id	sid	tid	token	lemma	pos
ejpam-1599	1	1	6_mary.dvi	6_mary.dvi	NUM
ejpam-1599	1	2	european	european	ADJ
ejpam-1599	1	3	journal	journal	PROPN
ejpam-1599	1	4	of	of	ADP
ejpam-1599	1	5	pure	pure	ADJ
ejpam-1599	1	6	and	and	CCONJ
ejpam-1599	1	7	applied	apply	VERB
ejpam-1599	1	8	mathematics	mathematic	NOUN
ejpam-1599	1	9	vol	vol	NOUN
ejpam-1599	1	10	.	.	PROPN
ejpam-1599	1	11	5	5	NUM
ejpam-1599	1	12	,	,	PUNCT
ejpam-1599	1	13	no	no	INTJ
ejpam-1599	1	14	.	.	NOUN
ejpam-1599	1	15	2	2	NUM
ejpam-1599	1	16	,	,	PUNCT
ejpam-1599	1	17	2012	2012	NUM
ejpam-1599	1	18	,	,	PUNCT
ejpam-1599	1	19	160	160	NUM
ejpam-1599	1	20	-	-	SYM
ejpam-1599	1	21	173	173	NUM
ejpam-1599	1	22	issn	issn	PROPN
ejpam-1599	1	23	1307	1307	NUM
ejpam-1599	1	24	-	-	SYM
ejpam-1599	1	25	5543	5543	NUM
ejpam-1599	1	26	–	–	PUNCT
ejpam-1599	1	27	www.ejpam.com	www.ejpam.com	X
ejpam-1599	1	28	natural	natural	ADJ
ejpam-1599	1	29	generalized	generalized	ADJ
ejpam-1599	1	30	inverse	inverse	NOUN
ejpam-1599	1	31	and	and	CCONJ
ejpam-1599	1	32	core	core	NOUN
ejpam-1599	1	33	of	of	ADP
ejpam-1599	1	34	an	an	DET
ejpam-1599	1	35	element	element	NOUN
ejpam-1599	1	36	in	in	ADP
ejpam-1599	1	37	semigroups	semigroup	NOUN
ejpam-1599	1	38	,	,	PUNCT
ejpam-1599	1	39	rings	ring	NOUN
ejpam-1599	1	40	and	and	CCONJ
ejpam-1599	1	41	banach	banach	NOUN
ejpam-1599	1	42	and	and	CCONJ
ejpam-1599	1	43	operator	operator	NOUN
ejpam-1599	1	44	algebras	algebras	PROPN
ejpam-1599	1	45	xavier	xavier	PROPN
ejpam-1599	1	46	mary	mary	PROPN
ejpam-1599	1	47	université	université	PROPN
ejpam-1599	1	48	paris	paris	PROPN
ejpam-1599	1	49	-	-	PUNCT
ejpam-1599	1	50	ouest	ouest	PROPN
ejpam-1599	1	51	nanterre	nanterre	PROPN
ejpam-1599	1	52	-	-	PUNCT
ejpam-1599	1	53	la	la	X
ejpam-1599	1	54	défense	défense	PROPN
ejpam-1599	1	55	,	,	PUNCT
ejpam-1599	1	56	laboratoire	laboratoire	PROPN
ejpam-1599	1	57	modal’x	modal’x	PROPN
ejpam-1599	1	58	,	,	PUNCT
ejpam-1599	1	59	paris	paris	PROPN
ejpam-1599	1	60	france	france	PROPN
ejpam-1599	1	61	abstract	abstract	NOUN
ejpam-1599	1	62	.	.	PUNCT
ejpam-1599	2	1	using	use	VERB
ejpam-1599	2	2	the	the	DET
ejpam-1599	2	3	recent	recent	ADJ
ejpam-1599	2	4	notion	notion	NOUN
ejpam-1599	2	5	of	of	ADP
ejpam-1599	2	6	inverse	inverse	NOUN
ejpam-1599	2	7	along	along	ADP
ejpam-1599	2	8	an	an	DET
ejpam-1599	2	9	element	element	NOUN
ejpam-1599	2	10	in	in	ADP
ejpam-1599	2	11	a	a	DET
ejpam-1599	2	12	semigroup	semigroup	NOUN
ejpam-1599	2	13	,	,	PUNCT
ejpam-1599	2	14	and	and	CCONJ
ejpam-1599	2	15	the	the	DET
ejpam-1599	2	16	natural	natural	ADJ
ejpam-1599	2	17	partial	partial	ADJ
ejpam-1599	2	18	order	order	NOUN
ejpam-1599	2	19	on	on	ADP
ejpam-1599	2	20	idempotents	idempotent	NOUN
ejpam-1599	2	21	,	,	PUNCT
ejpam-1599	2	22	we	we	PRON
ejpam-1599	2	23	study	study	VERB
ejpam-1599	2	24	bicommuting	bicommute	VERB
ejpam-1599	2	25	generalized	generalize	VERB
ejpam-1599	2	26	inverses	inverse	NOUN
ejpam-1599	2	27	and	and	CCONJ
ejpam-1599	2	28	define	define	VERB
ejpam-1599	2	29	a	a	DET
ejpam-1599	2	30	new	new	ADJ
ejpam-1599	2	31	inverse	inverse	NOUN
ejpam-1599	2	32	called	call	VERB
ejpam-1599	2	33	natural	natural	ADJ
ejpam-1599	2	34	inverse	inverse	NOUN
ejpam-1599	2	35	,	,	PUNCT
ejpam-1599	2	36	that	that	PRON
ejpam-1599	2	37	generalizes	generalize	VERB
ejpam-1599	2	38	the	the	DET
ejpam-1599	2	39	drazin	drazin	PROPN
ejpam-1599	2	40	inverse	inverse	NOUN
ejpam-1599	2	41	in	in	ADP
ejpam-1599	2	42	a	a	DET
ejpam-1599	2	43	semigroup	semigroup	NOUN
ejpam-1599	2	44	,	,	PUNCT
ejpam-1599	2	45	but	but	CCONJ
ejpam-1599	2	46	also	also	ADV
ejpam-1599	2	47	the	the	DET
ejpam-1599	2	48	koliha	koliha	VERB
ejpam-1599	2	49	-	-	PUNCT
ejpam-1599	2	50	drazin	drazin	NOUN
ejpam-1599	2	51	inverse	inverse	NOUN
ejpam-1599	2	52	in	in	ADP
ejpam-1599	2	53	a	a	DET
ejpam-1599	2	54	ring	ring	NOUN
ejpam-1599	2	55	.	.	PUNCT
ejpam-1599	3	1	in	in	ADP
ejpam-1599	3	2	this	this	DET
ejpam-1599	3	3	setting	setting	NOUN
ejpam-1599	3	4	we	we	PRON
ejpam-1599	3	5	get	get	VERB
ejpam-1599	3	6	a	a	DET
ejpam-1599	3	7	core	core	NOUN
ejpam-1599	3	8	decomposition	decomposition	NOUN
ejpam-1599	3	9	similar	similar	ADJ
ejpam-1599	3	10	to	to	ADP
ejpam-1599	3	11	the	the	DET
ejpam-1599	3	12	nilpotent	nilpotent	NOUN
ejpam-1599	3	13	,	,	PUNCT
ejpam-1599	3	14	kato	kato	PROPN
ejpam-1599	3	15	or	or	CCONJ
ejpam-1599	3	16	mbekhta	mbekhta	PROPN
ejpam-1599	3	17	decompositions	decomposition	NOUN
ejpam-1599	3	18	.	.	PUNCT
ejpam-1599	4	1	in	in	ADP
ejpam-1599	4	2	banach	banach	NOUN
ejpam-1599	4	3	and	and	CCONJ
ejpam-1599	4	4	operator	operator	NOUN
ejpam-1599	4	5	algebras	algebra	NOUN
ejpam-1599	4	6	,	,	PUNCT
ejpam-1599	4	7	we	we	PRON
ejpam-1599	4	8	show	show	VERB
ejpam-1599	4	9	that	that	SCONJ
ejpam-1599	4	10	the	the	DET
ejpam-1599	4	11	study	study	NOUN
ejpam-1599	4	12	of	of	ADP
ejpam-1599	4	13	the	the	DET
ejpam-1599	4	14	spectrum	spectrum	NOUN
ejpam-1599	4	15	is	be	AUX
ejpam-1599	4	16	not	not	PART
ejpam-1599	4	17	sufficient	sufficient	ADJ
ejpam-1599	4	18	,	,	PUNCT
ejpam-1599	4	19	and	and	CCONJ
ejpam-1599	4	20	use	use	VERB
ejpam-1599	4	21	ideas	idea	NOUN
ejpam-1599	4	22	from	from	ADP
ejpam-1599	4	23	local	local	ADJ
ejpam-1599	4	24	spectral	spectral	ADJ
ejpam-1599	4	25	theory	theory	NOUN
ejpam-1599	4	26	to	to	PART
ejpam-1599	4	27	study	study	VERB
ejpam-1599	4	28	this	this	DET
ejpam-1599	4	29	new	new	ADJ
ejpam-1599	4	30	inverse	inverse	NOUN
ejpam-1599	4	31	.	.	PUNCT
ejpam-1599	5	1	2010	2010	NUM
ejpam-1599	5	2	mathematics	mathematic	NOUN
ejpam-1599	5	3	subject	subject	NOUN
ejpam-1599	5	4	classifications	classification	NOUN
ejpam-1599	5	5	:	:	PUNCT
ejpam-1599	5	6	15a09	15a09	NUM
ejpam-1599	5	7	,	,	PUNCT
ejpam-1599	5	8	47a05	47a05	NUM
ejpam-1599	5	9	,	,	PUNCT
ejpam-1599	5	10	47a11	47a11	ADJ
ejpam-1599	5	11	key	key	ADJ
ejpam-1599	5	12	words	word	NOUN
ejpam-1599	5	13	and	and	CCONJ
ejpam-1599	5	14	phrases	phrase	NOUN
ejpam-1599	5	15	:	:	PUNCT
ejpam-1599	5	16	generalized	generalized	ADJ
ejpam-1599	5	17	inverses	inverse	NOUN
ejpam-1599	5	18	,	,	PUNCT
ejpam-1599	5	19	koliha	koliha	ADJ
ejpam-1599	5	20	-	-	PUNCT
ejpam-1599	5	21	drazin	drazin	PROPN
ejpam-1599	5	22	inverse	inverse	NOUN
ejpam-1599	5	23	1	1	NUM
ejpam-1599	5	24	.	.	PUNCT
ejpam-1599	6	1	introduction	introduction	NOUN
ejpam-1599	6	2	in	in	ADP
ejpam-1599	6	3	this	this	DET
ejpam-1599	6	4	paper	paper	NOUN
ejpam-1599	6	5	,	,	PUNCT
ejpam-1599	6	6	s	s	X
ejpam-1599	6	7	,	,	PUNCT
ejpam-1599	6	8	r	r	NOUN
ejpam-1599	6	9	and	and	CCONJ
ejpam-1599	6	10	a	a	DET
ejpam-1599	6	11	denote	denote	NOUN
ejpam-1599	6	12	respectively	respectively	ADV
ejpam-1599	6	13	a	a	DET
ejpam-1599	6	14	semigroup	semigroup	NOUN
ejpam-1599	6	15	,	,	PUNCT
ejpam-1599	6	16	a	a	DET
ejpam-1599	6	17	ring	ring	NOUN
ejpam-1599	6	18	and	and	CCONJ
ejpam-1599	6	19	a	a	DET
ejpam-1599	6	20	banach	banach	NOUN
ejpam-1599	6	21	algebra	algebra	NOUN
ejpam-1599	6	22	.	.	PUNCT
ejpam-1599	7	1	in	in	ADP
ejpam-1599	7	2	particular	particular	ADJ
ejpam-1599	7	3	,	,	PUNCT
ejpam-1599	7	4	r	r	NOUN
ejpam-1599	7	5	and	and	CCONJ
ejpam-1599	7	6	a	a	PRON
ejpam-1599	7	7	with	with	ADP
ejpam-1599	7	8	only	only	ADV
ejpam-1599	7	9	their	their	PRON
ejpam-1599	7	10	multiplication	multiplication	NOUN
ejpam-1599	7	11	structure	structure	NOUN
ejpam-1599	7	12	will	will	AUX
ejpam-1599	7	13	be	be	AUX
ejpam-1599	7	14	considered	consider	VERB
ejpam-1599	7	15	as	as	ADP
ejpam-1599	7	16	semigroups	semigroup	NOUN
ejpam-1599	7	17	.	.	PUNCT
ejpam-1599	8	1	for	for	ADP
ejpam-1599	8	2	any	any	DET
ejpam-1599	8	3	semigroup	semigroup	ADJ
ejpam-1599	8	4	s	s	NOUN
ejpam-1599	8	5	,	,	PUNCT
ejpam-1599	8	6	s1	s1	PROPN
ejpam-1599	8	7	denotes	denote	VERB
ejpam-1599	8	8	the	the	DET
ejpam-1599	8	9	monoid	monoid	NOUN
ejpam-1599	8	10	generated	generate	VERB
ejpam-1599	8	11	by	by	ADP
ejpam-1599	8	12	s.	s.	PROPN
ejpam-1599	8	13	e(s	e(s	PROPN
ejpam-1599	8	14	)	)	PUNCT
ejpam-1599	8	15	denotes	denote	VERB
ejpam-1599	8	16	the	the	DET
ejpam-1599	8	17	set	set	NOUN
ejpam-1599	8	18	of	of	ADP
ejpam-1599	8	19	idempotents	idempotent	NOUN
ejpam-1599	8	20	.	.	PUNCT
ejpam-1599	9	1	for	for	ADP
ejpam-1599	9	2	any	any	DET
ejpam-1599	9	3	subset	subset	NOUN
ejpam-1599	9	4	a	a	DET
ejpam-1599	9	5	of	of	ADP
ejpam-1599	9	6	s	s	NOUN
ejpam-1599	9	7	,	,	PUNCT
ejpam-1599	9	8	a′	a′	PROPN
ejpam-1599	9	9	=	=	SYM
ejpam-1599	9	10	{	{	PUNCT
ejpam-1599	9	11	x	x	PUNCT
ejpam-1599	9	12	∈	∈	PROPN
ejpam-1599	9	13	s	s	NOUN
ejpam-1599	9	14	,	,	PUNCT
ejpam-1599	9	15	xa	xa	X
ejpam-1599	9	16	=	=	NOUN
ejpam-1599	9	17	ax	ax	NOUN
ejpam-1599	9	18	∀a	∀a	NOUN
ejpam-1599	9	19	∈	∈	PROPN
ejpam-1599	9	20	a	a	DET
ejpam-1599	9	21	}	}	PUNCT
ejpam-1599	9	22	denotes	denote	NOUN
ejpam-1599	9	23	the	the	DET
ejpam-1599	9	24	commutant	commutant	NOUN
ejpam-1599	9	25	(	(	PUNCT
ejpam-1599	9	26	or	or	CCONJ
ejpam-1599	9	27	centralizer	centralizer	NOUN
ejpam-1599	9	28	)	)	PUNCT
ejpam-1599	9	29	of	of	ADP
ejpam-1599	9	30	a.	a.	NOUN
ejpam-1599	9	31	we	we	PRON
ejpam-1599	9	32	say	say	VERB
ejpam-1599	9	33	a	a	PRON
ejpam-1599	9	34	is	be	AUX
ejpam-1599	9	35	(	(	PUNCT
ejpam-1599	9	36	von	von	PROPN
ejpam-1599	9	37	neumann	neumann	PROPN
ejpam-1599	9	38	)	)	PUNCT
ejpam-1599	10	1	regular	regular	ADV
ejpam-1599	10	2	in	in	ADP
ejpam-1599	10	3	s	s	PRON
ejpam-1599	10	4	if	if	SCONJ
ejpam-1599	10	5	a	a	DET
ejpam-1599	10	6	∈	∈	PROPN
ejpam-1599	10	7	asa	asa	PROPN
ejpam-1599	10	8	.	.	PUNCT
ejpam-1599	11	1	a	a	DET
ejpam-1599	11	2	particular	particular	ADJ
ejpam-1599	11	3	solution	solution	NOUN
ejpam-1599	11	4	to	to	ADP
ejpam-1599	11	5	axa	axa	NOUN
ejpam-1599	11	6	=	=	PUNCT
ejpam-1599	11	7	a	a	PRON
ejpam-1599	11	8	is	be	AUX
ejpam-1599	11	9	called	call	VERB
ejpam-1599	11	10	an	an	DET
ejpam-1599	11	11	associate	associate	NOUN
ejpam-1599	11	12	,	,	PUNCT
ejpam-1599	11	13	or	or	CCONJ
ejpam-1599	11	14	inner	inner	ADJ
ejpam-1599	11	15	inverse	inverse	NOUN
ejpam-1599	11	16	,	,	PUNCT
ejpam-1599	11	17	of	of	ADP
ejpam-1599	11	18	a.	a.	NOUN
ejpam-1599	11	19	a	a	DET
ejpam-1599	11	20	solution	solution	NOUN
ejpam-1599	11	21	to	to	ADP
ejpam-1599	11	22	xax	xax	PROPN
ejpam-1599	11	23	=	=	PROPN
ejpam-1599	11	24	a	a	PROPN
ejpam-1599	11	25	is	be	AUX
ejpam-1599	11	26	called	call	VERB
ejpam-1599	11	27	a	a	DET
ejpam-1599	11	28	weak	weak	ADJ
ejpam-1599	11	29	(	(	PUNCT
ejpam-1599	11	30	or	or	CCONJ
ejpam-1599	11	31	outer	outer	ADJ
ejpam-1599	11	32	)	)	PUNCT
ejpam-1599	11	33	inverse	inverse	NOUN
ejpam-1599	11	34	.	.	PUNCT
ejpam-1599	12	1	finally	finally	ADV
ejpam-1599	12	2	,	,	PUNCT
ejpam-1599	12	3	an	an	DET
ejpam-1599	12	4	element	element	NOUN
ejpam-1599	12	5	that	that	PRON
ejpam-1599	12	6	satisfies	satisfy	VERB
ejpam-1599	12	7	axa	axa	NOUN
ejpam-1599	12	8	=	=	PUNCT
ejpam-1599	12	9	a	a	PROPN
ejpam-1599	12	10	and	and	CCONJ
ejpam-1599	12	11	xax	xax	PROPN
ejpam-1599	12	12	=	=	PROPN
ejpam-1599	12	13	x	x	PROPN
ejpam-1599	12	14	is	be	AUX
ejpam-1599	12	15	called	call	VERB
ejpam-1599	12	16	an	an	DET
ejpam-1599	12	17	inverse	inverse	NOUN
ejpam-1599	12	18	(	(	PUNCT
ejpam-1599	12	19	or	or	CCONJ
ejpam-1599	12	20	reflexive	reflexive	ADJ
ejpam-1599	12	21	inverse	inverse	NOUN
ejpam-1599	12	22	,	,	PUNCT
ejpam-1599	12	23	or	or	CCONJ
ejpam-1599	12	24	relative	relative	ADJ
ejpam-1599	12	25	inverse	inverse	NOUN
ejpam-1599	12	26	)	)	PUNCT
ejpam-1599	12	27	of	of	ADP
ejpam-1599	12	28	a	a	PRON
ejpam-1599	12	29	and	and	CCONJ
ejpam-1599	12	30	is	be	AUX
ejpam-1599	12	31	denoted	denote	VERB
ejpam-1599	12	32	by	by	ADP
ejpam-1599	12	33	a′.	a′.	NOUN
ejpam-1599	12	34	the	the	DET
ejpam-1599	12	35	set	set	NOUN
ejpam-1599	12	36	of	of	ADP
ejpam-1599	12	37	all	all	DET
ejpam-1599	12	38	associates	associate	NOUN
ejpam-1599	12	39	of	of	ADP
ejpam-1599	12	40	a	a	PRON
ejpam-1599	12	41	is	be	AUX
ejpam-1599	12	42	denoted	denote	VERB
ejpam-1599	12	43	by	by	ADP
ejpam-1599	12	44	a(a	a(a	PROPN
ejpam-1599	12	45	)	)	PUNCT
ejpam-1599	12	46	,	,	PUNCT
ejpam-1599	12	47	and	and	CCONJ
ejpam-1599	12	48	the	the	DET
ejpam-1599	12	49	set	set	NOUN
ejpam-1599	12	50	of	of	ADP
ejpam-1599	12	51	weak	weak	ADJ
ejpam-1599	12	52	inverses	inverse	NOUN
ejpam-1599	12	53	of	of	ADP
ejpam-1599	12	54	a	a	PRON
ejpam-1599	12	55	by	by	ADP
ejpam-1599	12	56	w	w	PROPN
ejpam-1599	12	57	(	(	PUNCT
ejpam-1599	12	58	a	a	NOUN
ejpam-1599	12	59	)	)	PUNCT
ejpam-1599	12	60	.	.	PUNCT
ejpam-1599	13	1	a	a	DET
ejpam-1599	13	2	commuting	commuting	NOUN
ejpam-1599	13	3	inverse	inverse	NOUN
ejpam-1599	13	4	,	,	PUNCT
ejpam-1599	13	5	if	if	SCONJ
ejpam-1599	13	6	it	it	PRON
ejpam-1599	13	7	exists	exist	VERB
ejpam-1599	13	8	,	,	PUNCT
ejpam-1599	13	9	is	be	AUX
ejpam-1599	13	10	unique	unique	ADJ
ejpam-1599	13	11	and	and	CCONJ
ejpam-1599	13	12	denoted	denote	VERB
ejpam-1599	13	13	by	by	ADP
ejpam-1599	13	14	a	a	DET
ejpam-1599	13	15	#	#	NOUN
ejpam-1599	13	16	.	.	PUNCT
ejpam-1599	14	1	it	it	PRON
ejpam-1599	14	2	is	be	AUX
ejpam-1599	14	3	usually	usually	ADV
ejpam-1599	14	4	called	call	VERB
ejpam-1599	14	5	the	the	DET
ejpam-1599	14	6	group	group	NOUN
ejpam-1599	14	7	inverse	inverse	NOUN
ejpam-1599	14	8	of	of	ADP
ejpam-1599	14	9	a.	a.	NOUN
ejpam-1599	14	10	a	a	DET
ejpam-1599	14	11	classical	classical	ADJ
ejpam-1599	14	12	reference	reference	NOUN
ejpam-1599	14	13	for	for	ADP
ejpam-1599	14	14	generalized	generalized	ADJ
ejpam-1599	14	15	inverses	inverse	NOUN
ejpam-1599	14	16	is	be	AUX
ejpam-1599	14	17	[	[	X
ejpam-1599	14	18	2	2	NUM
ejpam-1599	14	19	]	]	PUNCT
ejpam-1599	14	20	.	.	PUNCT
ejpam-1599	15	1	we	we	PRON
ejpam-1599	15	2	will	will	AUX
ejpam-1599	15	3	make	make	VERB
ejpam-1599	15	4	use	use	NOUN
ejpam-1599	15	5	of	of	ADP
ejpam-1599	15	6	the	the	DET
ejpam-1599	15	7	green	green	PROPN
ejpam-1599	15	8	’s	’s	PART
ejpam-1599	15	9	preorders	preorder	NOUN
ejpam-1599	15	10	and	and	CCONJ
ejpam-1599	15	11	relations	relation	NOUN
ejpam-1599	15	12	in	in	ADP
ejpam-1599	15	13	a	a	DET
ejpam-1599	15	14	semigroup	semigroup	NOUN
ejpam-1599	15	15	[	[	X
ejpam-1599	15	16	9	9	NUM
ejpam-1599	15	17	]	]	PUNCT
ejpam-1599	15	18	.	.	PUNCT
ejpam-1599	16	1	for	for	ADP
ejpam-1599	16	2	elements	element	NOUN
ejpam-1599	16	3	a	a	PRON
ejpam-1599	16	4	and	and	CCONJ
ejpam-1599	16	5	b	b	NOUN
ejpam-1599	16	6	of	of	ADP
ejpam-1599	16	7	s	s	PROPN
ejpam-1599	16	8	,	,	PUNCT
ejpam-1599	16	9	green	green	PROPN
ejpam-1599	16	10	’s	’s	PART
ejpam-1599	16	11	preorders	preorder	NOUN
ejpam-1599	16	12	≤l	≤l	NOUN
ejpam-1599	16	13	,	,	PUNCT
ejpam-1599	16	14	≤r	≤r	PROPN
ejpam-1599	16	15	and	and	CCONJ
ejpam-1599	16	16	≤h	≤h	NOUN
ejpam-1599	16	17	are	be	AUX
ejpam-1599	16	18	defined	define	VERB
ejpam-1599	16	19	by	by	ADP
ejpam-1599	16	20	a	a	DET
ejpam-1599	16	21	≤l	≤l	PROPN
ejpam-1599	16	22	b	b	NUM
ejpam-1599	16	23	⇐	⇐	ADJ
ejpam-1599	16	24	⇒	⇒	NOUN
ejpam-1599	16	25	s1a	s1a	NOUN
ejpam-1599	17	1	⊂	⊂	PROPN
ejpam-1599	17	2	s1	s1	PROPN
ejpam-1599	17	3	b	b	ADP
ejpam-1599	17	4	⇐	⇐	ADJ
ejpam-1599	17	5	⇒	⇒	NOUN
ejpam-1599	17	6	∃x	∃x	PROPN
ejpam-1599	17	7	∈	∈	PROPN
ejpam-1599	17	8	s1	s1	NOUN
ejpam-1599	17	9	,	,	PUNCT
ejpam-1599	17	10	a	a	DET
ejpam-1599	17	11	=	=	NOUN
ejpam-1599	17	12	x	x	SYM
ejpam-1599	17	13	b	b	PROPN
ejpam-1599	17	14	;	;	PUNCT
ejpam-1599	17	15	email	email	NOUN
ejpam-1599	17	16	address	address	NOUN
ejpam-1599	17	17	:	:	PUNCT
ejpam-1599	17	18	xavier.mary�u-paris10.fr	xavier.mary�u-paris10.fr	PROPN
ejpam-1599	17	19	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1599	18	1	160	160	NUM
ejpam-1599	18	2	c	c	NOUN
ejpam-1599	18	3	©	©	PROPN
ejpam-1599	18	4	2012	2012	NUM
ejpam-1599	18	5	ejpam	ejpam	VERB
ejpam-1599	18	6	all	all	DET
ejpam-1599	18	7	rights	right	NOUN
ejpam-1599	18	8	reserved	reserve	VERB
ejpam-1599	18	9	.	.	PUNCT
ejpam-1599	19	1	x.	x.	PROPN
ejpam-1599	19	2	mary	mary	PROPN
ejpam-1599	19	3	/	/	SYM
ejpam-1599	19	4	eur	eur	PROPN
ejpam-1599	19	5	.	.	PUNCT
ejpam-1599	20	1	j.	j.	PROPN
ejpam-1599	20	2	pure	pure	PROPN
ejpam-1599	20	3	appl	appl	PROPN
ejpam-1599	20	4	.	.	PROPN
ejpam-1599	20	5	math	math	PROPN
ejpam-1599	20	6	,	,	PUNCT
ejpam-1599	20	7	5	5	NUM
ejpam-1599	20	8	(	(	PUNCT
ejpam-1599	20	9	2012	2012	NUM
ejpam-1599	20	10	)	)	PUNCT
ejpam-1599	20	11	,	,	PUNCT
ejpam-1599	20	12	160	160	NUM
ejpam-1599	20	13	-	-	SYM
ejpam-1599	20	14	173	173	NUM
ejpam-1599	20	15	161	161	NUM
ejpam-1599	20	16	a	a	DET
ejpam-1599	20	17	≤r	≤r	PROPN
ejpam-1599	20	18	b	b	NOUN
ejpam-1599	20	19	⇐	⇐	ADJ
ejpam-1599	20	20	⇒	⇒	PROPN
ejpam-1599	20	21	as1	as1	PROPN
ejpam-1599	20	22	⊂	⊂	PROPN
ejpam-1599	20	23	bs1	bs1	PROPN
ejpam-1599	20	24	⇐	⇐	ADJ
ejpam-1599	20	25	⇒	⇒	PROPN
ejpam-1599	20	26	∃x	∃x	PROPN
ejpam-1599	20	27	∈	∈	PROPN
ejpam-1599	20	28	s1	s1	NOUN
ejpam-1599	20	29	,	,	PUNCT
ejpam-1599	20	30	a	a	DET
ejpam-1599	20	31	=	=	X
ejpam-1599	20	32	bx	bx	X
ejpam-1599	20	33	;	;	PUNCT
ejpam-1599	20	34	a	a	DET
ejpam-1599	20	35	≤h	≤h	NOUN
ejpam-1599	20	36	b	b	NUM
ejpam-1599	20	37	⇐	⇐	ADJ
ejpam-1599	20	38	⇒	⇒	NOUN
ejpam-1599	20	39	{	{	PUNCT
ejpam-1599	20	40	a	a	DET
ejpam-1599	20	41	≤l	≤l	PROPN
ejpam-1599	20	42	b	b	PROPN
ejpam-1599	20	43	and	and	CCONJ
ejpam-1599	20	44	a	a	DET
ejpam-1599	20	45	≤r	≤r	PROPN
ejpam-1599	20	46	b	b	NOUN
ejpam-1599	20	47	}	}	PUNCT
ejpam-1599	20	48	.	.	PUNCT
ejpam-1599	21	1	if	if	SCONJ
ejpam-1599	21	2	≤k	≤k	PROPN
ejpam-1599	21	3	is	be	AUX
ejpam-1599	21	4	one	one	NUM
ejpam-1599	21	5	of	of	ADP
ejpam-1599	21	6	these	these	DET
ejpam-1599	21	7	preorders	preorder	NOUN
ejpam-1599	21	8	,	,	PUNCT
ejpam-1599	21	9	then	then	ADV
ejpam-1599	21	10	ak	ak	PROPN
ejpam-1599	21	11	b	b	PROPN
ejpam-1599	21	12	⇐	⇐	PROPN
ejpam-1599	21	13	⇒	⇒	PROPN
ejpam-1599	21	14	{	{	PUNCT
ejpam-1599	21	15	a	a	DET
ejpam-1599	21	16	≤k	≤k	PROPN
ejpam-1599	21	17	b	b	PROPN
ejpam-1599	21	18	and	and	CCONJ
ejpam-1599	21	19	b	b	NOUN
ejpam-1599	21	20	≤k	≤k	PROPN
ejpam-1599	21	21	a	a	PRON
ejpam-1599	21	22	}	}	PUNCT
ejpam-1599	21	23	,	,	PUNCT
ejpam-1599	21	24	and	and	CCONJ
ejpam-1599	21	25	ka	ka	PROPN
ejpam-1599	22	1	=	=	PRON
ejpam-1599	22	2	{	{	PUNCT
ejpam-1599	22	3	b	b	PROPN
ejpam-1599	22	4	∈	∈	PROPN
ejpam-1599	22	5	s	s	PART
ejpam-1599	22	6	,	,	PUNCT
ejpam-1599	22	7	bk	bk	VERB
ejpam-1599	22	8	a	a	DET
ejpam-1599	22	9	}	}	PUNCT
ejpam-1599	22	10	denotes	denote	NOUN
ejpam-1599	22	11	the	the	DET
ejpam-1599	22	12	k	k	PROPN
ejpam-1599	22	13	-class	-class	PROPN
ejpam-1599	22	14	of	of	ADP
ejpam-1599	22	15	a.	a.	NOUN
ejpam-1599	22	16	we	we	PRON
ejpam-1599	22	17	recall	recall	VERB
ejpam-1599	22	18	the	the	DET
ejpam-1599	22	19	following	follow	VERB
ejpam-1599	22	20	characterization	characterization	NOUN
ejpam-1599	22	21	of	of	ADP
ejpam-1599	22	22	group	group	NOUN
ejpam-1599	22	23	invertibility	invertibility	NOUN
ejpam-1599	22	24	in	in	ADP
ejpam-1599	22	25	terms	term	NOUN
ejpam-1599	22	26	of	of	ADP
ejpam-1599	22	27	green	green	PROPN
ejpam-1599	22	28	’s	’s	PART
ejpam-1599	22	29	relation	relation	NOUN
ejpam-1599	22	30	h	h	NOUN
ejpam-1599	23	1	[	[	X
ejpam-1599	23	2	see	see	VERB
ejpam-1599	23	3	9	9	NUM
ejpam-1599	23	4	,	,	PUNCT
ejpam-1599	23	5	22	22	NUM
ejpam-1599	23	6	]	]	PUNCT
ejpam-1599	23	7	:	:	PUNCT
ejpam-1599	23	8	lemma	lemma	PROPN
ejpam-1599	23	9	1	1	X
ejpam-1599	23	10	.	.	PUNCT
ejpam-1599	24	1	a	a	DET
ejpam-1599	24	2	#	#	NOUN
ejpam-1599	24	3	exists	exist	VERB
ejpam-1599	24	4	if	if	SCONJ
ejpam-1599	24	5	and	and	CCONJ
ejpam-1599	24	6	only	only	ADV
ejpam-1599	24	7	if	if	SCONJ
ejpam-1599	24	8	ah	ah	INTJ
ejpam-1599	24	9	a2	a2	PROPN
ejpam-1599	24	10	if	if	SCONJ
ejpam-1599	24	11	and	and	CCONJ
ejpam-1599	24	12	only	only	ADV
ejpam-1599	24	13	ifha	ifha	NOUN
ejpam-1599	24	14	is	be	AUX
ejpam-1599	24	15	a	a	DET
ejpam-1599	24	16	group	group	NOUN
ejpam-1599	24	17	.	.	PUNCT
ejpam-1599	25	1	the	the	DET
ejpam-1599	25	2	study	study	NOUN
ejpam-1599	25	3	of	of	ADP
ejpam-1599	25	4	generalized	generalized	ADJ
ejpam-1599	25	5	inverses	inverse	NOUN
ejpam-1599	25	6	has	have	AUX
ejpam-1599	25	7	been	be	AUX
ejpam-1599	25	8	conducted	conduct	VERB
ejpam-1599	25	9	in	in	ADP
ejpam-1599	25	10	many	many	ADJ
ejpam-1599	25	11	different	different	ADJ
ejpam-1599	25	12	mathematical	mathematical	ADJ
ejpam-1599	25	13	areas	area	NOUN
ejpam-1599	25	14	,	,	PUNCT
ejpam-1599	25	15	from	from	ADP
ejpam-1599	25	16	semigroup	semigroup	PROPN
ejpam-1599	25	17	theory	theory	NOUN
ejpam-1599	25	18	to	to	ADP
ejpam-1599	25	19	operator	operator	NOUN
ejpam-1599	25	20	theory	theory	NOUN
ejpam-1599	25	21	,	,	PUNCT
ejpam-1599	25	22	and	and	CCONJ
ejpam-1599	25	23	applied	apply	VERB
ejpam-1599	25	24	to	to	ADP
ejpam-1599	25	25	various	various	ADJ
ejpam-1599	25	26	domains	domain	NOUN
ejpam-1599	25	27	such	such	ADJ
ejpam-1599	25	28	as	as	ADP
ejpam-1599	25	29	markov	markov	NOUN
ejpam-1599	25	30	chains	chain	NOUN
ejpam-1599	25	31	or	or	CCONJ
ejpam-1599	25	32	differential	differential	ADJ
ejpam-1599	25	33	equations	equation	NOUN
ejpam-1599	25	34	.	.	PUNCT
ejpam-1599	26	1	in	in	ADP
ejpam-1599	26	2	these	these	DET
ejpam-1599	26	3	studies	study	NOUN
ejpam-1599	26	4	,	,	PUNCT
ejpam-1599	26	5	it	it	PRON
ejpam-1599	26	6	may	may	AUX
ejpam-1599	26	7	be	be	AUX
ejpam-1599	26	8	useful	useful	ADJ
ejpam-1599	26	9	to	to	PART
ejpam-1599	26	10	consider	consider	VERB
ejpam-1599	26	11	commuting	commute	VERB
ejpam-1599	26	12	(	(	PUNCT
ejpam-1599	26	13	or	or	CCONJ
ejpam-1599	26	14	bicommuting	bicommute	VERB
ejpam-1599	26	15	)	)	PUNCT
ejpam-1599	26	16	inverses	inverse	VERB
ejpam-1599	26	17	.	.	PUNCT
ejpam-1599	27	1	since	since	SCONJ
ejpam-1599	27	2	the	the	DET
ejpam-1599	27	3	existence	existence	NOUN
ejpam-1599	27	4	of	of	ADP
ejpam-1599	27	5	a	a	DET
ejpam-1599	27	6	commuting	commute	VERB
ejpam-1599	27	7	inner	inner	ADJ
ejpam-1599	27	8	inverse	inverse	NOUN
ejpam-1599	27	9	is	be	AUX
ejpam-1599	27	10	a	a	DET
ejpam-1599	27	11	very	very	ADV
ejpam-1599	27	12	strong	strong	ADJ
ejpam-1599	27	13	property	property	NOUN
ejpam-1599	27	14	,	,	PUNCT
ejpam-1599	27	15	it	it	PRON
ejpam-1599	27	16	is	be	AUX
ejpam-1599	27	17	common	common	ADJ
ejpam-1599	27	18	to	to	PART
ejpam-1599	27	19	look	look	VERB
ejpam-1599	27	20	at	at	ADP
ejpam-1599	27	21	outer	outer	ADJ
ejpam-1599	27	22	commuting	commuting	NOUN
ejpam-1599	27	23	inverses	inverse	NOUN
ejpam-1599	27	24	,	,	PUNCT
ejpam-1599	27	25	following	follow	VERB
ejpam-1599	27	26	the	the	DET
ejpam-1599	27	27	seminal	seminal	ADJ
ejpam-1599	27	28	work	work	NOUN
ejpam-1599	27	29	of	of	ADP
ejpam-1599	27	30	m.	m.	NOUN
ejpam-1599	27	31	drazin	drazin	PROPN
ejpam-1599	28	1	[	[	X
ejpam-1599	28	2	4	4	NUM
ejpam-1599	28	3	]	]	PUNCT
ejpam-1599	28	4	,	,	PUNCT
ejpam-1599	28	5	who	who	PRON
ejpam-1599	28	6	introduced	introduce	VERB
ejpam-1599	28	7	the	the	DET
ejpam-1599	28	8	drazin	drazin	PROPN
ejpam-1599	28	9	inverse	inverse	NOUN
ejpam-1599	28	10	in	in	ADP
ejpam-1599	28	11	the	the	DET
ejpam-1599	28	12	context	context	NOUN
ejpam-1599	28	13	of	of	ADP
ejpam-1599	28	14	semigroups	semigroup	NOUN
ejpam-1599	28	15	and	and	CCONJ
ejpam-1599	28	16	rings	ring	NOUN
ejpam-1599	28	17	.	.	PUNCT
ejpam-1599	29	1	later	later	ADV
ejpam-1599	29	2	,	,	PUNCT
ejpam-1599	29	3	this	this	DET
ejpam-1599	29	4	inverse	inverse	NOUN
ejpam-1599	29	5	has	have	AUX
ejpam-1599	29	6	been	be	AUX
ejpam-1599	29	7	generalized	generalize	VERB
ejpam-1599	29	8	in	in	ADP
ejpam-1599	29	9	the	the	DET
ejpam-1599	29	10	setting	setting	NOUN
ejpam-1599	29	11	of	of	ADP
ejpam-1599	29	12	operators	operator	NOUN
ejpam-1599	29	13	by	by	ADP
ejpam-1599	29	14	koliha	koliha	NOUN
ejpam-1599	29	15	[	[	X
ejpam-1599	29	16	16	16	NUM
ejpam-1599	29	17	]	]	PUNCT
ejpam-1599	29	18	using	use	VERB
ejpam-1599	29	19	spectral	spectral	ADJ
ejpam-1599	29	20	properties	property	NOUN
ejpam-1599	29	21	and	and	CCONJ
ejpam-1599	29	22	functional	functional	ADJ
ejpam-1599	29	23	calculus	calculus	NOUN
ejpam-1599	29	24	.	.	PUNCT
ejpam-1599	30	1	this	this	DET
ejpam-1599	30	2	generalized	generalize	VERB
ejpam-1599	30	3	drazin	drazin	PROPN
ejpam-1599	30	4	inverse	inverse	NOUN
ejpam-1599	30	5	(	(	PUNCT
ejpam-1599	30	6	also	also	ADV
ejpam-1599	30	7	called	call	VERB
ejpam-1599	30	8	koliha	koliha	ADJ
ejpam-1599	30	9	-	-	PUNCT
ejpam-1599	30	10	drazin	drazin	PROPN
ejpam-1599	30	11	inverse	inverse	NOUN
ejpam-1599	30	12	)	)	PUNCT
ejpam-1599	30	13	finds	find	VERB
ejpam-1599	30	14	many	many	ADJ
ejpam-1599	30	15	applications	application	NOUN
ejpam-1599	30	16	,	,	PUNCT
ejpam-1599	30	17	in	in	ADP
ejpam-1599	30	18	particular	particular	ADJ
ejpam-1599	30	19	to	to	ADP
ejpam-1599	30	20	singular	singular	PROPN
ejpam-1599	30	21	differential	differential	ADJ
ejpam-1599	30	22	equations	equation	NOUN
ejpam-1599	30	23	.	.	PUNCT
ejpam-1599	31	1	in	in	ADP
ejpam-1599	31	2	[	[	X
ejpam-1599	31	3	18	18	NUM
ejpam-1599	31	4	]	]	PUNCT
ejpam-1599	31	5	the	the	DET
ejpam-1599	31	6	author	author	NOUN
ejpam-1599	31	7	introduced	introduce	VERB
ejpam-1599	31	8	a	a	DET
ejpam-1599	31	9	special	special	ADJ
ejpam-1599	31	10	outer	outer	ADJ
ejpam-1599	31	11	inverse	inverse	NOUN
ejpam-1599	31	12	,	,	PUNCT
ejpam-1599	31	13	called	call	VERB
ejpam-1599	31	14	inverse	inverse	NOUN
ejpam-1599	31	15	along	along	ADP
ejpam-1599	31	16	an	an	DET
ejpam-1599	31	17	element	element	NOUN
ejpam-1599	31	18	in	in	ADP
ejpam-1599	31	19	the	the	DET
ejpam-1599	31	20	context	context	NOUN
ejpam-1599	31	21	of	of	ADP
ejpam-1599	31	22	semigroups	semigroup	NOUN
ejpam-1599	31	23	.	.	PUNCT
ejpam-1599	32	1	the	the	DET
ejpam-1599	32	2	aim	aim	NOUN
ejpam-1599	32	3	of	of	ADP
ejpam-1599	32	4	this	this	DET
ejpam-1599	32	5	article	article	NOUN
ejpam-1599	32	6	is	be	AUX
ejpam-1599	32	7	to	to	PART
ejpam-1599	32	8	use	use	VERB
ejpam-1599	32	9	this	this	DET
ejpam-1599	32	10	new	new	ADJ
ejpam-1599	32	11	inverse	inverse	NOUN
ejpam-1599	32	12	to	to	PART
ejpam-1599	32	13	study	study	VERB
ejpam-1599	32	14	bicommuting	bicommute	VERB
ejpam-1599	32	15	generalized	generalize	VERB
ejpam-1599	32	16	inverses	inverse	NOUN
ejpam-1599	32	17	.	.	PUNCT
ejpam-1599	33	1	then	then	ADV
ejpam-1599	33	2	,	,	PUNCT
ejpam-1599	33	3	using	use	VERB
ejpam-1599	33	4	the	the	DET
ejpam-1599	33	5	natural	natural	ADJ
ejpam-1599	33	6	partial	partial	ADJ
ejpam-1599	33	7	order	order	NOUN
ejpam-1599	33	8	on	on	ADP
ejpam-1599	33	9	idempotents	idempotent	NOUN
ejpam-1599	33	10	,	,	PUNCT
ejpam-1599	33	11	we	we	PRON
ejpam-1599	33	12	will	will	AUX
ejpam-1599	33	13	define	define	VERB
ejpam-1599	33	14	a	a	DET
ejpam-1599	33	15	new	new	ADJ
ejpam-1599	33	16	inverse	inverse	NOUN
ejpam-1599	33	17	called	call	VERB
ejpam-1599	33	18	natural	natural	ADJ
ejpam-1599	33	19	inverse	inverse	NOUN
ejpam-1599	33	20	,	,	PUNCT
ejpam-1599	33	21	that	that	PRON
ejpam-1599	33	22	generalizes	generalize	VERB
ejpam-1599	33	23	the	the	DET
ejpam-1599	33	24	drazin	drazin	PROPN
ejpam-1599	33	25	inverse	inverse	NOUN
ejpam-1599	33	26	in	in	ADP
ejpam-1599	33	27	a	a	DET
ejpam-1599	33	28	semigroup	semigroup	NOUN
ejpam-1599	33	29	,	,	PUNCT
ejpam-1599	33	30	but	but	CCONJ
ejpam-1599	33	31	also	also	ADV
ejpam-1599	33	32	the	the	DET
ejpam-1599	33	33	koliha	koliha	VERB
ejpam-1599	33	34	-	-	PUNCT
ejpam-1599	33	35	drazin	drazin	NOUN
ejpam-1599	33	36	inverse	inverse	NOUN
ejpam-1599	33	37	in	in	ADP
ejpam-1599	33	38	a	a	DET
ejpam-1599	33	39	ring	ring	NOUN
ejpam-1599	33	40	.	.	PUNCT
ejpam-1599	34	1	in	in	ADP
ejpam-1599	34	2	this	this	DET
ejpam-1599	34	3	setting	setting	NOUN
ejpam-1599	34	4	,	,	PUNCT
ejpam-1599	34	5	this	this	PRON
ejpam-1599	34	6	provides	provide	VERB
ejpam-1599	34	7	a	a	DET
ejpam-1599	34	8	decomposition	decomposition	NOUN
ejpam-1599	34	9	of	of	ADP
ejpam-1599	34	10	an	an	DET
ejpam-1599	34	11	element	element	NOUN
ejpam-1599	34	12	similar	similar	ADJ
ejpam-1599	34	13	to	to	ADP
ejpam-1599	34	14	the	the	DET
ejpam-1599	34	15	nilpotent	nilpotent	NOUN
ejpam-1599	34	16	,	,	PUNCT
ejpam-1599	34	17	kato	kato	PROPN
ejpam-1599	34	18	or	or	CCONJ
ejpam-1599	34	19	mbekhta	mbekhta	PROPN
ejpam-1599	34	20	decompositions	decomposition	NOUN
ejpam-1599	34	21	[	[	X
ejpam-1599	34	22	21	21	NUM
ejpam-1599	34	23	]	]	PUNCT
ejpam-1599	34	24	.	.	PUNCT
ejpam-1599	35	1	in	in	ADP
ejpam-1599	35	2	the	the	DET
ejpam-1599	35	3	first	first	ADJ
ejpam-1599	35	4	sections	section	NOUN
ejpam-1599	35	5	we	we	PRON
ejpam-1599	35	6	introduce	introduce	VERB
ejpam-1599	35	7	the	the	DET
ejpam-1599	35	8	main	main	ADJ
ejpam-1599	35	9	notions	notion	NOUN
ejpam-1599	35	10	(	(	PUNCT
ejpam-1599	35	11	inverse	inverse	NOUN
ejpam-1599	35	12	along	along	ADP
ejpam-1599	35	13	an	an	DET
ejpam-1599	35	14	element	element	NOUN
ejpam-1599	35	15	,	,	PUNCT
ejpam-1599	35	16	natural	natural	ADJ
ejpam-1599	35	17	generalized	generalized	ADJ
ejpam-1599	35	18	inverse	inverse	NOUN
ejpam-1599	35	19	)	)	PUNCT
ejpam-1599	35	20	entirely	entirely	ADV
ejpam-1599	35	21	in	in	ADP
ejpam-1599	35	22	the	the	DET
ejpam-1599	35	23	semigroup	semigroup	ADJ
ejpam-1599	35	24	setting	setting	NOUN
ejpam-1599	35	25	.	.	PUNCT
ejpam-1599	36	1	we	we	PRON
ejpam-1599	36	2	then	then	ADV
ejpam-1599	36	3	study	study	VERB
ejpam-1599	36	4	further	further	ADJ
ejpam-1599	36	5	properties	property	NOUN
ejpam-1599	36	6	of	of	ADP
ejpam-1599	36	7	the	the	DET
ejpam-1599	36	8	natural	natural	ADJ
ejpam-1599	36	9	inverse	inverse	NOUN
ejpam-1599	36	10	in	in	ADP
ejpam-1599	36	11	rings	ring	NOUN
ejpam-1599	36	12	,	,	PUNCT
ejpam-1599	36	13	making	make	VERB
ejpam-1599	36	14	the	the	DET
ejpam-1599	36	15	link	link	NOUN
ejpam-1599	36	16	with	with	ADP
ejpam-1599	36	17	quasipolar	quasipolar	ADJ
ejpam-1599	36	18	(	(	PUNCT
ejpam-1599	36	19	generalized	generalize	VERB
ejpam-1599	36	20	drazin	drazin	PROPN
ejpam-1599	36	21	invertible	invertible	ADJ
ejpam-1599	36	22	)	)	PUNCT
ejpam-1599	36	23	elements	element	NOUN
ejpam-1599	36	24	[	[	X
ejpam-1599	36	25	10	10	NUM
ejpam-1599	36	26	,	,	PUNCT
ejpam-1599	36	27	11	11	NUM
ejpam-1599	36	28	,	,	PUNCT
ejpam-1599	36	29	16	16	NUM
ejpam-1599	36	30	,	,	PUNCT
ejpam-1599	36	31	17	17	NUM
ejpam-1599	36	32	]	]	PUNCT
ejpam-1599	36	33	.	.	PUNCT
ejpam-1599	37	1	in	in	ADP
ejpam-1599	37	2	the	the	DET
ejpam-1599	37	3	last	last	ADJ
ejpam-1599	37	4	sections	section	NOUN
ejpam-1599	37	5	,	,	PUNCT
ejpam-1599	37	6	a	a	DET
ejpam-1599	37	7	particular	particular	ADJ
ejpam-1599	37	8	attention	attention	NOUN
ejpam-1599	37	9	is	be	AUX
ejpam-1599	37	10	given	give	VERB
ejpam-1599	37	11	to	to	PART
ejpam-1599	37	12	banach	banach	VERB
ejpam-1599	37	13	and	and	CCONJ
ejpam-1599	37	14	operators	operator	NOUN
ejpam-1599	37	15	algebras	algebra	VERB
ejpam-1599	37	16	.	.	PUNCT
ejpam-1599	38	1	the	the	DET
ejpam-1599	38	2	main	main	ADJ
ejpam-1599	38	3	result	result	NOUN
ejpam-1599	38	4	is	be	AUX
ejpam-1599	38	5	that	that	SCONJ
ejpam-1599	38	6	this	this	DET
ejpam-1599	38	7	inverses	inverse	NOUN
ejpam-1599	38	8	relies	rely	VERB
ejpam-1599	38	9	on	on	ADP
ejpam-1599	38	10	finer	fine	ADJ
ejpam-1599	38	11	properties	property	NOUN
ejpam-1599	38	12	than	than	ADP
ejpam-1599	38	13	spectral	spectral	ADJ
ejpam-1599	38	14	properties	property	NOUN
ejpam-1599	38	15	only	only	ADV
ejpam-1599	38	16	.	.	PUNCT
ejpam-1599	39	1	local	local	ADJ
ejpam-1599	39	2	spectral	spectral	ADJ
ejpam-1599	39	3	theory[12	theory[12	NOUN
ejpam-1599	39	4	]	]	PUNCT
ejpam-1599	39	5	is	be	AUX
ejpam-1599	39	6	then	then	ADV
ejpam-1599	39	7	an	an	DET
ejpam-1599	39	8	interesting	interesting	ADJ
