCT
ejpam-2648	265	24	b	b	NOUN
ejpam-2648	265	25	)	)	PUNCT
ejpam-2648	265	26	a2	a2	PROPN
ejpam-2648	265	27	...	...	PUNCT
ejpam-2648	265	28	u	u	NOUN
ejpam-2648	265	29	(	(	PUNCT
ejpam-2648	265	30	b	b	NOUN
ejpam-2648	265	31	)	)	PUNCT
ejpam-2648	265	32	am(x	am(x	NOUN
ejpam-2648	265	33	)	)	PUNCT
ejpam-2648	265	34	,	,	PUNCT
ejpam-2648	265	35	where	where	SCONJ
ejpam-2648	265	36	ψ1(x	ψ1(x	NOUN
ejpam-2648	265	37	)	)	PUNCT
ejpam-2648	265	38	=	=	SYM
ejpam-2648	265	39	ϕ(x	ϕ(x	X
ejpam-2648	265	40	)	)	PUNCT
ejpam-2648	265	41	+	+	CCONJ
ejpam-2648	265	42	1	1	NUM
ejpam-2648	265	43	2	2	NUM
ejpam-2648	265	44	πnqa1	πnqa1	NOUN
ejpam-2648	265	45	(	(	PUNCT
ejpam-2648	265	46	∑	∑	ADV
ejpam-2648	265	47	i+j+h	i+j+h	ADJ
ejpam-2648	265	48	=	=	PRON
ejpam-2648	265	49	k+1	k+1	X
ejpam-2648	265	50	j≤k	j≤k	X
ejpam-2648	265	51	{	{	PUNCT
ejpam-2648	265	52	dib	dib	PROPN
ejpam-2648	265	53	,	,	PUNCT
ejpam-2648	265	54	dju	dju	PROPN
ejpam-2648	265	55	(	(	PUNCT
ejpam-2648	265	56	b	b	NOUN
ejpam-2648	265	57	)	)	PUNCT
ejpam-2648	265	58	a2	a2	PROPN
ejpam-2648	265	59	u	u	NOUN
ejpam-2648	265	60	(	(	PUNCT
ejpam-2648	265	61	b	b	NOUN
ejpam-2648	265	62	)	)	PUNCT
ejpam-2648	265	63	a3	a3	NOUN
ejpam-2648	265	64	...	...	PUNCT
ejpam-2648	265	65	u	u	NOUN
ejpam-2648	265	66	(	(	PUNCT
ejpam-2648	265	67	b	b	NOUN
ejpam-2648	265	68	)	)	PUNCT
ejpam-2648	265	69	amx	amx	PROPN
ejpam-2648	265	70	,	,	PUNCT
ejpam-2648	265	71	dhb	dhb	PROPN
ejpam-2648	265	72	}	}	PUNCT
ejpam-2648	265	73	)	)	PUNCT
ejpam-2648	265	74	ϕ(x	ϕ(x	X
ejpam-2648	265	75	)	)	PUNCT
ejpam-2648	265	76	=	=	SYM
ejpam-2648	265	77	1	1	NUM
ejpam-2648	265	78	4	4	NUM
ejpam-2648	265	79	πn	πn	INTJ
ejpam-2648	265	80	∑	∑	PUNCT
ejpam-2648	265	81	i+j+h	i+j+h	ADJ
ejpam-2648	265	82	=	=	PRON
ejpam-2648	265	83	k+1	k+1	X
ejpam-2648	265	84	j≤k	j≤k	X
ejpam-2648	265	85	{	{	PUNCT
ejpam-2648	265	86	dia1	dia1	PROPN
ejpam-2648	265	87	,	,	PUNCT
ejpam-2648	265	88	dj	dj	X
ejpam-2648	265	89	{	{	PUNCT
ejpam-2648	265	90	u	u	PROPN
ejpam-2648	265	91	(	(	PUNCT
ejpam-2648	265	92	b	b	NOUN
ejpam-2648	265	93	)	)	PUNCT
ejpam-2648	265	94	a1	a1	NOUN
ejpam-2648	265	95	u	u	NOUN
ejpam-2648	265	96	(	(	PUNCT
ejpam-2648	265	97	b	b	NOUN
ejpam-2648	265	98	)	)	PUNCT
ejpam-2648	265	99	a2	a2	PROPN
ejpam-2648	265	100	...	...	PUNCT
ejpam-2648	265	101	u	u	NOUN
ejpam-2648	265	102	(	(	PUNCT
ejpam-2648	265	103	b	b	NOUN
ejpam-2648	265	104	)	)	PUNCT
ejpam-2648	265	105	am(x	am(x	PUNCT
ejpam-2648	265	106	)	)	PUNCT
ejpam-2648	265	107	}	}	PUNCT
ejpam-2648	265	108	,	,	PUNCT
ejpam-2648	265	109	dha1	dha1	NOUN
ejpam-2648	265	110	}	}	PUNCT
ejpam-2648	265	111	are	be	AUX
ejpam-2648	265	112	clearly	clearly	ADV
ejpam-2648	265	113	continuous	continuous	ADJ
ejpam-2648	265	114	operators	operator	NOUN
ejpam-2648	265	115	.	.	PUNCT
ejpam-2648	266	1	by	by	ADP
ejpam-2648	266	2	iterating	iterate	VERB
ejpam-2648	266	3	the	the	DET
ejpam-2648	266	4	same	same	ADJ
ejpam-2648	266	5	process	process	NOUN
ejpam-2648	266	6	,	,	PUNCT
ejpam-2648	266	7	we	we	PRON
ejpam-2648	266	8	show	show	VERB
ejpam-2648	266	9	that	that	SCONJ
ejpam-2648	266	10	there	there	PRON
ejpam-2648	266	11	exits	exit	VERB
ejpam-2648	266	12	a	a	DET
ejpam-2648	266	13	continuous	continuous	ADJ
ejpam-2648	266	14	linear	linear	NOUN
ejpam-2648	266	15	operator	operator	NOUN
ejpam-2648	266	16	ψm	ψm	PRON
ejpam-2648	266	17	such	such	ADJ
ejpam-2648	266	18	that	that	SCONJ
ejpam-2648	266	19	πndk+1u	πndk+1u	PROPN
ejpam-2648	266	20	(	(	PUNCT
ejpam-2648	266	21	b	b	X
ejpam-2648	266	22	)	)	PUNCT
ejpam-2648	266	23	a1	a1	NOUN
ejpam-2648	266	24	u	u	NOUN
ejpam-2648	266	25	(	(	PUNCT
ejpam-2648	266	26	b	b	NOUN
ejpam-2648	266	27	)	)	PUNCT
ejpam-2648	266	28	a2	a2	PROPN
ejpam-2648	266	29	...	...	PUNCT
ejpam-2648	267	1	u	u	NOUN
ejpam-2648	267	2	(	(	PUNCT
ejpam-2648	267	3	b	b	NOUN
ejpam-2648	267	4	)	)	PUNCT
ejpam-2648	267	5	am(x	am(x	PUNCT
ejpam-2648	267	6	)	)	PUNCT
ejpam-2648	267	7	=	=	SYM
ejpam-2648	267	8	ψm(x	ψm(x	X
ejpam-2648	267	9	)	)	PUNCT
ejpam-2648	268	1	+	+	CCONJ
ejpam-2648	268	2	πnu	πnu	ADJ
ejpam-2648	268	3	(	(	PUNCT
ejpam-2648	268	4	b	b	NOUN
ejpam-2648	268	5	)	)	PUNCT
ejpam-2648	268	6	a1	a1	NOUN
ejpam-2648	268	7	u	u	NOUN
ejpam-2648	268	8	(	(	PUNCT
ejpam-2648	268	9	b	b	NOUN
ejpam-2648	268	10	)	)	PUNCT
ejpam-2648	268	11	a2	a2	PROPN
ejpam-2648	268	12	...	...	PUNCT
ejpam-2648	268	13	u	u	NOUN
ejpam-2648	268	14	(	(	PUNCT
ejpam-2648	268	15	b	b	NOUN
ejpam-2648	268	16	)	)	PUNCT
ejpam-2648	268	17	amdk+1(x	amdk+1(x	NOUN
ejpam-2648	268	18	)	)	PUNCT
ejpam-2648	268	19	.	.	PUNCT
ejpam-2648	269	1	but	but	CCONJ
ejpam-2648	269	2	we	we	PRON
ejpam-2648	269	3	have	have	VERB
ejpam-2648	269	4	πnu	πnu	ADJ
ejpam-2648	269	5	(	(	PUNCT
ejpam-2648	269	6	b	b	NOUN
ejpam-2648	269	7	)	)	PUNCT
ejpam-2648	269	8	a1	a1	NOUN
ejpam-2648	269	9	u	u	NOUN
ejpam-2648	269	10	(	(	PUNCT
ejpam-2648	269	11	b	b	NOUN
ejpam-2648	269	12	)	)	PUNCT
ejpam-2648	269	13	a2	a2	PROPN
ejpam-2648	269	14	...	...	PUNCT
ejpam-2648	270	1	u	u	NOUN
ejpam-2648	270	2	(	(	PUNCT
ejpam-2648	270	3	b	b	NOUN
ejpam-2648	270	4	)	)	PUNCT
ejpam-2648	270	5	amdk+1	amdk+1	VERB
ejpam-2648	271	1	=	=	SYM
ejpam-2648	271	2	0	0	NUM
ejpam-2648	271	3	when	when	SCONJ
ejpam-2648	271	4	n	n	ADP
ejpam-2648	271	5	<	<	X
ejpam-2648	271	6	m.	m.	NOUN
ejpam-2648	271	7	it	it	PRON
ejpam-2648	271	8	follows	follow	VERB
ejpam-2648	271	9	that	that	SCONJ
ejpam-2648	271	10	the	the	DET
ejpam-2648	271	11	operator	operator	NOUN
ejpam-2648	271	12	πndk+1u	πndk+1u	NUM
ejpam-2648	271	13	(	(	PUNCT
ejpam-2648	271	14	b	b	X
ejpam-2648	271	15	)	)	PUNCT
ejpam-2648	271	16	a1	a1	NOUN
ejpam-2648	271	17	u	u	NOUN
ejpam-2648	271	18	(	(	PUNCT
ejpam-2648	271	19	b	b	NOUN
ejpam-2648	271	20	)	)	PUNCT
ejpam-2648	271	21	a2	a2	PROPN
ejpam-2648	271	22	...	...	PUNCT
ejpam-2648	271	23	u	u	NOUN
ejpam-2648	271	24	(	(	PUNCT
ejpam-2648	271	25	b	b	NOUN
ejpam-2648	271	26	)	)	PUNCT
ejpam-2648	271	27	am	be	AUX
ejpam-2648	271	28	is	be	AUX
ejpam-2648	271	29	continuous	continuous	ADJ
ejpam-2648	271	30	.	.	PUNCT
ejpam-2648	272	1	now	now	ADV
ejpam-2648	272	2	,	,	PUNCT
ejpam-2648	272	3	lemma	lemma	PROPN
ejpam-2648	272	4	3	3	NUM
ejpam-2648	272	5	applies	apply	VERB
ejpam-2648	272	6	to	to	ADP
ejpam-2648	272	7	the	the	DET
ejpam-2648	272	8	sequences	sequence	NOUN
ejpam-2648	272	9	{	{	PUNCT
ejpam-2648	272	10	ri	ri	NOUN
ejpam-2648	272	11	}	}	PUNCT
ejpam-2648	272	12	and	and	CCONJ
ejpam-2648	272	13	{	{	PUNCT
ejpam-2648	272	14	ti	ti	NOUN
ejpam-2648	272	15	}	}	PUNCT
ejpam-2648	272	16	withri	withri	NOUN
ejpam-2648	273	1	=	=	PUNCT
ejpam-2648	273	2	πi	πi	ADV
ejpam-2648	273	3	and	and	CCONJ
ejpam-2648	273	4	ti	ti	X
ejpam-2648	273	5	=	=	SYM
ejpam-2648	273	6	u	u	PROPN
ejpam-2648	273	7	(	(	PUNCT
ejpam-2648	273	8	b	b	NOUN
ejpam-2648	273	9	)	)	PUNCT
ejpam-2648	273	10	ai	ai	VERB
ejpam-2648	273	11	to	to	PART
ejpam-2648	273	12	obtain	obtain	VERB
ejpam-2648	273	13	the	the	DET
ejpam-2648	273	14	continuity	continuity	NOUN
ejpam-2648	273	15	of	of	ADP
ejpam-2648	273	16	the	the	DET
ejpam-2648	273	17	operator	operator	NOUN
ejpam-2648	273	18	πndk+1u	πndk+1u	NUM
ejpam-2648	273	19	(	(	PUNCT
ejpam-2648	273	20	b	b	X
ejpam-2648	273	21	)	)	PUNCT
ejpam-2648	273	22	a1	a1	NOUN
ejpam-2648	273	23	u	u	NOUN
ejpam-2648	273	24	(	(	PUNCT
ejpam-2648	273	25	b	b	NOUN
ejpam-2648	273	26	)	)	PUNCT
ejpam-2648	273	27	a2	a2	PROPN
ejpam-2648	273	28	...	...	PUNCT
ejpam-2648	273	29	u	u	NOUN
ejpam-2648	273	30	(	(	PUNCT
ejpam-2648	273	31	b	b	NOUN
ejpam-2648	273	32	)	)	PUNCT
ejpam-2648	273	33	an	an	PRON
ejpam-2648	273	34	when	when	SCONJ
ejpam-2648	273	35	the	the	DET
ejpam-2648	273	36	integer	integer	NOUN
ejpam-2648	273	37	n	n	PRON
ejpam-2648	273	38	is	be	AUX
ejpam-2648	273	39	sufficiently	sufficiently	ADV
ejpam-2648	273	40	large	large	ADJ
ejpam-2648	273	41	.	.	PUNCT
ejpam-2648	274	1	that	that	PRON
ejpam-2648	274	2	is	be	AUX
ejpam-2648	274	3	s(πndk+1u	s(πndk+1u	PRON
ejpam-2648	274	4	(	(	PUNCT
ejpam-2648	274	5	b	b	X
ejpam-2648	274	6	)	)	PUNCT
ejpam-2648	274	7	a1	a1	NOUN
ejpam-2648	274	8	u	u	NOUN
ejpam-2648	274	9	(	(	PUNCT
ejpam-2648	274	10	b	b	NOUN
ejpam-2648	274	11	)	)	PUNCT
ejpam-2648	274	12	a2	a2	PROPN
ejpam-2648	274	13	...	...	PUNCT
ejpam-2648	275	1	u	u	NOUN
ejpam-2648	275	2	(	(	PUNCT
ejpam-2648	275	3	b	b	NOUN
ejpam-2648	275	4	)	)	PUNCT
ejpam-2648	275	5	an	an	PRON
ejpam-2648	275	6	)	)	PUNCT
ejpam-2648	275	7	=	=	SYM
ejpam-2648	275	8	0	0	X
ejpam-2648	275	9	.	.	PUNCT
ejpam-2648	276	1	but	but	CCONJ
ejpam-2648	276	2	since	since	SCONJ
ejpam-2648	276	3	πn(ai	πn(ai	PROPN
ejpam-2648	276	4	)	)	PUNCT
ejpam-2648	276	5	is	be	AUX
ejpam-2648	276	6	invertible	invertible	ADJ
ejpam-2648	276	7	for	for	ADP
ejpam-2648	276	8	i	i	PROPN
ejpam-2648	276	9	≤	≤	PROPN
ejpam-2648	276	10	n	n	CCONJ
ejpam-2648	276	11	,	,	PUNCT
ejpam-2648	276	12	we	we	PRON
ejpam-2648	276	13	have	have	VERB
ejpam-2648	276	14	s(πndk+1u	s(πndk+1u	PRON
ejpam-2648	276	15	(	(	PUNCT
ejpam-2648	276	16	b	b	X
ejpam-2648	276	17	)	)	PUNCT
ejpam-2648	276	18	a1	a1	NOUN
ejpam-2648	276	19	u	u	NOUN
ejpam-2648	276	20	(	(	PUNCT
ejpam-2648	276	21	b	b	NOUN
ejpam-2648	276	22	)	)	PUNCT
ejpam-2648	276	23	a2	a2	PROPN
ejpam-2648	276	24	...	...	PUNCT
ejpam-2648	277	1	u	u	NOUN
ejpam-2648	277	2	(	(	PUNCT
ejpam-2648	277	3	b	b	NOUN
ejpam-2648	277	4	)	)	PUNCT
ejpam-2648	277	5	an	an	PRON
ejpam-2648	277	6	)	)	PUNCT
ejpam-2648	277	7	=	=	SYM
ejpam-2648	278	1	s(πnu	s(πnu	PROPN
ejpam-2648	278	2	(	(	PUNCT
ejpam-2648	278	3	b	b	NOUN
ejpam-2648	278	4	)	)	PUNCT
ejpam-2648	278	5	a1	a1	NOUN
ejpam-2648	278	6	u	u	NOUN
ejpam-2648	278	7	(	(	PUNCT
ejpam-2648	278	8	b	b	NOUN
ejpam-2648	278	9	)	)	PUNCT
ejpam-2648	278	10	a2	a2	PROPN
