id	sid	tid	token	lemma	pos
ejpam-1528	1	1	european	european	PROPN
ejpam-1528	1	2	journal	journal	PROPN
ejpam-1528	1	3	of	of	ADP
ejpam-1528	1	4	pure	pure	ADJ
ejpam-1528	1	5	and	and	CCONJ
ejpam-1528	1	6	applied	apply	VERB
ejpam-1528	1	7	mathematics	mathematic	NOUN
ejpam-1528	1	8	vol	vol	NOUN
ejpam-1528	1	9	.	.	PROPN
ejpam-1528	2	1	6	6	NUM
ejpam-1528	2	2	,	,	PUNCT
ejpam-1528	2	3	no	no	INTJ
ejpam-1528	2	4	.	.	NOUN
ejpam-1528	2	5	4	4	NUM
ejpam-1528	2	6	,	,	PUNCT
ejpam-1528	2	7	2013	2013	NUM
ejpam-1528	2	8	,	,	PUNCT
ejpam-1528	2	9	413	413	NUM
ejpam-1528	2	10	-	-	SYM
ejpam-1528	2	11	427	427	NUM
ejpam-1528	2	12	issn	issn	PROPN
ejpam-1528	2	13	1307	1307	NUM
ejpam-1528	2	14	-	-	SYM
ejpam-1528	2	15	5543	5543	NUM
ejpam-1528	2	16	–	–	PUNCT
ejpam-1528	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-1528	2	18	natural	natural	ADJ
ejpam-1528	2	19	generalized	generalized	ADJ
ejpam-1528	2	20	inverse	inverse	NOUN
ejpam-1528	2	21	and	and	CCONJ
ejpam-1528	2	22	core	core	NOUN
ejpam-1528	2	23	of	of	ADP
ejpam-1528	2	24	an	an	DET
ejpam-1528	2	25	element	element	NOUN
ejpam-1528	2	26	in	in	ADP
ejpam-1528	2	27	semigroups	semigroup	NOUN
ejpam-1528	2	28	,	,	PUNCT
ejpam-1528	2	29	rings	ring	NOUN
ejpam-1528	2	30	and	and	CCONJ
ejpam-1528	2	31	banach	banach	NOUN
ejpam-1528	2	32	and	and	CCONJ
ejpam-1528	2	33	operator	operator	NOUN
ejpam-1528	2	34	algebras	algebras	PROPN
ejpam-1528	2	35	xavier	xavier	PROPN
ejpam-1528	2	36	mary	mary	PROPN
ejpam-1528	2	37	université	université	PROPN
ejpam-1528	2	38	paris	paris	PROPN
ejpam-1528	2	39	-	-	PUNCT
ejpam-1528	2	40	ouest	ouest	PROPN
ejpam-1528	2	41	nanterre	nanterre	PROPN
ejpam-1528	2	42	-	-	PUNCT
ejpam-1528	2	43	la	la	X
ejpam-1528	2	44	défense	défense	PROPN
ejpam-1528	2	45	,	,	PUNCT
ejpam-1528	2	46	laboratoire	laboratoire	PROPN
ejpam-1528	2	47	modal’x	modal’x	PROPN
ejpam-1528	2	48	abstract	abstract	NOUN
ejpam-1528	2	49	.	.	PUNCT
ejpam-1528	3	1	using	use	VERB
ejpam-1528	3	2	the	the	DET
ejpam-1528	3	3	recent	recent	ADJ
ejpam-1528	3	4	notion	notion	NOUN
ejpam-1528	3	5	of	of	ADP
ejpam-1528	3	6	inverse	inverse	NOUN
ejpam-1528	3	7	along	along	ADP
ejpam-1528	3	8	an	an	DET
ejpam-1528	3	9	element	element	NOUN
ejpam-1528	3	10	in	in	ADP
ejpam-1528	3	11	a	a	DET
ejpam-1528	3	12	semigroup	semigroup	NOUN
ejpam-1528	3	13	,	,	PUNCT
ejpam-1528	3	14	and	and	CCONJ
ejpam-1528	3	15	the	the	DET
ejpam-1528	3	16	natural	natural	ADJ
ejpam-1528	3	17	partial	partial	ADJ
ejpam-1528	3	18	order	order	NOUN
ejpam-1528	3	19	on	on	ADP
ejpam-1528	3	20	idempotents	idempotent	NOUN
ejpam-1528	3	21	,	,	PUNCT
ejpam-1528	3	22	we	we	PRON
ejpam-1528	3	23	study	study	VERB
ejpam-1528	3	24	bicommuting	bicommute	VERB
ejpam-1528	3	25	generalized	generalize	VERB
ejpam-1528	3	26	inverses	inverse	NOUN
ejpam-1528	3	27	and	and	CCONJ
ejpam-1528	3	28	define	define	VERB
ejpam-1528	3	29	a	a	DET
ejpam-1528	3	30	new	new	ADJ
ejpam-1528	3	31	inverse	inverse	NOUN
ejpam-1528	3	32	called	call	VERB
ejpam-1528	3	33	natural	natural	ADJ
ejpam-1528	3	34	inverse	inverse	NOUN
ejpam-1528	3	35	,	,	PUNCT
ejpam-1528	3	36	that	that	PRON
ejpam-1528	3	37	generalizes	generalize	VERB
ejpam-1528	3	38	the	the	DET
ejpam-1528	3	39	drazin	drazin	PROPN
ejpam-1528	3	40	inverse	inverse	NOUN
ejpam-1528	3	41	in	in	ADP
ejpam-1528	3	42	a	a	DET
ejpam-1528	3	43	semigroup	semigroup	NOUN
ejpam-1528	3	44	,	,	PUNCT
ejpam-1528	3	45	but	but	CCONJ
ejpam-1528	3	46	also	also	ADV
ejpam-1528	3	47	the	the	DET
ejpam-1528	3	48	koliha	koliha	VERB
ejpam-1528	3	49	-	-	PUNCT
ejpam-1528	3	50	drazin	drazin	NOUN
ejpam-1528	3	51	inverse	inverse	NOUN
ejpam-1528	3	52	in	in	ADP
ejpam-1528	3	53	a	a	DET
ejpam-1528	3	54	ring	ring	NOUN
ejpam-1528	3	55	.	.	PUNCT
ejpam-1528	4	1	in	in	ADP
ejpam-1528	4	2	this	this	DET
ejpam-1528	4	3	setting	setting	NOUN
ejpam-1528	4	4	we	we	PRON
ejpam-1528	4	5	get	get	VERB
ejpam-1528	4	6	a	a	DET
ejpam-1528	4	7	core	core	NOUN
ejpam-1528	4	8	decomposition	decomposition	NOUN
ejpam-1528	4	9	similar	similar	ADJ
ejpam-1528	4	10	to	to	ADP
ejpam-1528	4	11	the	the	DET
ejpam-1528	4	12	nilpotent	nilpotent	NOUN
ejpam-1528	4	13	,	,	PUNCT
ejpam-1528	4	14	kato	kato	PROPN
ejpam-1528	4	15	or	or	CCONJ
ejpam-1528	4	16	mbekhta	mbekhta	PROPN
ejpam-1528	4	17	decompositions	decomposition	NOUN
ejpam-1528	4	18	.	.	PUNCT
ejpam-1528	5	1	in	in	ADP
ejpam-1528	5	2	banach	banach	NOUN
ejpam-1528	5	3	and	and	CCONJ
ejpam-1528	5	4	operator	operator	NOUN
ejpam-1528	5	5	algebras	algebra	NOUN
ejpam-1528	5	6	,	,	PUNCT
ejpam-1528	5	7	we	we	PRON
ejpam-1528	5	8	show	show	VERB
ejpam-1528	5	9	that	that	SCONJ
ejpam-1528	5	10	the	the	DET
ejpam-1528	5	11	study	study	NOUN
ejpam-1528	5	12	of	of	ADP
ejpam-1528	5	13	the	the	DET
ejpam-1528	5	14	spectrum	spectrum	NOUN
ejpam-1528	5	15	is	be	AUX
ejpam-1528	5	16	not	not	PART
ejpam-1528	5	17	sufficient	sufficient	ADJ
ejpam-1528	5	18	,	,	PUNCT
ejpam-1528	5	19	and	and	CCONJ
ejpam-1528	5	20	use	use	VERB
ejpam-1528	5	21	ideas	idea	NOUN
ejpam-1528	5	22	from	from	ADP
ejpam-1528	5	23	local	local	ADJ
ejpam-1528	5	24	spectral	spectral	ADJ
ejpam-1528	5	25	theory	theory	NOUN
ejpam-1528	5	26	to	to	PART
ejpam-1528	5	27	study	study	VERB
ejpam-1528	5	28	this	this	DET
ejpam-1528	5	29	new	new	ADJ
ejpam-1528	5	30	inverse	inverse	NOUN
ejpam-1528	5	31	.	.	PUNCT
ejpam-1528	6	1	2010	2010	NUM
ejpam-1528	6	2	mathematics	mathematic	NOUN
ejpam-1528	6	3	subject	subject	NOUN
ejpam-1528	6	4	classifications	classification	NOUN
ejpam-1528	6	5	:	:	PUNCT
ejpam-1528	6	6	15a09	15a09	NUM
ejpam-1528	6	7	,	,	PUNCT
ejpam-1528	6	8	47a05	47a05	NUM
ejpam-1528	6	9	,	,	PUNCT
ejpam-1528	6	10	47a11	47a11	ADJ
ejpam-1528	6	11	key	key	ADJ
ejpam-1528	6	12	words	word	NOUN
ejpam-1528	6	13	and	and	CCONJ
ejpam-1528	6	14	phrases	phrase	NOUN
ejpam-1528	6	15	:	:	PUNCT
ejpam-1528	6	16	generalized	generalized	ADJ
ejpam-1528	6	17	inverses	inverse	NOUN
ejpam-1528	6	18	,	,	PUNCT
ejpam-1528	6	19	koliha	koliha	ADJ
ejpam-1528	6	20	-	-	PUNCT
ejpam-1528	6	21	drazin	drazin	PROPN
ejpam-1528	6	22	inverse	inverse	NOUN
ejpam-1528	6	23	1	1	NUM
ejpam-1528	6	24	.	.	PUNCT
ejpam-1528	7	1	introduction	introduction	NOUN
ejpam-1528	7	2	in	in	ADP
ejpam-1528	7	3	this	this	DET
ejpam-1528	7	4	paper	paper	NOUN
ejpam-1528	7	5	,	,	PUNCT
ejpam-1528	7	6	s	s	X
ejpam-1528	7	7	,	,	PUNCT
ejpam-1528	7	8	r	r	NOUN
ejpam-1528	7	9	and	and	CCONJ
ejpam-1528	7	10	a	a	DET
ejpam-1528	7	11	denote	denote	NOUN
ejpam-1528	7	12	respectively	respectively	ADV
ejpam-1528	7	13	a	a	DET
ejpam-1528	7	14	semigroup	semigroup	NOUN
ejpam-1528	7	15	,	,	PUNCT
ejpam-1528	7	16	a	a	DET
ejpam-1528	7	17	unital	unital	ADJ
ejpam-1528	7	18	ring	ring	NOUN
ejpam-1528	7	19	and	and	CCONJ
ejpam-1528	7	20	a	a	DET
ejpam-1528	7	21	unital	unital	ADJ
ejpam-1528	7	22	banach	banach	NOUN
ejpam-1528	7	23	algebra	algebra	NOUN
ejpam-1528	7	24	.	.	PUNCT
ejpam-1528	8	1	in	in	ADP
ejpam-1528	8	2	particular	particular	ADJ
ejpam-1528	8	3	,	,	PUNCT
ejpam-1528	8	4	r	r	NOUN
ejpam-1528	8	5	and	and	CCONJ
ejpam-1528	8	6	a	a	PRON
ejpam-1528	8	7	with	with	ADP
ejpam-1528	8	8	only	only	ADV
ejpam-1528	8	9	their	their	PRON
ejpam-1528	8	10	multiplication	multiplication	NOUN
ejpam-1528	8	11	structure	structure	NOUN
ejpam-1528	8	12	will	will	AUX
ejpam-1528	8	13	be	be	AUX
ejpam-1528	8	14	considered	consider	VERB
ejpam-1528	8	15	as	as	ADP
ejpam-1528	8	16	semigroups	semigroup	NOUN
ejpam-1528	8	17	.	.	PUNCT
ejpam-1528	9	1	for	for	ADP
ejpam-1528	9	2	any	any	DET
ejpam-1528	9	3	semigroup	semigroup	ADJ
ejpam-1528	9	4	s	s	NOUN
ejpam-1528	9	5	,	,	PUNCT
ejpam-1528	9	6	s1	s1	PROPN
ejpam-1528	9	7	denotes	denote	VERB
ejpam-1528	9	8	the	the	DET
ejpam-1528	9	9	monoid	monoid	NOUN
ejpam-1528	9	10	generated	generate	VERB
ejpam-1528	9	11	by	by	ADP
ejpam-1528	9	12	s	s	PROPN
ejpam-1528	9	13	(	(	PUNCT
ejpam-1528	10	1	r1	r1	NOUN
ejpam-1528	10	2	=	=	SYM
ejpam-1528	10	3	r	r	NOUN
ejpam-1528	10	4	,	,	PUNCT
ejpam-1528	10	5	a	a	DET
ejpam-1528	10	6	1	1	NUM
ejpam-1528	10	7	=	=	NOUN
ejpam-1528	10	8	a	a	PRON
ejpam-1528	10	9	)	)	PUNCT
ejpam-1528	10	10	.	.	PUNCT
ejpam-1528	11	1	e(s	e(s	PROPN
ejpam-1528	11	2	)	)	PUNCT
ejpam-1528	11	3	denotes	denote	VERB
ejpam-1528	11	4	the	the	DET
ejpam-1528	11	5	set	set	NOUN
ejpam-1528	11	6	of	of	ADP
ejpam-1528	11	7	idempotents	idempotent	NOUN
ejpam-1528	11	8	.	.	PUNCT
ejpam-1528	12	1	for	for	ADP
ejpam-1528	12	2	any	any	DET
ejpam-1528	12	3	subset	subset	NOUN
ejpam-1528	12	4	a	a	DET
ejpam-1528	12	5	of	of	ADP
ejpam-1528	12	6	s	s	NOUN
ejpam-1528	12	7	,	,	PUNCT
ejpam-1528	12	8	a′	a′	PROPN
ejpam-1528	12	9	=	=	SYM
ejpam-1528	12	10	{	{	PUNCT
ejpam-1528	12	11	x	x	PUNCT
ejpam-1528	12	12	∈	∈	PROPN
ejpam-1528	12	13	s	s	NOUN
ejpam-1528	12	14	,	,	PUNCT
ejpam-1528	12	15	(	(	PUNCT
ejpam-1528	12	16	∀a	∀a	NOUN
ejpam-1528	12	17	∈	∈	PROPN
ejpam-1528	12	18	a	a	NOUN
ejpam-1528	12	19	)	)	PUNCT
ejpam-1528	12	20	xa	xa	NOUN
ejpam-1528	12	21	=	=	NOUN
ejpam-1528	12	22	ax	ax	NOUN
ejpam-1528	12	23	}	}	PUNCT
ejpam-1528	12	24	denotes	denote	VERB
ejpam-1528	12	25	the	the	DET
ejpam-1528	12	26	commutant	commutant	NOUN
ejpam-1528	12	27	(	(	PUNCT
ejpam-1528	12	28	or	or	CCONJ
ejpam-1528	12	29	centralizer	centralizer	NOUN
ejpam-1528	12	30	)	)	PUNCT
ejpam-1528	12	31	of	of	ADP
ejpam-1528	12	32	a.	a.	NOUN
ejpam-1528	12	33	we	we	PRON
ejpam-1528	12	34	say	say	VERB
ejpam-1528	12	35	a	a	PRON
ejpam-1528	12	36	is	be	AUX
ejpam-1528	12	37	(	(	PUNCT
ejpam-1528	12	38	von	von	PROPN
ejpam-1528	12	39	neumann	neumann	PROPN
ejpam-1528	12	40	)	)	PUNCT
ejpam-1528	13	1	regular	regular	ADV
ejpam-1528	13	2	in	in	ADP
ejpam-1528	13	3	s	s	PRON
ejpam-1528	13	4	if	if	SCONJ
ejpam-1528	13	5	a	a	DET
ejpam-1528	13	6	∈	∈	PROPN
ejpam-1528	13	7	asa	asa	PROPN
ejpam-1528	13	8	.	.	PUNCT
ejpam-1528	14	1	a	a	DET
ejpam-1528	14	2	particular	particular	ADJ
ejpam-1528	14	3	solution	solution	NOUN
ejpam-1528	14	4	to	to	ADP
ejpam-1528	14	5	axa	axa	NOUN
ejpam-1528	14	6	=	=	PUNCT
ejpam-1528	14	7	a	a	PRON
ejpam-1528	14	8	is	be	AUX
ejpam-1528	14	9	called	call	VERB
ejpam-1528	14	10	an	an	DET
ejpam-1528	14	11	associate	associate	NOUN
ejpam-1528	14	12	,	,	PUNCT
ejpam-1528	14	13	or	or	CCONJ
ejpam-1528	14	14	inner	inner	ADJ
ejpam-1528	14	15	inverse	inverse	NOUN
ejpam-1528	14	16	,	,	PUNCT
ejpam-1528	14	17	of	of	ADP
ejpam-1528	14	18	a.	a.	NOUN
ejpam-1528	14	19	a	a	DET
ejpam-1528	14	20	solution	solution	NOUN