ejpam-1599	39	9	tool	tool	NOUN
ejpam-1599	39	10	.	.	PUNCT
ejpam-1599	40	1	2	2	X
ejpam-1599	40	2	.	.	X
ejpam-1599	40	3	inverse	inverse	NOUN
ejpam-1599	40	4	along	along	ADP
ejpam-1599	40	5	an	an	DET
ejpam-1599	40	6	element	element	NOUN
ejpam-1599	40	7	2.1	2.1	NUM
ejpam-1599	40	8	.	.	PUNCT
ejpam-1599	41	1	definition	definition	NOUN
ejpam-1599	41	2	and	and	CCONJ
ejpam-1599	41	3	first	first	ADJ
ejpam-1599	41	4	properties	property	NOUN
ejpam-1599	41	5	the	the	DET
ejpam-1599	41	6	inverse	inverse	NOUN
ejpam-1599	41	7	along	along	ADP
ejpam-1599	41	8	an	an	DET
ejpam-1599	41	9	element	element	NOUN
ejpam-1599	41	10	was	be	AUX
ejpam-1599	41	11	introduced	introduce	VERB
ejpam-1599	41	12	in	in	ADP
ejpam-1599	41	13	[	[	X
ejpam-1599	41	14	18	18	NUM
ejpam-1599	41	15	]	]	PUNCT
ejpam-1599	41	16	,	,	PUNCT
ejpam-1599	41	17	and	and	CCONJ
ejpam-1599	41	18	in	in	ADP
ejpam-1599	41	19	[	[	X
ejpam-1599	41	20	19	19	NUM
ejpam-1599	41	21	]	]	PUNCT
ejpam-1599	41	22	,	,	PUNCT
ejpam-1599	41	23	it	it	PRON
ejpam-1599	41	24	was	be	AUX
ejpam-1599	41	25	interpreted	interpret	VERB
ejpam-1599	41	26	as	as	ADP
ejpam-1599	41	27	a	a	DET
ejpam-1599	41	28	kind	kind	NOUN
ejpam-1599	41	29	of	of	ADP
ejpam-1599	41	30	inverse	inverse	NOUN
ejpam-1599	41	31	modulo	modulo	NOUN
ejpam-1599	41	32	h	h	NOUN
ejpam-1599	41	33	.	.	PUNCT
ejpam-1599	42	1	we	we	PRON
ejpam-1599	42	2	recall	recall	VERB
ejpam-1599	42	3	the	the	DET
ejpam-1599	42	4	definition	definition	NOUN
ejpam-1599	42	5	and	and	CCONJ
ejpam-1599	42	6	properties	property	NOUN
ejpam-1599	42	7	of	of	ADP
ejpam-1599	42	8	this	this	DET
ejpam-1599	42	9	inverse	inverse	NOUN
ejpam-1599	42	10	.	.	PUNCT
ejpam-1599	43	1	note	note	VERB
ejpam-1599	43	2	that	that	SCONJ
ejpam-1599	43	3	in	in	ADP
ejpam-1599	43	4	this	this	DET
ejpam-1599	43	5	article	article	NOUN
ejpam-1599	43	6	,	,	PUNCT
ejpam-1599	43	7	this	this	DET
ejpam-1599	43	8	new	new	ADJ
ejpam-1599	43	9	inverse	inverse	NOUN
ejpam-1599	43	10	is	be	AUX
ejpam-1599	43	11	denoted	denote	VERB
ejpam-1599	43	12	by	by	ADP
ejpam-1599	43	13	a−d	a−d	PROPN
ejpam-1599	43	14	instead	instead	ADV
ejpam-1599	43	15	of	of	ADP
ejpam-1599	43	16	a‖d	a‖d	NOUN
ejpam-1599	43	17	,	,	PUNCT
ejpam-1599	43	18	extending	extend	VERB
ejpam-1599	43	19	the	the	DET
ejpam-1599	43	20	case	case	NOUN
ejpam-1599	43	21	d	d	X
ejpam-1599	43	22	=	=	SYM
ejpam-1599	43	23	1	1	X
ejpam-1599	43	24	.	.	PUNCT
ejpam-1599	43	25	definition	definition	NOUN
ejpam-1599	43	26	1	1	NUM
ejpam-1599	43	27	.	.	PUNCT
ejpam-1599	44	1	given	give	VERB
ejpam-1599	44	2	a	a	PRON
ejpam-1599	44	3	,	,	PUNCT
ejpam-1599	44	4	d	d	X
ejpam-1599	44	5	in	in	ADP
ejpam-1599	44	6	s	s	PROPN
ejpam-1599	44	7	,	,	PUNCT
ejpam-1599	44	8	we	we	PRON
ejpam-1599	44	9	say	say	VERB
ejpam-1599	44	10	a	a	PRON
ejpam-1599	44	11	is	be	AUX
ejpam-1599	44	12	invertible	invertible	ADJ
ejpam-1599	44	13	along	along	ADP
ejpam-1599	44	14	d	d	PROPN
ejpam-1599	44	15	if	if	SCONJ
ejpam-1599	44	16	there	there	PRON
ejpam-1599	44	17	exists	exist	VERB
ejpam-1599	44	18	b	b	PROPN
ejpam-1599	44	19	∈	∈	PROPN
ejpam-1599	44	20	s	s	VERB
ejpam-1599	44	21	such	such	ADJ
ejpam-1599	44	22	that	that	ADV
ejpam-1599	44	23	bad	bad	ADJ
ejpam-1599	44	24	=	=	NOUN
ejpam-1599	44	25	d	d	NOUN
ejpam-1599	44	26	=	=	PUNCT
ejpam-1599	44	27	dab	dab	PROPN
ejpam-1599	44	28	and	and	CCONJ
ejpam-1599	44	29	b	b	NOUN
ejpam-1599	44	30	≤h	≤h	NOUN
ejpam-1599	44	31	d.	d.	NOUN
ejpam-1599	44	32	if	if	SCONJ
ejpam-1599	44	33	such	such	DET
ejpam-1599	44	34	an	an	DET
ejpam-1599	44	35	element	element	NOUN
ejpam-1599	44	36	exists	exist	VERB
ejpam-1599	44	37	then	then	ADV
ejpam-1599	44	38	it	it	PRON
ejpam-1599	44	39	is	be	AUX
ejpam-1599	44	40	unique	unique	ADJ
ejpam-1599	44	41	and	and	CCONJ
ejpam-1599	44	42	is	be	AUX
ejpam-1599	44	43	denoted	denote	VERB
ejpam-1599	44	44	by	by	ADP
ejpam-1599	44	45	a−d	a−d	PROPN
ejpam-1599	44	46	.	.	PUNCT
ejpam-1599	45	1	another	another	DET
ejpam-1599	45	2	characterization	characterization	NOUN
ejpam-1599	45	3	is	be	AUX
ejpam-1599	45	4	the	the	DET
ejpam-1599	45	5	following	following	NOUN
ejpam-1599	45	6	:	:	PUNCT
ejpam-1599	45	7	x.	x.	PROPN
ejpam-1599	45	8	mary	mary	PROPN
ejpam-1599	45	9	/	/	SYM
ejpam-1599	45	10	eur	eur	PROPN
ejpam-1599	45	11	.	.	PUNCT
ejpam-1599	46	1	j.	j.	PROPN
ejpam-1599	46	2	pure	pure	PROPN
ejpam-1599	46	3	appl	appl	PROPN
ejpam-1599	46	4	.	.	PROPN
ejpam-1599	46	5	math	math	PROPN
ejpam-1599	46	6	,	,	PUNCT
ejpam-1599	46	7	5	5	NUM
ejpam-1599	46	8	(	(	PUNCT
ejpam-1599	46	9	2012	2012	NUM
ejpam-1599	46	10	)	)	PUNCT
ejpam-1599	46	11	,	,	PUNCT
ejpam-1599	46	12	160	160	NUM
ejpam-1599	46	13	-	-	SYM
ejpam-1599	46	14	173	173	NUM
ejpam-1599	46	15	162	162	NUM
ejpam-1599	46	16	lemma	lemma	PROPN
ejpam-1599	46	17	2	2	NUM
ejpam-1599	46	18	.	.	PUNCT
ejpam-1599	47	1	a	a	PRON
ejpam-1599	47	2	is	be	AUX
ejpam-1599	47	3	invertible	invertible	ADJ
ejpam-1599	47	4	along	along	ADP
ejpam-1599	47	5	d	d	PROPN
ejpam-1599	47	6	if	if	SCONJ
ejpam-1599	48	1	and	and	CCONJ
ejpam-1599	48	2	only	only	ADV
ejpam-1599	48	3	if	if	SCONJ
ejpam-1599	48	4	there	there	PRON
ejpam-1599	48	5	exists	exist	VERB
ejpam-1599	48	6	b	b	PROPN
ejpam-1599	48	7	∈	∈	PROPN
ejpam-1599	48	8	s	s	VERB
ejpam-1599	48	9	such	such	ADJ
ejpam-1599	48	10	that	that	SCONJ
ejpam-1599	48	11	bab	bab	PROPN
ejpam-1599	48	12	=	=	SYM
ejpam-1599	48	13	b	b	PROPN
ejpam-1599	48	14	and	and	CCONJ
ejpam-1599	48	15	bh	bh	PROPN
ejpam-1599	48	16	d	d	NOUN
ejpam-1599	48	17	,	,	PUNCT
ejpam-1599	48	18	and	and	CCONJ
ejpam-1599	48	19	in	in	ADP
ejpam-1599	48	20	this	this	DET
ejpam-1599	48	21	case	case	NOUN
ejpam-1599	48	22	a−d	a−d	PROPN
ejpam-1599	48	23	=	=	SYM
ejpam-1599	48	24	b.	b.	PROPN
ejpam-1599	48	25	theorem	theorem	NOUN
ejpam-1599	48	26	1	1	X
ejpam-1599	48	27	.	.	PUNCT
ejpam-1599	49	1	let	let	VERB
ejpam-1599	49	2	a	a	PRON
ejpam-1599	49	3	,	,	PUNCT
ejpam-1599	49	4	d	d	PROPN
ejpam-1599	49	5	∈	∈	PROPN
ejpam-1599	49	6	s.	s.	PROPN
ejpam-1599	49	7	then	then	ADV
ejpam-1599	49	8	the	the	DET
ejpam-1599	49	9	following	follow	VERB
ejpam-1599	49	10	are	be	AUX
ejpam-1599	49	11	equivalent	equivalent	ADJ
ejpam-1599	49	12	:	:	PUNCT
ejpam-1599	49	13	1	1	X
ejpam-1599	49	14	.	.	X
ejpam-1599	49	15	a−d	a−d	PROPN
ejpam-1599	49	16	exists	exist	VERB
ejpam-1599	49	17	.	.	PUNCT
ejpam-1599	50	1	2	2	X
ejpam-1599	50	2	.	.	X
ejpam-1599	50	3	d	d	PROPN
ejpam-1599	50	4	≤r	≤r	PROPN
ejpam-1599	50	5	da	da	PROPN
ejpam-1599	50	6	and	and	CCONJ
ejpam-1599	50	7	(	(	PUNCT
ejpam-1599	50	8	da	da	ADJ
ejpam-1599	50	9	)	)	PUNCT
ejpam-1599	50	10	#	#	NOUN
ejpam-1599	50	11	exists	exist	VERB
ejpam-1599	50	12	.	.	PUNCT
ejpam-1599	51	1	3	3	X
ejpam-1599	51	2	.	.	X
ejpam-1599	51	3	d	d	NOUN
ejpam-1599	51	4	≤l	≤l	NOUN
ejpam-1599	51	5	ad	ad	NOUN
ejpam-1599	51	6	and	and	CCONJ
ejpam-1599	51	7	(	(	PUNCT
ejpam-1599	51	8	ad	ad	NOUN
ejpam-1599	51	9	)	)	PUNCT
ejpam-1599	51	10	#	#	NOUN
ejpam-1599	51	11	exists	exist	VERB
ejpam-1599	51	12	.	.	PUNCT
ejpam-1599	52	1	4	4	X
ejpam-1599	52	2	.	.	X
ejpam-1599	52	3	dadh	dadh	PROPN
ejpam-1599	52	4	d.	d.	PROPN
ejpam-1599	52	5	5	5	NUM
ejpam-1599	52	6	.	.	PUNCT
ejpam-1599	53	1	d	d	X
ejpam-1599	53	2	≤h	≤h	PROPN
ejpam-1599	53	3	dad	dad	NOUN
ejpam-1599	53	4	.	.	PUNCT
ejpam-1599	54	1	in	in	ADP
ejpam-1599	54	2	this	this	DET
ejpam-1599	54	3	case	case	NOUN
ejpam-1599	54	4	,	,	PUNCT
ejpam-1599	54	5	b	b	X
ejpam-1599	54	6	=	=	SYM
ejpam-1599	54	7	d(ad)♯	d(ad)♯	PROPN
ejpam-1599	54	8	=	=	SYM
ejpam-1599	54	9	(	(	PUNCT
ejpam-1599	54	10	da)♯d	da)♯d	NOUN
ejpam-1599	54	11	.	.	PUNCT
ejpam-1599	55	1	for	for	ADP
ejpam-1599	55	2	another	another	DET
ejpam-1599	55	3	look	look	NOUN
ejpam-1599	55	4	at	at	ADP
ejpam-1599	55	5	this	this	DET
ejpam-1599	55	6	inverse	inverse	NOUN
ejpam-1599	55	7	,	,	PUNCT
ejpam-1599	55	8	we	we	PRON
ejpam-1599	55	9	also	also	ADV
ejpam-1599	55	10	refer	refer	VERB
ejpam-1599	55	11	to	to	ADP
ejpam-1599	55	12	[	[	X
ejpam-1599	55	13	5	5	NUM
ejpam-1599	55	14	]	]	PUNCT
ejpam-1599	55	15	,	,	PUNCT
ejpam-1599	55	16	where	where	SCONJ
ejpam-1599	55	17	m.	m.	NOUN
ejpam-1599	55	18	drazin	drazin	PROPN
ejpam-1599	55	19	independently	independently	ADV
ejpam-1599	55	20	defined	define	VERB
ejpam-1599	55	21	an	an	DET
ejpam-1599	55	22	new	new	ADJ
ejpam-1599	55	23	outer	outer	ADJ
ejpam-1599	55	24	inverse	inverse	NOUN
ejpam-1599	55	25	that	that	PRON
ejpam-1599	55	26	is	be	AUX
ejpam-1599	55	27	actually	actually	ADV
ejpam-1599	55	28	similar	similar	ADJ
ejpam-1599	55	29	to	to	ADP
ejpam-1599	55	30	the	the	DET
ejpam-1599	55	31	inverse	inverse	NOUN
ejpam-1599	55	32	along	along	ADP
ejpam-1599	55	33	an	an	DET
ejpam-1599	55	34	element	element	NOUN
ejpam-1599	55	35	.	.	PUNCT
ejpam-1599	56	1	2.2	2.2	NUM
ejpam-1599	56	2	.	.	PUNCT
ejpam-1599	56	3	commutativity	commutativity	NOUN
ejpam-1599	56	4	and	and	CCONJ
ejpam-1599	56	5	idempotents	idempotent	VERB
ejpam-1599	56	6	a	a	DET
ejpam-1599	56	7	remarkable	remarkable	ADJ
ejpam-1599	56	8	feature	feature	NOUN
ejpam-1599	56	9	of	of	ADP
ejpam-1599	56	10	the	the	DET
ejpam-1599	56	11	inverse	inverse	NOUN
ejpam-1599	56	12	along	along	ADP
ejpam-1599	56	13	an	an	DET
ejpam-1599	56	14	element	element	NOUN
ejpam-1599	56	15	is	be	AUX
ejpam-1599	56	16	the	the	DET
ejpam-1599	56	17	following	follow	VERB
ejpam-1599	56	18	[	[	X
ejpam-1599	56	19	theorem	theorem	ADJ
ejpam-1599	56	20	10	10	NUM
ejpam-1599	56	21	in	in	ADP
ejpam-1599	56	22	18	18	NUM
ejpam-1599	56	23	]	]	PUNCT
ejpam-1599	56	24	.	.	PUNCT
ejpam-1599	57	1	theorem	theorem	NOUN
ejpam-1599	57	2	2	2	NUM
ejpam-1599	57	3	.	.	PUNCT
ejpam-1599	58	1	let	let	VERB
ejpam-1599	58	2	a	a	PRON
ejpam-1599	58	3	,	,	PUNCT
ejpam-1599	58	4	d	d	PROPN
ejpam-1599	58	5	∈	∈	PROPN
ejpam-1599	58	6	s	s	PART
ejpam-1599	58	7	and	and	CCONJ
ejpam-1599	58	8	pose	pose	VERB
ejpam-1599	58	9	a=	a=	ADJ
ejpam-1599	58	10	(	(	PUNCT
ejpam-1599	58	11	a	a	DET
ejpam-1599	58	12	,	,	PUNCT
ejpam-1599	58	13	d	d	NOUN
ejpam-1599	58	14	)	)	PUNCT
ejpam-1599	58	15	.	.	PUNCT
ejpam-1599	59	1	if	if	SCONJ
ejpam-1599	59	2	a	a	PRON
ejpam-1599	59	3	is	be	AUX
ejpam-1599	59	4	invertible	invertible	ADJ
ejpam-1599	59	5	along	along	ADP
ejpam-1599	59	6	d	d	PROPN
ejpam-1599	59	7	,	,	PUNCT
ejpam-1599	59	8	then	then	ADV
ejpam-1599	59	9	a−d	a−d	PROPN
ejpam-1599	59	10	∈	∈	PROPN
ejpam-1599	59	11	a′′.	a′′.	PROPN
ejpam-1599	59	12	as	as	ADP
ejpam-1599	59	13	a	a	DET
ejpam-1599	59	14	direct	direct	ADJ
ejpam-1599	59	15	corollary	corollary	NOUN
ejpam-1599	59	16	,	,	PUNCT
ejpam-1599	59	17	we	we	PRON
ejpam-1599	59	18	get	get	VERB
ejpam-1599	59	19	:	:	PUNCT
ejpam-1599	59	20	corollary	corollary	ADJ
ejpam-1599	59	21	1	1	X
ejpam-1599	59	22	.	.	PUNCT
ejpam-1599	60	1	let	let	VERB
ejpam-1599	60	2	a	a	DET
ejpam-1599	60	3	,	,	PUNCT
ejpam-1599	60	4	d	d	PROPN
ejpam-1599	60	5	∈	∈	PROPN
ejpam-1599	60	6	s	s	NOUN
ejpam-1599	60	7	,	,	PUNCT
ejpam-1599	60	8	dadh	dadh	NOUN
ejpam-1599	60	9	d	d	NOUN
ejpam-1599	60	10	and	and	CCONJ
ejpam-1599	60	11	pose	pose	VERB
ejpam-1599	60	12	b	b	PROPN
ejpam-1599	60	13	=	=	X
ejpam-1599	60	14	a−d	a−d	PROPN
ejpam-1599	60	15	.	.	PUNCT
ejpam-1599	61	1	if	if	SCONJ
ejpam-1599	61	2	ad	ad	NOUN
ejpam-1599	61	3	=	=	SYM
ejpam-1599	61	4	da	da	NOUN
ejpam-1599	61	5	,	,	PUNCT
ejpam-1599	61	6	then	then	ADV
ejpam-1599	61	7	ab	ab	PROPN
ejpam-1599	61	8	=	=	PUNCT
ejpam-1599	61	9	ba	ba	PROPN
ejpam-1599	61	10	and	and	CCONJ
ejpam-1599	61	11	bd	bd	PROPN
ejpam-1599	61	12	=	=	PROPN
ejpam-1599	61	13	d	d	PROPN
ejpam-1599	61	14	b.	b.	PROPN
ejpam-1599	62	1	we	we	PRON
ejpam-1599	62	2	define	define	VERB
ejpam-1599	62	3	the	the	DET
ejpam-1599	62	4	following	follow	VERB
ejpam-1599	62	5	sets	set	NOUN
ejpam-1599	62	6	:	:	PUNCT
ejpam-1599	63	1	1	1	X
ejpam-1599	63	2	.	.	X
ejpam-1599	63	3	σ0(a	σ0(a	X
ejpam-1599	63	4	)	)	PUNCT
ejpam-1599	63	5	=	=	PRON
ejpam-1599	63	6	{	{	PUNCT
ejpam-1599	63	7	e	e	PROPN
ejpam-1599	63	8	∈	∈	PROPN
ejpam-1599	63	9	e(s	e(s	PROPN
ejpam-1599	63	10	)	)	PUNCT
ejpam-1599	63	11	,	,	PUNCT
ejpam-1599	63	12	eaeh	eaeh	NOUN
ejpam-1599	63	13	e	e	NOUN
ejpam-1599	63	14	}	}	PUNCT
ejpam-1599	63	15	;	;	PUNCT
ejpam-1599	64	1	2	2	X
ejpam-1599	64	2	.	.	X
ejpam-1599	64	3	σ1(a	σ1(a	NUM
ejpam-1599	64	4	)	)	PUNCT
ejpam-1599	64	5	=	=	PRON
ejpam-1599	64	6	{	{	PUNCT
ejpam-1599	64	7	a	a	NOUN
ejpam-1599	64	8	}	}	PUNCT
ejpam-1599	64	9	′	′	NUM
ejpam-1599	64	10	∩σ0(a	∩σ0(a	NOUN
ejpam-1599	64	11	)	)	PUNCT
ejpam-1599	64	12	;	;	PUNCT
ejpam-1599	65	1	3	3	X
ejpam-1599	65	2	.	.	X
ejpam-1599	65	3	σ2(a	σ2(a	NUM
ejpam-1599	65	4	)	)	PUNCT
ejpam-1599	65	5	=	=	PRON
ejpam-1599	65	6	{	{	PUNCT
ejpam-1599	65	7	a	a	DET
ejpam-1599	65	8	}	}	PUNCT
ejpam-1599	65	9	′′	′′	PROPN
ejpam-1599	65	10	∩σ0(a	∩σ0(a	NOUN
ejpam-1599	65	11	)	)	PUNCT
ejpam-1599	65	12	.	.	PUNCT
ejpam-1599	66	1	(	(	PUNCT
ejpam-1599	66	2	if	if	SCONJ
ejpam-1599	66	3	s	s	NOUN
ejpam-1599	66	4	is	be	AUX
ejpam-1599	66	5	commutative	commutative	ADJ
ejpam-1599	66	6	,	,	PUNCT
ejpam-1599	66	7	or	or	CCONJ
ejpam-1599	66	8	the	the	DET
ejpam-1599	66	9	idempotents	idempotent	NOUN
ejpam-1599	66	10	are	be	AUX
ejpam-1599	66	11	central	central	ADJ
ejpam-1599	66	12	,	,	PUNCT
ejpam-1599	66	13	then	then	ADV
ejpam-1599	66	14	the	the	DET
ejpam-1599	66	15	three	three	NUM
ejpam-1599	66	16	sets	set	NOUN
ejpam-1599	66	17	are	be	AUX
ejpam-1599	66	18	equal	equal	ADJ
ejpam-1599	66	19	.	.	PUNCT
ejpam-1599	67	1	we	we	PRON
ejpam-1599	67	2	then	then	ADV
ejpam-1599	67	3	simply	simply	ADV
ejpam-1599	67	4	denote	denote	VERB
ejpam-1599	67	5	it	it	PRON
ejpam-1599	67	6	σ(a	σ(a	PROPN
ejpam-1599	67	7	)	)	PUNCT
ejpam-1599	67	8	.	.	PUNCT
ejpam-1599	67	9	)	)	PUNCT
ejpam-1599	68	1	lemma	lemma	PROPN
ejpam-1599	68	2	3	3	X
ejpam-1599	68	3	.	.	PUNCT
ejpam-1599	69	1	let	let	VERB
ejpam-1599	69	2	e	e	X
ejpam-1599	69	3	∈	∈	PROPN
ejpam-1599	69	4	e(s	e(s	PROPN
ejpam-1599	69	5	)	)	PUNCT
ejpam-1599	69	6	and	and	CCONJ
ejpam-1599	69	7	a	a	DET
ejpam-1599	69	8	∈	∈	NOUN
ejpam-1599	69	9	s	s	VERB
ejpam-1599	69	10	such	such	ADJ
ejpam-1599	69	11	that	that	SCONJ
ejpam-1599	69	12	ae	ae	PROPN
ejpam-1599	69	13	=	=	SYM
ejpam-1599	69	14	ea	ea	PROPN
ejpam-1599	69	15	.	.	PUNCT
ejpam-1599	70	1	then	then	ADV
ejpam-1599	70	2	e	e	PROPN
ejpam-1599	70	3	∈	∈	PROPN
ejpam-1599	70	4	σ0(a	σ0(a	PROPN
ejpam-1599	70	5	)	)	PUNCT
ejpam-1599	70	6	⇐	⇐	ADJ
ejpam-1599	70	7	⇒	⇒	NOUN
ejpam-1599	70	8	e	e	X
ejpam-1599	70	9	≤h	≤h	NOUN
ejpam-1599	70	10	a.	a.	NOUN
ejpam-1599	70	11	proof	proof	NOUN
ejpam-1599	70	12	.	.	PUNCT
ejpam-1599	71	1	assume	assume	VERB
ejpam-1599	71	2	e	e	X
ejpam-1599	71	3	∈	∈	PROPN
ejpam-1599	71	4	σ0(a	σ0(a	PROPN
ejpam-1599	71	5	)	)	PUNCT
ejpam-1599	71	6	.	.	PUNCT
ejpam-1599	72	1	then	then	ADV
ejpam-1599	72	2	e	e	X
ejpam-1599	72	3	≤h	≤h	NOUN
ejpam-1599	72	4	eae	eae	PROPN
ejpam-1599	72	5	=	=	SYM
ejpam-1599	72	6	ea	ea	PROPN
ejpam-1599	72	7	=	=	SYM
ejpam-1599	72	8	ae	ae	PROPN
ejpam-1599	72	9	≤h	≤h	NOUN
ejpam-1599	72	10	a.	a.	NOUN
ejpam-1599	72	11	conversely	conversely	ADV
ejpam-1599	72	12	,	,	PUNCT
ejpam-1599	72	13	if	if	SCONJ
ejpam-1599	72	14	e	e	PROPN
ejpam-1599	72	15	≤h	≤h	VERB
ejpam-1599	72	16	a	a	PRON
ejpam-1599	72	17	and	and	CCONJ
ejpam-1599	72	18	ae	ae	PROPN
ejpam-1599	72	19	=	=	SYM
ejpam-1599	72	20	ea	ea	PROPN
ejpam-1599	72	21	,	,	PUNCT
ejpam-1599	72	22	then	then	ADV
ejpam-1599	72	23	e	e	X
ejpam-1599	72	24	≤r	≤r	PROPN
ejpam-1599	72	25	a⇒	a⇒	PROPN
ejpam-1599	72	26	e	e	PROPN
ejpam-1599	72	27	=	=	PROPN
ejpam-1599	72	28	ee	ee	PROPN
ejpam-1599	72	29	≤r	≤r	PROPN
ejpam-1599	72	30	ea	ea	X
ejpam-1599	73	1	≤r	≤r	PROPN
ejpam-1599	73	2	e	e	PROPN
ejpam-1599	73	3	that	that	PRON
ejpam-1599	73	4	is	be	AUX
ejpam-1599	73	5	erea	erea	NOUN
ejpam-1599	73	6	.	.	PUNCT
ejpam-1599	74	1	but	but	CCONJ
ejpam-1599	74	2	ea	ea	X
ejpam-1599	74	3	=	=	SYM
ejpam-1599	74	4	ae	ae	PROPN
ejpam-1599	74	5	,	,	PUNCT
ejpam-1599	74	6	hence	hence	ADV
ejpam-1599	74	7	erea⇒	erea⇒	PROPN
ejpam-1599	74	8	erae⇒	erae⇒	NOUN
ejpam-1599	74	9	e	e	X
ejpam-1599	74	10	=	=	SYM
ejpam-1599	74	11	eereae	eereae	PROPN
ejpam-1599	74	12	.	.	PUNCT
ejpam-1599	75	1	by	by	ADP
ejpam-1599	75	2	symmetry	symmetry	NOUN
ejpam-1599	75	3	,	,	PUNCT
ejpam-1599	75	4	we	we	PRON
ejpam-1599	75	5	get	get	VERB
ejpam-1599	75	6	eh	eh	INTJ
ejpam-1599	75	7	eae	eae	PROPN
ejpam-1599	75	8	.	.	PUNCT
ejpam-1599	76	1	combining	combine	VERB
ejpam-1599	76	2	the	the	DET
ejpam-1599	76	3	previous	previous	ADJ
ejpam-1599	76	4	lemmas	lemma	NOUN
ejpam-1599	76	5	and	and	CCONJ
ejpam-1599	76	6	theorems	theorem	NOUN
ejpam-1599	76	7	we	we	PRON
ejpam-1599	76	8	get	get	VERB
ejpam-1599	76	9	:	:	PUNCT
ejpam-1599	76	10	x.	x.	PROPN
ejpam-1599	76	11	mary	mary	PROPN
ejpam-1599	76	12	/	/	SYM
ejpam-1599	76	13	eur	eur	PROPN
ejpam-1599	76	14	.	.	PUNCT
ejpam-1599	77	1	j.	j.	PROPN
ejpam-1599	77	2	pure	pure	PROPN
ejpam-1599	77	3	appl	appl	PROPN
ejpam-1599	77	4	.	.	PROPN
ejpam-1599	77	5	math	math	PROPN
ejpam-1599	77	6	,	,	PUNCT
ejpam-1599	77	7	5	5	NUM
ejpam-1599	77	8	(	(	PUNCT
ejpam-1599	77	9	2012	2012	NUM
ejpam-1599	77	10	)	)	PUNCT
ejpam-1599	77	11	,	,	PUNCT
ejpam-1599	77	12	160	160	NUM
ejpam-1599	77	13	-	-	SYM
ejpam-1599	77	14	173	173	NUM
ejpam-1599	77	15	163	163	NUM
ejpam-1599	77	16	theorem	theorem	NOUN
ejpam-1599	77	17	3	3	NUM
ejpam-1599	77	18	.	.	PUNCT
ejpam-1599	78	1	τa	τa	PROPN
ejpam-1599	78	2	:	:	PUNCT
ejpam-1599	78	3	w	w	X
ejpam-1599	78	4	(	(	PUNCT
ejpam-1599	78	5	a	a	X
ejpam-1599	78	6	)	)	PUNCT
ejpam-1599	78	7	−→	−→	NOUN
ejpam-1599	78	8	e(s	e(s	PROPN
ejpam-1599	78	9	)	)	PUNCT
ejpam-1599	79	1	x	x	SYM
ejpam-1599	79	2	7−→	7−→	NOUN
ejpam-1599	79	3	ax	ax	NOUN
ejpam-1599	79	4	•	•	NOUN
ejpam-1599	79	5	is	be	AUX
ejpam-1599	79	6	one	one	NUM
ejpam-1599	79	7	to	to	ADP
ejpam-1599	79	8	one	one	NUM
ejpam-1599	79	9	from	from	ADP
ejpam-1599	79	10	w	w	PROPN
ejpam-1599	79	11	(	(	PUNCT
ejpam-1599	79	12	a)∩	a)∩	X
ejpam-1599	79	13	{	{	PUNCT
ejpam-1599	79	14	a}′	a}′	NOUN
ejpam-1599	79	15	onto	onto	ADP
ejpam-1599	79	16	σ1(a	σ1(a	NOUN
ejpam-1599	79	17	)	)	PUNCT
ejpam-1599	79	18	;	;	PUNCT
ejpam-1599	79	19	•	•	NUM
ejpam-1599	79	20	is	be	AUX
ejpam-1599	79	21	one	one	NUM
ejpam-1599	79	22	to	to	ADP
ejpam-1599	79	23	one	one	NUM
ejpam-1599	79	24	from	from	ADP
ejpam-1599	79	25	w	w	PROPN
ejpam-1599	79	26	(	(	PUNCT
ejpam-1599	79	27	a)∩	a)∩	X
ejpam-1599	79	28	{	{	PUNCT
ejpam-1599	79	29	a}′′	a}′′	NOUN
ejpam-1599	79	30	onto	onto	ADP
ejpam-1599	79	31	σ2(a	σ2(a	NUM
ejpam-1599	79	32	)	)	PUNCT
ejpam-1599	79	33	.	.	PUNCT
ejpam-1599	80	1	its	its	PRON
ejpam-1599	80	2	reciprocal	reciprocal	ADJ
ejpam-1599	80	3	τ−1	τ−1	PROPN
ejpam-1599	80	4	a	a	DET
ejpam-1599	80	5	associates	associate	NOUN
ejpam-1599	80	6	e	e	NOUN
ejpam-1599	80	7	to	to	ADP
ejpam-1599	80	8	b	b	NOUN
ejpam-1599	80	9	=	=	NOUN
ejpam-1599	80	10	a−e	a−e	NOUN
ejpam-1599	80	11	.	.	PUNCT
ejpam-1599	81	1	proof	proof	NOUN
ejpam-1599	81	2	.	.	PUNCT
ejpam-1599	82	1	let	let	VERB
ejpam-1599	82	2	b	b	X
ejpam-1599	82	3	,	,	PUNCT
ejpam-1599	82	4	c	c	PROPN
ejpam-1599	82	5	∈	∈	PROPN
ejpam-1599	82	6	w	w	PROPN
ejpam-1599	82	7	(	(	PUNCT
ejpam-1599	82	8	a	a	NOUN
ejpam-1599	82	9	)	)	PUNCT
ejpam-1599	82	10	∩	∩	NOUN
ejpam-1599	82	11	{	{	PUNCT
ejpam-1599	82	12	a}′.	a}′.	ADV
ejpam-1599	82	13	then	then	ADV
ejpam-1599	83	1	ab	ab	PROPN
ejpam-1599	83	2	=	=	PUNCT
ejpam-1599	83	3	ac	ac	PROPN
ejpam-1599	83	4	⇒	⇒	PROPN
ejpam-1599	83	5	b	b	PROPN
ejpam-1599	83	6	=	=	SYM
ejpam-1599	83	7	bab	bab	PROPN
ejpam-1599	83	8	=	=	SYM
ejpam-1599	83	9	bac	bac	PROPN
ejpam-1599	83	10	.	.	PUNCT
ejpam-1599	84	1	but	but	CCONJ
ejpam-1599	84	2	also	also	ADV
ejpam-1599	84	3	ba	ba	PROPN
ejpam-1599	85	1	=	=	PUNCT
ejpam-1599	85	2	ca	can	AUX
ejpam-1599	85	3	by	by	ADP
ejpam-1599	85	4	commutativity	commutativity	NOUN
ejpam-1599	85	5	and	and	CCONJ
ejpam-1599	85	6	bac	bac	NOUN
ejpam-1599	85	7	=	=	PROPN
ejpam-1599	85	8	cac	cac	PROPN
ejpam-1599	85	9	=	=	PROPN
ejpam-1599	85	10	c.	c.	PROPN
ejpam-1599	85	11	finally	finally	ADV
ejpam-1599	85	12	b	b	X
ejpam-1599	85	13	=	=	PROPN
ejpam-1599	85	14	c.	c.	PROPN
ejpam-1599	85	15	obviously	obviously	ADV
ejpam-1599	85	16	,	,	PUNCT
ejpam-1599	85	17	ab	ab	PROPN
ejpam-1599	85	18	=	=	PUNCT
ejpam-1599	85	19	ba	ba	PROPN
ejpam-1599	86	1	=	=	PUNCT
ejpam-1599	86	2	e	e	PROPN
ejpam-1599	86	3	is	be	AUX
ejpam-1599	86	4	an	an	DET
ejpam-1599	86	5	idempotent	idempotent	NOUN
ejpam-1599	86	6	commuting	commuting	NOUN
ejpam-1599	86	7	with	with	ADP
ejpam-1599	86	8	a.	a.	NOUN
ejpam-1599	86	9	conversely	conversely	ADV
ejpam-1599	86	10	,	,	PUNCT
ejpam-1599	86	11	if	if	SCONJ
ejpam-1599	86	12	e	e	PROPN
ejpam-1599	86	13	∈	∈	PROPN
ejpam-1599	86	14	σ1(a	σ1(a	PROPN
ejpam-1599	86	15	)	)	PUNCT
ejpam-1599	86	16	,	,	PUNCT
ejpam-1599	86	17	then	then	ADV
ejpam-1599	86	18	e	e	PROPN
ejpam-1599	86	19	≤r	≤r	VERB
ejpam-1599	86	20	a	a	DET
ejpam-1599	86	21	⇒	⇒	NOUN
ejpam-1599	86	22	e	e	X
ejpam-1599	86	23	=	=	SYM
ejpam-1599	86	24	ee	ee	PROPN
ejpam-1599	86	25	≤r	≤r	PROPN
ejpam-1599	86	26	ea	ea	PROPN
ejpam-1599	87	1	=	=	SYM
ejpam-1599	87	2	ae	ae	PROPN
ejpam-1599	87	3	≤r	≤r	PROPN
ejpam-1599	87	4	e.	e.	PROPN
ejpam-1599	87	5	also	also	ADV
ejpam-1599	87	6	e	e	VERB
ejpam-1599	87	7	≤l	≤l	NOUN
ejpam-1599	87	8	a⇒	a⇒	PRON
ejpam-1599	87	9	e	e	PROPN
ejpam-1599	87	10	=	=	PROPN
ejpam-1599	87	11	ee	ee	PROPN
ejpam-1599	87	12	≤r	≤r	PROPN
ejpam-1599	87	13	ae	ae	PROPN
ejpam-1599	87	14	=	=	SYM
ejpam-1599	87	15	ea	ea	PROPN
ejpam-1599	87	16	≤l	≤l	PROPN
ejpam-1599	87	17	e.	e.	PROPN
ejpam-1599	88	1	it	it	PRON
ejpam-1599	88	2	follows	follow	VERB
ejpam-1599	88	3	that	that	PRON
ejpam-1599	88	4	ea	ea	PROPN
ejpam-1599	89	1	=	=	SYM
ejpam-1599	89	2	eah	eah	PROPN
ejpam-1599	89	3	e	e	PROPN
ejpam-1599	89	4	,	,	PUNCT
ejpam-1599	89	5	a	a	PRON
ejpam-1599	89	6	is	be	AUX
ejpam-1599	89	7	invertible	invertible	ADJ
ejpam-1599	89	8	along	along	ADP
ejpam-1599	89	9	e.	e.	PROPN
ejpam-1599	89	10	pose	pose	PROPN
ejpam-1599	89	11	b	b	NOUN
ejpam-1599	89	12	=	=	NOUN
ejpam-1599	89	13	a−e	a−e	NOUN
ejpam-1599	89	14	.	.	PUNCT
ejpam-1599	90	1	then	then	ADV
ejpam-1599	90	2	b	b	X
ejpam-1599	90	3	∈	∈	PROPN
ejpam-1599	90	4	{	{	PUNCT
ejpam-1599	90	5	a	a	NOUN
ejpam-1599	90	6	,	,	PUNCT
ejpam-1599	90	7	e}′′	e}′′	PROPN
ejpam-1599	90	8	hence	hence	ADV
ejpam-1599	90	9	ab	ab	PROPN
ejpam-1599	90	10	=	=	PUNCT
ejpam-1599	90	11	ba	ba	PROPN
ejpam-1599	90	12	and	and	CCONJ
ejpam-1599	90	13	ab	ab	NOUN
ejpam-1599	90	14	=	=	PROPN
ejpam-1599	90	15	abe	abe	PROPN
ejpam-1599	90	16	=	=	PROPN
ejpam-1599	90	17	bae	bae	PROPN
ejpam-1599	90	18	=	=	PROPN
ejpam-1599	90	19	e.	e.	PROPN
ejpam-1599	90	20	for	for	ADP
ejpam-1599	90	21	the	the	DET
ejpam-1599	90	22	second	second	ADJ
ejpam-1599	90	23	statement	statement	NOUN
ejpam-1599	90	24	,	,	PUNCT
ejpam-1599	90	25	we	we	PRON
ejpam-1599	90	26	have	have	VERB
ejpam-1599	90	27	only	only	ADV
ejpam-1599	90	28	to	to	PART
ejpam-1599	90	29	prove	prove	VERB
ejpam-1599	90	30	that	that	SCONJ
ejpam-1599	90	31	τa	τa	ADP
ejpam-1599	90	32	maps	maps	PROPN
ejpam-1599	90	33	w	w	PROPN
ejpam-1599	90	34	(	(	PUNCT
ejpam-1599	90	35	a	a	NOUN
ejpam-1599	90	36	)	)	PUNCT
ejpam-1599	90	37	∩	∩	NOUN
ejpam-1599	90	38	{	{	PUNCT
ejpam-1599	90	39	a}′′	a}′′	NOUN
ejpam-1599	90	40	onto	onto	ADP
ejpam-1599	90	41	σ2(a	σ2(a	NUM
ejpam-1599	90	42	)	)	PUNCT
ejpam-1599	90	43	,	,	PUNCT
ejpam-1599	90	44	but	but	CCONJ
ejpam-1599	90	45	this	this	PRON
ejpam-1599	90	46	follows	follow	VERB
ejpam-1599	90	47	from	from	ADP
ejpam-1599	90	48	theorem	theorem	ADJ
ejpam-1599	90	49	2	2	NUM
ejpam-1599	90	50	.	.	PUNCT
ejpam-1599	90	51	as	as	ADP
ejpam-1599	90	52	a	a	DET
ejpam-1599	90	53	consequence	consequence	NOUN
ejpam-1599	90	54	,	,	PUNCT
ejpam-1599	90	55	looking	look	VERB
ejpam-1599	90	56	for	for	ADP
ejpam-1599	90	57	commuting	commute	VERB
ejpam-1599	90	58	or	or	CCONJ
ejpam-1599	90	59	bicommuting	bicommute	VERB
ejpam-1599	90	60	outer	outer	ADJ
ejpam-1599	90	61	inverses	inverse	NOUN
ejpam-1599	90	62	can	can	AUX
ejpam-1599	90	63	be	be	AUX
ejpam-1599	90	64	handled	handle	VERB
ejpam-1599	90	65	through	through	ADP
ejpam-1599	90	66	idempotents	idempotent	NOUN
ejpam-1599	90	67	.	.	PUNCT
ejpam-1599	91	1	recall	recall	VERB
ejpam-1599	91	2	that	that	SCONJ
ejpam-1599	91	3	any	any	DET
ejpam-1599	91	4	set	set	NOUN
ejpam-1599	91	5	of	of	ADP
ejpam-1599	91	6	idempotents	idempotent	NOUN
ejpam-1599	91	7	may	may	AUX
ejpam-1599	91	8	be	be	AUX
ejpam-1599	91	9	partially	partially	ADV
ejpam-1599	91	10	ordered	order	VERB
ejpam-1599	91	11	by	by	ADP
ejpam-1599	91	12	e	e	PROPN
ejpam-1599	91	13	≤	≤	PROPN
ejpam-1599	92	1	f	f	X
ejpam-1599	92	2	⇐	⇐	ADJ
ejpam-1599	92	3	⇒	⇒	NOUN
ejpam-1599	92	4	e	e	X
ejpam-1599	92	5	f	f	X
ejpam-1599	92	6	=	=	SYM
ejpam-1599	92	7	f	f	X
ejpam-1599	92	8	e	e	X
ejpam-1599	92	9	=	=	SYM
ejpam-1599	92	10	e	e	PROPN
ejpam-1599	92	11	,	,	PUNCT
ejpam-1599	92	12	the	the	DET
ejpam-1599	92	13	natural	natural	ADJ
ejpam-1599	92	14	partial	partial	ADJ
ejpam-1599	92	15	order	order	NOUN
ejpam-1599	92	16	,	,	PUNCT
ejpam-1599	92	17	and	and	CCONJ
ejpam-1599	92	18	if	if	SCONJ
ejpam-1599	92	19	this	this	DET
ejpam-1599	92	20	set	set	NOUN
ejpam-1599	92	21	is	be	AUX
ejpam-1599	92	22	commutative	commutative	ADJ
ejpam-1599	92	23	,	,	PUNCT
ejpam-1599	92	24	then	then	ADV
ejpam-1599	92	25	this	this	DET
ejpam-1599	92	26	partial	partial	ADJ
ejpam-1599	92	27	order	order	NOUN
ejpam-1599	92	28	is	be	AUX
ejpam-1599	92	29	compatible	compatible	ADJ
ejpam-1599	92	30	with	with	ADP
ejpam-1599	92	31	multiplication	multiplication	NOUN
ejpam-1599	92	32	.	.	PUNCT
ejpam-1599	93	1	we	we	PRON
ejpam-1599	93	2	then	then	ADV
ejpam-1599	93	3	have	have	VERB
ejpam-1599	93	4	two	two	NUM
ejpam-1599	93	5	partial	partial	ADJ
ejpam-1599	93	6	orders	order	NOUN
ejpam-1599	93	7	on	on	ADP
ejpam-1599	93	8	e(s	e(s	PROPN
ejpam-1599	93	9	)	)	PUNCT
ejpam-1599	93	10	,	,	PUNCT
ejpam-1599	93	11	the	the	DET
ejpam-1599	93	12	natural	natural	ADJ
ejpam-1599	93	13	partial	partial	ADJ
ejpam-1599	93	14	order	order	NOUN
ejpam-1599	93	15	and	and	CCONJ
ejpam-1599	93	16	the	the	DET
ejpam-1599	93	17	h	h	NOUN
ejpam-1599	93	18	preorder	preorder	NOUN
ejpam-1599	93	19	(	(	PUNCT
ejpam-1599	93	20	that	that	PRON
ejpam-1599	93	21	reduces	reduce	VERB
ejpam-1599	93	22	to	to	ADP
ejpam-1599	93	23	a	a	DET
ejpam-1599	93	24	partial	partial	ADJ
ejpam-1599	93	25	order	order	NOUN
ejpam-1599	93	26	for	for	ADP
ejpam-1599	93	27	idempotents	idempotent	NOUN
ejpam-1599	93	28	since	since	SCONJ
ejpam-1599	93	29	a	a	DET
ejpam-1599	93	30	h	h	NOUN
ejpam-1599	93	31	-class	-class	NOUN
ejpam-1599	93	32	contains	contain	VERB
ejpam-1599	93	33	at	at	ADP
ejpam-1599	93	34	most	most	ADJ
ejpam-1599	93	35	one	one	NUM
ejpam-1599	93	36	idempotent	idempotent	NOUN
ejpam-1599	94	1	[	[	X
ejpam-1599	94	2	9	9	NUM
ejpam-1599	94	3	]	]	PUNCT
ejpam-1599	94	4	)	)	PUNCT
ejpam-1599	94	5	.	.	PUNCT
ejpam-1599	95	1	actually	actually	ADV
ejpam-1599	95	2	,	,	PUNCT
ejpam-1599	95	3	they	they	PRON
ejpam-1599	95	4	coincide	coincide	VERB
ejpam-1599	95	5	for	for	ADP
ejpam-1599	95	6	idempotents	idempotent	NOUN
ejpam-1599	95	7	.	.	PUNCT
ejpam-1599	96	1	if	if	SCONJ
ejpam-1599	96	2	e	e	PROPN
ejpam-1599	96	3	≤	≤	X
ejpam-1599	96	4	f	f	NOUN
ejpam-1599	96	5	,	,	PUNCT
ejpam-1599	96	6	then	then	ADV
ejpam-1599	96	7	e	e	X
ejpam-1599	96	8	=	=	PUNCT
ejpam-1599	96	9	e	e	X
ejpam-1599	96	10	f	f	PROPN
ejpam-1599	96	11	=	=	SYM
ejpam-1599	96	12	f	f	PROPN
ejpam-1599	96	13	e	e	PROPN
ejpam-1599	96	14	and	and	CCONJ
ejpam-1599	96	15	e	e	X
ejpam-1599	96	16	≤h	≤h	NOUN
ejpam-1599	96	17	f	f	PROPN
ejpam-1599	96	18	and	and	CCONJ
ejpam-1599	96	19	conversely	conversely	ADV
ejpam-1599	96	20	,	,	PUNCT
ejpam-1599	96	21	if	if	SCONJ
ejpam-1599	96	22	e	e	NOUN
ejpam-1599	96	23	=	=	NOUN
ejpam-1599	96	24	f	f	X
ejpam-1599	97	1	x	x	X
ejpam-1599	97	2	=	=	PUNCT
ejpam-1599	97	3	y	y	PROPN
ejpam-1599	97	4	f	f	PROPN
ejpam-1599	97	5	then	then	ADV
ejpam-1599	97	6	f	f	PROPN
ejpam-1599	97	7	e	e	PROPN
ejpam-1599	97	8	=	=	PUNCT
ejpam-1599	98	1	f	f	PROPN
ejpam-1599	98	2	f	f	NOUN
ejpam-1599	98	3	x	x	X
ejpam-1599	98	4	=	=	PUNCT
ejpam-1599	98	5	f	f	NOUN
ejpam-1599	98	6	x	x	PUNCT
ejpam-1599	99	1	=	=	PUNCT
ejpam-1599	99	2	e	e	X
ejpam-1599	99	3	=	=	SYM
ejpam-1599	99	4	y	y	PROPN
ejpam-1599	100	1	f	f	PROPN
ejpam-1599	100	2	=	=	SYM
ejpam-1599	101	1	y	y	PROPN
ejpam-1599	101	2	f	f	X
ejpam-1599	101	3	f	f	PROPN
ejpam-1599	101	4	=	=	SYM
ejpam-1599	101	5	e	e	X
ejpam-1599	101	6	f	f	PROPN
ejpam-1599	101	7	.	.	PUNCT
ejpam-1599	102	1	it	it	PRON
ejpam-1599	102	2	is	be	AUX
ejpam-1599	102	3	interesting	interesting	ADJ
ejpam-1599	102	4	to	to	PART
ejpam-1599	102	5	notice	notice	VERB
ejpam-1599	102	6	that	that	SCONJ
ejpam-1599	102	7	even	even	ADV
ejpam-1599	102	8	in	in	ADP
ejpam-1599	102	9	the	the	DET
ejpam-1599	102	10	noncommutative	noncommutative	ADJ
ejpam-1599	102	11	case	case	NOUN
ejpam-1599	102	12	,	,	PUNCT
ejpam-1599	102	13	invertibilty	invertibilty	NOUN
ejpam-1599	102	14	along	along	ADP
ejpam-1599	102	15	an	an	DET
ejpam-1599	102	16	idempotent	idempotent	NOUN
ejpam-1599	102	17	e	e	NOUN
ejpam-1599	102	18	can	can	AUX
ejpam-1599	102	19	be	be	AUX
ejpam-1599	102	20	expressed	express	VERB
ejpam-1599	102	21	as	as	ADP
ejpam-1599	102	22	invertibity	invertibity	NOUN
ejpam-1599	102	23	in	in	ADP
ejpam-1599	102	24	the	the	DET
ejpam-1599	102	25	local	local	ADJ
ejpam-1599	102	26	submonoid	submonoid	ADJ
ejpam-1599	102	27	ese	ese	NOUN
ejpam-1599	102	28	(	(	PUNCT
ejpam-1599	102	29	ring	ring	NOUN
ejpam-1599	102	30	theorists	theorist	NOUN
ejpam-1599	102	31	use	use	VERB
ejpam-1599	102	32	the	the	DET
ejpam-1599	102	33	word	word	NOUN
ejpam-1599	102	34	“	"	PUNCT
ejpam-1599	102	35	corner	corner	NOUN
ejpam-1599	102	36	ring	ring	NOUN
ejpam-1599	102	37	”	"	PUNCT
ejpam-1599	102	38	)	)	PUNCT
ejpam-1599	102	39	.	.	PUNCT
ejpam-1599	103	1	lemma	lemma	PROPN
ejpam-1599	103	2	4	4	X
ejpam-1599	103	3	.	.	PUNCT
ejpam-1599	103	4	let	let	VERB
ejpam-1599	103	5	a	a	DET
ejpam-1599	103	6	∈	∈	ADJ
ejpam-1599	103	7	s	s	NOUN
ejpam-1599	103	8	,	,	PUNCT
ejpam-1599	103	9	e	e	PROPN
ejpam-1599	103	10	∈	∈	PROPN
ejpam-1599	103	11	e(s	e(s	PROPN
ejpam-1599	103	12	)	)	PUNCT
ejpam-1599	103	13	.	.	PUNCT
ejpam-1599	104	1	then	then	ADV
ejpam-1599	104	2	e	e	PROPN
ejpam-1599	104	3	∈	∈	PROPN
ejpam-1599	104	4	σ0(a	σ0(a	PROPN
ejpam-1599	104	5	)	)	PUNCT
ejpam-1599	104	6	(	(	PUNCT
ejpam-1599	104	7	a−e	a−e	NOUN
ejpam-1599	104	8	exists	exist	VERB
ejpam-1599	104	9	)	)	PUNCT
ejpam-1599	105	1	if	if	SCONJ
ejpam-1599	105	2	and	and	CCONJ
ejpam-1599	105	3	only	only	ADV
ejpam-1599	105	4	if	if	SCONJ
ejpam-1599	105	5	eae	eae	PROPN
ejpam-1599	105	6	is	be	AUX
ejpam-1599	105	7	invertible	invertible	ADJ
ejpam-1599	105	8	in	in	ADP
ejpam-1599	105	9	the	the	DET
ejpam-1599	105	10	local	local	ADJ
ejpam-1599	105	11	submonoid	submonoid	ADJ
ejpam-1599	105	12	ese	ese	NOUN
ejpam-1599	105	13	.	.	PUNCT
ejpam-1599	106	1	in	in	ADP
ejpam-1599	106	2	this	this	DET
ejpam-1599	106	3	case	case	NOUN
ejpam-1599	106	4	a−e	a−e	NOUN
ejpam-1599	106	5	=	=	PUNCT
ejpam-1599	106	6	(	(	PUNCT
ejpam-1599	106	7	ea)#e	ea)#e	NOUN
ejpam-1599	106	8	=	=	PUNCT
ejpam-1599	106	9	e(ae	e(ae	NOUN
ejpam-1599	106	10	)	)	PUNCT
ejpam-1599	106	11	#	#	NOUN
ejpam-1599	106	12	=	=	SYM
ejpam-1599	106	13	(	(	PUNCT
ejpam-1599	106	14	eae	eae	NOUN
ejpam-1599	106	15	)	)	PUNCT
ejpam-1599	106	16	#	#	NOUN