ejpam-2648	278	11	...	...	PUNCT
ejpam-2648	278	12	u	u	NOUN
ejpam-2648	278	13	(	(	PUNCT
ejpam-2648	278	14	b	b	NOUN
ejpam-2648	278	15	)	)	PUNCT
ejpam-2648	278	16	an	an	DET
ejpam-2648	278	17	dk+1	dk+1	NOUN
ejpam-2648	278	18	)	)	PUNCT
ejpam-2648	278	19	h.	h.	PROPN
ejpam-2648	278	20	marhnine	marhnine	PROPN
ejpam-2648	278	21	,	,	PUNCT
ejpam-2648	278	22	c.	c.	PROPN
ejpam-2648	278	23	zarhouti	zarhouti	PROPN
ejpam-2648	278	24	/	/	SYM
ejpam-2648	278	25	eur	eur	PROPN
ejpam-2648	278	26	.	.	PUNCT
ejpam-2648	279	1	j.	j.	PROPN
ejpam-2648	279	2	pure	pure	PROPN
ejpam-2648	279	3	appl	appl	PROPN
ejpam-2648	279	4	.	.	PROPN
ejpam-2648	279	5	math	math	PROPN
ejpam-2648	279	6	,	,	PUNCT
ejpam-2648	279	7	10	10	NUM
ejpam-2648	279	8	(	(	PUNCT
ejpam-2648	279	9	4	4	NUM
ejpam-2648	279	10	)	)	PUNCT
ejpam-2648	279	11	(	(	PUNCT
ejpam-2648	279	12	2017	2017	NUM
ejpam-2648	279	13	)	)	PUNCT
ejpam-2648	279	14	,	,	PUNCT
ejpam-2648	279	15	749	749	NUM
ejpam-2648	279	16	-	-	SYM
ejpam-2648	279	17	762	762	NUM
ejpam-2648	279	18	759	759	NUM
ejpam-2648	279	19	=	=	NOUN
ejpam-2648	279	20	cl(u	cl(u	X
ejpam-2648	279	21	(	(	PUNCT
ejpam-2648	279	22	b	b	NOUN
ejpam-2648	279	23	)	)	PUNCT
ejpam-2648	279	24	π1a1u	π1a1u	X
ejpam-2648	279	25	(	(	PUNCT
ejpam-2648	279	26	b	b	X
ejpam-2648	279	27	)	)	PUNCT
ejpam-2648	279	28	π2a2	π2a2	PROPN
ejpam-2648	279	29	...	...	PUNCT
ejpam-2648	279	30	u	u	NOUN
ejpam-2648	279	31	(	(	PUNCT
ejpam-2648	279	32	b	b	NOUN
ejpam-2648	279	33	)	)	PUNCT
ejpam-2648	279	34	πnans(πndk+1	πnans(πndk+1	NOUN
ejpam-2648	279	35	)	)	PUNCT
ejpam-2648	279	36	)	)	PUNCT
ejpam-2648	280	1	=	=	SYM
ejpam-2648	280	2	cl(s(πndk+1	cl(s(πndk+1	VERB
ejpam-2648	280	3	)	)	PUNCT
ejpam-2648	280	4	)	)	PUNCT
ejpam-2648	280	5	,	,	PUNCT
ejpam-2648	280	6	which	which	PRON
ejpam-2648	280	7	is	be	AUX
ejpam-2648	280	8	a	a	DET
ejpam-2648	280	9	contradiction	contradiction	NOUN
ejpam-2648	280	10	because	because	SCONJ
ejpam-2648	280	11	cl(s(πndk+1	cl(s(πndk+1	NOUN
ejpam-2648	280	12	)	)	PUNCT
ejpam-2648	280	13	)	)	PUNCT
ejpam-2648	281	1	6=	6=	ADP
ejpam-2648	281	2	0	0	NUM
ejpam-2648	281	3	since	since	SCONJ
ejpam-2648	281	4	otherwise	otherwise	ADV
ejpam-2648	281	5	we	we	PRON
ejpam-2648	281	6	will	will	AUX
ejpam-2648	281	7	have	have	VERB
ejpam-2648	281	8	s(dk+1	s(dk+1	NOUN
ejpam-2648	281	9	)	)	PUNCT
ejpam-2648	281	10	⊆	⊆	NUM
ejpam-2648	281	11	pn	pn	NOUN
ejpam-2648	281	12	for	for	ADP
ejpam-2648	281	13	any	any	DET
ejpam-2648	281	14	positive	positive	ADJ
ejpam-2648	281	15	integer	integer	NOUN
ejpam-2648	281	16	n.	n.	NOUN
ejpam-2648	281	17	the	the	DET
ejpam-2648	281	18	set	set	NOUN
ejpam-2648	281	19	γ	γ	PROPN
ejpam-2648	281	20	is	be	AUX
ejpam-2648	281	21	actually	actually	ADV
ejpam-2648	281	22	finite	finite	ADJ
ejpam-2648	281	23	,	,	PUNCT
ejpam-2648	281	24	say	say	VERB
ejpam-2648	281	25	γ	γ	X
ejpam-2648	281	26	=	=	SYM
ejpam-2648	281	27	{	{	PUNCT
ejpam-2648	281	28	p1	p1	PROPN
ejpam-2648	281	29	,	,	PUNCT
ejpam-2648	281	30	...	...	PUNCT
ejpam-2648	281	31	,	,	PUNCT
ejpam-2648	281	32	pn	pn	PROPN
ejpam-2648	281	33	}	}	PUNCT
ejpam-2648	281	34	.	.	PUNCT
ejpam-2648	282	1	set	set	VERB
ejpam-2648	282	2	h	h	NOUN
ejpam-2648	282	3	=	=	SYM
ejpam-2648	282	4	∩	∩	NOUN
ejpam-2648	282	5	p	p	NOUN
ejpam-2648	282	6	/∈γ	/∈γ	PUNCT
ejpam-2648	282	7	p	p	X
ejpam-2648	282	8	.	.	PUNCT
ejpam-2648	283	1	the	the	DET
ejpam-2648	283	2	ideals	ideal	NOUN
ejpam-2648	283	3	p1	p1	NOUN
ejpam-2648	283	4	,	,	PUNCT
ejpam-2648	283	5	p2	p2	NOUN
ejpam-2648	283	6	,	,	PUNCT
ejpam-2648	283	7	...	...	PUNCT
ejpam-2648	283	8	,	,	PUNCT
ejpam-2648	283	9	pn	pn	PROPN
ejpam-2648	283	10	and	and	CCONJ
ejpam-2648	283	11	h	h	NOUN
ejpam-2648	283	12	satisfy	satisfy	VERB
ejpam-2648	283	13	the	the	DET
ejpam-2648	283	14	requirements	requirement	NOUN
ejpam-2648	283	15	of	of	ADP
ejpam-2648	283	16	lemma	lemma	PROPN
ejpam-2648	283	17	4	4	NUM
ejpam-2648	283	18	since	since	SCONJ
ejpam-2648	283	19	(	(	PUNCT
ejpam-2648	283	20	n	n	PRON
ejpam-2648	283	21	∩	∩	NOUN
ejpam-2648	283	22	i=1	i=1	ADP
ejpam-2648	283	23	pi)∩h	pi)∩h	NOUN
ejpam-2648	283	24	=	=	SYM
ejpam-2648	283	25	rad(v	rad(v	NOUN
ejpam-2648	283	26	)	)	PUNCT
ejpam-2648	283	27	is	be	AUX
ejpam-2648	283	28	the	the	DET
ejpam-2648	283	29	intersection	intersection	NOUN
ejpam-2648	283	30	of	of	ADP
ejpam-2648	283	31	all	all	DET
ejpam-2648	283	32	primitive	primitive	ADJ
ejpam-2648	283	33	ideals	ideal	NOUN
ejpam-2648	283	34	of	of	ADP
ejpam-2648	283	35	v	v	NOUN
ejpam-2648	283	36	(	(	PUNCT
ejpam-2648	283	37	2.4	2.4	NUM
ejpam-2648	283	38	)	)	PUNCT
ejpam-2648	283	39	and	and	CCONJ
ejpam-2648	283	40	rad(v	rad(v	NOUN
ejpam-2648	283	41	)	)	PUNCT
ejpam-2648	283	42	=	=	SYM
ejpam-2648	284	1	0	0	X
ejpam-2648	284	2	.	.	PUNCT
ejpam-2648	285	1	we	we	PRON
ejpam-2648	285	2	conclude	conclude	VERB
ejpam-2648	285	3	that	that	PRON
ejpam-2648	285	4	h	h	NOUN
ejpam-2648	285	5	=	=	NOUN
ejpam-2648	285	6	0	0	PROPN
ejpam-2648	285	7	.	.	PUNCT
ejpam-2648	286	1	but	but	CCONJ
ejpam-2648	286	2	s(dk+1	s(dk+1	NOUN
ejpam-2648	286	3	)	)	PUNCT
ejpam-2648	286	4	⊆	⊆	NUM
ejpam-2648	286	5	p	p	NOUN
ejpam-2648	286	6	for	for	ADP
ejpam-2648	286	7	any	any	DET
ejpam-2648	286	8	primitive	primitive	ADJ
ejpam-2648	286	9	ideal	ideal	NOUN
ejpam-2648	286	10	p	p	NOUN
ejpam-2648	286	11	not	not	PART
ejpam-2648	286	12	contained	contain	VERB
ejpam-2648	286	13	in	in	ADP
ejpam-2648	286	14	γ	γ	PROPN
ejpam-2648	286	15	,	,	PUNCT
ejpam-2648	286	16	then	then	ADV
ejpam-2648	286	17	s(dk+1	s(dk+1	NOUN
ejpam-2648	286	18	)	)	PUNCT
ejpam-2648	286	19	⊆	⊆	NUM
ejpam-2648	286	20	∩	∩	X
ejpam-2648	286	21	p	p	NOUN
ejpam-2648	286	22	/∈γ	/∈γ	PUNCT
ejpam-2648	287	1	p	p	X
ejpam-2648	287	2	=	=	NOUN
ejpam-2648	287	3	h	h	NOUN
ejpam-2648	287	4	=	=	SYM
ejpam-2648	287	5	0	0	PROPN
ejpam-2648	287	6	,	,	PUNCT
ejpam-2648	287	7	which	which	PRON
ejpam-2648	287	8	is	be	AUX
ejpam-2648	287	9	a	a	DET
ejpam-2648	287	10	contradiction	contradiction	NOUN
ejpam-2648	287	11	.	.	PUNCT
ejpam-2648	288	1	dk+1	dk+1	NOUN
ejpam-2648	288	2	is	be	AUX
ejpam-2648	288	3	finally	finally	ADV
ejpam-2648	288	4	continuous	continuous	ADJ
ejpam-2648	288	5	.	.	PUNCT
ejpam-2648	289	1	as	as	SCONJ
ejpam-2648	289	2	it	it	PRON
ejpam-2648	289	3	is	be	AUX
ejpam-2648	289	4	pointed	point	VERB
ejpam-2648	289	5	out	out	ADP
ejpam-2648	289	6	,	,	PUNCT
ejpam-2648	289	7	any	any	DET
ejpam-2648	289	8	jordan	jordan	PROPN
ejpam-2648	289	9	algebra	algebra	PROPN
ejpam-2648	289	10	gives	give	VERB
ejpam-2648	289	11	rise	rise	NOUN
ejpam-2648	289	12	to	to	ADP
ejpam-2648	289	13	a	a	DET
ejpam-2648	289	14	jordan	jordan	PROPN
ejpam-2648	289	15	pair	pair	PROPN
ejpam-2648	289	16	(	(	PUNCT
ejpam-2648	289	17	j	j	PROPN
ejpam-2648	289	18	,	,	PUNCT
ejpam-2648	289	19	j	j	PROPN
ejpam-2648	289	20	)	)	PUNCT
ejpam-2648	289	21	with	with	ADP
ejpam-2648	289	22	the	the	DET
ejpam-2648	289	23	quadratic	quadratic	ADJ
ejpam-2648	289	24	map	map	NOUN
ejpam-2648	289	25	qa	qa	PROPN
ejpam-2648	289	26	=	=	SYM
ejpam-2648	289	27	ua	ua	PROPN
ejpam-2648	289	28	defined	define	VERB
ejpam-2648	289	29	by	by	ADP
ejpam-2648	289	30	uab	uab	PROPN
ejpam-2648	289	31	=	=	PROPN
ejpam-2648	289	32	2a(ab)−	2a(ab)−	PROPN
ejpam-2648	289	33	a2b	a2b	NOUN
ejpam-2648	289	34	.	.	PUNCT
ejpam-2648	290	1	a	a	DET
ejpam-2648	290	2	family	family	NOUN
ejpam-2648	290	3	{	{	PUNCT
ejpam-2648	290	4	dn	dn	PROPN
ejpam-2648	290	5	}	}	PUNCT
ejpam-2648	290	6	(	(	PUNCT
ejpam-2648	290	7	n	n	NOUN
ejpam-2648	290	8	=	=	SYM
ejpam-2648	290	9	0	0	NUM
ejpam-2648	290	10	,	,	PUNCT
ejpam-2648	290	11	1	1	NUM
ejpam-2648	290	12	,	,	PUNCT
ejpam-2648	290	13	2	2	NUM
ejpam-2648	290	14	,	,	PUNCT
ejpam-2648	290	15	...	...	PUNCT
ejpam-2648	290	16	,	,	PUNCT
ejpam-2648	290	17	k	k	PROPN
ejpam-2648	290	18	,	,	PUNCT
ejpam-2648	290	19	k	k	PROPN
ejpam-2648	290	20	may	may	AUX
ejpam-2648	290	21	be	be	AUX
ejpam-2648	290	22	∞	∞	NUM
ejpam-2648	290	23	)	)	PUNCT
ejpam-2648	290	24	of	of	ADP
ejpam-2648	290	25	linear	linear	PROPN
ejpam-2648	290	26	operators	operator	NOUN
ejpam-2648	290	27	defined	define	VERB
ejpam-2648	290	28	on	on	ADP
ejpam-2648	290	29	j	j	PROPN
ejpam-2648	290	30	is	be	AUX
ejpam-2648	290	31	said	say	VERB
ejpam-2648	290	32	to	to	PART
ejpam-2648	290	33	be	be	AUX
ejpam-2648	290	34	a	a	DET
ejpam-2648	290	35	higher	high	ADJ
ejpam-2648	290	36	derivation	derivation	NOUN
ejpam-2648	290	37	if	if	SCONJ
ejpam-2648	290	38	,	,	PUNCT
ejpam-2648	290	39	for	for	ADP
ejpam-2648	290	40	all	all	DET
ejpam-2648	290	41	a	a	DET
ejpam-2648	290	42	,	,	PUNCT
ejpam-2648	290	43	b	b	NOUN
ejpam-2648	290	44	in	in	ADP
ejpam-2648	290	45	j	j	PROPN
ejpam-2648	290	46	,	,	PUNCT
ejpam-2648	290	47	we	we	PRON
ejpam-2648	290	48	have	have	VERB
ejpam-2648	290	49	dn(ab	dn(ab	PUNCT
ejpam-2648	290	50	)	)	PUNCT
ejpam-2648	291	1	=	=	SYM
ejpam-2648	291	2	k	k	X
ejpam-2648	292	1	=	=	PROPN
ejpam-2648	292	2	n∑	n∑	NOUN
ejpam-2648	292	3	k=1	k=1	NOUN
ejpam-2648	292	4	dk(a)dn−k(b	dk(a)dn−k(b	NOUN
ejpam-2648	292	5	)	)	PUNCT
ejpam-2648	292	6	.	.	PUNCT
ejpam-2648	293	1	a	a	DET
ejpam-2648	293	2	tedious	tedious	ADJ
ejpam-2648	293	3	computation	computation	NOUN
ejpam-2648	293	4	enables	enable	VERB
ejpam-2648	293	5	to	to	PART
ejpam-2648	293	6	prove	prove	VERB
ejpam-2648	293	7	that	that	SCONJ
ejpam-2648	293	8	any	any	DET
ejpam-2648	293	9	higher	high	ADJ
ejpam-2648	293	10	derivation	derivation	NOUN
ejpam-2648	293	11	{	{	PUNCT
ejpam-2648	293	12	dn}n≥0	dn}n≥0	NOUN
ejpam-2648	293	13	on	on	ADP
ejpam-2648	293	14	a	a	DET
ejpam-2648	293	15	jordan	jordan	PROPN
ejpam-2648	293	16	algebra	algebra	PROPN
ejpam-2648	293	17	gives	give	VERB
ejpam-2648	293	18	rise	rise	NOUN