ejpam-1528	14	21	to	to	ADP
ejpam-1528	14	22	xax	xax	PROPN
ejpam-1528	14	23	=	=	PROPN
ejpam-1528	14	24	a	a	PROPN
ejpam-1528	14	25	is	be	AUX
ejpam-1528	14	26	called	call	VERB
ejpam-1528	14	27	a	a	DET
ejpam-1528	14	28	weak	weak	ADJ
ejpam-1528	14	29	(	(	PUNCT
ejpam-1528	14	30	or	or	CCONJ
ejpam-1528	14	31	outer	outer	ADJ
ejpam-1528	14	32	)	)	PUNCT
ejpam-1528	14	33	inverse	inverse	NOUN
ejpam-1528	14	34	.	.	PUNCT
ejpam-1528	15	1	finally	finally	ADV
ejpam-1528	15	2	,	,	PUNCT
ejpam-1528	15	3	an	an	DET
ejpam-1528	15	4	element	element	NOUN
ejpam-1528	15	5	that	that	PRON
ejpam-1528	15	6	satisfies	satisfy	VERB
ejpam-1528	15	7	axa	axa	NOUN
ejpam-1528	15	8	=	=	PUNCT
ejpam-1528	15	9	a	a	PROPN
ejpam-1528	15	10	and	and	CCONJ
ejpam-1528	15	11	xax	xax	PROPN
ejpam-1528	15	12	=	=	PROPN
ejpam-1528	15	13	x	x	PROPN
ejpam-1528	15	14	is	be	AUX
ejpam-1528	15	15	called	call	VERB
ejpam-1528	15	16	an	an	DET
ejpam-1528	15	17	inverse	inverse	NOUN
ejpam-1528	15	18	(	(	PUNCT
ejpam-1528	15	19	or	or	CCONJ
ejpam-1528	15	20	reflexive	reflexive	ADJ
ejpam-1528	15	21	inverse	inverse	NOUN
ejpam-1528	15	22	,	,	PUNCT
ejpam-1528	15	23	or	or	CCONJ
ejpam-1528	15	24	relative	relative	ADJ
ejpam-1528	15	25	inverse	inverse	NOUN
ejpam-1528	15	26	)	)	PUNCT
ejpam-1528	15	27	of	of	ADP
ejpam-1528	15	28	a	a	PRON
ejpam-1528	15	29	and	and	CCONJ
ejpam-1528	15	30	is	be	AUX
ejpam-1528	15	31	denoted	denote	VERB
ejpam-1528	15	32	by	by	ADP
ejpam-1528	15	33	a′.	a′.	NOUN
ejpam-1528	15	34	the	the	DET
ejpam-1528	15	35	set	set	NOUN
ejpam-1528	15	36	of	of	ADP
ejpam-1528	15	37	all	all	DET
ejpam-1528	15	38	associates	associate	NOUN
ejpam-1528	15	39	of	of	ADP
ejpam-1528	15	40	a	a	PRON
ejpam-1528	15	41	is	be	AUX
ejpam-1528	15	42	denoted	denote	VERB
ejpam-1528	15	43	by	by	ADP
ejpam-1528	15	44	a(a	a(a	PROPN
ejpam-1528	15	45	)	)	PUNCT
ejpam-1528	15	46	,	,	PUNCT
ejpam-1528	15	47	and	and	CCONJ
ejpam-1528	15	48	the	the	DET
ejpam-1528	15	49	set	set	NOUN
ejpam-1528	15	50	of	of	ADP
ejpam-1528	15	51	weak	weak	ADJ
ejpam-1528	15	52	inverses	inverse	NOUN
ejpam-1528	15	53	of	of	ADP
ejpam-1528	15	54	a	a	PRON
ejpam-1528	15	55	by	by	ADP
ejpam-1528	15	56	w	w	PROPN
ejpam-1528	15	57	(	(	PUNCT
ejpam-1528	15	58	a	a	NOUN
ejpam-1528	15	59	)	)	PUNCT
ejpam-1528	15	60	.	.	PUNCT
ejpam-1528	16	1	a	a	DET
ejpam-1528	16	2	commuting	commuting	NOUN
ejpam-1528	16	3	inverse	inverse	NOUN
ejpam-1528	16	4	,	,	PUNCT
ejpam-1528	16	5	if	if	SCONJ
ejpam-1528	16	6	it	it	PRON
ejpam-1528	16	7	exists	exist	VERB
ejpam-1528	16	8	,	,	PUNCT
ejpam-1528	16	9	is	be	AUX
ejpam-1528	16	10	unique	unique	ADJ
ejpam-1528	16	11	and	and	CCONJ
ejpam-1528	16	12	denoted	denote	VERB
ejpam-1528	16	13	by	by	ADP
ejpam-1528	16	14	a	a	DET
ejpam-1528	16	15	#	#	NOUN
ejpam-1528	16	16	.	.	PUNCT
ejpam-1528	17	1	it	it	PRON
ejpam-1528	17	2	is	be	AUX
ejpam-1528	17	3	usually	usually	ADV
ejpam-1528	17	4	called	call	VERB
ejpam-1528	17	5	the	the	DET
ejpam-1528	17	6	group	group	NOUN
ejpam-1528	17	7	inverse	inverse	NOUN
ejpam-1528	17	8	of	of	ADP
ejpam-1528	17	9	a.	a.	NOUN
ejpam-1528	17	10	a	a	DET
ejpam-1528	17	11	classical	classical	ADJ
ejpam-1528	17	12	reference	reference	NOUN
ejpam-1528	17	13	for	for	ADP
ejpam-1528	17	14	generalized	generalized	ADJ
ejpam-1528	17	15	inverses	inverse	NOUN
ejpam-1528	17	16	is	be	AUX
ejpam-1528	17	17	[	[	X
ejpam-1528	17	18	2	2	NUM
ejpam-1528	17	19	]	]	PUNCT
ejpam-1528	17	20	.	.	PUNCT
ejpam-1528	18	1	email	email	NOUN
ejpam-1528	18	2	address	address	NOUN
ejpam-1528	18	3	:	:	PUNCT
ejpam-1528	18	4	xavier.mary@u-paris10.fr	xavier.mary@u-paris10.fr	X
ejpam-1528	18	5	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1528	19	1	413	413	NUM
ejpam-1528	20	1	c	c	X
ejpam-1528	20	2	©	©	PROPN
ejpam-1528	20	3	2013	2013	NUM
ejpam-1528	20	4	ejpam	ejpam	NOUN
ejpam-1528	20	5	all	all	DET
ejpam-1528	20	6	rights	right	NOUN
ejpam-1528	20	7	reserved	reserve	VERB
ejpam-1528	20	8	.	.	PUNCT
ejpam-1528	21	1	x.	x.	PROPN
ejpam-1528	21	2	mary	mary	PROPN
ejpam-1528	21	3	/	/	SYM
ejpam-1528	21	4	eur	eur	PROPN
ejpam-1528	21	5	.	.	PUNCT
ejpam-1528	22	1	j.	j.	PROPN
ejpam-1528	22	2	pure	pure	PROPN
ejpam-1528	22	3	appl	appl	PROPN
ejpam-1528	22	4	.	.	PROPN
ejpam-1528	22	5	math	math	PROPN
ejpam-1528	22	6	,	,	PUNCT
ejpam-1528	22	7	6	6	NUM
ejpam-1528	22	8	(	(	PUNCT
ejpam-1528	22	9	2013	2013	NUM
ejpam-1528	22	10	)	)	PUNCT
ejpam-1528	22	11	,	,	PUNCT
ejpam-1528	22	12	413	413	NUM
ejpam-1528	22	13	-	-	SYM
ejpam-1528	22	14	427	427	NUM
ejpam-1528	22	15	414	414	NUM
ejpam-1528	22	16	we	we	PRON
ejpam-1528	22	17	will	will	AUX
ejpam-1528	22	18	make	make	VERB
ejpam-1528	22	19	use	use	NOUN
ejpam-1528	22	20	of	of	ADP
ejpam-1528	22	21	the	the	DET
ejpam-1528	22	22	green	green	PROPN
ejpam-1528	22	23	’s	’s	PART
ejpam-1528	22	24	preorders	preorder	NOUN
ejpam-1528	22	25	and	and	CCONJ
ejpam-1528	22	26	relations	relation	NOUN
ejpam-1528	22	27	in	in	ADP
ejpam-1528	22	28	a	a	DET
ejpam-1528	22	29	semigroup	semigroup	NOUN
ejpam-1528	23	1	[	[	X
ejpam-1528	23	2	9	9	NUM
ejpam-1528	23	3	]	]	PUNCT
ejpam-1528	23	4	.	.	PUNCT
ejpam-1528	24	1	for	for	ADP
ejpam-1528	24	2	elements	element	NOUN
ejpam-1528	24	3	a	a	PRON
ejpam-1528	24	4	and	and	CCONJ
ejpam-1528	24	5	b	b	NOUN
ejpam-1528	24	6	of	of	ADP
ejpam-1528	24	7	s	s	PROPN
ejpam-1528	24	8	,	,	PUNCT
ejpam-1528	24	9	green	green	PROPN
ejpam-1528	24	10	’s	’s	PART
ejpam-1528	24	11	preorders	preorder	NOUN
ejpam-1528	24	12	≤l	≤l	NOUN
ejpam-1528	24	13	,	,	PUNCT
ejpam-1528	24	14	≤r	≤r	PROPN
ejpam-1528	24	15	and	and	CCONJ
ejpam-1528	24	16	≤h	≤h	NOUN
ejpam-1528	24	17	are	be	AUX
ejpam-1528	24	18	defined	define	VERB
ejpam-1528	24	19	by	by	ADP
ejpam-1528	24	20	a	a	DET
ejpam-1528	24	21	≤l	≤l	PROPN
ejpam-1528	24	22	b	b	NUM
ejpam-1528	24	23	⇐	⇐	ADJ
ejpam-1528	24	24	⇒	⇒	NOUN
ejpam-1528	24	25	s1a	s1a	NOUN
ejpam-1528	25	1	⊂	⊂	PROPN
ejpam-1528	25	2	s1	s1	PROPN
ejpam-1528	25	3	b	b	NUM
ejpam-1528	25	4	⇐	⇐	ADJ
ejpam-1528	25	5	⇒∃x	⇒∃x	NOUN
ejpam-1528	25	6	∈	∈	NOUN
ejpam-1528	25	7	s1	s1	NOUN
ejpam-1528	25	8	,	,	PUNCT
ejpam-1528	25	9	a	a	DET
ejpam-1528	25	10	=	=	NOUN
ejpam-1528	25	11	x	x	SYM
ejpam-1528	25	12	b	b	PROPN
ejpam-1528	25	13	;	;	PUNCT
ejpam-1528	25	14	a	a	DET
ejpam-1528	25	15	≤r	≤r	PROPN
ejpam-1528	25	16	b	b	X
ejpam-1528	25	17	⇐	⇐	ADJ
ejpam-1528	25	18	⇒	⇒	PROPN
ejpam-1528	25	19	as1	as1	PROPN
ejpam-1528	25	20	⊂	⊂	PROPN
ejpam-1528	25	21	bs1	bs1	PROPN
ejpam-1528	25	22	⇐	⇐	ADJ
ejpam-1528	25	23	⇒∃x	⇒∃x	NOUN
ejpam-1528	25	24	∈	∈	NOUN
ejpam-1528	25	25	s1	s1	NOUN
ejpam-1528	25	26	,	,	PUNCT
ejpam-1528	25	27	a	a	DET
ejpam-1528	25	28	=	=	X
ejpam-1528	25	29	bx	bx	X
ejpam-1528	25	30	;	;	PUNCT
ejpam-1528	25	31	a	a	DET
ejpam-1528	25	32	≤h	≤h	NOUN
ejpam-1528	25	33	b	b	NUM
ejpam-1528	25	34	⇐	⇐	ADJ
ejpam-1528	25	35	⇒	⇒	NOUN
ejpam-1528	25	36	{	{	PUNCT
ejpam-1528	25	37	a	a	DET
ejpam-1528	25	38	≤l	≤l	PROPN
ejpam-1528	25	39	b	b	PROPN
ejpam-1528	25	40	and	and	CCONJ
ejpam-1528	25	41	a	a	DET
ejpam-1528	25	42	≤r	≤r	PROPN
ejpam-1528	25	43	b	b	NOUN
ejpam-1528	25	44	}	}	PUNCT
ejpam-1528	25	45	.	.	PUNCT
ejpam-1528	26	1	if	if	SCONJ
ejpam-1528	26	2	≤k	≤k	PROPN
ejpam-1528	26	3	is	be	AUX
ejpam-1528	26	4	one	one	NUM
ejpam-1528	26	5	of	of	ADP
ejpam-1528	26	6	these	these	DET
ejpam-1528	26	7	preorders	preorder	NOUN
ejpam-1528	26	8	,	,	PUNCT
ejpam-1528	26	9	then	then	ADV
ejpam-1528	26	10	ak	ak	PROPN
ejpam-1528	26	11	b	b	PROPN
ejpam-1528	26	12	⇐	⇐	PROPN
ejpam-1528	26	13	⇒	⇒	PROPN
ejpam-1528	26	14	{	{	PUNCT
ejpam-1528	26	15	a	a	DET
ejpam-1528	26	16	≤k	≤k	PROPN
ejpam-1528	26	17	b	b	PROPN
ejpam-1528	26	18	and	and	CCONJ
ejpam-1528	26	19	b	b	NOUN
ejpam-1528	26	20	≤k	≤k	PROPN
ejpam-1528	26	21	a	a	PRON
ejpam-1528	26	22	}	}	PUNCT
ejpam-1528	26	23	,	,	PUNCT
ejpam-1528	26	24	and	and	CCONJ
ejpam-1528	26	25	ka	ka	PROPN
ejpam-1528	27	1	=	=	PRON
ejpam-1528	27	2	{	{	PUNCT
ejpam-1528	27	3	b	b	PROPN
ejpam-1528	27	4	∈	∈	PROPN
ejpam-1528	27	5	s	s	PART
ejpam-1528	27	6	,	,	PUNCT
ejpam-1528	27	7	bk	bk	VERB
ejpam-1528	27	8	a	a	DET
ejpam-1528	27	9	}	}	PUNCT
ejpam-1528	27	10	denotes	denote	NOUN
ejpam-1528	27	11	the	the	DET
ejpam-1528	27	12	k	k	PROPN
ejpam-1528	27	13	-class	-class	PROPN
ejpam-1528	27	14	of	of	ADP
ejpam-1528	27	15	a.	a.	NOUN
ejpam-1528	27	16	we	we	PRON
ejpam-1528	27	17	recall	recall	VERB
ejpam-1528	27	18	the	the	DET
ejpam-1528	27	19	following	follow	VERB
ejpam-1528	27	20	characterization	characterization	NOUN
ejpam-1528	27	21	of	of	ADP
ejpam-1528	27	22	group	group	NOUN
ejpam-1528	27	23	invertibility	invertibility	NOUN
ejpam-1528	27	24	in	in	ADP
ejpam-1528	27	25	terms	term	NOUN
ejpam-1528	27	26	of	of	ADP
ejpam-1528	27	27	green	green	PROPN
ejpam-1528	27	28	’s	’s	PART
ejpam-1528	27	29	relation	relation	NOUN
ejpam-1528	27	30	h	h	PROPN
ejpam-1528	27	31	(	(	PUNCT
ejpam-1528	27	32	see	see	VERB
ejpam-1528	27	33	[	[	X
ejpam-1528	27	34	9	9	NUM
ejpam-1528	27	35	,	,	PUNCT
ejpam-1528	27	36	22	22	NUM
ejpam-1528	27	37	]	]	PUNCT
ejpam-1528	27	38	):	):	PUNCT
ejpam-1528	27	39	lemma	lemma	PROPN
ejpam-1528	27	40	1	1	NUM
ejpam-1528	27	41	.	.	PUNCT
ejpam-1528	28	1	a	a	DET
ejpam-1528	28	2	#	#	NOUN
ejpam-1528	28	3	exists	exist	VERB
ejpam-1528	28	4	if	if	SCONJ
ejpam-1528	28	5	and	and	CCONJ
ejpam-1528	28	6	only	only	ADV
ejpam-1528	28	7	if	if	SCONJ
ejpam-1528	28	8	ah	ah	INTJ
ejpam-1528	28	9	a2	a2	PROPN
ejpam-1528	28	10	if	if	SCONJ
ejpam-1528	28	11	and	and	CCONJ
ejpam-1528	28	12	only	only	ADV
ejpam-1528	28	13	ifha	ifha	NOUN
ejpam-1528	28	14	is	be	AUX
ejpam-1528	28	15	a	a	DET
ejpam-1528	28	16	group	group	NOUN
ejpam-1528	28	17	.	.	PUNCT
ejpam-1528	29	1	the	the	DET
ejpam-1528	29	2	study	study	NOUN
ejpam-1528	29	3	of	of	ADP
ejpam-1528	29	4	generalized	generalized	ADJ
ejpam-1528	29	5	inverses	inverse	NOUN
ejpam-1528	29	6	has	have	AUX
ejpam-1528	29	7	been	be	AUX
ejpam-1528	29	8	conducted	conduct	VERB
ejpam-1528	29	9	in	in	ADP
ejpam-1528	29	10	many	many	ADJ
ejpam-1528	29	11	different	different	ADJ
ejpam-1528	29	12	mathematical	mathematical	ADJ
ejpam-1528	29	13	areas	area	NOUN
ejpam-1528	29	14	,	,	PUNCT
ejpam-1528	29	15	from	from	ADP
ejpam-1528	29	16	semigroup	semigroup	PROPN
ejpam-1528	29	17	theory	theory	NOUN
ejpam-1528	29	18	to	to	ADP
ejpam-1528	29	19	operator	operator	NOUN
ejpam-1528	29	20	theory	theory	NOUN
ejpam-1528	29	21	,	,	PUNCT
ejpam-1528	29	22	and	and	CCONJ
ejpam-1528	29	23	applied	apply	VERB
ejpam-1528	29	24	to	to	ADP