ejpam-1599	106	17	=	=	SYM
ejpam-1599	106	18	(	(	PUNCT
ejpam-1599	106	19	eae)−1	eae)−1	NOUN
ejpam-1599	106	20	.	.	PUNCT
ejpam-1599	107	1	proof	proof	NOUN
ejpam-1599	107	2	.	.	PUNCT
ejpam-1599	108	1	assume	assume	VERB
ejpam-1599	108	2	a−e	a−e	NOUN
ejpam-1599	108	3	exists	exist	VERB
ejpam-1599	108	4	.	.	PUNCT
ejpam-1599	109	1	then	then	ADV
ejpam-1599	109	2	a−eh	a−eh	PRON
ejpam-1599	109	3	e	e	NOUN
ejpam-1599	109	4	hence	hence	ADV
ejpam-1599	109	5	a−e	a−e	NOUN
ejpam-1599	109	6	=	=	SYM
ejpam-1599	109	7	ea−e	ea−e	NOUN
ejpam-1599	109	8	=	=	PUNCT
ejpam-1599	109	9	a−ee	a−ee	PROPN
ejpam-1599	109	10	=	=	SYM
ejpam-1599	109	11	ea−ee	ea−ee	PRON
ejpam-1599	109	12	∈	∈	PROPN
ejpam-1599	109	13	ese	ese	NOUN
ejpam-1599	109	14	.	.	PUNCT
ejpam-1599	110	1	it	it	PRON
ejpam-1599	110	2	also	also	ADV
ejpam-1599	110	3	satisfies	satisfy	VERB
ejpam-1599	110	4	a−eae	a−eae	ADP
ejpam-1599	110	5	=	=	SYM
ejpam-1599	110	6	e	e	NOUN
ejpam-1599	110	7	=	=	SYM
ejpam-1599	110	8	eaa−e	eaa−e	PROPN
ejpam-1599	110	9	hence	hence	ADV
ejpam-1599	110	10	a−e(eae	a−e(eae	NUM
ejpam-1599	110	11	)	)	PUNCT
ejpam-1599	110	12	=	=	PUNCT
ejpam-1599	110	13	e	e	X
ejpam-1599	110	14	=	=	PUNCT
ejpam-1599	110	15	(	(	PUNCT
ejpam-1599	110	16	eae)a−e	eae)a−e	NOUN
ejpam-1599	110	17	and	and	CCONJ
ejpam-1599	110	18	eae	eae	PROPN
ejpam-1599	110	19	is	be	AUX
ejpam-1599	110	20	invertible	invertible	ADJ
ejpam-1599	110	21	in	in	ADP
ejpam-1599	110	22	the	the	DET
ejpam-1599	110	23	monoid	monoid	NOUN
ejpam-1599	110	24	ese	ese	NOUN
ejpam-1599	110	25	(	(	PUNCT
ejpam-1599	110	26	with	with	ADP
ejpam-1599	110	27	unit	unit	NOUN
ejpam-1599	110	28	e	e	NOUN
ejpam-1599	110	29	)	)	PUNCT
ejpam-1599	110	30	.	.	PUNCT
ejpam-1599	111	1	conversely	conversely	ADV
ejpam-1599	111	2	,	,	PUNCT
ejpam-1599	111	3	assume	assume	VERB
ejpam-1599	111	4	eae	eae	PROPN
ejpam-1599	111	5	is	be	AUX
ejpam-1599	111	6	invertible	invertible	ADJ
ejpam-1599	111	7	in	in	ADP
ejpam-1599	111	8	ese	ese	NOUN
ejpam-1599	111	9	with	with	ADP
ejpam-1599	111	10	inverse	inverse	NOUN
ejpam-1599	111	11	b	b	PROPN
ejpam-1599	111	12	∈	∈	PROPN
ejpam-1599	111	13	ese	ese	NOUN
ejpam-1599	111	14	.	.	PUNCT
ejpam-1599	112	1	then	then	ADV
ejpam-1599	112	2	b	b	X
ejpam-1599	112	3	≤h	≤h	NOUN
ejpam-1599	112	4	e	e	NOUN
ejpam-1599	112	5	and	and	CCONJ
ejpam-1599	112	6	bae	bae	PROPN
ejpam-1599	112	7	=	=	SYM
ejpam-1599	112	8	b(eae	b(eae	PROPN
ejpam-1599	112	9	)	)	PUNCT
ejpam-1599	113	1	=	=	PUNCT
ejpam-1599	113	2	e	e	X
ejpam-1599	113	3	=	=	PUNCT
ejpam-1599	113	4	(	(	PUNCT
ejpam-1599	113	5	eae)b	eae)b	ADJ
ejpam-1599	113	6	=	=	SYM
ejpam-1599	113	7	eab	eab	NOUN
ejpam-1599	113	8	and	and	CCONJ
ejpam-1599	113	9	b	b	PROPN
ejpam-1599	113	10	is	be	AUX
ejpam-1599	113	11	the	the	DET
ejpam-1599	113	12	inverse	inverse	NOUN
ejpam-1599	113	13	of	of	ADP
ejpam-1599	113	14	a	a	PRON
ejpam-1599	113	15	along	along	NOUN
ejpam-1599	113	16	e.	e.	PROPN
ejpam-1599	113	17	finally	finally	ADV
ejpam-1599	113	18	,	,	PUNCT
ejpam-1599	113	19	note	note	VERB
ejpam-1599	113	20	that	that	SCONJ
ejpam-1599	113	21	σ2(a	σ2(a	NOUN
ejpam-1599	113	22	)	)	PUNCT
ejpam-1599	113	23	is	be	AUX
ejpam-1599	113	24	a	a	DET
ejpam-1599	113	25	commutative	commutative	ADJ
ejpam-1599	113	26	band	band	NOUN
ejpam-1599	113	27	(	(	PUNCT
ejpam-1599	113	28	commutative	commutative	ADJ
ejpam-1599	113	29	semigroup	semigroup	NOUN
ejpam-1599	113	30	of	of	ADP
ejpam-1599	113	31	idempotents	idempotent	NOUN
ejpam-1599	113	32	,	,	PUNCT
ejpam-1599	113	33	semilattice	semilattice	NOUN
ejpam-1599	113	34	with	with	ADP
ejpam-1599	113	35	e	e	PROPN
ejpam-1599	113	36	∨	∨	X
ejpam-1599	113	37	f	f	X
ejpam-1599	113	38	=	=	SYM
ejpam-1599	113	39	e	e	X
ejpam-1599	113	40	f	f	PROPN
ejpam-1599	113	41	=	=	SYM
ejpam-1599	113	42	f	f	PROPN
ejpam-1599	113	43	e	e	NOUN
ejpam-1599	113	44	)	)	PUNCT
ejpam-1599	113	45	.	.	PUNCT
ejpam-1599	114	1	proposition	proposition	NOUN
ejpam-1599	114	2	1	1	NUM
ejpam-1599	114	3	.	.	PUNCT
ejpam-1599	114	4	σ2(a	σ2(a	NUM
ejpam-1599	114	5	)	)	PUNCT
ejpam-1599	114	6	is	be	AUX
ejpam-1599	114	7	a	a	DET
ejpam-1599	114	8	commutative	commutative	ADJ
ejpam-1599	114	9	subsemigroup	subsemigroup	NOUN
ejpam-1599	114	10	of	of	ADP
ejpam-1599	114	11	s.	s.	PROPN
ejpam-1599	114	12	proof	proof	PROPN
ejpam-1599	114	13	.	.	PUNCT
ejpam-1599	115	1	if	if	SCONJ
ejpam-1599	115	2	e	e	X
ejpam-1599	115	3	,	,	PUNCT
ejpam-1599	115	4	f	f	PROPN
ejpam-1599	115	5	∈	∈	PROPN
ejpam-1599	115	6	σ2(a	σ2(a	PROPN
ejpam-1599	115	7	)	)	PUNCT
ejpam-1599	115	8	,	,	PUNCT
ejpam-1599	115	9	then	then	ADV
ejpam-1599	115	10	e	e	PROPN
ejpam-1599	115	11	f	f	PROPN
ejpam-1599	115	12	=	=	SYM
ejpam-1599	115	13	f	f	PROPN
ejpam-1599	115	14	e	e	NOUN
ejpam-1599	115	15	≤h	≤h	PROPN
ejpam-1599	115	16	e	e	NOUN
ejpam-1599	115	17	≤h	≤h	NOUN
ejpam-1599	115	18	a.	a.	NOUN
ejpam-1599	115	19	we	we	PRON
ejpam-1599	115	20	have	have	VERB
ejpam-1599	115	21	to	to	PART
ejpam-1599	115	22	show	show	VERB
ejpam-1599	115	23	that	that	SCONJ
ejpam-1599	115	24	e	e	PROPN
ejpam-1599	115	25	f	f	PROPN
ejpam-1599	115	26	is	be	AUX
ejpam-1599	115	27	an	an	DET
ejpam-1599	115	28	idempotent	idempotent	NOUN
ejpam-1599	115	29	.	.	PUNCT
ejpam-1599	116	1	e	e	X
ejpam-1599	116	2	f	f	X
ejpam-1599	116	3	e	e	X
ejpam-1599	116	4	f	f	PROPN
ejpam-1599	116	5	=	=	SYM
ejpam-1599	116	6	e	e	PROPN
ejpam-1599	116	7	f	f	X
ejpam-1599	116	8	f	f	PROPN
ejpam-1599	116	9	e	e	PROPN
ejpam-1599	116	10	=	=	SYM
ejpam-1599	116	11	e	e	X
ejpam-1599	116	12	f	f	X
ejpam-1599	116	13	e	e	PROPN
ejpam-1599	116	14	=	=	PROPN
ejpam-1599	116	15	ee	ee	PROPN
ejpam-1599	116	16	f	f	PROPN
ejpam-1599	116	17	=	=	SYM
ejpam-1599	116	18	e	e	PROPN
ejpam-1599	116	19	f	f	PROPN
ejpam-1599	116	20	and	and	CCONJ
ejpam-1599	116	21	e	e	PROPN
ejpam-1599	116	22	f	f	PROPN
ejpam-1599	116	23	is	be	AUX
ejpam-1599	116	24	an	an	DET
ejpam-1599	116	25	idempotent	idempotent	NOUN
ejpam-1599	116	26	.	.	PUNCT
ejpam-1599	117	1	x.	x.	PROPN
ejpam-1599	117	2	mary	mary	PROPN
ejpam-1599	117	3	/	/	SYM
ejpam-1599	117	4	eur	eur	PROPN
ejpam-1599	117	5	.	.	PUNCT
ejpam-1599	118	1	j.	j.	PROPN
ejpam-1599	118	2	pure	pure	PROPN
ejpam-1599	118	3	appl	appl	PROPN
ejpam-1599	118	4	.	.	PROPN
ejpam-1599	118	5	math	math	PROPN
ejpam-1599	118	6	,	,	PUNCT
ejpam-1599	118	7	5	5	NUM
ejpam-1599	118	8	(	(	PUNCT
ejpam-1599	118	9	2012	2012	NUM
ejpam-1599	118	10	)	)	PUNCT
ejpam-1599	118	11	,	,	PUNCT
ejpam-1599	118	12	160	160	NUM
ejpam-1599	118	13	-	-	SYM
ejpam-1599	118	14	173	173	NUM
ejpam-1599	118	15	164	164	NUM
ejpam-1599	118	16	3	3	NUM
ejpam-1599	118	17	.	.	PUNCT
ejpam-1599	119	1	the	the	DET
ejpam-1599	119	2	natural	natural	ADJ
ejpam-1599	119	3	generalized	generalized	ADJ
ejpam-1599	119	4	inverse	inverse	NOUN
ejpam-1599	119	5	in	in	ADP
ejpam-1599	119	6	a	a	DET
ejpam-1599	119	7	semigroup	semigroup	ADJ
ejpam-1599	119	8	3.1	3.1	NUM
ejpam-1599	119	9	.	.	PUNCT
ejpam-1599	119	10	definition	definition	NOUN
ejpam-1599	119	11	and	and	CCONJ
ejpam-1599	119	12	first	first	ADJ
ejpam-1599	119	13	properties	property	NOUN
ejpam-1599	119	14	definition	definition	NOUN
ejpam-1599	119	15	2	2	X
ejpam-1599	119	16	.	.	PUNCT
ejpam-1599	120	1	let	let	VERB
ejpam-1599	120	2	s	s	PRON
ejpam-1599	120	3	be	be	AUX
ejpam-1599	120	4	a	a	DET
ejpam-1599	120	5	semigroup	semigroup	NOUN
ejpam-1599	120	6	,	,	PUNCT
ejpam-1599	120	7	a	a	DET
ejpam-1599	120	8	∈	∈	NOUN
ejpam-1599	120	9	s.	s.	PROPN
ejpam-1599	120	10	1	1	NUM
ejpam-1599	120	11	.	.	PUNCT
ejpam-1599	121	1	let	let	VERB
ejpam-1599	121	2	j	j	PROPN
ejpam-1599	121	3	=	=	NOUN
ejpam-1599	121	4	0,1,2	0,1,2	NUM
ejpam-1599	121	5	.	.	PUNCT
ejpam-1599	122	1	the	the	DET
ejpam-1599	122	2	element	element	NOUN
ejpam-1599	122	3	a	a	PRON
ejpam-1599	122	4	is	be	AUX
ejpam-1599	122	5	j−maximally	j−maximally	ADV
ejpam-1599	122	6	invertible	invertible	ADJ
ejpam-1599	122	7	if	if	SCONJ
ejpam-1599	122	8	the	the	DET
ejpam-1599	122	9	set	set	NOUN
ejpam-1599	122	10	σ	σ	PROPN
ejpam-1599	122	11	j(a	j(a	PROPN
ejpam-1599	122	12	)	)	PUNCT
ejpam-1599	122	13	admits	admit	VERB
ejpam-1599	122	14	maximal	maximal	ADJ
ejpam-1599	122	15	elements	element	NOUN
ejpam-1599	122	16	for	for	ADP
ejpam-1599	122	17	the	the	DET
ejpam-1599	122	18	natural	natural	ADJ
ejpam-1599	122	19	partial	partial	ADJ
ejpam-1599	122	20	order	order	NOUN
ejpam-1599	122	21	.	.	PUNCT
ejpam-1599	123	1	elements	element	NOUN
ejpam-1599	123	2	b	b	X
ejpam-1599	124	1	=	=	PUNCT
ejpam-1599	124	2	a−e	a−e	NOUN
ejpam-1599	124	3	where	where	SCONJ
ejpam-1599	124	4	e	e	NOUN
ejpam-1599	124	5	is	be	AUX
ejpam-1599	124	6	maximal	maximal	ADJ
ejpam-1599	124	7	are	be	AUX
ejpam-1599	124	8	then	then	ADV
ejpam-1599	124	9	called	call	VERB
ejpam-1599	124	10	j−maximal	j−maximal	PROPN
ejpam-1599	124	11	generalized	generalize	VERB
ejpam-1599	124	12	inverses	inverse	NOUN
ejpam-1599	124	13	of	of	ADP
ejpam-1599	124	14	a.	a.	NOUN
ejpam-1599	124	15	2	2	NUM
ejpam-1599	124	16	.	.	PUNCT
ejpam-1599	125	1	if	if	SCONJ
ejpam-1599	125	2	there	there	PRON
ejpam-1599	125	3	exists	exist	VERB
ejpam-1599	125	4	a	a	DET
ejpam-1599	125	5	greatest	great	ADJ
ejpam-1599	125	6	element	element	NOUN
ejpam-1599	125	7	m	m	PROPN
ejpam-1599	125	8	∈	∈	PROPN
ejpam-1599	125	9	σ	σ	NUM
ejpam-1599	125	10	j(a	j(a	PROPN
ejpam-1599	125	11	)	)	PUNCT
ejpam-1599	125	12	,	,	PUNCT
ejpam-1599	125	13	then	then	ADV
ejpam-1599	125	14	we	we	PRON
ejpam-1599	125	15	say	say	VERB
ejpam-1599	125	16	that	that	SCONJ
ejpam-1599	125	17	a	a	PRON
ejpam-1599	125	18	is	be	AUX
ejpam-1599	125	19	j−naturally	j−naturally	ADV
ejpam-1599	125	20	invertible	invertible	ADJ
ejpam-1599	125	21	,	,	PUNCT
ejpam-1599	125	22	and	and	CCONJ
ejpam-1599	125	23	b	b	X
ejpam-1599	125	24	=	=	NOUN
ejpam-1599	125	25	a−m	a−m	NOUN
ejpam-1599	125	26	is	be	AUX
ejpam-1599	125	27	called	call	VERB
ejpam-1599	125	28	the	the	DET
ejpam-1599	125	29	j−natural	j−natural	ADJ
ejpam-1599	125	30	(	(	PUNCT
ejpam-1599	125	31	generalized	generalized	ADJ
ejpam-1599	125	32	)	)	PUNCT
ejpam-1599	125	33	inverse	inverse	NOUN
ejpam-1599	125	34	of	of	ADP
ejpam-1599	125	35	a.	a.	NOUN
ejpam-1599	125	36	3	3	NUM
ejpam-1599	125	37	.	.	PUNCT
ejpam-1599	126	1	finally	finally	ADV
ejpam-1599	126	2	,	,	PUNCT
ejpam-1599	126	3	if	if	SCONJ
ejpam-1599	126	4	a	a	PRON
ejpam-1599	126	5	is	be	AUX
ejpam-1599	126	6	2−naturally	2−naturally	ADV
ejpam-1599	126	7	invertible	invertible	ADJ
ejpam-1599	126	8	,	,	PUNCT
ejpam-1599	126	9	the	the	DET
ejpam-1599	126	10	element	element	NOUN
ejpam-1599	126	11	am	be	AUX
ejpam-1599	126	12	=	=	PUNCT
ejpam-1599	126	13	aba	aba	PROPN
ejpam-1599	126	14	is	be	AUX
ejpam-1599	126	15	called	call	VERB
ejpam-1599	126	16	the	the	DET
ejpam-1599	126	17	core	core	NOUN
ejpam-1599	126	18	of	of	ADP
ejpam-1599	126	19	a.	a.	NOUN
ejpam-1599	126	20	we	we	PRON
ejpam-1599	126	21	will	will	AUX
ejpam-1599	126	22	mainly	mainly	ADV
ejpam-1599	126	23	deal	deal	VERB
ejpam-1599	126	24	with	with	ADP
ejpam-1599	126	25	the	the	DET
ejpam-1599	126	26	2−natural	2−natural	ADJ
ejpam-1599	126	27	inverse	inverse	NOUN
ejpam-1599	126	28	in	in	ADP
ejpam-1599	126	29	the	the	DET
ejpam-1599	126	30	sequel	sequel	NOUN
ejpam-1599	126	31	,	,	PUNCT
ejpam-1599	126	32	and	and	CCONJ
ejpam-1599	126	33	we	we	PRON
ejpam-1599	126	34	will	will	AUX
ejpam-1599	126	35	also	also	ADV
ejpam-1599	126	36	refer	refer	VERB
ejpam-1599	126	37	to	to	ADP
ejpam-1599	126	38	it	it	PRON
ejpam-1599	126	39	as	as	ADP
ejpam-1599	126	40	the	the	DET
ejpam-1599	126	41	natural	natural	ADJ
ejpam-1599	126	42	inverse	inverse	NOUN
ejpam-1599	126	43	.	.	PUNCT
ejpam-1599	127	1	as	as	SCONJ
ejpam-1599	127	2	noted	note	VERB
ejpam-1599	127	3	before	before	ADV
ejpam-1599	127	4	,	,	PUNCT
ejpam-1599	127	5	if	if	SCONJ
ejpam-1599	127	6	s	s	NOUN
ejpam-1599	127	7	is	be	AUX
ejpam-1599	127	8	commutative	commutative	ADJ
ejpam-1599	127	9	or	or	CCONJ
ejpam-1599	127	10	the	the	DET
ejpam-1599	127	11	idempotents	idempotent	NOUN
ejpam-1599	127	12	central	central	ADJ
ejpam-1599	127	13	then	then	ADV
ejpam-1599	127	14	the	the	DET
ejpam-1599	127	15	three	three	NUM
ejpam-1599	127	16	notions	notion	NOUN
ejpam-1599	127	17	coincide	coincide	NOUN
ejpam-1599	127	18	.	.	PUNCT
ejpam-1599	128	1	recall	recall	VERB
ejpam-1599	128	2	that	that	SCONJ
ejpam-1599	128	3	a	a	DET
ejpam-1599	128	4	semillatice	semillatice	NOUN
ejpam-1599	128	5	is	be	AUX
ejpam-1599	128	6	distributive	distributive	ADJ
ejpam-1599	128	7	if	if	SCONJ
ejpam-1599	128	8	e	e	PROPN
ejpam-1599	128	9	∨	∨	X
ejpam-1599	128	10	f	f	PROPN
ejpam-1599	128	11	≤	≤	NUM
ejpam-1599	128	12	x	x	PUNCT
ejpam-1599	128	13	implies	imply	VERB
ejpam-1599	128	14	the	the	DET
ejpam-1599	128	15	existence	existence	NOUN
ejpam-1599	128	16	of	of	ADP
ejpam-1599	128	17	e′	e′	PROPN
ejpam-1599	128	18	,	,	PUNCT
ejpam-1599	128	19	f	f	PROPN
ejpam-1599	128	20	′	′	NUM
ejpam-1599	128	21	such	such	ADJ
ejpam-1599	128	22	that	that	SCONJ
ejpam-1599	128	23	e	e	PROPN
ejpam-1599	128	24	≤	≤	NOUN
ejpam-1599	128	25	e′	e′	PROPN
ejpam-1599	128	26	,	,	PUNCT
ejpam-1599	129	1	f	f	PROPN
ejpam-1599	129	2	≤	≤	PROPN
ejpam-1599	130	1	f	f	PROPN
ejpam-1599	131	1	′	′	NOUN
ejpam-1599	132	1	and	and	CCONJ
ejpam-1599	132	2	x	x	X
ejpam-1599	132	3	=	=	SYM
ejpam-1599	132	4	e′	e′	X
ejpam-1599	132	5	∨	∨	PROPN
ejpam-1599	132	6	f	f	PROPN
ejpam-1599	132	7	′	′	NUM
ejpam-1599	132	8	.	.	PUNCT
ejpam-1599	133	1	proposition	proposition	NOUN
ejpam-1599	133	2	2	2	NUM
ejpam-1599	133	3	.	.	PUNCT
ejpam-1599	134	1	if	if	SCONJ
ejpam-1599	134	2	the	the	DET
ejpam-1599	134	3	semilattice	semilattice	NOUN
ejpam-1599	134	4	σ2(a	σ2(a	NOUN
ejpam-1599	134	5	)	)	PUNCT
ejpam-1599	134	6	is	be	AUX
ejpam-1599	134	7	distributive	distributive	ADJ
ejpam-1599	134	8	,	,	PUNCT
ejpam-1599	134	9	then	then	ADV
ejpam-1599	134	10	any	any	DET
ejpam-1599	134	11	2−maximally	2−maximally	ADV
ejpam-1599	134	12	invertible	invertible	ADJ
ejpam-1599	134	13	element	element	NOUN
ejpam-1599	134	14	is	be	AUX
ejpam-1599	134	15	naturally	naturally	ADV
ejpam-1599	134	16	invertible	invertible	ADJ
ejpam-1599	134	17	.	.	PUNCT
ejpam-1599	135	1	proof	proof	NOUN
ejpam-1599	135	2	.	.	PUNCT
ejpam-1599	136	1	let	let	VERB
ejpam-1599	136	2	e	e	PRON
ejpam-1599	136	3	be	be	AUX
ejpam-1599	136	4	a	a	DET
ejpam-1599	136	5	maximal	maximal	ADJ
ejpam-1599	136	6	element	element	NOUN
ejpam-1599	136	7	of	of	ADP
ejpam-1599	136	8	σ2(a	σ2(a	PROPN
ejpam-1599	136	9	)	)	PUNCT
ejpam-1599	136	10	,	,	PUNCT
ejpam-1599	136	11	f	f	PROPN
ejpam-1599	136	12	∈	∈	PROPN
ejpam-1599	136	13	σ2(a	σ2(a	PROPN
ejpam-1599	136	14	)	)	PUNCT
ejpam-1599	136	15	.	.	PUNCT
ejpam-1599	137	1	then	then	ADV
ejpam-1599	137	2	e	e	X
ejpam-1599	137	3	f	f	PROPN
ejpam-1599	137	4	=	=	SYM
ejpam-1599	137	5	f	f	PROPN
ejpam-1599	137	6	e	e	NOUN
ejpam-1599	137	7	≤	≤	NOUN
ejpam-1599	137	8	e	e	NOUN
ejpam-1599	137	9	and	and	CCONJ
ejpam-1599	137	10	exists	exist	VERB
ejpam-1599	137	11	e′	e′	PROPN
ejpam-1599	137	12	,	,	PUNCT
ejpam-1599	137	13	f	f	PROPN
ejpam-1599	137	14	′	′	NUM
ejpam-1599	137	15	such	such	ADJ
ejpam-1599	137	16	that	that	SCONJ
ejpam-1599	137	17	e	e	PROPN
ejpam-1599	137	18	≤	≤	NOUN
ejpam-1599	137	19	e′	e′	PROPN
ejpam-1599	137	20	,	,	PUNCT
ejpam-1599	137	21	f	f	PROPN
ejpam-1599	137	22	≤	≤	PROPN
ejpam-1599	138	1	f	f	X
ejpam-1599	138	2	′	′	NOUN
ejpam-1599	139	1	and	and	CCONJ
ejpam-1599	139	2	e	e	X
ejpam-1599	139	3	=	=	PUNCT
ejpam-1599	139	4	e′	e′	PROPN
ejpam-1599	139	5	f	f	PROPN
ejpam-1599	139	6	′.	′.	NOUN
ejpam-1599	139	7	by	by	ADP
ejpam-1599	139	8	maximality	maximality	PROPN
ejpam-1599	139	9	,	,	PUNCT
ejpam-1599	139	10	e′	e′	X
ejpam-1599	139	11	=	=	SYM
ejpam-1599	139	12	e	e	PROPN
ejpam-1599	139	13	and	and	CCONJ
ejpam-1599	139	14	we	we	PRON
ejpam-1599	139	15	get	get	VERB
ejpam-1599	139	16	e	e	NOUN
ejpam-1599	139	17	=	=	SYM
ejpam-1599	140	1	e	e	X
ejpam-1599	140	2	f	f	NOUN
ejpam-1599	140	3	′	′	NUM
ejpam-1599	140	4	=	=	PUNCT
ejpam-1599	140	5	f	f	PROPN
ejpam-1599	140	6	′e	′e	PROPN
ejpam-1599	140	7	.	.	PUNCT
ejpam-1599	141	1	it	it	PRON
ejpam-1599	141	2	follows	follow	VERB
ejpam-1599	141	3	that	that	SCONJ
ejpam-1599	141	4	e	e	NOUN
ejpam-1599	141	5	≤	≤	X
ejpam-1599	141	6	f	f	NOUN
ejpam-1599	142	1	′	′	NOUN
ejpam-1599	142	2	hence	hence	ADV
ejpam-1599	142	3	e	e	X
ejpam-1599	143	1	=	=	SYM
ejpam-1599	143	2	f	f	X
ejpam-1599	143	3	′	′	NOUN
ejpam-1599	143	4	and	and	CCONJ
ejpam-1599	143	5	f	f	PROPN
ejpam-1599	143	6	≤	≤	PROPN
ejpam-1599	143	7	e.	e.	PROPN
ejpam-1599	143	8	e	e	PROPN
ejpam-1599	143	9	is	be	AUX
ejpam-1599	143	10	the	the	DET
ejpam-1599	143	11	greatest	great	ADJ
ejpam-1599	143	12	element	element	NOUN
ejpam-1599	143	13	in	in	ADP
ejpam-1599	143	14	σ2(a	σ2(a	PROPN
ejpam-1599	143	15	)	)	PUNCT
ejpam-1599	143	16	.	.	PUNCT
ejpam-1599	144	1	the	the	DET
ejpam-1599	144	2	natural	natural	ADJ
ejpam-1599	144	3	inverse	inverse	NOUN
ejpam-1599	144	4	generalizes	generalize	VERB
ejpam-1599	144	5	the	the	DET
ejpam-1599	144	6	drazin	drazin	PROPN
ejpam-1599	144	7	inverse	inverse	NOUN
ejpam-1599	145	1	[	[	X
ejpam-1599	145	2	4	4	NUM
ejpam-1599	145	3	]	]	PUNCT
ejpam-1599	145	4	.	.	PUNCT
ejpam-1599	146	1	theorem	theorem	ADJ
ejpam-1599	146	2	4	4	NUM
ejpam-1599	146	3	.	.	PUNCT
ejpam-1599	146	4	assume	assume	VERB
ejpam-1599	146	5	a	a	PRON
ejpam-1599	146	6	is	be	AUX
ejpam-1599	146	7	drazin	drazin	NOUN
ejpam-1599	146	8	invertible	invertible	ADJ
ejpam-1599	146	9	with	with	ADP
ejpam-1599	146	10	inverse	inverse	NOUN
ejpam-1599	146	11	ad	ad	NOUN
ejpam-1599	146	12	.	.	PUNCT
ejpam-1599	147	1	then	then	ADV
ejpam-1599	147	2	a	a	PRON
ejpam-1599	147	3	is	be	AUX
ejpam-1599	147	4	1	1	NUM
ejpam-1599	147	5	and	and	CCONJ
ejpam-1599	147	6	2−naturally	2−naturally	ADV
ejpam-1599	147	7	invertible	invertible	ADJ
ejpam-1599	147	8	with	with	ADP
ejpam-1599	147	9	inverse	inverse	NOUN
ejpam-1599	147	10	a−m	a−m	NOUN
ejpam-1599	147	11	=	=	SYM
ejpam-1599	147	12	ad	ad	NOUN
ejpam-1599	147	13	.	.	PUNCT
ejpam-1599	148	1	proof	proof	NOUN
ejpam-1599	148	2	.	.	PUNCT
ejpam-1599	149	1	let	let	VERB
ejpam-1599	149	2	a	a	PRON
ejpam-1599	149	3	be	be	AUX
ejpam-1599	149	4	drazin	drazin	NOUN
ejpam-1599	149	5	invertible	invertible	ADJ
ejpam-1599	149	6	with	with	ADP
ejpam-1599	149	7	index	index	NOUN
ejpam-1599	149	8	n	n	NOUN
ejpam-1599	149	9	and	and	CCONJ
ejpam-1599	149	10	inverse	inverse	NOUN
ejpam-1599	149	11	ad	ad	NOUN
ejpam-1599	149	12	.	.	PUNCT
ejpam-1599	150	1	then	then	ADV
ejpam-1599	150	2	e	e	X
ejpam-1599	150	3	=	=	PUNCT
ejpam-1599	150	4	aad	aad	PROPN
ejpam-1599	150	5	=	=	PROPN
ejpam-1599	150	6	ada	ada	PROPN
ejpam-1599	150	7	∈	∈	PROPN
ejpam-1599	150	8	σ2(a	σ2(a	PROPN
ejpam-1599	150	9	)	)	PUNCT
ejpam-1599	151	1	⊂	⊂	PROPN
ejpam-1599	151	2	σ1(a	σ1(a	NUM
ejpam-1599	151	3	)	)	PUNCT
ejpam-1599	151	4	,	,	PUNCT
ejpam-1599	151	5	and	and	CCONJ
ejpam-1599	151	6	adan+1	adan+1	PROPN
ejpam-1599	151	7	=	=	SYM
ejpam-1599	151	8	an+1ad	an+1ad	PROPN
ejpam-1599	151	9	=	=	SYM
ejpam-1599	151	10	an	an	X
ejpam-1599	151	11	.	.	PUNCT
ejpam-1599	152	1	let	let	VERB
ejpam-1599	152	2	f	f	PROPN
ejpam-1599	152	3	∈	∈	PROPN
ejpam-1599	152	4	σ1(a	σ1(a	PROPN
ejpam-1599	152	5	)	)	PUNCT
ejpam-1599	152	6	.	.	PUNCT
ejpam-1599	153	1	then	then	ADV
ejpam-1599	153	2	a−	a−	PROPN
ejpam-1599	153	3	f	f	PROPN
ejpam-1599	153	4	satisfies	satisfy	VERB
ejpam-1599	153	5	a−	a−	PROPN
ejpam-1599	153	6	f	f	PROPN
ejpam-1599	153	7	a	a	DET
ejpam-1599	153	8	f	f	X
ejpam-1599	153	9	=	=	SYM
ejpam-1599	153	10	f	f	PROPN
ejpam-1599	153	11	=	=	PUNCT
ejpam-1599	153	12	aa−	aa−	PROPN
ejpam-1599	153	13	f	f	X
ejpam-1599	153	14	f	f	PROPN
ejpam-1599	153	15	=	=	SYM
ejpam-1599	153	16	f	f	PROPN
ejpam-1599	153	17	aa−	aa−	PROPN
ejpam-1599	153	18	f	f	X
ejpam-1599	153	19	=	=	SYM
ejpam-1599	153	20	f	f	PROPN
ejpam-1599	153	21	a−	a−	PROPN
ejpam-1599	153	22	f	f	PROPN
ejpam-1599	153	23	a.	a.	NOUN
ejpam-1599	153	24	it	it	PRON
ejpam-1599	153	25	follows	follow	VERB
ejpam-1599	153	26	that	that	SCONJ
ejpam-1599	153	27	f	f	PROPN
ejpam-1599	153	28	=	=	SYM
ejpam-1599	153	29	f	f	PROPN
ejpam-1599	153	30	�	�	PROPN
ejpam-1599	153	31	a−	a−	PROPN
ejpam-1599	153	32	f	f	PROPN
ejpam-1599	153	33	�	�	PROPN
ejpam-1599	153	34	n+1	n+1	PROPN
ejpam-1599	153	35	an+1	an+1	NOUN
ejpam-1599	153	36	.	.	PUNCT
ejpam-1599	154	1	then	then	ADV
ejpam-1599	154	2	f	f	PROPN
ejpam-1599	154	3	e	e	PROPN
ejpam-1599	154	4	=	=	SYM
ejpam-1599	154	5	f	f	PROPN
ejpam-1599	154	6	�	�	PROPN
ejpam-1599	154	7	a−	a−	PROPN
ejpam-1599	154	8	f	f	PROPN
ejpam-1599	154	9	�	�	PROPN
ejpam-1599	154	10	n+1	n+1	PROPN
ejpam-1599	154	11	an+1ada	an+1ada	PUNCT
ejpam-1599	154	12	=	=	SYM
ejpam-1599	155	1	f	f	PROPN
ejpam-1599	155	2	.	.	PUNCT
ejpam-1599	156	1	also	also	ADV
ejpam-1599	156	2	f	f	X
ejpam-1599	156	3	e	e	NOUN
ejpam-1599	156	4	=	=	SYM
ejpam-1599	156	5	e	e	X
ejpam-1599	156	6	f	f	X
ejpam-1599	156	7	(	(	PUNCT
ejpam-1599	156	8	e	e	NOUN
ejpam-1599	156	9	=	=	NOUN
ejpam-1599	156	10	aad	aad	PROPN
ejpam-1599	156	11	=	=	PROPN
ejpam-1599	156	12	ada	ada	PROPN
ejpam-1599	156	13	∈	∈	PROPN
ejpam-1599	156	14	σ2(a	σ2(a	PROPN
ejpam-1599	156	15	)	)	PUNCT
ejpam-1599	156	16	)	)	PUNCT
ejpam-1599	157	1	hence	hence	ADV
ejpam-1599	157	2	f	f	PROPN
ejpam-1599	157	3	≤	≤	PROPN
ejpam-1599	157	4	e.	e.	PROPN
ejpam-1599	157	5	3.2	3.2	NUM
ejpam-1599	157	6	.	.	PUNCT
ejpam-1599	158	1	examples	example	NOUN
ejpam-1599	158	2	many	many	ADJ
ejpam-1599	158	3	maximal	maximal	ADJ
ejpam-1599	158	4	inverses	inverse	NOUN
ejpam-1599	158	5	.	.	PUNCT
ejpam-1599	159	1	let	let	VERB
ejpam-1599	159	2	s	s	PRON
ejpam-1599	159	3	be	be	AUX
ejpam-1599	159	4	the	the	DET
ejpam-1599	159	5	semigroup	semigroup	NOUN
ejpam-1599	159	6	generated	generate	VERB
ejpam-1599	159	7	by	by	ADP
ejpam-1599	159	8	three	three	NUM
ejpam-1599	159	9	elements	element	NOUN
ejpam-1599	159	10	e	e	NOUN
ejpam-1599	159	11	,	,	PUNCT
ejpam-1599	159	12	f	f	PROPN
ejpam-1599	159	13	,	,	PUNCT
ejpam-1599	159	14	a	a	DET
ejpam-1599	159	15	subject	subject	NOUN
ejpam-1599	159	16	to	to	ADP
ejpam-1599	159	17	the	the	DET
ejpam-1599	159	18	conditions	condition	NOUN
ejpam-1599	159	19	e	e	X
ejpam-1599	159	20	=	=	SYM
ejpam-1599	159	21	e2	e2	PROPN
ejpam-1599	159	22	=	=	SYM
ejpam-1599	159	23	ea	ea	PROPN
ejpam-1599	159	24	=	=	SYM
ejpam-1599	159	25	ae	ae	PROPN
ejpam-1599	159	26	,	,	PUNCT
ejpam-1599	159	27	f	f	PROPN
ejpam-1599	159	28	=	=	SYM
ejpam-1599	159	29	f	f	PROPN
ejpam-1599	159	30	2	2	NUM
ejpam-1599	159	31	=	=	SYM
ejpam-1599	159	32	f	f	PROPN
ejpam-1599	160	1	a	a	NOUN
ejpam-1599	160	2	=	=	X
ejpam-1599	160	3	a	a	DET
ejpam-1599	160	4	f	f	NOUN
ejpam-1599	160	5	and	and	CCONJ
ejpam-1599	161	1	e	e	X
ejpam-1599	161	2	f	f	PROPN
ejpam-1599	161	3	=	=	SYM
ejpam-1599	161	4	f	f	PROPN
ejpam-1599	161	5	e.	e.	PROPN
ejpam-1599	161	6	then	then	ADV
ejpam-1599	161	7	s	s	VERB
ejpam-1599	161	8	is	be	AUX
ejpam-1599	161	9	commutative	commutative	ADJ
ejpam-1599	161	10	,	,	PUNCT
ejpam-1599	161	11	a	a	PRON
ejpam-1599	161	12	is	be	AUX
ejpam-1599	161	13	maximally	maximally	ADV
ejpam-1599	161	14	invertible	invertible	ADJ
ejpam-1599	161	15	but	but	CCONJ
ejpam-1599	161	16	not	not	PART
ejpam-1599	161	17	naturally	naturally	ADV
ejpam-1599	161	18	invertible	invertible	ADJ
ejpam-1599	161	19	,	,	PUNCT
ejpam-1599	161	20	with	with	ADP
ejpam-1599	161	21	two	two	NUM
ejpam-1599	161	22	maximal	maximal	ADJ
ejpam-1599	161	23	inverses	inverse	NOUN
ejpam-1599	161	24	a−e	a−e	NOUN
ejpam-1599	161	25	=	=	SYM
ejpam-1599	161	26	e	e	NOUN
ejpam-1599	161	27	and	and	CCONJ
ejpam-1599	161	28	a−	a−	PROPN
ejpam-1599	161	29	f	f	PROPN
ejpam-1599	162	1	=	=	SYM
ejpam-1599	162	2	f	f	PROPN
ejpam-1599	162	3	.	.	PUNCT
ejpam-1599	163	1	x.	x.	PROPN
ejpam-1599	163	2	mary	mary	PROPN
ejpam-1599	163	3	/	/	SYM
ejpam-1599	163	4	eur	eur	PROPN
ejpam-1599	163	5	.	.	PUNCT
ejpam-1599	164	1	j.	j.	PROPN
ejpam-1599	164	2	pure	pure	PROPN
ejpam-1599	164	3	appl	appl	PROPN
ejpam-1599	164	4	.	.	PROPN
ejpam-1599	164	5	math	math	PROPN
ejpam-1599	164	6	,	,	PUNCT
ejpam-1599	164	7	5	5	NUM
ejpam-1599	164	8	(	(	PUNCT
ejpam-1599	164	9	2012	2012	NUM
ejpam-1599	164	10	)	)	PUNCT
ejpam-1599	164	11	,	,	PUNCT
ejpam-1599	164	12	160	160	NUM
ejpam-1599	164	13	-	-	SYM
ejpam-1599	164	14	173	173	NUM
ejpam-1599	164	15	165	165	NUM
ejpam-1599	164	16	we	we	PRON
ejpam-1599	164	17	consider	consider	VERB
ejpam-1599	164	18	now	now	ADV
ejpam-1599	164	19	a	a	DET
ejpam-1599	164	20	simple	simple	ADJ
ejpam-1599	164	21	variant	variant	NOUN
ejpam-1599	164	22	of	of	ADP
ejpam-1599	164	23	the	the	DET
ejpam-1599	164	24	previous	previous	ADJ
ejpam-1599	164	25	example	example	NOUN
ejpam-1599	164	26	.	.	PUNCT
ejpam-1599	165	1	let	let	VERB
ejpam-1599	165	2	s′	s′	PROPN
ejpam-1599	165	3	be	be	AUX
ejpam-1599	165	4	the	the	DET
ejpam-1599	165	5	semigroup	semigroup	NOUN
ejpam-1599	165	6	generated	generate	VERB
ejpam-1599	165	7	by	by	ADP
ejpam-1599	165	8	three	three	NUM
ejpam-1599	165	9	elements	element	NOUN
ejpam-1599	165	10	e	e	NOUN
ejpam-1599	165	11	,	,	PUNCT
ejpam-1599	165	12	f	f	PROPN
ejpam-1599	165	13	,	,	PUNCT
ejpam-1599	165	14	a	a	DET
ejpam-1599	165	15	subject	subject	NOUN
ejpam-1599	165	16	to	to	ADP
ejpam-1599	165	17	the	the	DET
ejpam-1599	165	18	conditions	condition	NOUN
ejpam-1599	165	19	e	e	X
ejpam-1599	165	20	=	=	SYM
ejpam-1599	165	21	e2	e2	PROPN
ejpam-1599	165	22	=	=	SYM
ejpam-1599	165	23	ea	ea	PROPN
ejpam-1599	165	24	=	=	SYM
ejpam-1599	165	25	ae	ae	PROPN
ejpam-1599	165	26	,	,	PUNCT
ejpam-1599	165	27	f	f	PROPN
ejpam-1599	165	28	=	=	SYM
ejpam-1599	165	29	f	f	PROPN
ejpam-1599	165	30	2	2	NUM
ejpam-1599	165	31	=	=	SYM
ejpam-1599	165	32	f	f	PROPN
ejpam-1599	166	1	a	a	NOUN
ejpam-1599	166	2	=	=	X
ejpam-1599	166	3	a	a	DET
ejpam-1599	166	4	f	f	NOUN
ejpam-1599	166	5	and	and	CCONJ
ejpam-1599	166	6	e	e	X
ejpam-1599	166	7	f	f	PROPN
ejpam-1599	166	8	=	=	SYM
ejpam-1599	166	9	e	e	PROPN
ejpam-1599	166	10	,	,	PUNCT
ejpam-1599	166	11	f	f	PROPN
ejpam-1599	166	12	e	e	PROPN
ejpam-1599	166	13	=	=	PROPN
ejpam-1599	166	14	f	f	PROPN
ejpam-1599	166	15	.	.	PUNCT
ejpam-1599	167	1	then	then	ADV
ejpam-1599	167	2	σ1(a	σ1(a	NUM
ejpam-1599	167	3	)	)	PUNCT
ejpam-1599	167	4	=	=	PRON
ejpam-1599	167	5	{	{	PUNCT
ejpam-1599	167	6	e	e	PROPN
ejpam-1599	167	7	,	,	PUNCT
ejpam-1599	167	8	f	f	PROPN
ejpam-1599	167	9	}	}	PUNCT
ejpam-1599	167	10	but	but	CCONJ
ejpam-1599	167	11	σ2(a	σ2(a	NUM
ejpam-1599	167	12	)	)	PUNCT
ejpam-1599	167	13	is	be	AUX
ejpam-1599	167	14	empty	empty	ADJ
ejpam-1599	167	15	since	since	SCONJ
ejpam-1599	167	16	e	e	PROPN
ejpam-1599	167	17	and	and	CCONJ
ejpam-1599	167	18	f	f	X
ejpam-1599	167	19	do	do	AUX
ejpam-1599	167	20	not	not	PART
ejpam-1599	167	21	commute	commute	VERB
ejpam-1599	167	22	.	.	PUNCT
ejpam-1599	168	1	right	right	ADJ
ejpam-1599	168	2	hereditary	hereditary	ADJ
ejpam-1599	168	3	semigroups	semigroup	NOUN
ejpam-1599	168	4	with	with	ADP
ejpam-1599	168	5	central	central	ADJ
ejpam-1599	168	6	idempotents	idempotent	NOUN
ejpam-1599	168	7	[	[	X
ejpam-1599	168	8	6	6	NUM
ejpam-1599	168	9	]	]	PUNCT
ejpam-1599	168	10	.	.	PUNCT
ejpam-1599	169	1	in	in	ADP
ejpam-1599	169	2	this	this	DET
ejpam-1599	169	3	example	example	NOUN
ejpam-1599	169	4	we	we	PRON
ejpam-1599	169	5	notably	notably	ADV
ejpam-1599	169	6	show	show	VERB
ejpam-1599	169	7	that	that	SCONJ
ejpam-1599	169	8	elements	element	NOUN
ejpam-1599	169	9	of	of	ADP
ejpam-1599	169	10	a	a	DET
ejpam-1599	169	11	right	right	ADJ
ejpam-1599	169	12	hereditary	hereditary	ADJ
ejpam-1599	169	13	semigroup	semigroup	NOUN
ejpam-1599	169	14	with	with	ADP
ejpam-1599	169	15	central	central	ADJ
ejpam-1599	169	16	idempotents	idempotent	NOUN
ejpam-1599	169	17	are	be	AUX
ejpam-1599	169	18	naturally	naturally	ADV
ejpam-1599	169	19	invertible	invertible	ADJ
ejpam-1599	169	20	,	,	PUNCT
ejpam-1599	169	21	and	and	CCONJ
ejpam-1599	169	22	describe	describe	VERB
ejpam-1599	169	23	the	the	DET
ejpam-1599	169	24	set	set	NOUN
ejpam-1599	169	25	σ(a	σ(a	PROPN
ejpam-1599	169	26	)	)	PUNCT
ejpam-1599	169	27	.	.	PUNCT
ejpam-1599	170	1	let	let	VERB
ejpam-1599	170	2	s	s	PRON
ejpam-1599	170	3	be	be	AUX
ejpam-1599	170	4	a	a	DET
ejpam-1599	170	5	right	right	ADJ
ejpam-1599	170	6	p.p	p.p	PROPN
ejpam-1599	170	7	.	.	PUNCT
ejpam-1599	170	8	(	(	PUNCT
ejpam-1599	170	9	principal	principal	NOUN
ejpam-1599	170	10	projective	projective	NOUN
ejpam-1599	170	11	)	)	PUNCT
ejpam-1599	170	12	semigroup	semigroup	NOUN
ejpam-1599	170	13	with	with	ADP
ejpam-1599	170	14	central	central	ADJ
ejpam-1599	170	15	idempotents	idempotent	NOUN
ejpam-1599	170	16	as	as	SCONJ
ejpam-1599	170	17	defined	define	VERB
ejpam-1599	170	18	in	in	ADP
ejpam-1599	170	19	[	[	X
ejpam-1599	170	20	6	6	NUM
ejpam-1599	170	21	]	]	PUNCT
ejpam-1599	170	22	.	.	PUNCT
ejpam-1599	171	1	then	then	ADV
ejpam-1599	171	2	e(s	e(s	PROPN
ejpam-1599	171	3	)	)	PUNCT
ejpam-1599	171	4	is	be	AUX
ejpam-1599	171	5	a	a	DET
ejpam-1599	171	6	semillatice	semillatice	NOUN
ejpam-1599	171	7	(	(	PUNCT
ejpam-1599	171	8	for	for	ADP
ejpam-1599	171	9	the	the	DET
ejpam-1599	171	10	natural	natural	ADJ
ejpam-1599	171	11	partial	partial	ADJ
ejpam-1599	171	12	order	order	NOUN
ejpam-1599	171	13	)	)	PUNCT
ejpam-1599	171	14	.	.	PUNCT
ejpam-1599	172	1	for	for	ADP
ejpam-1599	172	2	any	any	DET
ejpam-1599	172	3	e	e	PROPN
ejpam-1599	172	4	∈	∈	PROPN
ejpam-1599	172	5	e(s	e(s	PROPN
ejpam-1599	172	6	)	)	PUNCT
ejpam-1599	172	7	,	,	PUNCT
ejpam-1599	172	8	define	define	VERB
ejpam-1599	172	9	ye	ye	NUM
ejpam-1599	172	10	=	=	SYM
ejpam-1599	172	11	{	{	PUNCT
ejpam-1599	172	12	x	x	PUNCT
ejpam-1599	172	13	∈	∈	PROPN
ejpam-1599	172	14	s	s	NOUN
ejpam-1599	172	15	,	,	PUNCT
ejpam-1599	172	16	xe	xe	PROPN
ejpam-1599	172	17	=	=	PROPN
ejpam-1599	172	18	x	x	PROPN
ejpam-1599	172	19	and	and	CCONJ
ejpam-1599	172	20	xs	xs	PROPN
ejpam-1599	172	21	=	=	PUNCT
ejpam-1599	172	22	x	x	SYM
ejpam-1599	172	23	t	t	NOUN
ejpam-1599	172	24	⇒	⇒	NOUN
ejpam-1599	172	25	es	es	X
ejpam-1599	172	26	=	=	PUNCT
ejpam-1599	172	27	et	et	NOUN
ejpam-1599	172	28	}	}	PUNCT
ejpam-1599	172	29	(	(	PUNCT
ejpam-1599	172	30	that	that	PRON
ejpam-1599	172	31	is	be	AUX
ejpam-1599	172	32	the	the	DET
ejpam-1599	172	33	l	l	NOUN
ejpam-1599	172	34	∗−class	∗−class	NOUN
ejpam-1599	172	35	of	of	ADP
ejpam-1599	172	36	e	e	PROPN
ejpam-1599	172	37	for	for	ADP
ejpam-1599	172	38	the	the	DET
ejpam-1599	172	39	extended	extend	VERB
ejpam-1599	172	40	green	green	NOUN
ejpam-1599	172	41	’s	’s	PART
ejpam-1599	172	42	relation	relation	NOUN
ejpam-1599	172	43	l	l	PROPN
ejpam-1599	172	44	∗	∗	NOUN
ejpam-1599	173	1	[	[	X
ejpam-1599	173	2	7	7	NUM
ejpam-1599	173	3	]	]	NUM
ejpam-1599	173	4	)	)	PUNCT
ejpam-1599	173	5	.	.	PUNCT
ejpam-1599	174	1	then	then	ADV
ejpam-1599	174	2	ye	ye	PRON
ejpam-1599	174	3	is	be	AUX
ejpam-1599	174	4	a	a	DET
ejpam-1599	174	5	cancellative	cancellative	ADJ
ejpam-1599	174	6	monoid	monoid	NOUN
ejpam-1599	174	7	(	(	PUNCT
ejpam-1599	174	8	with	with	ADP
ejpam-1599	174	9	unit	unit	NOUN
ejpam-1599	174	10	e	e	NOUN
ejpam-1599	174	11	)	)	PUNCT
ejpam-1599	174	12	and	and	CCONJ
ejpam-1599	174	13	the	the	DET
ejpam-1599	174	14	structure	structure	NOUN
ejpam-1599	174	15	theorem	theorem	NOUN
ejpam-1599	174	16	of	of	ADP
ejpam-1599	174	17	fountain	fountain	NOUN
ejpam-1599	174	18	says	say	VERB
ejpam-1599	174	19	that	that	SCONJ
ejpam-1599	174	20	s	s	VERB
ejpam-1599	174	21	is	be	AUX