ejpam-2648	293	19	to	to	ADP
ejpam-2648	293	20	a	a	DET
ejpam-2648	293	21	higher	high	ADJ
ejpam-2648	293	22	derivation	derivation	NOUN
ejpam-2648	293	23	{	{	PUNCT
ejpam-2648	293	24	(	(	PUNCT
ejpam-2648	293	25	dn	dn	PROPN
ejpam-2648	293	26	,	,	PUNCT
ejpam-2648	293	27	dn)}n≥0	dn)}n≥0	VERB
ejpam-2648	293	28	on	on	ADP
ejpam-2648	293	29	the	the	DET
ejpam-2648	293	30	jordan	jordan	PROPN
ejpam-2648	293	31	pair	pair	PROPN
ejpam-2648	293	32	(	(	PUNCT
ejpam-2648	293	33	j	j	PROPN
ejpam-2648	293	34	,	,	PUNCT
ejpam-2648	293	35	j	j	PROPN
ejpam-2648	293	36	)	)	PUNCT
ejpam-2648	293	37	with	with	ADP
ejpam-2648	293	38	respect	respect	NOUN
ejpam-2648	293	39	to	to	ADP
ejpam-2648	293	40	the	the	DET
ejpam-2648	293	41	triple	triple	ADJ
ejpam-2648	293	42	product	product	NOUN
ejpam-2648	293	43	{	{	PUNCT
ejpam-2648	293	44	x	x	NOUN
ejpam-2648	293	45	,	,	PUNCT
ejpam-2648	293	46	y	y	PROPN
ejpam-2648	293	47	,	,	PUNCT
ejpam-2648	293	48	z	z	NOUN
ejpam-2648	293	49	}	}	PUNCT
ejpam-2648	293	50	=	=	SYM
ejpam-2648	293	51	(	(	PUNCT
ejpam-2648	293	52	xy)z	xy)z	PROPN
ejpam-2648	293	53	+	+	NUM
ejpam-2648	293	54	(	(	PUNCT
ejpam-2648	293	55	yz)x−	yz)x−	NOUN
ejpam-2648	293	56	(	(	PUNCT
ejpam-2648	293	57	zx)y	zx)y	PROPN
ejpam-2648	293	58	.	.	PUNCT
ejpam-2648	294	1	the	the	DET
ejpam-2648	294	2	jordan	jordan	PROPN
ejpam-2648	294	3	pair	pair	PROPN
ejpam-2648	294	4	is	be	AUX
ejpam-2648	294	5	semiprimitive	semiprimitive	ADJ
ejpam-2648	294	6	if	if	SCONJ
ejpam-2648	294	7	so	so	ADV
ejpam-2648	294	8	is	be	AUX
ejpam-2648	294	9	j.	j.	PROPN
ejpam-2648	294	10	hence	hence	PROPN
ejpam-2648	294	11	,	,	PUNCT
ejpam-2648	294	12	according	accord	VERB
ejpam-2648	294	13	to	to	ADP
ejpam-2648	294	14	theorem	theorem	NOUN
ejpam-2648	294	15	2	2	NUM
ejpam-2648	294	16	,	,	PUNCT
ejpam-2648	294	17	we	we	PRON
ejpam-2648	294	18	have	have	VERB
ejpam-2648	294	19	the	the	DET
ejpam-2648	294	20	following	following	NOUN
ejpam-2648	294	21	.	.	PUNCT
ejpam-2648	295	1	corollary	corollary	ADJ
ejpam-2648	295	2	2	2	NUM
ejpam-2648	295	3	.	.	PUNCT
ejpam-2648	295	4	.	.	PUNCT
ejpam-2648	296	1	any	any	DET
ejpam-2648	296	2	higher	high	ADJ
ejpam-2648	296	3	derivation	derivation	NOUN
ejpam-2648	296	4	{	{	PUNCT
ejpam-2648	296	5	dn}n≥0	dn}n≥0	NOUN
ejpam-2648	296	6	on	on	ADP
ejpam-2648	296	7	a	a	DET
ejpam-2648	296	8	semiprimitive	semiprimitive	ADJ
ejpam-2648	296	9	banach	banach	NOUN
ejpam-2648	296	10	-	-	PUNCT
ejpam-2648	296	11	jordan	jordan	PROPN
ejpam-2648	296	12	algebra	algebra	PROPN
ejpam-2648	296	13	consists	consist	VERB
ejpam-2648	296	14	of	of	ADP
ejpam-2648	296	15	continuous	continuous	ADJ
ejpam-2648	296	16	operators	operator	NOUN
ejpam-2648	296	17	.	.	PUNCT
ejpam-2648	297	1	5	5	X
ejpam-2648	297	2	.	.	X
ejpam-2648	297	3	higher	high	ADJ
ejpam-2648	297	4	derivations	derivation	NOUN
ejpam-2648	297	5	on	on	ADP
ejpam-2648	297	6	banach	banach	NOUN
ejpam-2648	297	7	alternative	alternative	ADJ
ejpam-2648	297	8	pairs	pair	NOUN
ejpam-2648	297	9	and	and	CCONJ
ejpam-2648	297	10	jb∗-triples	jb∗-triple	VERB
ejpam-2648	297	11	the	the	DET
ejpam-2648	297	12	reader	reader	NOUN
ejpam-2648	297	13	is	be	AUX
ejpam-2648	297	14	referred	refer	VERB
ejpam-2648	297	15	to	to	ADP
ejpam-2648	297	16	[	[	X
ejpam-2648	297	17	18	18	NUM
ejpam-2648	297	18	]	]	PUNCT
ejpam-2648	297	19	for	for	ADP
ejpam-2648	297	20	definitions	definition	NOUN
ejpam-2648	297	21	and	and	CCONJ
ejpam-2648	297	22	basic	basic	ADJ
ejpam-2648	297	23	results	result	NOUN
ejpam-2648	297	24	on	on	ADP
ejpam-2648	297	25	alternative	alternative	ADJ
ejpam-2648	297	26	pairs	pair	NOUN
ejpam-2648	297	27	.	.	PUNCT
ejpam-2648	298	1	given	give	VERB
ejpam-2648	298	2	an	an	DET
ejpam-2648	298	3	alternative	alternative	ADJ
ejpam-2648	298	4	pair	pair	NOUN
ejpam-2648	298	5	a	a	PRON
ejpam-2648	298	6	=	=	SYM
ejpam-2648	298	7	(	(	PUNCT
ejpam-2648	298	8	a+	a+	NOUN
ejpam-2648	298	9	,	,	PUNCT
ejpam-2648	298	10	a−	a−	PROPN
ejpam-2648	298	11	)	)	PUNCT
ejpam-2648	298	12	,	,	PUNCT
ejpam-2648	298	13	we	we	PRON
ejpam-2648	298	14	write	write	VERB
ejpam-2648	298	15	(	(	PUNCT
ejpam-2648	298	16	x	x	NOUN
ejpam-2648	298	17	,	,	PUNCT
ejpam-2648	298	18	y	y	PROPN
ejpam-2648	298	19	,	,	PUNCT
ejpam-2648	298	20	z	z	NOUN
ejpam-2648	298	21	)	)	PUNCT
ejpam-2648	298	22	7−→	7−→	NOUN
ejpam-2648	298	23	〈	〈	PROPN
ejpam-2648	298	24	xyz	xyz	PROPN
ejpam-2648	298	25	〉	〉	PROPN
ejpam-2648	298	26	to	to	PART
ejpam-2648	298	27	denote	denote	VERB
ejpam-2648	298	28	the	the	DET
ejpam-2648	298	29	triple	triple	ADJ
ejpam-2648	298	30	product	product	NOUN
ejpam-2648	298	31	of	of	ADP
ejpam-2648	298	32	(	(	PUNCT
ejpam-2648	298	33	x	x	NOUN
ejpam-2648	298	34	,	,	PUNCT
ejpam-2648	298	35	y	y	PROPN
ejpam-2648	298	36	,	,	PUNCT
ejpam-2648	298	37	z	z	NOUN
ejpam-2648	298	38	)	)	PUNCT
ejpam-2648	298	39	in	in	ADP
ejpam-2648	298	40	aσ	aσ	NOUN
ejpam-2648	298	41	×a−σ	×a−σ	NOUN
ejpam-2648	298	42	×aσ	×aσ	PROPN
ejpam-2648	298	43	(	(	PUNCT
ejpam-2648	298	44	σ	σ	NOUN
ejpam-2648	298	45	=	=	SYM
ejpam-2648	298	46	±	±	PROPN
ejpam-2648	298	47	)	)	PUNCT
ejpam-2648	298	48	.	.	PUNCT
ejpam-2648	299	1	by	by	ADP
ejpam-2648	299	2	a	a	DET
ejpam-2648	299	3	normed	normed	ADJ
ejpam-2648	299	4	alternative	alternative	ADJ
ejpam-2648	299	5	pair	pair	NOUN
ejpam-2648	299	6	we	we	PRON
ejpam-2648	299	7	mean	mean	VERB
ejpam-2648	299	8	a	a	DET
ejpam-2648	299	9	complex	complex	ADJ
ejpam-2648	299	10	alternative	alternative	ADJ
ejpam-2648	299	11	pair	pair	NOUN
ejpam-2648	299	12	a	a	PRON
ejpam-2648	299	13	=	=	SYM
ejpam-2648	299	14	(	(	PUNCT
ejpam-2648	299	15	a+	a+	NOUN
ejpam-2648	299	16	,	,	PUNCT
ejpam-2648	299	17	a−	a−	PROPN
ejpam-2648	299	18	)	)	PUNCT
ejpam-2648	299	19	,	,	PUNCT
ejpam-2648	299	20	where	where	SCONJ
ejpam-2648	299	21	the	the	DET
ejpam-2648	299	22	vector	vector	NOUN
ejpam-2648	299	23	spaces	space	VERB
ejpam-2648	299	24	a+	a+	PUNCT
ejpam-2648	299	25	and	and	CCONJ
ejpam-2648	299	26	a−	a−	PROPN
ejpam-2648	299	27	are	be	AUX
ejpam-2648	299	28	equipped	equip	VERB
ejpam-2648	299	29	with	with	ADP
ejpam-2648	299	30	norms	norm	NOUN
ejpam-2648	299	31	‖.‖σ	‖.‖σ	NOUN
ejpam-2648	299	32	making	make	VERB
ejpam-2648	299	33	continuous	continuous	ADJ
ejpam-2648	299	34	the	the	DET
ejpam-2648	299	35	triple	triple	ADJ
ejpam-2648	299	36	product	product	NOUN
ejpam-2648	299	37	〈	〈	PROPN
ejpam-2648	299	38	xyz	xyz	PROPN
ejpam-2648	299	39	〉	〉	PROPN
ejpam-2648	299	40	.	.	PUNCT
ejpam-2648	300	1	a	a	PRON
ejpam-2648	300	2	=	=	SYM
ejpam-2648	300	3	(	(	PUNCT
ejpam-2648	300	4	a+	a+	NOUN
ejpam-2648	300	5	,	,	PUNCT
ejpam-2648	300	6	a−	a−	NOUN
ejpam-2648	300	7	)	)	PUNCT
ejpam-2648	300	8	is	be	AUX
ejpam-2648	300	9	said	say	VERB
ejpam-2648	300	10	to	to	ADP
ejpam-2648	300	11	b	b	PROPN
ejpam-2648	300	12	banach	banach	ADV
ejpam-2648	300	13	alternative	alternative	ADJ
ejpam-2648	300	14	pair	pair	NOUN
ejpam-2648	300	15	provided	provide	VERB
ejpam-2648	300	16	the	the	DET
ejpam-2648	300	17	norms	norm	NOUN
ejpam-2648	300	18	‖.‖σ	‖.‖σ	NOUN
ejpam-2648	300	19	are	be	AUX
ejpam-2648	300	20	complete	complete	ADJ
ejpam-2648	300	21	.	.	PUNCT
ejpam-2648	301	1	the	the	DET
ejpam-2648	301	2	banach	banach	NOUN
ejpam-2648	301	3	spaces	space	VERB
ejpam-2648	301	4	mp	mp	PROPN
ejpam-2648	301	5	,	,	PUNCT
ejpam-2648	301	6	q(c	q(c	PROPN
ejpam-2648	301	7	)	)	PUNCT
ejpam-2648	301	8	,	,	PUNCT
ejpam-2648	301	9	mq	mq	PROPN
ejpam-2648	301	10	,	,	PUNCT
ejpam-2648	301	11	p(c	p(c	NOUN
ejpam-2648	301	12	)	)	PUNCT
ejpam-2648	301	13	of	of	ADP
ejpam-2648	301	14	rectangular	rectangular	ADJ
ejpam-2648	301	15	matrices	matrix	NOUN
ejpam-2648	301	16	with	with	ADP
ejpam-2648	301	17	entries	entry	NOUN
ejpam-2648	301	18	in	in	ADP
ejpam-2648	301	19	the	the	DET
ejpam-2648	301	20	complex	complex	ADJ
ejpam-2648	301	21	field	field	NOUN
ejpam-2648	301	22	c	c	AUX
ejpam-2648	301	23	define	define	VERB
ejpam-2648	301	24	a	a	DET
ejpam-2648	301	25	banach	banach	NOUN
ejpam-2648	301	26	alternative	alternative	ADJ
ejpam-2648	301	27	pair	pair	NOUN
ejpam-2648	301	28	a	a	PRON
ejpam-2648	301	29	=	=	X
ejpam-2648	301	30	(	(	PUNCT
ejpam-2648	301	31	mp	mp	PROPN
ejpam-2648	301	32	,	,	PUNCT
ejpam-2648	301	33	q(c),mq	q(c),mq	PROPN
ejpam-2648	301	34	,	,	PUNCT
ejpam-2648	301	35	p(c	p(c	NOUN
ejpam-2648	301	36	)	)	PUNCT
ejpam-2648	301	37	)	)	PUNCT
ejpam-2648	301	38	,	,	PUNCT
ejpam-2648	301	39	with	with	ADP
ejpam-2648	301	40	respect	respect	NOUN
ejpam-2648	301	41	to	to	ADP
ejpam-2648	301	42	the	the	DET
ejpam-2648	301	43	triple	triple	ADJ
ejpam-2648	301	44	product	product	NOUN
ejpam-2648	301	45	〈	〈	PROPN
ejpam-2648	301	46	rst	rst	PROPN
ejpam-2648	301	47	〉	〉	PROPN
ejpam-2648	301	48	=	=	SYM
ejpam-2648	301	49	rst	rst	PROPN
ejpam-2648	301	50	,	,	PUNCT
ejpam-2648	301	51	the	the	DET
ejpam-2648	301	52	usual	usual	ADJ
ejpam-2648	301	53	matrices	matrix	NOUN
ejpam-2648	301	54	product	product	NOUN
ejpam-2648	301	55	.	.	PUNCT
ejpam-2648	302	1	h.	h.	PROPN
ejpam-2648	302	2	marhnine	marhnine	PROPN
ejpam-2648	302	3	,	,	PUNCT
ejpam-2648	302	4	c.	c.	PROPN
ejpam-2648	302	5	zarhouti	zarhouti	PROPN
ejpam-2648	302	6	/	/	SYM
ejpam-2648	302	7	eur	eur	PROPN
ejpam-2648	302	8	.	.	PUNCT
ejpam-2648	303	1	j.	j.	PROPN
ejpam-2648	303	2	pure	pure	PROPN
ejpam-2648	303	3	appl	appl	PROPN
ejpam-2648	303	4	.	.	PROPN
ejpam-2648	303	5	math	math	PROPN
ejpam-2648	303	6	,	,	PUNCT
ejpam-2648	303	7	10	10	NUM
ejpam-2648	303	8	(	(	PUNCT
ejpam-2648	303	9	4	4	NUM
ejpam-2648	303	10	)	)	PUNCT
ejpam-2648	303	11	(	(	PUNCT
ejpam-2648	303	12	2017	2017	NUM
ejpam-2648	303	13	)	)	PUNCT
ejpam-2648	303	14	,	,	PUNCT
ejpam-2648	303	15	749	749	NUM
ejpam-2648	303	16	-	-	SYM
ejpam-2648	303	17	762	762	NUM