ejpam-1528	29	25	various	various	ADJ
ejpam-1528	29	26	domains	domain	NOUN
ejpam-1528	29	27	such	such	ADJ
ejpam-1528	29	28	as	as	ADP
ejpam-1528	29	29	markov	markov	NOUN
ejpam-1528	29	30	chains	chain	NOUN
ejpam-1528	29	31	or	or	CCONJ
ejpam-1528	29	32	differential	differential	ADJ
ejpam-1528	29	33	equations	equation	NOUN
ejpam-1528	29	34	.	.	PUNCT
ejpam-1528	30	1	in	in	ADP
ejpam-1528	30	2	these	these	DET
ejpam-1528	30	3	studies	study	NOUN
ejpam-1528	30	4	,	,	PUNCT
ejpam-1528	30	5	it	it	PRON
ejpam-1528	30	6	may	may	AUX
ejpam-1528	30	7	be	be	AUX
ejpam-1528	30	8	useful	useful	ADJ
ejpam-1528	30	9	to	to	PART
ejpam-1528	30	10	consider	consider	VERB
ejpam-1528	30	11	commuting	commute	VERB
ejpam-1528	30	12	(	(	PUNCT
ejpam-1528	30	13	or	or	CCONJ
ejpam-1528	30	14	bicommuting	bicommute	VERB
ejpam-1528	30	15	)	)	PUNCT
ejpam-1528	30	16	inverses	inverse	VERB
ejpam-1528	30	17	.	.	PUNCT
ejpam-1528	31	1	since	since	SCONJ
ejpam-1528	31	2	the	the	DET
ejpam-1528	31	3	existence	existence	NOUN
ejpam-1528	31	4	of	of	ADP
ejpam-1528	31	5	a	a	DET
ejpam-1528	31	6	commuting	commute	VERB
ejpam-1528	31	7	inner	inner	ADJ
ejpam-1528	31	8	inverse	inverse	NOUN
ejpam-1528	31	9	is	be	AUX
ejpam-1528	31	10	a	a	DET
ejpam-1528	31	11	very	very	ADV
ejpam-1528	31	12	strong	strong	ADJ
ejpam-1528	31	13	property	property	NOUN
ejpam-1528	31	14	,	,	PUNCT
ejpam-1528	31	15	it	it	PRON
ejpam-1528	31	16	is	be	AUX
ejpam-1528	31	17	common	common	ADJ
ejpam-1528	31	18	to	to	PART
ejpam-1528	31	19	look	look	VERB
ejpam-1528	31	20	at	at	ADP
ejpam-1528	31	21	outer	outer	ADJ
ejpam-1528	31	22	commuting	commuting	NOUN
ejpam-1528	31	23	inverses	inverse	NOUN
ejpam-1528	31	24	,	,	PUNCT
ejpam-1528	31	25	following	follow	VERB
ejpam-1528	31	26	the	the	DET
ejpam-1528	31	27	seminal	seminal	ADJ
ejpam-1528	31	28	work	work	NOUN
ejpam-1528	31	29	of	of	ADP
ejpam-1528	31	30	m.	m.	NOUN
ejpam-1528	31	31	drazin	drazin	PROPN
ejpam-1528	32	1	[	[	X
ejpam-1528	32	2	4	4	NUM
ejpam-1528	32	3	]	]	PUNCT
ejpam-1528	32	4	,	,	PUNCT
ejpam-1528	32	5	who	who	PRON
ejpam-1528	32	6	introduced	introduce	VERB
ejpam-1528	32	7	the	the	DET
ejpam-1528	32	8	drazin	drazin	PROPN
ejpam-1528	32	9	inverse	inverse	NOUN
ejpam-1528	32	10	in	in	ADP
ejpam-1528	32	11	the	the	DET
ejpam-1528	32	12	context	context	NOUN
ejpam-1528	32	13	of	of	ADP
ejpam-1528	32	14	semigroups	semigroup	NOUN
ejpam-1528	32	15	and	and	CCONJ
ejpam-1528	32	16	rings	ring	NOUN
ejpam-1528	32	17	.	.	PUNCT
ejpam-1528	33	1	later	later	ADV
ejpam-1528	33	2	,	,	PUNCT
ejpam-1528	33	3	this	this	DET
ejpam-1528	33	4	inverse	inverse	NOUN
ejpam-1528	33	5	has	have	AUX
ejpam-1528	33	6	been	be	AUX
ejpam-1528	33	7	generalized	generalize	VERB
ejpam-1528	33	8	in	in	ADP
ejpam-1528	33	9	the	the	DET
ejpam-1528	33	10	setting	setting	NOUN
ejpam-1528	33	11	of	of	ADP
ejpam-1528	33	12	operators	operator	NOUN
ejpam-1528	33	13	by	by	ADP
ejpam-1528	33	14	koliha	koliha	NOUN
ejpam-1528	33	15	[	[	X
ejpam-1528	33	16	16	16	NUM
ejpam-1528	33	17	]	]	PUNCT
ejpam-1528	33	18	using	use	VERB
ejpam-1528	33	19	spectral	spectral	ADJ
ejpam-1528	33	20	properties	property	NOUN
ejpam-1528	33	21	and	and	CCONJ
ejpam-1528	33	22	functional	functional	ADJ
ejpam-1528	33	23	calculus	calculus	NOUN
ejpam-1528	33	24	.	.	PUNCT
ejpam-1528	34	1	this	this	DET
ejpam-1528	34	2	generalized	generalize	VERB
ejpam-1528	34	3	drazin	drazin	PROPN
ejpam-1528	34	4	inverse	inverse	NOUN
ejpam-1528	34	5	(	(	PUNCT
ejpam-1528	34	6	also	also	ADV
ejpam-1528	34	7	called	call	VERB
ejpam-1528	34	8	koliha	koliha	ADJ
ejpam-1528	34	9	-	-	PUNCT
ejpam-1528	34	10	drazin	drazin	PROPN
ejpam-1528	34	11	inverse	inverse	NOUN
ejpam-1528	34	12	)	)	PUNCT
ejpam-1528	34	13	finds	find	VERB
ejpam-1528	34	14	many	many	ADJ
ejpam-1528	34	15	applications	application	NOUN
ejpam-1528	34	16	,	,	PUNCT
ejpam-1528	34	17	in	in	ADP
ejpam-1528	34	18	particular	particular	ADJ
ejpam-1528	34	19	to	to	ADP
ejpam-1528	34	20	singular	singular	PROPN
ejpam-1528	34	21	differential	differential	ADJ
ejpam-1528	34	22	equations	equation	NOUN
ejpam-1528	34	23	.	.	PUNCT
ejpam-1528	35	1	in	in	ADP
ejpam-1528	35	2	[	[	X
ejpam-1528	35	3	18	18	NUM
ejpam-1528	35	4	]	]	PUNCT
ejpam-1528	35	5	the	the	DET
ejpam-1528	35	6	author	author	NOUN
ejpam-1528	35	7	introduced	introduce	VERB
ejpam-1528	35	8	a	a	DET
ejpam-1528	35	9	special	special	ADJ
ejpam-1528	35	10	outer	outer	ADJ
ejpam-1528	35	11	inverse	inverse	NOUN
ejpam-1528	35	12	,	,	PUNCT
ejpam-1528	35	13	called	call	VERB
ejpam-1528	35	14	inverse	inverse	NOUN
ejpam-1528	35	15	along	along	ADP
ejpam-1528	35	16	an	an	DET
ejpam-1528	35	17	element	element	NOUN
ejpam-1528	35	18	in	in	ADP
ejpam-1528	35	19	the	the	DET
ejpam-1528	35	20	context	context	NOUN
ejpam-1528	35	21	of	of	ADP
ejpam-1528	35	22	semigroups	semigroup	NOUN
ejpam-1528	35	23	.	.	PUNCT
ejpam-1528	36	1	the	the	DET
ejpam-1528	36	2	aim	aim	NOUN
ejpam-1528	36	3	of	of	ADP
ejpam-1528	36	4	this	this	DET
ejpam-1528	36	5	article	article	NOUN
ejpam-1528	36	6	is	be	AUX
ejpam-1528	36	7	to	to	PART
ejpam-1528	36	8	use	use	VERB
ejpam-1528	36	9	this	this	DET
ejpam-1528	36	10	new	new	ADJ
ejpam-1528	36	11	inverse	inverse	NOUN
ejpam-1528	36	12	to	to	PART
ejpam-1528	36	13	study	study	VERB
ejpam-1528	36	14	bicommuting	bicommute	VERB
ejpam-1528	36	15	generalized	generalize	VERB
ejpam-1528	36	16	inverses	inverse	NOUN
ejpam-1528	36	17	.	.	PUNCT
ejpam-1528	37	1	then	then	ADV
ejpam-1528	37	2	,	,	PUNCT
ejpam-1528	37	3	using	use	VERB
ejpam-1528	37	4	the	the	DET
ejpam-1528	37	5	natural	natural	ADJ
ejpam-1528	37	6	partial	partial	ADJ
ejpam-1528	37	7	order	order	NOUN
ejpam-1528	37	8	on	on	ADP
ejpam-1528	37	9	idempotents	idempotent	NOUN
ejpam-1528	37	10	,	,	PUNCT
ejpam-1528	37	11	we	we	PRON
ejpam-1528	37	12	will	will	AUX
ejpam-1528	37	13	define	define	VERB
ejpam-1528	37	14	a	a	DET
ejpam-1528	37	15	new	new	ADJ
ejpam-1528	37	16	inverse	inverse	NOUN
ejpam-1528	37	17	called	call	VERB
ejpam-1528	37	18	natural	natural	ADJ
ejpam-1528	37	19	inverse	inverse	NOUN
ejpam-1528	37	20	,	,	PUNCT
ejpam-1528	37	21	that	that	PRON
ejpam-1528	37	22	generalizes	generalize	VERB
ejpam-1528	37	23	the	the	DET
ejpam-1528	37	24	drazin	drazin	PROPN
ejpam-1528	37	25	inverse	inverse	NOUN
ejpam-1528	37	26	in	in	ADP
ejpam-1528	37	27	a	a	DET
ejpam-1528	37	28	semigroup	semigroup	NOUN
ejpam-1528	37	29	,	,	PUNCT
ejpam-1528	37	30	but	but	CCONJ
ejpam-1528	37	31	also	also	ADV
ejpam-1528	37	32	the	the	DET
ejpam-1528	37	33	koliha	koliha	VERB
ejpam-1528	37	34	-	-	PUNCT
ejpam-1528	37	35	drazin	drazin	NOUN
ejpam-1528	37	36	inverse	inverse	NOUN
ejpam-1528	37	37	in	in	ADP
ejpam-1528	37	38	a	a	DET
ejpam-1528	37	39	ring	ring	NOUN
ejpam-1528	37	40	.	.	PUNCT
ejpam-1528	38	1	in	in	ADP
ejpam-1528	38	2	this	this	DET
ejpam-1528	38	3	setting	setting	NOUN
ejpam-1528	38	4	,	,	PUNCT
ejpam-1528	38	5	this	this	PRON
ejpam-1528	38	6	provides	provide	VERB
ejpam-1528	38	7	a	a	DET
ejpam-1528	38	8	decomposition	decomposition	NOUN
ejpam-1528	38	9	of	of	ADP
ejpam-1528	38	10	an	an	DET
ejpam-1528	38	11	element	element	NOUN
ejpam-1528	38	12	similar	similar	ADJ
ejpam-1528	38	13	to	to	ADP
ejpam-1528	38	14	the	the	DET
ejpam-1528	38	15	nilpotent	nilpotent	NOUN
ejpam-1528	38	16	,	,	PUNCT
ejpam-1528	38	17	kato	kato	PROPN
ejpam-1528	38	18	or	or	CCONJ
ejpam-1528	38	19	mbekhta	mbekhta	PROPN
ejpam-1528	38	20	decompositions	decomposition	NOUN
ejpam-1528	38	21	[	[	X
ejpam-1528	38	22	21	21	NUM
ejpam-1528	38	23	]	]	PUNCT
ejpam-1528	38	24	.	.	PUNCT
ejpam-1528	39	1	in	in	ADP
ejpam-1528	39	2	the	the	DET
ejpam-1528	39	3	first	first	ADJ
ejpam-1528	39	4	sections	section	NOUN
ejpam-1528	39	5	we	we	PRON
ejpam-1528	39	6	introduce	introduce	VERB
ejpam-1528	39	7	the	the	DET
ejpam-1528	39	8	main	main	ADJ
ejpam-1528	39	9	notions	notion	NOUN
ejpam-1528	39	10	(	(	PUNCT
ejpam-1528	39	11	inverse	inverse	NOUN
ejpam-1528	39	12	along	along	ADP
ejpam-1528	39	13	an	an	DET
ejpam-1528	39	14	element	element	NOUN
ejpam-1528	39	15	,	,	PUNCT
ejpam-1528	39	16	natural	natural	ADJ
ejpam-1528	39	17	generalized	generalized	ADJ
ejpam-1528	39	18	inverse	inverse	NOUN
ejpam-1528	39	19	)	)	PUNCT
ejpam-1528	39	20	entirely	entirely	ADV
ejpam-1528	39	21	in	in	ADP
ejpam-1528	39	22	the	the	DET
ejpam-1528	39	23	semigroup	semigroup	ADJ
ejpam-1528	39	24	setting	setting	NOUN
ejpam-1528	39	25	.	.	PUNCT
ejpam-1528	40	1	we	we	PRON
ejpam-1528	40	2	then	then	ADV
ejpam-1528	40	3	study	study	VERB
ejpam-1528	40	4	further	further	ADJ
ejpam-1528	40	5	properties	property	NOUN
ejpam-1528	40	6	of	of	ADP
ejpam-1528	40	7	the	the	DET
ejpam-1528	40	8	natural	natural	ADJ
ejpam-1528	40	9	inverse	inverse	NOUN
ejpam-1528	40	10	in	in	ADP
ejpam-1528	40	11	rings	ring	NOUN
ejpam-1528	40	12	,	,	PUNCT
ejpam-1528	40	13	making	make	VERB
ejpam-1528	40	14	the	the	DET
ejpam-1528	40	15	link	link	NOUN
ejpam-1528	40	16	with	with	ADP
ejpam-1528	40	17	quasipolar	quasipolar	ADJ
ejpam-1528	40	18	(	(	PUNCT
ejpam-1528	40	19	generalized	generalize	VERB
ejpam-1528	40	20	drazin	drazin	PROPN
ejpam-1528	40	21	invertible	invertible	ADJ
ejpam-1528	40	22	)	)	PUNCT
ejpam-1528	40	23	elements	element	NOUN
ejpam-1528	40	24	[	[	X
ejpam-1528	40	25	10	10	NUM
ejpam-1528	40	26	,	,	PUNCT
ejpam-1528	40	27	11	11	NUM
ejpam-1528	40	28	,	,	PUNCT
ejpam-1528	40	29	16	16	NUM
ejpam-1528	40	30	,	,	PUNCT
ejpam-1528	40	31	17	17	NUM
ejpam-1528	40	32	]	]	PUNCT
ejpam-1528	40	33	.	.	PUNCT
ejpam-1528	41	1	in	in	ADP
ejpam-1528	41	2	the	the	DET
ejpam-1528	41	3	last	last	ADJ
ejpam-1528	41	4	sections	section	NOUN
ejpam-1528	41	5	,	,	PUNCT
ejpam-1528	41	6	a	a	DET
ejpam-1528	41	7	particular	particular	ADJ
ejpam-1528	41	8	attention	attention	NOUN
ejpam-1528	41	9	is	be	AUX
ejpam-1528	41	10	given	give	VERB
ejpam-1528	41	11	to	to	PART
ejpam-1528	41	12	banach	banach	VERB
ejpam-1528	41	13	and	and	CCONJ
ejpam-1528	41	14	operators	operator	NOUN
ejpam-1528	41	15	algebras	algebra	VERB
ejpam-1528	41	16	.	.	PUNCT
ejpam-1528	42	1	the	the	DET
ejpam-1528	42	2	main	main	ADJ
ejpam-1528	42	3	result	result	NOUN
ejpam-1528	42	4	is	be	AUX
ejpam-1528	42	5	that	that	SCONJ
ejpam-1528	42	6	this	this	DET
ejpam-1528	42	7	inverse	inverse	NOUN
ejpam-1528	42	8	relies	rely	VERB
ejpam-1528	42	9	on	on	ADP
ejpam-1528	42	10	finer	fine	ADJ
ejpam-1528	42	11	properties	property	NOUN
ejpam-1528	42	12	than	than	ADP