ejpam-1599	174	22	the	the	DET
ejpam-1599	174	23	semillatice	semillatice	NOUN
ejpam-1599	174	24	of	of	ADP
ejpam-1599	174	25	these	these	DET
ejpam-1599	174	26	disjoints	disjoint	NOUN
ejpam-1599	174	27	monoids	monoid	NOUN
ejpam-1599	174	28	.	.	PUNCT
ejpam-1599	175	1	if	if	SCONJ
ejpam-1599	175	2	s	s	NOUN
ejpam-1599	175	3	is	be	AUX
ejpam-1599	175	4	right	right	ADJ
ejpam-1599	175	5	semi	semi	ADJ
ejpam-1599	175	6	-	-	ADJ
ejpam-1599	175	7	hereditary	hereditary	ADJ
ejpam-1599	175	8	then	then	ADV
ejpam-1599	175	9	it	it	PRON
ejpam-1599	175	10	is	be	AUX
ejpam-1599	175	11	right	right	ADJ
ejpam-1599	175	12	p.p	p.p	PROPN
ejpam-1599	175	13	.	.	PROPN
ejpam-1599	175	14	and	and	CCONJ
ejpam-1599	175	15	incomparable	incomparable	ADJ
ejpam-1599	175	16	principal	principal	ADJ
ejpam-1599	175	17	right	right	ADJ
ejpam-1599	175	18	ideals	ideal	NOUN
ejpam-1599	175	19	are	be	AUX
ejpam-1599	175	20	disjoints	disjoint	NOUN
ejpam-1599	175	21	[	[	X
ejpam-1599	175	22	3	3	NUM
ejpam-1599	175	23	]	]	PUNCT
ejpam-1599	175	24	.	.	PUNCT
ejpam-1599	176	1	it	it	PRON
ejpam-1599	176	2	follows	follow	VERB
ejpam-1599	176	3	notably	notably	ADV
ejpam-1599	176	4	that	that	SCONJ
ejpam-1599	176	5	e(s	e(s	PROPN
ejpam-1599	176	6	)	)	PUNCT
ejpam-1599	176	7	is	be	AUX
ejpam-1599	176	8	a	a	DET
ejpam-1599	176	9	chain	chain	NOUN
ejpam-1599	176	10	(	(	PUNCT
ejpam-1599	176	11	any	any	DET
ejpam-1599	176	12	two	two	NUM
ejpam-1599	176	13	idempotents	idempotent	NOUN
ejpam-1599	176	14	are	be	AUX
ejpam-1599	176	15	comparable	comparable	ADJ
ejpam-1599	176	16	)	)	PUNCT
ejpam-1599	176	17	,	,	PUNCT
ejpam-1599	176	18	and	and	CCONJ
ejpam-1599	176	19	maximal	maximal	ADJ
ejpam-1599	176	20	invertibility	invertibility	NOUN
ejpam-1599	176	21	implies	imply	VERB
ejpam-1599	176	22	natural	natural	ADJ
ejpam-1599	176	23	invertibility	invertibility	NOUN
ejpam-1599	176	24	.	.	PUNCT
ejpam-1599	177	1	let	let	VERB
ejpam-1599	177	2	now	now	ADV
ejpam-1599	177	3	a	a	DET
ejpam-1599	177	4	∈	∈	NOUN
ejpam-1599	177	5	s.	s.	PROPN
ejpam-1599	177	6	if	if	SCONJ
ejpam-1599	177	7	a	a	PRON
ejpam-1599	177	8	is	be	AUX
ejpam-1599	177	9	regular	regular	ADJ
ejpam-1599	177	10	,	,	PUNCT
ejpam-1599	177	11	then	then	ADV
ejpam-1599	177	12	a	a	PRON
ejpam-1599	177	13	is	be	AUX
ejpam-1599	177	14	group	group	NOUN
ejpam-1599	177	15	invertible	invertible	ADJ
ejpam-1599	177	16	hence	hence	ADV
ejpam-1599	177	17	naturally	naturally	ADV
ejpam-1599	177	18	invertible	invertible	ADJ
ejpam-1599	177	19	.	.	PUNCT
ejpam-1599	178	1	we	we	PRON
ejpam-1599	178	2	assume	assume	VERB
ejpam-1599	178	3	in	in	ADP
ejpam-1599	178	4	the	the	DET
ejpam-1599	178	5	sequel	sequel	NOUN
ejpam-1599	178	6	that	that	SCONJ
ejpam-1599	178	7	a	a	PRON
ejpam-1599	178	8	is	be	AUX
ejpam-1599	178	9	not	not	PART
ejpam-1599	178	10	regular	regular	ADJ
ejpam-1599	178	11	.	.	PUNCT
ejpam-1599	179	1	by	by	ADP
ejpam-1599	179	2	centrality	centrality	NOUN
ejpam-1599	179	3	of	of	ADP
ejpam-1599	179	4	the	the	DET
ejpam-1599	179	5	idempotents	idempotent	NOUN
ejpam-1599	179	6	,	,	PUNCT
ejpam-1599	179	7	σ0(a	σ0(a	NUM
ejpam-1599	179	8	)	)	PUNCT
ejpam-1599	179	9	=	=	SYM
ejpam-1599	179	10	σ1(a	σ1(a	PROPN
ejpam-1599	179	11	)	)	PUNCT
ejpam-1599	179	12	=	=	SYM
ejpam-1599	179	13	σ2(a	σ2(a	PROPN
ejpam-1599	179	14	)	)	PUNCT
ejpam-1599	179	15	=	=	PRON
ejpam-1599	179	16	{	{	PUNCT
ejpam-1599	179	17	e	e	PROPN
ejpam-1599	179	18	∈	∈	PROPN
ejpam-1599	179	19	e(s	e(s	PROPN
ejpam-1599	179	20	)	)	PUNCT
ejpam-1599	179	21	,	,	PUNCT
ejpam-1599	179	22	e	e	NOUN
ejpam-1599	179	23	≤h	≤h	NOUN
ejpam-1599	179	24	a	a	X
ejpam-1599	179	25	}	}	PUNCT
ejpam-1599	179	26	.	.	PUNCT
ejpam-1599	180	1	let	let	VERB
ejpam-1599	180	2	a0	a0	PROPN
ejpam-1599	180	3	∈	∈	PROPN
ejpam-1599	180	4	e(s	e(s	PROPN
ejpam-1599	180	5	)	)	PUNCT
ejpam-1599	180	6	be	be	AUX
ejpam-1599	180	7	the	the	DET
ejpam-1599	180	8	idempotent	idempotent	NOUN
ejpam-1599	180	9	such	such	DET
ejpam-1599	180	10	that	that	SCONJ
ejpam-1599	180	11	a	a	DET
ejpam-1599	180	12	∈	∈	PROPN
ejpam-1599	180	13	ya0	ya0	NOUN
ejpam-1599	180	14	.	.	PUNCT
ejpam-1599	181	1	since	since	SCONJ
ejpam-1599	181	2	aa0	aa0	NOUN
ejpam-1599	181	3	=	=	SYM
ejpam-1599	181	4	a0a	a0a	PROPN
ejpam-1599	181	5	=	=	SYM
ejpam-1599	181	6	a	a	NOUN
ejpam-1599	181	7	,	,	PUNCT
ejpam-1599	181	8	any	any	DET
ejpam-1599	181	9	e	e	NOUN
ejpam-1599	181	10	≤h	≤h	NOUN
ejpam-1599	181	11	a	a	DET
ejpam-1599	181	12	satisfies	satisfie	NOUN
ejpam-1599	181	13	e	e	X
ejpam-1599	181	14	≤	≤	ADJ
ejpam-1599	181	15	a0	a0	NOUN
ejpam-1599	181	16	for	for	ADP
ejpam-1599	181	17	the	the	DET
ejpam-1599	181	18	h	h	NOUN
ejpam-1599	181	19	order	order	NOUN
ejpam-1599	181	20	hence	hence	ADV
ejpam-1599	181	21	the	the	DET
ejpam-1599	181	22	natural	natural	ADJ
ejpam-1599	181	23	partial	partial	ADJ
ejpam-1599	181	24	order	order	NOUN
ejpam-1599	181	25	,	,	PUNCT
ejpam-1599	181	26	and	and	CCONJ
ejpam-1599	181	27	since	since	SCONJ
ejpam-1599	181	28	a	a	PRON
ejpam-1599	181	29	is	be	AUX
ejpam-1599	181	30	not	not	PART
ejpam-1599	181	31	regular	regular	ADJ
ejpam-1599	181	32	,	,	PUNCT
ejpam-1599	181	33	e	e	X
ejpam-1599	181	34	<	<	X
ejpam-1599	181	35	a0	a0	PROPN
ejpam-1599	181	36	.	.	PUNCT
ejpam-1599	182	1	conversely	conversely	ADV
ejpam-1599	182	2	,	,	PUNCT
ejpam-1599	182	3	let	let	VERB
ejpam-1599	182	4	e	e	PRON
ejpam-1599	182	5	<	<	X
ejpam-1599	182	6	a0	a0	PROPN
ejpam-1599	182	7	and	and	CCONJ
ejpam-1599	182	8	assume	assume	VERB
ejpam-1599	182	9	s	s	X
ejpam-1599	182	10	is	be	AUX
ejpam-1599	182	11	semi	semi	ADJ
ejpam-1599	182	12	-	-	ADJ
ejpam-1599	182	13	hereditary	hereditary	ADJ
ejpam-1599	182	14	.	.	PUNCT
ejpam-1599	183	1	from	from	ADP
ejpam-1599	183	2	ae	ae	PROPN
ejpam-1599	183	3	=	=	SYM
ejpam-1599	183	4	ea	ea	PROPN
ejpam-1599	183	5	∈	∈	NOUN
ejpam-1599	183	6	es	es	NOUN
ejpam-1599	183	7	∩	∩	NOUN
ejpam-1599	183	8	as	as	ADP
ejpam-1599	183	9	,	,	PUNCT
ejpam-1599	183	10	es	es	NOUN
ejpam-1599	183	11	and	and	CCONJ
ejpam-1599	183	12	as	as	SCONJ
ejpam-1599	183	13	are	be	AUX
ejpam-1599	183	14	comparable	comparable	ADJ
ejpam-1599	183	15	,	,	PUNCT
ejpam-1599	183	16	and	and	CCONJ
ejpam-1599	183	17	from	from	ADP
ejpam-1599	183	18	e	e	X
ejpam-1599	183	19	<	<	X
ejpam-1599	183	20	a0	a0	PROPN
ejpam-1599	183	21	we	we	PRON
ejpam-1599	183	22	get	get	VERB
ejpam-1599	183	23	es	es	ADP
ejpam-1599	183	24	⊂	⊂	PRON
ejpam-1599	183	25	as	as	ADP
ejpam-1599	183	26	(	(	PUNCT
ejpam-1599	183	27	ae	ae	PROPN
ejpam-1599	183	28	∈	∈	PROPN
ejpam-1599	183	29	ye	ye	PRON
ejpam-1599	183	30	disjoint	disjoint	NOUN
ejpam-1599	183	31	from	from	ADP
ejpam-1599	183	32	ya0	ya0	PROPN
ejpam-1599	183	33	hence	hence	ADV
ejpam-1599	183	34	ae	ae	PROPN
ejpam-1599	183	35	6=	6=	PROPN
ejpam-1599	183	36	a	a	PRON
ejpam-1599	183	37	)	)	PUNCT
ejpam-1599	183	38	.	.	PUNCT
ejpam-1599	184	1	it	it	PRON
ejpam-1599	184	2	follows	follow	VERB
ejpam-1599	184	3	that	that	SCONJ
ejpam-1599	184	4	e	e	PROPN
ejpam-1599	184	5	≤r	≤r	VERB
ejpam-1599	184	6	a	a	PRON
ejpam-1599	184	7	and	and	CCONJ
ejpam-1599	184	8	in	in	ADP
ejpam-1599	184	9	particular	particular	ADJ
ejpam-1599	184	10	ea	ea	NOUN
ejpam-1599	185	1	=	=	SYM
ejpam-1599	185	2	aere	aere	X
ejpam-1599	185	3	is	be	AUX
ejpam-1599	185	4	regular	regular	ADJ
ejpam-1599	185	5	.	.	PUNCT
ejpam-1599	186	1	since	since	SCONJ
ejpam-1599	186	2	for	for	ADP
ejpam-1599	186	3	regular	regular	ADJ
ejpam-1599	186	4	elements	element	NOUN
ejpam-1599	186	5	,	,	PUNCT
ejpam-1599	186	6	the	the	DET
ejpam-1599	186	7	appartenance	appartenance	NOUN
ejpam-1599	186	8	in	in	ADP
ejpam-1599	186	9	ye	ye	PRON
ejpam-1599	186	10	is	be	AUX
ejpam-1599	186	11	simply	simply	ADV
ejpam-1599	186	12	green	green	PROPN
ejpam-1599	186	13	’s	’s	PART
ejpam-1599	186	14	relation	relation	NOUN
ejpam-1599	186	15	l	l	NOUN
ejpam-1599	186	16	,	,	PUNCT
ejpam-1599	186	17	we	we	PRON
ejpam-1599	186	18	get	get	VERB
ejpam-1599	186	19	that	that	PRON
ejpam-1599	186	20	ae	ae	PROPN
ejpam-1599	187	1	=	=	PUNCT
ejpam-1599	188	1	eah	eah	PROPN
ejpam-1599	188	2	e	e	PROPN
ejpam-1599	188	3	and	and	CCONJ
ejpam-1599	188	4	e	e	X
ejpam-1599	188	5	≤h	≤h	NOUN
ejpam-1599	188	6	a.	a.	NOUN
ejpam-1599	188	7	finally	finally	ADV
ejpam-1599	188	8	,	,	PUNCT
ejpam-1599	188	9	we	we	PRON
ejpam-1599	188	10	have	have	AUX
ejpam-1599	188	11	proved	prove	VERB
ejpam-1599	188	12	that	that	SCONJ
ejpam-1599	188	13	σ(a	σ(a	PROPN
ejpam-1599	188	14	)	)	PUNCT
ejpam-1599	188	15	is	be	AUX
ejpam-1599	188	16	the	the	DET
ejpam-1599	188	17	chain	chain	NOUN
ejpam-1599	188	18	of	of	ADP
ejpam-1599	188	19	idempotents	idempotent	NOUN
ejpam-1599	188	20	{	{	PUNCT
ejpam-1599	188	21	e	e	NOUN
ejpam-1599	188	22	∈	∈	PROPN
ejpam-1599	188	23	e(s	e(s	PROPN
ejpam-1599	188	24	)	)	PUNCT
ejpam-1599	188	25	,	,	PUNCT
ejpam-1599	189	1	e	e	X
ejpam-1599	189	2	<	<	X
ejpam-1599	189	3	a0	a0	PROPN
ejpam-1599	189	4	}	}	PUNCT
ejpam-1599	189	5	.	.	PUNCT
ejpam-1599	190	1	if	if	SCONJ
ejpam-1599	190	2	we	we	PRON
ejpam-1599	190	3	finally	finally	ADV
ejpam-1599	190	4	assume	assume	VERB
ejpam-1599	190	5	that	that	SCONJ
ejpam-1599	190	6	s	s	VERB
ejpam-1599	190	7	is	be	AUX
ejpam-1599	190	8	right	right	ADJ
ejpam-1599	190	9	hereditary	hereditary	ADJ
ejpam-1599	190	10	(	(	PUNCT
ejpam-1599	190	11	right	right	ADJ
ejpam-1599	190	12	ideals	ideal	NOUN
ejpam-1599	190	13	are	be	AUX
ejpam-1599	190	14	projective	projective	ADJ
ejpam-1599	190	15	)	)	PUNCT
ejpam-1599	190	16	,	,	PUNCT
ejpam-1599	190	17	then	then	ADV
ejpam-1599	190	18	dorofeeva	dorofeeva	VERB
ejpam-1599	190	19	[	[	X
ejpam-1599	190	20	3	3	X
ejpam-1599	190	21	]	]	PUNCT
ejpam-1599	190	22	showed	show	VERB
ejpam-1599	190	23	that	that	SCONJ
ejpam-1599	190	24	s	s	NOUN
ejpam-1599	190	25	satifisies	satifisie	NOUN
ejpam-1599	190	26	the	the	DET
ejpam-1599	190	27	maximum	maximum	ADJ
ejpam-1599	190	28	condition	condition	NOUN
ejpam-1599	190	29	for	for	ADP
ejpam-1599	190	30	principal	principal	ADJ
ejpam-1599	190	31	right	right	ADJ
ejpam-1599	190	32	ideals	ideal	NOUN
ejpam-1599	190	33	.	.	PUNCT
ejpam-1599	191	1	as	as	ADP
ejpam-1599	191	2	a	a	DET
ejpam-1599	191	3	consequence	consequence	NOUN
ejpam-1599	191	4	,	,	PUNCT
ejpam-1599	191	5	the	the	DET
ejpam-1599	191	6	chain	chain	NOUN
ejpam-1599	191	7	of	of	ADP
ejpam-1599	191	8	idempotents	idempotent	NOUN
ejpam-1599	191	9	{	{	PUNCT
ejpam-1599	191	10	e	e	NOUN
ejpam-1599	191	11	∈	∈	PROPN
ejpam-1599	191	12	e(s	e(s	PROPN
ejpam-1599	191	13	)	)	PUNCT
ejpam-1599	191	14	,	,	PUNCT
ejpam-1599	191	15	e	e	PROPN
ejpam-1599	191	16	<	<	X
ejpam-1599	191	17	a0	a0	PROPN
ejpam-1599	191	18	}	}	PUNCT
ejpam-1599	191	19	has	have	VERB
ejpam-1599	191	20	a	a	DET
ejpam-1599	191	21	greatest	great	ADJ
ejpam-1599	191	22	element	element	NOUN
ejpam-1599	191	23	m	m	PROPN
ejpam-1599	191	24	and	and	CCONJ
ejpam-1599	191	25	a	a	PRON
ejpam-1599	191	26	is	be	AUX
ejpam-1599	191	27	naturally	naturally	ADV
ejpam-1599	191	28	invertible	invertible	ADJ
ejpam-1599	191	29	with	with	ADP
ejpam-1599	191	30	inverse	inverse	NOUN
ejpam-1599	191	31	a−m	a−m	NOUN
ejpam-1599	191	32	.	.	PUNCT
ejpam-1599	192	1	4	4	X
ejpam-1599	192	2	.	.	X
ejpam-1599	192	3	the	the	DET
ejpam-1599	192	4	ring	ring	NOUN
ejpam-1599	192	5	case	case	NOUN
ejpam-1599	192	6	4.1	4.1	NUM
ejpam-1599	192	7	.	.	PUNCT
ejpam-1599	193	1	invertibility	invertibility	NOUN
ejpam-1599	193	2	along	along	ADP
ejpam-1599	193	3	an	an	DET
ejpam-1599	193	4	element	element	NOUN
ejpam-1599	193	5	in	in	ADP
ejpam-1599	193	6	a	a	DET
ejpam-1599	193	7	ring	ring	NOUN
ejpam-1599	193	8	in	in	ADP
ejpam-1599	193	9	this	this	DET
ejpam-1599	193	10	section	section	NOUN
ejpam-1599	193	11	,	,	PUNCT
ejpam-1599	193	12	r	r	NOUN
ejpam-1599	193	13	denotes	denote	VERB
ejpam-1599	193	14	a	a	DET
ejpam-1599	193	15	unital	unital	ADJ
ejpam-1599	193	16	ring	ring	NOUN
ejpam-1599	193	17	.	.	PUNCT
ejpam-1599	194	1	in	in	ADP
ejpam-1599	194	2	particular	particular	ADJ
ejpam-1599	194	3	,	,	PUNCT
ejpam-1599	194	4	it	it	PRON
ejpam-1599	194	5	is	be	AUX
ejpam-1599	194	6	a	a	DET
ejpam-1599	194	7	semigroup	semigroup	NOUN
ejpam-1599	194	8	and	and	CCONJ
ejpam-1599	194	9	the	the	DET
ejpam-1599	194	10	previous	previous	ADJ
ejpam-1599	194	11	notations	notation	NOUN
ejpam-1599	194	12	and	and	CCONJ
ejpam-1599	194	13	results	result	NOUN
ejpam-1599	194	14	apply	apply	VERB
ejpam-1599	194	15	.	.	PUNCT
ejpam-1599	195	1	the	the	DET
ejpam-1599	195	2	ring	ring	NOUN
ejpam-1599	195	3	being	be	AUX
ejpam-1599	195	4	unital	unital	ADJ
ejpam-1599	195	5	,	,	PUNCT
ejpam-1599	195	6	r1	r1	PROPN
ejpam-1599	195	7	=	=	PUNCT
ejpam-1599	195	8	r.	r.	PROPN
ejpam-1599	195	9	in	in	ADP
ejpam-1599	195	10	[	[	X
ejpam-1599	195	11	19	19	NUM
ejpam-1599	195	12	]	]	PUNCT
ejpam-1599	195	13	,	,	PUNCT
ejpam-1599	195	14	invertibilty	invertibilty	NOUN
ejpam-1599	195	15	along	along	ADP
ejpam-1599	195	16	an	an	DET
ejpam-1599	195	17	element	element	NOUN
ejpam-1599	195	18	was	be	AUX
ejpam-1599	195	19	characterized	characterize	VERB
ejpam-1599	195	20	in	in	ADP
ejpam-1599	195	21	terms	term	NOUN
ejpam-1599	195	22	of	of	ADP
ejpam-1599	195	23	existence	existence	NOUN
ejpam-1599	195	24	of	of	ADP
ejpam-1599	195	25	units	unit	NOUN
ejpam-1599	195	26	.	.	PUNCT
ejpam-1599	196	1	theorem	theorem	NOUN
ejpam-1599	196	2	5	5	NUM
ejpam-1599	196	3	.	.	PUNCT
ejpam-1599	197	1	let	let	VERB
ejpam-1599	197	2	d	d	PRON
ejpam-1599	197	3	be	be	AUX
ejpam-1599	197	4	a	a	DET
ejpam-1599	197	5	regular	regular	ADJ
ejpam-1599	197	6	element	element	NOUN
ejpam-1599	197	7	of	of	ADP
ejpam-1599	197	8	a	a	DET
ejpam-1599	197	9	ring	ring	NOUN
ejpam-1599	197	10	r	r	NOUN
ejpam-1599	197	11	,	,	PUNCT
ejpam-1599	197	12	d	d	NOUN
ejpam-1599	197	13	′	′	NUM
ejpam-1599	197	14	∈	∈	PROPN
ejpam-1599	197	15	a(d	a(d	PROPN
ejpam-1599	197	16	)	)	PUNCT
ejpam-1599	197	17	.	.	PUNCT
ejpam-1599	198	1	then	then	ADV
ejpam-1599	198	2	the	the	DET
ejpam-1599	198	3	following	follow	VERB
ejpam-1599	198	4	are	be	AUX
ejpam-1599	198	5	equivalent	equivalent	ADJ
ejpam-1599	198	6	:	:	PUNCT
ejpam-1599	198	7	x.	x.	PROPN
ejpam-1599	198	8	mary	mary	PROPN
ejpam-1599	198	9	/	/	SYM
ejpam-1599	198	10	eur	eur	PROPN
ejpam-1599	198	11	.	.	PUNCT
ejpam-1599	199	1	j.	j.	PROPN
ejpam-1599	199	2	pure	pure	PROPN
ejpam-1599	199	3	appl	appl	PROPN
ejpam-1599	199	4	.	.	PROPN
ejpam-1599	199	5	math	math	PROPN
ejpam-1599	199	6	,	,	PUNCT
ejpam-1599	199	7	5	5	NUM
ejpam-1599	199	8	(	(	PUNCT
ejpam-1599	199	9	2012	2012	NUM
ejpam-1599	199	10	)	)	PUNCT
ejpam-1599	199	11	,	,	PUNCT
ejpam-1599	199	12	160	160	NUM
ejpam-1599	199	13	-	-	SYM
ejpam-1599	199	14	173	173	NUM
ejpam-1599	199	15	166	166	NUM
ejpam-1599	199	16	1	1	NUM
ejpam-1599	199	17	.	.	PUNCT
ejpam-1599	200	1	a−d	a−d	PROPN
ejpam-1599	200	2	exists	exist	VERB
ejpam-1599	200	3	.	.	PUNCT
ejpam-1599	201	1	2	2	X
ejpam-1599	201	2	.	.	X
ejpam-1599	201	3	u	u	NOUN
ejpam-1599	201	4	=	=	PRON
ejpam-1599	201	5	da+	da+	VERB
ejpam-1599	201	6	1−	1−	NUM
ejpam-1599	201	7	dd	dd	NOUN
ejpam-1599	201	8	′	′	NUM
ejpam-1599	201	9	is	be	AUX
ejpam-1599	201	10	a	a	DET
ejpam-1599	201	11	unit	unit	NOUN
ejpam-1599	201	12	.	.	PUNCT
ejpam-1599	202	1	3	3	X
ejpam-1599	202	2	.	.	X
ejpam-1599	202	3	v	v	NOUN
ejpam-1599	202	4	=	=	SYM
ejpam-1599	202	5	ad	ad	NOUN
ejpam-1599	202	6	+	+	CCONJ
ejpam-1599	202	7	1−	1−	NUM
ejpam-1599	203	1	d	d	NOUN
ejpam-1599	203	2	′d	′d	NOUN
ejpam-1599	203	3	is	be	AUX
ejpam-1599	203	4	a	a	DET
ejpam-1599	203	5	unit	unit	NOUN
ejpam-1599	203	6	.	.	PUNCT
ejpam-1599	204	1	in	in	ADP
ejpam-1599	204	2	this	this	DET
ejpam-1599	204	3	case	case	NOUN
ejpam-1599	204	4	,	,	PUNCT
ejpam-1599	204	5	a−d	a−d	NOUN
ejpam-1599	204	6	=	=	X
ejpam-1599	204	7	u−1d	u−1d	NOUN
ejpam-1599	204	8	=	=	SYM
ejpam-1599	204	9	dv−1	dv−1	PROPN
ejpam-1599	204	10	.	.	PUNCT
ejpam-1599	205	1	note	note	VERB
ejpam-1599	205	2	that	that	SCONJ
ejpam-1599	205	3	in	in	ADP
ejpam-1599	205	4	the	the	DET
ejpam-1599	205	5	particular	particular	ADJ
ejpam-1599	205	6	case	case	NOUN
ejpam-1599	205	7	of	of	ADP
ejpam-1599	205	8	invertibility	invertibility	NOUN
ejpam-1599	205	9	along	along	ADP
ejpam-1599	205	10	an	an	DET
ejpam-1599	205	11	idempotent	idempotent	ADJ
ejpam-1599	205	12	e	e	NOUN
ejpam-1599	205	13	,	,	PUNCT
ejpam-1599	205	14	this	this	PRON
ejpam-1599	205	15	reduces	reduce	VERB
ejpam-1599	205	16	to	to	PART
ejpam-1599	205	17	:	:	PUNCT
ejpam-1599	205	18	corollary	corollary	ADJ
ejpam-1599	205	19	2	2	X
ejpam-1599	205	20	.	.	PUNCT
ejpam-1599	206	1	let	let	VERB
ejpam-1599	206	2	e	e	PRON
ejpam-1599	206	3	∈	∈	PROPN
ejpam-1599	206	4	e(r	e(r	X
ejpam-1599	206	5	)	)	PUNCT
ejpam-1599	206	6	be	be	AUX
ejpam-1599	206	7	a	a	DET
ejpam-1599	206	8	idempotent	idempotent	ADJ
ejpam-1599	206	9	element	element	NOUN
ejpam-1599	206	10	of	of	ADP
ejpam-1599	206	11	a	a	DET
ejpam-1599	206	12	ring	ring	NOUN
ejpam-1599	206	13	r.	r.	PROPN
ejpam-1599	206	14	then	then	ADV
ejpam-1599	206	15	the	the	DET
ejpam-1599	206	16	following	follow	VERB
ejpam-1599	206	17	are	be	AUX
ejpam-1599	206	18	equivalent	equivalent	ADJ
ejpam-1599	206	19	:	:	PUNCT
ejpam-1599	206	20	1	1	X
ejpam-1599	206	21	.	.	X
ejpam-1599	206	22	a−e	a−e	NOUN
ejpam-1599	206	23	exists	exist	VERB
ejpam-1599	206	24	.	.	PUNCT
ejpam-1599	207	1	2	2	X
ejpam-1599	207	2	.	.	X
ejpam-1599	207	3	u	u	NOUN
ejpam-1599	207	4	=	=	PROPN
ejpam-1599	207	5	ea+	ea+	NOUN
ejpam-1599	207	6	1−	1−	NUM
ejpam-1599	207	7	e	e	NOUN
ejpam-1599	207	8	is	be	AUX
ejpam-1599	207	9	a	a	DET
ejpam-1599	207	10	unit	unit	NOUN
ejpam-1599	207	11	.	.	PUNCT
ejpam-1599	208	1	3	3	X
ejpam-1599	208	2	.	.	X
ejpam-1599	208	3	v	v	NOUN
ejpam-1599	208	4	=	=	SYM
ejpam-1599	208	5	ae+	ae+	NOUN
ejpam-1599	208	6	1−	1−	NUM
ejpam-1599	208	7	e	e	NOUN
ejpam-1599	208	8	is	be	AUX
ejpam-1599	208	9	a	a	DET
ejpam-1599	208	10	unit	unit	NOUN
ejpam-1599	208	11	.	.	PUNCT
ejpam-1599	209	1	in	in	ADP
ejpam-1599	209	2	this	this	DET
ejpam-1599	209	3	case	case	NOUN
ejpam-1599	209	4	,	,	PUNCT
ejpam-1599	209	5	a−e	a−e	NOUN
ejpam-1599	209	6	=	=	SYM
ejpam-1599	209	7	u−1e	u−1e	NOUN
ejpam-1599	209	8	=	=	SYM
ejpam-1599	209	9	ev−1	ev−1	PROPN
ejpam-1599	209	10	.	.	PROPN
ejpam-1599	209	11	corollary	corollary	ADJ
ejpam-1599	209	12	3	3	X
ejpam-1599	209	13	.	.	PUNCT
ejpam-1599	210	1	if	if	SCONJ
ejpam-1599	210	2	ae	ae	PROPN
ejpam-1599	210	3	=	=	SYM
ejpam-1599	210	4	ea	ea	PROPN
ejpam-1599	210	5	,	,	PUNCT
ejpam-1599	210	6	then	then	ADV
ejpam-1599	210	7	e	e	X
ejpam-1599	210	8	≤h	≤h	NOUN
ejpam-1599	210	9	a	a	DET
ejpam-1599	210	10	if	if	NOUN
ejpam-1599	210	11	and	and	CCONJ
ejpam-1599	210	12	only	only	ADV
ejpam-1599	210	13	if	if	SCONJ
ejpam-1599	210	14	u=	u=	ADJ
ejpam-1599	210	15	1	1	NUM
ejpam-1599	210	16	+	+	NUM
ejpam-1599	210	17	ae−	ae−	PUNCT
ejpam-1599	210	18	e	e	NOUN
ejpam-1599	210	19	is	be	AUX
ejpam-1599	210	20	a	a	DET
ejpam-1599	210	21	unit	unit	NOUN
ejpam-1599	210	22	.	.	PUNCT
ejpam-1599	211	1	remark	remark	VERB
ejpam-1599	211	2	that	that	SCONJ
ejpam-1599	211	3	a	a	DET
ejpam-1599	211	4	sufficient	sufficient	ADJ
ejpam-1599	211	5	condition	condition	NOUN
ejpam-1599	211	6	for	for	SCONJ
ejpam-1599	211	7	this	this	PRON
ejpam-1599	211	8	to	to	PART
ejpam-1599	211	9	happen	happen	VERB
ejpam-1599	211	10	is	be	AUX
ejpam-1599	211	11	the	the	DET
ejpam-1599	211	12	following	following	NOUN
ejpam-1599	211	13	:	:	PUNCT
ejpam-1599	211	14	lemma	lemma	PROPN
ejpam-1599	211	15	5	5	X
ejpam-1599	211	16	.	.	PUNCT
ejpam-1599	212	1	if	if	SCONJ
ejpam-1599	212	2	ae	ae	PROPN
ejpam-1599	212	3	=	=	SYM
ejpam-1599	212	4	ea	ea	PROPN
ejpam-1599	212	5	and	and	CCONJ
ejpam-1599	212	6	a+	a+	PUNCT
ejpam-1599	212	7	1−	1−	NUM
ejpam-1599	212	8	e	e	NOUN
ejpam-1599	212	9	is	be	AUX
ejpam-1599	212	10	a	a	DET
ejpam-1599	212	11	unit	unit	NOUN
ejpam-1599	212	12	,	,	PUNCT
ejpam-1599	212	13	then	then	ADV
ejpam-1599	212	14	e	e	X
ejpam-1599	212	15	≤h	≤h	NOUN
ejpam-1599	212	16	a.	a.	NOUN
ejpam-1599	212	17	proof	proof	NOUN
ejpam-1599	212	18	.	.	PUNCT
ejpam-1599	213	1	let	let	VERB
ejpam-1599	213	2	u	u	PRON
ejpam-1599	213	3	=	=	X
ejpam-1599	213	4	a+	a+	PUNCT
ejpam-1599	213	5	1−	1−	NUM
ejpam-1599	213	6	e.	e.	PROPN
ejpam-1599	213	7	then	then	ADV
ejpam-1599	213	8	ue	ue	PROPN
ejpam-1599	214	1	=	=	SYM
ejpam-1599	214	2	ae	ae	PROPN
ejpam-1599	214	3	=	=	SYM
ejpam-1599	214	4	ea	ea	PROPN
ejpam-1599	214	5	hence	hence	ADV
ejpam-1599	214	6	e	e	NOUN
ejpam-1599	214	7	=	=	NOUN
ejpam-1599	214	8	u−1ea	u−1ea	X
ejpam-1599	214	9	=	=	SYM
ejpam-1599	214	10	au−1e	au−1e	PROPN
ejpam-1599	214	11	.	.	PUNCT
ejpam-1599	215	1	4.2	4.2	NUM
ejpam-1599	215	2	.	.	PUNCT
ejpam-1599	215	3	natural	natural	ADJ
ejpam-1599	215	4	inverse	inverse	NOUN
ejpam-1599	215	5	in	in	ADP
ejpam-1599	215	6	a	a	DET
ejpam-1599	215	7	ring	ring	NOUN
ejpam-1599	215	8	let	let	VERB
ejpam-1599	215	9	r	r	PRON
ejpam-1599	215	10	be	be	AUX
ejpam-1599	215	11	a	a	DET
ejpam-1599	215	12	ring	ring	NOUN
ejpam-1599	215	13	,	,	PUNCT
ejpam-1599	215	14	and	and	CCONJ
ejpam-1599	215	15	let	let	VERB
ejpam-1599	215	16	a	a	DET
ejpam-1599	215	17	∈	∈	PROPN
ejpam-1599	215	18	r.	r.	NOUN
ejpam-1599	215	19	then	then	ADV
ejpam-1599	215	20	the	the	DET
ejpam-1599	215	21	semilattice	semilattice	NOUN
ejpam-1599	215	22	σ2(a	σ2(a	NUM
ejpam-1599	215	23	)	)	PUNCT
ejpam-1599	215	24	is	be	AUX
ejpam-1599	215	25	actually	actually	ADV
ejpam-1599	215	26	a	a	DET
ejpam-1599	215	27	distributive	distributive	ADJ
ejpam-1599	215	28	lattice	lattice	NOUN
ejpam-1599	215	29	(	(	PUNCT
ejpam-1599	215	30	with	with	ADP
ejpam-1599	215	31	e	e	PROPN
ejpam-1599	215	32	∧	∧	NOUN
ejpam-1599	215	33	f	f	PROPN
ejpam-1599	215	34	=	=	SYM
ejpam-1599	215	35	e	e	PROPN
ejpam-1599	215	36	+	+	NOUN
ejpam-1599	216	1	f	f	PROPN
ejpam-1599	216	2	−	−	PROPN
ejpam-1599	216	3	e	e	X
ejpam-1599	216	4	f	f	PROPN
ejpam-1599	216	5	)	)	PUNCT
ejpam-1599	216	6	hence	hence	ADV
ejpam-1599	216	7	a	a	PRON
ejpam-1599	216	8	is	be	AUX
ejpam-1599	216	9	2−maximally	2−maximally	ADV
ejpam-1599	216	10	invertible	invertible	ADJ
ejpam-1599	216	11	if	if	SCONJ
ejpam-1599	216	12	and	and	CCONJ
ejpam-1599	216	13	only	only	ADV
ejpam-1599	216	14	if	if	SCONJ
ejpam-1599	216	15	it	it	PRON
ejpam-1599	216	16	is	be	AUX
ejpam-1599	216	17	naturally	naturally	ADV
ejpam-1599	216	18	invertible	invertible	ADJ
ejpam-1599	216	19	.	.	PUNCT
ejpam-1599	217	1	we	we	PRON
ejpam-1599	217	2	derive	derive	VERB
ejpam-1599	217	3	new	new	ADJ
ejpam-1599	217	4	criterion	criterion	NOUN
ejpam-1599	217	5	for	for	ADP
ejpam-1599	217	6	the	the	DET
ejpam-1599	217	7	natural	natural	ADJ
ejpam-1599	217	8	inverse	inverse	NOUN
ejpam-1599	217	9	to	to	ADP
ejpam-1599	217	10	exists	exist	NOUN
ejpam-1599	217	11	.	.	PUNCT
ejpam-1599	218	1	theorem	theorem	VERB
ejpam-1599	218	2	6	6	NUM
ejpam-1599	218	3	.	.	PUNCT
ejpam-1599	219	1	let	let	VERB
ejpam-1599	219	2	a	a	DET
ejpam-1599	219	3	∈	∈	PROPN
ejpam-1599	219	4	r.	r.	NOUN
ejpam-1599	219	5	then	then	ADV
ejpam-1599	219	6	the	the	DET
ejpam-1599	219	7	following	follow	VERB
ejpam-1599	219	8	are	be	AUX
ejpam-1599	219	9	equivalent	equivalent	ADJ
ejpam-1599	219	10	:	:	PUNCT
ejpam-1599	219	11	1	1	X
ejpam-1599	219	12	.	.	X
ejpam-1599	219	13	a	a	PRON
ejpam-1599	219	14	is	be	AUX
ejpam-1599	219	15	naturally	naturally	ADV
ejpam-1599	219	16	invertible	invertible	ADJ
ejpam-1599	219	17	with	with	ADP
ejpam-1599	219	18	inverse	inverse	NOUN
ejpam-1599	219	19	a−m	a−m	NOUN
ejpam-1599	219	20	;	;	PUNCT
ejpam-1599	219	21	2	2	X
ejpam-1599	219	22	.	.	X
ejpam-1599	219	23	there	there	PRON
ejpam-1599	219	24	exists	exist	VERB
ejpam-1599	219	25	b	b	PROPN
ejpam-1599	219	26	∈	∈	PROPN
ejpam-1599	219	27	{	{	PUNCT
ejpam-1599	219	28	a}′′	a}′′	PROPN
ejpam-1599	219	29	,	,	PUNCT
ejpam-1599	219	30	bab	bab	PROPN
ejpam-1599	219	31	=	=	SYM
ejpam-1599	219	32	b	b	PROPN
ejpam-1599	219	33	and	and	CCONJ
ejpam-1599	219	34	σ2(a−	σ2(a−	NUM
ejpam-1599	219	35	aba	aba	PROPN
ejpam-1599	219	36	)	)	PUNCT
ejpam-1599	219	37	=	=	PRON
ejpam-1599	220	1	{	{	PUNCT
ejpam-1599	220	2	0	0	NUM
ejpam-1599	220	3	}	}	PUNCT
ejpam-1599	220	4	;	;	PUNCT
ejpam-1599	220	5	3	3	X
ejpam-1599	220	6	.	.	X
ejpam-1599	221	1	a	a	PRON
ejpam-1599	221	2	=	=	PUNCT
ejpam-1599	221	3	x	x	SYM
ejpam-1599	222	1	+	+	NUM
ejpam-1599	222	2	y	y	NOUN
ejpam-1599	222	3	with	with	ADP
ejpam-1599	222	4	x	x	PROPN
ejpam-1599	222	5	∈	∈	PROPN
ejpam-1599	222	6	{	{	PUNCT
ejpam-1599	222	7	a}′′	a}′′	NUM
ejpam-1599	222	8	,	,	PUNCT
ejpam-1599	222	9	x	x	ADJ
ejpam-1599	222	10	#	#	NOUN
ejpam-1599	222	11	exists	exist	VERB
ejpam-1599	222	12	,	,	PUNCT
ejpam-1599	222	13	x	x	X
ejpam-1599	222	14	y	y	NOUN
ejpam-1599	222	15	=	=	SYM
ejpam-1599	222	16	0	0	NUM
ejpam-1599	222	17	and	and	CCONJ
ejpam-1599	222	18	σ2(y	σ2(y	X
ejpam-1599	222	19	)	)	PUNCT
ejpam-1599	222	20	=	=	PRON
ejpam-1599	222	21	{	{	PUNCT
ejpam-1599	222	22	0	0	NUM
ejpam-1599	222	23	}	}	PUNCT
ejpam-1599	222	24	.	.	PUNCT
ejpam-1599	223	1	in	in	ADP
ejpam-1599	223	2	this	this	DET
ejpam-1599	223	3	case	case	NOUN
ejpam-1599	223	4	,	,	PUNCT
ejpam-1599	223	5	a−m	a−m	NOUN
ejpam-1599	223	6	=	=	SYM
ejpam-1599	223	7	b	b	SYM
ejpam-1599	223	8	=	=	SYM
ejpam-1599	223	9	x	x	NOUN
ejpam-1599	223	10	#	#	X
ejpam-1599	223	11	.	.	PUNCT
ejpam-1599	223	12	x.	x.	PROPN
ejpam-1599	223	13	mary	mary	PROPN
ejpam-1599	223	14	/	/	SYM
ejpam-1599	223	15	eur	eur	PROPN
ejpam-1599	223	16	.	.	PUNCT
ejpam-1599	224	1	j.	j.	PROPN
ejpam-1599	224	2	pure	pure	PROPN
ejpam-1599	224	3	appl	appl	PROPN
ejpam-1599	224	4	.	.	PROPN
ejpam-1599	224	5	math	math	PROPN
ejpam-1599	224	6	,	,	PUNCT
ejpam-1599	224	7	5	5	NUM
ejpam-1599	224	8	(	(	PUNCT
ejpam-1599	224	9	2012	2012	NUM
ejpam-1599	224	10	)	)	PUNCT
ejpam-1599	224	11	,	,	PUNCT
ejpam-1599	224	12	160	160	NUM
ejpam-1599	224	13	-	-	SYM
ejpam-1599	224	14	173	173	NUM
ejpam-1599	224	15	167	167	NUM
ejpam-1599	224	16	proof	proof	NOUN
ejpam-1599	224	17	.	.	PUNCT
ejpam-1599	225	1	1.⇒	1.⇒	ADJ
ejpam-1599	225	2	2	2	X
ejpam-1599	225	3	.	.	PUNCT
ejpam-1599	225	4	assume	assume	VERB
ejpam-1599	225	5	a	a	PRON
ejpam-1599	225	6	is	be	AUX
ejpam-1599	225	7	naturally	naturally	ADV
ejpam-1599	225	8	invertible	invertible	ADJ
ejpam-1599	225	9	with	with	ADP
ejpam-1599	225	10	inverse	inverse	NOUN
ejpam-1599	225	11	b	b	NOUN
ejpam-1599	225	12	=	=	NOUN
ejpam-1599	225	13	a−m	a−m	NOUN
ejpam-1599	225	14	.	.	PUNCT
ejpam-1599	226	1	then	then	ADV
ejpam-1599	226	2	m	m	VERB
ejpam-1599	226	3	=	=	ADJ
ejpam-1599	226	4	ab	ab	PROPN
ejpam-1599	226	5	=	=	SYM
ejpam-1599	226	6	ba	ba	PROPN
ejpam-1599	226	7	.	.	PUNCT
ejpam-1599	227	1	let	let	VERB
ejpam-1599	227	2	e	e	PROPN
ejpam-1599	227	3	∈	∈	PROPN
ejpam-1599	227	4	σ2(a−	σ2(a−	PROPN
ejpam-1599	227	5	aba	aba	PROPN
ejpam-1599	227	6	)	)	PUNCT
ejpam-1599	227	7	.	.	PUNCT
ejpam-1599	228	1	the	the	DET
ejpam-1599	228	2	ca	ca	NOUN
ejpam-1599	228	3	=	=	SYM
ejpam-1599	228	4	ac⇒	ac⇒	X
ejpam-1599	228	5	cb	cb	NOUN
ejpam-1599	228	6	=	=	PUNCT
ejpam-1599	228	7	bc⇒	bc⇒	PROPN
ejpam-1599	228	8	c(a−	c(a−	PROPN
ejpam-1599	228	9	aba	aba	PROPN
ejpam-1599	228	10	)	)	PUNCT
ejpam-1599	229	1	=	=	PUNCT
ejpam-1599	229	2	(	(	PUNCT
ejpam-1599	229	3	a−	a−	PROPN
ejpam-1599	229	4	aba)c⇒	aba)c⇒	X
ejpam-1599	229	5	ec	ec	PROPN
ejpam-1599	229	6	=	=	SYM
ejpam-1599	229	7	ce	ce	PROPN
ejpam-1599	229	8	.	.	PROPN
ejpam-1599	229	9	hence	hence	ADV
ejpam-1599	229	10	e	e	X
ejpam-1599	229	11	∈	∈	PROPN
ejpam-1599	229	12	{	{	PUNCT
ejpam-1599	229	13	a}′′.	a}′′.	ADJ
ejpam-1599	229	14	but	but	CCONJ
ejpam-1599	229	15	also	also	ADV
ejpam-1599	229	16	∃t	∃t	PROPN
ejpam-1599	229	17	,	,	PUNCT
ejpam-1599	229	18	s	s	PART
ejpam-1599	229	19	∈	∈	PROPN
ejpam-1599	229	20	r	r	NOUN
ejpam-1599	229	21	,	,	PUNCT
ejpam-1599	229	22	e	e	NOUN
ejpam-1599	229	23	=	=	PUNCT
ejpam-1599	229	24	a(1−	a(1−	NOUN
ejpam-1599	229	25	ba)t	ba)t	ADV
ejpam-1599	229	26	=	=	SYM
ejpam-1599	229	27	s(1−	s(1−	NOUN
ejpam-1599	229	28	ab)a	ab)a	PROPN
ejpam-1599	229	29	and	and	CCONJ
ejpam-1599	229	30	e	e	X
ejpam-1599	229	31	≤h	≤h	NOUN
ejpam-1599	229	32	a.	a.	NOUN
ejpam-1599	229	33	finally	finally	ADV
ejpam-1599	229	34	,	,	PUNCT
ejpam-1599	229	35	e	e	PROPN
ejpam-1599	229	36	∈	∈	PROPN
ejpam-1599	229	37	σ2(a	σ2(a	NUM
ejpam-1599	229	38	)	)	PUNCT
ejpam-1599	229	39	hence	hence	ADV
ejpam-1599	229	40	e	e	X
ejpam-1599	229	41	≤	≤	NUM
ejpam-1599	229	42	m	m	VERB
ejpam-1599	229	43	,	,	PUNCT
ejpam-1599	229	44	em	em	PRON
ejpam-1599	229	45	=	=	NUM
ejpam-1599	229	46	me	i	PRON
ejpam-1599	230	1	=	=	PUNCT
ejpam-1599	230	2	e.	e.	PROPN
ejpam-1599	230	3	computation	computation	PROPN
ejpam-1599	230	4	give	give	VERB
ejpam-1599	230	5	e	e	X
ejpam-1599	230	6	=	=	SYM
ejpam-1599	230	7	em	em	PROPN
ejpam-1599	230	8	=	=	SYM
ejpam-1599	230	9	s(1−	s(1−	PROPN
ejpam-1599	230	10	ab)aba	ab)aba	PROPN
ejpam-1599	231	1	=	=	SYM
ejpam-1599	231	2	0	0	X
ejpam-1599	231	3	.	.	PUNCT
ejpam-1599	231	4	2.⇒	2.⇒	PROPN
ejpam-1599	231	5	3	3	X
ejpam-1599	231	6	.	.	PUNCT
ejpam-1599	232	1	let	let	VERB
ejpam-1599	232	2	b	b	X
ejpam-1599	232	3	∈	∈	PROPN
ejpam-1599	232	4	{	{	PUNCT
ejpam-1599	232	5	a}′′	a}′′	PROPN
ejpam-1599	232	6	,	,	PUNCT
ejpam-1599	232	7	bab	bab	PROPN
ejpam-1599	232	8	=	=	SYM
ejpam-1599	232	9	b	b	PROPN
ejpam-1599	232	10	and	and	CCONJ
ejpam-1599	232	11	σ(a−	σ(a−	PROPN
ejpam-1599	232	12	aba	aba	PROPN
ejpam-1599	232	13	)	)	PUNCT
ejpam-1599	232	14	=	=	PUNCT
ejpam-1599	233	1	{	{	PUNCT
ejpam-1599	233	2	0	0	NUM
ejpam-1599	233	3	}	}	PUNCT
ejpam-1599	233	4	.	.	PUNCT
ejpam-1599	234	1	then	then	ADV
ejpam-1599	234	2	x	x	X
ejpam-1599	234	3	=	=	VERB
ejpam-1599	234	4	aba	aba	PROPN
ejpam-1599	234	5	and	and	CCONJ
ejpam-1599	234	6	y	y	PROPN
ejpam-1599	234	7	=	=	PROPN
ejpam-1599	235	1	a	a	DET
ejpam-1599	235	2	−	−	PROPN
ejpam-1599	235	3	aba	aba	PROPN
ejpam-1599	235	4	satisfy	satisfy	VERB
ejpam-1599	235	5	the	the	DET
ejpam-1599	235	6	required	require	VERB
ejpam-1599	235	7	relations	relation	NOUN
ejpam-1599	235	8	(	(	PUNCT
ejpam-1599	235	9	x	x	X
ejpam-1599	235	10	#	#	NOUN
ejpam-1599	235	11	=	=	SYM
ejpam-1599	235	12	b	b	NOUN
ejpam-1599	235	13	)	)	PUNCT
ejpam-1599	235	14	.	.	PUNCT
ejpam-1599	236	1	3.⇒	3.⇒	PROPN
ejpam-1599	236	2	1	1	X
ejpam-1599	236	3	.	.	PUNCT
ejpam-1599	237	1	finally	finally	ADV
ejpam-1599	237	2	,	,	PUNCT
ejpam-1599	237	3	let	let	VERB
ejpam-1599	237	4	a	a	DET
ejpam-1599	237	5	=	=	PUNCT
ejpam-1599	237	6	x+	x+	ADJ
ejpam-1599	237	7	y	y	NOUN
ejpam-1599	237	8	with	with	ADP
ejpam-1599	237	9	x	x	PROPN
ejpam-1599	237	10	∈	∈	PROPN
ejpam-1599	237	11	{	{	PUNCT
ejpam-1599	237	12	a}′′	a}′′	NUM
ejpam-1599	237	13	,	,	PUNCT
ejpam-1599	237	14	x	x	ADJ
ejpam-1599	237	15	#	#	NOUN
ejpam-1599	237	16	exists	exist	VERB
ejpam-1599	237	17	,	,	PUNCT
ejpam-1599	237	18	x	x	X
ejpam-1599	237	19	y	y	NOUN
ejpam-1599	237	20	=	=	SYM
ejpam-1599	237	21	0	0	NUM
ejpam-1599	237	22	and	and	CCONJ
ejpam-1599	237	23	σ(y	σ(y	NOUN
ejpam-1599	237	24	)	)	PUNCT
ejpam-1599	237	25	=	=	PUNCT
ejpam-1599	237	26	{	{	PUNCT
ejpam-1599	237	27	0	0	NUM
ejpam-1599	237	28	}	}	PUNCT
ejpam-1599	237	29	.	.	PUNCT
ejpam-1599	238	1	by	by	ADP
ejpam-1599	238	2	properties	property	NOUN
ejpam-1599	238	3	of	of	ADP
ejpam-1599	238	4	the	the	DET
ejpam-1599	238	5	group	group	NOUN
ejpam-1599	238	6	inverse	inverse	NOUN
ejpam-1599	238	7	,	,	PUNCT
ejpam-1599	238	8	x	x	NOUN
ejpam-1599	238	9	#	#	NOUN
ejpam-1599	238	10	∈	∈	NOUN
ejpam-1599	238	11	{	{	PUNCT
ejpam-1599	238	12	x}′′⇒	x}′′⇒	NOUN
ejpam-1599	238	13	x	x	X
ejpam-1599	238	14	x	x	SYM