ejpam-2648	303	18	760	760	NUM
ejpam-2648	303	19	a	a	DET
ejpam-2648	303	20	higher	high	ADJ
ejpam-2648	303	21	derivation	derivation	NOUN
ejpam-2648	303	22	on	on	ADP
ejpam-2648	303	23	an	an	DET
ejpam-2648	303	24	alternative	alternative	ADJ
ejpam-2648	303	25	paira	paira	NOUN
ejpam-2648	303	26	=	=	SYM
ejpam-2648	303	27	(	(	PUNCT
ejpam-2648	303	28	a+	a+	NOUN
ejpam-2648	303	29	,	,	PUNCT
ejpam-2648	303	30	a−	a−	NOUN
ejpam-2648	303	31	)	)	PUNCT
ejpam-2648	303	32	is	be	AUX
ejpam-2648	303	33	a	a	DET
ejpam-2648	303	34	sequence	sequence	NOUN
ejpam-2648	303	35	{	{	PUNCT
ejpam-2648	303	36	dn	dn	NOUN
ejpam-2648	303	37	=	=	SYM
ejpam-2648	303	38	(	(	PUNCT
ejpam-2648	303	39	d+	d+	X
ejpam-2648	303	40	n	n	X
ejpam-2648	303	41	,	,	PUNCT
ejpam-2648	303	42	d	d	PROPN
ejpam-2648	303	43	−	−	PROPN
ejpam-2648	303	44	n	n	NOUN
ejpam-2648	303	45	)	)	PUNCT
ejpam-2648	303	46	}	}	PUNCT
ejpam-2648	303	47	n≥0	n≥0	NOUN
ejpam-2648	303	48	of	of	ADP
ejpam-2648	303	49	linear	linear	PROPN
ejpam-2648	303	50	operators	operator	NOUN
ejpam-2648	303	51	dσ	dσ	VERB
ejpam-2648	303	52	n	n	PROPN
ejpam-2648	303	53	:	:	PUNCT
ejpam-2648	303	54	aσ	aσ	ADP
ejpam-2648	303	55	7−→	7−→	NOUN
ejpam-2648	303	56	aσ	aσ	ADV
ejpam-2648	303	57	satisfying	satisfy	VERB
ejpam-2648	303	58	the	the	DET
ejpam-2648	303	59	formula	formula	NOUN
ejpam-2648	303	60	dσ	dσ	VERB
ejpam-2648	303	61	n	n	CCONJ
ejpam-2648	303	62	(	(	PUNCT
ejpam-2648	303	63	<	<	X
ejpam-2648	303	64	xyz	xyz	X
ejpam-2648	303	65	>	>	PUNCT
ejpam-2648	303	66	)	)	PUNCT
ejpam-2648	304	1	=	=	SYM
ejpam-2648	304	2	∑	∑	PUNCT
ejpam-2648	304	3	i+j+h	i+j+h	X
ejpam-2648	304	4	=	=	PRON
ejpam-2648	304	5	n	n	NOUN
ejpam-2648	304	6	<	<	X
ejpam-2648	304	7	dσ	dσ	PROPN
ejpam-2648	304	8	i	i	PRON
ejpam-2648	304	9	(	(	PUNCT
ejpam-2648	304	10	x)d−σj	x)d−σj	X
ejpam-2648	304	11	(	(	PUNCT
ejpam-2648	304	12	y)dσ	y)dσ	PROPN
ejpam-2648	304	13	h(z	h(z	NOUN
ejpam-2648	304	14	)	)	PUNCT
ejpam-2648	304	15	>	>	PUNCT
ejpam-2648	304	16	,	,	PUNCT
ejpam-2648	304	17	(	(	PUNCT
ejpam-2648	304	18	x	x	X
ejpam-2648	304	19	,	,	PUNCT
ejpam-2648	304	20	z	z	PROPN
ejpam-2648	304	21	∈	∈	PROPN
ejpam-2648	304	22	aσ	aσ	NOUN
ejpam-2648	304	23	,	,	PUNCT
ejpam-2648	304	24	y	y	PROPN
ejpam-2648	304	25	∈	∈	PROPN
ejpam-2648	304	26	a−σ	a−σ	NOUN
ejpam-2648	304	27	,	,	PUNCT
ejpam-2648	304	28	n	n	NOUN
ejpam-2648	304	29	=	=	SYM
ejpam-2648	304	30	0	0	NUM
ejpam-2648	304	31	,	,	PUNCT
ejpam-2648	304	32	1	1	NUM
ejpam-2648	304	33	,	,	PUNCT
ejpam-2648	304	34	2	2	NUM
ejpam-2648	304	35	,	,	PUNCT
ejpam-2648	304	36	...	...	PUNCT
ejpam-2648	304	37	with	with	ADP
ejpam-2648	304	38	dσ	dσ	PROPN
ejpam-2648	304	39	0	0	NUM
ejpam-2648	304	40	=	=	SYM
ejpam-2648	304	41	idaσ	idaσ	PROPN
ejpam-2648	304	42	.	.	PUNCT
ejpam-2648	305	1	corollary	corollary	ADJ
ejpam-2648	305	2	3	3	X
ejpam-2648	305	3	.	.	PUNCT
ejpam-2648	306	1	let	let	VERB
ejpam-2648	306	2	{	{	PUNCT
ejpam-2648	306	3	dn	dn	VERB
ejpam-2648	306	4	=	=	SYM
ejpam-2648	306	5	(	(	PUNCT
ejpam-2648	306	6	d+	d+	X
ejpam-2648	306	7	n	n	X
ejpam-2648	306	8	,	,	PUNCT
ejpam-2648	306	9	d	d	PROPN
ejpam-2648	306	10	−	−	PROPN
ejpam-2648	306	11	n	n	NOUN
ejpam-2648	306	12	)	)	PUNCT
ejpam-2648	306	13	}	}	PUNCT
ejpam-2648	306	14	n≥0	n≥0	NOUN
ejpam-2648	306	15	be	be	AUX
ejpam-2648	306	16	a	a	DET
ejpam-2648	306	17	higher	high	ADJ
ejpam-2648	306	18	derivation	derivation	NOUN
ejpam-2648	306	19	on	on	ADP
ejpam-2648	306	20	a	a	DET
ejpam-2648	306	21	banach	banach	NOUN
ejpam-2648	306	22	alternative	alternative	ADJ
ejpam-2648	306	23	pair	pair	NOUN
ejpam-2648	306	24	a	a	PRON
ejpam-2648	306	25	=	=	SYM
ejpam-2648	306	26	(	(	PUNCT
ejpam-2648	306	27	a+	a+	NOUN
ejpam-2648	306	28	,	,	PUNCT
ejpam-2648	306	29	a−	a−	PROPN
ejpam-2648	306	30	)	)	PUNCT
ejpam-2648	306	31	.	.	PUNCT
ejpam-2648	307	1	if	if	SCONJ
ejpam-2648	307	2	a	a	PRON
ejpam-2648	307	3	is	be	AUX
ejpam-2648	307	4	semiprimitive	semiprimitive	ADJ
ejpam-2648	307	5	,	,	PUNCT
ejpam-2648	307	6	then	then	ADV
ejpam-2648	307	7	dσ	dσ	PROPN
ejpam-2648	307	8	k	k	PROPN
ejpam-2648	307	9	is	be	AUX
ejpam-2648	307	10	continuous	continuous	ADJ
ejpam-2648	307	11	for	for	ADP
ejpam-2648	307	12	every	every	DET
ejpam-2648	307	13	positive	positive	ADJ
ejpam-2648	307	14	integer	integer	NOUN
ejpam-2648	307	15	k.	k.	PROPN
ejpam-2648	307	16	proof	proof	PROPN
ejpam-2648	307	17	.	.	PUNCT
ejpam-2648	308	1	it	it	PRON
ejpam-2648	308	2	is	be	AUX
ejpam-2648	308	3	known	know	VERB
ejpam-2648	308	4	that	that	SCONJ
ejpam-2648	308	5	any	any	DET
ejpam-2648	308	6	alternative	alternative	ADJ
ejpam-2648	308	7	pair	pair	NOUN
ejpam-2648	308	8	a	a	PRON
ejpam-2648	308	9	=	=	SYM
ejpam-2648	308	10	(	(	PUNCT
ejpam-2648	308	11	a+	a+	NOUN
ejpam-2648	308	12	,	,	PUNCT
ejpam-2648	308	13	a−	a−	ADJ
ejpam-2648	308	14	)	)	PUNCT
ejpam-2648	308	15	gives	give	VERB
ejpam-2648	308	16	rise	rise	NOUN
ejpam-2648	308	17	to	to	ADP
ejpam-2648	308	18	a	a	DET
ejpam-2648	308	19	jordan	jordan	PROPN
ejpam-2648	308	20	pair	pair	PROPN
ejpam-2648	308	21	frequently	frequently	ADV
ejpam-2648	308	22	denoted	denote	VERB
ejpam-2648	308	23	by	by	ADP
ejpam-2648	308	24	aj	aj	PROPN
ejpam-2648	308	25	(	(	PUNCT
ejpam-2648	308	26	see	see	VERB
ejpam-2648	308	27	[	[	X
ejpam-2648	308	28	18	18	NUM
ejpam-2648	308	29	,	,	PUNCT
ejpam-2648	308	30	theorem	theorem	VERB
ejpam-2648	308	31	7.1	7.1	NUM
ejpam-2648	308	32	]	]	PUNCT
ejpam-2648	308	33	)	)	PUNCT
ejpam-2648	308	34	by	by	ADP
ejpam-2648	308	35	considering	consider	VERB
ejpam-2648	308	36	the	the	DET
ejpam-2648	308	37	quadratic	quadratic	ADJ
ejpam-2648	308	38	operators	operator	NOUN
ejpam-2648	308	39	qxy	qxy	NOUN
ejpam-2648	309	1	=	=	SYM
ejpam-2648	309	2	〈	〈	PROPN
ejpam-2648	309	3	xyx	xyx	PROPN
ejpam-2648	309	4	〉	〉	PROPN
ejpam-2648	309	5	for	for	ADP
ejpam-2648	309	6	all	all	PRON
ejpam-2648	309	7	(	(	PUNCT
ejpam-2648	309	8	x	x	NOUN
ejpam-2648	309	9	,	,	PUNCT
ejpam-2648	309	10	y	y	NOUN
ejpam-2648	309	11	)	)	PUNCT
ejpam-2648	309	12	in	in	ADP
ejpam-2648	309	13	aσ	aσ	NOUN
ejpam-2648	309	14	×a−σ	×a−σ	NOUN
ejpam-2648	309	15	.	.	PUNCT
ejpam-2648	310	1	clearlyaj	clearlyaj	NOUN
ejpam-2648	310	2	is	be	AUX
ejpam-2648	310	3	a	a	DET
ejpam-2648	310	4	banach	banach	NOUN
ejpam-2648	310	5	-	-	PUNCT
ejpam-2648	310	6	jordan	jordan	NOUN
ejpam-2648	310	7	pair	pair	PROPN
ejpam-2648	310	8	whenevera	whenevera	NOUN
ejpam-2648	310	9	is	be	AUX
ejpam-2648	310	10	a	a	DET
ejpam-2648	310	11	banach	banach	NOUN
ejpam-2648	310	12	alternative	alternative	ADJ
ejpam-2648	310	13	pair	pair	NOUN
ejpam-2648	310	14	.	.	PUNCT
ejpam-2648	311	1	by	by	ADP
ejpam-2648	311	2	[	[	X
ejpam-2648	311	3	18	18	NUM
ejpam-2648	311	4	,	,	PUNCT
ejpam-2648	311	5	7.9(1	7.9(1	NUM
ejpam-2648	311	6	)	)	PUNCT
ejpam-2648	311	7	]	]	PUNCT
ejpam-2648	311	8	,	,	PUNCT
ejpam-2648	311	9	aj	aj	PROPN
ejpam-2648	311	10	is	be	AUX
ejpam-2648	311	11	semiprimitive	semiprimitive	ADJ
ejpam-2648	311	12	if	if	SCONJ
ejpam-2648	312	1	and	and	CCONJ
ejpam-2648	312	2	only	only	ADV
ejpam-2648	312	3	if	if	SCONJ
ejpam-2648	312	4	so	so	ADV
ejpam-2648	312	5	is	be	AUX
ejpam-2648	312	6	a.	a.	NOUN
ejpam-2648	312	7	moreover	moreover	ADV
ejpam-2648	312	8	,	,	PUNCT
ejpam-2648	312	9	a	a	DET
ejpam-2648	312	10	simple	simple	ADJ
ejpam-2648	312	11	computation	computation	NOUN
ejpam-2648	312	12	enables	enable	VERB
ejpam-2648	312	13	to	to	PART
ejpam-2648	312	14	verify	verify	VERB
ejpam-2648	312	15	that	that	SCONJ
ejpam-2648	312	16	every	every	DET
ejpam-2648	312	17	higher	high	ADJ
ejpam-2648	312	18	derivation	derivation	NOUN
ejpam-2648	312	19	{	{	PUNCT
ejpam-2648	312	20	dn	dn	NOUN
ejpam-2648	312	21	=	=	SYM
ejpam-2648	312	22	(	(	PUNCT
ejpam-2648	312	23	d+	d+	X
ejpam-2648	312	24	n	n	X
ejpam-2648	312	25	,	,	PUNCT
ejpam-2648	312	26	d	d	PROPN
ejpam-2648	312	27	−	−	PROPN
ejpam-2648	312	28	n	n	PROPN
ejpam-2648	312	29	)	)	PUNCT
ejpam-2648	312	30	}	}	PUNCT
ejpam-2648	312	31	on	on	ADP
ejpam-2648	312	32	a	a	DET
ejpam-2648	312	33	induces	induce	NOUN
ejpam-2648	312	34	a	a	DET
ejpam-2648	312	35	higher	high	ADJ
ejpam-2648	312	36	derivation	derivation	NOUN
ejpam-2648	312	37	on	on	ADP
ejpam-2648	312	38	aj	aj	PROPN
ejpam-2648	312	39	with	with	ADP
ejpam-2648	312	40	respect	respect	NOUN
ejpam-2648	312	41	to	to	ADP
ejpam-2648	312	42	its	its	PRON
ejpam-2648	312	43	triple	triple	ADJ
ejpam-2648	312	44	product	product	NOUN
ejpam-2648	312	45	defined	define	VERB
ejpam-2648	312	46	by	by	ADP
ejpam-2648	312	47	{	{	PUNCT
ejpam-2648	312	48	x	x	PROPN
ejpam-2648	312	49	,	,	PUNCT
ejpam-2648	312	50	y	y	PROPN
ejpam-2648	312	51	,	,	PUNCT
ejpam-2648	312	52	z	z	NOUN
ejpam-2648	312	53	}	}	PUNCT
ejpam-2648	312	54	=	=	SYM
ejpam-2648	312	55	q(x	q(x	NOUN
ejpam-2648	312	56	,	,	PUNCT
ejpam-2648	312	57	z)y	z)y	NOUN
ejpam-2648	312	58	=	=	PUNCT
ejpam-2648	312	59	〈	〈	PROPN
ejpam-2648	312	60	xyz〉+	xyz〉+	PROPN
ejpam-2648	312	61	〈	〈	PROPN
ejpam-2648	312	62	zyx	zyx	PROPN
ejpam-2648	312	63	〉	〉	PROPN
ejpam-2648	312	64	for	for	ADP
ejpam-2648	312	65	all	all	DET
ejpam-2648	312	66	(	(	PUNCT
ejpam-2648	312	67	x	x	NOUN
ejpam-2648	312	68	,	,	PUNCT
ejpam-2648	312	69	y	y	PROPN
ejpam-2648	312	70	,	,	PUNCT
ejpam-2648	312	71	z	z	NOUN
ejpam-2648	312	72	)	)	PUNCT
ejpam-2648	312	73	in	in	ADP
ejpam-2648	312	74	aσ	aσ	ADP
ejpam-2648	312	75	×a−σ	×a−σ	NOUN
ejpam-2648	312	76	×aσ	×aσ	PROPN
ejpam-2648	312	77	.	.	PUNCT
ejpam-2648	313	1	actually	actually	ADV
ejpam-2648	313	2	,	,	PUNCT
ejpam-2648	313	3	theorem	theorem	VERB
ejpam-2648	313	4	2	2	NUM
ejpam-2648	313	5	applies	apply	VERB
ejpam-2648	313	6	to	to	PART
ejpam-2648	313	7	deduce	deduce	VERB
ejpam-2648	313	8	that	that	SCONJ
ejpam-2648	313	9	dσ	dσ	PROPN
ejpam-2648	313	10	n	n	PRON