ejpam-1528	42	13	spectral	spectral	ADJ
ejpam-1528	42	14	properties	property	NOUN
ejpam-1528	42	15	only	only	ADV
ejpam-1528	42	16	.	.	PUNCT
ejpam-1528	43	1	local	local	ADJ
ejpam-1528	43	2	spectral	spectral	ADJ
ejpam-1528	43	3	theory[12	theory[12	NOUN
ejpam-1528	43	4	]	]	PUNCT
ejpam-1528	43	5	is	be	AUX
ejpam-1528	43	6	then	then	ADV
ejpam-1528	43	7	an	an	DET
ejpam-1528	43	8	interesting	interesting	ADJ
ejpam-1528	43	9	tool	tool	NOUN
ejpam-1528	43	10	.	.	PUNCT
ejpam-1528	44	1	2	2	X
ejpam-1528	44	2	.	.	X
ejpam-1528	44	3	inverse	inverse	NOUN
ejpam-1528	44	4	along	along	ADP
ejpam-1528	44	5	an	an	DET
ejpam-1528	44	6	element	element	NOUN
ejpam-1528	44	7	2.1	2.1	NUM
ejpam-1528	44	8	.	.	PUNCT
ejpam-1528	45	1	definition	definition	NOUN
ejpam-1528	45	2	and	and	CCONJ
ejpam-1528	45	3	first	first	ADJ
ejpam-1528	45	4	properties	property	NOUN
ejpam-1528	45	5	the	the	DET
ejpam-1528	45	6	inverse	inverse	NOUN
ejpam-1528	45	7	along	along	ADP
ejpam-1528	45	8	an	an	DET
ejpam-1528	45	9	element	element	NOUN
ejpam-1528	45	10	was	be	AUX
ejpam-1528	45	11	introduced	introduce	VERB
ejpam-1528	45	12	in	in	ADP
ejpam-1528	45	13	[	[	X
ejpam-1528	45	14	18	18	NUM
ejpam-1528	45	15	]	]	PUNCT
ejpam-1528	45	16	,	,	PUNCT
ejpam-1528	45	17	and	and	CCONJ
ejpam-1528	45	18	in	in	ADP
ejpam-1528	45	19	[	[	X
ejpam-1528	45	20	19	19	NUM
ejpam-1528	45	21	]	]	PUNCT
ejpam-1528	45	22	,	,	PUNCT
ejpam-1528	45	23	it	it	PRON
ejpam-1528	45	24	was	be	AUX
ejpam-1528	45	25	interpreted	interpret	VERB
ejpam-1528	45	26	as	as	ADP
ejpam-1528	45	27	a	a	DET
ejpam-1528	45	28	kind	kind	NOUN
ejpam-1528	45	29	of	of	ADP
ejpam-1528	45	30	inverse	inverse	NOUN
ejpam-1528	45	31	modulo	modulo	NOUN
ejpam-1528	45	32	h	h	NOUN
ejpam-1528	45	33	.	.	PUNCT
ejpam-1528	46	1	we	we	PRON
ejpam-1528	46	2	recall	recall	VERB
ejpam-1528	46	3	the	the	DET
ejpam-1528	46	4	definition	definition	NOUN
ejpam-1528	46	5	and	and	CCONJ
ejpam-1528	46	6	properties	property	NOUN
ejpam-1528	46	7	of	of	ADP
ejpam-1528	46	8	this	this	DET
ejpam-1528	46	9	inverse	inverse	NOUN
ejpam-1528	46	10	.	.	PUNCT
ejpam-1528	47	1	note	note	VERB
ejpam-1528	47	2	that	that	SCONJ
ejpam-1528	47	3	in	in	ADP
ejpam-1528	47	4	this	this	DET
ejpam-1528	47	5	article	article	NOUN
ejpam-1528	47	6	,	,	PUNCT
ejpam-1528	47	7	this	this	DET
ejpam-1528	47	8	new	new	ADJ
ejpam-1528	47	9	inverse	inverse	NOUN
ejpam-1528	47	10	is	be	AUX
ejpam-1528	47	11	denoted	denote	VERB
ejpam-1528	47	12	by	by	ADP
ejpam-1528	47	13	a−d	a−d	PROPN
ejpam-1528	47	14	instead	instead	ADV
ejpam-1528	47	15	of	of	ADP
ejpam-1528	47	16	a‖d	a‖d	NOUN
ejpam-1528	47	17	,	,	PUNCT
ejpam-1528	47	18	extending	extend	VERB
ejpam-1528	47	19	the	the	DET
ejpam-1528	47	20	case	case	NOUN
ejpam-1528	47	21	d	d	X
ejpam-1528	47	22	=	=	SYM
ejpam-1528	47	23	1	1	X
ejpam-1528	47	24	.	.	PUNCT
ejpam-1528	47	25	x.	x.	PROPN
ejpam-1528	47	26	mary	mary	PROPN
ejpam-1528	47	27	/	/	SYM
ejpam-1528	47	28	eur	eur	PROPN
ejpam-1528	47	29	.	.	PUNCT
ejpam-1528	48	1	j.	j.	PROPN
ejpam-1528	48	2	pure	pure	PROPN
ejpam-1528	48	3	appl	appl	PROPN
ejpam-1528	48	4	.	.	PROPN
ejpam-1528	48	5	math	math	PROPN
ejpam-1528	48	6	,	,	PUNCT
ejpam-1528	48	7	6	6	NUM
ejpam-1528	48	8	(	(	PUNCT
ejpam-1528	48	9	2013	2013	NUM
ejpam-1528	48	10	)	)	PUNCT
ejpam-1528	48	11	,	,	PUNCT
ejpam-1528	48	12	413	413	NUM
ejpam-1528	48	13	-	-	SYM
ejpam-1528	48	14	427	427	NUM
ejpam-1528	48	15	415	415	NUM
ejpam-1528	48	16	definition	definition	NOUN
ejpam-1528	48	17	1	1	NUM
ejpam-1528	48	18	.	.	PUNCT
ejpam-1528	48	19	given	give	VERB
ejpam-1528	48	20	a	a	PRON
ejpam-1528	48	21	,	,	PUNCT
ejpam-1528	48	22	d	d	X
ejpam-1528	48	23	in	in	ADP
ejpam-1528	48	24	s	s	PROPN
ejpam-1528	48	25	,	,	PUNCT
ejpam-1528	48	26	we	we	PRON
ejpam-1528	48	27	say	say	VERB
ejpam-1528	48	28	a	a	PRON
ejpam-1528	48	29	is	be	AUX
ejpam-1528	48	30	invertible	invertible	ADJ
ejpam-1528	48	31	along	along	ADP
ejpam-1528	48	32	d	d	PROPN
ejpam-1528	48	33	if	if	SCONJ
ejpam-1528	48	34	there	there	PRON
ejpam-1528	48	35	exists	exist	VERB
ejpam-1528	48	36	b	b	PROPN
ejpam-1528	48	37	∈	∈	PROPN
ejpam-1528	48	38	s	s	VERB
ejpam-1528	48	39	such	such	ADJ
ejpam-1528	48	40	that	that	ADV
ejpam-1528	48	41	bad	bad	ADJ
ejpam-1528	48	42	=	=	NOUN
ejpam-1528	48	43	d	d	NOUN
ejpam-1528	48	44	=	=	PUNCT
ejpam-1528	48	45	dab	dab	PROPN
ejpam-1528	48	46	and	and	CCONJ
ejpam-1528	48	47	b	b	NOUN
ejpam-1528	48	48	≤h	≤h	NOUN
ejpam-1528	48	49	d.	d.	NOUN
ejpam-1528	48	50	if	if	SCONJ
ejpam-1528	48	51	such	such	DET
ejpam-1528	48	52	an	an	DET
ejpam-1528	48	53	element	element	NOUN
ejpam-1528	48	54	exists	exist	VERB
ejpam-1528	48	55	then	then	ADV
ejpam-1528	48	56	it	it	PRON
ejpam-1528	48	57	is	be	AUX
ejpam-1528	48	58	unique	unique	ADJ
ejpam-1528	48	59	and	and	CCONJ
ejpam-1528	48	60	is	be	AUX
ejpam-1528	48	61	denoted	denote	VERB
ejpam-1528	48	62	by	by	ADP
ejpam-1528	48	63	a−d	a−d	PROPN
ejpam-1528	48	64	.	.	PUNCT
ejpam-1528	49	1	another	another	DET
ejpam-1528	49	2	characterization	characterization	NOUN
ejpam-1528	49	3	is	be	AUX
ejpam-1528	49	4	the	the	DET
ejpam-1528	49	5	following	following	NOUN
ejpam-1528	49	6	:	:	PUNCT
ejpam-1528	49	7	lemma	lemma	PROPN
ejpam-1528	49	8	2	2	X
ejpam-1528	49	9	.	.	PUNCT
ejpam-1528	50	1	a	a	PRON
ejpam-1528	50	2	is	be	AUX
ejpam-1528	50	3	invertible	invertible	ADJ
ejpam-1528	50	4	along	along	ADP
ejpam-1528	50	5	d	d	PROPN
ejpam-1528	50	6	if	if	SCONJ
ejpam-1528	51	1	and	and	CCONJ
ejpam-1528	51	2	only	only	ADV
ejpam-1528	51	3	if	if	SCONJ
ejpam-1528	51	4	there	there	PRON
ejpam-1528	51	5	exists	exist	VERB
ejpam-1528	51	6	b	b	PROPN
ejpam-1528	51	7	∈	∈	PROPN
ejpam-1528	51	8	s	s	VERB
ejpam-1528	51	9	such	such	ADJ
ejpam-1528	51	10	that	that	SCONJ
ejpam-1528	51	11	bab	bab	PROPN
ejpam-1528	51	12	=	=	SYM
ejpam-1528	51	13	b	b	PROPN
ejpam-1528	51	14	and	and	CCONJ
ejpam-1528	51	15	bh	bh	PROPN
ejpam-1528	51	16	d	d	NOUN
ejpam-1528	51	17	,	,	PUNCT
ejpam-1528	51	18	and	and	CCONJ
ejpam-1528	51	19	in	in	ADP
ejpam-1528	51	20	this	this	DET
ejpam-1528	51	21	case	case	NOUN
ejpam-1528	51	22	a−d	a−d	PROPN
ejpam-1528	51	23	=	=	SYM
ejpam-1528	51	24	b.	b.	PROPN
ejpam-1528	51	25	theorem	theorem	NOUN
ejpam-1528	51	26	1	1	X
ejpam-1528	51	27	.	.	PUNCT
ejpam-1528	52	1	let	let	VERB
ejpam-1528	52	2	a	a	PRON
ejpam-1528	52	3	,	,	PUNCT
ejpam-1528	52	4	d	d	PROPN
ejpam-1528	52	5	∈	∈	PROPN
ejpam-1528	52	6	s.	s.	PROPN
ejpam-1528	52	7	then	then	ADV
ejpam-1528	52	8	the	the	DET
ejpam-1528	52	9	following	follow	VERB
ejpam-1528	52	10	are	be	AUX
ejpam-1528	52	11	equivalent	equivalent	ADJ
ejpam-1528	52	12	:	:	PUNCT
ejpam-1528	52	13	i	i	PRON
ejpam-1528	52	14	)	)	PUNCT
ejpam-1528	52	15	a−d	a−d	PROPN
ejpam-1528	52	16	exists	exist	VERB
ejpam-1528	52	17	.	.	PUNCT
ejpam-1528	53	1	ii	ii	X
ejpam-1528	53	2	)	)	PUNCT
ejpam-1528	53	3	d	d	PROPN
ejpam-1528	53	4	≤r	≤r	PROPN
ejpam-1528	53	5	da	da	PROPN
ejpam-1528	53	6	and	and	CCONJ
ejpam-1528	53	7	(	(	PUNCT
ejpam-1528	53	8	da	da	ADJ
ejpam-1528	53	9	)	)	PUNCT
ejpam-1528	53	10	#	#	NOUN
ejpam-1528	53	11	exists	exist	VERB
ejpam-1528	53	12	.	.	PUNCT
ejpam-1528	54	1	iii	iii	X
ejpam-1528	54	2	)	)	PUNCT
ejpam-1528	54	3	d	d	NOUN
ejpam-1528	54	4	≤l	≤l	NOUN
ejpam-1528	54	5	ad	ad	NOUN
ejpam-1528	54	6	and	and	CCONJ
ejpam-1528	54	7	(	(	PUNCT
ejpam-1528	54	8	ad	ad	NOUN
ejpam-1528	54	9	)	)	PUNCT
ejpam-1528	54	10	#	#	NOUN
ejpam-1528	54	11	exists	exist	VERB
ejpam-1528	54	12	.	.	PUNCT
ejpam-1528	55	1	iv	iv	X
ejpam-1528	55	2	)	)	PUNCT
ejpam-1528	55	3	dadh	dadh	NOUN
ejpam-1528	55	4	d.	d.	PROPN
ejpam-1528	55	5	v	v	PROPN
ejpam-1528	55	6	)	)	PUNCT
ejpam-1528	56	1	d	d	X
ejpam-1528	56	2	≤h	≤h	NOUN
ejpam-1528	56	3	dad	dad	NOUN
ejpam-1528	56	4	.	.	PUNCT
ejpam-1528	57	1	in	in	ADP
ejpam-1528	57	2	this	this	DET
ejpam-1528	57	3	case	case	NOUN
ejpam-1528	57	4	,	,	PUNCT
ejpam-1528	57	5	b	b	NOUN
ejpam-1528	57	6	=	=	SYM
ejpam-1528	57	7	d(ad	d(ad	PROPN
ejpam-1528	57	8	)	)	PUNCT
ejpam-1528	57	9	]	]	PUNCT
ejpam-1528	58	1	=	=	SYM
ejpam-1528	58	2	(	(	PUNCT
ejpam-1528	58	3	da)]d	da)]d	PROPN
ejpam-1528	58	4	.	.	PUNCT
ejpam-1528	59	1	for	for	ADP
ejpam-1528	59	2	another	another	DET
ejpam-1528	59	3	look	look	NOUN
ejpam-1528	59	4	at	at	ADP
ejpam-1528	59	5	this	this	DET
ejpam-1528	59	6	inverse	inverse	NOUN
ejpam-1528	59	7	,	,	PUNCT
ejpam-1528	59	8	we	we	PRON
ejpam-1528	59	9	also	also	ADV
ejpam-1528	59	10	refer	refer	VERB
ejpam-1528	59	11	to	to	ADP
ejpam-1528	59	12	[	[	X
ejpam-1528	59	13	5	5	NUM
ejpam-1528	59	14	]	]	PUNCT
ejpam-1528	59	15	,	,	PUNCT
ejpam-1528	59	16	where	where	SCONJ
ejpam-1528	59	17	m.	m.	NOUN
ejpam-1528	59	18	drazin	drazin	PROPN
ejpam-1528	59	19	independently	independently	ADV
ejpam-1528	59	20	defined	define	VERB
ejpam-1528	59	21	an	an	DET
ejpam-1528	59	22	new	new	ADJ
ejpam-1528	59	23	outer	outer	ADJ
ejpam-1528	59	24	inverse	inverse	NOUN
ejpam-1528	59	25	that	that	PRON
ejpam-1528	59	26	is	be	AUX
ejpam-1528	59	27	actually	actually	ADV
ejpam-1528	59	28	similar	similar	ADJ
ejpam-1528	59	29	to	to	ADP
ejpam-1528	59	30	the	the	DET
ejpam-1528	59	31	inverse	inverse	NOUN
ejpam-1528	59	32	along	along	ADP
ejpam-1528	59	33	an	an	DET
ejpam-1528	59	34	element	element	NOUN
ejpam-1528	59	35	.	.	PUNCT
ejpam-1528	60	1	2.2	2.2	NUM
ejpam-1528	60	2	.	.	PUNCT
ejpam-1528	60	3	commutativity	commutativity	NOUN
ejpam-1528	60	4	and	and	CCONJ
ejpam-1528	60	5	idempotents	idempotent	VERB
ejpam-1528	60	6	a	a	DET
ejpam-1528	60	7	remarkable	remarkable	ADJ
ejpam-1528	60	8	feature	feature	NOUN
ejpam-1528	60	9	of	of	ADP
ejpam-1528	60	10	the	the	DET
ejpam-1528	60	11	inverse	inverse	NOUN
ejpam-1528	60	12	along	along	ADP
ejpam-1528	60	13	an	an	DET
ejpam-1528	60	14	element	element	NOUN
ejpam-1528	60	15	is	be	AUX
ejpam-1528	60	16	the	the	DET
ejpam-1528	60	17	following	following	NOUN
ejpam-1528	60	18	[	[	X
ejpam-1528	60	19	18	18	NUM
ejpam-1528	60	20	,	,	PUNCT
ejpam-1528	60	21	theorem	theorem	VERB
ejpam-1528	60	22	10	10	NUM
ejpam-1528	60	23	]	]	PUNCT
ejpam-1528	60	24	.	.	PUNCT
ejpam-1528	61	1	theorem	theorem	NOUN
ejpam-1528	61	2	2	2	NUM
ejpam-1528	61	3	.	.	PUNCT
ejpam-1528	62	1	let	let	VERB
ejpam-1528	62	2	a	a	PRON
ejpam-1528	62	3	,	,	PUNCT
ejpam-1528	62	4	d	d	PROPN
ejpam-1528	62	5	∈	∈	PROPN
ejpam-1528	62	6	s	s	PART
ejpam-1528	62	7	and	and	CCONJ
ejpam-1528	62	8	pose	pose	VERB
ejpam-1528	62	9	a=	a=	ADJ
ejpam-1528	62	10	(	(	PUNCT
ejpam-1528	62	11	a	a	DET
ejpam-1528	62	12	,	,	PUNCT