ejpam-1599	238	15	#	#	NOUN
ejpam-1599	238	16	∈	∈	NOUN
ejpam-1599	238	17	{	{	PUNCT
ejpam-1599	238	18	a}′′.	a}′′.	NOUN
ejpam-1599	238	19	pose	pose	VERB
ejpam-1599	238	20	m	m	VERB
ejpam-1599	238	21	=	=	PUNCT
ejpam-1599	238	22	x	x	PUNCT
ejpam-1599	238	23	x	x	X
ejpam-1599	238	24	#	#	NOUN
ejpam-1599	238	25	.	.	PUNCT
ejpam-1599	239	1	since	since	SCONJ
ejpam-1599	239	2	x	x	X
ejpam-1599	239	3	=	=	PUNCT
ejpam-1599	239	4	x	x	PUNCT
ejpam-1599	239	5	x#x	x#x	PROPN
ejpam-1599	239	6	=	=	PUNCT
ejpam-1599	240	1	x	x	PUNCT
ejpam-1599	240	2	x#a	x#a	NOUN
ejpam-1599	240	3	=	=	PUNCT
ejpam-1599	240	4	ax	ax	NOUN
ejpam-1599	240	5	x	x	NOUN
ejpam-1599	240	6	#	#	NOUN
ejpam-1599	240	7	,	,	PUNCT
ejpam-1599	240	8	m	m	VERB
ejpam-1599	240	9	≤h	≤h	NOUN
ejpam-1599	240	10	a	a	DET
ejpam-1599	240	11	and	and	CCONJ
ejpam-1599	240	12	m	m	PROPN
ejpam-1599	240	13	∈	∈	PROPN
ejpam-1599	240	14	σ2(a	σ2(a	PROPN
ejpam-1599	240	15	)	)	PUNCT
ejpam-1599	240	16	.	.	PUNCT
ejpam-1599	241	1	let	let	VERB
ejpam-1599	241	2	e	e	PRON
ejpam-1599	241	3	∈	∈	PROPN
ejpam-1599	241	4	σ2(a	σ2(a	PROPN
ejpam-1599	241	5	)	)	PUNCT
ejpam-1599	241	6	.	.	PUNCT
ejpam-1599	242	1	then	then	ADV
ejpam-1599	242	2	e	e	X
ejpam-1599	242	3	=	=	PUNCT
ejpam-1599	242	4	a−eae	a−eae	ADV
ejpam-1599	242	5	,	,	PUNCT
ejpam-1599	242	6	and	and	CCONJ
ejpam-1599	242	7	e	e	NOUN
ejpam-1599	242	8	is	be	AUX
ejpam-1599	242	9	in	in	ADP
ejpam-1599	242	10	the	the	DET
ejpam-1599	242	11	bicommutant	bicommutant	NOUN
ejpam-1599	242	12	of	of	ADP
ejpam-1599	242	13	y	y	PROPN
ejpam-1599	242	14	=	=	SYM
ejpam-1599	242	15	a−	a−	PROPN
ejpam-1599	242	16	x	x	X
ejpam-1599	242	17	.	.	PUNCT
ejpam-1599	243	1	then	then	ADV
ejpam-1599	243	2	e−	e−	NUM
ejpam-1599	243	3	em	em	PRON
ejpam-1599	244	1	=	=	PUNCT
ejpam-1599	244	2	e(1−	e(1−	PROPN
ejpam-1599	244	3	x	x	SYM
ejpam-1599	244	4	x	x	NOUN
ejpam-1599	244	5	#	#	NOUN
ejpam-1599	244	6	)	)	PUNCT
ejpam-1599	244	7	=	=	SYM
ejpam-1599	245	1	ea−ea(1−	ea−ea(1−	PROPN
ejpam-1599	245	2	x	x	PUNCT
ejpam-1599	245	3	x	x	X
ejpam-1599	245	4	#	#	NOUN
ejpam-1599	245	5	)	)	PUNCT
ejpam-1599	245	6	=	=	PUNCT
ejpam-1599	245	7	ea−e(x	ea−e(x	PROPN
ejpam-1599	246	1	+	+	CCONJ
ejpam-1599	246	2	y)(1−	y)(1−	PROPN
ejpam-1599	246	3	x	x	SYM
ejpam-1599	246	4	x	x	NOUN
ejpam-1599	246	5	#	#	NOUN
ejpam-1599	246	6	)	)	PUNCT
ejpam-1599	246	7	=	=	SYM
ejpam-1599	246	8	ea−e	ea−e	NOUN
ejpam-1599	246	9	y	y	PROPN
ejpam-1599	246	10	and	and	CCONJ
ejpam-1599	246	11	e−	e−	NUM
ejpam-1599	246	12	em	em	PROPN
ejpam-1599	246	13	∈	∈	PROPN
ejpam-1599	246	14	σ2(y	σ2(y	ADJ
ejpam-1599	246	15	)	)	PUNCT
ejpam-1599	246	16	.	.	PUNCT
ejpam-1599	247	1	by	by	ADP
ejpam-1599	247	2	hypothesis	hypothesis	NOUN
ejpam-1599	247	3	,	,	PUNCT
ejpam-1599	247	4	e−	e−	PROPN
ejpam-1599	247	5	em	em	PRON
ejpam-1599	247	6	=	=	PUNCT
ejpam-1599	247	7	0	0	PUNCT
ejpam-1599	247	8	and	and	CCONJ
ejpam-1599	247	9	e	e	X
ejpam-1599	247	10	≤	≤	NUM
ejpam-1599	247	11	m	m	VERB
ejpam-1599	247	12	,	,	PUNCT
ejpam-1599	247	13	m	m	VERB
ejpam-1599	247	14	is	be	AUX
ejpam-1599	247	15	the	the	DET
ejpam-1599	247	16	greatest	great	ADJ
ejpam-1599	247	17	element	element	NOUN
ejpam-1599	247	18	of	of	ADP
ejpam-1599	247	19	σ2(a	σ2(a	PROPN
ejpam-1599	247	20	)	)	PUNCT
ejpam-1599	247	21	and	and	CCONJ
ejpam-1599	247	22	a	a	PRON
ejpam-1599	247	23	is	be	AUX
ejpam-1599	247	24	naturally	naturally	ADV
ejpam-1599	247	25	invertible	invertible	ADJ
ejpam-1599	247	26	with	with	ADP
ejpam-1599	247	27	inverse	inverse	NOUN
ejpam-1599	247	28	a−x	a−x	NOUN
ejpam-1599	247	29	x	x	SYM
ejpam-1599	247	30	#	#	NOUN
ejpam-1599	247	31	.	.	PUNCT
ejpam-1599	248	1	the	the	DET
ejpam-1599	248	2	unique	unique	ADJ
ejpam-1599	248	3	decomposition	decomposition	NOUN
ejpam-1599	248	4	a	a	DET
ejpam-1599	248	5	=	=	SYM
ejpam-1599	248	6	x	x	SYM
ejpam-1599	248	7	+	+	CCONJ
ejpam-1599	248	8	y	y	NOUN
ejpam-1599	248	9	=	=	PRON
ejpam-1599	248	10	am	be	AUX
ejpam-1599	248	11	+	+	X
ejpam-1599	248	12	(	(	PUNCT
ejpam-1599	248	13	a	a	DET
ejpam-1599	248	14	−	−	NOUN
ejpam-1599	248	15	am	am	NOUN
ejpam-1599	248	16	)	)	PUNCT
ejpam-1599	248	17	=	=	PUNCT
ejpam-1599	248	18	aba	aba	PROPN
ejpam-1599	248	19	+	+	CCONJ
ejpam-1599	248	20	(	(	PUNCT
ejpam-1599	248	21	a	a	DET
ejpam-1599	248	22	−	−	PROPN
ejpam-1599	248	23	aba	aba	PROPN
ejpam-1599	248	24	)	)	PUNCT
ejpam-1599	248	25	as	as	ADP
ejpam-1599	248	26	in	in	ADP
ejpam-1599	248	27	the	the	DET
ejpam-1599	248	28	previous	previous	ADJ
ejpam-1599	248	29	theorem	theorem	NOUN
ejpam-1599	248	30	will	will	AUX
ejpam-1599	248	31	be	be	AUX
ejpam-1599	248	32	called	call	VERB
ejpam-1599	248	33	the	the	DET
ejpam-1599	248	34	natural	natural	ADJ
ejpam-1599	248	35	core	core	NOUN
ejpam-1599	248	36	decomposition	decomposition	NOUN
ejpam-1599	248	37	of	of	ADP
ejpam-1599	248	38	a.	a.	NOUN
ejpam-1599	248	39	4.3	4.3	NUM
ejpam-1599	248	40	.	.	PUNCT
ejpam-1599	249	1	link	link	VERB
ejpam-1599	249	2	with	with	ADP
ejpam-1599	249	3	the	the	DET
ejpam-1599	249	4	koliha	koliha	VERB
ejpam-1599	249	5	-	-	PUNCT
ejpam-1599	249	6	drazin	drazin	NOUN
ejpam-1599	249	7	inverse	inverse	NOUN
ejpam-1599	249	8	we	we	PRON
ejpam-1599	249	9	recall	recall	VERB
ejpam-1599	249	10	the	the	DET
ejpam-1599	249	11	following	follow	VERB
ejpam-1599	249	12	definitions	definition	NOUN
ejpam-1599	249	13	of	of	ADP
ejpam-1599	249	14	quasinilpotency	quasinilpotency	NOUN
ejpam-1599	249	15	and	and	CCONJ
ejpam-1599	249	16	quasipolarity	quasipolarity	NOUN
ejpam-1599	249	17	in	in	ADP
ejpam-1599	249	18	rings	ring	NOUN
ejpam-1599	249	19	due	due	ADP
ejpam-1599	249	20	to	to	ADP
ejpam-1599	249	21	r.	r.	PROPN
ejpam-1599	249	22	harte	harte	PROPN
ejpam-1599	250	1	[	[	X
ejpam-1599	250	2	10	10	NUM
ejpam-1599	250	3	]	]	PUNCT
ejpam-1599	250	4	.	.	PUNCT
ejpam-1599	251	1	definition	definition	NOUN
ejpam-1599	251	2	3	3	NUM
ejpam-1599	251	3	.	.	PUNCT
ejpam-1599	252	1	an	an	DET
ejpam-1599	252	2	element	element	NOUN
ejpam-1599	252	3	q	q	NOUN
ejpam-1599	252	4	of	of	ADP
ejpam-1599	252	5	a	a	DET
ejpam-1599	252	6	ring	ring	NOUN
ejpam-1599	252	7	r	r	NOUN
ejpam-1599	252	8	is	be	AUX
ejpam-1599	252	9	quasinilpotent	quasinilpotent	NOUN
ejpam-1599	252	10	if	if	SCONJ
ejpam-1599	252	11	∀x	∀x	X
ejpam-1599	252	12	∈	∈	PROPN
ejpam-1599	252	13	{	{	PUNCT
ejpam-1599	252	14	q}′	q}′	NOUN
ejpam-1599	252	15	,	,	PUNCT
ejpam-1599	252	16	1	1	NUM
ejpam-1599	252	17	+	+	NUM
ejpam-1599	252	18	xq	xq	PROPN
ejpam-1599	252	19	∈	∈	PROPN
ejpam-1599	252	20	r−1	r−1	PROPN
ejpam-1599	252	21	,	,	PUNCT
ejpam-1599	252	22	and	and	CCONJ
ejpam-1599	252	23	quasiquasinilpotent	quasiquasinilpotent	VERB
ejpam-1599	252	24	if	if	SCONJ
ejpam-1599	252	25	∀x	∀x	X
ejpam-1599	252	26	∈	∈	PROPN
ejpam-1599	252	27	{	{	PUNCT
ejpam-1599	252	28	q}′′	q}′′	NUM
ejpam-1599	252	29	,	,	PUNCT
ejpam-1599	252	30	1	1	NUM
ejpam-1599	252	31	+	+	NUM
ejpam-1599	252	32	xq	xq	PROPN
ejpam-1599	252	33	∈	∈	PROPN
ejpam-1599	252	34	r−1	r−1	PROPN
ejpam-1599	252	35	note	note	VERB
ejpam-1599	252	36	that	that	SCONJ
ejpam-1599	252	37	quasi	quasi	ADJ
ejpam-1599	252	38	-	-	ADJ
ejpam-1599	252	39	quasinilpotent	quasinilpotent	ADJ
ejpam-1599	252	40	elements	element	NOUN
ejpam-1599	252	41	need	need	AUX
ejpam-1599	252	42	not	not	PART
ejpam-1599	252	43	be	be	AUX
ejpam-1599	252	44	quasinilpotent	quasinilpotent	ADJ
ejpam-1599	252	45	in	in	ADP
ejpam-1599	252	46	general	general	ADJ
ejpam-1599	252	47	.	.	PUNCT
ejpam-1599	253	1	the	the	DET
ejpam-1599	253	2	two	two	NUM
ejpam-1599	253	3	notions	notion	NOUN
ejpam-1599	253	4	however	however	ADV
ejpam-1599	253	5	coincide	coincide	VERB
ejpam-1599	253	6	for	for	ADP
ejpam-1599	253	7	banach	banach	NOUN
ejpam-1599	253	8	algebras	algebra	NOUN
ejpam-1599	253	9	.	.	PUNCT
ejpam-1599	254	1	definition	definition	NOUN
ejpam-1599	254	2	4	4	NUM
ejpam-1599	254	3	.	.	PUNCT
ejpam-1599	255	1	an	an	DET
ejpam-1599	255	2	element	element	NOUN
ejpam-1599	255	3	a	a	PRON
ejpam-1599	255	4	of	of	ADP
ejpam-1599	255	5	a	a	DET
ejpam-1599	255	6	ring	ring	NOUN
ejpam-1599	255	7	r	r	NOUN
ejpam-1599	255	8	is	be	AUX
ejpam-1599	255	9	quasipolar	quasipolar	ADJ
ejpam-1599	255	10	(	(	PUNCT
ejpam-1599	255	11	resp	resp	NOUN
ejpam-1599	255	12	.	.	PUNCT
ejpam-1599	256	1	quasi	quasi	ADJ
ejpam-1599	256	2	-	-	ADJ
ejpam-1599	256	3	quasipolar	quasipolar	ADJ
ejpam-1599	256	4	)	)	PUNCT
ejpam-1599	256	5	if	if	SCONJ
ejpam-1599	256	6	there	there	PRON
ejpam-1599	256	7	exists	exist	VERB
ejpam-1599	256	8	a	a	DET
ejpam-1599	256	9	idempotent	idempotent	NOUN
ejpam-1599	256	10	(	(	PUNCT
ejpam-1599	256	11	called	call	VERB
ejpam-1599	256	12	spectral	spectral	ADJ
ejpam-1599	256	13	idempotent	idempotent	NOUN
ejpam-1599	256	14	)	)	PUNCT
ejpam-1599	256	15	p	p	NOUN
ejpam-1599	256	16	in	in	ADP
ejpam-1599	256	17	{	{	PUNCT
ejpam-1599	256	18	a}′′	a}′′	NUM
ejpam-1599	256	19	such	such	ADJ
ejpam-1599	256	20	that	that	SCONJ
ejpam-1599	256	21	ap	ap	PROPN
ejpam-1599	256	22	is	be	AUX
ejpam-1599	256	23	quasinilpotent	quasinilpotent	NOUN
ejpam-1599	256	24	(	(	PUNCT
ejpam-1599	256	25	resp	resp	NOUN
ejpam-1599	256	26	.	.	PUNCT
ejpam-1599	257	1	quasiquasinilpotent	quasiquasinilpotent	NOUN
ejpam-1599	257	2	)	)	PUNCT
ejpam-1599	258	1	and	and	CCONJ
ejpam-1599	258	2	a+	a+	PUNCT
ejpam-1599	258	3	p	p	PROPN
ejpam-1599	258	4	∈	∈	PROPN
ejpam-1599	258	5	r−1	r−1	PROPN
ejpam-1599	258	6	.	.	PUNCT
ejpam-1599	259	1	it	it	PRON
ejpam-1599	259	2	was	be	AUX
ejpam-1599	259	3	remarked	remark	VERB
ejpam-1599	259	4	in	in	ADP
ejpam-1599	259	5	[	[	X
ejpam-1599	259	6	17	17	NUM
ejpam-1599	259	7	]	]	PUNCT
ejpam-1599	259	8	that	that	SCONJ
ejpam-1599	259	9	the	the	DET
ejpam-1599	259	10	last	last	ADJ
ejpam-1599	259	11	condition	condition	NOUN
ejpam-1599	259	12	can	can	AUX
ejpam-1599	259	13	be	be	AUX
ejpam-1599	259	14	replaced	replace	VERB
ejpam-1599	259	15	by	by	ADP
ejpam-1599	259	16	the	the	DET
ejpam-1599	259	17	following	follow	VERB
ejpam-1599	259	18	one	one	NUM
ejpam-1599	259	19	1−	1−	NUM
ejpam-1599	260	1	p	p	NOUN
ejpam-1599	260	2	≤h	≤h	NOUN
ejpam-1599	260	3	a.	a.	NOUN
ejpam-1599	260	4	this	this	PRON
ejpam-1599	260	5	is	be	AUX
ejpam-1599	260	6	the	the	DET
ejpam-1599	260	7	content	content	NOUN
ejpam-1599	260	8	of	of	ADP
ejpam-1599	260	9	lemma	lemma	PROPN
ejpam-1599	260	10	5	5	NUM
ejpam-1599	260	11	.	.	PUNCT
ejpam-1599	261	1	it	it	PRON
ejpam-1599	261	2	was	be	AUX
ejpam-1599	261	3	proved	prove	VERB
ejpam-1599	261	4	by	by	ADP
ejpam-1599	261	5	j.	j.	PROPN
ejpam-1599	261	6	koliha	koliha	PROPN
ejpam-1599	261	7	and	and	CCONJ
ejpam-1599	261	8	p.	p.	PROPN
ejpam-1599	261	9	patricio	patricio	PROPN
ejpam-1599	262	1	[	[	X
ejpam-1599	262	2	theorem	theorem	VERB
ejpam-1599	262	3	4.2	4.2	NUM
ejpam-1599	262	4	in	in	ADP
ejpam-1599	262	5	17	17	NUM
ejpam-1599	262	6	]	]	PUNCT
ejpam-1599	262	7	that	that	SCONJ
ejpam-1599	262	8	quasipolar	quasipolar	ADJ
ejpam-1599	262	9	elements	element	NOUN
ejpam-1599	262	10	are	be	AUX
ejpam-1599	262	11	exactly	exactly	ADV
ejpam-1599	262	12	the	the	DET
ejpam-1599	262	13	generalized	generalized	ADJ
ejpam-1599	262	14	drazin	drazin	NOUN
ejpam-1599	262	15	invertible	invertible	ADJ
ejpam-1599	262	16	elements	element	NOUN
ejpam-1599	262	17	(	(	PUNCT
ejpam-1599	262	18	also	also	ADV
ejpam-1599	262	19	called	call	VERB
ejpam-1599	262	20	koliha	koliha	ADJ
ejpam-1599	262	21	-	-	PUNCT
ejpam-1599	262	22	drazin	drazin	PROPN
ejpam-1599	262	23	invertible	invertible	ADJ
ejpam-1599	262	24	elements	element	NOUN
ejpam-1599	262	25	):	):	PUNCT
ejpam-1599	262	26	definition	definition	NOUN
ejpam-1599	262	27	5	5	NUM
ejpam-1599	262	28	.	.	PUNCT
ejpam-1599	263	1	an	an	DET
ejpam-1599	263	2	element	element	NOUN
ejpam-1599	263	3	a	a	PRON
ejpam-1599	263	4	of	of	ADP
ejpam-1599	263	5	a	a	DET
ejpam-1599	263	6	ring	ring	NOUN
ejpam-1599	263	7	r	r	NOUN
ejpam-1599	263	8	is	be	AUX
ejpam-1599	263	9	generalized	generalize	VERB
ejpam-1599	263	10	drazin	drazin	NOUN
ejpam-1599	263	11	invertible	invertible	ADJ
ejpam-1599	263	12	if	if	SCONJ
ejpam-1599	263	13	there	there	PRON
ejpam-1599	263	14	exists	exist	VERB
ejpam-1599	263	15	b	b	PROPN
ejpam-1599	263	16	in	in	ADP
ejpam-1599	263	17	{	{	PUNCT
ejpam-1599	263	18	a}′′	a}′′	NUM
ejpam-1599	263	19	such	such	ADJ
ejpam-1599	263	20	that	that	PRON
ejpam-1599	263	21	bab	bab	PROPN
ejpam-1599	263	22	=	=	SYM
ejpam-1599	263	23	b	b	PROPN
ejpam-1599	263	24	and	and	CCONJ
ejpam-1599	263	25	a2	a2	PROPN
ejpam-1599	263	26	b−	b−	PROPN
ejpam-1599	263	27	a	a	PRON
ejpam-1599	263	28	is	be	AUX
ejpam-1599	263	29	quasinilpotent	quasinilpotent	NOUN
ejpam-1599	263	30	.	.	PUNCT
ejpam-1599	264	1	x.	x.	PROPN
ejpam-1599	264	2	mary	mary	PROPN
ejpam-1599	264	3	/	/	SYM
ejpam-1599	264	4	eur	eur	PROPN
ejpam-1599	264	5	.	.	PUNCT
ejpam-1599	265	1	j.	j.	PROPN
ejpam-1599	265	2	pure	pure	PROPN
ejpam-1599	265	3	appl	appl	PROPN
ejpam-1599	265	4	.	.	PROPN
ejpam-1599	265	5	math	math	PROPN
ejpam-1599	265	6	,	,	PUNCT
ejpam-1599	265	7	5	5	NUM
ejpam-1599	265	8	(	(	PUNCT
ejpam-1599	265	9	2012	2012	NUM
ejpam-1599	265	10	)	)	PUNCT
ejpam-1599	265	11	,	,	PUNCT
ejpam-1599	265	12	160	160	NUM
ejpam-1599	265	13	-	-	SYM
ejpam-1599	265	14	173	173	NUM
ejpam-1599	265	15	168	168	NUM
ejpam-1599	265	16	theorem	theorem	NOUN
ejpam-1599	265	17	7	7	NUM
ejpam-1599	265	18	.	.	PUNCT
ejpam-1599	266	1	an	an	DET
ejpam-1599	266	2	element	element	NOUN
ejpam-1599	266	3	a	a	PRON
ejpam-1599	266	4	of	of	ADP
ejpam-1599	266	5	a	a	DET
ejpam-1599	266	6	ring	ring	NOUN
ejpam-1599	266	7	r	r	NOUN
ejpam-1599	266	8	is	be	AUX
ejpam-1599	266	9	generalized	generalize	VERB
ejpam-1599	266	10	drazin	drazin	NOUN
ejpam-1599	266	11	invertible	invertible	ADJ
ejpam-1599	266	12	if	if	SCONJ
ejpam-1599	266	13	and	and	CCONJ
ejpam-1599	266	14	only	only	ADV
ejpam-1599	266	15	if	if	SCONJ
ejpam-1599	266	16	it	it	PRON
ejpam-1599	266	17	is	be	AUX
ejpam-1599	266	18	quasipolar	quasipolar	ADJ
ejpam-1599	266	19	.	.	PUNCT
ejpam-1599	267	1	in	in	ADP
ejpam-1599	267	2	this	this	DET
ejpam-1599	267	3	case	case	NOUN
ejpam-1599	267	4	b	b	X
ejpam-1599	267	5	=	=	SYM
ejpam-1599	267	6	(	(	PUNCT
ejpam-1599	267	7	a+	a+	PUNCT
ejpam-1599	267	8	p)−1(1−	p)−1(1−	NUM
ejpam-1599	267	9	p	p	NOUN
ejpam-1599	267	10	)	)	PUNCT
ejpam-1599	267	11	.	.	PUNCT
ejpam-1599	268	1	next	next	ADJ
ejpam-1599	268	2	theorem	theorem	NOUN
ejpam-1599	268	3	proves	prove	VERB
ejpam-1599	268	4	that	that	SCONJ
ejpam-1599	268	5	the	the	DET
ejpam-1599	268	6	natural	natural	ADJ
ejpam-1599	268	7	inverse	inverse	NOUN
ejpam-1599	268	8	generalizes	generalize	VERB
ejpam-1599	268	9	not	not	PART
ejpam-1599	268	10	only	only	ADV
ejpam-1599	268	11	the	the	DET
ejpam-1599	268	12	drazin	drazin	PROPN
ejpam-1599	268	13	inverse	inverse	NOUN
ejpam-1599	268	14	,	,	PUNCT
ejpam-1599	268	15	but	but	CCONJ
ejpam-1599	268	16	also	also	ADV
ejpam-1599	268	17	the	the	DET
ejpam-1599	268	18	koliha	koliha	VERB
ejpam-1599	268	19	-	-	PUNCT
ejpam-1599	268	20	drazin	drazin	NOUN
ejpam-1599	268	21	inverse	inverse	NOUN
ejpam-1599	268	22	in	in	ADP
ejpam-1599	268	23	a	a	DET
ejpam-1599	268	24	ring	ring	NOUN
ejpam-1599	268	25	:	:	PUNCT
ejpam-1599	268	26	theorem	theorem	NOUN
ejpam-1599	268	27	8	8	NUM
ejpam-1599	268	28	.	.	PUNCT
ejpam-1599	269	1	let	let	VERB
ejpam-1599	269	2	r	r	PRON
ejpam-1599	269	3	be	be	AUX
ejpam-1599	269	4	a	a	DET
ejpam-1599	269	5	ring	ring	NOUN
ejpam-1599	269	6	,	,	PUNCT
ejpam-1599	269	7	and	and	CCONJ
ejpam-1599	269	8	a	a	DET
ejpam-1599	269	9	∈	∈	NOUN
ejpam-1599	269	10	r	r	AUX
ejpam-1599	269	11	be	be	VERB
ejpam-1599	269	12	quasi	quasi	ADJ
ejpam-1599	269	13	-	-	ADJ
ejpam-1599	269	14	quasipolar	quasipolar	ADJ
ejpam-1599	269	15	with	with	ADP
ejpam-1599	269	16	spectral	spectral	ADJ
ejpam-1599	269	17	idempotent	idempotent	NOUN
ejpam-1599	269	18	p	p	NOUN
ejpam-1599	269	19	and	and	CCONJ
ejpam-1599	269	20	koliha	koliha	ADJ
ejpam-1599	269	21	-	-	PUNCT
ejpam-1599	269	22	drazin	drazin	PROPN
ejpam-1599	269	23	inverse	inverse	PROPN
ejpam-1599	269	24	b.	b.	PROPN
ejpam-1599	270	1	then	then	ADV
ejpam-1599	270	2	a	a	PRON
ejpam-1599	270	3	is	be	AUX
ejpam-1599	270	4	naturally	naturally	ADV
ejpam-1599	270	5	invertible	invertible	ADJ
ejpam-1599	270	6	,	,	PUNCT
ejpam-1599	270	7	m	m	VERB
ejpam-1599	270	8	=	=	NOUN
ejpam-1599	270	9	1	1	NUM
ejpam-1599	270	10	−	−	PROPN
ejpam-1599	270	11	p	p	NOUN
ejpam-1599	270	12	is	be	AUX
ejpam-1599	270	13	the	the	DET
ejpam-1599	270	14	greatest	great	ADJ
ejpam-1599	270	15	element	element	NOUN
ejpam-1599	270	16	of	of	ADP
ejpam-1599	270	17	σ2(a	σ2(a	PROPN
ejpam-1599	270	18	)	)	PUNCT
ejpam-1599	270	19	and	and	CCONJ
ejpam-1599	270	20	the	the	DET
ejpam-1599	270	21	generalized	generalized	ADJ
ejpam-1599	270	22	drazin	drazin	PROPN
ejpam-1599	270	23	inverse	inverse	PROPN
ejpam-1599	270	24	b	b	PROPN
ejpam-1599	270	25	is	be	AUX
ejpam-1599	270	26	equal	equal	ADJ
ejpam-1599	270	27	to	to	ADP
ejpam-1599	270	28	a−m	a−m	NOUN
ejpam-1599	270	29	,	,	PUNCT
ejpam-1599	270	30	the	the	DET
ejpam-1599	270	31	natural	natural	ADJ
ejpam-1599	270	32	generalized	generalized	ADJ
ejpam-1599	270	33	inverse	inverse	NOUN
ejpam-1599	270	34	of	of	ADP
ejpam-1599	270	35	a.	a.	NOUN
ejpam-1599	270	36	proof	proof	NOUN
ejpam-1599	270	37	.	.	PUNCT
ejpam-1599	271	1	assume	assume	VERB
ejpam-1599	271	2	a	a	PRON
ejpam-1599	271	3	is	be	AUX
ejpam-1599	271	4	quasi	quasi	ADJ
ejpam-1599	271	5	-	-	ADJ
ejpam-1599	271	6	quasipolar	quasipolar	ADJ
ejpam-1599	271	7	in	in	ADP
ejpam-1599	271	8	the	the	DET
ejpam-1599	271	9	ring	ring	NOUN
ejpam-1599	271	10	sense	sense	NOUN
ejpam-1599	271	11	.	.	PUNCT
ejpam-1599	272	1	then	then	ADV
ejpam-1599	272	2	exists	exist	VERB
ejpam-1599	272	3	spectral	spectral	ADJ
ejpam-1599	272	4	idempotent	idempotent	NOUN
ejpam-1599	272	5	p	p	NOUN
ejpam-1599	272	6	in	in	ADP
ejpam-1599	272	7	{	{	PUNCT
ejpam-1599	272	8	a}′′	a}′′	NUM
ejpam-1599	272	9	such	such	ADJ
ejpam-1599	272	10	that	that	SCONJ
ejpam-1599	272	11	ap	ap	PROPN
ejpam-1599	272	12	is	be	AUX
ejpam-1599	272	13	quasi	quasi	ADJ
ejpam-1599	272	14	-	-	NOUN
ejpam-1599	272	15	quasinilpotent	quasinilpotent	ADJ
ejpam-1599	272	16	and	and	CCONJ
ejpam-1599	272	17	a+	a+	PUNCT
ejpam-1599	272	18	p	p	PROPN
ejpam-1599	272	19	∈	∈	PROPN
ejpam-1599	272	20	r−1	r−1	PROPN
ejpam-1599	272	21	.	.	PUNCT
ejpam-1599	273	1	by	by	ADP
ejpam-1599	273	2	lemma	lemma	PROPN
ejpam-1599	273	3	5	5	NUM
ejpam-1599	273	4	,	,	PUNCT
ejpam-1599	273	5	m	m	VERB
ejpam-1599	273	6	=	=	NOUN
ejpam-1599	273	7	1−	1−	NUM
ejpam-1599	273	8	p	p	NOUN
ejpam-1599	273	9	≤h	≤h	PROPN
ejpam-1599	273	10	a	a	PRON
ejpam-1599	273	11	,	,	PUNCT
ejpam-1599	273	12	hence	hence	ADV
ejpam-1599	273	13	it	it	PRON
ejpam-1599	273	14	is	be	AUX
ejpam-1599	273	15	in	in	ADP
ejpam-1599	273	16	σ2(a	σ2(a	NOUN
ejpam-1599	273	17	)	)	PUNCT
ejpam-1599	273	18	.	.	PUNCT
ejpam-1599	274	1	let	let	VERB
ejpam-1599	274	2	f	f	PROPN
ejpam-1599	274	3	∈	∈	PROPN
ejpam-1599	274	4	σ2(a	σ2(a	PROPN
ejpam-1599	274	5	)	)	PUNCT
ejpam-1599	274	6	.	.	PUNCT
ejpam-1599	275	1	then	then	ADV
ejpam-1599	275	2	exists	exist	VERB
ejpam-1599	275	3	x	x	X
ejpam-1599	275	4	∈	∈	PROPN
ejpam-1599	275	5	s	s	PROPN
ejpam-1599	275	6	,	,	PUNCT
ejpam-1599	275	7	f	f	PROPN
ejpam-1599	275	8	=	=	SYM
ejpam-1599	275	9	xa	xa	PROPN
ejpam-1599	275	10	.	.	PUNCT
ejpam-1599	276	1	by	by	ADP
ejpam-1599	276	2	quasi	quasi	NOUN
ejpam-1599	276	3	-	-	NOUN
ejpam-1599	276	4	quasinilpotency	quasinilpotency	NOUN
ejpam-1599	276	5	,	,	PUNCT
ejpam-1599	276	6	(	(	PUNCT
ejpam-1599	276	7	1−	1−	NUM
ejpam-1599	276	8	f	f	NOUN
ejpam-1599	276	9	p	p	NOUN
ejpam-1599	276	10	)	)	PUNCT
ejpam-1599	276	11	=	=	SYM
ejpam-1599	276	12	(	(	PUNCT
ejpam-1599	276	13	1−	1−	NUM
ejpam-1599	276	14	xap	xap	PROPN
ejpam-1599	276	15	)	)	PUNCT
ejpam-1599	276	16	∈	∈	PROPN
ejpam-1599	276	17	r−1	r−1	PROPN
ejpam-1599	276	18	.	.	PUNCT
ejpam-1599	277	1	but	but	CCONJ
ejpam-1599	277	2	by	by	ADP
ejpam-1599	277	3	commutativity	commutativity	NOUN
ejpam-1599	277	4	of	of	ADP
ejpam-1599	277	5	{	{	PUNCT
ejpam-1599	277	6	a}′′	a}′′	PROPN
ejpam-1599	277	7	and	and	CCONJ
ejpam-1599	277	8	the	the	DET
ejpam-1599	277	9	fact	fact	NOUN
ejpam-1599	277	10	that	that	SCONJ
ejpam-1599	277	11	f	f	X
ejpam-1599	277	12	,	,	PUNCT
ejpam-1599	277	13	p	p	PROPN
ejpam-1599	277	14	∈	∈	PROPN
ejpam-1599	277	15	e(s	e(s	PROPN
ejpam-1599	277	16	)	)	PUNCT
ejpam-1599	277	17	,	,	PUNCT
ejpam-1599	277	18	we	we	PRON
ejpam-1599	277	19	have	have	VERB
ejpam-1599	277	20	(	(	PUNCT
ejpam-1599	277	21	1−	1−	NUM
ejpam-1599	277	22	f	f	X
ejpam-1599	277	23	p)(1	p)(1	PROPN
ejpam-1599	278	1	+	+	CCONJ
ejpam-1599	278	2	f	f	PROPN
ejpam-1599	278	3	p	p	NOUN
ejpam-1599	278	4	)	)	PUNCT
ejpam-1599	278	5	=	=	SYM
ejpam-1599	279	1	1−	1−	NUM
ejpam-1599	279	2	f	f	X
ejpam-1599	280	1	p.	p.	NOUN
ejpam-1599	280	2	by	by	ADP
ejpam-1599	280	3	invertibility	invertibility	NOUN
ejpam-1599	280	4	,	,	PUNCT
ejpam-1599	280	5	1	1	NUM
ejpam-1599	280	6	+	+	NUM
ejpam-1599	280	7	f	f	X
ejpam-1599	280	8	p	p	NOUN
ejpam-1599	280	9	=	=	NOUN
ejpam-1599	280	10	1	1	NUM
ejpam-1599	281	1	hence	hence	ADV
ejpam-1599	281	2	f	f	X
ejpam-1599	281	3	p	p	X
ejpam-1599	281	4	=	=	NOUN
ejpam-1599	281	5	0	0	NUM
ejpam-1599	281	6	.	.	PUNCT
ejpam-1599	282	1	it	it	PRON
ejpam-1599	282	2	follows	follow	VERB
ejpam-1599	282	3	that	that	SCONJ
ejpam-1599	282	4	f	f	PROPN
ejpam-1599	282	5	m	m	NOUN
ejpam-1599	282	6	=	=	ADJ
ejpam-1599	282	7	f	f	X
ejpam-1599	282	8	(	(	PUNCT
ejpam-1599	282	9	1−	1−	NUM
ejpam-1599	282	10	p	p	NOUN
ejpam-1599	282	11	)	)	PUNCT
ejpam-1599	282	12	=	=	PUNCT
ejpam-1599	283	1	f	f	X
ejpam-1599	284	1	−	−	NOUN
ejpam-1599	284	2	f	f	X
ejpam-1599	285	1	p	p	X
ejpam-1599	285	2	=	=	PUNCT
ejpam-1599	285	3	f	f	PROPN
ejpam-1599	285	4	and	and	CCONJ
ejpam-1599	285	5	f	f	PROPN
ejpam-1599	285	6	≤	≤	PROPN
ejpam-1599	285	7	m	m	VERB
ejpam-1599	285	8	for	for	ADP
ejpam-1599	285	9	the	the	DET
ejpam-1599	285	10	natural	natural	ADJ
ejpam-1599	285	11	partial	partial	ADJ
ejpam-1599	285	12	order	order	NOUN
ejpam-1599	285	13	.	.	PUNCT
ejpam-1599	286	1	m	m	PROPN
ejpam-1599	286	2	is	be	AUX
ejpam-1599	286	3	the	the	DET
ejpam-1599	286	4	greatest	great	ADJ
ejpam-1599	286	5	element	element	NOUN
ejpam-1599	286	6	of	of	ADP
ejpam-1599	286	7	σ2(a	σ2(a	PROPN
ejpam-1599	286	8	)	)	PUNCT
ejpam-1599	286	9	.	.	PUNCT
ejpam-1599	287	1	now	now	ADV
ejpam-1599	287	2	the	the	DET
ejpam-1599	287	3	generalized	generalized	ADJ
ejpam-1599	287	4	drazin	drazin	PROPN
ejpam-1599	287	5	inverse	inverse	NOUN
ejpam-1599	287	6	of	of	ADP
ejpam-1599	287	7	a	a	DET
ejpam-1599	287	8	b	b	NOUN
ejpam-1599	287	9	=	=	SYM
ejpam-1599	287	10	(	(	PUNCT
ejpam-1599	287	11	a+	a+	PUNCT
ejpam-1599	287	12	p)−1(1−	p)−1(1−	NUM
ejpam-1599	287	13	p	p	NOUN
ejpam-1599	287	14	)	)	PUNCT
ejpam-1599	287	15	is	be	AUX
ejpam-1599	287	16	obviously	obviously	ADV
ejpam-1599	287	17	inh(1−p	inh(1−p	PROPN
ejpam-1599	287	18	)	)	PUNCT
ejpam-1599	287	19	and	and	CCONJ
ejpam-1599	287	20	is	be	AUX
ejpam-1599	287	21	an	an	DET
ejpam-1599	287	22	outer	outer	ADJ
ejpam-1599	287	23	inverse	inverse	NOUN
ejpam-1599	287	24	of	of	ADP
ejpam-1599	287	25	a	a	PRON
ejpam-1599	287	26	by	by	ADP
ejpam-1599	287	27	definition	definition	NOUN
ejpam-1599	287	28	.	.	PUNCT
ejpam-1599	288	1	by	by	ADP
ejpam-1599	288	2	unicity	unicity	NOUN
ejpam-1599	288	3	,	,	PUNCT
ejpam-1599	288	4	it	it	PRON
ejpam-1599	288	5	is	be	AUX
ejpam-1599	288	6	a−m	a−m	NOUN
ejpam-1599	288	7	.	.	PUNCT
ejpam-1599	289	1	if	if	SCONJ
ejpam-1599	289	2	we	we	PRON
ejpam-1599	289	3	require	require	VERB
ejpam-1599	289	4	the	the	DET
ejpam-1599	289	5	element	element	NOUN
ejpam-1599	289	6	a	a	PRON
ejpam-1599	289	7	to	to	PART
ejpam-1599	289	8	be	be	AUX
ejpam-1599	289	9	quasipolar	quasipolar	ADJ
ejpam-1599	289	10	instead	instead	ADV
ejpam-1599	289	11	of	of	ADP
ejpam-1599	289	12	quasi	quasi	ADJ
ejpam-1599	289	13	-	-	ADJ
ejpam-1599	289	14	quasipolar	quasipolar	ADJ
ejpam-1599	289	15	with	with	ADP
ejpam-1599	289	16	koliha	koliha	VERB
ejpam-1599	289	17	-	-	PUNCT
ejpam-1599	289	18	drazin	drazin	PROPN
ejpam-1599	289	19	inverse	inverse	PROPN
ejpam-1599	289	20	b	b	PROPN
ejpam-1599	289	21	,	,	PUNCT
ejpam-1599	289	22	then	then	ADV
ejpam-1599	289	23	the	the	DET
ejpam-1599	289	24	idempotent	idempotent	NOUN
ejpam-1599	289	25	m	m	VERB
ejpam-1599	289	26	=	=	SYM
ejpam-1599	289	27	1−	1−	NUM
ejpam-1599	289	28	p	p	NOUN
ejpam-1599	289	29	is	be	AUX
ejpam-1599	289	30	actually	actually	ADV
ejpam-1599	289	31	the	the	DET
ejpam-1599	289	32	greatest	great	ADJ
ejpam-1599	289	33	element	element	NOUN
ejpam-1599	289	34	σ1(a	σ1(a	NOUN
ejpam-1599	289	35	)	)	PUNCT
ejpam-1599	289	36	and	and	CCONJ
ejpam-1599	289	37	b	b	X
ejpam-1599	289	38	=	=	NOUN
ejpam-1599	289	39	a−m	a−m	NOUN
ejpam-1599	289	40	is	be	AUX
ejpam-1599	289	41	the	the	DET
ejpam-1599	289	42	1−natural	1−natural	ADJ
ejpam-1599	289	43	generalized	generalized	ADJ
ejpam-1599	289	44	inverse	inverse	NOUN
ejpam-1599	289	45	of	of	ADP
ejpam-1599	289	46	a.	a.	NOUN
ejpam-1599	289	47	it	it	PRON
ejpam-1599	289	48	is	be	AUX
ejpam-1599	289	49	not	not	PART
ejpam-1599	289	50	in	in	ADP
ejpam-1599	289	51	{	{	PUNCT
ejpam-1599	289	52	a}′′	a}′′	PROPN
ejpam-1599	289	53	in	in	ADP
ejpam-1599	289	54	general	general	ADJ
ejpam-1599	289	55	.	.	PUNCT
ejpam-1599	290	1	5	5	X
ejpam-1599	290	2	.	.	X
ejpam-1599	290	3	the	the	DET
ejpam-1599	290	4	banach	banach	NOUN
ejpam-1599	290	5	algebra	algebra	NOUN
ejpam-1599	290	6	case	case	NOUN
ejpam-1599	290	7	in	in	ADP
ejpam-1599	290	8	this	this	DET
ejpam-1599	290	9	section	section	NOUN
ejpam-1599	290	10	,	,	PUNCT
ejpam-1599	290	11	a	a	DET
ejpam-1599	290	12	denotes	denote	NOUN
ejpam-1599	290	13	a	a	DET
ejpam-1599	290	14	unital	unital	ADJ
ejpam-1599	290	15	banach	banach	NOUN
ejpam-1599	290	16	algebra	algebra	NOUN
ejpam-1599	290	17	.	.	PUNCT
ejpam-1599	291	1	for	for	ADP
ejpam-1599	291	2	any	any	DET
ejpam-1599	291	3	a	a	DET
ejpam-1599	291	4	∈	∈	PROPN
ejpam-1599	291	5	a	a	PRON
ejpam-1599	291	6	,	,	PUNCT
ejpam-1599	291	7	we	we	PRON
ejpam-1599	291	8	denote	denote	VERB
ejpam-1599	291	9	its	its	PRON
ejpam-1599	291	10	spectrum	spectrum	NOUN
ejpam-1599	291	11	by	by	ADP
ejpam-1599	291	12	σ(a	σ(a	PROPN
ejpam-1599	291	13	)	)	PUNCT
ejpam-1599	291	14	and	and	CCONJ
ejpam-1599	291	15	its	its	PRON
ejpam-1599	291	16	spectral	spectral	ADJ
ejpam-1599	291	17	radius	radius	NOUN
ejpam-1599	291	18	by	by	ADP
ejpam-1599	291	19	r(a	r(a	PROPN
ejpam-1599	291	20	)	)	PUNCT
ejpam-1599	291	21	.	.	PUNCT
ejpam-1599	292	1	recall	recall	VERB
ejpam-1599	292	2	that	that	SCONJ
ejpam-1599	292	3	in	in	ADP
ejpam-1599	292	4	a	a	DET
ejpam-1599	292	5	banach	banach	NOUN
ejpam-1599	292	6	algebra	algebra	NOUN
ejpam-1599	292	7	,	,	PUNCT
ejpam-1599	292	8	an	an	DET
ejpam-1599	292	9	element	element	NOUN
ejpam-1599	292	10	is	be	AUX
ejpam-1599	292	11	quasinilpotent	quasinilpotent	ADJ
ejpam-1599	292	12	if	if	SCONJ
ejpam-1599	292	13	its	its	PRON
ejpam-1599	292	14	spectrum	spectrum	NOUN
ejpam-1599	292	15	reduces	reduce	VERB
ejpam-1599	292	16	to	to	ADP
ejpam-1599	292	17	0	0	NUM
ejpam-1599	292	18	,	,	PUNCT
ejpam-1599	292	19	or	or	CCONJ
ejpam-1599	292	20	equivalently	equivalently	ADV
ejpam-1599	292	21	if	if	SCONJ
ejpam-1599	292	22	its	its	PRON
ejpam-1599	292	23	spectral	spectral	ADJ
ejpam-1599	292	24	radius	radius	NOUN
ejpam-1599	292	25	is	be	AUX
ejpam-1599	292	26	0	0	NUM
ejpam-1599	292	27	,	,	PUNCT
ejpam-1599	292	28	and	and	CCONJ
ejpam-1599	292	29	quasipolar	quasipolar	ADJ
ejpam-1599	292	30	if	if	SCONJ
ejpam-1599	292	31	0	0	NUM
ejpam-1599	292	32	an	an	DET
ejpam-1599	292	33	isolated	isolated	ADJ
ejpam-1599	292	34	point	point	NOUN
ejpam-1599	292	35	of	of	ADP
ejpam-1599	292	36	the	the	DET
ejpam-1599	292	37	spectrum	spectrum	NOUN
ejpam-1599	292	38	.	.	PUNCT
ejpam-1599	293	1	it	it	PRON
ejpam-1599	293	2	is	be	AUX
ejpam-1599	293	3	known	know	VERB
ejpam-1599	293	4	[	[	PUNCT
ejpam-1599	293	5	10	10	NUM
ejpam-1599	293	6	]	]	PUNCT
ejpam-1599	293	7	that	that	SCONJ
ejpam-1599	293	8	these	these	DET
ejpam-1599	293	9	notions	notion	NOUN
ejpam-1599	293	10	coincide	coincide	VERB
ejpam-1599	293	11	with	with	ADP
ejpam-1599	293	12	their	their	PRON
ejpam-1599	293	13	ring	ring	NOUN
ejpam-1599	293	14	counterpart	counterpart	NOUN
ejpam-1599	293	15	,	,	PUNCT
ejpam-1599	293	16	and	and	CCONJ
ejpam-1599	293	17	also	also	ADV
ejpam-1599	293	18	with	with	ADP
ejpam-1599	293	19	the	the	DET
ejpam-1599	293	20	quasi	quasi	ADJ
ejpam-1599	293	21	-	-	ADJ
ejpam-1599	293	22	quasi	quasi	ADJ
ejpam-1599	293	23	notion	notion	NOUN
ejpam-1599	293	24	(	(	PUNCT
ejpam-1599	293	25	for	for	ADP
ejpam-1599	293	26	instance	instance	NOUN
ejpam-1599	293	27	,	,	PUNCT
ejpam-1599	293	28	σ(a	σ(a	PROPN
ejpam-1599	293	29	)	)	PUNCT
ejpam-1599	294	1	=	=	PRON
ejpam-1599	294	2	{	{	PUNCT
ejpam-1599	294	3	0c	0c	NOUN
ejpam-1599	294	4	}	}	PUNCT
ejpam-1599	294	5	if	if	SCONJ
ejpam-1599	294	6	and	and	CCONJ
ejpam-1599	294	7	only	only	ADV
ejpam-1599	294	8	if	if	SCONJ
ejpam-1599	294	9	a	a	PRON
ejpam-1599	294	10	is	be	AUX
ejpam-1599	294	11	quasinilpotent	quasinilpotent	NOUN
ejpam-1599	294	12	in	in	ADP
ejpam-1599	294	13	the	the	DET
ejpam-1599	294	14	ring	ring	NOUN
ejpam-1599	294	15	sense	sense	NOUN
ejpam-1599	294	16	if	if	SCONJ
ejpam-1599	294	17	and	and	CCONJ
ejpam-1599	294	18	only	only	ADV
ejpam-1599	294	19	if	if	SCONJ
ejpam-1599	294	20	a	a	PRON
ejpam-1599	294	21	is	be	AUX
ejpam-1599	294	22	quasi	quasi	ADJ
ejpam-1599	294	23	-	-	NOUN
ejpam-1599	294	24	quasinilpotent	quasinilpotent	ADJ
ejpam-1599	294	25	in	in	ADP
ejpam-1599	294	26	the	the	DET
ejpam-1599	294	27	ring	ring	NOUN
ejpam-1599	294	28	sense	sense	NOUN
ejpam-1599	294	29	)	)	PUNCT
ejpam-1599	294	30	.	.	PUNCT
ejpam-1599	295	1	corollary	corollary	ADJ
ejpam-1599	295	2	4	4	NUM
ejpam-1599	295	3	.	.	PUNCT
ejpam-1599	295	4	let	let	VERB
ejpam-1599	295	5	a	a	DET
ejpam-1599	295	6	∈	∈	PROPN
ejpam-1599	295	7	a	a	PRON
ejpam-1599	295	8	.	.	PUNCT
ejpam-1599	296	1	if	if	SCONJ
ejpam-1599	296	2	0	0	NUM
ejpam-1599	296	3	is	be	AUX
ejpam-1599	296	4	an	an	DET
ejpam-1599	296	5	isolated	isolated	ADJ
ejpam-1599	296	6	point	point	NOUN
ejpam-1599	296	7	of	of	ADP
ejpam-1599	296	8	the	the	DET
ejpam-1599	296	9	spectrum	spectrum	NOUN
ejpam-1599	296	10	of	of	ADP
ejpam-1599	296	11	a	a	PRON
ejpam-1599	296	12	,	,	PUNCT
ejpam-1599	296	13	then	then	ADV
ejpam-1599	296	14	a	a	PRON
ejpam-1599	296	15	is	be	AUX
ejpam-1599	296	16	naturally	naturally	ADV
ejpam-1599	296	17	invertible	invertible	ADJ
ejpam-1599	296	18	.	.	PUNCT
ejpam-1599	297	1	proof	proof	NOUN
ejpam-1599	297	2	.	.	PUNCT
ejpam-1599	298	1	if	if	SCONJ
ejpam-1599	298	2	0	0	NUM
ejpam-1599	298	3	is	be	AUX
ejpam-1599	298	4	an	an	DET
ejpam-1599	298	5	isolated	isolated	ADJ
ejpam-1599	298	6	point	point	NOUN
ejpam-1599	298	7	of	of	ADP
ejpam-1599	298	8	the	the	DET
ejpam-1599	298	9	spectrum	spectrum	NOUN
ejpam-1599	298	10	of	of	ADP
ejpam-1599	298	11	a	a	PRON
ejpam-1599	298	12	,	,	PUNCT
ejpam-1599	298	13	then	then	ADV
ejpam-1599	298	14	a	a	PRON
ejpam-1599	298	15	is	be	AUX
ejpam-1599	298	16	quasi	quasi	ADJ
ejpam-1599	298	17	-	-	ADJ
ejpam-1599	298	18	quasipolar	quasipolar	ADJ
ejpam-1599	298	19	in	in	ADP
ejpam-1599	298	20	the	the	DET
ejpam-1599	298	21	banach	banach	NOUN
ejpam-1599	298	22	sense	sense	NOUN
ejpam-1599	298	23	,	,	PUNCT
ejpam-1599	298	24	hence	hence	ADV
ejpam-1599	298	25	it	it	PRON
ejpam-1599	298	26	is	be	AUX