ejpam-2648	313	11	is	be	AUX
ejpam-2648	313	12	continuous	continuous	ADJ
ejpam-2648	313	13	for	for	ADP
ejpam-2648	313	14	every	every	DET
ejpam-2648	313	15	natural	natural	ADJ
ejpam-2648	313	16	number	number	NOUN
ejpam-2648	313	17	n.	n.	NOUN
ejpam-2648	313	18	following	follow	VERB
ejpam-2648	313	19	[	[	X
ejpam-2648	313	20	4	4	NUM
ejpam-2648	313	21	]	]	PUNCT
ejpam-2648	313	22	,	,	PUNCT
ejpam-2648	313	23	we	we	PRON
ejpam-2648	313	24	mean	mean	VERB
ejpam-2648	313	25	by	by	ADP
ejpam-2648	313	26	a	a	DET
ejpam-2648	313	27	higher	high	ADJ
ejpam-2648	313	28	derivation	derivation	NOUN
ejpam-2648	313	29	on	on	ADP
ejpam-2648	313	30	a	a	DET
ejpam-2648	313	31	jb∗−triple	jb∗−triple	NOUN
ejpam-2648	313	32	e	e	NOUN
ejpam-2648	313	33	,	,	PUNCT
ejpam-2648	313	34	a	a	DET
ejpam-2648	313	35	sequence	sequence	NOUN
ejpam-2648	313	36	{	{	PUNCT
ejpam-2648	313	37	δn}n≥0	δn}n≥0	NOUN
ejpam-2648	313	38	of	of	ADP
ejpam-2648	313	39	linear	linear	PROPN
ejpam-2648	313	40	operators	operator	NOUN
ejpam-2648	313	41	δk	δk	PRON
ejpam-2648	313	42	:	:	PUNCT
ejpam-2648	313	43	e	e	X
ejpam-2648	313	44	−→	−→	NOUN
ejpam-2648	313	45	e	e	NOUN
ejpam-2648	313	46	satisfying	satisfy	VERB
ejpam-2648	313	47	δn({x	δn({x	NOUN
ejpam-2648	313	48	,	,	PUNCT
ejpam-2648	313	49	y	y	PROPN
ejpam-2648	313	50	,	,	PUNCT
ejpam-2648	313	51	z	z	NOUN
ejpam-2648	313	52	}	}	PUNCT
ejpam-2648	313	53	)	)	PUNCT
ejpam-2648	313	54	=	=	SYM
ejpam-2648	313	55	∑	∑	PUNCT
ejpam-2648	313	56	i+j+k	i+j+k	NOUN
ejpam-2648	313	57	=	=	SYM
ejpam-2648	313	58	n	n	PROPN
ejpam-2648	313	59	{	{	PUNCT
ejpam-2648	313	60	δix	δix	NOUN
ejpam-2648	313	61	,	,	PUNCT
ejpam-2648	313	62	δjy	δjy	NOUN
ejpam-2648	313	63	,	,	PUNCT
ejpam-2648	313	64	δkz	δkz	PROPN
ejpam-2648	313	65	}	}	PUNCT
ejpam-2648	313	66	,	,	PUNCT
ejpam-2648	313	67	for	for	ADP
ejpam-2648	313	68	all	all	DET
ejpam-2648	313	69	x	x	NOUN
ejpam-2648	313	70	,	,	PUNCT
ejpam-2648	313	71	y	y	PROPN
ejpam-2648	313	72	,	,	PUNCT
ejpam-2648	313	73	z	z	NOUN
ejpam-2648	313	74	in	in	ADP
ejpam-2648	313	75	e	e	NOUN
ejpam-2648	313	76	,	,	PUNCT
ejpam-2648	313	77	where	where	SCONJ
ejpam-2648	313	78	δ0	δ0	NOUN
ejpam-2648	313	79	=	=	NOUN
ejpam-2648	313	80	ide	ide	NOUN
ejpam-2648	313	81	.	.	PUNCT
ejpam-2648	314	1	corollary	corollary	ADJ
ejpam-2648	314	2	4	4	NUM
ejpam-2648	314	3	.	.	PUNCT
ejpam-2648	315	1	any	any	DET
ejpam-2648	315	2	higher	high	ADJ
ejpam-2648	315	3	derivation	derivation	NOUN
ejpam-2648	315	4	{	{	PUNCT
ejpam-2648	315	5	δn}n≥0	δn}n≥0	NOUN
ejpam-2648	315	6	on	on	ADP
ejpam-2648	315	7	a	a	DET
ejpam-2648	315	8	jb∗-triple	jb∗-triple	NOUN
ejpam-2648	315	9	e	e	NOUN
ejpam-2648	315	10	is	be	AUX
ejpam-2648	315	11	continuous	continuous	ADJ
ejpam-2648	315	12	.	.	PUNCT
ejpam-2648	316	1	proof	proof	NOUN
ejpam-2648	316	2	.	.	PUNCT
ejpam-2648	317	1	since	since	SCONJ
ejpam-2648	317	2	every	every	DET
ejpam-2648	317	3	jb∗−triple	jb∗−triple	NOUN
ejpam-2648	317	4	e	e	NOUN
ejpam-2648	317	5	gives	give	VERB
ejpam-2648	317	6	rise	rise	NOUN
ejpam-2648	317	7	to	to	ADP
ejpam-2648	317	8	a	a	DET
ejpam-2648	317	9	complex	complex	ADJ
ejpam-2648	317	10	semiprimitive	semiprimitive	ADJ
ejpam-2648	317	11	banach	banach	NOUN
ejpam-2648	317	12	-	-	PUNCT
ejpam-2648	317	13	jordan	jordan	NOUN
ejpam-2648	317	14	pair	pair	PROPN
ejpam-2648	317	15	v	v	NOUN
ejpam-2648	317	16	=	=	PUNCT
ejpam-2648	317	17	(	(	PUNCT
ejpam-2648	317	18	v	v	ADP
ejpam-2648	317	19	+	+	NOUN
ejpam-2648	317	20	,	,	PUNCT
ejpam-2648	317	21	v	v	ADP
ejpam-2648	317	22	−	−	NOUN
ejpam-2648	317	23	)	)	PUNCT
ejpam-2648	317	24	,	,	PUNCT
ejpam-2648	317	25	where	where	SCONJ
ejpam-2648	317	26	v	v	NOUN
ejpam-2648	317	27	+	+	NOUN
ejpam-2648	317	28	=	=	SYM
ejpam-2648	317	29	e	e	NOUN
ejpam-2648	317	30	as	as	ADP
ejpam-2648	317	31	vector	vector	NOUN
ejpam-2648	317	32	space	space	NOUN
ejpam-2648	317	33	and	and	CCONJ
ejpam-2648	317	34	v	v	NOUN
ejpam-2648	317	35	−	−	PROPN
ejpam-2648	317	36	is	be	AUX
ejpam-2648	317	37	the	the	DET
ejpam-2648	317	38	conjugate	conjugate	ADJ
ejpam-2648	317	39	complex	complex	ADJ
ejpam-2648	317	40	vector	vector	NOUN
ejpam-2648	317	41	space	space	NOUN
ejpam-2648	317	42	of	of	ADP
ejpam-2648	317	43	e	e	PROPN
ejpam-2648	317	44	that	that	PRON
ejpam-2648	317	45	is	be	AUX
ejpam-2648	317	46	the	the	DET
ejpam-2648	317	47	vector	vector	NOUN
ejpam-2648	317	48	space	space	NOUN
ejpam-2648	317	49	with	with	ADP
ejpam-2648	317	50	the	the	DET
ejpam-2648	317	51	new	new	ADJ
ejpam-2648	317	52	scalar	scalar	ADJ
ejpam-2648	317	53	multiplication	multiplication	NOUN
ejpam-2648	317	54	λ.x	λ.x	PROPN
ejpam-2648	317	55	=	=	SYM
ejpam-2648	317	56	λx	λx	PROPN
ejpam-2648	317	57	for	for	ADP
ejpam-2648	317	58	x	x	PROPN
ejpam-2648	317	59	∈	∈	PROPN
ejpam-2648	317	60	e	e	NOUN
ejpam-2648	317	61	and	and	CCONJ
ejpam-2648	317	62	λ	λ	PROPN
ejpam-2648	317	63	∈	∈	PROPN
ejpam-2648	317	64	c.	c.	NOUN
ejpam-2648	317	65	moreover	moreover	ADV
ejpam-2648	317	66	,	,	PUNCT
ejpam-2648	317	67	{	{	PUNCT
ejpam-2648	317	68	δn}n≥0	δn}n≥0	NOUN
ejpam-2648	317	69	defines	define	VERB
ejpam-2648	317	70	a	a	DET
ejpam-2648	317	71	higher	high	ADJ
ejpam-2648	317	72	derivation	derivation	NOUN
ejpam-2648	317	73	{	{	PUNCT
ejpam-2648	317	74	(	(	PUNCT
ejpam-2648	317	75	δn	δn	NOUN
ejpam-2648	317	76	,	,	PUNCT
ejpam-2648	317	77	δn)}n≥0	δn)}n≥0	NOUN
ejpam-2648	317	78	on	on	ADP
ejpam-2648	317	79	the	the	DET
ejpam-2648	317	80	complex	complex	ADJ
ejpam-2648	317	81	semiprimitive	semiprimitive	ADJ
ejpam-2648	317	82	banach	banach	NOUN
ejpam-2648	317	83	-	-	PUNCT
ejpam-2648	317	84	jordan	jordan	NOUN
ejpam-2648	317	85	pair	pair	PROPN
ejpam-2648	317	86	v	v	NOUN
ejpam-2648	317	87	=	=	PUNCT
ejpam-2648	317	88	(	(	PUNCT
ejpam-2648	317	89	v	v	ADP
ejpam-2648	317	90	+	+	NOUN
ejpam-2648	317	91	,	,	PUNCT
ejpam-2648	317	92	v	v	ADP
ejpam-2648	317	93	−	−	NOUN
ejpam-2648	317	94	)	)	PUNCT
ejpam-2648	317	95	.	.	PUNCT
ejpam-2648	318	1	thus	thus	ADV
ejpam-2648	318	2	the	the	DET
ejpam-2648	318	3	continuity	continuity	NOUN
ejpam-2648	318	4	of	of	ADP
ejpam-2648	318	5	δn	δn	NOUN
ejpam-2648	318	6	holds	hold	NOUN
ejpam-2648	318	7	by	by	ADP
ejpam-2648	318	8	theorem	theorem	NOUN
ejpam-2648	318	9	2	2	NUM
ejpam-2648	318	10	.	.	PUNCT
ejpam-2648	318	11	h.	h.	PROPN
ejpam-2648	318	12	marhnine	marhnine	PROPN
ejpam-2648	318	13	,	,	PUNCT
ejpam-2648	318	14	c.	c.	PROPN
ejpam-2648	318	15	zarhouti	zarhouti	PROPN
ejpam-2648	318	16	/	/	SYM
ejpam-2648	318	17	eur	eur	PROPN
ejpam-2648	318	18	.	.	PUNCT
ejpam-2648	319	1	j.	j.	PROPN
ejpam-2648	319	2	pure	pure	PROPN
ejpam-2648	319	3	appl	appl	PROPN
ejpam-2648	319	4	.	.	PROPN
ejpam-2648	319	5	math	math	PROPN
ejpam-2648	319	6	,	,	PUNCT
ejpam-2648	319	7	10	10	NUM
ejpam-2648	319	8	(	(	PUNCT
ejpam-2648	319	9	4	4	NUM
ejpam-2648	319	10	)	)	PUNCT
ejpam-2648	319	11	(	(	PUNCT
ejpam-2648	319	12	2017	2017	NUM
ejpam-2648	319	13	)	)	PUNCT
ejpam-2648	319	14	,	,	PUNCT
ejpam-2648	319	15	749	749	NUM
ejpam-2648	319	16	-	-	SYM
ejpam-2648	319	17	762	762	NUM
ejpam-2648	319	18	761	761	NUM
ejpam-2648	319	19	references	reference	NOUN
ejpam-2648	319	20	[	[	X
ejpam-2648	319	21	1	1	NUM
ejpam-2648	319	22	]	]	PUNCT
ejpam-2648	319	23	j.	j.	PROPN
ejpam-2648	319	24	anquela	anquela	PROPN
ejpam-2648	319	25	and	and	CCONJ
ejpam-2648	319	26	t.	t.	PROPN
ejpam-2648	319	27	cortes	corte	NOUN
ejpam-2648	319	28	,	,	PUNCT
ejpam-2648	319	29	primitive	primitive	ADJ
ejpam-2648	319	30	jordan	jordan	PROPN
ejpam-2648	319	31	pairs	pair	NOUN
ejpam-2648	319	32	and	and	CCONJ
ejpam-2648	319	33	triple	triple	ADJ
ejpam-2648	319	34	systems	system	NOUN
ejpam-2648	319	35	,	,	PUNCT
ejpam-2648	319	36	j.	j.	PROPN
ejpam-2648	319	37	algebra	algebra	PROPN
ejpam-2648	319	38	184	184	NUM
ejpam-2648	319	39	(	(	PUNCT
ejpam-2648	319	40	1996	1996	NUM
ejpam-2648	319	41	)	)	PUNCT
ejpam-2648	319	42	,	,	PUNCT
ejpam-2648	319	43	632	632	NUM
ejpam-2648	319	44	-	-	SYM
ejpam-2648	319	45	678	678	NUM
ejpam-2648	319	46	.	.	PUNCT
ejpam-2648	320	1	[	[	X
ejpam-2648	320	2	2	2	X
ejpam-2648	320	3	]	]	PUNCT
ejpam-2648	320	4	j.	j.	PROPN
ejpam-2648	320	5	anquela	anquela	PROPN
ejpam-2648	320	6	and	and	CCONJ
ejpam-2648	320	7	t.	t.	PROPN
ejpam-2648	320	8	cortes	corte	NOUN
ejpam-2648	320	9	,	,	PUNCT
ejpam-2648	320	10	primitivity	primitivity	NOUN
ejpam-2648	320	11	in	in	ADP
ejpam-2648	320	12	jordan	jordan	PROPN
ejpam-2648	320	13	systems	systems	PROPN
ejpam-2648	320	14	is	be	AUX
ejpam-2648	320	15	ubiquitous	ubiquitous	ADJ
ejpam-2648	320	16	,	,	PUNCT
ejpam-2648	320	17	j.	j.	PROPN
ejpam-2648	320	18	algebra	algebra	PROPN
ejpam-2648	320	19	202	202	NUM
ejpam-2648	320	20	(	(	PUNCT
ejpam-2648	320	21	1998	1998	NUM
ejpam-2648	320	22	)	)	PUNCT
ejpam-2648	320	23	,	,	PUNCT
ejpam-2648	320	24	295	295	NUM
ejpam-2648	320	25	-	-	SYM
ejpam-2648	320	26	314	314	NUM
ejpam-2648	320	27	.	.	PUNCT
ejpam-2648	321	1	[	[	X
ejpam-2648	321	2	3	3	X
ejpam-2648	321	3	]	]	X
ejpam-2648	321	4	j.	j.	PROPN
ejpam-2648	321	5	anquela	anquela	PROPN
ejpam-2648	321	6	,	,	PUNCT
ejpam-2648	321	7	t.	t.	NOUN
ejpam-2648	321	8	cortes	corte	NOUN
ejpam-2648	321	9	,	,	PUNCT
ejpam-2648	321	10	and	and	CCONJ
ejpam-2648	321	11	f.	f.	PROPN
ejpam-2648	321	12	montaner	montaner	PROPN
ejpam-2648	321	13	,	,	PUNCT
ejpam-2648	321	14	on	on	ADP
ejpam-2648	321	15	primitive	primitive	ADJ
ejpam-2648	321	16	jordan	jordan	PROPN
ejpam-2648	321	17	algebras	algebras	PROPN
ejpam-2648	321	18	,	,	PUNCT
ejpam-2648	321	19	j.	j.	PROPN
ejpam-2648	321	20	algebra	algebra	PROPN
ejpam-2648	321	21	163	163	NUM
ejpam-2648	321	22	(	(	PUNCT
ejpam-2648	321	23	1998	1998	NUM
ejpam-2648	321	24	)	)	PUNCT
ejpam-2648	321	25	,	,	PUNCT
ejpam-2648	321	26	663	663	NUM