ejpam-1528	62	13	d	d	NOUN
ejpam-1528	62	14	)	)	PUNCT
ejpam-1528	62	15	.	.	PUNCT
ejpam-1528	63	1	if	if	SCONJ
ejpam-1528	63	2	a	a	PRON
ejpam-1528	63	3	is	be	AUX
ejpam-1528	63	4	invertible	invertible	ADJ
ejpam-1528	63	5	along	along	ADP
ejpam-1528	63	6	d	d	PROPN
ejpam-1528	63	7	,	,	PUNCT
ejpam-1528	63	8	then	then	ADV
ejpam-1528	63	9	a−d	a−d	PROPN
ejpam-1528	63	10	∈	∈	PROPN
ejpam-1528	63	11	a′′.	a′′.	PROPN
ejpam-1528	63	12	as	as	ADP
ejpam-1528	63	13	a	a	DET
ejpam-1528	63	14	direct	direct	ADJ
ejpam-1528	63	15	corollary	corollary	NOUN
ejpam-1528	63	16	,	,	PUNCT
ejpam-1528	63	17	we	we	PRON
ejpam-1528	63	18	get	get	VERB
ejpam-1528	63	19	:	:	PUNCT
ejpam-1528	63	20	corollary	corollary	ADJ
ejpam-1528	63	21	1	1	X
ejpam-1528	63	22	.	.	PUNCT
ejpam-1528	64	1	let	let	VERB
ejpam-1528	64	2	a	a	DET
ejpam-1528	64	3	,	,	PUNCT
ejpam-1528	64	4	d	d	PROPN
ejpam-1528	64	5	∈	∈	PROPN
ejpam-1528	64	6	s	s	NOUN
ejpam-1528	64	7	,	,	PUNCT
ejpam-1528	64	8	dadh	dadh	NOUN
ejpam-1528	64	9	d	d	NOUN
ejpam-1528	64	10	and	and	CCONJ
ejpam-1528	64	11	pose	pose	VERB
ejpam-1528	64	12	b	b	PROPN
ejpam-1528	64	13	=	=	X
ejpam-1528	64	14	a−d	a−d	PROPN
ejpam-1528	64	15	.	.	PUNCT
ejpam-1528	65	1	if	if	SCONJ
ejpam-1528	65	2	ad	ad	NOUN
ejpam-1528	65	3	=	=	SYM
ejpam-1528	65	4	da	da	NOUN
ejpam-1528	65	5	,	,	PUNCT
ejpam-1528	65	6	then	then	ADV
ejpam-1528	65	7	ab	ab	PROPN
ejpam-1528	65	8	=	=	PUNCT
ejpam-1528	65	9	ba	ba	PROPN
ejpam-1528	65	10	and	and	CCONJ
ejpam-1528	65	11	bd	bd	PROPN
ejpam-1528	65	12	=	=	PROPN
ejpam-1528	65	13	d	d	PROPN
ejpam-1528	65	14	b.	b.	PROPN
ejpam-1528	66	1	we	we	PRON
ejpam-1528	66	2	define	define	VERB
ejpam-1528	66	3	the	the	DET
ejpam-1528	66	4	following	follow	VERB
ejpam-1528	66	5	sets	set	NOUN
ejpam-1528	66	6	:	:	PUNCT
ejpam-1528	66	7	i	i	NOUN
ejpam-1528	66	8	)	)	PUNCT
ejpam-1528	66	9	σ0(a	σ0(a	PROPN
ejpam-1528	66	10	)	)	PUNCT
ejpam-1528	66	11	=	=	PRON
ejpam-1528	66	12	{	{	PUNCT
ejpam-1528	66	13	e	e	PROPN
ejpam-1528	66	14	∈	∈	PROPN
ejpam-1528	66	15	e(s	e(s	PROPN
ejpam-1528	66	16	)	)	PUNCT
ejpam-1528	66	17	,	,	PUNCT
ejpam-1528	66	18	eaeh	eaeh	NOUN
ejpam-1528	66	19	e	e	NOUN
ejpam-1528	66	20	}	}	PUNCT
ejpam-1528	66	21	;	;	PUNCT
ejpam-1528	66	22	ii	ii	X
ejpam-1528	66	23	)	)	PUNCT
ejpam-1528	66	24	σ1(a	σ1(a	NUM
ejpam-1528	66	25	)	)	PUNCT
ejpam-1528	66	26	=	=	PRON
ejpam-1528	66	27	{	{	PUNCT
ejpam-1528	66	28	a}′	a}′	NOUN
ejpam-1528	66	29	∩σ0(a	∩σ0(a	NOUN
ejpam-1528	66	30	)	)	PUNCT
ejpam-1528	66	31	;	;	PUNCT
ejpam-1528	66	32	iii	iii	X
ejpam-1528	66	33	)	)	PUNCT
ejpam-1528	66	34	σ2(a	σ2(a	PROPN
ejpam-1528	66	35	)	)	PUNCT
ejpam-1528	66	36	=	=	PRON
ejpam-1528	66	37	{	{	PUNCT
ejpam-1528	66	38	a}′′	a}′′	PROPN
ejpam-1528	66	39	∩σ0(a	∩σ0(a	NOUN
ejpam-1528	66	40	)	)	PUNCT
ejpam-1528	66	41	.	.	PUNCT
ejpam-1528	67	1	(	(	PUNCT
ejpam-1528	67	2	if	if	SCONJ
ejpam-1528	67	3	s	s	NOUN
ejpam-1528	67	4	is	be	AUX
ejpam-1528	67	5	commutative	commutative	ADJ
ejpam-1528	67	6	,	,	PUNCT
ejpam-1528	67	7	or	or	CCONJ
ejpam-1528	67	8	the	the	DET
ejpam-1528	67	9	idempotents	idempotent	NOUN
ejpam-1528	67	10	are	be	AUX
ejpam-1528	67	11	central	central	ADJ
ejpam-1528	67	12	,	,	PUNCT
ejpam-1528	67	13	then	then	ADV
ejpam-1528	67	14	the	the	DET
ejpam-1528	67	15	three	three	NUM
ejpam-1528	67	16	sets	set	NOUN
ejpam-1528	67	17	are	be	AUX
ejpam-1528	67	18	equal	equal	ADJ
ejpam-1528	67	19	.	.	PUNCT
ejpam-1528	68	1	we	we	PRON
ejpam-1528	68	2	then	then	ADV
ejpam-1528	68	3	simply	simply	ADV
ejpam-1528	68	4	denote	denote	VERB
ejpam-1528	68	5	it	it	PRON
ejpam-1528	68	6	σ(a	σ(a	PROPN
ejpam-1528	68	7	)	)	PUNCT
ejpam-1528	68	8	.	.	PUNCT
ejpam-1528	68	9	)	)	PUNCT
ejpam-1528	69	1	lemma	lemma	PROPN
ejpam-1528	69	2	3	3	X
ejpam-1528	69	3	.	.	PUNCT
ejpam-1528	70	1	let	let	VERB
ejpam-1528	70	2	e	e	X
ejpam-1528	70	3	∈	∈	PROPN
ejpam-1528	70	4	e(s	e(s	PROPN
ejpam-1528	70	5	)	)	PUNCT
ejpam-1528	70	6	and	and	CCONJ
ejpam-1528	70	7	a	a	DET
ejpam-1528	70	8	∈	∈	NOUN
ejpam-1528	70	9	s	s	VERB
ejpam-1528	70	10	such	such	ADJ
ejpam-1528	70	11	that	that	SCONJ
ejpam-1528	70	12	ae	ae	PROPN
ejpam-1528	70	13	=	=	SYM
ejpam-1528	70	14	ea	ea	PROPN
ejpam-1528	70	15	.	.	PUNCT
ejpam-1528	71	1	then	then	ADV
ejpam-1528	71	2	e	e	PROPN
ejpam-1528	71	3	∈	∈	PROPN
ejpam-1528	71	4	σ0(a	σ0(a	PROPN
ejpam-1528	71	5	)	)	PUNCT
ejpam-1528	71	6	⇐	⇐	ADJ
ejpam-1528	71	7	⇒	⇒	NOUN
ejpam-1528	71	8	e	e	X
ejpam-1528	71	9	≤h	≤h	NOUN
ejpam-1528	71	10	a.	a.	NOUN
ejpam-1528	71	11	x.	x.	NOUN
ejpam-1528	71	12	mary	mary	PROPN
ejpam-1528	71	13	/	/	SYM
ejpam-1528	71	14	eur	eur	PROPN
ejpam-1528	71	15	.	.	PUNCT
ejpam-1528	72	1	j.	j.	PROPN
ejpam-1528	72	2	pure	pure	PROPN
ejpam-1528	72	3	appl	appl	PROPN
ejpam-1528	72	4	.	.	PROPN
ejpam-1528	72	5	math	math	PROPN
ejpam-1528	72	6	,	,	PUNCT
ejpam-1528	72	7	6	6	NUM
ejpam-1528	72	8	(	(	PUNCT
ejpam-1528	72	9	2013	2013	NUM
ejpam-1528	72	10	)	)	PUNCT
ejpam-1528	72	11	,	,	PUNCT
ejpam-1528	72	12	413	413	NUM
ejpam-1528	72	13	-	-	SYM
ejpam-1528	72	14	427	427	NUM
ejpam-1528	72	15	416	416	NUM
ejpam-1528	72	16	proof	proof	NOUN
ejpam-1528	72	17	.	.	PUNCT
ejpam-1528	73	1	assume	assume	VERB
ejpam-1528	73	2	e	e	X
ejpam-1528	73	3	∈	∈	PROPN
ejpam-1528	73	4	σ0(a	σ0(a	PROPN
ejpam-1528	73	5	)	)	PUNCT
ejpam-1528	73	6	.	.	PUNCT
ejpam-1528	74	1	then	then	ADV
ejpam-1528	74	2	e	e	X
ejpam-1528	74	3	≤h	≤h	NOUN
ejpam-1528	74	4	eae	eae	PROPN
ejpam-1528	74	5	=	=	SYM
ejpam-1528	74	6	ea	ea	PROPN
ejpam-1528	74	7	=	=	SYM
ejpam-1528	74	8	ae	ae	PROPN
ejpam-1528	74	9	≤h	≤h	NOUN
ejpam-1528	74	10	a.	a.	NOUN
ejpam-1528	74	11	conversely	conversely	ADV
ejpam-1528	74	12	,	,	PUNCT
ejpam-1528	74	13	if	if	SCONJ
ejpam-1528	74	14	e	e	PROPN
ejpam-1528	74	15	≤h	≤h	VERB
ejpam-1528	74	16	a	a	PRON
ejpam-1528	74	17	and	and	CCONJ
ejpam-1528	74	18	ae	ae	PROPN
ejpam-1528	74	19	=	=	SYM
ejpam-1528	74	20	ea	ea	PROPN
ejpam-1528	74	21	,	,	PUNCT
ejpam-1528	74	22	then	then	ADV
ejpam-1528	74	23	e	e	X
ejpam-1528	74	24	≤r	≤r	PROPN
ejpam-1528	74	25	a⇒	a⇒	PROPN
ejpam-1528	74	26	e	e	PROPN
ejpam-1528	74	27	=	=	PROPN
ejpam-1528	74	28	ee	ee	PROPN
ejpam-1528	74	29	≤r	≤r	PROPN
ejpam-1528	74	30	ea	ea	X
ejpam-1528	75	1	≤r	≤r	PROPN
ejpam-1528	75	2	e	e	PROPN
ejpam-1528	75	3	that	that	PRON
ejpam-1528	75	4	is	be	AUX
ejpam-1528	75	5	erea	erea	NOUN
ejpam-1528	75	6	.	.	PUNCT
ejpam-1528	76	1	but	but	CCONJ
ejpam-1528	76	2	ea	ea	X
ejpam-1528	76	3	=	=	SYM
ejpam-1528	76	4	ae	ae	PROPN
ejpam-1528	76	5	,	,	PUNCT
ejpam-1528	76	6	hence	hence	ADV
ejpam-1528	76	7	erea⇒	erea⇒	PROPN
ejpam-1528	76	8	erae⇒	erae⇒	NOUN
ejpam-1528	76	9	e	e	X
ejpam-1528	76	10	=	=	SYM
ejpam-1528	76	11	eereae	eereae	PROPN
ejpam-1528	76	12	.	.	PUNCT
ejpam-1528	77	1	by	by	ADP
ejpam-1528	77	2	symmetry	symmetry	NOUN
ejpam-1528	77	3	,	,	PUNCT
ejpam-1528	77	4	we	we	PRON
ejpam-1528	77	5	get	get	VERB
ejpam-1528	77	6	eh	eh	INTJ
ejpam-1528	77	7	eae	eae	PROPN
ejpam-1528	77	8	.	.	PUNCT
ejpam-1528	78	1	combining	combine	VERB
ejpam-1528	78	2	the	the	DET
ejpam-1528	78	3	previous	previous	ADJ
ejpam-1528	78	4	lemmas	lemma	NOUN
ejpam-1528	78	5	and	and	CCONJ
ejpam-1528	78	6	theorems	theorem	NOUN
ejpam-1528	78	7	we	we	PRON
ejpam-1528	78	8	get	get	VERB
ejpam-1528	78	9	:	:	PUNCT
ejpam-1528	78	10	theorem	theorem	ADJ
ejpam-1528	78	11	3	3	NUM
ejpam-1528	78	12	.	.	PUNCT
ejpam-1528	79	1	τa	τa	PROPN
ejpam-1528	79	2	:	:	PUNCT
ejpam-1528	79	3	w	w	X
ejpam-1528	79	4	(	(	PUNCT
ejpam-1528	79	5	a	a	X
ejpam-1528	79	6	)	)	PUNCT
ejpam-1528	79	7	−→	−→	NOUN
ejpam-1528	79	8	e(s	e(s	PROPN
ejpam-1528	79	9	)	)	PUNCT
ejpam-1528	80	1	x	x	SYM
ejpam-1528	80	2	7−→	7−→	NOUN
ejpam-1528	80	3	ax	ax	NOUN
ejpam-1528	80	4	•	•	NOUN
ejpam-1528	80	5	is	be	AUX
ejpam-1528	80	6	one	one	NUM
ejpam-1528	80	7	to	to	ADP
ejpam-1528	80	8	one	one	NUM
ejpam-1528	80	9	from	from	ADP
ejpam-1528	80	10	w	w	PROPN
ejpam-1528	80	11	(	(	PUNCT
ejpam-1528	80	12	a)∩	a)∩	X
ejpam-1528	80	13	{	{	PUNCT
ejpam-1528	80	14	a}′	a}′	NOUN
ejpam-1528	80	15	onto	onto	ADP
ejpam-1528	80	16	σ1(a	σ1(a	NOUN
ejpam-1528	80	17	)	)	PUNCT
ejpam-1528	80	18	;	;	PUNCT
ejpam-1528	80	19	•	•	NUM
ejpam-1528	80	20	is	be	AUX
ejpam-1528	80	21	one	one	NUM
ejpam-1528	80	22	to	to	ADP
ejpam-1528	80	23	one	one	NUM
ejpam-1528	80	24	from	from	ADP
ejpam-1528	80	25	w	w	PROPN
ejpam-1528	80	26	(	(	PUNCT
ejpam-1528	80	27	a)∩	a)∩	X
ejpam-1528	80	28	{	{	PUNCT
ejpam-1528	80	29	a}′′	a}′′	NOUN
ejpam-1528	80	30	onto	onto	ADP
ejpam-1528	80	31	σ2(a	σ2(a	NUM
ejpam-1528	80	32	)	)	PUNCT
ejpam-1528	80	33	.	.	PUNCT
ejpam-1528	81	1	its	its	PRON
ejpam-1528	81	2	reciprocal	reciprocal	ADJ
ejpam-1528	81	3	τ−1	τ−1	PROPN
ejpam-1528	81	4	a	a	DET
ejpam-1528	81	5	associates	associate	NOUN
ejpam-1528	81	6	e	e	NOUN
ejpam-1528	81	7	to	to	ADP
ejpam-1528	81	8	b	b	NOUN
ejpam-1528	81	9	=	=	NOUN
ejpam-1528	81	10	a−e	a−e	NOUN
ejpam-1528	81	11	.	.	PUNCT
ejpam-1528	82	1	proof	proof	NOUN
ejpam-1528	82	2	.	.	PUNCT
ejpam-1528	83	1	let	let	VERB
ejpam-1528	83	2	b	b	X
ejpam-1528	83	3	,	,	PUNCT
ejpam-1528	83	4	c	c	PROPN
ejpam-1528	83	5	∈	∈	PROPN
ejpam-1528	83	6	w	w	PROPN
ejpam-1528	83	7	(	(	PUNCT
ejpam-1528	83	8	a	a	NOUN
ejpam-1528	83	9	)	)	PUNCT
ejpam-1528	83	10	∩	∩	NOUN
ejpam-1528	83	11	{	{	PUNCT
ejpam-1528	83	12	a}′.	a}′.	ADV
ejpam-1528	83	13	then	then	ADV
ejpam-1528	84	1	ab	ab	PROPN
ejpam-1528	84	2	=	=	PUNCT
ejpam-1528	84	3	ac	ac	PROPN
ejpam-1528	84	4	⇒	⇒	PROPN
ejpam-1528	84	5	b	b	PROPN
ejpam-1528	84	6	=	=	SYM
ejpam-1528	84	7	bab	bab	PROPN
ejpam-1528	84	8	=	=	SYM
ejpam-1528	84	9	bac	bac	PROPN
ejpam-1528	84	10	.	.	PUNCT
ejpam-1528	85	1	but	but	CCONJ
ejpam-1528	85	2	also	also	ADV
ejpam-1528	85	3	ba	ba	PROPN
ejpam-1528	86	1	=	=	PUNCT
ejpam-1528	86	2	ca	can	AUX
ejpam-1528	86	3	by	by	ADP
ejpam-1528	86	4	commutativity	commutativity	NOUN
ejpam-1528	86	5	and	and	CCONJ
ejpam-1528	86	6	bac	bac	NOUN
ejpam-1528	86	7	=	=	PROPN
ejpam-1528	86	8	cac	cac	PROPN
ejpam-1528	86	9	=	=	PROPN
ejpam-1528	86	10	c.	c.	PROPN
ejpam-1528	86	11	finally	finally	ADV
ejpam-1528	86	12	b	b	X
ejpam-1528	86	13	=	=	PROPN
ejpam-1528	86	14	c.	c.	PROPN
ejpam-1528	86	15	obviously	obviously	ADV
ejpam-1528	86	16	,	,	PUNCT
ejpam-1528	86	17	ab	ab	PROPN
ejpam-1528	86	18	=	=	PUNCT
ejpam-1528	86	19	ba	ba	PROPN
ejpam-1528	87	1	=	=	PUNCT
ejpam-1528	87	2	e	e	PROPN
ejpam-1528	87	3	is	be	AUX
ejpam-1528	87	4	an	an	DET
ejpam-1528	87	5	idempotent	idempotent	NOUN
ejpam-1528	87	6	commuting	commuting	NOUN
ejpam-1528	87	7	with	with	ADP