ejpam-1599	298	27	quasi	quasi	ADJ
ejpam-1599	298	28	-	-	ADJ
ejpam-1599	298	29	quasipolar	quasipolar	ADJ
ejpam-1599	298	30	ring	ring	NOUN
ejpam-1599	298	31	sense	sense	NOUN
ejpam-1599	298	32	.	.	PUNCT
ejpam-1599	299	1	we	we	PRON
ejpam-1599	299	2	then	then	ADV
ejpam-1599	299	3	apply	apply	VERB
ejpam-1599	299	4	theorem	theorem	ADJ
ejpam-1599	299	5	8	8	NUM
ejpam-1599	299	6	.	.	PUNCT
ejpam-1599	300	1	we	we	PRON
ejpam-1599	300	2	now	now	ADV
ejpam-1599	300	3	investigate	investigate	VERB
ejpam-1599	300	4	the	the	DET
ejpam-1599	300	5	link	link	NOUN
ejpam-1599	300	6	between	between	ADP
ejpam-1599	300	7	σi(a	σi(a	PROPN
ejpam-1599	300	8	)	)	PUNCT
ejpam-1599	300	9	,	,	PUNCT
ejpam-1599	300	10	i	i	NOUN
ejpam-1599	300	11	=	=	NOUN
ejpam-1599	300	12	1,2	1,2	NUM
ejpam-1599	300	13	and	and	CCONJ
ejpam-1599	300	14	σ(a	σ(a	NUM
ejpam-1599	300	15	)	)	PUNCT
ejpam-1599	300	16	.	.	PUNCT
ejpam-1599	301	1	theorem	theorem	VERB
ejpam-1599	301	2	9	9	NUM
ejpam-1599	301	3	.	.	PUNCT
ejpam-1599	302	1	leta	leta	PROPN
ejpam-1599	302	2	be	be	AUX
ejpam-1599	302	3	a	a	DET
ejpam-1599	302	4	unital	unital	ADJ
ejpam-1599	302	5	banach	banach	NOUN
ejpam-1599	302	6	algebra	algebra	NOUN
ejpam-1599	302	7	,	,	PUNCT
ejpam-1599	302	8	a	a	DET
ejpam-1599	302	9	∈a	∈a	NOUN
ejpam-1599	302	10	.	.	PUNCT
ejpam-1599	303	1	then	then	ADV
ejpam-1599	303	2	1	1	X
ejpam-1599	303	3	.	.	PUNCT
ejpam-1599	304	1	σ(a	σ(a	NUM
ejpam-1599	304	2	)	)	PUNCT
ejpam-1599	305	1	=	=	PRON
ejpam-1599	305	2	{	{	PUNCT
ejpam-1599	305	3	0c	0c	NOUN
ejpam-1599	305	4	}	}	PUNCT
ejpam-1599	305	5	⇒	⇒	NOUN
ejpam-1599	305	6	σ1(a	σ1(a	PRON
ejpam-1599	305	7	)	)	PUNCT
ejpam-1599	305	8	=	=	PRON
ejpam-1599	305	9	{	{	PUNCT
ejpam-1599	305	10	0	0	NUM
ejpam-1599	305	11	}	}	PUNCT
ejpam-1599	305	12	.	.	PUNCT
ejpam-1599	306	1	2	2	X
ejpam-1599	306	2	.	.	X
ejpam-1599	306	3	σ2(a	σ2(a	NUM
ejpam-1599	306	4	)	)	PUNCT
ejpam-1599	306	5	=	=	PRON
ejpam-1599	306	6	{	{	PUNCT
ejpam-1599	306	7	0	0	NUM
ejpam-1599	306	8	}	}	PUNCT
ejpam-1599	306	9	⇒	⇒	NOUN
ejpam-1599	306	10	σ(a	σ(a	PROPN
ejpam-1599	306	11	)	)	PUNCT
ejpam-1599	306	12	is	be	AUX
ejpam-1599	306	13	connected	connect	VERB
ejpam-1599	306	14	and	and	CCONJ
ejpam-1599	306	15	contains	contain	VERB
ejpam-1599	306	16	0c	0c	NOUN
ejpam-1599	306	17	.	.	PUNCT
ejpam-1599	307	1	x.	x.	PROPN
ejpam-1599	307	2	mary	mary	PROPN
ejpam-1599	307	3	/	/	SYM
ejpam-1599	307	4	eur	eur	PROPN
ejpam-1599	307	5	.	.	PUNCT
ejpam-1599	308	1	j.	j.	PROPN
ejpam-1599	308	2	pure	pure	PROPN
ejpam-1599	308	3	appl	appl	PROPN
ejpam-1599	308	4	.	.	PROPN
ejpam-1599	308	5	math	math	PROPN
ejpam-1599	308	6	,	,	PUNCT
ejpam-1599	308	7	5	5	NUM
ejpam-1599	308	8	(	(	PUNCT
ejpam-1599	308	9	2012	2012	NUM
ejpam-1599	308	10	)	)	PUNCT
ejpam-1599	308	11	,	,	PUNCT
ejpam-1599	308	12	160	160	NUM
ejpam-1599	308	13	-	-	SYM
ejpam-1599	308	14	173	173	NUM
ejpam-1599	308	15	169	169	NUM
ejpam-1599	308	16	proof	proof	NOUN
ejpam-1599	308	17	.	.	PUNCT
ejpam-1599	309	1	1	1	X
ejpam-1599	309	2	.	.	X
ejpam-1599	310	1	if	if	SCONJ
ejpam-1599	310	2	the	the	DET
ejpam-1599	310	3	spectrum	spectrum	NOUN
ejpam-1599	310	4	of	of	ADP
ejpam-1599	310	5	a	a	DET
ejpam-1599	310	6	reduces	reduce	NOUN
ejpam-1599	310	7	to	to	ADP
ejpam-1599	310	8	0	0	NUM
ejpam-1599	310	9	,	,	PUNCT
ejpam-1599	310	10	the	the	DET
ejpam-1599	310	11	its	its	PRON
ejpam-1599	310	12	spectral	spectral	ADJ
ejpam-1599	310	13	radius	radius	NOUN
ejpam-1599	310	14	is	be	AUX
ejpam-1599	310	15	equal	equal	ADJ
ejpam-1599	310	16	to	to	ADP
ejpam-1599	310	17	0	0	NUM
ejpam-1599	310	18	.	.	PUNCT
ejpam-1599	311	1	let	let	VERB
ejpam-1599	311	2	e	e	X
ejpam-1599	311	3	∈	∈	PROPN
ejpam-1599	311	4	σ1(a	σ1(a	PROPN
ejpam-1599	311	5	)	)	PUNCT
ejpam-1599	311	6	.	.	PUNCT
ejpam-1599	312	1	then	then	ADV
ejpam-1599	312	2	e	e	X
ejpam-1599	312	3	=	=	SYM
ejpam-1599	312	4	aa−e	aa−e	NOUN
ejpam-1599	312	5	=	=	NOUN
ejpam-1599	312	6	a−ea	a−ea	NOUN
ejpam-1599	312	7	.	.	PUNCT
ejpam-1599	313	1	we	we	PRON
ejpam-1599	313	2	get	get	VERB
ejpam-1599	313	3	||e||	||e||	ADJ
ejpam-1599	313	4	1	1	NUM
ejpam-1599	313	5	n	n	NOUN
ejpam-1599	313	6	=	=	SYM
ejpam-1599	313	7	||en||	||en||	VERB
ejpam-1599	313	8	1	1	NUM
ejpam-1599	313	9	n	n	NOUN
ejpam-1599	313	10	=	=	PUNCT
ejpam-1599	313	11	||an(a−e)n||	||an(a−e)n||	VERB
ejpam-1599	313	12	1	1	NUM
ejpam-1599	313	13	n	n	NOUN
ejpam-1599	313	14	≤	≤	NUM
ejpam-1599	313	15	||an||	||an||	ADJ
ejpam-1599	313	16	1	1	NUM
ejpam-1599	313	17	n	n	NOUN
ejpam-1599	313	18	||(a−e)||	||(a−e)||	NUM
ejpam-1599	313	19	→	→	SYM
ejpam-1599	313	20	0	0	NUM
ejpam-1599	313	21	and	and	CCONJ
ejpam-1599	313	22	||e||=	||e||=	NOUN
ejpam-1599	313	23	0	0	NUM
ejpam-1599	313	24	.	.	PUNCT
ejpam-1599	314	1	2	2	NUM
ejpam-1599	314	2	.	.	X
ejpam-1599	314	3	if	if	SCONJ
ejpam-1599	314	4	a	a	PRON
ejpam-1599	314	5	is	be	AUX
ejpam-1599	314	6	invertible	invertible	ADJ
ejpam-1599	314	7	,	,	PUNCT
ejpam-1599	314	8	then	then	ADV
ejpam-1599	314	9	1	1	NUM
ejpam-1599	314	10	∈	∈	NOUN
ejpam-1599	314	11	σ2(a	σ2(a	NUM
ejpam-1599	314	12	)	)	PUNCT
ejpam-1599	314	13	.	.	PUNCT
ejpam-1599	315	1	hence	hence	ADV
ejpam-1599	315	2	assume	assume	VERB
ejpam-1599	315	3	σ(a	σ(a	PROPN
ejpam-1599	315	4	)	)	PUNCT
ejpam-1599	315	5	contains	contain	VERB
ejpam-1599	315	6	0	0	NUM
ejpam-1599	316	1	but	but	CCONJ
ejpam-1599	316	2	is	be	AUX
ejpam-1599	316	3	not	not	PART
ejpam-1599	316	4	connected	connect	VERB
ejpam-1599	316	5	.	.	PUNCT
ejpam-1599	317	1	then	then	ADV
ejpam-1599	317	2	σ(a	σ(a	PROPN
ejpam-1599	317	3	)	)	PUNCT
ejpam-1599	317	4	=	=	PUNCT
ejpam-1599	317	5	c0∪c1	c0∪c1	NOUN
ejpam-1599	317	6	with	with	ADP
ejpam-1599	317	7	0	0	NUM
ejpam-1599	317	8	∈	∈	PROPN
ejpam-1599	317	9	c0	c0	NOUN
ejpam-1599	317	10	and	and	CCONJ
ejpam-1599	317	11	c0	c0	PROPN
ejpam-1599	317	12	,	,	PUNCT
ejpam-1599	317	13	c1	c1	PROPN
ejpam-1599	317	14	disjoint	disjoint	NOUN
ejpam-1599	317	15	and	and	CCONJ
ejpam-1599	317	16	open	open	VERB
ejpam-1599	317	17	and	and	CCONJ
ejpam-1599	317	18	closed	close	VERB
ejpam-1599	317	19	in	in	ADP
ejpam-1599	317	20	σ(a	σ(a	PROPN
ejpam-1599	317	21	)	)	PUNCT
ejpam-1599	317	22	.	.	PUNCT
ejpam-1599	318	1	then	then	ADV
ejpam-1599	318	2	the	the	DET
ejpam-1599	318	3	holomorphic	holomorphic	ADJ
ejpam-1599	318	4	calculus	calculus	NOUN
ejpam-1599	318	5	for	for	ADP
ejpam-1599	318	6	f	f	PROPN
ejpam-1599	318	7	(	(	PUNCT
ejpam-1599	318	8	z	z	NOUN
ejpam-1599	318	9	)	)	PUNCT
ejpam-1599	318	10	=	=	SYM
ejpam-1599	318	11	1	1	NUM
ejpam-1599	318	12	z	z	NOUN
ejpam-1599	318	13	on	on	ADP
ejpam-1599	318	14	u	u	PRON
ejpam-1599	318	15	open	open	ADJ
ejpam-1599	318	16	set	set	NOUN
ejpam-1599	318	17	containing	contain	VERB
ejpam-1599	318	18	c1	c1	NOUN
ejpam-1599	318	19	and	and	CCONJ
ejpam-1599	318	20	0	0	NUM
ejpam-1599	318	21	outside	outside	ADP
ejpam-1599	318	22	u	u	NOUN
ejpam-1599	318	23	,	,	PUNCT
ejpam-1599	318	24	such	such	ADJ
ejpam-1599	318	25	that	that	SCONJ
ejpam-1599	318	26	u	u	PROPN
ejpam-1599	318	27	contains	contain	VERB
ejpam-1599	318	28	an	an	DET
ejpam-1599	318	29	open	open	ADJ
ejpam-1599	318	30	neighbourhood	neighbourhood	NOUN
ejpam-1599	318	31	of	of	ADP
ejpam-1599	318	32	c0	c0	PROPN
ejpam-1599	318	33	,	,	PUNCT
ejpam-1599	318	34	defines	define	VERB
ejpam-1599	318	35	an	an	DET
ejpam-1599	318	36	element	element	NOUN
ejpam-1599	318	37	x	x	X
ejpam-1599	319	1	=	=	SYM
ejpam-1599	319	2	f	f	X
ejpam-1599	319	3	(	(	PUNCT
ejpam-1599	319	4	a	a	NOUN
ejpam-1599	319	5	)	)	PUNCT
ejpam-1599	319	6	of	of	ADP
ejpam-1599	319	7	{	{	PUNCT
ejpam-1599	319	8	a}′′	a}′′	NUM
ejpam-1599	319	9	such	such	ADJ
ejpam-1599	319	10	that	that	DET
ejpam-1599	319	11	ax	ax	NOUN
ejpam-1599	319	12	=	=	X
ejpam-1599	319	13	xa	xa	PROPN
ejpam-1599	320	1	=	=	SYM
ejpam-1599	320	2	e	e	PROPN
ejpam-1599	320	3	is	be	AUX
ejpam-1599	320	4	idempotent	idempotent	ADJ
ejpam-1599	320	5	and	and	CCONJ
ejpam-1599	320	6	non	non	ADJ
ejpam-1599	320	7	zero	zero	NUM
ejpam-1599	320	8	,	,	PUNCT
ejpam-1599	320	9	and	and	CCONJ
ejpam-1599	320	10	σ2(a	σ2(a	NUM
ejpam-1599	320	11	)	)	PUNCT
ejpam-1599	320	12	does	do	AUX
ejpam-1599	320	13	not	not	PART
ejpam-1599	320	14	reduce	reduce	VERB
ejpam-1599	320	15	to	to	ADP
ejpam-1599	320	16	{	{	PUNCT
ejpam-1599	320	17	0	0	NUM
ejpam-1599	320	18	}	}	PUNCT
ejpam-1599	320	19	.	.	PUNCT
ejpam-1599	321	1	now	now	ADV
ejpam-1599	321	2	,	,	PUNCT
ejpam-1599	321	3	we	we	PRON
ejpam-1599	321	4	consider	consider	VERB
ejpam-1599	321	5	three	three	NUM
ejpam-1599	321	6	different	different	ADJ
ejpam-1599	321	7	(	(	PUNCT
ejpam-1599	321	8	commutative	commutative	ADJ
ejpam-1599	321	9	)	)	PUNCT
ejpam-1599	321	10	banach	banach	NOUN
ejpam-1599	321	11	algebras	algebra	VERB
ejpam-1599	321	12	to	to	PART
ejpam-1599	321	13	show	show	VERB
ejpam-1599	321	14	that	that	SCONJ
ejpam-1599	321	15	we	we	PRON
ejpam-1599	321	16	can	can	AUX
ejpam-1599	321	17	not	not	PART
ejpam-1599	321	18	do	do	VERB
ejpam-1599	321	19	better	well	ADV
ejpam-1599	321	20	in	in	ADP
ejpam-1599	321	21	the	the	DET
ejpam-1599	321	22	theorem	theorem	NOUN
ejpam-1599	321	23	,	,	PUNCT
ejpam-1599	321	24	nor	nor	CCONJ
ejpam-1599	321	25	define	define	VERB
ejpam-1599	321	26	natural	natural	ADJ
ejpam-1599	321	27	invertibility	invertibility	NOUN
ejpam-1599	321	28	in	in	ADP
ejpam-1599	321	29	terms	term	NOUN
ejpam-1599	321	30	of	of	ADP
ejpam-1599	321	31	the	the	DET
ejpam-1599	321	32	spectrum	spectrum	NOUN
ejpam-1599	321	33	.	.	PUNCT
ejpam-1599	322	1	•	•	NUM
ejpam-1599	322	2	consider	consider	VERB
ejpam-1599	322	3	the	the	DET
ejpam-1599	322	4	banach	banach	NOUN
ejpam-1599	322	5	algebra	algebra	NOUN
ejpam-1599	322	6	a	a	DET
ejpam-1599	322	7	=	=	SYM
ejpam-1599	322	8	c0([0,1	c0([0,1	NOUN
ejpam-1599	322	9	]	]	PUNCT
ejpam-1599	322	10	)	)	PUNCT
ejpam-1599	322	11	of	of	ADP
ejpam-1599	322	12	continuous	continuous	ADJ
ejpam-1599	322	13	functions	function	NOUN
ejpam-1599	322	14	on	on	ADP
ejpam-1599	322	15	[	[	X
ejpam-1599	322	16	0,1	0,1	NUM
ejpam-1599	322	17	]	]	PUNCT
ejpam-1599	322	18	,	,	PUNCT
ejpam-1599	322	19	and	and	CCONJ
ejpam-1599	322	20	let	let	VERB
ejpam-1599	322	21	a(t	a(t	VERB
ejpam-1599	322	22	)	)	PUNCT
ejpam-1599	323	1	=	=	SYM
ejpam-1599	324	1	t.	t.	NOUN
ejpam-1599	324	2	then	then	ADV
ejpam-1599	324	3	σ(a	σ(a	PROPN
ejpam-1599	324	4	)	)	PUNCT
ejpam-1599	324	5	=	=	PUNCT
ejpam-1599	325	1	[	[	X
ejpam-1599	325	2	0,1	0,1	NUM
ejpam-1599	325	3	]	]	PUNCT
ejpam-1599	325	4	and	and	CCONJ
ejpam-1599	325	5	σ(a	σ(a	PROPN
ejpam-1599	325	6	)	)	PUNCT
ejpam-1599	325	7	=	=	PRON
ejpam-1599	325	8	{	{	PUNCT
ejpam-1599	325	9	0	0	NUM
ejpam-1599	325	10	}	}	PUNCT
ejpam-1599	325	11	.	.	PUNCT
ejpam-1599	326	1	a	a	PRON
ejpam-1599	326	2	is	be	AUX
ejpam-1599	326	3	naturally	naturally	ADV
ejpam-1599	326	4	invertible	invertible	ADJ
ejpam-1599	326	5	with	with	ADP
ejpam-1599	326	6	b	b	NOUN
ejpam-1599	326	7	=	=	SYM
ejpam-1599	326	8	0	0	PROPN
ejpam-1599	326	9	.	.	NOUN
ejpam-1599	326	10	•	•	NUM
ejpam-1599	326	11	consider	consider	VERB
ejpam-1599	326	12	the	the	DET
ejpam-1599	326	13	banach	banach	NOUN
ejpam-1599	326	14	algebraa	algebraa	NOUN
ejpam-1599	326	15	=	=	PUNCT
ejpam-1599	327	1	c0([0,1]∪	c0([0,1]∪	NOUN
ejpam-1599	328	1	[	[	X
ejpam-1599	328	2	2,3	2,3	NUM
ejpam-1599	328	3	]	]	PUNCT
ejpam-1599	328	4	)	)	PUNCT
ejpam-1599	328	5	of	of	ADP
ejpam-1599	328	6	continuous	continuous	ADJ
ejpam-1599	328	7	functions	function	NOUN
ejpam-1599	328	8	on	on	ADP
ejpam-1599	328	9	[	[	PUNCT
ejpam-1599	328	10	0,1]∪	0,1]∪	NOUN
ejpam-1599	329	1	[	[	X
ejpam-1599	329	2	2,3	2,3	NUM
ejpam-1599	329	3	]	]	PUNCT
ejpam-1599	329	4	,	,	PUNCT
ejpam-1599	329	5	and	and	CCONJ
ejpam-1599	329	6	let	let	VERB
ejpam-1599	329	7	a(t	a(t	VERB
ejpam-1599	329	8	)	)	PUNCT
ejpam-1599	330	1	=	=	SYM
ejpam-1599	330	2	t	t	PROPN
ejpam-1599	330	3	,	,	PUNCT
ejpam-1599	330	4	0	0	NUM
ejpam-1599	330	5	≤	≤	NUM
ejpam-1599	330	6	t	t	NOUN
ejpam-1599	330	7	≤	≤	NUM
ejpam-1599	330	8	1	1	NUM
ejpam-1599	330	9	and	and	CCONJ
ejpam-1599	330	10	a(t	a(t	VERB
ejpam-1599	330	11	)	)	PUNCT
ejpam-1599	331	1	=	=	SYM
ejpam-1599	331	2	t	t	PROPN
ejpam-1599	332	1	−	−	NUM
ejpam-1599	332	2	1,2≤	1,2≤	PROPN
ejpam-1599	332	3	t	t	PROPN
ejpam-1599	332	4	≤	≤	NUM
ejpam-1599	332	5	3	3	NUM
ejpam-1599	332	6	.	.	PUNCT
ejpam-1599	333	1	then	then	ADV
ejpam-1599	333	2	σ(a	σ(a	PROPN
ejpam-1599	333	3	)	)	PUNCT
ejpam-1599	333	4	=	=	PUNCT
ejpam-1599	334	1	[	[	X
ejpam-1599	334	2	0,2	0,2	NUM
ejpam-1599	334	3	]	]	PUNCT
ejpam-1599	334	4	and	and	CCONJ
ejpam-1599	334	5	σ(a	σ(a	PROPN
ejpam-1599	334	6	)	)	PUNCT
ejpam-1599	334	7	=	=	PRON
ejpam-1599	334	8	{	{	PUNCT
ejpam-1599	334	9	1[2,3	1[2,3	NOUN
ejpam-1599	334	10	]	]	X
ejpam-1599	334	11	}	}	PUNCT
ejpam-1599	334	12	.	.	PUNCT
ejpam-1599	335	1	a	a	PRON
ejpam-1599	335	2	is	be	AUX
ejpam-1599	335	3	naturally	naturally	ADV
ejpam-1599	335	4	invertible	invertible	ADJ
ejpam-1599	335	5	with	with	ADP
ejpam-1599	335	6	b(t	b(t	NOUN
ejpam-1599	335	7	)	)	PUNCT
ejpam-1599	336	1	=	=	SYM
ejpam-1599	336	2	0,0≤	0,0≤	NUM
ejpam-1599	336	3	t	t	X
ejpam-1599	336	4	≤	≤	NUM
ejpam-1599	336	5	1	1	NUM
ejpam-1599	336	6	and	and	CCONJ
ejpam-1599	336	7	b(t	b(t	VERB
ejpam-1599	336	8	)	)	PUNCT
ejpam-1599	336	9	=	=	SYM
ejpam-1599	337	1	1	1	NUM
ejpam-1599	337	2	t−1	t−1	NOUN
ejpam-1599	337	3	,	,	PUNCT
ejpam-1599	337	4	2≤	2≤	NUM
ejpam-1599	337	5	t	t	NOUN
ejpam-1599	337	6	≤	≤	ADJ
ejpam-1599	337	7	3	3	NUM
ejpam-1599	337	8	.	.	NOUN
ejpam-1599	337	9	•	•	NUM
ejpam-1599	337	10	consider	consider	VERB
ejpam-1599	337	11	now	now	ADV
ejpam-1599	337	12	the	the	DET
ejpam-1599	337	13	banach	banach	NOUN
ejpam-1599	337	14	algebra	algebra	NOUN
ejpam-1599	337	15	a	a	DET
ejpam-1599	337	16	=	=	NOUN
ejpam-1599	337	17	l∞([0,1	l∞([0,1	NOUN
ejpam-1599	337	18	]	]	X
ejpam-1599	337	19	)	)	PUNCT
ejpam-1599	337	20	of	of	ADP
ejpam-1599	337	21	essentially	essentially	ADV
ejpam-1599	337	22	bounded	bound	VERB
ejpam-1599	337	23	measurable	measurable	ADJ
ejpam-1599	337	24	functions	function	NOUN
ejpam-1599	337	25	on	on	ADP
ejpam-1599	337	26	[	[	X
ejpam-1599	337	27	0,1	0,1	NUM
ejpam-1599	337	28	]	]	PUNCT
ejpam-1599	337	29	,	,	PUNCT
ejpam-1599	337	30	and	and	CCONJ
ejpam-1599	337	31	let	let	VERB
ejpam-1599	337	32	a(t	a(t	VERB
ejpam-1599	337	33	)	)	PUNCT
ejpam-1599	338	1	=	=	SYM
ejpam-1599	339	1	t.	t.	NOUN
ejpam-1599	339	2	then	then	ADV
ejpam-1599	339	3	σ(a	σ(a	PROPN
ejpam-1599	339	4	)	)	PUNCT
ejpam-1599	339	5	=	=	PUNCT
ejpam-1599	340	1	[	[	X
ejpam-1599	340	2	0,1	0,1	NUM
ejpam-1599	340	3	]	]	PUNCT
ejpam-1599	340	4	and	and	CCONJ
ejpam-1599	340	5	σ(a	σ(a	PROPN
ejpam-1599	340	6	)	)	PUNCT
ejpam-1599	340	7	=	=	PRON
ejpam-1599	340	8	{	{	PUNCT
ejpam-1599	340	9	1a	1a	NOUN
ejpam-1599	340	10	,	,	PUNCT
ejpam-1599	340	11	∃0	∃0	NOUN
ejpam-1599	340	12	<	<	X
ejpam-1599	340	13	c	c	X
ejpam-1599	340	14	≤	≤	NOUN
ejpam-1599	340	15	1,λ(a	1,λ(a	NUM
ejpam-1599	340	16	∩	∩	NOUN
ejpam-1599	340	17	[	[	X
ejpam-1599	340	18	0	0	NUM
ejpam-1599	340	19	,	,	PUNCT
ejpam-1599	340	20	c	c	NOUN
ejpam-1599	340	21	]	]	X
ejpam-1599	340	22	)	)	PUNCT
ejpam-1599	340	23	=	=	PUNCT
ejpam-1599	340	24	0	0	NUM
ejpam-1599	340	25	}	}	PUNCT
ejpam-1599	340	26	.	.	PUNCT
ejpam-1599	341	1	this	this	DET
ejpam-1599	341	2	set	set	NOUN
ejpam-1599	341	3	admits	admit	VERB
ejpam-1599	341	4	no	no	DET
ejpam-1599	341	5	maximal	maximal	ADJ
ejpam-1599	341	6	element	element	NOUN
ejpam-1599	341	7	,	,	PUNCT
ejpam-1599	341	8	hence	hence	ADV
ejpam-1599	341	9	a(t	a(t	VERB
ejpam-1599	341	10	)	)	PUNCT
ejpam-1599	342	1	=	=	SYM
ejpam-1599	342	2	t	t	NOUN
ejpam-1599	342	3	is	be	AUX
ejpam-1599	342	4	not	not	PART
ejpam-1599	342	5	naturally	naturally	ADV
ejpam-1599	342	6	invertible	invertible	ADJ
ejpam-1599	342	7	.	.	PUNCT
ejpam-1599	343	1	it	it	PRON
ejpam-1599	343	2	appears	appear	VERB
ejpam-1599	343	3	that	that	SCONJ
ejpam-1599	343	4	natural	natural	ADJ
ejpam-1599	343	5	invertibility	invertibility	NOUN
ejpam-1599	343	6	is	be	AUX
ejpam-1599	343	7	strongly	strongly	ADV
ejpam-1599	343	8	linked	link	VERB
ejpam-1599	343	9	with	with	ADP
ejpam-1599	343	10	the	the	DET
ejpam-1599	343	11	nature	nature	NOUN
ejpam-1599	343	12	of	of	ADP
ejpam-1599	343	13	the	the	DET
ejpam-1599	343	14	structure	structure	NOUN
ejpam-1599	343	15	space	space	NOUN
ejpam-1599	343	16	(	(	PUNCT
ejpam-1599	343	17	or	or	CCONJ
ejpam-1599	343	18	spectrum	spectrum	NOUN
ejpam-1599	343	19	)	)	PUNCT
ejpam-1599	343	20	of	of	ADP
ejpam-1599	343	21	the	the	DET
ejpam-1599	343	22	whole	whole	ADJ
ejpam-1599	343	23	commutative	commutative	ADJ
ejpam-1599	343	24	banach	banach	NOUN
ejpam-1599	343	25	algebrab	algebrab	NOUN
ejpam-1599	343	26	=	=	PUNCT
ejpam-1599	343	27	{	{	PUNCT
ejpam-1599	343	28	a}′′	a}′′	NUM
ejpam-1599	343	29	,	,	PUNCT
ejpam-1599	343	30	independently	independently	ADV
ejpam-1599	343	31	of	of	ADP
ejpam-1599	343	32	the	the	DET
ejpam-1599	343	33	nature	nature	NOUN
ejpam-1599	343	34	of	of	ADP
ejpam-1599	343	35	the	the	DET
ejpam-1599	343	36	spectrum	spectrum	NOUN
ejpam-1599	343	37	of	of	ADP
ejpam-1599	343	38	the	the	DET
ejpam-1599	343	39	element	element	NOUN
ejpam-1599	343	40	a.	a.	NOUN
ejpam-1599	343	41	obviously	obviously	ADV
ejpam-1599	343	42	,	,	PUNCT
ejpam-1599	343	43	if	if	SCONJ
ejpam-1599	343	44	the	the	DET
ejpam-1599	343	45	spectrum	spectrum	NOUN
ejpam-1599	343	46	of	of	ADP
ejpam-1599	343	47	{	{	PUNCT
ejpam-1599	343	48	a}′′	a}′′	PROPN
ejpam-1599	343	49	is	be	AUX
ejpam-1599	343	50	not	not	PART
ejpam-1599	343	51	connected	connect	VERB
ejpam-1599	343	52	,	,	PUNCT
ejpam-1599	343	53	then	then	ADV
ejpam-1599	343	54	shilov	shilov	VERB
ejpam-1599	343	55	’s	’s	PART
ejpam-1599	343	56	idempotent	idempotent	NOUN
ejpam-1599	343	57	theorem	theorem	NOUN
ejpam-1599	343	58	gives	give	VERB
ejpam-1599	343	59	the	the	DET
ejpam-1599	343	60	existence	existence	NOUN
ejpam-1599	343	61	of	of	ADP
ejpam-1599	343	62	a	a	DET
ejpam-1599	343	63	nontrivial	nontrivial	ADJ
ejpam-1599	343	64	idempotent	idempotent	NOUN
ejpam-1599	343	65	.	.	PUNCT
ejpam-1599	344	1	this	this	DET
ejpam-1599	344	2	idempotent	idempotent	NOUN
ejpam-1599	344	3	needs	need	VERB
ejpam-1599	344	4	not	not	PART
ejpam-1599	344	5	to	to	PART
ejpam-1599	344	6	be	be	AUX
ejpam-1599	344	7	in	in	ADP
ejpam-1599	344	8	σ(a	σ(a	PROPN
ejpam-1599	344	9	)	)	PUNCT
ejpam-1599	344	10	.	.	PUNCT
ejpam-1599	345	1	next	next	ADJ
ejpam-1599	345	2	theorem	theorem	NOUN
ejpam-1599	345	3	uses	use	VERB
ejpam-1599	345	4	the	the	DET
ejpam-1599	345	5	generalized	generalized	ADJ
ejpam-1599	345	6	spectral	spectral	ADJ
ejpam-1599	345	7	theory	theory	NOUN
ejpam-1599	345	8	of	of	ADP
ejpam-1599	345	9	hile	hile	NOUN
ejpam-1599	345	10	and	and	CCONJ
ejpam-1599	345	11	pfaffenberger	pfaffenberger	ADV
ejpam-1599	345	12	[	[	X
ejpam-1599	345	13	14	14	NUM
ejpam-1599	345	14	,	,	PUNCT
ejpam-1599	345	15	15	15	NUM
ejpam-1599	345	16	]	]	PUNCT
ejpam-1599	345	17	and	and	CCONJ
ejpam-1599	345	18	the	the	DET
ejpam-1599	345	19	associated	associated	ADJ
ejpam-1599	345	20	functional	functional	ADJ
ejpam-1599	345	21	calculus	calculus	NOUN
ejpam-1599	345	22	to	to	PART
ejpam-1599	345	23	construct	construct	VERB
ejpam-1599	345	24	elements	element	NOUN
ejpam-1599	345	25	in	in	ADP
ejpam-1599	345	26	σ	σ	PROPN
ejpam-1599	345	27	j(a	j(a	PROPN
ejpam-1599	345	28	)	)	PUNCT
ejpam-1599	345	29	,	,	PUNCT
ejpam-1599	345	30	j	j	PROPN
ejpam-1599	345	31	=	=	SYM
ejpam-1599	345	32	1,2	1,2	NUM
ejpam-1599	345	33	.	.	PUNCT
ejpam-1599	346	1	the	the	DET
ejpam-1599	346	2	construction	construction	NOUN
ejpam-1599	346	3	is	be	AUX
ejpam-1599	346	4	similar	similar	ADJ
ejpam-1599	346	5	to	to	ADP
ejpam-1599	346	6	the	the	DET
ejpam-1599	346	7	case	case	NOUN
ejpam-1599	346	8	of	of	ADP
ejpam-1599	346	9	a	a	DET
ejpam-1599	346	10	disconnected	disconnected	ADJ
ejpam-1599	346	11	spectrum	spectrum	NOUN
ejpam-1599	346	12	,	,	PUNCT
ejpam-1599	346	13	but	but	CCONJ
ejpam-1599	346	14	instead	instead	ADV
ejpam-1599	346	15	of	of	ADP
ejpam-1599	346	16	using	use	VERB
ejpam-1599	346	17	σ(a	σ(a	PROPN
ejpam-1599	346	18	)	)	PUNCT
ejpam-1599	346	19	(	(	PUNCT
ejpam-1599	346	20	that	that	PRON
ejpam-1599	346	21	can	can	AUX
ejpam-1599	346	22	be	be	AUX
ejpam-1599	346	23	connected	connect	VERB
ejpam-1599	346	24	)	)	PUNCT
ejpam-1599	346	25	,	,	PUNCT
ejpam-1599	346	26	we	we	PRON
ejpam-1599	346	27	use	use	VERB
ejpam-1599	346	28	the	the	DET
ejpam-1599	346	29	generalized	generalized	ADJ
ejpam-1599	346	30	spectrum	spectrum	NOUN
ejpam-1599	346	31	of	of	ADP
ejpam-1599	346	32	hile	hile	NOUN
ejpam-1599	346	33	and	and	CCONJ
ejpam-1599	346	34	pfaffenberger	pfaffenberger	ADV
ejpam-1599	346	35	.	.	PUNCT
ejpam-1599	347	1	if	if	SCONJ
ejpam-1599	347	2	a	a	PRON
ejpam-1599	347	3	,	,	PUNCT
ejpam-1599	347	4	q	q	NOUN
ejpam-1599	347	5	∈	∈	PROPN
ejpam-1599	347	6	a	a	PRON
ejpam-1599	347	7	,	,	PUNCT
ejpam-1599	347	8	then	then	ADV
ejpam-1599	347	9	the	the	DET
ejpam-1599	347	10	spectrum	spectrum	NOUN
ejpam-1599	347	11	of	of	ADP
ejpam-1599	347	12	a	a	DET
ejpam-1599	347	13	relative	relative	NOUN
ejpam-1599	347	14	to	to	ADP
ejpam-1599	347	15	q	q	NOUN
ejpam-1599	347	16	,	,	PUNCT
ejpam-1599	347	17	or	or	CCONJ
ejpam-1599	347	18	q−spectrum	q−spectrum	PRON
ejpam-1599	347	19	of	of	ADP
ejpam-1599	347	20	a	a	DET
ejpam-1599	347	21	σq(a	σq(a	NOUN
ejpam-1599	347	22	)	)	PUNCT
ejpam-1599	347	23	,	,	PUNCT
ejpam-1599	347	24	is	be	AUX
ejpam-1599	347	25	the	the	DET
ejpam-1599	347	26	set	set	NOUN
ejpam-1599	347	27	of	of	ADP
ejpam-1599	347	28	points	point	NOUN
ejpam-1599	347	29	z	z	NOUN
ejpam-1599	347	30	such	such	ADJ
ejpam-1599	347	31	that	that	SCONJ
ejpam-1599	347	32	a−	a−	PROPN
ejpam-1599	347	33	z.1−	z.1−	NOUN
ejpam-1599	347	34	z̄q	z̄q	PROPN
ejpam-1599	347	35	is	be	AUX
ejpam-1599	347	36	not	not	PART
ejpam-1599	347	37	invertible	invertible	ADJ
ejpam-1599	347	38	in	in	ADP
ejpam-1599	347	39	a.	a.	NOUN
ejpam-1599	347	40	theorem	theorem	NOUN
ejpam-1599	347	41	10	10	NUM
ejpam-1599	347	42	.	.	PUNCT
ejpam-1599	348	1	let	let	VERB
ejpam-1599	348	2	a	a	DET
ejpam-1599	348	3	,	,	PUNCT
ejpam-1599	348	4	q	q	NOUN
ejpam-1599	348	5	∈	∈	PROPN
ejpam-1599	348	6	a	a	PRON
ejpam-1599	348	7	,	,	PUNCT
ejpam-1599	348	8	with	with	ADP
ejpam-1599	348	9	σ(a	σ(a	PROPN
ejpam-1599	348	10	)	)	PUNCT
ejpam-1599	348	11	connected	connect	VERB
ejpam-1599	348	12	set	set	NOUN
ejpam-1599	348	13	that	that	PRON
ejpam-1599	348	14	contains	contain	VERB
ejpam-1599	348	15	0	0	PROPN
ejpam-1599	348	16	.	.	PUNCT
ejpam-1599	349	1	assume	assume	VERB
ejpam-1599	349	2	σ(q	σ(q	PROPN
ejpam-1599	349	3	)	)	PUNCT
ejpam-1599	350	1	∩	∩	NOUN
ejpam-1599	350	2	t	t	NOUN
ejpam-1599	350	3	=	=	PUNCT
ejpam-1599	350	4	;	;	PUNCT
ejpam-1599	350	5	,	,	PUNCT
ejpam-1599	350	6	where	where	SCONJ
ejpam-1599	350	7	t	t	PROPN
ejpam-1599	350	8	is	be	AUX
ejpam-1599	350	9	the	the	DET
ejpam-1599	350	10	unit	unit	NOUN
ejpam-1599	350	11	circle	circle	NOUN
ejpam-1599	350	12	,	,	PUNCT
ejpam-1599	350	13	and	and	CCONJ
ejpam-1599	350	14	σq(a	σq(a	NOUN
ejpam-1599	350	15	)	)	PUNCT
ejpam-1599	350	16	is	be	AUX
ejpam-1599	350	17	not	not	PART
ejpam-1599	350	18	connected	connect	VERB
ejpam-1599	350	19	.	.	PUNCT
ejpam-1599	351	1	then	then	ADV
ejpam-1599	351	2	x.	x.	PROPN
ejpam-1599	351	3	mary	mary	PROPN
ejpam-1599	351	4	/	/	SYM
ejpam-1599	351	5	eur	eur	PROPN
ejpam-1599	351	6	.	.	PUNCT
ejpam-1599	352	1	j.	j.	PROPN
ejpam-1599	352	2	pure	pure	PROPN
ejpam-1599	352	3	appl	appl	PROPN
ejpam-1599	352	4	.	.	PROPN
ejpam-1599	352	5	math	math	PROPN
ejpam-1599	352	6	,	,	PUNCT
ejpam-1599	352	7	5	5	NUM
ejpam-1599	352	8	(	(	PUNCT
ejpam-1599	352	9	2012	2012	NUM
ejpam-1599	352	10	)	)	PUNCT
ejpam-1599	352	11	,	,	PUNCT
ejpam-1599	352	12	160	160	NUM
ejpam-1599	352	13	-	-	SYM
ejpam-1599	352	14	173	173	NUM
ejpam-1599	352	15	170	170	NUM
ejpam-1599	352	16	1	1	NUM
ejpam-1599	352	17	.	.	PUNCT
ejpam-1599	353	1	if	if	SCONJ
ejpam-1599	353	2	q	q	PROPN
ejpam-1599	353	3	∈	∈	PROPN
ejpam-1599	353	4	{	{	PUNCT
ejpam-1599	353	5	a}′	a}′	NOUN
ejpam-1599	353	6	,	,	PUNCT
ejpam-1599	353	7	σ1(a	σ1(a	PRON
ejpam-1599	353	8	)	)	PUNCT
ejpam-1599	353	9	is	be	AUX
ejpam-1599	353	10	not	not	PART
ejpam-1599	353	11	empty	empty	ADJ
ejpam-1599	353	12	;	;	PUNCT
ejpam-1599	353	13	2	2	X
ejpam-1599	353	14	.	.	X
ejpam-1599	353	15	if	if	SCONJ
ejpam-1599	353	16	q	q	X
ejpam-1599	353	17	∈	∈	PROPN
ejpam-1599	353	18	{	{	PUNCT
ejpam-1599	353	19	a}′′	a}′′	NUM
ejpam-1599	353	20	,	,	PUNCT
ejpam-1599	353	21	σ2(a	σ2(a	NUM
ejpam-1599	353	22	)	)	PUNCT
ejpam-1599	353	23	is	be	AUX
ejpam-1599	353	24	not	not	PART
ejpam-1599	353	25	empty	empty	ADJ
ejpam-1599	353	26	.	.	PUNCT
ejpam-1599	354	1	proof	proof	NOUN
ejpam-1599	354	2	.	.	PUNCT
ejpam-1599	355	1	this	this	PRON
ejpam-1599	355	2	is	be	AUX
ejpam-1599	355	3	a	a	DET
ejpam-1599	355	4	consequence	consequence	NOUN
ejpam-1599	355	5	of	of	ADP
ejpam-1599	355	6	theorem	theorem	NOUN
ejpam-1599	355	7	12	12	NUM
ejpam-1599	355	8	in	in	ADP
ejpam-1599	355	9	[	[	X
ejpam-1599	355	10	14	14	NUM
ejpam-1599	355	11	]	]	PUNCT
ejpam-1599	355	12	.	.	PUNCT
ejpam-1599	356	1	indeed	indeed	ADV
ejpam-1599	356	2	,	,	PUNCT
ejpam-1599	356	3	since	since	SCONJ
ejpam-1599	356	4	a	a	PRON
ejpam-1599	356	5	is	be	AUX
ejpam-1599	356	6	not	not	PART
ejpam-1599	356	7	invertible	invertible	ADJ
ejpam-1599	356	8	,	,	PUNCT
ejpam-1599	356	9	0	0	NUM
ejpam-1599	356	10	is	be	AUX
ejpam-1599	356	11	in	in	ADP
ejpam-1599	356	12	the	the	DET
ejpam-1599	356	13	q	q	NOUN
ejpam-1599	356	14	spectrum	spectrum	NOUN
ejpam-1599	356	15	of	of	ADP
ejpam-1599	356	16	a.	a.	NOUN
ejpam-1599	356	17	since	since	SCONJ
ejpam-1599	356	18	σq(a	σq(a	NOUN
ejpam-1599	356	19	)	)	PUNCT
ejpam-1599	356	20	is	be	AUX
ejpam-1599	356	21	not	not	PART
ejpam-1599	356	22	connected	connect	VERB
ejpam-1599	356	23	,	,	PUNCT
ejpam-1599	356	24	we	we	PRON
ejpam-1599	356	25	can	can	AUX
ejpam-1599	356	26	find	find	VERB
ejpam-1599	356	27	a	a	DET
ejpam-1599	356	28	closed	closed	ADJ
ejpam-1599	356	29	rectifiable	rectifiable	ADJ
ejpam-1599	356	30	curve	curve	NOUN
ejpam-1599	356	31	γ	γ	NOUN
ejpam-1599	356	32	in	in	ADP
ejpam-1599	356	33	the	the	DET
ejpam-1599	356	34	q	q	X
ejpam-1599	356	35	resolvent	resolvent	NOUN
ejpam-1599	356	36	such	such	ADJ
ejpam-1599	356	37	that	that	SCONJ
ejpam-1599	356	38	0	0	NUM
ejpam-1599	356	39	is	be	AUX
ejpam-1599	356	40	in	in	ADP
ejpam-1599	356	41	its	its	PRON
ejpam-1599	356	42	exterior	exterior	NOUN
ejpam-1599	356	43	and	and	CCONJ
ejpam-1599	356	44	its	its	PRON
ejpam-1599	356	45	interior	interior	NOUN
ejpam-1599	356	46	contains	contain	VERB
ejpam-1599	356	47	elements	element	NOUN
ejpam-1599	356	48	of	of	ADP
ejpam-1599	356	49	σq(a	σq(a	NOUN
ejpam-1599	356	50	)	)	PUNCT
ejpam-1599	356	51	(	(	PUNCT
ejpam-1599	356	52	a	a	DET
ejpam-1599	356	53	component	component	NOUN
ejpam-1599	356	54	of	of	ADP
ejpam-1599	356	55	σq(a	σq(a	NOUN
ejpam-1599	356	56	)	)	PUNCT
ejpam-1599	356	57	that	that	PRON
ejpam-1599	356	58	does	do	AUX
ejpam-1599	356	59	not	not	PART
ejpam-1599	356	60	contains	contain	VERB
ejpam-1599	356	61	0	0	NUM
ejpam-1599	356	62	)	)	PUNCT
ejpam-1599	356	63	.	.	PUNCT
ejpam-1599	357	1	choosing	choose	VERB
ejpam-1599	357	2	z	z	PROPN
ejpam-1599	357	3	=	=	SYM
ejpam-1599	357	4	0	0	NUM
ejpam-1599	357	5	in	in	ADP
ejpam-1599	357	6	equation	equation	NOUN
ejpam-1599	357	7	4.3	4.3	NUM
ejpam-1599	357	8	gives	give	VERB
ejpam-1599	357	9	an	an	DET
ejpam-1599	357	10	idempotent	idempotent	NOUN
ejpam-1599	357	11	p	p	X
ejpam-1599	357	12	≤r	≤r	PROPN
ejpam-1599	357	13	a.	a.	NOUN
ejpam-1599	357	14	the	the	DET
ejpam-1599	357	15	rest	rest	NOUN
ejpam-1599	357	16	follows	follow	VERB
ejpam-1599	357	17	from	from	ADP
ejpam-1599	357	18	commutation	commutation	NOUN
ejpam-1599	357	19	properties	property	NOUN
ejpam-1599	357	20	.	.	PUNCT
ejpam-1599	358	1	6	6	X
ejpam-1599	358	2	.	.	X
ejpam-1599	358	3	operators	operator	NOUN
ejpam-1599	358	4	finally	finally	ADV
ejpam-1599	358	5	,	,	PUNCT
ejpam-1599	358	6	we	we	PRON
ejpam-1599	358	7	apply	apply	VERB
ejpam-1599	358	8	the	the	DET
ejpam-1599	358	9	previous	previous	ADJ
ejpam-1599	358	10	results	result	NOUN
ejpam-1599	358	11	to	to	ADP
ejpam-1599	358	12	the	the	DET
ejpam-1599	358	13	operator	operator	NOUN
ejpam-1599	358	14	algebra	algebra	VERB
ejpam-1599	358	15	a	a	DET
ejpam-1599	358	16	=	=	X
ejpam-1599	358	17	b(x	b(x	NOUN
ejpam-1599	358	18	)	)	PUNCT
ejpam-1599	358	19	of	of	ADP
ejpam-1599	358	20	bounded	bounded	ADJ
ejpam-1599	358	21	operators	operator	NOUN
ejpam-1599	358	22	on	on	ADP
ejpam-1599	358	23	a	a	DET
ejpam-1599	358	24	banach	banach	NOUN
ejpam-1599	358	25	space	space	NOUN
ejpam-1599	358	26	x	x	X
ejpam-1599	358	27	.	.	PUNCT
ejpam-1599	359	1	6.1	6.1	NUM
ejpam-1599	359	2	.	.	PUNCT
ejpam-1599	360	1	local	local	ADJ
ejpam-1599	360	2	spectral	spectral	ADJ
ejpam-1599	360	3	theory	theory	NOUN
ejpam-1599	360	4	in	in	ADP
ejpam-1599	360	5	the	the	DET
ejpam-1599	360	6	operator	operator	NOUN
ejpam-1599	360	7	case	case	NOUN
ejpam-1599	360	8	,	,	PUNCT
ejpam-1599	360	9	we	we	PRON
ejpam-1599	360	10	can	can	AUX
ejpam-1599	360	11	improve	improve	VERB
ejpam-1599	360	12	somehow	somehow	ADV
ejpam-1599	360	13	the	the	DET
ejpam-1599	360	14	results	result	NOUN
ejpam-1599	360	15	of	of	ADP
ejpam-1599	360	16	the	the	DET
ejpam-1599	360	17	previous	previous	ADJ
ejpam-1599	360	18	section	section	NOUN
ejpam-1599	360	19	.	.	PUNCT
ejpam-1599	361	1	let	let	VERB
ejpam-1599	361	2	x	x	PRON
ejpam-1599	361	3	be	be	AUX
ejpam-1599	361	4	a	a	DET
ejpam-1599	361	5	banach	banach	NOUN
ejpam-1599	361	6	space	space	NOUN
ejpam-1599	361	7	and	and	CCONJ
ejpam-1599	361	8	t	t	NOUN
ejpam-1599	361	9	∈	∈	PROPN
ejpam-1599	361	10	b(x	b(x	PROPN
ejpam-1599	361	11	)	)	PUNCT
ejpam-1599	361	12	.	.	PUNCT
ejpam-1599	362	1	t	t	PROPN
ejpam-1599	362	2	(	(	PUNCT
ejpam-1599	362	3	x	x	PROPN
ejpam-1599	362	4	)	)	PUNCT
ejpam-1599	362	5	,	,	PUNCT
ejpam-1599	362	6	or	or	CCONJ
ejpam-1599	362	7	r(t	r(t	NOUN
ejpam-1599	362	8	)	)	PUNCT
ejpam-1599	362	9	denotes	denote	VERB
ejpam-1599	362	10	its	its	PRON
ejpam-1599	362	11	range	range	NOUN
ejpam-1599	362	12	,	,	PUNCT
ejpam-1599	362	13	n(t	n(t	PROPN
ejpam-1599	362	14	)	)	PUNCT
ejpam-1599	362	15	its	its	PRON
ejpam-1599	362	16	kernel	kernel	NOUN
ejpam-1599	362	17	.	.	PUNCT
ejpam-1599	363	1	we	we	PRON
ejpam-1599	363	2	use	use	VERB
ejpam-1599	363	3	ideas	idea	NOUN
ejpam-1599	363	4	from	from	ADP
ejpam-1599	363	5	local	local	ADJ
ejpam-1599	363	6	spectral	spectral	ADJ
ejpam-1599	363	7	theory	theory	NOUN
ejpam-1599	363	8	[	[	X
ejpam-1599	363	9	21	21	NUM
ejpam-1599	363	10	,	,	PUNCT
ejpam-1599	363	11	20	20	NUM
ejpam-1599	363	12	,	,	PUNCT
ejpam-1599	363	13	1	1	NUM
ejpam-1599	363	14	,	,	PUNCT
ejpam-1599	363	15	12	12	NUM
ejpam-1599	363	16	]	]	PUNCT
ejpam-1599	363	17	and	and	CCONJ
ejpam-1599	363	18	define	define	VERB
ejpam-1599	363	19	the	the	DET
ejpam-1599	363	20	following	follow	VERB
ejpam-1599	363	21	sets	set	NOUN
ejpam-1599	363	22	:	:	PUNCT
ejpam-1599	363	23	definition	definition	NOUN
ejpam-1599	363	24	6	6	NUM
ejpam-1599	363	25	.	.	NOUN
ejpam-1599	363	26	•	•	NUM
ejpam-1599	363	27	the	the	DET
ejpam-1599	363	28	hyperrange	hyperrange	NOUN
ejpam-1599	363	29	of	of	ADP
ejpam-1599	363	30	t	t	PROPN
ejpam-1599	363	31	is	be	AUX
ejpam-1599	363	32	the	the	DET
ejpam-1599	363	33	linear	linear	ADJ
ejpam-1599	363	34	space	space	NOUN
ejpam-1599	363	35	t∞(x	t∞(x	NOUN