ejpam-2648	321	27	-	-	SYM
ejpam-2648	321	28	674	674	NUM
ejpam-2648	321	29	.	.	PUNCT
ejpam-2648	322	1	[	[	X
ejpam-2648	322	2	4	4	X
ejpam-2648	322	3	]	]	PUNCT
ejpam-2648	322	4	t.	t.	PROPN
ejpam-2648	322	5	j.	j.	PROPN
ejpam-2648	322	6	barton	barton	PROPN
ejpam-2648	322	7	and	and	CCONJ
ejpam-2648	322	8	y.	y.	PROPN
ejpam-2648	322	9	friedman	friedman	PROPN
ejpam-2648	322	10	,	,	PUNCT
ejpam-2648	322	11	bounded	bounded	ADJ
ejpam-2648	322	12	derivations	derivation	NOUN
ejpam-2648	322	13	on	on	ADP
ejpam-2648	322	14	jb∗−triples	jb∗−triples	PROPN
ejpam-2648	322	15	,	,	PUNCT
ejpam-2648	322	16	quart	quart	NOUN
ejpam-2648	322	17	.	.	PUNCT
ejpam-2648	323	1	j.	j.	PROPN
ejpam-2648	323	2	math	math	PROPN
ejpam-2648	323	3	.	.	PUNCT
ejpam-2648	324	1	41	41	NUM
ejpam-2648	324	2	(	(	PUNCT
ejpam-2648	324	3	1990	1990	NUM
ejpam-2648	324	4	)	)	PUNCT
ejpam-2648	324	5	,	,	PUNCT
ejpam-2648	324	6	255	255	NUM
ejpam-2648	324	7	-	-	SYM
ejpam-2648	324	8	268	268	NUM
ejpam-2648	324	9	.	.	PUNCT
ejpam-2648	325	1	[	[	X
ejpam-2648	325	2	5	5	NUM
ejpam-2648	325	3	]	]	X
ejpam-2648	325	4	p.e	p.e	PROPN
ejpam-2648	325	5	.	.	PROPN
ejpam-2648	325	6	bland	bland	ADJ
ejpam-2648	325	7	,	,	PUNCT
ejpam-2648	325	8	higher	high	ADJ
ejpam-2648	325	9	derivations	derivation	NOUN
ejpam-2648	325	10	on	on	ADP
ejpam-2648	325	11	rings	ring	NOUN
ejpam-2648	325	12	and	and	CCONJ
ejpam-2648	325	13	modules	module	NOUN
ejpam-2648	325	14	,	,	PUNCT
ejpam-2648	325	15	int	int	NOUN
ejpam-2648	325	16	.	.	PUNCT
ejpam-2648	326	1	j.	j.	PROPN
ejpam-2648	326	2	math	math	PROPN
ejpam-2648	326	3	.	.	PUNCT
ejpam-2648	327	1	sci	sci	PROPN
ejpam-2648	327	2	.	.	PROPN
ejpam-2648	327	3	15	15	NUM
ejpam-2648	327	4	(	(	PUNCT
ejpam-2648	327	5	2001	2001	NUM
ejpam-2648	327	6	)	)	PUNCT
ejpam-2648	327	7	,	,	PUNCT
ejpam-2648	327	8	2373	2373	NUM
ejpam-2648	327	9	-	-	SYM
ejpam-2648	327	10	2387	2387	NUM
ejpam-2648	327	11	.	.	PUNCT
ejpam-2648	328	1	[	[	X
ejpam-2648	328	2	6	6	NUM
ejpam-2648	328	3	]	]	X
ejpam-2648	328	4	n.	n.	PROPN
ejpam-2648	328	5	boudi	boudi	PROPN
ejpam-2648	328	6	,	,	PUNCT
ejpam-2648	328	7	h.	h.	PROPN
ejpam-2648	328	8	marhnine	marhnine	PROPN
ejpam-2648	328	9	,	,	PUNCT
ejpam-2648	328	10	and	and	CCONJ
ejpam-2648	328	11	c.	c.	PROPN
ejpam-2648	328	12	zarhouti	zarhouti	PROPN
ejpam-2648	328	13	,	,	PUNCT
ejpam-2648	328	14	additive	additive	ADJ
ejpam-2648	328	15	derivations	derivation	NOUN
ejpam-2648	328	16	on	on	ADP
ejpam-2648	328	17	jordan	jordan	PROPN
ejpam-2648	328	18	banach	banach	NOUN
ejpam-2648	328	19	pairs	pair	NOUN
ejpam-2648	328	20	,	,	PUNCT
ejpam-2648	328	21	comm	comm	NOUN
ejpam-2648	328	22	.	.	PUNCT
ejpam-2648	329	1	in	in	ADP
ejpam-2648	329	2	algebra	algebra	NOUN
ejpam-2648	329	3	,	,	PUNCT
ejpam-2648	329	4	vol	vol	NOUN
ejpam-2648	329	5	.	.	PROPN
ejpam-2648	329	6	32	32	NUM
ejpam-2648	329	7	n.	n.	NOUN
ejpam-2648	329	8	9	9	NUM
ejpam-2648	329	9	,	,	PUNCT
ejpam-2648	329	10	(	(	PUNCT
ejpam-2648	329	11	2004	2004	NUM
ejpam-2648	329	12	)	)	PUNCT
ejpam-2648	329	13	,	,	PUNCT
ejpam-2648	329	14	pp	pp	PROPN
ejpam-2648	329	15	.	.	PUNCT
ejpam-2648	329	16	3609	3609	NUM
ejpam-2648	329	17	-	-	SYM
ejpam-2648	329	18	3625	3625	NUM
ejpam-2648	329	19	.	.	PUNCT
ejpam-2648	330	1	[	[	X
ejpam-2648	330	2	7	7	X
ejpam-2648	330	3	]	]	X
ejpam-2648	330	4	w.	w.	NOUN
ejpam-2648	330	5	cortes	corte	NOUN
ejpam-2648	330	6	and	and	CCONJ
ejpam-2648	330	7	c.	c.	NOUN
ejpam-2648	330	8	haetinger	haetinger	NOUN
ejpam-2648	330	9	,	,	PUNCT
ejpam-2648	330	10	on	on	ADP
ejpam-2648	330	11	jordan	jordan	PROPN
ejpam-2648	330	12	generalized	generalize	VERB
ejpam-2648	330	13	higher	high	ADJ
ejpam-2648	330	14	derivations	derivation	NOUN
ejpam-2648	330	15	on	on	ADP
ejpam-2648	330	16	rings	ring	NOUN
ejpam-2648	330	17	,	,	PUNCT
ejpam-2648	330	18	turk	turk	PROPN
ejpam-2648	330	19	.	.	PUNCT
ejpam-2648	331	1	j.	j.	PROPN
ejpam-2648	331	2	math	math	PROPN
ejpam-2648	331	3	,	,	PUNCT
ejpam-2648	331	4	29	29	NUM
ejpam-2648	331	5	(	(	PUNCT
ejpam-2648	331	6	2005	2005	NUM
ejpam-2648	331	7	)	)	PUNCT
ejpam-2648	331	8	,	,	PUNCT
ejpam-2648	331	9	1	1	NUM
ejpam-2648	331	10	-	-	SYM
ejpam-2648	331	11	10	10	NUM
ejpam-2648	331	12	.	.	PUNCT
ejpam-2648	332	1	[	[	X
ejpam-2648	332	2	8	8	NUM
ejpam-2648	332	3	]	]	PUNCT
ejpam-2648	332	4	m.	m.	NOUN
ejpam-2648	332	5	cabrera	cabrera	PROPN
ejpam-2648	332	6	garcia	garcia	PROPN
ejpam-2648	332	7	,	,	PUNCT
ejpam-2648	332	8	a.	a.	PROPN
ejpam-2648	332	9	moreno	moreno	PROPN
ejpam-2648	332	10	galindo	galindo	PROPN
ejpam-2648	332	11	,	,	PUNCT
ejpam-2648	332	12	and	and	CCONJ
ejpam-2648	332	13	a.	a.	NOUN
ejpam-2648	332	14	rodriguez	rodriguez	NOUN
ejpam-2648	332	15	palacios	palacio	NOUN
ejpam-2648	332	16	,	,	PUNCT
ejpam-2648	332	17	zel’manov	zel’manov	PROPN
ejpam-2648	332	18	’s	’s	PART
ejpam-2648	332	19	theorem	theorem	NOUN
ejpam-2648	332	20	for	for	ADP
ejpam-2648	332	21	primitive	primitive	ADJ
ejpam-2648	332	22	banach	banach	NOUN
ejpam-2648	332	23	-	-	PUNCT
ejpam-2648	332	24	jordan	jordan	PROPN
ejpam-2648	332	25	algebras	algebras	PROPN
ejpam-2648	332	26	,	,	PUNCT
ejpam-2648	332	27	j.	j.	PROPN
ejpam-2648	332	28	london	london	PROPN
ejpam-2648	332	29	math	math	PROPN
ejpam-2648	332	30	.	.	PUNCT
ejpam-2648	333	1	soc	soc	PROPN
ejpam-2648	333	2	.	.	PUNCT
ejpam-2648	334	1	(	(	PUNCT
ejpam-2648	334	2	2	2	X
ejpam-2648	334	3	)	)	PUNCT
ejpam-2648	334	4	57	57	NUM
ejpam-2648	334	5	(	(	PUNCT
ejpam-2648	334	6	1998	1998	NUM
ejpam-2648	334	7	)	)	PUNCT
ejpam-2648	334	8	231244	231244	NUM
ejpam-2648	334	9	.	.	PUNCT
ejpam-2648	335	1	[	[	X
ejpam-2648	335	2	9	9	NUM
ejpam-2648	335	3	]	]	PUNCT
ejpam-2648	335	4	a.	a.	NOUN
ejpam-2648	335	5	d’amour	d’amour	PRON
ejpam-2648	335	6	ant	ant	PROPN
ejpam-2648	335	7	k.	k.	PROPN
ejpam-2648	335	8	mccrimmon	mccrimmon	PROPN
ejpam-2648	335	9	,	,	PUNCT
ejpam-2648	335	10	the	the	DET
ejpam-2648	335	11	local	local	ADJ
ejpam-2648	335	12	algebra	algebra	NOUN
ejpam-2648	335	13	of	of	ADP
ejpam-2648	335	14	jordan	jordan	PROPN
ejpam-2648	335	15	systems	systems	PROPN
ejpam-2648	335	16	,	,	PUNCT
ejpam-2648	335	17	j.	j.	PROPN
ejpam-2648	335	18	algebra	algebra	PROPN
ejpam-2648	335	19	177	177	NUM
ejpam-2648	335	20	(	(	PUNCT
ejpam-2648	335	21	1995	1995	NUM
ejpam-2648	335	22	)	)	PUNCT
ejpam-2648	335	23	,	,	PUNCT
ejpam-2648	335	24	199	199	NUM
ejpam-2648	335	25	-	-	SYM
ejpam-2648	335	26	239	239	NUM
ejpam-2648	335	27	.	.	PUNCT
ejpam-2648	336	1	[	[	X
ejpam-2648	336	2	10	10	NUM
ejpam-2648	336	3	]	]	PUNCT
ejpam-2648	336	4	a.	a.	NOUN
ejpam-2648	336	5	fernandez	fernandez	PROPN
ejpam-2648	336	6	lopez	lopez	PROPN
ejpam-2648	336	7	,	,	PUNCT
ejpam-2648	336	8	h.	h.	PROPN
ejpam-2648	336	9	marhnine	marhnine	PROPN
ejpam-2648	336	10	and	and	CCONJ
ejpam-2648	336	11	c.	c.	PROPN
ejpam-2648	336	12	zarhouti	zarhouti	PROPN
ejpam-2648	336	13	,	,	PUNCT
ejpam-2648	336	14	derivations	derivation	NOUN
ejpam-2648	336	15	on	on	ADP
ejpam-2648	336	16	banach	banach	NOUN
ejpam-2648	336	17	-	-	PUNCT
ejpam-2648	336	18	jordan	jordan	NOUN
ejpam-2648	336	19	pairs	pair	NOUN
ejpam-2648	336	20	,	,	PUNCT
ejpam-2648	336	21	quart	quart	NOUN
ejpam-2648	336	22	.	.	PUNCT
ejpam-2648	337	1	j.	j.	PROPN
ejpam-2648	337	2	math	math	PROPN
ejpam-2648	337	3	.	.	PUNCT
ejpam-2648	338	1	3	3	NUM
ejpam-2648	338	2	(	(	PUNCT
ejpam-2648	338	3	2001	2001	NUM
ejpam-2648	338	4	)	)	PUNCT
ejpam-2648	338	5	,	,	PUNCT
ejpam-2648	338	6	1	1	NUM
ejpam-2648	338	7	-	-	SYM
ejpam-2648	338	8	15	15	NUM
ejpam-2648	338	9	.	.	PUNCT
ejpam-2648	339	1	[	[	X
ejpam-2648	339	2	11	11	NUM
ejpam-2648	339	3	]	]	X
ejpam-2648	339	4	c.	c.	NOUN
ejpam-2648	339	5	haetinger	haetinger	NOUN
ejpam-2648	339	6	,	,	PUNCT
ejpam-2648	339	7	higher	high	ADJ
ejpam-2648	339	8	derivations	derivation	NOUN
ejpam-2648	339	9	on	on	ADP
ejpam-2648	339	10	lie	lie	NOUN
ejpam-2648	339	11	ideals	ideal	NOUN
ejpam-2648	339	12	,	,	PUNCT
ejpam-2648	339	13	tendencias	tendencias	PROPN
ejpam-2648	339	14	em	em	PROPN
ejpam-2648	339	15	matematica	matematica	PROPN
ejpam-2648	339	16	e	e	PROPN
ejpam-2648	339	17	computacional	computacional	ADJ
ejpam-2648	339	18	3	3	NUM
ejpam-2648	339	19	(	(	PUNCT
ejpam-2648	339	20	2002),141	2002),141	NOUN
ejpam-2648	339	21	-	-	SYM
ejpam-2648	339	22	145	145	NUM
ejpam-2648	339	23	.	.	PUNCT
ejpam-2648	340	1	[	[	X
ejpam-2648	340	2	12	12	NUM
ejpam-2648	340	3	]	]	X
ejpam-2648	340	4	h.	h.	PROPN
ejpam-2648	340	5	hasse	hasse	PROPN
ejpam-2648	340	6	and	and	CCONJ
ejpam-2648	340	7	f.	f.	PROPN
ejpam-2648	340	8	k.	k.	PROPN
ejpam-2648	340	9	shmidt	shmidt	PROPN
ejpam-2648	340	10	,	,	PUNCT
ejpam-2648	340	11	noch	noch	PROPN
ejpam-2648	340	12	eine	eine	PROPN
ejpam-2648	340	13	begrüdung	begrüdung	PUNCT
ejpam-2648	340	14	der	der	PROPN
ejpam-2648	340	15	theorie	theorie	PROPN
ejpam-2648	340	16	der	der	PROPN
ejpam-2648	340	17	höheren	höheren	PROPN
ejpam-2648	340	18	differential	differential	PROPN
ejpam-2648	340	19	quotienten	quotienten	PROPN
ejpam-2648	340	20	einem	einem	PROPN
ejpam-2648	340	21	algebraischen	algebraischen	ADV
ejpam-2648	340	22	funtionenkörper	funtionenkörper	PRON
ejpam-2648	340	23	einer	einer	PROPN
ejpam-2648	340	24	unbestimmeten	unbestimmeten	PROPN
ejpam-2648	340	25	,	,	PUNCT
ejpam-2648	340	26	j.	j.	PROPN
ejpam-2648	340	27	reine	reine	PROPN
ejpam-2648	340	28	angew	angew	PROPN
ejpam-2648	340	29	math	math	PROPN
ejpam-2648	340	30	.	.	PUNCT
ejpam-2648	341	1	177	177	NUM
ejpam-2648	341	2	(	(	PUNCT
ejpam-2648	341	3	1937	1937	NUM
ejpam-2648	341	4	)	)	PUNCT
ejpam-2648	341	5	,	,	PUNCT
ejpam-2648	341	6	215	215	NUM
ejpam-2648	341	7	-	-	SYM
ejpam-2648	341	8	237	237	NUM
ejpam-2648	341	9	.	.	PUNCT
ejpam-2648	342	1	[	[	X