ejpam-1528	87	8	a.	a.	NOUN
ejpam-1528	87	9	conversely	conversely	ADV
ejpam-1528	87	10	,	,	PUNCT
ejpam-1528	87	11	if	if	SCONJ
ejpam-1528	87	12	e	e	PROPN
ejpam-1528	87	13	∈	∈	PROPN
ejpam-1528	87	14	σ1(a	σ1(a	PROPN
ejpam-1528	87	15	)	)	PUNCT
ejpam-1528	87	16	,	,	PUNCT
ejpam-1528	87	17	then	then	ADV
ejpam-1528	87	18	e	e	PROPN
ejpam-1528	87	19	≤r	≤r	VERB
ejpam-1528	87	20	a	a	DET
ejpam-1528	87	21	⇒	⇒	NOUN
ejpam-1528	87	22	e	e	X
ejpam-1528	87	23	=	=	SYM
ejpam-1528	87	24	ee	ee	PROPN
ejpam-1528	87	25	≤r	≤r	PROPN
ejpam-1528	87	26	ea	ea	PROPN
ejpam-1528	88	1	=	=	SYM
ejpam-1528	88	2	ae	ae	PROPN
ejpam-1528	88	3	≤r	≤r	PROPN
ejpam-1528	88	4	e.	e.	PROPN
ejpam-1528	88	5	also	also	ADV
ejpam-1528	88	6	e	e	VERB
ejpam-1528	88	7	≤l	≤l	NOUN
ejpam-1528	88	8	a⇒	a⇒	PRON
ejpam-1528	88	9	e	e	PROPN
ejpam-1528	88	10	=	=	PROPN
ejpam-1528	88	11	ee	ee	PROPN
ejpam-1528	88	12	≤r	≤r	PROPN
ejpam-1528	88	13	ae	ae	PROPN
ejpam-1528	88	14	=	=	SYM
ejpam-1528	88	15	ea	ea	PROPN
ejpam-1528	88	16	≤l	≤l	PROPN
ejpam-1528	88	17	e.	e.	PROPN
ejpam-1528	89	1	it	it	PRON
ejpam-1528	89	2	follows	follow	VERB
ejpam-1528	89	3	that	that	PRON
ejpam-1528	89	4	ea	ea	PROPN
ejpam-1528	90	1	=	=	SYM
ejpam-1528	90	2	eah	eah	PROPN
ejpam-1528	90	3	e	e	PROPN
ejpam-1528	90	4	,	,	PUNCT
ejpam-1528	90	5	a	a	PRON
ejpam-1528	90	6	is	be	AUX
ejpam-1528	90	7	invertible	invertible	ADJ
ejpam-1528	90	8	along	along	ADP
ejpam-1528	90	9	e.	e.	PROPN
ejpam-1528	90	10	pose	pose	PROPN
ejpam-1528	90	11	b	b	NOUN
ejpam-1528	90	12	=	=	NOUN
ejpam-1528	90	13	a−e	a−e	NOUN
ejpam-1528	90	14	.	.	PUNCT
ejpam-1528	91	1	then	then	ADV
ejpam-1528	91	2	b	b	X
ejpam-1528	91	3	∈	∈	PROPN
ejpam-1528	91	4	{	{	PUNCT
ejpam-1528	91	5	a	a	NOUN
ejpam-1528	91	6	,	,	PUNCT
ejpam-1528	91	7	e}′′	e}′′	PROPN
ejpam-1528	91	8	hence	hence	ADV
ejpam-1528	91	9	ab	ab	PROPN
ejpam-1528	91	10	=	=	PUNCT
ejpam-1528	91	11	ba	ba	PROPN
ejpam-1528	91	12	and	and	CCONJ
ejpam-1528	91	13	ab	ab	NOUN
ejpam-1528	91	14	=	=	PROPN
ejpam-1528	91	15	abe	abe	PROPN
ejpam-1528	91	16	=	=	PROPN
ejpam-1528	91	17	bae	bae	PROPN
ejpam-1528	91	18	=	=	PROPN
ejpam-1528	91	19	e.	e.	PROPN
ejpam-1528	91	20	for	for	ADP
ejpam-1528	91	21	the	the	DET
ejpam-1528	91	22	second	second	ADJ
ejpam-1528	91	23	statement	statement	NOUN
ejpam-1528	91	24	,	,	PUNCT
ejpam-1528	91	25	we	we	PRON
ejpam-1528	91	26	have	have	VERB
ejpam-1528	91	27	only	only	ADV
ejpam-1528	91	28	to	to	PART
ejpam-1528	91	29	prove	prove	VERB
ejpam-1528	91	30	that	that	SCONJ
ejpam-1528	91	31	τa	τa	ADP
ejpam-1528	91	32	maps	maps	PROPN
ejpam-1528	91	33	w	w	PROPN
ejpam-1528	91	34	(	(	PUNCT
ejpam-1528	91	35	a	a	NOUN
ejpam-1528	91	36	)	)	PUNCT
ejpam-1528	91	37	∩	∩	NOUN
ejpam-1528	91	38	{	{	PUNCT
ejpam-1528	91	39	a}′′	a}′′	NOUN
ejpam-1528	91	40	onto	onto	ADP
ejpam-1528	91	41	σ2(a	σ2(a	NUM
ejpam-1528	91	42	)	)	PUNCT
ejpam-1528	91	43	,	,	PUNCT
ejpam-1528	91	44	but	but	CCONJ
ejpam-1528	91	45	this	this	PRON
ejpam-1528	91	46	follows	follow	VERB
ejpam-1528	91	47	from	from	ADP
ejpam-1528	91	48	theorem	theorem	ADJ
ejpam-1528	91	49	2	2	NUM
ejpam-1528	91	50	.	.	PUNCT
ejpam-1528	91	51	as	as	ADP
ejpam-1528	91	52	a	a	DET
ejpam-1528	91	53	consequence	consequence	NOUN
ejpam-1528	91	54	,	,	PUNCT
ejpam-1528	91	55	looking	look	VERB
ejpam-1528	91	56	for	for	ADP
ejpam-1528	91	57	commuting	commute	VERB
ejpam-1528	91	58	or	or	CCONJ
ejpam-1528	91	59	bicommuting	bicommute	VERB
ejpam-1528	91	60	outer	outer	ADJ
ejpam-1528	91	61	inverses	inverse	NOUN
ejpam-1528	91	62	can	can	AUX
ejpam-1528	91	63	be	be	AUX
ejpam-1528	91	64	handled	handle	VERB
ejpam-1528	91	65	through	through	ADP
ejpam-1528	91	66	idempotents	idempotent	NOUN
ejpam-1528	91	67	.	.	PUNCT
ejpam-1528	92	1	recall	recall	VERB
ejpam-1528	92	2	that	that	SCONJ
ejpam-1528	92	3	any	any	DET
ejpam-1528	92	4	set	set	NOUN
ejpam-1528	92	5	of	of	ADP
ejpam-1528	92	6	idempotents	idempotent	NOUN
ejpam-1528	92	7	may	may	AUX
ejpam-1528	92	8	be	be	AUX
ejpam-1528	92	9	partially	partially	ADV
ejpam-1528	92	10	ordered	order	VERB
ejpam-1528	92	11	by	by	ADP
ejpam-1528	92	12	e	e	PROPN
ejpam-1528	92	13	≤	≤	PROPN
ejpam-1528	93	1	f	f	X
ejpam-1528	93	2	⇐	⇐	ADJ
ejpam-1528	93	3	⇒	⇒	NOUN
ejpam-1528	93	4	e	e	X
ejpam-1528	93	5	f	f	X
ejpam-1528	93	6	=	=	SYM
ejpam-1528	93	7	f	f	X
ejpam-1528	93	8	e	e	X
ejpam-1528	93	9	=	=	SYM
ejpam-1528	93	10	e	e	PROPN
ejpam-1528	93	11	,	,	PUNCT
ejpam-1528	93	12	the	the	DET
ejpam-1528	93	13	natural	natural	ADJ
ejpam-1528	93	14	partial	partial	ADJ
ejpam-1528	93	15	order	order	NOUN
ejpam-1528	93	16	,	,	PUNCT
ejpam-1528	93	17	and	and	CCONJ
ejpam-1528	93	18	if	if	SCONJ
ejpam-1528	93	19	this	this	DET
ejpam-1528	93	20	set	set	NOUN
ejpam-1528	93	21	is	be	AUX
ejpam-1528	93	22	commutative	commutative	ADJ
ejpam-1528	93	23	,	,	PUNCT
ejpam-1528	93	24	then	then	ADV
ejpam-1528	93	25	this	this	DET
ejpam-1528	93	26	partial	partial	ADJ
ejpam-1528	93	27	order	order	NOUN
ejpam-1528	93	28	is	be	AUX
ejpam-1528	93	29	compatible	compatible	ADJ
ejpam-1528	93	30	with	with	ADP
ejpam-1528	93	31	multiplication	multiplication	NOUN
ejpam-1528	93	32	.	.	PUNCT
ejpam-1528	94	1	we	we	PRON
ejpam-1528	94	2	then	then	ADV
ejpam-1528	94	3	have	have	VERB
ejpam-1528	94	4	two	two	NUM
ejpam-1528	94	5	partial	partial	ADJ
ejpam-1528	94	6	orders	order	NOUN
ejpam-1528	94	7	on	on	ADP
ejpam-1528	94	8	e(s	e(s	PROPN
ejpam-1528	94	9	)	)	PUNCT
ejpam-1528	94	10	,	,	PUNCT
ejpam-1528	94	11	the	the	DET
ejpam-1528	94	12	natural	natural	ADJ
ejpam-1528	94	13	partial	partial	ADJ
ejpam-1528	94	14	order	order	NOUN
ejpam-1528	94	15	and	and	CCONJ
ejpam-1528	94	16	the	the	DET
ejpam-1528	94	17	h	h	NOUN
ejpam-1528	94	18	preorder	preorder	NOUN
ejpam-1528	94	19	(	(	PUNCT
ejpam-1528	94	20	that	that	PRON
ejpam-1528	94	21	reduces	reduce	VERB
ejpam-1528	94	22	to	to	ADP
ejpam-1528	94	23	a	a	DET
ejpam-1528	94	24	partial	partial	ADJ
ejpam-1528	94	25	order	order	NOUN
ejpam-1528	94	26	for	for	ADP
ejpam-1528	94	27	idempotents	idempotent	NOUN
ejpam-1528	94	28	since	since	SCONJ
ejpam-1528	94	29	a	a	DET
ejpam-1528	94	30	h	h	NOUN
ejpam-1528	94	31	-class	-class	NOUN
ejpam-1528	94	32	contains	contain	VERB
ejpam-1528	94	33	at	at	ADP
ejpam-1528	94	34	most	most	ADJ
ejpam-1528	94	35	one	one	NUM
ejpam-1528	94	36	idempotent	idempotent	NOUN
ejpam-1528	95	1	[	[	X
ejpam-1528	95	2	9	9	NUM
ejpam-1528	95	3	]	]	PUNCT
ejpam-1528	95	4	)	)	PUNCT
ejpam-1528	95	5	.	.	PUNCT
ejpam-1528	96	1	actually	actually	ADV
ejpam-1528	96	2	,	,	PUNCT
ejpam-1528	96	3	they	they	PRON
ejpam-1528	96	4	coincide	coincide	VERB
ejpam-1528	96	5	for	for	ADP
ejpam-1528	96	6	idempotents	idempotent	NOUN
ejpam-1528	96	7	.	.	PUNCT
ejpam-1528	97	1	if	if	SCONJ
ejpam-1528	97	2	e	e	PROPN
ejpam-1528	97	3	≤	≤	X
ejpam-1528	97	4	f	f	NOUN
ejpam-1528	97	5	,	,	PUNCT
ejpam-1528	97	6	then	then	ADV
ejpam-1528	97	7	e	e	X
ejpam-1528	97	8	=	=	PUNCT
ejpam-1528	97	9	e	e	X
ejpam-1528	97	10	f	f	PROPN
ejpam-1528	97	11	=	=	SYM
ejpam-1528	97	12	f	f	PROPN
ejpam-1528	97	13	e	e	PROPN
ejpam-1528	97	14	and	and	CCONJ
ejpam-1528	97	15	e	e	X
ejpam-1528	97	16	≤h	≤h	NOUN
ejpam-1528	97	17	f	f	PROPN
ejpam-1528	97	18	and	and	CCONJ
ejpam-1528	97	19	conversely	conversely	ADV
ejpam-1528	97	20	,	,	PUNCT
ejpam-1528	97	21	if	if	SCONJ
ejpam-1528	97	22	e	e	NOUN
ejpam-1528	97	23	=	=	NOUN
ejpam-1528	97	24	f	f	X
ejpam-1528	98	1	x	x	X
ejpam-1528	98	2	=	=	PUNCT
ejpam-1528	98	3	y	y	PROPN
ejpam-1528	98	4	f	f	PROPN
ejpam-1528	98	5	then	then	ADV
ejpam-1528	98	6	f	f	PROPN
ejpam-1528	98	7	e	e	PROPN
ejpam-1528	98	8	=	=	PUNCT
ejpam-1528	99	1	f	f	PROPN
ejpam-1528	99	2	f	f	NOUN
ejpam-1528	99	3	x	x	X
ejpam-1528	99	4	=	=	PUNCT
ejpam-1528	99	5	f	f	NOUN
ejpam-1528	99	6	x	x	PUNCT
ejpam-1528	100	1	=	=	PUNCT
ejpam-1528	100	2	e	e	X
ejpam-1528	100	3	=	=	SYM
ejpam-1528	100	4	y	y	PROPN
ejpam-1528	101	1	f	f	PROPN
ejpam-1528	101	2	=	=	SYM
ejpam-1528	102	1	y	y	PROPN
ejpam-1528	102	2	f	f	X
ejpam-1528	102	3	f	f	PROPN
ejpam-1528	102	4	=	=	SYM
ejpam-1528	102	5	e	e	X
ejpam-1528	102	6	f	f	PROPN
ejpam-1528	102	7	.	.	PUNCT
ejpam-1528	103	1	it	it	PRON
ejpam-1528	103	2	is	be	AUX
ejpam-1528	103	3	interesting	interesting	ADJ
ejpam-1528	103	4	to	to	PART
ejpam-1528	103	5	notice	notice	VERB
ejpam-1528	103	6	that	that	SCONJ
ejpam-1528	103	7	even	even	ADV
ejpam-1528	103	8	in	in	ADP
ejpam-1528	103	9	the	the	DET
ejpam-1528	103	10	noncommutative	noncommutative	ADJ
ejpam-1528	103	11	case	case	NOUN
ejpam-1528	103	12	,	,	PUNCT
ejpam-1528	103	13	invertibilty	invertibilty	NOUN
ejpam-1528	103	14	along	along	ADP
ejpam-1528	103	15	an	an	DET
ejpam-1528	103	16	idempotent	idempotent	NOUN
ejpam-1528	103	17	e	e	NOUN
ejpam-1528	103	18	can	can	AUX
ejpam-1528	103	19	be	be	AUX
ejpam-1528	103	20	expressed	express	VERB
ejpam-1528	103	21	as	as	ADP
ejpam-1528	103	22	invertibity	invertibity	NOUN
ejpam-1528	103	23	in	in	ADP
ejpam-1528	103	24	the	the	DET
ejpam-1528	103	25	local	local	ADJ
ejpam-1528	103	26	submonoid	submonoid	ADJ
ejpam-1528	103	27	ese	ese	NOUN
ejpam-1528	103	28	(	(	PUNCT
ejpam-1528	103	29	ring	ring	NOUN
ejpam-1528	103	30	theorists	theorist	NOUN
ejpam-1528	103	31	use	use	VERB
ejpam-1528	103	32	the	the	DET
ejpam-1528	103	33	word	word	NOUN
ejpam-1528	103	34	“	"	PUNCT
ejpam-1528	103	35	corner	corner	NOUN
ejpam-1528	103	36	ring	ring	NOUN
ejpam-1528	103	37	”	"	PUNCT
ejpam-1528	103	38	)	)	PUNCT
ejpam-1528	103	39	.	.	PUNCT
ejpam-1528	104	1	lemma	lemma	PROPN
ejpam-1528	104	2	4	4	X
ejpam-1528	104	3	.	.	PUNCT
ejpam-1528	104	4	let	let	VERB
ejpam-1528	104	5	a	a	DET
ejpam-1528	104	6	∈	∈	ADJ
ejpam-1528	104	7	s	s	NOUN
ejpam-1528	104	8	,	,	PUNCT
ejpam-1528	104	9	e	e	PROPN
ejpam-1528	104	10	∈	∈	PROPN
ejpam-1528	104	11	e(s	e(s	PROPN
ejpam-1528	104	12	)	)	PUNCT
ejpam-1528	104	13	.	.	PUNCT
ejpam-1528	105	1	then	then	ADV
ejpam-1528	105	2	e	e	PROPN
ejpam-1528	105	3	∈	∈	PROPN
ejpam-1528	105	4	σ0(a	σ0(a	PROPN
ejpam-1528	105	5	)	)	PUNCT
ejpam-1528	105	6	(	(	PUNCT
ejpam-1528	105	7	a−e	a−e	NOUN
ejpam-1528	105	8	exists	exist	VERB
ejpam-1528	105	9	)	)	PUNCT
ejpam-1528	106	1	if	if	SCONJ
ejpam-1528	106	2	and	and	CCONJ
ejpam-1528	106	3	only	only	ADV
ejpam-1528	106	4	if	if	SCONJ
ejpam-1528	106	5	eae	eae	PROPN
ejpam-1528	106	6	is	be	AUX
ejpam-1528	106	7	invertible	invertible	ADJ
ejpam-1528	106	8	in	in	ADP
ejpam-1528	106	9	the	the	DET
ejpam-1528	106	10	local	local	ADJ
ejpam-1528	106	11	submonoid	submonoid	ADJ