ejpam-1599	363	36	)	)	PUNCT
ejpam-1599	364	1	=	=	SYM
ejpam-1599	365	1	⋂	⋂	PROPN
ejpam-1599	365	2	n∈n	n∈n	NOUN
ejpam-1599	365	3	t	t	NOUN
ejpam-1599	365	4	n(x	n(x	PROPN
ejpam-1599	365	5	)	)	PUNCT
ejpam-1599	365	6	;	;	PUNCT
ejpam-1599	365	7	•	•	NUM
ejpam-1599	365	8	the	the	DET
ejpam-1599	365	9	hyperkernel	hyperkernel	NOUN
ejpam-1599	365	10	of	of	ADP
ejpam-1599	365	11	t	t	PROPN
ejpam-1599	365	12	is	be	AUX
ejpam-1599	365	13	the	the	DET
ejpam-1599	365	14	linear	linear	ADJ
ejpam-1599	365	15	space	space	NOUN
ejpam-1599	365	16	n∞(t	n∞(t	ADJ
ejpam-1599	365	17	)	)	PUNCT
ejpam-1599	366	1	=	=	PUNCT
ejpam-1599	366	2	⋃	⋃	NOUN
ejpam-1599	366	3	n∈n	n∈n	DET
ejpam-1599	366	4	n(t	n(t	PROPN
ejpam-1599	366	5	n	n	CCONJ
ejpam-1599	366	6	)	)	PUNCT
ejpam-1599	366	7	;	;	PUNCT
ejpam-1599	366	8	•	•	ADP
ejpam-1599	366	9	the	the	DET
ejpam-1599	366	10	quasinilpotent	quasinilpotent	NOUN
ejpam-1599	366	11	part	part	NOUN
ejpam-1599	366	12	(	(	PUNCT
ejpam-1599	366	13	or	or	CCONJ
ejpam-1599	366	14	transfinite	transfinite	ADJ
ejpam-1599	366	15	kernel	kernel	NOUN
ejpam-1599	366	16	)	)	PUNCT
ejpam-1599	366	17	of	of	ADP
ejpam-1599	366	18	t	t	PROPN
ejpam-1599	366	19	is	be	AUX
ejpam-1599	366	20	the	the	DET
ejpam-1599	366	21	linear	linear	ADJ
ejpam-1599	366	22	space	space	NOUN
ejpam-1599	366	23	h0(t	h0(t	X
ejpam-1599	366	24	)	)	PUNCT
ejpam-1599	366	25	=	=	SYM
ejpam-1599	367	1	{	{	PUNCT
ejpam-1599	367	2	x	x	SYM
ejpam-1599	367	3	∈	∈	PROPN
ejpam-1599	367	4	x	x	X
ejpam-1599	367	5	,	,	PUNCT
ejpam-1599	367	6	||t	||t	VERB
ejpam-1599	367	7	nx	nx	PROPN
ejpam-1599	367	8	||	||	ADP
ejpam-1599	367	9	1	1	NUM
ejpam-1599	367	10	n	n	PROPN
ejpam-1599	367	11	→	→	SYM
ejpam-1599	367	12	0	0	NUM
ejpam-1599	367	13	}	}	PUNCT
ejpam-1599	367	14	;	;	PUNCT
ejpam-1599	367	15	•	•	ADP
ejpam-1599	367	16	the	the	DET
ejpam-1599	367	17	algebraic	algebraic	ADJ
ejpam-1599	367	18	core	core	NOUN
ejpam-1599	367	19	c(t	c(t	PROPN
ejpam-1599	367	20	)	)	PUNCT
ejpam-1599	367	21	of	of	ADP
ejpam-1599	367	22	t	t	PROPN
ejpam-1599	367	23	is	be	AUX
ejpam-1599	367	24	the	the	DET
ejpam-1599	367	25	largest	large	ADJ
ejpam-1599	367	26	subspace	subspace	NOUN
ejpam-1599	367	27	such	such	ADJ
ejpam-1599	367	28	that	that	SCONJ
ejpam-1599	367	29	t	t	PROPN
ejpam-1599	367	30	(	(	PUNCT
ejpam-1599	367	31	m	m	NOUN
ejpam-1599	367	32	)	)	PUNCT
ejpam-1599	367	33	=	=	SYM
ejpam-1599	367	34	m	m	PROPN
ejpam-1599	367	35	;	;	PUNCT
ejpam-1599	367	36	•	•	ADP
ejpam-1599	367	37	the	the	DET
ejpam-1599	367	38	analytic	analytic	ADJ
ejpam-1599	367	39	core	core	NOUN
ejpam-1599	367	40	(	(	PUNCT
ejpam-1599	367	41	or	or	CCONJ
ejpam-1599	367	42	transfinite	transfinite	VERB
ejpam-1599	367	43	range	range	NOUN
ejpam-1599	367	44	)	)	PUNCT
ejpam-1599	367	45	k(t	k(t	PROPN
ejpam-1599	367	46	)	)	PUNCT
ejpam-1599	367	47	of	of	ADP
ejpam-1599	367	48	t	t	PROPN
ejpam-1599	367	49	consists	consist	VERB
ejpam-1599	367	50	of	of	ADP
ejpam-1599	367	51	all	all	DET
ejpam-1599	367	52	vectors	vector	NOUN
ejpam-1599	367	53	x0	x0	PROPN
ejpam-1599	367	54	∈	∈	PROPN
ejpam-1599	367	55	x	x	PUNCT
ejpam-1599	367	56	for	for	ADP
ejpam-1599	367	57	which	which	PRON
ejpam-1599	367	58	there	there	PRON
ejpam-1599	367	59	exist	exist	VERB
ejpam-1599	367	60	a	a	DET
ejpam-1599	367	61	sequence	sequence	NOUN
ejpam-1599	367	62	xn	xn	SYM
ejpam-1599	367	63	∈	∈	PROPN
ejpam-1599	367	64	x	x	PUNCT
ejpam-1599	367	65	such	such	ADJ
ejpam-1599	367	66	that	that	SCONJ
ejpam-1599	367	67	t	t	NOUN
ejpam-1599	367	68	xn	xn	PUNCT
ejpam-1599	368	1	=	=	SYM
ejpam-1599	368	2	xn−1	xn−1	PROPN
ejpam-1599	368	3	and	and	CCONJ
ejpam-1599	368	4	exists	exist	VERB
ejpam-1599	368	5	c	c	PROPN
ejpam-1599	368	6	>	>	X
ejpam-1599	368	7	0	0	PROPN
ejpam-1599	368	8	,	,	PUNCT
ejpam-1599	368	9	||xn||	||xn||	VERB
ejpam-1599	368	10	≤	≤	NOUN
ejpam-1599	368	11	cn||x0||	cn||x0||	PROPN
ejpam-1599	368	12	.	.	PUNCT
ejpam-1599	369	1	the	the	DET
ejpam-1599	369	2	algebraic	algebraic	PROPN
ejpam-1599	369	3	core	core	NOUN
ejpam-1599	369	4	can	can	AUX
ejpam-1599	369	5	also	also	ADV
ejpam-1599	369	6	be	be	AUX
ejpam-1599	369	7	defined	define	VERB
ejpam-1599	369	8	as	as	SCONJ
ejpam-1599	369	9	follows	follow	VERB
ejpam-1599	369	10	:	:	PUNCT
ejpam-1599	369	11	c(t	c(t	PROPN
ejpam-1599	369	12	)	)	PUNCT
ejpam-1599	369	13	consists	consist	VERB
ejpam-1599	369	14	of	of	ADP
ejpam-1599	369	15	all	all	DET
ejpam-1599	369	16	vectors	vector	NOUN
ejpam-1599	369	17	x0	x0	PROPN
ejpam-1599	369	18	∈	∈	PROPN
ejpam-1599	369	19	x	x	PUNCT
ejpam-1599	369	20	for	for	ADP
ejpam-1599	369	21	which	which	PRON
ejpam-1599	369	22	there	there	PRON
ejpam-1599	369	23	exist	exist	VERB
ejpam-1599	369	24	a	a	DET
ejpam-1599	369	25	sequence	sequence	NOUN
ejpam-1599	369	26	xn	xn	SYM
ejpam-1599	369	27	∈	∈	PROPN
ejpam-1599	369	28	x	x	PUNCT
ejpam-1599	370	1	such	such	ADJ
ejpam-1599	370	2	that	that	SCONJ
ejpam-1599	370	3	t	t	NOUN
ejpam-1599	370	4	xn	xn	PUNCT
ejpam-1599	370	5	=	=	SYM
ejpam-1599	370	6	xn−1	xn−1	PROPN
ejpam-1599	370	7	.	.	PUNCT
ejpam-1599	371	1	we	we	PRON
ejpam-1599	371	2	then	then	ADV
ejpam-1599	371	3	have	have	VERB
ejpam-1599	371	4	the	the	DET
ejpam-1599	371	5	following	follow	VERB
ejpam-1599	371	6	inclusions	inclusion	NOUN
ejpam-1599	371	7	:	:	PUNCT
ejpam-1599	371	8	k(t	k(t	X
ejpam-1599	371	9	)	)	PUNCT
ejpam-1599	372	1	⊂	⊂	PROPN
ejpam-1599	372	2	c(t	c(t	PROPN
ejpam-1599	372	3	)	)	PUNCT
ejpam-1599	372	4	⊂	⊂	PROPN
ejpam-1599	372	5	t∞(x	t∞(x	PROPN
ejpam-1599	372	6	)	)	PUNCT
ejpam-1599	372	7	,	,	PUNCT
ejpam-1599	372	8	n∞(t	n∞(t	INTJ
ejpam-1599	372	9	)	)	PUNCT
ejpam-1599	373	1	⊂	⊂	PROPN
ejpam-1599	373	2	h0(t	h0(t	X
ejpam-1599	373	3	)	)	PUNCT
ejpam-1599	373	4	.	.	PUNCT
ejpam-1599	374	1	in	in	ADP
ejpam-1599	374	2	[	[	X
ejpam-1599	374	3	12	12	NUM
ejpam-1599	374	4	]	]	PUNCT
ejpam-1599	374	5	,	,	PUNCT
ejpam-1599	374	6	it	it	PRON
ejpam-1599	374	7	is	be	AUX
ejpam-1599	374	8	proved	prove	VERB
ejpam-1599	374	9	that	that	SCONJ
ejpam-1599	374	10	for	for	ADP
ejpam-1599	374	11	a	a	DET
ejpam-1599	374	12	bounded	bounded	ADJ
ejpam-1599	374	13	operator	operator	NOUN
ejpam-1599	374	14	t	t	NOUN
ejpam-1599	374	15	,	,	PUNCT
ejpam-1599	374	16	the	the	DET
ejpam-1599	374	17	analytic	analytic	ADJ
ejpam-1599	374	18	core	core	NOUN
ejpam-1599	374	19	corresponds	correspond	VERB
ejpam-1599	374	20	to	to	ADP
ejpam-1599	374	21	the	the	DET
ejpam-1599	374	22	holomorphic	holomorphic	ADJ
ejpam-1599	374	23	range	range	NOUN
ejpam-1599	374	24	{	{	PUNCT
ejpam-1599	374	25	limz→0(t	limz→0(t	NOUN
ejpam-1599	374	26	−	−	PROPN
ejpam-1599	374	27	zi	zi	PROPN
ejpam-1599	374	28	)	)	PUNCT
ejpam-1599	374	29	f	f	PROPN
ejpam-1599	374	30	(	(	PUNCT
ejpam-1599	374	31	z	z	NOUN
ejpam-1599	374	32	)	)	PUNCT
ejpam-1599	374	33	,	,	PUNCT
ejpam-1599	374	34	f	f	PROPN
ejpam-1599	374	35	∈	∈	PROPN
ejpam-1599	374	36	holo(0	holo(0	PROPN
ejpam-1599	374	37	,	,	PUNCT
ejpam-1599	374	38	x	x	NOUN
ejpam-1599	374	39	)	)	PUNCT
ejpam-1599	374	40	}	}	PUNCT
ejpam-1599	374	41	,	,	PUNCT
ejpam-1599	374	42	and	and	CCONJ
ejpam-1599	374	43	that	that	SCONJ
ejpam-1599	374	44	the	the	DET
ejpam-1599	374	45	intersection	intersection	NOUN
ejpam-1599	374	46	if	if	SCONJ
ejpam-1599	374	47	the	the	DET
ejpam-1599	374	48	analytic	analytic	ADJ
ejpam-1599	374	49	core	core	NOUN
ejpam-1599	374	50	with	with	ADP
ejpam-1599	374	51	n(t	n(t	PROPN
ejpam-1599	374	52	)	)	PUNCT
ejpam-1599	374	53	is	be	AUX
ejpam-1599	374	54	the	the	DET
ejpam-1599	374	55	holomorphic	holomorphic	ADJ
ejpam-1599	374	56	kernel	kernel	NOUN
ejpam-1599	374	57	of	of	ADP
ejpam-1599	374	58	t	t	PROPN
ejpam-1599	374	59	{	{	PUNCT
ejpam-1599	374	60	g(0	g(0	PROPN
ejpam-1599	374	61	)	)	PUNCT
ejpam-1599	374	62	,	,	PUNCT
ejpam-1599	374	63	(	(	PUNCT
ejpam-1599	374	64	t	t	PROPN
ejpam-1599	374	65	−	−	PROPN
ejpam-1599	374	66	zi)g(z	zi)g(z	NUM
ejpam-1599	374	67	)	)	PUNCT
ejpam-1599	374	68	=	=	PUNCT
ejpam-1599	374	69	0	0	NUM
ejpam-1599	374	70	,	,	PUNCT
ejpam-1599	374	71	g	g	PROPN
ejpam-1599	374	72	∈	∈	PROPN
ejpam-1599	374	73	holo(0	holo(0	NOUN
ejpam-1599	374	74	,	,	PUNCT
ejpam-1599	374	75	x	x	NOUN
ejpam-1599	374	76	)	)	PUNCT
ejpam-1599	374	77	}	}	PUNCT
ejpam-1599	374	78	.	.	PUNCT
ejpam-1599	375	1	we	we	PRON
ejpam-1599	375	2	have	have	VERB
ejpam-1599	375	3	the	the	DET
ejpam-1599	375	4	following	follow	VERB
ejpam-1599	375	5	relations	relation	NOUN
ejpam-1599	375	6	:	:	PUNCT
ejpam-1599	375	7	x.	x.	PROPN
ejpam-1599	375	8	mary	mary	PROPN
ejpam-1599	375	9	/	/	SYM
ejpam-1599	375	10	eur	eur	PROPN
ejpam-1599	375	11	.	.	PUNCT
ejpam-1599	376	1	j.	j.	PROPN
ejpam-1599	376	2	pure	pure	PROPN
ejpam-1599	376	3	appl	appl	PROPN
ejpam-1599	376	4	.	.	PROPN
ejpam-1599	376	5	math	math	PROPN
ejpam-1599	376	6	,	,	PUNCT
ejpam-1599	376	7	5	5	NUM
ejpam-1599	376	8	(	(	PUNCT
ejpam-1599	376	9	2012	2012	NUM
ejpam-1599	376	10	)	)	PUNCT
ejpam-1599	376	11	,	,	PUNCT
ejpam-1599	376	12	160	160	NUM
ejpam-1599	376	13	-	-	SYM
ejpam-1599	376	14	173	173	NUM
ejpam-1599	376	15	171	171	NUM
ejpam-1599	376	16	proposition	proposition	NOUN
ejpam-1599	376	17	3	3	NUM
ejpam-1599	376	18	.	.	PUNCT
ejpam-1599	377	1	let	let	VERB
ejpam-1599	377	2	p	p	PROPN
ejpam-1599	377	3	∈	∈	PROPN
ejpam-1599	377	4	σ1(t	σ1(t	X
ejpam-1599	377	5	)	)	PUNCT
ejpam-1599	377	6	.	.	PUNCT
ejpam-1599	378	1	then	then	ADV
ejpam-1599	378	2	p(x	p(x	PROPN
ejpam-1599	378	3	)	)	PUNCT
ejpam-1599	378	4	⊂	⊂	PROPN
ejpam-1599	378	5	k(t	k(t	PUNCT
ejpam-1599	378	6	)	)	PUNCT
ejpam-1599	378	7	and	and	CCONJ
ejpam-1599	378	8	h0(t	h0(t	X
ejpam-1599	378	9	)	)	PUNCT
ejpam-1599	378	10	⊂	⊂	PROPN
ejpam-1599	378	11	n(p	n(p	PROPN
ejpam-1599	378	12	)	)	PUNCT
ejpam-1599	378	13	.	.	PUNCT
ejpam-1599	379	1	proof	proof	NOUN
ejpam-1599	379	2	.	.	PUNCT
ejpam-1599	380	1	let	let	VERB
ejpam-1599	380	2	p	p	PRON
ejpam-1599	380	3	∈	∈	PROPN
ejpam-1599	380	4	σ1(t	σ1(t	X
ejpam-1599	380	5	)	)	PUNCT
ejpam-1599	380	6	.	.	PUNCT
ejpam-1599	381	1	then	then	ADV
ejpam-1599	381	2	p	p	X
ejpam-1599	381	3	=	=	X
ejpam-1599	381	4	t	t	PROPN
ejpam-1599	381	5	t−p	t−p	NUM
ejpam-1599	381	6	p	p	NOUN
ejpam-1599	381	7	=	=	X
ejpam-1599	381	8	t	t	NOUN
ejpam-1599	381	9	t−p	t−p	NUM
ejpam-1599	381	10	=	=	SYM
ejpam-1599	381	11	t−p	t−p	NUM
ejpam-1599	381	12	t	t	NOUN
ejpam-1599	381	13	.	.	PUNCT
ejpam-1599	382	1	let	let	VERB
ejpam-1599	382	2	x0	x0	PROPN
ejpam-1599	382	3	∈	∈	PROPN
ejpam-1599	382	4	p(x	p(x	PROPN
ejpam-1599	382	5	)	)	PUNCT
ejpam-1599	382	6	,	,	PUNCT
ejpam-1599	382	7	and	and	CCONJ
ejpam-1599	382	8	for	for	ADP
ejpam-1599	382	9	all	all	DET
ejpam-1599	382	10	n	n	CCONJ
ejpam-1599	382	11	>	>	X
ejpam-1599	382	12	0	0	NUM
ejpam-1599	382	13	,	,	PUNCT
ejpam-1599	382	14	pose	pose	VERB
ejpam-1599	382	15	xn	xn	PROPN
ejpam-1599	383	1	=	=	SYM
ejpam-1599	383	2	(	(	PUNCT
ejpam-1599	383	3	t	t	PROPN
ejpam-1599	383	4	−p)n	−p)n	NOUN
ejpam-1599	383	5	x0	x0	PROPN
ejpam-1599	383	6	.	.	PUNCT
ejpam-1599	384	1	then	then	ADV
ejpam-1599	384	2	t	t	X
ejpam-1599	384	3	xn	xn	PROPN
ejpam-1599	385	1	=	=	SYM
ejpam-1599	385	2	t	t	PROPN
ejpam-1599	385	3	(	(	PUNCT
ejpam-1599	385	4	t−p)n	t−p)n	PROPN
ejpam-1599	385	5	x0	x0	PROPN
ejpam-1599	385	6	=	=	SYM
ejpam-1599	385	7	p(t−p	p(t−p	ADJ
ejpam-1599	385	8	)	)	PUNCT
ejpam-1599	386	1	n−1	n−1	PROPN
ejpam-1599	386	2	x0	x0	PROPN
ejpam-1599	386	3	=	=	PRON
ejpam-1599	387	1	(	(	PUNCT
ejpam-1599	387	2	t	t	NOUN
ejpam-1599	387	3	−p)n−1p	−p)n−1p	NOUN
ejpam-1599	387	4	x0	x0	PROPN
ejpam-1599	387	5	=	=	PRON
ejpam-1599	388	1	(	(	PUNCT
ejpam-1599	388	2	t	t	PROPN
ejpam-1599	388	3	−p)n−1	−p)n−1	X
ejpam-1599	388	4	x0	x0	PROPN
ejpam-1599	388	5	=	=	PUNCT
ejpam-1599	388	6	xn−1	xn−1	PROPN
ejpam-1599	388	7	.	.	PUNCT
ejpam-1599	388	8	also	also	ADV
ejpam-1599	388	9	||xn||	||xn||	VERB
ejpam-1599	388	10	≤	≤	ADJ
ejpam-1599	388	11	||t	||t	ADJ
ejpam-1599	388	12	−p	−p	ADJ
ejpam-1599	388	13	||n||x0||	||n||x0||	NOUN
ejpam-1599	388	14	,	,	PUNCT
ejpam-1599	388	15	hence	hence	ADV
ejpam-1599	388	16	x0	x0	PROPN
ejpam-1599	388	17	∈	∈	PROPN
ejpam-1599	388	18	k(t	k(t	PROPN
ejpam-1599	388	19	)	)	PUNCT
ejpam-1599	388	20	.	.	PUNCT
ejpam-1599	389	1	let	let	VERB
ejpam-1599	389	2	now	now	ADV
ejpam-1599	389	3	x	x	X
ejpam-1599	389	4	∈	∈	PROPN
ejpam-1599	389	5	h0(t	h0(t	X
ejpam-1599	389	6	)	)	PUNCT
ejpam-1599	389	7	.	.	PUNCT
ejpam-1599	390	1	then	then	ADV
ejpam-1599	390	2	p(x	p(x	VERB
ejpam-1599	390	3	)	)	PUNCT
ejpam-1599	390	4	=	=	PUNCT
ejpam-1599	390	5	t−p	t−p	NUM
ejpam-1599	390	6	t	t	NOUN
ejpam-1599	390	7	(	(	PUNCT
ejpam-1599	390	8	x	x	NOUN
ejpam-1599	390	9	)	)	PUNCT
ejpam-1599	390	10	=	=	SYM
ejpam-1599	390	11	(	(	PUNCT
ejpam-1599	390	12	t−p)nt	t−p)nt	PUNCT
ejpam-1599	390	13	n(x	n(x	PROPN
ejpam-1599	390	14	)	)	PUNCT
ejpam-1599	390	15	forall	forall	NOUN
ejpam-1599	390	16	n	n	CCONJ
ejpam-1599	390	17	>	>	X
ejpam-1599	390	18	0	0	NUM
ejpam-1599	391	1	and	and	CCONJ
ejpam-1599	391	2	||p(x)||	||p(x)||	NUM
ejpam-1599	391	3	1	1	NUM
ejpam-1599	391	4	n	n	NOUN
ejpam-1599	391	5	≤	≤	X
ejpam-1599	391	6	||(t−p)n||	||(t−p)n||	VERB
ejpam-1599	391	7	1	1	NUM
ejpam-1599	391	8	n	n	DET
ejpam-1599	391	9	||t	||t	NOUN
ejpam-1599	391	10	n(x)||	n(x)||	ADJ
ejpam-1599	391	11	1	1	NUM
ejpam-1599	391	12	n	n	CCONJ
ejpam-1599	391	13	≤	≤	NUM
ejpam-1599	391	14	||(t−p)||||t	||(t−p)||||t	NOUN
ejpam-1599	391	15	n(x)||	n(x)||	NOUN
ejpam-1599	391	16	1	1	NUM
ejpam-1599	391	17	n	n	NOUN
ejpam-1599	391	18	→	→	SYM
ejpam-1599	391	19	0	0	NUM
ejpam-1599	391	20	and	and	CCONJ
ejpam-1599	391	21	p(x	p(x	PROPN
ejpam-1599	391	22	)	)	PUNCT
ejpam-1599	391	23	=	=	SYM
ejpam-1599	391	24	0	0	X
ejpam-1599	391	25	.	.	PUNCT
ejpam-1599	391	26	corollary	corollary	ADJ
ejpam-1599	391	27	5	5	NUM
ejpam-1599	391	28	.	.	PUNCT
ejpam-1599	391	29	k(t	k(t	PUNCT
ejpam-1599	391	30	)	)	PUNCT
ejpam-1599	392	1	=	=	PUNCT
ejpam-1599	392	2	{	{	PUNCT
ejpam-1599	392	3	0	0	NUM
ejpam-1599	392	4	}	}	PUNCT
ejpam-1599	392	5	⇒	⇒	NOUN
ejpam-1599	392	6	σ1(t	σ1(t	X
ejpam-1599	392	7	)	)	PUNCT
ejpam-1599	392	8	=	=	SYM
ejpam-1599	392	9	{	{	PUNCT
ejpam-1599	392	10	0	0	NUM
ejpam-1599	392	11	}	}	PUNCT
ejpam-1599	392	12	;	;	PUNCT
ejpam-1599	392	13	h0(t	h0(t	X
ejpam-1599	392	14	)	)	PUNCT
ejpam-1599	392	15	=	=	PUNCT
ejpam-1599	392	16	x	x	SYM
ejpam-1599	392	17	⇒	⇒	NOUN
ejpam-1599	392	18	σ1(t	σ1(t	X
ejpam-1599	392	19	)	)	PUNCT
ejpam-1599	392	20	=	=	SYM
ejpam-1599	392	21	{	{	PUNCT
ejpam-1599	392	22	0	0	NUM
ejpam-1599	392	23	}	}	PUNCT
ejpam-1599	392	24	.	.	PUNCT
ejpam-1599	393	1	obviously	obviously	ADV
ejpam-1599	393	2	,	,	PUNCT
ejpam-1599	393	3	the	the	DET
ejpam-1599	393	4	existence	existence	NOUN
ejpam-1599	393	5	of	of	ADP
ejpam-1599	393	6	a	a	DET
ejpam-1599	393	7	greatest	great	ADJ
ejpam-1599	393	8	element	element	NOUN
ejpam-1599	393	9	in	in	ADP
ejpam-1599	393	10	σ2(t	σ2(t	PROPN
ejpam-1599	393	11	)	)	PUNCT
ejpam-1599	393	12	is	be	AUX
ejpam-1599	393	13	guaranteed	guarantee	VERB
ejpam-1599	393	14	by	by	ADP
ejpam-1599	393	15	a	a	DET
ejpam-1599	393	16	decomposition	decomposition	NOUN
ejpam-1599	393	17	of	of	ADP
ejpam-1599	393	18	the	the	DET
ejpam-1599	393	19	form	form	NOUN
ejpam-1599	393	20	x	x	PUNCT
ejpam-1599	393	21	=	=	SYM
ejpam-1599	393	22	h0(t	h0(t	X
ejpam-1599	393	23	)	)	PUNCT
ejpam-1599	393	24	⊕k(t	⊕k(t	PROPN
ejpam-1599	393	25	)	)	PUNCT
ejpam-1599	393	26	,	,	PUNCT
ejpam-1599	393	27	with	with	SCONJ
ejpam-1599	393	28	both	both	DET
ejpam-1599	393	29	subspaces	subspace	NOUN
ejpam-1599	393	30	closed	close	VERB
ejpam-1599	393	31	(	(	PUNCT
ejpam-1599	393	32	choose	choose	VERB
ejpam-1599	393	33	p	p	X
ejpam-1599	393	34	the	the	DET
ejpam-1599	393	35	associated	associated	ADJ
ejpam-1599	393	36	projection	projection	NOUN
ejpam-1599	393	37	on	on	ADP
ejpam-1599	393	38	k(t	k(t	PROPN
ejpam-1599	393	39	)	)	PUNCT
ejpam-1599	393	40	)	)	PUNCT
ejpam-1599	393	41	.	.	PUNCT
ejpam-1599	394	1	but	but	CCONJ
ejpam-1599	394	2	such	such	DET
ejpam-1599	394	3	a	a	DET
ejpam-1599	394	4	decomposition	decomposition	NOUN
ejpam-1599	394	5	occurs	occur	VERB
ejpam-1599	394	6	only	only	ADV
ejpam-1599	394	7	for	for	ADP
ejpam-1599	394	8	quasipolar	quasipolar	ADJ
ejpam-1599	394	9	elements	element	NOUN
ejpam-1599	394	10	:	:	PUNCT
ejpam-1599	394	11	theorem	theorem	VERB
ejpam-1599	394	12	11	11	NUM
ejpam-1599	394	13	.	.	PUNCT
ejpam-1599	395	1	[	[	X
ejpam-1599	395	2	21	21	NUM
ejpam-1599	395	3	,	,	PUNCT
ejpam-1599	395	4	theorem	theorem	VERB
ejpam-1599	395	5	1.6	1.6	NUM
ejpam-1599	395	6	]	]	PUNCT
ejpam-1599	395	7	let	let	VERB
ejpam-1599	395	8	t	t	PROPN
ejpam-1599	395	9	∈	∈	PROPN
ejpam-1599	395	10	b(x	b(x	PROPN
ejpam-1599	395	11	)	)	PUNCT
ejpam-1599	395	12	.	.	PUNCT
ejpam-1599	396	1	then	then	ADV
ejpam-1599	396	2	0	0	NUM
ejpam-1599	396	3	is	be	AUX
ejpam-1599	396	4	an	an	DET
ejpam-1599	396	5	isolated	isolated	ADJ
ejpam-1599	396	6	point	point	NOUN
ejpam-1599	396	7	of	of	ADP
ejpam-1599	396	8	the	the	DET
ejpam-1599	396	9	spectrum	spectrum	NOUN
ejpam-1599	396	10	if	if	SCONJ
ejpam-1599	396	11	and	and	CCONJ
ejpam-1599	396	12	only	only	ADV
ejpam-1599	396	13	if	if	SCONJ
ejpam-1599	396	14	h0(t	h0(t	PROPN
ejpam-1599	396	15	)	)	PUNCT
ejpam-1599	396	16	,	,	PUNCT
ejpam-1599	396	17	k(t	k(t	PROPN
ejpam-1599	396	18	)	)	PUNCT
ejpam-1599	396	19	are	be	AUX
ejpam-1599	396	20	closed	closed	ADJ
ejpam-1599	396	21	and	and	CCONJ
ejpam-1599	396	22	x	x	SYM
ejpam-1599	396	23	=	=	SYM
ejpam-1599	396	24	h0(t	h0(t	X
ejpam-1599	396	25	)	)	PUNCT
ejpam-1599	396	26	⊕	⊕	PROPN
ejpam-1599	396	27	k(t	k(t	PROPN
ejpam-1599	396	28	)	)	PUNCT
ejpam-1599	396	29	.	.	PUNCT
ejpam-1599	397	1	theorem	theorem	NOUN
ejpam-1599	397	2	12	12	NUM
ejpam-1599	397	3	.	.	PUNCT
ejpam-1599	398	1	assume	assume	VERB
ejpam-1599	398	2	k(t	k(t	PROPN
ejpam-1599	398	3	)	)	PUNCT
ejpam-1599	399	1	is	be	AUX
ejpam-1599	399	2	closed	close	VERB
ejpam-1599	399	3	and	and	CCONJ
ejpam-1599	399	4	complemented	complement	VERB
ejpam-1599	399	5	with	with	ADP
ejpam-1599	399	6	complement	complement	NOUN
ejpam-1599	399	7	n	n	DET
ejpam-1599	399	8	hyperinvariant	hyperinvariant	NOUN
ejpam-1599	399	9	,	,	PUNCT
ejpam-1599	399	10	and	and	CCONJ
ejpam-1599	399	11	n(t	n(t	PROPN
ejpam-1599	399	12	)	)	PUNCT
ejpam-1599	399	13	∩	∩	PROPN
ejpam-1599	399	14	k(t	k(t	NOUN
ejpam-1599	399	15	)	)	PUNCT
ejpam-1599	400	1	=	=	PUNCT
ejpam-1599	400	2	{	{	PUNCT
ejpam-1599	400	3	0	0	NUM
ejpam-1599	400	4	}	}	PUNCT
ejpam-1599	400	5	.	.	PUNCT
ejpam-1599	401	1	then	then	ADV
ejpam-1599	401	2	t	t	PROPN
ejpam-1599	401	3	is	be	AUX
ejpam-1599	401	4	naturally	naturally	ADV
ejpam-1599	401	5	invertible	invertible	ADJ
ejpam-1599	401	6	with	with	ADP
ejpam-1599	401	7	greatest	great	ADJ
ejpam-1599	401	8	idempotent	idempotent	NOUN
ejpam-1599	401	9	the	the	DET
ejpam-1599	401	10	projection	projection	NOUN
ejpam-1599	401	11	on	on	ADP
ejpam-1599	401	12	k(t	k(t	PROPN
ejpam-1599	401	13	)	)	PUNCT
ejpam-1599	402	1	parallel	parallel	ADJ
ejpam-1599	402	2	to	to	ADP
ejpam-1599	402	3	n.	n.	NOUN
ejpam-1599	402	4	proof	proof	NOUN
ejpam-1599	402	5	.	.	PUNCT
ejpam-1599	403	1	let	let	VERB
ejpam-1599	403	2	x	x	PUNCT
ejpam-1599	403	3	=	=	PUNCT
ejpam-1599	403	4	k(t	k(t	X
ejpam-1599	403	5	)	)	PUNCT
ejpam-1599	404	1	⊕	⊕	PROPN
ejpam-1599	404	2	n	n	PROPN
ejpam-1599	404	3	and	and	CCONJ
ejpam-1599	404	4	m	m	VERB
ejpam-1599	404	5	the	the	DET
ejpam-1599	404	6	idempotent	idempotent	NOUN
ejpam-1599	404	7	of	of	ADP
ejpam-1599	404	8	the	the	DET
ejpam-1599	404	9	theorem	theorem	NOUN
ejpam-1599	404	10	.	.	PUNCT
ejpam-1599	405	1	first	first	ADV
ejpam-1599	405	2	,	,	PUNCT
ejpam-1599	405	3	we	we	PRON
ejpam-1599	405	4	must	must	AUX
ejpam-1599	405	5	prove	prove	VERB
ejpam-1599	405	6	that	that	SCONJ
ejpam-1599	405	7	m	m	VERB
ejpam-1599	405	8	∈	∈	NOUN
ejpam-1599	405	9	σ2(t	σ2(t	PROPN
ejpam-1599	405	10	)	)	PUNCT
ejpam-1599	405	11	.	.	PUNCT
ejpam-1599	406	1	since	since	SCONJ
ejpam-1599	406	2	k(t	k(t	PROPN
ejpam-1599	406	3	)	)	PUNCT
ejpam-1599	406	4	and	and	CCONJ
ejpam-1599	406	5	n	n	PRON
ejpam-1599	406	6	are	be	AUX
ejpam-1599	406	7	hyperinvariant	hyperinvariant	ADJ
ejpam-1599	406	8	,	,	PUNCT
ejpam-1599	406	9	we	we	PRON
ejpam-1599	406	10	only	only	ADV
ejpam-1599	406	11	have	have	VERB
ejpam-1599	406	12	to	to	PART
ejpam-1599	406	13	prove	prove	VERB
ejpam-1599	406	14	that	that	SCONJ
ejpam-1599	406	15	m	m	VERB
ejpam-1599	406	16	≤h	≤h	NOUN
ejpam-1599	406	17	t	t	NOUN
ejpam-1599	406	18	.	.	PUNCT
ejpam-1599	407	1	consider	consider	VERB
ejpam-1599	407	2	t|k(t	t|k(t	ADP
ejpam-1599	407	3	)	)	PUNCT
ejpam-1599	407	4	:	:	PUNCT
ejpam-1599	407	5	k(t	k(t	X
ejpam-1599	407	6	)	)	PUNCT
ejpam-1599	408	1	→	→	PUNCT
ejpam-1599	408	2	k(t	k(t	NOUN
ejpam-1599	408	3	)	)	PUNCT
ejpam-1599	408	4	the	the	DET
ejpam-1599	408	5	restriction	restriction	NOUN
ejpam-1599	408	6	of	of	ADP
ejpam-1599	408	7	t	t	NOUN
ejpam-1599	408	8	to	to	ADP
ejpam-1599	408	9	k(t	k(t	PROPN
ejpam-1599	408	10	)	)	PUNCT
ejpam-1599	408	11	.	.	PUNCT
ejpam-1599	409	1	t|k(t	t|k(t	X
ejpam-1599	409	2	)	)	PUNCT
ejpam-1599	409	3	is	be	AUX
ejpam-1599	409	4	well	well	ADV
ejpam-1599	409	5	defined	define	VERB
ejpam-1599	409	6	since	since	SCONJ
ejpam-1599	409	7	t	t	PROPN
ejpam-1599	409	8	(	(	PUNCT
ejpam-1599	409	9	k(t	k(t	PROPN
ejpam-1599	409	10	)	)	PUNCT
ejpam-1599	409	11	)	)	PUNCT
ejpam-1599	410	1	⊂	⊂	PROPN
ejpam-1599	410	2	k(t	k(t	X
ejpam-1599	410	3	)	)	PUNCT
ejpam-1599	410	4	,	,	PUNCT
ejpam-1599	410	5	and	and	CCONJ
ejpam-1599	410	6	surjective	surjective	VERB
ejpam-1599	410	7	since	since	SCONJ
ejpam-1599	410	8	t	t	PROPN
ejpam-1599	410	9	(	(	PUNCT
ejpam-1599	410	10	k(t	k(t	PROPN
ejpam-1599	410	11	)	)	PUNCT
ejpam-1599	410	12	)	)	PUNCT
ejpam-1599	411	1	=	=	PUNCT
ejpam-1599	411	2	k(t	k(t	NOUN
ejpam-1599	411	3	)	)	PUNCT
ejpam-1599	411	4	.	.	PUNCT
ejpam-1599	412	1	but	but	CCONJ
ejpam-1599	412	2	from	from	ADP
ejpam-1599	412	3	the	the	DET
ejpam-1599	412	4	hypothesis	hypothesis	NOUN
ejpam-1599	412	5	n(t	n(t	PROPN
ejpam-1599	412	6	)	)	PUNCT
ejpam-1599	412	7	⊂	⊂	PROPN
ejpam-1599	413	1	n	n	CCONJ
ejpam-1599	413	2	it	it	PRON
ejpam-1599	413	3	is	be	AUX
ejpam-1599	413	4	also	also	ADV
ejpam-1599	413	5	injective	injective	ADJ
ejpam-1599	413	6	,	,	PUNCT
ejpam-1599	413	7	hence	hence	ADV
ejpam-1599	413	8	invertible	invertible	ADJ
ejpam-1599	413	9	and	and	CCONJ
ejpam-1599	413	10	exists	exist	VERB
ejpam-1599	413	11	s	s	PART
ejpam-1599	413	12	bounded	bounded	ADJ
ejpam-1599	413	13	operator	operator	NOUN
ejpam-1599	413	14	,	,	PUNCT
ejpam-1599	413	15	ts	ts	ADP
ejpam-1599	413	16	=	=	PROPN
ejpam-1599	413	17	st	st	PROPN
ejpam-1599	414	1	=	=	NOUN
ejpam-1599	414	2	m	m	PROPN
ejpam-1599	414	3	.	.	PUNCT
ejpam-1599	415	1	let	let	VERB
ejpam-1599	415	2	now	now	ADV
ejpam-1599	415	3	p	p	X
ejpam-1599	415	4	be	be	AUX
ejpam-1599	415	5	and	and	CCONJ
ejpam-1599	415	6	idempotent	idempotent	ADJ
ejpam-1599	415	7	in	in	ADP
ejpam-1599	415	8	σ2(t	σ2(t	PROPN
ejpam-1599	415	9	)	)	PUNCT
ejpam-1599	415	10	.	.	PUNCT
ejpam-1599	416	1	then	then	ADV
ejpam-1599	416	2	p(x	p(x	PROPN
ejpam-1599	416	3	)	)	PUNCT
ejpam-1599	416	4	⊂	⊂	PROPN
ejpam-1599	416	5	k(t	k(t	PUNCT
ejpam-1599	416	6	)	)	PUNCT
ejpam-1599	416	7	from	from	ADP
ejpam-1599	416	8	proposition	proposition	NOUN
ejpam-1599	416	9	3	3	NUM
ejpam-1599	416	10	,	,	PUNCT
ejpam-1599	416	11	hence	hence	ADV
ejpam-1599	416	12	p(x	p(x	PROPN
ejpam-1599	416	13	)	)	PUNCT
ejpam-1599	416	14	⊂	⊂	PROPN
ejpam-1599	416	15	m(x	m(x	PROPN
ejpam-1599	416	16	)	)	PUNCT
ejpam-1599	416	17	.	.	PUNCT
ejpam-1599	417	1	it	it	PRON
ejpam-1599	417	2	follows	follow	VERB
ejpam-1599	417	3	that	that	DET
ejpam-1599	417	4	pm	pm	NOUN
ejpam-1599	417	5	p	p	NOUN
ejpam-1599	417	6	=	=	PUNCT
ejpam-1599	417	7	p	p	NOUN
ejpam-1599	417	8	and	and	CCONJ
ejpam-1599	417	9	by	by	ADP
ejpam-1599	417	10	commutation	commutation	NOUN
ejpam-1599	417	11	(	(	PUNCT
ejpam-1599	417	12	σ2(t	σ2(t	PROPN
ejpam-1599	417	13	)	)	PUNCT
ejpam-1599	417	14	is	be	AUX
ejpam-1599	417	15	a	a	DET
ejpam-1599	417	16	commutative	commutative	ADJ
ejpam-1599	417	17	semigroup	semigroup	NOUN
ejpam-1599	417	18	)	)	PUNCT
ejpam-1599	417	19	,	,	PUNCT
ejpam-1599	417	20	pm	pm	NOUN
ejpam-1599	417	21	=	=	PUNCT
ejpam-1599	417	22	m	m	VERB
ejpam-1599	417	23	p	p	NOUN
ejpam-1599	417	24	=	=	PUNCT
ejpam-1599	417	25	pm	pm	NOUN
ejpam-1599	417	26	p	p	NOUN
ejpam-1599	417	27	=	=	PROPN
ejpam-1599	417	28	p	p	PROPN
ejpam-1599	417	29	and	and	CCONJ
ejpam-1599	417	30	m	m	PROPN
ejpam-1599	417	31	is	be	AUX
ejpam-1599	417	32	the	the	DET
ejpam-1599	417	33	greatest	great	ADJ
ejpam-1599	417	34	element	element	NOUN
ejpam-1599	417	35	of	of	ADP
ejpam-1599	417	36	σ2(t	σ2(t	PROPN
ejpam-1599	417	37	)	)	PUNCT
ejpam-1599	417	38	.	.	PUNCT
ejpam-1599	418	1	by	by	ADP
ejpam-1599	418	2	the	the	DET
ejpam-1599	418	3	results	result	NOUN
ejpam-1599	418	4	of	of	ADP
ejpam-1599	418	5	harte	harte	PROPN
ejpam-1599	418	6	[	[	X
ejpam-1599	418	7	12	12	NUM
ejpam-1599	418	8	]	]	PUNCT
ejpam-1599	418	9	,	,	PUNCT
ejpam-1599	418	10	n(t	n(t	NOUN
ejpam-1599	418	11	)	)	PUNCT
ejpam-1599	418	12	∩k(t	∩k(t	NOUN
ejpam-1599	418	13	)	)	PUNCT
ejpam-1599	418	14	is	be	AUX
ejpam-1599	418	15	the	the	DET
ejpam-1599	418	16	holomorphic	holomorphic	ADJ
ejpam-1599	418	17	kernel	kernel	NOUN
ejpam-1599	418	18	of	of	ADP
ejpam-1599	418	19	t	t	PROPN
ejpam-1599	418	20	,	,	PUNCT
ejpam-1599	418	21	and	and	CCONJ
ejpam-1599	418	22	it	it	PRON
ejpam-1599	418	23	reduces	reduce	VERB
ejpam-1599	418	24	to	to	ADP
ejpam-1599	418	25	0	0	NUM
ejpam-1599	418	26	precisely	precisely	ADV
ejpam-1599	418	27	when	when	SCONJ
ejpam-1599	418	28	t	t	PROPN
ejpam-1599	418	29	has	have	VERB
ejpam-1599	418	30	the	the	DET
ejpam-1599	418	31	single	single	ADJ
ejpam-1599	418	32	valued	value	VERB
ejpam-1599	418	33	extension	extension	NOUN
ejpam-1599	418	34	property	property	NOUN
ejpam-1599	418	35	(	(	PUNCT
ejpam-1599	418	36	svep	svep	NOUN
ejpam-1599	418	37	)	)	PUNCT
ejpam-1599	418	38	at	at	ADP
ejpam-1599	418	39	0	0	NUM
ejpam-1599	418	40	(	(	PUNCT
ejpam-1599	418	41	theorem	theorem	NOUN
ejpam-1599	418	42	9	9	NUM
ejpam-1599	418	43	p.	p.	NOUN
ejpam-1599	418	44	180	180	NUM
ejpam-1599	418	45	)	)	PUNCT
ejpam-1599	418	46	.	.	PUNCT
ejpam-1599	419	1	we	we	PRON
ejpam-1599	419	2	get	get	VERB
ejpam-1599	419	3	the	the	DET
ejpam-1599	419	4	following	follow	VERB
ejpam-1599	419	5	corollary	corollary	NOUN
ejpam-1599	419	6	.	.	PUNCT
ejpam-1599	420	1	corollary	corollary	ADJ
ejpam-1599	420	2	6	6	NUM
ejpam-1599	420	3	.	.	PUNCT
ejpam-1599	421	1	let	let	VERB
ejpam-1599	421	2	t	t	PROPN
ejpam-1599	421	3	be	be	AUX
ejpam-1599	421	4	a	a	DET
ejpam-1599	421	5	bounded	bounded	ADJ
ejpam-1599	421	6	operator	operator	NOUN
ejpam-1599	421	7	on	on	ADP
ejpam-1599	421	8	x	x	PUNCT
ejpam-1599	421	9	with	with	ADP
ejpam-1599	421	10	the	the	DET
ejpam-1599	421	11	svep	svep	NOUN
ejpam-1599	421	12	at	at	ADP
ejpam-1599	421	13	0	0	NUM
ejpam-1599	421	14	.	.	PUNCT
ejpam-1599	422	1	if	if	SCONJ
ejpam-1599	422	2	k(t	k(t	PROPN
ejpam-1599	422	3	)	)	PUNCT
ejpam-1599	422	4	is	be	AUX
ejpam-1599	422	5	closed	close	VERB
ejpam-1599	422	6	and	and	CCONJ
ejpam-1599	422	7	hyperinvariantly	hyperinvariantly	ADV
ejpam-1599	422	8	complemented	complement	VERB
ejpam-1599	422	9	,	,	PUNCT
ejpam-1599	422	10	then	then	ADV
ejpam-1599	422	11	t	t	PROPN
ejpam-1599	422	12	is	be	AUX
ejpam-1599	422	13	naturally	naturally	ADV
ejpam-1599	422	14	invertible	invertible	ADJ
ejpam-1599	422	15	.	.	PUNCT
ejpam-1599	423	1	as	as	ADP
ejpam-1599	423	2	a	a	DET
ejpam-1599	423	3	final	final	ADJ
ejpam-1599	423	4	result	result	NOUN
ejpam-1599	423	5	,	,	PUNCT
ejpam-1599	423	6	we	we	PRON
ejpam-1599	423	7	investigate	investigate	VERB
ejpam-1599	423	8	the	the	DET
ejpam-1599	423	9	range	range	NOUN
ejpam-1599	423	10	of	of	ADP
ejpam-1599	423	11	the	the	DET
ejpam-1599	423	12	core	core	NOUN
ejpam-1599	423	13	of	of	ADP
ejpam-1599	423	14	a	a	DET
ejpam-1599	423	15	naturally	naturally	ADV
ejpam-1599	423	16	invertible	invertible	ADJ
ejpam-1599	423	17	element	element	NOUN
ejpam-1599	423	18	:	:	PUNCT
ejpam-1599	423	19	proposition	proposition	NOUN
ejpam-1599	423	20	4	4	NUM
ejpam-1599	423	21	.	.	PUNCT
ejpam-1599	424	1	let	let	VERB
ejpam-1599	424	2	t	t	PROPN
ejpam-1599	424	3	be	be	AUX
ejpam-1599	424	4	naturally	naturally	ADV
ejpam-1599	424	5	invertible	invertible	ADJ
ejpam-1599	424	6	with	with	ADP
ejpam-1599	424	7	natural	natural	ADJ
ejpam-1599	424	8	inverse	inverse	NOUN
ejpam-1599	424	9	b	b	PROPN
ejpam-1599	424	10	,	,	PUNCT
ejpam-1599	424	11	greatest	great	ADJ
ejpam-1599	424	12	idempotent	idempotent	NOUN
ejpam-1599	425	1	m	m	NOUN
ejpam-1599	425	2	=	=	PROPN
ejpam-1599	425	3	t	t	PROPN
ejpam-1599	425	4	b	b	PROPN
ejpam-1599	425	5	=	=	SYM
ejpam-1599	425	6	bt	bt	PROPN
ejpam-1599	425	7	and	and	CCONJ
ejpam-1599	425	8	core	core	PROPN
ejpam-1599	425	9	t	t	PROPN
ejpam-1599	425	10	m	m	PROPN
ejpam-1599	425	11	=	=	PROPN
ejpam-1599	425	12	t	t	PROPN
ejpam-1599	425	13	bt	bt	PROPN
ejpam-1599	425	14	.	.	PUNCT
ejpam-1599	426	1	then	then	ADV
ejpam-1599	426	2	kν(t	kν(t	NOUN
ejpam-1599	426	3	)	)	PUNCT
ejpam-1599	427	1	=	=	SYM
ejpam-1599	427	2	t	t	PROPN
ejpam-1599	427	3	m(x	m(x	PROPN
ejpam-1599	427	4	)	)	PUNCT
ejpam-1599	427	5	is	be	AUX
ejpam-1599	427	6	a	a	DET
ejpam-1599	427	7	closed	closed	ADJ
ejpam-1599	427	8	,	,	PUNCT
ejpam-1599	427	9	hyperinvariant	hyperinvariant	NOUN
ejpam-1599	427	10	,	,	PUNCT
ejpam-1599	427	11	complemented	complement	VERB
ejpam-1599	427	12	(	(	PUNCT
ejpam-1599	427	13	with	with	ADP
ejpam-1599	427	14	hyperinvariant	hyperinvariant	PROPN
ejpam-1599	427	15	complement	complement	PROPN
ejpam-1599	427	16	)	)	PUNCT
ejpam-1599	427	17	subspace	subspace	NOUN
ejpam-1599	427	18	of	of	ADP
ejpam-1599	427	19	the	the	DET
ejpam-1599	427	20	analytic	analytic	ADJ
ejpam-1599	427	21	core	core	NOUN
ejpam-1599	427	22	k(t	k(t	PROPN
ejpam-1599	427	23	)	)	PUNCT
ejpam-1599	427	24	,	,	PUNCT
ejpam-1599	427	25	and	and	CCONJ
ejpam-1599	427	26	t	t	PROPN
ejpam-1599	427	27	kν(t	kν(t	PUNCT
ejpam-1599	427	28	)	)	PUNCT
ejpam-1599	428	1	=	=	SYM
ejpam-1599	428	2	kν(t	kν(t	NOUN
ejpam-1599	428	3	)	)	PUNCT
ejpam-1599	428	4	.	.	PUNCT
ejpam-1599	429	1	references	reference	NOUN
ejpam-1599	429	2	172	172	NUM
ejpam-1599	429	3	proof	proof	NOUN
ejpam-1599	429	4	.	.	PUNCT
ejpam-1599	430	1	by	by	ADP
ejpam-1599	430	2	commutation	commutation	NOUN
ejpam-1599	430	3	,	,	PUNCT
ejpam-1599	430	4	t	t	PROPN
ejpam-1599	430	5	m(x	m(x	PROPN
ejpam-1599	430	6	)	)	PUNCT
ejpam-1599	430	7	⊂	⊂	PROPN
ejpam-1599	430	8	m(x	m(x	PROPN
ejpam-1599	430	9	)	)	PUNCT
ejpam-1599	430	10	.	.	PUNCT
ejpam-1599	431	1	but	but	CCONJ
ejpam-1599	431	2	also	also	ADV
ejpam-1599	431	3	m(x	m(x	NOUN
ejpam-1599	431	4	)	)	PUNCT
ejpam-1599	432	1	=	=	PUNCT
ejpam-1599	432	2	m2(x	m2(x	PROPN
ejpam-1599	432	3	)	)	PUNCT
ejpam-1599	433	1	=	=	SYM
ejpam-1599	433	2	bt	bt	X
ejpam-1599	433	3	m(x	m(x	PROPN
ejpam-1599	433	4	)	)	PUNCT
ejpam-1599	434	1	⊂	⊂	PROPN
ejpam-1599	434	2	t	t	PROPN
ejpam-1599	434	3	m(x	m(x	PROPN
ejpam-1599	434	4	)	)	PUNCT
ejpam-1599	434	5	and	and	CCONJ
ejpam-1599	434	6	the	the	DET
ejpam-1599	434	7	two	two	NUM
ejpam-1599	434	8	subspaces	subspace	NOUN
ejpam-1599	434	9	are	be	AUX
ejpam-1599	434	10	equal	equal	ADJ
ejpam-1599	434	11	.	.	PUNCT
ejpam-1599	435	1	the	the	DET
ejpam-1599	435	2	other	other	ADJ
ejpam-1599	435	3	properties	property	NOUN
ejpam-1599	435	4	follow	follow	VERB
ejpam-1599	435	5	.	.	PUNCT