ejpam-2648	342	2	13	13	NUM
ejpam-2648	342	3	]	]	PUNCT
ejpam-2648	342	4	s.	s.	PROPN
ejpam-2648	342	5	hejazian	hejazian	PROPN
ejpam-2648	342	6	and	and	CCONJ
ejpam-2648	342	7	l.	l.	PROPN
ejpam-2648	342	8	shatery	shatery	PROPN
ejpam-2648	342	9	,	,	PUNCT
ejpam-2648	342	10	automatic	automatic	ADJ
ejpam-2648	342	11	continuity	continuity	NOUN
ejpam-2648	342	12	of	of	ADP
ejpam-2648	342	13	higher	high	ADJ
ejpam-2648	342	14	derivations	derivation	NOUN
ejpam-2648	342	15	on	on	ADP
ejpam-2648	342	16	jb∗−algebras	jb∗−algebras	PROPN
ejpam-2648	342	17	,	,	PUNCT
ejpam-2648	342	18	bull	bull	NOUN
ejpam-2648	342	19	.	.	PUNCT
ejpam-2648	343	1	iranian	iranian	ADJ
ejpam-2648	343	2	math	math	PROPN
ejpam-2648	343	3	.	.	PUNCT
ejpam-2648	344	1	soc	soc	PROPN
ejpam-2648	344	2	.	.	PUNCT
ejpam-2648	345	1	vol	vol	NOUN
ejpam-2648	345	2	.	.	PROPN
ejpam-2648	346	1	33	33	NUM
ejpam-2648	346	2	,	,	PUNCT
ejpam-2648	346	3	1	1	NUM
ejpam-2648	346	4	(	(	PUNCT
ejpam-2648	346	5	2007	2007	NUM
ejpam-2648	346	6	)	)	PUNCT
ejpam-2648	346	7	,	,	PUNCT
ejpam-2648	346	8	pp	pp	ADP
ejpam-2648	346	9	11	11	NUM
ejpam-2648	346	10	-	-	SYM
ejpam-2648	346	11	23	23	NUM
ejpam-2648	346	12	.	.	PUNCT
ejpam-2648	347	1	[	[	X
ejpam-2648	347	2	14	14	NUM
ejpam-2648	347	3	]	]	X
ejpam-2648	347	4	g.	g.	PROPN
ejpam-2648	347	5	hessenberger	hessenberger	PROPN
ejpam-2648	347	6	,	,	PUNCT
ejpam-2648	347	7	riesz	riesz	VERB
ejpam-2648	347	8	und	und	NOUN
ejpam-2648	347	9	fredholm	fredholm	NOUN
ejpam-2648	347	10	-	-	PUNCT
ejpam-2648	347	11	theorie	theorie	NOUN
ejpam-2648	347	12	in	in	ADP
ejpam-2648	347	13	banach	banach	NOUN
ejpam-2648	347	14	-	-	PUNCT
ejpam-2648	347	15	jordan	jordan	PROPN
ejpam-2648	347	16	systemen	systemen	PROPN
ejpam-2648	347	17	,	,	PUNCT
ejpam-2648	347	18	universität	universität	PROPN
ejpam-2648	347	19	innsbruck	innsbruck	PROPN
ejpam-2648	347	20	,	,	PUNCT
ejpam-2648	347	21	1994	1994	NUM
ejpam-2648	347	22	.	.	PUNCT
ejpam-2648	348	1	[	[	X
ejpam-2648	348	2	15	15	NUM
ejpam-2648	348	3	]	]	X
ejpam-2648	348	4	n.	n.	PROPN
ejpam-2648	348	5	p.	p.	PROPN
ejpam-2648	348	6	jewell	jewell	PROPN
ejpam-2648	348	7	,	,	PUNCT
ejpam-2648	348	8	continuity	continuity	NOUN
ejpam-2648	348	9	of	of	ADP
ejpam-2648	348	10	modules	module	NOUN
ejpam-2648	348	11	and	and	CCONJ
ejpam-2648	348	12	higher	high	ADJ
ejpam-2648	348	13	derivations	derivation	NOUN
ejpam-2648	348	14	,	,	PUNCT
ejpam-2648	348	15	pacific	pacific	PROPN
ejpam-2648	348	16	j.	j.	PROPN
ejpam-2648	348	17	math	math	PROPN
ejpam-2648	348	18	.	.	PUNCT
ejpam-2648	349	1	68	68	NUM
ejpam-2648	349	2	(	(	PUNCT
ejpam-2648	349	3	1977	1977	NUM
ejpam-2648	349	4	)	)	PUNCT
ejpam-2648	349	5	,	,	PUNCT
ejpam-2648	349	6	91	91	NUM
ejpam-2648	349	7	-	-	SYM
ejpam-2648	349	8	98	98	NUM
ejpam-2648	349	9	.	.	PUNCT
ejpam-2648	350	1	[	[	X
ejpam-2648	350	2	16	16	NUM
ejpam-2648	350	3	]	]	X
ejpam-2648	350	4	n.	n.	PROPN
ejpam-2648	350	5	p.	p.	PROPN
ejpam-2648	350	6	jewell	jewell	PROPN
ejpam-2648	350	7	and	and	CCONJ
ejpam-2648	350	8	a.	a.	PROPN
ejpam-2648	350	9	m.	m.	PROPN
ejpam-2648	350	10	sinclair	sinclair	PROPN
ejpam-2648	350	11	,	,	PUNCT
ejpam-2648	350	12	epimorphisms	epimorphism	NOUN
ejpam-2648	350	13	and	and	CCONJ
ejpam-2648	350	14	derivations	derivation	NOUN
ejpam-2648	350	15	on	on	ADP
ejpam-2648	350	16	l1(0	l1(0	PROPN
ejpam-2648	350	17	,	,	PUNCT
ejpam-2648	350	18	1	1	NUM
ejpam-2648	350	19	)	)	PUNCT
ejpam-2648	350	20	are	be	AUX
ejpam-2648	350	21	continuous	continuous	ADJ
ejpam-2648	350	22	,	,	PUNCT
ejpam-2648	350	23	bull	bull	NOUN
ejpam-2648	350	24	.	.	PUNCT
ejpam-2648	351	1	london	london	PROPN
ejpam-2648	351	2	math	math	PROPN
ejpam-2648	351	3	.	.	PUNCT
ejpam-2648	352	1	soc	soc	PROPN
ejpam-2648	352	2	.	.	PUNCT
ejpam-2648	353	1	8	8	NUM
ejpam-2648	353	2	(	(	PUNCT
ejpam-2648	353	3	1976	1976	NUM
ejpam-2648	353	4	)	)	PUNCT
ejpam-2648	353	5	135	135	NUM
ejpam-2648	353	6	-	-	SYM
ejpam-2648	353	7	139	139	NUM
ejpam-2648	353	8	.	.	PUNCT
ejpam-2648	354	1	[	[	X
ejpam-2648	354	2	17	17	NUM
ejpam-2648	354	3	]	]	X
ejpam-2648	354	4	k.w	k.w	PROPN
ejpam-2648	354	5	.	.	PROPN
ejpam-2648	354	6	jun	jun	PROPN
ejpam-2648	354	7	and	and	CCONJ
ejpam-2648	354	8	y.w	y.w	PROPN
ejpam-2648	354	9	.	.	PROPN
ejpam-2648	354	10	lee	lee	PROPN
ejpam-2648	354	11	,	,	PUNCT
ejpam-2648	354	12	the	the	DET
ejpam-2648	354	13	image	image	NOUN
ejpam-2648	354	14	of	of	ADP
ejpam-2648	354	15	a	a	DET
ejpam-2648	354	16	continuous	continuous	ADJ
ejpam-2648	354	17	strong	strong	ADJ
ejpam-2648	354	18	higher	high	ADJ
ejpam-2648	354	19	derivation	derivation	NOUN
ejpam-2648	354	20	is	be	AUX
ejpam-2648	354	21	contained	contain	VERB
ejpam-2648	354	22	in	in	ADP
ejpam-2648	354	23	the	the	DET
ejpam-2648	354	24	radical	radical	ADJ
ejpam-2648	354	25	,	,	PUNCT
ejpam-2648	354	26	bull	bull	NOUN
ejpam-2648	354	27	.	.	PUNCT
ejpam-2648	355	1	korean	korean	ADJ
ejpam-2648	355	2	math	math	PROPN
ejpam-2648	355	3	.	.	PUNCT
ejpam-2648	356	1	soc	soc	PROPN
ejpam-2648	356	2	.	.	PUNCT
ejpam-2648	357	1	33	33	NUM
ejpam-2648	357	2	(	(	PUNCT
ejpam-2648	357	3	1996	1996	NUM
ejpam-2648	357	4	)	)	PUNCT
ejpam-2648	357	5	,	,	PUNCT
ejpam-2648	357	6	229	229	NUM
ejpam-2648	357	7	-	-	SYM
ejpam-2648	357	8	232	232	NUM
ejpam-2648	357	9	.	.	PUNCT
ejpam-2648	358	1	[	[	X
ejpam-2648	358	2	18	18	NUM
ejpam-2648	358	3	]	]	X
ejpam-2648	358	4	o.	o.	NOUN
ejpam-2648	358	5	loos	loos	PROPN
ejpam-2648	358	6	,	,	PUNCT
ejpam-2648	358	7	jordan	jordan	PROPN
ejpam-2648	358	8	pairs	pair	NOUN
ejpam-2648	358	9	,	,	PUNCT
ejpam-2648	358	10	lecture	lecture	NOUN
ejpam-2648	358	11	notes	note	NOUN
ejpam-2648	358	12	in	in	ADP
ejpam-2648	358	13	mathematics	mathematic	NOUN
ejpam-2648	358	14	,	,	PUNCT
ejpam-2648	358	15	vol	vol	NOUN
ejpam-2648	358	16	460	460	NUM
ejpam-2648	358	17	,	,	PUNCT
ejpam-2648	358	18	springer	springer	NOUN
ejpam-2648	358	19	verlag	verlag	PROPN
ejpam-2648	358	20	,	,	PUNCT
ejpam-2648	358	21	new	new	PROPN
ejpam-2648	358	22	york	york	PROPN
ejpam-2648	358	23	,	,	PUNCT
ejpam-2648	358	24	1975	1975	NUM
ejpam-2648	358	25	.	.	PUNCT
ejpam-2648	359	1	[	[	X
ejpam-2648	359	2	19	19	NUM
ejpam-2648	359	3	]	]	X
ejpam-2648	359	4	o.	o.	NOUN
ejpam-2648	359	5	loos	loo	NOUN
ejpam-2648	359	6	,	,	PUNCT
ejpam-2648	359	7	recent	recent	ADJ
ejpam-2648	359	8	results	result	NOUN
ejpam-2648	359	9	on	on	ADP
ejpam-2648	359	10	finiteness	finiteness	ADJ
ejpam-2648	359	11	conditions	condition	NOUN
ejpam-2648	359	12	in	in	ADP
ejpam-2648	359	13	jordan	jordan	PROPN
ejpam-2648	359	14	pairs	pairs	PROPN
ejpam-2648	359	15	,	,	PUNCT
ejpam-2648	359	16	jordan	jordan	PROPN
ejpam-2648	359	17	algebras	algebras	PROPN
ejpam-2648	359	18	,	,	PUNCT
ejpam-2648	359	19	proceedings	proceeding	NOUN
ejpam-2648	359	20	of	of	ADP
ejpam-2648	359	21	a	a	DET
ejpam-2648	359	22	conference	conference	NOUN
ejpam-2648	359	23	in	in	ADP
ejpam-2648	359	24	overwolfach	overwolfach	NOUN
ejpam-2648	359	25	,	,	PUNCT
ejpam-2648	359	26	1992	1992	NUM
ejpam-2648	359	27	,	,	PUNCT
ejpam-2648	359	28	de	de	NOUN
ejpam-2648	359	29	gruyter	gruyter	NOUN
ejpam-2648	359	30	,	,	PUNCT
ejpam-2648	359	31	pp	pp	ADJ
ejpam-2648	359	32	.	.	PUNCT
ejpam-2648	360	1	83	83	NUM
ejpam-2648	360	2	-	-	SYM
ejpam-2648	360	3	95	95	NUM
ejpam-2648	360	4	.	.	PUNCT
ejpam-2648	361	1	h.	h.	PROPN
ejpam-2648	361	2	marhnine	marhnine	PROPN
ejpam-2648	361	3	,	,	PUNCT
ejpam-2648	361	4	c.	c.	PROPN
ejpam-2648	361	5	zarhouti	zarhouti	PROPN
ejpam-2648	361	6	/	/	SYM
ejpam-2648	361	7	eur	eur	PROPN
ejpam-2648	361	8	.	.	PUNCT
ejpam-2648	362	1	j.	j.	PROPN
ejpam-2648	362	2	pure	pure	PROPN
ejpam-2648	362	3	appl	appl	PROPN
ejpam-2648	362	4	.	.	PROPN
ejpam-2648	362	5	math	math	PROPN
ejpam-2648	362	6	,	,	PUNCT
ejpam-2648	362	7	10	10	NUM
ejpam-2648	362	8	(	(	PUNCT
ejpam-2648	362	9	4	4	NUM
ejpam-2648	362	10	)	)	PUNCT
ejpam-2648	362	11	(	(	PUNCT
ejpam-2648	362	12	2017	2017	NUM
ejpam-2648	362	13	)	)	PUNCT
ejpam-2648	362	14	,	,	PUNCT
ejpam-2648	362	15	749	749	NUM
ejpam-2648	362	16	-	-	SYM
ejpam-2648	362	17	762	762	NUM
ejpam-2648	362	18	762	762	NUM
ejpam-2648	363	1	[	[	X
ejpam-2648	363	2	20	20	NUM
ejpam-2648	363	3	]	]	PUNCT
ejpam-2648	363	4	o.	o.	NOUN
ejpam-2648	363	5	loos	loo	VERB
ejpam-2648	363	6	properly	properly	ADV
ejpam-2648	363	7	algebraic	algebraic	ADJ
ejpam-2648	363	8	and	and	CCONJ
ejpam-2648	363	9	spectrum	spectrum	NOUN
ejpam-2648	363	10	-	-	PUNCT
ejpam-2648	363	11	finite	finite	PROPN
ejpam-2648	363	12	ideals	ideal	NOUN
ejpam-2648	363	13	in	in	ADP
ejpam-2648	363	14	jordan	jordan	PROPN
ejpam-2648	363	15	systems	systems	PROPN
ejpam-2648	363	16	,	,	PUNCT
ejpam-2648	363	17	math	math	NOUN
ejpam-2648	363	18	.	.	PUNCT
ejpam-2648	364	1	proc	proc	PROPN
ejpam-2648	364	2	.	.	PUNCT
ejpam-2648	365	1	camb	camb	PROPN
ejpam-2648	365	2	.	.	PUNCT
ejpam-2648	366	1	phil	phil	PROPN
ejpam-2648	366	2	.	.	PUNCT
ejpam-2648	367	1	soc	soc	PROPN
ejpam-2648	367	2	.	.	PUNCT
ejpam-2648	368	1	(	(	PUNCT
ejpam-2648	368	2	1993	1993	NUM
ejpam-2648	368	3	)	)	PUNCT
ejpam-2648	368	4	,	,	PUNCT
ejpam-2648	368	5	114	114	NUM
ejpam-2648	368	6	,	,	PUNCT
ejpam-2648	368	7	149	149	NUM
ejpam-2648	368	8	-	-	SYM
ejpam-2648	368	9	161	161	NUM
ejpam-2648	368	10	.	.	PUNCT
ejpam-2648	369	1	[	[	X
ejpam-2648	369	2	21	21	NUM
ejpam-2648	369	3	]	]	X
ejpam-2648	369	4	o.	o.	NOUN
ejpam-2648	369	5	loos	loos	PROPN
ejpam-2648	369	6	,	,	PUNCT
ejpam-2648	369	7	bounded	bound	VERB
ejpam-2648	369	8	symmetric	symmetric	ADJ
ejpam-2648	369	9	domains	domain	NOUN
ejpam-2648	369	10	and	and	CCONJ
ejpam-2648	369	11	jordan	jordan	PROPN
ejpam-2648	369	12	pairs	pair	NOUN
ejpam-2648	369	13	,	,	PUNCT
ejpam-2648	369	14	lecture	lecture	NOUN