ejpam-1528	106	12	ese	ese	NOUN
ejpam-1528	106	13	.	.	PUNCT
ejpam-1528	107	1	in	in	ADP
ejpam-1528	107	2	this	this	DET
ejpam-1528	107	3	case	case	NOUN
ejpam-1528	107	4	a−e	a−e	NOUN
ejpam-1528	107	5	=	=	PUNCT
ejpam-1528	107	6	(	(	PUNCT
ejpam-1528	107	7	ea)#e	ea)#e	NOUN
ejpam-1528	107	8	=	=	PUNCT
ejpam-1528	107	9	e(ae	e(ae	NOUN
ejpam-1528	107	10	)	)	PUNCT
ejpam-1528	107	11	#	#	NOUN
ejpam-1528	107	12	=	=	SYM
ejpam-1528	107	13	(	(	PUNCT
ejpam-1528	107	14	eae	eae	NOUN
ejpam-1528	107	15	)	)	PUNCT
ejpam-1528	107	16	#	#	NOUN
ejpam-1528	107	17	=	=	SYM
ejpam-1528	107	18	(	(	PUNCT
ejpam-1528	107	19	eae)−1	eae)−1	NOUN
ejpam-1528	107	20	.	.	PUNCT
ejpam-1528	108	1	proof	proof	NOUN
ejpam-1528	108	2	.	.	PUNCT
ejpam-1528	109	1	assume	assume	VERB
ejpam-1528	109	2	a−e	a−e	NOUN
ejpam-1528	109	3	exists	exist	VERB
ejpam-1528	109	4	.	.	PUNCT
ejpam-1528	110	1	then	then	ADV
ejpam-1528	110	2	a−eh	a−eh	PRON
ejpam-1528	110	3	e	e	NOUN
ejpam-1528	110	4	hence	hence	ADV
ejpam-1528	110	5	a−e	a−e	NOUN
ejpam-1528	110	6	=	=	SYM
ejpam-1528	110	7	ea−e	ea−e	NOUN
ejpam-1528	110	8	=	=	PUNCT
ejpam-1528	110	9	a−ee	a−ee	PROPN
ejpam-1528	110	10	=	=	SYM
ejpam-1528	110	11	ea−ee	ea−ee	PRON
ejpam-1528	110	12	∈	∈	PROPN
ejpam-1528	110	13	ese	ese	NOUN
ejpam-1528	110	14	.	.	PUNCT
ejpam-1528	111	1	it	it	PRON
ejpam-1528	111	2	also	also	ADV
ejpam-1528	111	3	satisfies	satisfy	VERB
ejpam-1528	111	4	a−eae	a−eae	ADP
ejpam-1528	111	5	=	=	SYM
ejpam-1528	111	6	e	e	NOUN
ejpam-1528	111	7	=	=	SYM
ejpam-1528	111	8	eaa−e	eaa−e	PROPN
ejpam-1528	111	9	hence	hence	ADV
ejpam-1528	111	10	a−e(eae	a−e(eae	NUM
ejpam-1528	111	11	)	)	PUNCT
ejpam-1528	111	12	=	=	PUNCT
ejpam-1528	111	13	e	e	X
ejpam-1528	111	14	=	=	PUNCT
ejpam-1528	111	15	(	(	PUNCT
ejpam-1528	111	16	eae)a−e	eae)a−e	NOUN
ejpam-1528	111	17	and	and	CCONJ
ejpam-1528	111	18	eae	eae	PROPN
ejpam-1528	111	19	is	be	AUX
ejpam-1528	111	20	invertible	invertible	ADJ
ejpam-1528	111	21	in	in	ADP
ejpam-1528	111	22	the	the	DET
ejpam-1528	111	23	monoid	monoid	NOUN
ejpam-1528	111	24	ese	ese	NOUN
ejpam-1528	111	25	(	(	PUNCT
ejpam-1528	111	26	with	with	ADP
ejpam-1528	111	27	unit	unit	NOUN
ejpam-1528	111	28	e	e	NOUN
ejpam-1528	111	29	)	)	PUNCT
ejpam-1528	111	30	.	.	PUNCT
ejpam-1528	112	1	conversely	conversely	ADV
ejpam-1528	112	2	,	,	PUNCT
ejpam-1528	112	3	assume	assume	VERB
ejpam-1528	112	4	eae	eae	PROPN
ejpam-1528	112	5	is	be	AUX
ejpam-1528	112	6	invertible	invertible	ADJ
ejpam-1528	112	7	in	in	ADP
ejpam-1528	112	8	ese	ese	NOUN
ejpam-1528	112	9	with	with	ADP
ejpam-1528	112	10	inverse	inverse	NOUN
ejpam-1528	112	11	b	b	PROPN
ejpam-1528	112	12	∈	∈	PROPN
ejpam-1528	112	13	ese	ese	NOUN
ejpam-1528	112	14	.	.	PUNCT
ejpam-1528	113	1	then	then	ADV
ejpam-1528	113	2	b	b	X
ejpam-1528	113	3	≤h	≤h	NOUN
ejpam-1528	113	4	e	e	NOUN
ejpam-1528	113	5	and	and	CCONJ
ejpam-1528	113	6	bae	bae	PROPN
ejpam-1528	113	7	=	=	SYM
ejpam-1528	113	8	b(eae	b(eae	PROPN
ejpam-1528	113	9	)	)	PUNCT
ejpam-1528	114	1	=	=	PUNCT
ejpam-1528	114	2	e	e	X
ejpam-1528	114	3	=	=	PUNCT
ejpam-1528	114	4	(	(	PUNCT
ejpam-1528	114	5	eae)b	eae)b	ADJ
ejpam-1528	114	6	=	=	SYM
ejpam-1528	114	7	eab	eab	NOUN
ejpam-1528	114	8	and	and	CCONJ
ejpam-1528	114	9	b	b	PROPN
ejpam-1528	114	10	is	be	AUX
ejpam-1528	114	11	the	the	DET
ejpam-1528	114	12	inverse	inverse	NOUN
ejpam-1528	114	13	of	of	ADP
ejpam-1528	114	14	a	a	PRON
ejpam-1528	114	15	along	along	NOUN
ejpam-1528	114	16	e.	e.	PROPN
ejpam-1528	114	17	finally	finally	ADV
ejpam-1528	114	18	,	,	PUNCT
ejpam-1528	114	19	note	note	VERB
ejpam-1528	114	20	that	that	SCONJ
ejpam-1528	114	21	σ2(a	σ2(a	NOUN
ejpam-1528	114	22	)	)	PUNCT
ejpam-1528	114	23	is	be	AUX
ejpam-1528	114	24	a	a	DET
ejpam-1528	114	25	commutative	commutative	ADJ
ejpam-1528	114	26	band	band	NOUN
ejpam-1528	114	27	(	(	PUNCT
ejpam-1528	114	28	commutative	commutative	ADJ
ejpam-1528	114	29	semigroup	semigroup	NOUN
ejpam-1528	114	30	of	of	ADP
ejpam-1528	114	31	idempotents	idempotent	NOUN
ejpam-1528	114	32	,	,	PUNCT
ejpam-1528	114	33	semilattice	semilattice	NOUN
ejpam-1528	114	34	with	with	ADP
ejpam-1528	114	35	e	e	PROPN
ejpam-1528	114	36	∧	∧	PROPN
ejpam-1528	114	37	f	f	PROPN
ejpam-1528	114	38	=	=	SYM
ejpam-1528	114	39	e	e	X
ejpam-1528	114	40	f	f	PROPN
ejpam-1528	114	41	=	=	SYM
ejpam-1528	114	42	f	f	PROPN
ejpam-1528	114	43	e	e	NOUN
ejpam-1528	114	44	)	)	PUNCT
ejpam-1528	114	45	.	.	PUNCT
ejpam-1528	115	1	x.	x.	PROPN
ejpam-1528	115	2	mary	mary	PROPN
ejpam-1528	115	3	/	/	SYM
ejpam-1528	115	4	eur	eur	PROPN
ejpam-1528	115	5	.	.	PUNCT
ejpam-1528	116	1	j.	j.	PROPN
ejpam-1528	116	2	pure	pure	PROPN
ejpam-1528	116	3	appl	appl	PROPN
ejpam-1528	116	4	.	.	PROPN
ejpam-1528	116	5	math	math	PROPN
ejpam-1528	116	6	,	,	PUNCT
ejpam-1528	116	7	6	6	NUM
ejpam-1528	116	8	(	(	PUNCT
ejpam-1528	116	9	2013	2013	NUM
ejpam-1528	116	10	)	)	PUNCT
ejpam-1528	116	11	,	,	PUNCT
ejpam-1528	116	12	413	413	NUM
ejpam-1528	116	13	-	-	SYM
ejpam-1528	116	14	427	427	NUM
ejpam-1528	116	15	417	417	NUM
ejpam-1528	116	16	proposition	proposition	NOUN
ejpam-1528	116	17	1	1	NUM
ejpam-1528	116	18	.	.	PUNCT
ejpam-1528	116	19	σ2(a	σ2(a	NUM
ejpam-1528	116	20	)	)	PUNCT
ejpam-1528	116	21	is	be	AUX
ejpam-1528	116	22	a	a	DET
ejpam-1528	116	23	commutative	commutative	ADJ
ejpam-1528	116	24	subsemigroup	subsemigroup	NOUN
ejpam-1528	116	25	of	of	ADP
ejpam-1528	116	26	s.	s.	PROPN
ejpam-1528	116	27	proof	proof	PROPN
ejpam-1528	116	28	.	.	PUNCT
ejpam-1528	117	1	if	if	SCONJ
ejpam-1528	117	2	e	e	X
ejpam-1528	117	3	,	,	PUNCT
ejpam-1528	117	4	f	f	PROPN
ejpam-1528	117	5	∈	∈	PROPN
ejpam-1528	117	6	σ2(a	σ2(a	PROPN
ejpam-1528	117	7	)	)	PUNCT
ejpam-1528	117	8	,	,	PUNCT
ejpam-1528	117	9	then	then	ADV
ejpam-1528	117	10	e	e	PROPN
ejpam-1528	117	11	f	f	PROPN
ejpam-1528	117	12	=	=	SYM
ejpam-1528	117	13	f	f	PROPN
ejpam-1528	117	14	e	e	NOUN
ejpam-1528	117	15	≤h	≤h	PROPN
ejpam-1528	117	16	e	e	NOUN
ejpam-1528	117	17	≤h	≤h	NOUN
ejpam-1528	117	18	a.	a.	NOUN
ejpam-1528	117	19	we	we	PRON
ejpam-1528	117	20	have	have	VERB
ejpam-1528	117	21	to	to	PART
ejpam-1528	117	22	show	show	VERB
ejpam-1528	117	23	that	that	SCONJ
ejpam-1528	117	24	e	e	PROPN
ejpam-1528	117	25	f	f	PROPN
ejpam-1528	117	26	is	be	AUX
ejpam-1528	117	27	an	an	DET
ejpam-1528	117	28	idempotent	idempotent	NOUN
ejpam-1528	117	29	.	.	PUNCT
ejpam-1528	118	1	e	e	X
ejpam-1528	118	2	f	f	X
ejpam-1528	118	3	e	e	X
ejpam-1528	118	4	f	f	PROPN
ejpam-1528	118	5	=	=	SYM
ejpam-1528	118	6	e	e	PROPN
ejpam-1528	118	7	f	f	X
ejpam-1528	118	8	f	f	PROPN
ejpam-1528	118	9	e	e	PROPN
ejpam-1528	118	10	=	=	SYM
ejpam-1528	118	11	e	e	X
ejpam-1528	118	12	f	f	X
ejpam-1528	118	13	e	e	PROPN
ejpam-1528	118	14	=	=	PROPN
ejpam-1528	118	15	ee	ee	PROPN
ejpam-1528	118	16	f	f	PROPN
ejpam-1528	118	17	=	=	SYM
ejpam-1528	118	18	e	e	PROPN
ejpam-1528	118	19	f	f	PROPN
ejpam-1528	118	20	and	and	CCONJ
ejpam-1528	118	21	e	e	PROPN
ejpam-1528	118	22	f	f	PROPN
ejpam-1528	118	23	is	be	AUX
ejpam-1528	118	24	an	an	DET
ejpam-1528	118	25	idempotent	idempotent	NOUN
ejpam-1528	118	26	.	.	PUNCT
ejpam-1528	119	1	3	3	X
ejpam-1528	119	2	.	.	X
ejpam-1528	119	3	the	the	DET
ejpam-1528	119	4	natural	natural	ADJ
ejpam-1528	119	5	generalized	generalized	ADJ
ejpam-1528	119	6	inverse	inverse	NOUN
ejpam-1528	119	7	in	in	ADP
ejpam-1528	119	8	a	a	DET
ejpam-1528	119	9	semigroup	semigroup	ADJ
ejpam-1528	119	10	3.1	3.1	NUM
ejpam-1528	119	11	.	.	PUNCT
ejpam-1528	119	12	definition	definition	NOUN
ejpam-1528	119	13	and	and	CCONJ
ejpam-1528	119	14	first	first	ADJ
ejpam-1528	119	15	properties	property	NOUN
ejpam-1528	119	16	definition	definition	NOUN
ejpam-1528	119	17	2	2	X
ejpam-1528	119	18	.	.	PUNCT
ejpam-1528	120	1	let	let	VERB
ejpam-1528	120	2	s	s	PRON
ejpam-1528	120	3	be	be	AUX
ejpam-1528	120	4	a	a	DET
ejpam-1528	120	5	semigroup	semigroup	NOUN
ejpam-1528	120	6	,	,	PUNCT
ejpam-1528	120	7	a	a	DET
ejpam-1528	120	8	∈	∈	NOUN
ejpam-1528	120	9	s.	s.	PROPN
ejpam-1528	120	10	i	i	PRON
ejpam-1528	120	11	)	)	PUNCT
ejpam-1528	120	12	let	let	VERB
ejpam-1528	120	13	j	j	PROPN
ejpam-1528	120	14	=	=	SYM
ejpam-1528	120	15	0	0	NUM
ejpam-1528	120	16	,	,	PUNCT
ejpam-1528	120	17	1,2	1,2	NUM
ejpam-1528	120	18	.	.	PUNCT
ejpam-1528	121	1	the	the	DET
ejpam-1528	121	2	element	element	NOUN
ejpam-1528	121	3	a	a	PRON
ejpam-1528	121	4	is	be	AUX
ejpam-1528	121	5	j−maximally	j−maximally	ADV
ejpam-1528	121	6	invertible	invertible	ADJ
ejpam-1528	121	7	if	if	SCONJ
ejpam-1528	121	8	the	the	DET
ejpam-1528	121	9	set	set	NOUN
ejpam-1528	121	10	σ	σ	PROPN
ejpam-1528	121	11	j(a	j(a	PROPN
ejpam-1528	121	12	)	)	PUNCT
ejpam-1528	121	13	admits	admit	VERB
ejpam-1528	121	14	maximal	maximal	ADJ
ejpam-1528	121	15	elements	element	NOUN
ejpam-1528	121	16	for	for	ADP
ejpam-1528	121	17	the	the	DET
ejpam-1528	121	18	natural	natural	ADJ
ejpam-1528	121	19	partial	partial	ADJ
ejpam-1528	121	20	order	order	NOUN
ejpam-1528	121	21	.	.	PUNCT
ejpam-1528	122	1	elements	element	NOUN
ejpam-1528	122	2	b	b	X
ejpam-1528	123	1	=	=	PUNCT
ejpam-1528	123	2	a−e	a−e	NOUN
ejpam-1528	123	3	where	where	SCONJ
ejpam-1528	123	4	e	e	NOUN
ejpam-1528	123	5	is	be	AUX
ejpam-1528	123	6	maximal	maximal	ADJ
ejpam-1528	123	7	are	be	AUX
ejpam-1528	123	8	then	then	ADV
ejpam-1528	123	9	called	call	VERB
ejpam-1528	123	10	j−maximal	j−maximal	PROPN
ejpam-1528	123	11	generalized	generalize	VERB
ejpam-1528	123	12	inverses	inverse	NOUN
ejpam-1528	123	13	of	of	ADP
ejpam-1528	123	14	a.	a.	PROPN
ejpam-1528	123	15	ii	ii	PROPN
ejpam-1528	123	16	)	)	PUNCT
ejpam-1528	123	17	if	if	SCONJ
ejpam-1528	123	18	there	there	PRON
ejpam-1528	123	19	exists	exist	VERB
ejpam-1528	123	20	a	a	DET
ejpam-1528	123	21	greatest	great	ADJ
ejpam-1528	123	22	element	element	NOUN
ejpam-1528	123	23	m	m	PROPN
ejpam-1528	123	24	∈	∈	PROPN
ejpam-1528	123	25	σ	σ	NUM
ejpam-1528	123	26	j(a	j(a	PROPN
ejpam-1528	123	27	)	)	PUNCT
ejpam-1528	123	28	,	,	PUNCT
ejpam-1528	123	29	then	then	ADV
ejpam-1528	123	30	we	we	PRON
ejpam-1528	123	31	say	say	VERB
ejpam-1528	123	32	that	that	SCONJ
ejpam-1528	123	33	a	a	PRON
ejpam-1528	123	34	is	be	AUX
ejpam-1528	123	35	j−naturally	j−naturally	ADV
ejpam-1528	123	36	invertible	invertible	ADJ
ejpam-1528	123	37	,	,	PUNCT
ejpam-1528	123	38	and	and	CCONJ
ejpam-1528	123	39	b	b	X
ejpam-1528	123	40	=	=	NOUN
ejpam-1528	123	41	a−m	a−m	NOUN
ejpam-1528	123	42	is	be	AUX
ejpam-1528	123	43	called	call	VERB