ejpam-1599	436	1	6.2	6.2	NUM
ejpam-1599	436	2	.	.	PUNCT
ejpam-1599	437	1	miscellaneous	miscellaneous	ADJ
ejpam-1599	437	2	in	in	ADP
ejpam-1599	437	3	this	this	DET
ejpam-1599	437	4	last	last	ADJ
ejpam-1599	437	5	section	section	NOUN
ejpam-1599	437	6	we	we	PRON
ejpam-1599	437	7	give	give	VERB
ejpam-1599	437	8	examples	example	NOUN
ejpam-1599	437	9	and	and	CCONJ
ejpam-1599	437	10	results	result	NOUN
ejpam-1599	437	11	relative	relative	ADJ
ejpam-1599	437	12	to	to	ADP
ejpam-1599	437	13	natural	natural	ADJ
ejpam-1599	437	14	invertiblity	invertiblity	NOUN
ejpam-1599	437	15	.	.	PUNCT
ejpam-1599	438	1	the	the	DET
ejpam-1599	438	2	shift	shift	NOUN
ejpam-1599	438	3	operator	operator	NOUN
ejpam-1599	438	4	let	let	VERB
ejpam-1599	438	5	s	s	PRON
ejpam-1599	438	6	be	be	AUX
ejpam-1599	438	7	the	the	DET
ejpam-1599	438	8	shift	shift	NOUN
ejpam-1599	438	9	operator	operator	NOUN
ejpam-1599	438	10	on	on	ADP
ejpam-1599	438	11	l2(n	l2(n	NOUN
ejpam-1599	438	12	)	)	PUNCT
ejpam-1599	438	13	.	.	PUNCT
ejpam-1599	439	1	then	then	ADV
ejpam-1599	439	2	s	s	VERB
ejpam-1599	439	3	is	be	AUX
ejpam-1599	439	4	not	not	PART
ejpam-1599	439	5	quasinilpotent	quasinilpotent	ADJ
ejpam-1599	439	6	,	,	PUNCT
ejpam-1599	439	7	but	but	CCONJ
ejpam-1599	439	8	its	its	PRON
ejpam-1599	439	9	hyperrange	hyperrange	NOUN
ejpam-1599	439	10	reduces	reduce	VERB
ejpam-1599	439	11	to	to	ADP
ejpam-1599	439	12	0	0	NUM
ejpam-1599	439	13	.	.	PUNCT
ejpam-1599	440	1	as	as	ADP
ejpam-1599	440	2	a	a	DET
ejpam-1599	440	3	consequence	consequence	NOUN
ejpam-1599	440	4	,	,	PUNCT
ejpam-1599	440	5	σ1(s	σ1(s	X
ejpam-1599	440	6	)	)	PUNCT
ejpam-1599	440	7	=	=	SYM
ejpam-1599	440	8	{	{	PUNCT
ejpam-1599	440	9	0	0	NUM
ejpam-1599	440	10	}	}	PUNCT
ejpam-1599	440	11	.	.	PUNCT
ejpam-1599	441	1	the	the	DET
ejpam-1599	441	2	spectrum	spectrum	NOUN
ejpam-1599	441	3	of	of	ADP
ejpam-1599	441	4	s	s	PROPN
ejpam-1599	441	5	is	be	AUX
ejpam-1599	441	6	the	the	DET
ejpam-1599	441	7	unit	unit	NOUN
ejpam-1599	441	8	disk	disk	NOUN
ejpam-1599	441	9	.	.	PUNCT
ejpam-1599	442	1	strongly	strongly	ADV
ejpam-1599	442	2	irreducible	irreducible	ADJ
ejpam-1599	442	3	operators	operator	NOUN
ejpam-1599	442	4	in	in	ADP
ejpam-1599	442	5	1972	1972	NUM
ejpam-1599	442	6	,	,	PUNCT
ejpam-1599	442	7	f.	f.	PROPN
ejpam-1599	442	8	gilfeather	gilfeather	NOUN
ejpam-1599	443	1	[	[	X
ejpam-1599	443	2	8	8	NUM
ejpam-1599	443	3	]	]	PUNCT
ejpam-1599	443	4	introduced	introduce	VERB
ejpam-1599	443	5	the	the	DET
ejpam-1599	443	6	concept	concept	NOUN
ejpam-1599	443	7	of	of	ADP
ejpam-1599	443	8	strongly	strongly	ADV
ejpam-1599	443	9	irreducible	irreducible	ADJ
ejpam-1599	443	10	operator	operator	NOUN
ejpam-1599	443	11	.	.	PUNCT
ejpam-1599	444	1	a	a	DET
ejpam-1599	444	2	bounded	bounded	ADJ
ejpam-1599	444	3	linear	linear	ADJ
ejpam-1599	444	4	operator	operator	NOUN
ejpam-1599	444	5	t	t	NOUN
ejpam-1599	444	6	is	be	AUX
ejpam-1599	444	7	said	say	VERB
ejpam-1599	444	8	to	to	PART
ejpam-1599	444	9	be	be	AUX
ejpam-1599	444	10	strongly	strongly	ADV
ejpam-1599	444	11	irreducible	irreducible	ADJ
ejpam-1599	444	12	,	,	PUNCT
ejpam-1599	444	13	if	if	SCONJ
ejpam-1599	444	14	there	there	PRON
ejpam-1599	444	15	exists	exist	VERB
ejpam-1599	444	16	no	no	DET
ejpam-1599	444	17	non	non	ADJ
ejpam-1599	444	18	-	-	ADJ
ejpam-1599	444	19	trivial	trivial	ADJ
ejpam-1599	444	20	idempotent	idempotent	NOUN
ejpam-1599	444	21	p	p	NOUN
ejpam-1599	444	22	in	in	ADP
ejpam-1599	444	23	the	the	DET
ejpam-1599	444	24	commutant	commutant	NOUN
ejpam-1599	444	25	of	of	ADP
ejpam-1599	444	26	t	t	PROPN
ejpam-1599	444	27	.	.	PUNCT
ejpam-1599	445	1	this	this	DET
ejpam-1599	445	2	concept	concept	NOUN
ejpam-1599	445	3	actually	actually	ADV
ejpam-1599	445	4	coincides	coincide	VERB
ejpam-1599	445	5	with	with	ADP
ejpam-1599	445	6	the	the	DET
ejpam-1599	445	7	concept	concept	NOUN
ejpam-1599	445	8	of	of	ADP
ejpam-1599	445	9	banach	banach	ADV
ejpam-1599	445	10	irreducible	irreducible	ADJ
ejpam-1599	445	11	operator	operator	NOUN
ejpam-1599	445	12	(	(	PUNCT
ejpam-1599	445	13	a	a	DET
ejpam-1599	445	14	bounded	bounded	ADJ
ejpam-1599	445	15	linear	linear	ADJ
ejpam-1599	445	16	operator	operator	NOUN
ejpam-1599	445	17	t	t	NOUN
ejpam-1599	445	18	is	be	AUX
ejpam-1599	445	19	said	say	VERB
ejpam-1599	445	20	to	to	PART
ejpam-1599	445	21	be	be	AUX
ejpam-1599	445	22	banach	banach	ADV
ejpam-1599	445	23	irreducible	irreducible	ADJ
ejpam-1599	445	24	,	,	PUNCT
ejpam-1599	445	25	if	if	SCONJ
ejpam-1599	445	26	t	t	PROPN
ejpam-1599	445	27	can	can	AUX
ejpam-1599	445	28	not	not	PART
ejpam-1599	445	29	be	be	AUX
ejpam-1599	445	30	written	write	VERB
ejpam-1599	445	31	as	as	ADP
ejpam-1599	445	32	a	a	DET
ejpam-1599	445	33	direct	direct	ADJ
ejpam-1599	445	34	sum	sum	NOUN
ejpam-1599	445	35	of	of	ADP
ejpam-1599	445	36	two	two	NUM
ejpam-1599	445	37	bounded	bounded	ADJ
ejpam-1599	445	38	linear	linear	PROPN
ejpam-1599	445	39	operators	operator	NOUN
ejpam-1599	445	40	)	)	PUNCT
ejpam-1599	445	41	.	.	PUNCT
ejpam-1599	446	1	it	it	PRON
ejpam-1599	446	2	is	be	AUX
ejpam-1599	446	3	clear	clear	ADJ
ejpam-1599	446	4	that	that	SCONJ
ejpam-1599	446	5	strongly	strongly	ADV
ejpam-1599	446	6	irreducible	irreducible	ADJ
ejpam-1599	446	7	operators	operator	NOUN
ejpam-1599	446	8	satisfy	satisfy	VERB
ejpam-1599	446	9	σ1(t	σ1(t	PUNCT
ejpam-1599	446	10	)	)	PUNCT
ejpam-1599	446	11	=	=	SYM
ejpam-1599	446	12	{	{	PUNCT
ejpam-1599	446	13	0	0	NUM
ejpam-1599	446	14	}	}	PUNCT
ejpam-1599	446	15	.	.	PUNCT
ejpam-1599	447	1	also	also	ADV
ejpam-1599	447	2	,	,	PUNCT
ejpam-1599	447	3	the	the	DET
ejpam-1599	447	4	following	follow	VERB
ejpam-1599	447	5	spectral	spectral	ADJ
ejpam-1599	447	6	result	result	NOUN
ejpam-1599	447	7	is	be	AUX
ejpam-1599	447	8	due	due	ADJ
ejpam-1599	447	9	to	to	ADP
ejpam-1599	447	10	herrero	herrero	PROPN
ejpam-1599	447	11	and	and	CCONJ
ejpam-1599	447	12	jiang	jiang	PROPN
ejpam-1599	448	1	[	[	X
ejpam-1599	448	2	13	13	NUM
ejpam-1599	448	3	]	]	NUM
ejpam-1599	448	4	:	:	PUNCT
ejpam-1599	448	5	theorem	theorem	VERB
ejpam-1599	448	6	13	13	NUM
ejpam-1599	448	7	.	.	PUNCT
ejpam-1599	449	1	σ(t	σ(t	PROPN
ejpam-1599	449	2	)	)	PUNCT
ejpam-1599	449	3	is	be	AUX
ejpam-1599	449	4	connected	connect	VERB
ejpam-1599	449	5	if	if	SCONJ
ejpam-1599	449	6	and	and	CCONJ
ejpam-1599	449	7	only	only	ADV
ejpam-1599	449	8	if	if	SCONJ
ejpam-1599	449	9	t	t	PROPN
ejpam-1599	449	10	is	be	AUX
ejpam-1599	449	11	in	in	ADP
ejpam-1599	449	12	the	the	DET
ejpam-1599	449	13	norm	norm	NOUN
ejpam-1599	449	14	closure	closure	NOUN
ejpam-1599	449	15	of	of	ADP
ejpam-1599	449	16	strongly	strongly	ADV
ejpam-1599	449	17	irreducible	irreducible	ADJ
ejpam-1599	449	18	operators	operator	NOUN
ejpam-1599	449	19	.	.	PUNCT
ejpam-1599	450	1	rosenblum	rosenblum	PROPN
ejpam-1599	450	2	’s	’s	PART
ejpam-1599	450	3	corollary	corollary	ADJ
ejpam-1599	450	4	,	,	PUNCT
ejpam-1599	450	5	commutant	commutant	ADJ
ejpam-1599	450	6	and	and	CCONJ
ejpam-1599	450	7	bicommutant	bicommutant	NOUN
ejpam-1599	450	8	let	let	AUX
ejpam-1599	450	9	t	t	PROPN
ejpam-1599	450	10	=	=	SYM
ejpam-1599	450	11	�	�	PROPN
ejpam-1599	450	12	x	x	SYM
ejpam-1599	450	13	0	0	NUM
ejpam-1599	450	14	0	0	NUM
ejpam-1599	450	15	y	y	PROPN
ejpam-1599	450	16	�	�	PROPN
ejpam-1599	450	17	be	be	AUX
ejpam-1599	450	18	the	the	DET
ejpam-1599	450	19	a	a	DET
ejpam-1599	450	20	decomposition	decomposition	NOUN
ejpam-1599	450	21	of	of	ADP
ejpam-1599	450	22	t	t	PROPN
ejpam-1599	450	23	with	with	ADP
ejpam-1599	450	24	x	x	SYM
ejpam-1599	450	25	invertible	invertible	ADJ
ejpam-1599	450	26	and	and	CCONJ
ejpam-1599	450	27	m	m	NOUN
ejpam-1599	450	28	=	=	ADJ
ejpam-1599	450	29	�	�	PROPN
ejpam-1599	450	30	x	x	PUNCT
ejpam-1599	451	1	x−1	x−1	NOUN
ejpam-1599	451	2	0	0	NUM
ejpam-1599	451	3	0	0	SYM
ejpam-1599	451	4	0	0	NUM
ejpam-1599	451	5	�	�	PROPN
ejpam-1599	451	6	the	the	DET
ejpam-1599	451	7	greatest	great	ADJ
ejpam-1599	451	8	element	element	NOUN
ejpam-1599	451	9	of	of	ADP
ejpam-1599	451	10	σ1(t	σ1(t	PROPN
ejpam-1599	451	11	)	)	PUNCT
ejpam-1599	451	12	.	.	PUNCT
ejpam-1599	452	1	if	if	SCONJ
ejpam-1599	452	2	σ(x	σ(x	PROPN
ejpam-1599	452	3	)	)	PUNCT
ejpam-1599	452	4	∩σ(y	∩σ(y	NOUN
ejpam-1599	452	5	)	)	PUNCT
ejpam-1599	453	1	=	=	PUNCT
ejpam-1599	453	2	{	{	PUNCT
ejpam-1599	453	3	0	0	NUM
ejpam-1599	453	4	}	}	PUNCT
ejpam-1599	453	5	,	,	PUNCT
ejpam-1599	453	6	then	then	ADV
ejpam-1599	453	7	by	by	ADP
ejpam-1599	453	8	rosenblum	rosenblum	PROPN
ejpam-1599	453	9	’s	’s	PART
ejpam-1599	453	10	corollary	corollary	NOUN
ejpam-1599	453	11	[	[	X
ejpam-1599	453	12	see	see	NOUN
ejpam-1599	453	13	23	23	NUM
ejpam-1599	453	14	]	]	PUNCT
ejpam-1599	453	15	,	,	PUNCT
ejpam-1599	453	16	�	�	PROPN
ejpam-1599	453	17	x	x	SYM
ejpam-1599	453	18	0	0	NUM
ejpam-1599	453	19	0	0	SYM
ejpam-1599	453	20	0	0	NUM
ejpam-1599	453	21	�	�	PROPN
ejpam-1599	453	22	,	,	PUNCT
ejpam-1599	453	23	�	�	PROPN
ejpam-1599	453	24	0	0	NUM
ejpam-1599	453	25	0	0	NUM
ejpam-1599	453	26	0	0	NUM
ejpam-1599	453	27	y	y	PROPN
ejpam-1599	453	28	�	�	PROPN
ejpam-1599	453	29	∈	∈	PROPN
ejpam-1599	453	30	{	{	PUNCT
ejpam-1599	453	31	t}′′	t}′′	PROPN
ejpam-1599	453	32	and	and	CCONJ
ejpam-1599	453	33	t	t	PROPN
ejpam-1599	453	34	=	=	SYM
ejpam-1599	453	35	�	�	PROPN
ejpam-1599	453	36	x	x	SYM
ejpam-1599	453	37	0	0	NUM
ejpam-1599	453	38	0	0	NUM
ejpam-1599	453	39	0	0	NUM
ejpam-1599	453	40	�	�	PROPN
ejpam-1599	453	41	+	+	CCONJ
ejpam-1599	453	42	�	�	PROPN
ejpam-1599	453	43	0	0	NUM
ejpam-1599	453	44	0	0	NUM
ejpam-1599	453	45	0	0	NUM
ejpam-1599	454	1	y	y	PROPN
ejpam-1599	454	2	�	�	PROPN
ejpam-1599	454	3	is	be	AUX
ejpam-1599	454	4	the	the	DET
ejpam-1599	454	5	natural	natural	ADJ
ejpam-1599	454	6	core	core	NOUN
ejpam-1599	454	7	decomposition	decomposition	NOUN
ejpam-1599	454	8	of	of	ADP
ejpam-1599	454	9	t	t	PROPN
ejpam-1599	454	10	,	,	PUNCT
ejpam-1599	454	11	with	with	ADP
ejpam-1599	454	12	m	m	PROPN
ejpam-1599	454	13	=	=	SYM
ejpam-1599	454	14	�	�	PROPN
ejpam-1599	454	15	x	x	PUNCT
ejpam-1599	454	16	x−1	x−1	NOUN
ejpam-1599	454	17	0	0	NUM
ejpam-1599	454	18	0	0	SYM
ejpam-1599	454	19	0	0	NUM
ejpam-1599	454	20	�	�	PROPN
ejpam-1599	454	21	the	the	DET
ejpam-1599	454	22	greatest	great	ADJ
ejpam-1599	454	23	element	element	NOUN
ejpam-1599	454	24	of	of	ADP
ejpam-1599	454	25	σ2(t	σ2(t	PROPN
ejpam-1599	454	26	)	)	PUNCT
ejpam-1599	454	27	.	.	PUNCT
ejpam-1599	455	1	this	this	PRON
ejpam-1599	455	2	is	be	AUX
ejpam-1599	455	3	the	the	DET
ejpam-1599	455	4	case	case	NOUN
ejpam-1599	455	5	for	for	ADP
ejpam-1599	455	6	instance	instance	NOUN
ejpam-1599	455	7	when	when	SCONJ
ejpam-1599	455	8	y	y	PROPN
ejpam-1599	455	9	is	be	AUX
ejpam-1599	455	10	quasinilpotent	quasinilpotent	NOUN
ejpam-1599	455	11	.	.	PUNCT
ejpam-1599	456	1	references	reference	NOUN
ejpam-1599	456	2	[	[	X
ejpam-1599	456	3	1	1	X
ejpam-1599	456	4	]	]	X
ejpam-1599	456	5	p	p	X
ejpam-1599	456	6	aiena	aiena	NOUN
ejpam-1599	456	7	.	.	PUNCT
ejpam-1599	457	1	fredholm	fredholm	NOUN
ejpam-1599	457	2	and	and	CCONJ
ejpam-1599	457	3	local	local	ADJ
ejpam-1599	457	4	spectral	spectral	ADJ
ejpam-1599	457	5	theory	theory	NOUN
ejpam-1599	457	6	,	,	PUNCT
ejpam-1599	457	7	with	with	ADP
ejpam-1599	457	8	applications	application	NOUN
ejpam-1599	457	9	to	to	ADP
ejpam-1599	457	10	multipliers	multiplier	NOUN
ejpam-1599	457	11	,	,	PUNCT
ejpam-1599	457	12	kluwer	kluwer	NOUN
ejpam-1599	457	13	academic	academic	ADJ
ejpam-1599	457	14	publishers	publisher	NOUN
ejpam-1599	457	15	2004	2004	NUM
ejpam-1599	457	16	.	.	PUNCT
ejpam-1599	458	1	[	[	X
ejpam-1599	458	2	2	2	X
ejpam-1599	458	3	]	]	PUNCT
ejpam-1599	458	4	a	a	DET
ejpam-1599	458	5	ben	ben	PROPN
ejpam-1599	458	6	israel	israel	PROPN
ejpam-1599	458	7	and	and	CCONJ
ejpam-1599	458	8	t	t	PROPN
ejpam-1599	458	9	greville	greville	NOUN
ejpam-1599	458	10	.	.	PUNCT
ejpam-1599	459	1	generalized	generalized	ADJ
ejpam-1599	459	2	inverses	inverse	NOUN
ejpam-1599	459	3	,	,	PUNCT
ejpam-1599	459	4	theory	theory	NOUN
ejpam-1599	459	5	and	and	CCONJ
ejpam-1599	459	6	applications	application	NOUN
ejpam-1599	459	7	,	,	PUNCT
ejpam-1599	459	8	2nd	2nd	PROPN
ejpam-1599	459	9	edition	edition	NOUN
ejpam-1599	459	10	,	,	PUNCT
ejpam-1599	459	11	springer	springer	NOUN
ejpam-1599	459	12	2003	2003	NUM
ejpam-1599	459	13	.	.	PUNCT
ejpam-1599	460	1	[	[	X
ejpam-1599	460	2	3	3	NUM
ejpam-1599	460	3	]	]	X
ejpam-1599	460	4	m	m	NOUN
ejpam-1599	460	5	dorofeeva	dorofeeva	NOUN
ejpam-1599	460	6	.	.	PUNCT
ejpam-1599	461	1	hereditary	hereditary	ADJ
ejpam-1599	461	2	and	and	CCONJ
ejpam-1599	461	3	semi	semi	ADJ
ejpam-1599	461	4	-	-	ADJ
ejpam-1599	461	5	hereditary	hereditary	ADJ
ejpam-1599	461	6	monoids	monoid	NOUN
ejpam-1599	461	7	,	,	PUNCT
ejpam-1599	461	8	semigroup	semigroup	PROPN
ejpam-1599	461	9	forum	forum	PROPN
ejpam-1599	461	10	4	4	NUM
ejpam-1599	461	11	,	,	PUNCT
ejpam-1599	461	12	301–311	301–311	NUM
ejpam-1599	461	13	.	.	PUNCT
ejpam-1599	461	14	1972	1972	NUM
ejpam-1599	461	15	.	.	PUNCT
ejpam-1599	462	1	references	reference	NOUN
ejpam-1599	462	2	173	173	NUM
ejpam-1599	463	1	[	[	X
ejpam-1599	463	2	4	4	NUM
ejpam-1599	463	3	]	]	X
ejpam-1599	463	4	m	m	VERB
ejpam-1599	463	5	drazin	drazin	NOUN
ejpam-1599	463	6	.	.	PUNCT
ejpam-1599	464	1	pseudo	pseudo	NOUN
ejpam-1599	464	2	-	-	NOUN
ejpam-1599	464	3	inverses	inverse	NOUN
ejpam-1599	464	4	in	in	ADP
ejpam-1599	464	5	associative	associative	ADJ
ejpam-1599	464	6	rings	ring	NOUN
ejpam-1599	464	7	and	and	CCONJ
ejpam-1599	464	8	semigroups	semigroup	NOUN
ejpam-1599	464	9	,	,	PUNCT
ejpam-1599	464	10	am	be	AUX
ejpam-1599	464	11	.	.	PUNCT
ejpam-1599	464	12	math	math	NOUN
ejpam-1599	464	13	.	.	PUNCT
ejpam-1599	465	1	monthly	monthly	ADJ
ejpam-1599	465	2	65	65	NUM
ejpam-1599	465	3	,	,	PUNCT
ejpam-1599	465	4	no	no	INTJ
ejpam-1599	465	5	.	.	NOUN
ejpam-1599	465	6	7	7	NUM
ejpam-1599	465	7	,	,	PUNCT
ejpam-1599	465	8	506–514	506–514	NUM
ejpam-1599	465	9	.	.	NOUN
ejpam-1599	465	10	1958	1958	NUM
ejpam-1599	465	11	.	.	PUNCT
ejpam-1599	466	1	[	[	X
ejpam-1599	466	2	5	5	NUM
ejpam-1599	466	3	]	]	SYM
ejpam-1599	466	4	m	m	VERB
ejpam-1599	466	5	drazin	drazin	NOUN
ejpam-1599	466	6	.	.	PUNCT
ejpam-1599	467	1	a	a	DET
ejpam-1599	467	2	class	class	NOUN
ejpam-1599	467	3	of	of	ADP
ejpam-1599	467	4	outer	outer	ADJ
ejpam-1599	467	5	generalized	generalize	VERB
ejpam-1599	467	6	inverses	inverse	NOUN
ejpam-1599	467	7	,	,	PUNCT
ejpam-1599	467	8	linear	linear	PROPN
ejpam-1599	467	9	algebra	algebra	NOUN
ejpam-1599	467	10	appl	appl	NOUN
ejpam-1599	467	11	.	.	PUNCT
ejpam-1599	468	1	436	436	NUM
ejpam-1599	468	2	,	,	PUNCT
ejpam-1599	468	3	no	no	INTJ
ejpam-1599	468	4	.	.	NOUN
ejpam-1599	468	5	7	7	NUM
ejpam-1599	468	6	,	,	PUNCT
ejpam-1599	468	7	1909	1909	NUM
ejpam-1599	468	8	–	–	PUNCT
ejpam-1599	468	9	1923	1923	NUM
ejpam-1599	468	10	.	.	PUNCT
ejpam-1599	469	1	2012	2012	NUM
ejpam-1599	469	2	.	.	PUNCT
ejpam-1599	470	1	[	[	X
ejpam-1599	470	2	6	6	NUM
ejpam-1599	470	3	]	]	PUNCT
ejpam-1599	470	4	j	j	PROPN
ejpam-1599	470	5	fountain	fountain	NOUN
ejpam-1599	470	6	.	.	PUNCT
ejpam-1599	471	1	right	right	INTJ
ejpam-1599	471	2	pp	pp	ADV
ejpam-1599	471	3	monoids	monoid	NOUN
ejpam-1599	471	4	with	with	ADP
ejpam-1599	471	5	central	central	ADJ
ejpam-1599	471	6	idempotents	idempotent	NOUN
ejpam-1599	471	7	,	,	PUNCT
ejpam-1599	471	8	semigroup	semigroup	PROPN
ejpam-1599	471	9	forum	forum	PROPN
ejpam-1599	471	10	13	13	NUM
ejpam-1599	471	11	,	,	PUNCT
ejpam-1599	471	12	no	no	INTJ
ejpam-1599	471	13	.	.	NOUN
ejpam-1599	471	14	3	3	NUM
ejpam-1599	471	15	,	,	PUNCT
ejpam-1599	471	16	229ű-237	229ű-237	NUM
ejpam-1599	471	17	.	.	NOUN
ejpam-1599	471	18	1977	1977	NUM
ejpam-1599	471	19	.	.	PUNCT
ejpam-1599	472	1	[	[	X
ejpam-1599	472	2	7	7	X
ejpam-1599	472	3	]	]	PUNCT
ejpam-1599	472	4	j	j	PROPN
ejpam-1599	472	5	fountain	fountain	NOUN
ejpam-1599	472	6	.	.	PUNCT
ejpam-1599	473	1	abundant	abundant	ADJ
ejpam-1599	473	2	semigroups	semigroup	NOUN
ejpam-1599	473	3	,	,	PUNCT
ejpam-1599	473	4	proc	proc	NOUN
ejpam-1599	473	5	.	.	PUNCT
ejpam-1599	474	1	london	london	PROPN
ejpam-1599	474	2	math	math	PROPN
ejpam-1599	474	3	.	.	PUNCT
ejpam-1599	475	1	soc	soc	PROPN
ejpam-1599	475	2	.	.	PUNCT
ejpam-1599	476	1	3	3	NUM
ejpam-1599	476	2	,	,	PUNCT
ejpam-1599	476	3	no	no	INTJ
ejpam-1599	476	4	.	.	NOUN
ejpam-1599	476	5	1	1	NUM
ejpam-1599	476	6	,	,	PUNCT
ejpam-1599	476	7	103–129	103–129	NUM
ejpam-1599	476	8	.	.	PUNCT
ejpam-1599	476	9	1982	1982	NUM
ejpam-1599	476	10	.	.	PUNCT
ejpam-1599	477	1	[	[	X
ejpam-1599	477	2	8	8	NUM
ejpam-1599	477	3	]	]	SYM
ejpam-1599	477	4	f	f	PROPN
ejpam-1599	477	5	gilfeather	gilfeather	NOUN
ejpam-1599	477	6	.	.	PUNCT
ejpam-1599	478	1	strong	strong	ADJ
ejpam-1599	478	2	reducibility	reducibility	NOUN
ejpam-1599	478	3	of	of	ADP
ejpam-1599	478	4	operators	operator	NOUN
ejpam-1599	478	5	,	,	PUNCT
ejpam-1599	478	6	indiana	indiana	PROPN
ejpam-1599	478	7	univ	univ	PROPN
ejpam-1599	478	8	.	.	PUNCT
ejpam-1599	479	1	math	math	PROPN
ejpam-1599	479	2	.	.	PUNCT
ejpam-1599	480	1	j.	j.	PROPN
ejpam-1599	480	2	22	22	NUM
ejpam-1599	480	3	,	,	PUNCT
ejpam-1599	480	4	393–397	393–397	NUM
ejpam-1599	480	5	.	.	NOUN
ejpam-1599	480	6	1972	1972	NUM
ejpam-1599	480	7	.	.	PUNCT
ejpam-1599	481	1	[	[	X
ejpam-1599	481	2	9	9	NUM
ejpam-1599	481	3	]	]	X
ejpam-1599	481	4	j	j	PROPN
ejpam-1599	481	5	green	green	PROPN
ejpam-1599	481	6	.	.	PUNCT
ejpam-1599	482	1	on	on	ADP
ejpam-1599	482	2	the	the	DET
ejpam-1599	482	3	structure	structure	NOUN
ejpam-1599	482	4	of	of	ADP
ejpam-1599	482	5	semigroups	semigroup	NOUN
ejpam-1599	482	6	,	,	PUNCT
ejpam-1599	482	7	ann	ann	PROPN
ejpam-1599	482	8	.	.	PROPN
ejpam-1599	482	9	of	of	ADP
ejpam-1599	482	10	math	math	NOUN
ejpam-1599	482	11	.	.	PUNCT
ejpam-1599	483	1	54	54	NUM
ejpam-1599	483	2	,	,	PUNCT
ejpam-1599	483	3	no	no	INTJ
ejpam-1599	483	4	.	.	NOUN
ejpam-1599	483	5	1	1	NUM
ejpam-1599	483	6	,	,	PUNCT
ejpam-1599	483	7	163–172	163–172	NUM
ejpam-1599	483	8	.	.	PUNCT
ejpam-1599	484	1	1951	1951	NUM
ejpam-1599	484	2	.	.	PUNCT
ejpam-1599	485	1	[	[	X
ejpam-1599	485	2	10	10	NUM
ejpam-1599	485	3	]	]	X
ejpam-1599	485	4	r	r	NOUN
ejpam-1599	485	5	harte	harte	NOUN
ejpam-1599	485	6	.	.	PUNCT
ejpam-1599	486	1	on	on	ADP
ejpam-1599	486	2	quasinilpotents	quasinilpotent	NOUN
ejpam-1599	486	3	in	in	ADP
ejpam-1599	486	4	rings	ring	NOUN
ejpam-1599	486	5	,	,	PUNCT
ejpam-1599	486	6	panamer	panamer	NOUN
ejpam-1599	486	7	.	.	PUNCT
ejpam-1599	486	8	math	math	PROPN
ejpam-1599	486	9	.	.	PUNCT
ejpam-1599	487	1	j.	j.	PROPN
ejpam-1599	487	2	1	1	PROPN
ejpam-1599	487	3	,	,	PUNCT
ejpam-1599	487	4	10–16	10–16	NUM
ejpam-1599	487	5	.	.	NOUN
ejpam-1599	487	6	1991	1991	NUM
ejpam-1599	487	7	.	.	PUNCT
ejpam-1599	488	1	[	[	X
ejpam-1599	488	2	11	11	NUM
ejpam-1599	488	3	]	]	X
ejpam-1599	488	4	d	d	X
ejpam-1599	488	5	kitson	kitson	PROPN
ejpam-1599	488	6	and	and	CCONJ
ejpam-1599	488	7	r	r	PROPN
ejpam-1599	488	8	harte	harte	NOUN
ejpam-1599	488	9	.	.	PUNCT
ejpam-1599	489	1	on	on	ADP
ejpam-1599	489	2	browder	browder	PROPN
ejpam-1599	489	3	tuples	tuples	PROPN
ejpam-1599	489	4	,	,	PUNCT
ejpam-1599	489	5	acta	acta	PROPN
ejpam-1599	489	6	sci	sci	PROPN
ejpam-1599	489	7	.	.	PUNCT
ejpam-1599	489	8	math	math	PROPN
ejpam-1599	489	9	.	.	PUNCT
ejpam-1599	490	1	75	75	NUM
ejpam-1599	490	2	,	,	PUNCT
ejpam-1599	490	3	no	no	INTJ
ejpam-1599	490	4	.	.	PUNCT
ejpam-1599	491	1	3–4	3–4	NUM
ejpam-1599	491	2	,	,	PUNCT
ejpam-1599	491	3	665–677	665–677	NUM
ejpam-1599	491	4	.	.	PUNCT
ejpam-1599	492	1	2009	2009	NUM
ejpam-1599	492	2	.	.	PUNCT
ejpam-1599	493	1	[	[	X
ejpam-1599	493	2	12	12	NUM
ejpam-1599	493	3	]	]	X
ejpam-1599	493	4	r	r	NOUN
ejpam-1599	493	5	harte	harte	NOUN
ejpam-1599	493	6	.	.	PUNCT
ejpam-1599	494	1	on	on	ADP
ejpam-1599	494	2	local	local	ADJ
ejpam-1599	494	3	spectral	spectral	ADJ
ejpam-1599	494	4	theory	theory	NOUN
ejpam-1599	494	5	,	,	PUNCT
ejpam-1599	494	6	recent	recent	ADJ
ejpam-1599	494	7	advances	advance	NOUN
ejpam-1599	494	8	in	in	ADP
ejpam-1599	494	9	operator	operator	NOUN
ejpam-1599	494	10	theory	theory	NOUN
ejpam-1599	494	11	and	and	CCONJ
ejpam-1599	494	12	applications	application	NOUN
ejpam-1599	494	13	175–183	175–183	NUM
ejpam-1599	494	14	,	,	PUNCT
ejpam-1599	494	15	oper	oper	NOUN
ejpam-1599	494	16	.	.	PROPN
ejpam-1599	494	17	theory	theory	PROPN
ejpam-1599	494	18	adv	adv	PROPN
ejpam-1599	494	19	.	.	PUNCT
ejpam-1599	494	20	appl	appl	PROPN
ejpam-1599	494	21	.	.	PROPN
ejpam-1599	494	22	,	,	PUNCT
ejpam-1599	494	23	187	187	NUM
ejpam-1599	494	24	,	,	PUNCT
ejpam-1599	494	25	birkhäuser	birkhäuser	NOUN
ejpam-1599	494	26	,	,	PUNCT
ejpam-1599	494	27	basel	basel	PROPN
ejpam-1599	494	28	,	,	PUNCT
ejpam-1599	494	29	2009	2009	NUM
ejpam-1599	494	30	.	.	PUNCT
ejpam-1599	495	1	[	[	X
ejpam-1599	495	2	13	13	NUM
ejpam-1599	495	3	]	]	X
ejpam-1599	495	4	d	d	X
ejpam-1599	495	5	herrero	herrero	PROPN
ejpam-1599	495	6	and	and	CCONJ
ejpam-1599	495	7	c	c	PROPN
ejpam-1599	495	8	jiang	jiang	PROPN
ejpam-1599	495	9	.	.	PUNCT
ejpam-1599	496	1	limits	limit	NOUN
ejpam-1599	496	2	of	of	ADP
ejpam-1599	496	3	strongly	strongly	ADV
ejpam-1599	496	4	irreducible	irreducible	ADJ
ejpam-1599	496	5	operators	operator	NOUN
ejpam-1599	496	6	,	,	PUNCT
ejpam-1599	496	7	and	and	CCONJ
ejpam-1599	496	8	the	the	DET
ejpam-1599	496	9	riesz	riesz	PROPN
ejpam-1599	496	10	decomposition	decomposition	NOUN
ejpam-1599	496	11	theorem	theorem	NOUN
ejpam-1599	496	12	,	,	PUNCT
ejpam-1599	496	13	michigan	michigan	PROPN
ejpam-1599	496	14	math	math	PROPN
ejpam-1599	496	15	.	.	PUNCT
ejpam-1599	497	1	j.	j.	PROPN
ejpam-1599	497	2	37	37	PROPN
ejpam-1599	497	3	,	,	PUNCT
ejpam-1599	497	4	no	no	INTJ
ejpam-1599	497	5	.	.	NOUN
ejpam-1599	497	6	2	2	NUM
ejpam-1599	497	7	,	,	PUNCT
ejpam-1599	497	8	283–291	283–291	NUM
ejpam-1599	497	9	.	.	PUNCT
ejpam-1599	497	10	1990	1990	NUM
ejpam-1599	497	11	.	.	PUNCT
ejpam-1599	498	1	[	[	X
ejpam-1599	498	2	14	14	NUM
ejpam-1599	498	3	]	]	X
ejpam-1599	498	4	g	g	PROPN
ejpam-1599	498	5	hile	hile	NOUN
ejpam-1599	498	6	and	and	CCONJ
ejpam-1599	498	7	w	w	NOUN
ejpam-1599	498	8	pfaffenberger	pfaffenberger	ADV
ejpam-1599	498	9	.	.	PUNCT
ejpam-1599	499	1	generalized	generalized	ADJ
ejpam-1599	499	2	spectral	spectral	ADJ
ejpam-1599	499	3	theory	theory	NOUN
ejpam-1599	499	4	in	in	ADP
ejpam-1599	499	5	complex	complex	ADJ
ejpam-1599	499	6	banach	banach	NOUN
ejpam-1599	499	7	algebras	algebra	NOUN
ejpam-1599	499	8	,	,	PUNCT
ejpam-1599	499	9	canad	canad	PROPN
ejpam-1599	499	10	.	.	PUNCT
ejpam-1599	500	1	j.	j.	PROPN
ejpam-1599	500	2	math	math	PROPN
ejpam-1599	500	3	.	.	PUNCT
ejpam-1599	501	1	37	37	NUM
ejpam-1599	501	2	,	,	PUNCT
ejpam-1599	501	3	no	no	INTJ
ejpam-1599	501	4	.	.	NOUN
ejpam-1599	501	5	6	6	NUM
ejpam-1599	501	6	,	,	PUNCT
ejpam-1599	501	7	1211–1236	1211–1236	NUM
ejpam-1599	501	8	.	.	PUNCT
ejpam-1599	501	9	1985	1985	NUM
ejpam-1599	501	10	.	.	PUNCT
ejpam-1599	502	1	[	[	X
ejpam-1599	502	2	15	15	NUM
ejpam-1599	502	3	]	]	X
ejpam-1599	502	4	g	g	NOUN
ejpam-1599	502	5	hile	hile	NOUN
ejpam-1599	502	6	and	and	CCONJ
ejpam-1599	502	7	w	w	NOUN
ejpam-1599	502	8	pfaffenberger	pfaffenberger	ADV
ejpam-1599	502	9	.	.	PUNCT
ejpam-1599	503	1	idempotents	idempotent	NOUN
ejpam-1599	503	2	in	in	ADP
ejpam-1599	503	3	complex	complex	ADJ
ejpam-1599	503	4	banach	banach	NOUN
ejpam-1599	503	5	algebras	algebra	NOUN
ejpam-1599	503	6	,	,	PUNCT
ejpam-1599	503	7	canad	canad	PROPN
ejpam-1599	503	8	.	.	PUNCT
ejpam-1599	504	1	j.	j.	PROPN
ejpam-1599	504	2	math	math	PROPN
ejpam-1599	504	3	.	.	PUNCT
ejpam-1599	505	1	39	39	NUM
ejpam-1599	505	2	,	,	PUNCT
ejpam-1599	505	3	no	no	INTJ
ejpam-1599	505	4	.	.	NOUN
ejpam-1599	505	5	3	3	NUM
ejpam-1599	505	6	,	,	PUNCT
ejpam-1599	505	7	625–630	625–630	NUM
ejpam-1599	505	8	.	.	PUNCT
ejpam-1599	506	1	1987	1987	NUM
ejpam-1599	506	2	.	.	PUNCT
ejpam-1599	507	1	[	[	X
ejpam-1599	507	2	16	16	NUM
ejpam-1599	507	3	]	]	X
ejpam-1599	507	4	j	j	PROPN
ejpam-1599	507	5	koliha	koliha	VERB
ejpam-1599	507	6	.	.	PUNCT
ejpam-1599	508	1	a	a	DET
ejpam-1599	508	2	generalized	generalized	ADJ
ejpam-1599	508	3	drazin	drazin	NOUN
ejpam-1599	508	4	inverse	inverse	NOUN
ejpam-1599	508	5	,	,	PUNCT
ejpam-1599	508	6	glasgow	glasgow	NOUN
ejpam-1599	508	7	math	math	NOUN
ejpam-1599	508	8	.	.	PUNCT
ejpam-1599	509	1	j.	j.	PROPN
ejpam-1599	509	2	38	38	PROPN
ejpam-1599	509	3	,	,	PUNCT
ejpam-1599	509	4	no	no	INTJ
ejpam-1599	509	5	.	.	NOUN
ejpam-1599	509	6	3	3	NUM
ejpam-1599	509	7	,	,	PUNCT
ejpam-1599	509	8	367–381	367–381	NUM
ejpam-1599	509	9	.	.	NOUN
ejpam-1599	509	10	1996	1996	NUM
ejpam-1599	509	11	.	.	PUNCT
ejpam-1599	510	1	[	[	X
ejpam-1599	510	2	17	17	NUM
ejpam-1599	510	3	]	]	X
ejpam-1599	510	4	j	j	PROPN
ejpam-1599	510	5	koliha	koliha	VERB
ejpam-1599	510	6	and	and	CCONJ
ejpam-1599	510	7	p	p	PROPN
ejpam-1599	510	8	patricio	patricio	NOUN
ejpam-1599	510	9	.	.	PUNCT
ejpam-1599	511	1	elements	element	NOUN
ejpam-1599	511	2	of	of	ADP
ejpam-1599	511	3	rings	ring	NOUN
ejpam-1599	511	4	with	with	ADP
ejpam-1599	511	5	equal	equal	ADJ
ejpam-1599	511	6	spectral	spectral	ADJ
ejpam-1599	511	7	idempotents	idempotent	NOUN
ejpam-1599	511	8	,	,	PUNCT
ejpam-1599	511	9	j.	j.	PROPN
ejpam-1599	511	10	austral	austral	PROPN
ejpam-1599	511	11	.	.	PUNCT
ejpam-1599	512	1	math	math	NOUN
ejpam-1599	512	2	.	.	PUNCT
ejpam-1599	513	1	soc	soc	PROPN
ejpam-1599	513	2	.	.	PUNCT
ejpam-1599	514	1	72	72	NUM
ejpam-1599	514	2	,	,	PUNCT
ejpam-1599	514	3	137–152	137–152	NUM
ejpam-1599	514	4	.	.	PUNCT
ejpam-1599	515	1	2002	2002	NUM
ejpam-1599	515	2	.	.	PUNCT
ejpam-1599	516	1	[	[	X
ejpam-1599	516	2	18	18	NUM
ejpam-1599	516	3	]	]	X
ejpam-1599	516	4	x	x	SYM
ejpam-1599	516	5	mary	mary	PROPN
ejpam-1599	516	6	.	.	PUNCT
ejpam-1599	517	1	on	on	ADP
ejpam-1599	517	2	generalized	generalize	VERB
ejpam-1599	517	3	inverses	inverse	NOUN
ejpam-1599	517	4	and	and	CCONJ
ejpam-1599	517	5	green	green	PROPN
ejpam-1599	517	6	’s	’s	PART
ejpam-1599	517	7	relations	relation	NOUN
ejpam-1599	517	8	,	,	PUNCT
ejpam-1599	517	9	linear	linear	PROPN
ejpam-1599	517	10	algebra	algebra	PROPN
ejpam-1599	517	11	appl	appl	NOUN
ejpam-1599	517	12	.	.	PROPN
ejpam-1599	517	13	434	434	NUM
ejpam-1599	517	14	,	,	PUNCT
ejpam-1599	517	15	no	no	INTJ
ejpam-1599	517	16	.	.	NOUN
ejpam-1599	517	17	8	8	NUM
ejpam-1599	517	18	,	,	PUNCT
ejpam-1599	517	19	1836–1844	1836–1844	NUM
ejpam-1599	517	20	.	.	PUNCT
ejpam-1599	517	21	2011	2011	NUM
ejpam-1599	517	22	.	.	PUNCT
ejpam-1599	518	1	[	[	X
ejpam-1599	518	2	19	19	NUM
ejpam-1599	518	3	]	]	X
ejpam-1599	518	4	x	x	PART
ejpam-1599	518	5	mary	mary	PROPN
ejpam-1599	518	6	and	and	CCONJ
ejpam-1599	518	7	p	p	PROPN
ejpam-1599	518	8	patricio	patricio	PROPN
ejpam-1599	518	9	.	.	PUNCT
ejpam-1599	519	1	generalized	generalized	ADJ
ejpam-1599	519	2	invertibilty	invertibilty	NOUN
ejpam-1599	519	3	modulo	modulo	PROPN
ejpam-1599	519	4	h	h	NOUN
ejpam-1599	519	5	in	in	ADP
ejpam-1599	519	6	semigroups	semigroup	NOUN
ejpam-1599	519	7	and	and	CCONJ
ejpam-1599	519	8	rings	ring	NOUN
ejpam-1599	519	9	,	,	PUNCT
ejpam-1599	519	10	to	to	PART
ejpam-1599	519	11	appear	appear	VERB
ejpam-1599	519	12	.	.	PUNCT
ejpam-1599	520	1	[	[	X
ejpam-1599	520	2	20	20	NUM
ejpam-1599	520	3	]	]	X
ejpam-1599	520	4	m	m	VERB
ejpam-1599	520	5	gonzalez	gonzalez	PROPN
ejpam-1599	520	6	,	,	PUNCT
ejpam-1599	520	7	m	m	PROPN
ejpam-1599	520	8	mbekhta	mbekhta	PROPN
ejpam-1599	520	9	and	and	CCONJ
ejpam-1599	520	10	m	m	VERB
ejpam-1599	520	11	oudghiri	oudghiri	NOUN
ejpam-1599	520	12	.	.	PUNCT
ejpam-1599	521	1	on	on	ADP
ejpam-1599	521	2	the	the	DET
ejpam-1599	521	3	isolated	isolated	ADJ
ejpam-1599	521	4	points	point	NOUN
ejpam-1599	521	5	of	of	ADP
ejpam-1599	521	6	the	the	DET
ejpam-1599	521	7	surjective	surjective	ADJ
ejpam-1599	521	8	spectrum	spectrum	NOUN
ejpam-1599	521	9	of	of	ADP
ejpam-1599	521	10	a	a	DET
ejpam-1599	521	11	bounded	bounded	ADJ
ejpam-1599	521	12	operator	operator	NOUN
ejpam-1599	521	13	,	,	PUNCT
ejpam-1599	521	14	proc	proc	NOUN
ejpam-1599	521	15	.	.	PUNCT
ejpam-1599	522	1	amer	amer	PROPN
ejpam-1599	522	2	.	.	PUNCT
ejpam-1599	522	3	math	math	PROPN
ejpam-1599	522	4	.	.	PUNCT
ejpam-1599	523	1	soc	soc	PROPN
ejpam-1599	523	2	.	.	PUNCT
ejpam-1599	524	1	136	136	NUM
ejpam-1599	524	2	,	,	PUNCT
ejpam-1599	524	3	no	no	INTJ
ejpam-1599	524	4	.	.	NOUN
ejpam-1599	524	5	10	10	NUM
ejpam-1599	524	6	,	,	PUNCT
ejpam-1599	524	7	3521–3528	3521–3528	NUM
ejpam-1599	524	8	.	.	PUNCT
ejpam-1599	524	9	2008	2008	NUM
ejpam-1599	524	10	.	.	PUNCT
ejpam-1599	525	1	[	[	X
ejpam-1599	525	2	21	21	NUM
ejpam-1599	525	3	]	]	X
ejpam-1599	525	4	m	m	VERB
ejpam-1599	525	5	mbekhta	mbekhta	PROPN
ejpam-1599	525	6	.	.	PUNCT
ejpam-1599	526	1	généralisation	généralisation	PROPN
ejpam-1599	526	2	de	de	PROPN
ejpam-1599	526	3	la	la	PROPN
ejpam-1599	526	4	décomposition	décomposition	PROPN
ejpam-1599	526	5	de	de	PROPN
ejpam-1599	526	6	kato	kato	PROPN
ejpam-1599	526	7	aux	aux	PROPN
ejpam-1599	526	8	opérateurs	opérateur	VERB
ejpam-1599	526	9	paranormaux	paranormaux	PROPN
ejpam-1599	526	10	et	et	PROPN
ejpam-1599	526	11	spectraux	spectraux	NOUN
ejpam-1599	526	12	,	,	PUNCT
ejpam-1599	526	13	glasgow	glasgow	PROPN
ejpam-1599	526	14	math	math	NOUN
ejpam-1599	526	15	.	.	PUNCT
ejpam-1599	527	1	j.	j.	PROPN
ejpam-1599	527	2	29	29	PROPN
ejpam-1599	527	3	,	,	PUNCT
ejpam-1599	527	4	no	no	INTJ
ejpam-1599	527	5	.	.	NOUN
ejpam-1599	527	6	2	2	NUM
ejpam-1599	527	7	,	,	PUNCT
ejpam-1599	527	8	159–175	159–175	NUM
ejpam-1599	527	9	.	.	PUNCT
ejpam-1599	527	10	1987	1987	NUM
ejpam-1599	527	11	.	.	PUNCT
ejpam-1599	528	1	[	[	X
ejpam-1599	528	2	22	22	NUM
ejpam-1599	528	3	]	]	X
ejpam-1599	528	4	d	d	X
ejpam-1599	528	5	miller	miller	PROPN
ejpam-1599	528	6	and	and	CCONJ
ejpam-1599	528	7	a	a	DET
ejpam-1599	528	8	clifford	clifford	PROPN
ejpam-1599	528	9	.	.	PUNCT
ejpam-1599	529	1	regular	regular	ADJ
ejpam-1599	529	2	d	d	NOUN
ejpam-1599	529	3	-	-	PUNCT
ejpam-1599	529	4	classes	class	NOUN
ejpam-1599	529	5	in	in	ADP
ejpam-1599	529	6	semigroups	semigroup	NOUN
ejpam-1599	529	7	,	,	PUNCT
ejpam-1599	529	8	trans	trans	PROPN
ejpam-1599	529	9	.	.	PROPN
ejpam-1599	530	1	amer	amer	PROPN
ejpam-1599	530	2	.	.	PUNCT
ejpam-1599	530	3	math	math	PROPN
ejpam-1599	530	4	.	.	PUNCT
ejpam-1599	531	1	soc	soc	PROPN
ejpam-1599	531	2	.	.	PUNCT
ejpam-1599	532	1	82	82	NUM
ejpam-1599	532	2	,	,	PUNCT
ejpam-1599	532	3	no	no	INTJ
ejpam-1599	532	4	.	.	NOUN
ejpam-1599	532	5	1	1	NUM
ejpam-1599	532	6	,	,	PUNCT
ejpam-1599	532	7	270–280	270–280	NUM
ejpam-1599	532	8	.	.	PUNCT
ejpam-1599	533	1	1956	1956	NUM
ejpam-1599	533	2	.	.	PUNCT
ejpam-1599	534	1	[	[	X
ejpam-1599	534	2	23	23	NUM
ejpam-1599	534	3	]	]	PUNCT
ejpam-1599	534	4	h	h	NOUN
ejpam-1599	534	5	radjavi	radjavi	VERB
ejpam-1599	534	6	and	and	CCONJ
ejpam-1599	534	7	p	p	NOUN
ejpam-1599	534	8	rosenthal	rosenthal	NOUN
ejpam-1599	534	9	.	.	PUNCT
ejpam-1599	535	1	invariants	invariants	PROPN
ejpam-1599	535	2	subspaces	subspace	NOUN
ejpam-1599	535	3	,	,	PUNCT
ejpam-1599	535	4	springer	springer	NOUN
ejpam-1599	535	5	-	-	PUNCT
ejpam-1599	535	6	verlag	verlag	PROPN
ejpam-1599	535	7	,	,	PUNCT
ejpam-1599	535	8	berlin	berlin	PROPN
ejpam-1599	535	9	,	,	PUNCT
ejpam-1599	535	10	1973	1973	NUM
ejpam-1599	535	11	.	.	PUNCT