ejpam-2648	369	15	notes	note	NOUN
ejpam-2648	369	16	,	,	PUNCT
ejpam-2648	369	17	university	university	PROPN
ejpam-2648	369	18	of	of	ADP
ejpam-2648	369	19	california	california	PROPN
ejpam-2648	369	20	,	,	PUNCT
ejpam-2648	369	21	1975	1975	NUM
ejpam-2648	369	22	.	.	PUNCT
ejpam-2648	370	1	[	[	X
ejpam-2648	370	2	22	22	NUM
ejpam-2648	370	3	]	]	PUNCT
ejpam-2648	370	4	r.	r.	PROPN
ejpam-2648	370	5	j.	j.	PROPN
ejpam-2648	370	6	loy	loy	PROPN
ejpam-2648	370	7	,	,	PUNCT
ejpam-2648	370	8	continuity	continuity	NOUN
ejpam-2648	370	9	of	of	ADP
ejpam-2648	370	10	higher	high	ADJ
ejpam-2648	370	11	derivations	derivation	NOUN
ejpam-2648	370	12	,	,	PUNCT
ejpam-2648	370	13	proc	proc	NOUN
ejpam-2648	370	14	.	.	PUNCT
ejpam-2648	371	1	amer	amer	PROPN
ejpam-2648	371	2	.	.	PUNCT
ejpam-2648	371	3	math	math	PROPN
ejpam-2648	371	4	.	.	PUNCT
ejpam-2648	372	1	soc	soc	PROPN
ejpam-2648	372	2	.	.	PUNCT
ejpam-2648	373	1	37	37	NUM
ejpam-2648	373	2	(	(	PUNCT
ejpam-2648	373	3	1973	1973	NUM
ejpam-2648	373	4	)	)	PUNCT
ejpam-2648	373	5	505	505	NUM
ejpam-2648	373	6	-	-	SYM
ejpam-2648	373	7	510	510	NUM
ejpam-2648	373	8	.	.	PUNCT
ejpam-2648	374	1	[	[	X
ejpam-2648	374	2	23	23	NUM
ejpam-2648	374	3	]	]	X
ejpam-2648	374	4	h.	h.	PROPN
ejpam-2648	374	5	marhnine	marhnine	PROPN
ejpam-2648	374	6	,	,	PUNCT
ejpam-2648	374	7	caractérisation	caractérisation	NOUN
ejpam-2648	374	8	de	de	X
ejpam-2648	374	9	certaines	certaines	X
ejpam-2648	374	10	classes	class	NOUN
ejpam-2648	374	11	de	de	X
ejpam-2648	374	12	paires	paire	NOUN
ejpam-2648	374	13	de	de	ADP
ejpam-2648	374	14	banach	banach	NOUN
ejpam-2648	374	15	-	-	PUNCT
ejpam-2648	374	16	jordan	jordan	PROPN
ejpam-2648	374	17	,	,	PUNCT
ejpam-2648	374	18	thèse	thèse	PROPN
ejpam-2648	374	19	doctorale	doctorale	NOUN
ejpam-2648	374	20	,	,	PUNCT
ejpam-2648	374	21	université	université	ADJ
ejpam-2648	374	22	abdelmalek	abdelmalek	NOUN
ejpam-2648	374	23	essaadi	essaadi	NOUN
ejpam-2648	374	24	,	,	PUNCT
ejpam-2648	374	25	faculté	faculté	NOUN
ejpam-2648	374	26	des	des	PROPN
ejpam-2648	374	27	sciences	sciences	PROPN
ejpam-2648	374	28	de	de	PROPN
ejpam-2648	374	29	tétouan	tétouan	PROPN
ejpam-2648	374	30	,	,	PUNCT
ejpam-2648	374	31	maroc	maroc	PROPN
ejpam-2648	374	32	(	(	PUNCT
ejpam-2648	374	33	2000	2000	NUM
ejpam-2648	374	34	)	)	PUNCT
ejpam-2648	374	35	.	.	PUNCT
ejpam-2648	375	1	[	[	X
ejpam-2648	375	2	24	24	NUM
ejpam-2648	375	3	]	]	PUNCT
ejpam-2648	375	4	m.	m.	NOUN
ejpam-2648	375	5	mirzavaziri	mirzavaziri	PROPN
ejpam-2648	375	6	,	,	PUNCT
ejpam-2648	375	7	characterization	characterization	NOUN
ejpam-2648	375	8	of	of	ADP
ejpam-2648	375	9	higher	high	ADJ
ejpam-2648	375	10	derivations	derivation	NOUN
ejpam-2648	375	11	on	on	ADP
ejpam-2648	375	12	algebras	algebras	PROPN
ejpam-2648	375	13	,	,	PUNCT
ejpam-2648	375	14	comm	comm	NOUN
ejpam-2648	375	15	.	.	PUNCT
ejpam-2648	376	1	in	in	ADP
ejpam-2648	376	2	algebra	algebra	NOUN
ejpam-2648	376	3	,	,	PUNCT
ejpam-2648	376	4	38	38	NUM
ejpam-2648	376	5	(	(	PUNCT
ejpam-2648	376	6	2010	2010	NUM
ejpam-2648	376	7	)	)	PUNCT
ejpam-2648	376	8	,	,	PUNCT
ejpam-2648	376	9	no	no	DET
ejpam-2648	376	10	3	3	NUM
ejpam-2648	376	11	,	,	PUNCT
ejpam-2648	376	12	981	981	NUM
ejpam-2648	376	13	-	-	SYM
ejpam-2648	376	14	987	987	NUM
ejpam-2648	376	15	.	.	PUNCT
ejpam-2648	377	1	[	[	X
ejpam-2648	377	2	25	25	NUM
ejpam-2648	377	3	]	]	X
ejpam-2648	377	4	f.	f.	PROPN
ejpam-2648	377	5	montaner	montaner	PROPN
ejpam-2648	377	6	,	,	PUNCT
ejpam-2648	377	7	local	local	ADJ
ejpam-2648	377	8	pitheory	pitheory	NOUN
ejpam-2648	377	9	of	of	ADP
ejpam-2648	377	10	jordan	jordan	PROPN
ejpam-2648	377	11	systems	systems	PROPN
ejpam-2648	377	12	,	,	PUNCT
ejpam-2648	377	13	j.	j.	PROPN
ejpam-2648	377	14	algebra	algebra	PROPN
ejpam-2648	377	15	216	216	NUM
ejpam-2648	377	16	(	(	PUNCT
ejpam-2648	377	17	1999	1999	NUM
ejpam-2648	377	18	)	)	PUNCT
ejpam-2648	377	19	,	,	PUNCT
ejpam-2648	377	20	302	302	NUM
ejpam-2648	377	21	-	-	SYM
ejpam-2648	377	22	327	327	NUM
ejpam-2648	377	23	.	.	PUNCT
ejpam-2648	378	1	[	[	X
ejpam-2648	378	2	26	26	NUM
ejpam-2648	378	3	]	]	X
ejpam-2648	378	4	j.	j.	PROPN
ejpam-2648	378	5	m.	m.	PROPN
ejpam-2648	378	6	osborn	osborn	PROPN
ejpam-2648	378	7	and	and	CCONJ
ejpam-2648	378	8	m.	m.	PROPN
ejpam-2648	378	9	l.	l.	PROPN
ejpam-2648	378	10	racine	racine	PROPN
ejpam-2648	378	11	,	,	PUNCT
ejpam-2648	378	12	jordan	jordan	PROPN
ejpam-2648	378	13	rings	rings	PROPN
ejpam-2648	378	14	with	with	ADP
ejpam-2648	378	15	nonzero	nonzero	PROPN
ejpam-2648	378	16	socle	socle	PROPN
ejpam-2648	378	17	,	,	PUNCT
ejpam-2648	378	18	trans	trans	PROPN
ejpam-2648	378	19	.	.	PROPN
ejpam-2648	379	1	amer	amer	PROPN
ejpam-2648	379	2	.	.	PUNCT
ejpam-2648	379	3	math	math	PROPN
ejpam-2648	379	4	.	.	PUNCT
ejpam-2648	380	1	soc	soc	PROPN
ejpam-2648	380	2	.	.	PUNCT
ejpam-2648	381	1	251	251	NUM
ejpam-2648	381	2	(	(	PUNCT
ejpam-2648	381	3	1979	1979	NUM
ejpam-2648	381	4	)	)	PUNCT
ejpam-2648	381	5	,	,	PUNCT
ejpam-2648	381	6	375	375	NUM
ejpam-2648	381	7	-	-	SYM
ejpam-2648	381	8	387	387	NUM
ejpam-2648	381	9	.	.	PUNCT
ejpam-2648	382	1	[	[	X
ejpam-2648	382	2	27	27	NUM
ejpam-2648	382	3	]	]	PUNCT
ejpam-2648	382	4	a.	a.	PROPN
ejpam-2648	382	5	roy	roy	PROPN
ejpam-2648	382	6	and	and	CCONJ
ejpam-2648	382	7	r.	r.	PROPN
ejpam-2648	382	8	sridharan	sridharan	ADJ
ejpam-2648	382	9	,	,	PUNCT
ejpam-2648	382	10	higher	high	ADJ
ejpam-2648	382	11	derivations	derivation	NOUN
ejpam-2648	382	12	and	and	CCONJ
ejpam-2648	382	13	central	central	ADJ
ejpam-2648	382	14	simple	simple	ADJ
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ejpam-2648	382	16	,	,	PUNCT
ejpam-2648	382	17	nagoya	nagoya	PROPN
ejpam-2648	382	18	math	math	PROPN
ejpam-2648	382	19	.	.	PUNCT
ejpam-2648	383	1	j.	j.	PROPN
ejpam-2648	383	2	32	32	NUM
ejpam-2648	383	3	(	(	PUNCT
ejpam-2648	383	4	1968	1968	NUM
ejpam-2648	383	5	)	)	PUNCT
ejpam-2648	383	6	,	,	PUNCT
ejpam-2648	383	7	21	21	NUM
ejpam-2648	383	8	-	-	SYM
ejpam-2648	383	9	30	30	NUM
ejpam-2648	383	10	.	.	PUNCT
ejpam-2648	384	1	[	[	X
ejpam-2648	384	2	28	28	NUM
ejpam-2648	384	3	]	]	X
ejpam-2648	384	4	s.	s.	PROPN
ejpam-2648	384	5	satô	satô	PROPN
ejpam-2648	384	6	,	,	PUNCT
ejpam-2648	384	7	on	on	ADP
ejpam-2648	384	8	rings	ring	NOUN
ejpam-2648	384	9	with	with	ADP
ejpam-2648	384	10	a	a	DET
ejpam-2648	384	11	higher	high	ADJ
ejpam-2648	384	12	derivation	derivation	NOUN
ejpam-2648	384	13	,	,	PUNCT
ejpam-2648	384	14	proc	proc	NOUN
ejpam-2648	384	15	.	.	PUNCT
ejpam-2648	384	16	amer	amer	PROPN
ejpam-2648	384	17	.	.	PUNCT
ejpam-2648	384	18	math	math	PROPN
ejpam-2648	384	19	.	.	PUNCT
ejpam-2648	385	1	soc	soc	PROPN
ejpam-2648	385	2	.	.	PUNCT
ejpam-2648	386	1	30	30	NUM
ejpam-2648	386	2	(	(	PUNCT
ejpam-2648	386	3	1971	1971	NUM
ejpam-2648	386	4	)	)	PUNCT
ejpam-2648	386	5	,	,	PUNCT
ejpam-2648	386	6	21	21	NUM
ejpam-2648	386	7	-	-	SYM
ejpam-2648	386	8	30	30	NUM
ejpam-2648	386	9	.	.	PUNCT
ejpam-2648	387	1	[	[	X
ejpam-2648	387	2	29	29	NUM
ejpam-2648	387	3	]	]	PUNCT
ejpam-2648	387	4	m.	m.	NOUN
ejpam-2648	387	5	p.	p.	PROPN
ejpam-2648	387	6	thomas	thomas	PROPN
ejpam-2648	387	7	,	,	PUNCT
ejpam-2648	387	8	primitive	primitive	ADJ
ejpam-2648	387	9	ideals	ideal	NOUN
ejpam-2648	387	10	and	and	CCONJ
ejpam-2648	387	11	derivations	derivation	NOUN
ejpam-2648	387	12	on	on	ADP
ejpam-2648	387	13	noncommutative	noncommutative	ADJ
ejpam-2648	387	14	banach	banach	NOUN
ejpam-2648	387	15	algebras	algebra	NOUN
ejpam-2648	387	16	,	,	PUNCT
ejpam-2648	387	17	pacific	pacific	PROPN
ejpam-2648	387	18	j.	j.	PROPN
ejpam-2648	387	19	math	math	PROPN
ejpam-2648	387	20	,	,	PUNCT
ejpam-2648	387	21	159	159	NUM
ejpam-2648	387	22	(	(	PUNCT
ejpam-2648	387	23	1993	1993	NUM
ejpam-2648	387	24	)	)	PUNCT
ejpam-2648	387	25	139	139	NUM
ejpam-2648	387	26	-	-	SYM
ejpam-2648	387	27	152	152	NUM
ejpam-2648	387	28	.	.	PUNCT
ejpam-2648	388	1	[	[	X
ejpam-2648	388	2	30	30	NUM
ejpam-2648	388	3	]	]	X
ejpam-2648	388	4	y.	y.	NOUN
ejpam-2648	388	5	uchino	uchino	PROPN
ejpam-2648	388	6	and	and	CCONJ
ejpam-2648	388	7	t.	t.	NOUN
ejpam-2648	388	8	satoh	satoh	NOUN
ejpam-2648	388	9	,	,	PUNCT
ejpam-2648	388	10	function	function	NOUN
ejpam-2648	388	11	field	field	NOUN
ejpam-2648	388	12	modular	modular	ADJ
ejpam-2648	388	13	forms	form	NOUN
ejpam-2648	388	14	and	and	CCONJ
ejpam-2648	388	15	higher	high	ADJ
ejpam-2648	388	16	derivations	derivation	NOUN
ejpam-2648	388	17	,	,	PUNCT
ejpam-2648	388	18	math	math	NOUN
ejpam-2648	388	19	.	.	PUNCT
ejpam-2648	389	1	ann	ann	PROPN
ejpam-2648	389	2	.	.	PROPN
ejpam-2648	390	1	311	311	NUM
ejpam-2648	390	2	(	(	PUNCT
ejpam-2648	390	3	1998	1998	NUM
ejpam-2648	390	4	)	)	PUNCT
ejpam-2648	390	5	,	,	PUNCT
ejpam-2648	390	6	439	439	NUM
ejpam-2648	390	7	-	-	SYM
ejpam-2648	390	8	466	466	NUM
ejpam-2648	390	9	.	.	PUNCT
ejpam-2648	391	1	[	[	X
ejpam-2648	391	2	31	31	NUM
ejpam-2648	391	3	]	]	PUNCT
ejpam-2648	391	4	e.	e.	PROPN
ejpam-2648	391	5	i.	i.	PROPN
ejpam-2648	391	6	zelmanov	zelmanov	PROPN
ejpam-2648	391	7	,	,	PUNCT
ejpam-2648	391	8	primary	primary	ADJ
ejpam-2648	391	9	jordan	jordan	PROPN
ejpam-2648	391	10	triple	triple	PROPN
ejpam-2648	391	11	systems	systems	PROPN
ejpam-2648	391	12	iii	iii	PROPN
ejpam-2648	391	13	,	,	PUNCT
ejpam-2648	391	14	sib	sib	PROPN
ejpam-2648	391	15	.	.	PROPN
ejpam-2648	391	16	math	math	PROPN
ejpam-2648	391	17	.	.	PUNCT
ejpam-2648	392	1	j.	j.	PROPN
ejpam-2648	392	2	26	26	NUM
ejpam-2648	392	3	(	(	PUNCT
ejpam-2648	392	4	1985	1985	NUM
ejpam-2648	392	5	)	)	PUNCT
ejpam-2648	392	6	,	,	PUNCT
ejpam-2648	392	7	55	55	NUM
ejpam-2648	392	8	-	-	SYM
ejpam-2648	392	9	64	64	NUM
ejpam-2648	392	10	.	.	PUNCT