ejpam-1528	123	44	the	the	DET
ejpam-1528	123	45	j−natural	j−natural	ADJ
ejpam-1528	123	46	(	(	PUNCT
ejpam-1528	123	47	generalized	generalized	ADJ
ejpam-1528	123	48	)	)	PUNCT
ejpam-1528	123	49	inverse	inverse	NOUN
ejpam-1528	123	50	of	of	ADP
ejpam-1528	123	51	a.	a.	PROPN
ejpam-1528	123	52	iii	iii	PROPN
ejpam-1528	123	53	)	)	PUNCT
ejpam-1528	123	54	finally	finally	ADV
ejpam-1528	123	55	,	,	PUNCT
ejpam-1528	123	56	if	if	SCONJ
ejpam-1528	123	57	a	a	PRON
ejpam-1528	123	58	is	be	AUX
ejpam-1528	123	59	2−naturally	2−naturally	ADV
ejpam-1528	123	60	invertible	invertible	ADJ
ejpam-1528	123	61	,	,	PUNCT
ejpam-1528	123	62	the	the	DET
ejpam-1528	123	63	element	element	NOUN
ejpam-1528	123	64	am	be	AUX
ejpam-1528	123	65	=	=	PUNCT
ejpam-1528	123	66	aba	aba	PROPN
ejpam-1528	123	67	is	be	AUX
ejpam-1528	123	68	called	call	VERB
ejpam-1528	123	69	the	the	DET
ejpam-1528	123	70	core	core	NOUN
ejpam-1528	123	71	of	of	ADP
ejpam-1528	123	72	a.	a.	NOUN
ejpam-1528	123	73	we	we	PRON
ejpam-1528	123	74	will	will	AUX
ejpam-1528	123	75	mainly	mainly	ADV
ejpam-1528	123	76	deal	deal	VERB
ejpam-1528	123	77	with	with	ADP
ejpam-1528	123	78	the	the	DET
ejpam-1528	123	79	2−natural	2−natural	ADJ
ejpam-1528	123	80	inverse	inverse	NOUN
ejpam-1528	123	81	in	in	ADP
ejpam-1528	123	82	the	the	DET
ejpam-1528	123	83	sequel	sequel	NOUN
ejpam-1528	123	84	,	,	PUNCT
ejpam-1528	123	85	and	and	CCONJ
ejpam-1528	123	86	we	we	PRON
ejpam-1528	123	87	will	will	AUX
ejpam-1528	123	88	also	also	ADV
ejpam-1528	123	89	refer	refer	VERB
ejpam-1528	123	90	to	to	ADP
ejpam-1528	123	91	it	it	PRON
ejpam-1528	123	92	as	as	ADP
ejpam-1528	123	93	the	the	DET
ejpam-1528	123	94	natural	natural	ADJ
ejpam-1528	123	95	inverse	inverse	NOUN
ejpam-1528	123	96	.	.	PUNCT
ejpam-1528	124	1	as	as	SCONJ
ejpam-1528	124	2	noted	note	VERB
ejpam-1528	124	3	before	before	ADV
ejpam-1528	124	4	,	,	PUNCT
ejpam-1528	124	5	if	if	SCONJ
ejpam-1528	124	6	s	s	NOUN
ejpam-1528	124	7	is	be	AUX
ejpam-1528	124	8	commutative	commutative	ADJ
ejpam-1528	124	9	or	or	CCONJ
ejpam-1528	124	10	the	the	DET
ejpam-1528	124	11	idempotents	idempotent	NOUN
ejpam-1528	124	12	central	central	ADJ
ejpam-1528	124	13	then	then	ADV
ejpam-1528	124	14	the	the	DET
ejpam-1528	124	15	three	three	NUM
ejpam-1528	124	16	notions	notion	NOUN
ejpam-1528	124	17	coincide	coincide	NOUN
ejpam-1528	124	18	.	.	PUNCT
ejpam-1528	125	1	recall	recall	VERB
ejpam-1528	125	2	that	that	SCONJ
ejpam-1528	125	3	a	a	DET
ejpam-1528	125	4	semilattice	semilattice	NOUN
ejpam-1528	125	5	is	be	AUX
ejpam-1528	125	6	distributive	distributive	ADJ
ejpam-1528	125	7	if	if	SCONJ
ejpam-1528	125	8	e	e	PROPN
ejpam-1528	125	9	∧	∧	NOUN
ejpam-1528	125	10	f	f	PROPN
ejpam-1528	125	11	≤	≤	NUM
ejpam-1528	125	12	x	x	PUNCT
ejpam-1528	125	13	implies	imply	VERB
ejpam-1528	125	14	the	the	DET
ejpam-1528	125	15	existence	existence	NOUN
ejpam-1528	125	16	of	of	ADP
ejpam-1528	125	17	e′	e′	PROPN
ejpam-1528	125	18	,	,	PUNCT
ejpam-1528	125	19	f	f	PROPN
ejpam-1528	125	20	′	′	NUM
ejpam-1528	125	21	such	such	ADJ
ejpam-1528	125	22	that	that	SCONJ
ejpam-1528	125	23	e	e	PROPN
ejpam-1528	125	24	≤	≤	NOUN
ejpam-1528	125	25	e′	e′	PROPN
ejpam-1528	125	26	,	,	PUNCT
ejpam-1528	125	27	f	f	PROPN
ejpam-1528	125	28	≤	≤	PROPN
ejpam-1528	126	1	f	f	PROPN
ejpam-1528	127	1	′	′	NOUN
ejpam-1528	128	1	and	and	CCONJ
ejpam-1528	128	2	x	x	X
ejpam-1528	128	3	=	=	SYM
ejpam-1528	128	4	e′	e′	X
ejpam-1528	128	5	∧	∧	PROPN
ejpam-1528	128	6	f	f	PROPN
ejpam-1528	128	7	′.	′.	PROPN
ejpam-1528	128	8	proposition	proposition	NOUN
ejpam-1528	128	9	2	2	X
ejpam-1528	128	10	.	.	PUNCT
ejpam-1528	129	1	if	if	SCONJ
ejpam-1528	129	2	the	the	DET
ejpam-1528	129	3	semilattice	semilattice	NOUN
ejpam-1528	129	4	σ2(a	σ2(a	NOUN
ejpam-1528	129	5	)	)	PUNCT
ejpam-1528	129	6	is	be	AUX
ejpam-1528	129	7	distributive	distributive	ADJ
ejpam-1528	129	8	,	,	PUNCT
ejpam-1528	129	9	then	then	ADV
ejpam-1528	129	10	any	any	DET
ejpam-1528	129	11	2−maximally	2−maximally	ADV
ejpam-1528	129	12	invertible	invertible	ADJ
ejpam-1528	129	13	element	element	NOUN
ejpam-1528	129	14	is	be	AUX
ejpam-1528	129	15	naturally	naturally	ADV
ejpam-1528	129	16	invertible	invertible	ADJ
ejpam-1528	129	17	.	.	PUNCT
ejpam-1528	130	1	proof	proof	NOUN
ejpam-1528	130	2	.	.	PUNCT
ejpam-1528	131	1	let	let	VERB
ejpam-1528	131	2	e	e	PRON
ejpam-1528	131	3	be	be	AUX
ejpam-1528	131	4	a	a	DET
ejpam-1528	131	5	maximal	maximal	ADJ
ejpam-1528	131	6	element	element	NOUN
ejpam-1528	131	7	of	of	ADP
ejpam-1528	131	8	σ2(a	σ2(a	PROPN
ejpam-1528	131	9	)	)	PUNCT
ejpam-1528	131	10	,	,	PUNCT
ejpam-1528	131	11	f	f	PROPN
ejpam-1528	131	12	∈	∈	PROPN
ejpam-1528	131	13	σ2(a	σ2(a	PROPN
ejpam-1528	131	14	)	)	PUNCT
ejpam-1528	131	15	.	.	PUNCT
ejpam-1528	132	1	then	then	ADV
ejpam-1528	132	2	e	e	X
ejpam-1528	132	3	f	f	PROPN
ejpam-1528	132	4	=	=	SYM
ejpam-1528	132	5	f	f	PROPN
ejpam-1528	132	6	e	e	NOUN
ejpam-1528	132	7	≤	≤	NOUN
ejpam-1528	132	8	e	e	NOUN
ejpam-1528	132	9	and	and	CCONJ
ejpam-1528	132	10	exists	exist	VERB
ejpam-1528	132	11	e′	e′	PROPN
ejpam-1528	132	12	,	,	PUNCT
ejpam-1528	132	13	f	f	PROPN
ejpam-1528	132	14	′	′	NUM
ejpam-1528	132	15	such	such	ADJ
ejpam-1528	132	16	that	that	SCONJ
ejpam-1528	132	17	e	e	PROPN
ejpam-1528	132	18	≤	≤	NOUN
ejpam-1528	132	19	e′	e′	PROPN
ejpam-1528	132	20	,	,	PUNCT
ejpam-1528	132	21	f	f	PROPN
ejpam-1528	132	22	≤	≤	PROPN
ejpam-1528	133	1	f	f	X
ejpam-1528	133	2	′	′	NOUN
ejpam-1528	134	1	and	and	CCONJ
ejpam-1528	134	2	e	e	X
ejpam-1528	134	3	=	=	PUNCT
ejpam-1528	134	4	e′	e′	PROPN
ejpam-1528	134	5	f	f	PROPN
ejpam-1528	134	6	′.	′.	NOUN
ejpam-1528	134	7	by	by	ADP
ejpam-1528	134	8	maximality	maximality	PROPN
ejpam-1528	134	9	,	,	PUNCT
ejpam-1528	134	10	e′	e′	X
ejpam-1528	134	11	=	=	SYM
ejpam-1528	134	12	e	e	PROPN
ejpam-1528	134	13	and	and	CCONJ
ejpam-1528	134	14	we	we	PRON
ejpam-1528	134	15	get	get	VERB
ejpam-1528	134	16	e	e	NOUN
ejpam-1528	134	17	=	=	SYM
ejpam-1528	135	1	e	e	X
ejpam-1528	135	2	f	f	NOUN
ejpam-1528	135	3	′	′	NUM
ejpam-1528	135	4	=	=	PUNCT
ejpam-1528	135	5	f	f	PROPN
ejpam-1528	135	6	′e	′e	PROPN
ejpam-1528	135	7	.	.	PUNCT
ejpam-1528	136	1	it	it	PRON
ejpam-1528	136	2	follows	follow	VERB
ejpam-1528	136	3	that	that	SCONJ
ejpam-1528	136	4	e	e	NOUN
ejpam-1528	136	5	≤	≤	X
ejpam-1528	136	6	f	f	NOUN
ejpam-1528	137	1	′	′	NOUN
ejpam-1528	137	2	hence	hence	ADV
ejpam-1528	137	3	e	e	X
ejpam-1528	138	1	=	=	SYM
ejpam-1528	138	2	f	f	X
ejpam-1528	138	3	′	′	NOUN
ejpam-1528	138	4	and	and	CCONJ
ejpam-1528	138	5	f	f	PROPN
ejpam-1528	138	6	≤	≤	PROPN
ejpam-1528	138	7	e.	e.	PROPN
ejpam-1528	138	8	e	e	PROPN
ejpam-1528	138	9	is	be	AUX
ejpam-1528	138	10	the	the	DET
ejpam-1528	138	11	greatest	great	ADJ
ejpam-1528	138	12	element	element	NOUN
ejpam-1528	138	13	in	in	ADP
ejpam-1528	138	14	σ2(a	σ2(a	PROPN
ejpam-1528	138	15	)	)	PUNCT
ejpam-1528	138	16	.	.	PUNCT
ejpam-1528	139	1	the	the	DET
ejpam-1528	139	2	natural	natural	ADJ
ejpam-1528	139	3	inverse	inverse	NOUN
ejpam-1528	139	4	generalizes	generalize	VERB
ejpam-1528	139	5	the	the	DET
ejpam-1528	139	6	drazin	drazin	PROPN
ejpam-1528	139	7	inverse	inverse	NOUN
ejpam-1528	140	1	[	[	X
ejpam-1528	140	2	4	4	NUM
ejpam-1528	140	3	]	]	PUNCT
ejpam-1528	140	4	.	.	PUNCT
ejpam-1528	141	1	theorem	theorem	ADJ
ejpam-1528	141	2	4	4	NUM
ejpam-1528	141	3	.	.	PUNCT
ejpam-1528	141	4	assume	assume	VERB
ejpam-1528	141	5	a	a	PRON
ejpam-1528	141	6	is	be	AUX
ejpam-1528	141	7	drazin	drazin	NOUN
ejpam-1528	141	8	invertible	invertible	ADJ
ejpam-1528	141	9	with	with	ADP
ejpam-1528	141	10	inverse	inverse	NOUN
ejpam-1528	141	11	ad	ad	NOUN
ejpam-1528	141	12	.	.	PUNCT
ejpam-1528	142	1	then	then	ADV
ejpam-1528	142	2	a	a	PRON
ejpam-1528	142	3	is	be	AUX
ejpam-1528	142	4	1	1	NUM
ejpam-1528	142	5	and	and	CCONJ
ejpam-1528	142	6	2−naturally	2−naturally	ADV
ejpam-1528	142	7	invertible	invertible	ADJ
ejpam-1528	142	8	with	with	ADP
ejpam-1528	142	9	inverse	inverse	NOUN
ejpam-1528	142	10	a−m	a−m	NOUN
ejpam-1528	142	11	=	=	SYM
ejpam-1528	142	12	ad	ad	NOUN
ejpam-1528	142	13	.	.	PUNCT
ejpam-1528	143	1	proof	proof	NOUN
ejpam-1528	143	2	.	.	PUNCT
ejpam-1528	144	1	let	let	VERB
ejpam-1528	144	2	a	a	PRON
ejpam-1528	144	3	be	be	AUX
ejpam-1528	144	4	drazin	drazin	NOUN
ejpam-1528	144	5	invertible	invertible	ADJ
ejpam-1528	144	6	with	with	ADP
ejpam-1528	144	7	index	index	NOUN
ejpam-1528	144	8	n	n	NOUN
ejpam-1528	144	9	and	and	CCONJ
ejpam-1528	144	10	inverse	inverse	NOUN
ejpam-1528	144	11	ad	ad	NOUN
ejpam-1528	144	12	.	.	PUNCT
ejpam-1528	145	1	then	then	ADV
ejpam-1528	145	2	e	e	X
ejpam-1528	145	3	=	=	PUNCT
ejpam-1528	145	4	aad	aad	PROPN
ejpam-1528	145	5	=	=	PROPN
ejpam-1528	145	6	ada	ada	PROPN
ejpam-1528	145	7	∈	∈	PROPN
ejpam-1528	145	8	σ2(a)⊆	σ2(a)⊆	NOUN
ejpam-1528	145	9	σ1(a	σ1(a	NOUN
ejpam-1528	145	10	)	)	PUNCT
ejpam-1528	145	11	,	,	PUNCT
ejpam-1528	145	12	and	and	CCONJ
ejpam-1528	145	13	adan+1	adan+1	PROPN
ejpam-1528	145	14	=	=	SYM
ejpam-1528	145	15	an+1ad	an+1ad	PROPN
ejpam-1528	145	16	=	=	SYM
ejpam-1528	145	17	an	an	X
ejpam-1528	145	18	.	.	PUNCT
ejpam-1528	146	1	let	let	VERB
ejpam-1528	146	2	f	f	PROPN
ejpam-1528	146	3	∈	∈	PROPN
ejpam-1528	146	4	σ1(a	σ1(a	PROPN
ejpam-1528	146	5	)	)	PUNCT
ejpam-1528	146	6	.	.	PUNCT
ejpam-1528	147	1	then	then	ADV
ejpam-1528	147	2	a−	a−	PROPN
ejpam-1528	147	3	f	f	PROPN
ejpam-1528	147	4	satisfies	satisfy	VERB
ejpam-1528	147	5	a−	a−	PROPN
ejpam-1528	147	6	f	f	PROPN
ejpam-1528	147	7	a	a	DET
ejpam-1528	147	8	f	f	X
ejpam-1528	147	9	=	=	SYM
ejpam-1528	147	10	f	f	PROPN
ejpam-1528	147	11	=	=	PUNCT
ejpam-1528	147	12	aa−	aa−	PROPN
ejpam-1528	147	13	f	f	X
ejpam-1528	147	14	f	f	PROPN
ejpam-1528	147	15	=	=	SYM
ejpam-1528	147	16	f	f	PROPN
ejpam-1528	147	17	aa−	aa−	PROPN
ejpam-1528	147	18	f	f	X
ejpam-1528	147	19	=	=	SYM
ejpam-1528	147	20	f	f	PROPN
ejpam-1528	147	21	a−	a−	PROPN
ejpam-1528	147	22	f	f	PROPN
ejpam-1528	147	23	a.	a.	NOUN
ejpam-1528	147	24	it	it	PRON
ejpam-1528	147	25	follows	follow	VERB
ejpam-1528	147	26	that	that	SCONJ
ejpam-1528	147	27	f	f	PROPN
ejpam-1528	147	28	=	=	SYM
ejpam-1528	147	29	f	f	PROPN
ejpam-1528	147	30	�	�	PROPN
ejpam-1528	147	31	a−	a−	PROPN
ejpam-1528	147	32	f	f	PROPN
ejpam-1528	147	33	�	�	PROPN
ejpam-1528	147	34	n+1	n+1	PROPN
ejpam-1528	147	35	an+1	an+1	NOUN
ejpam-1528	147	36	.	.	PUNCT
ejpam-1528	148	1	then	then	ADV
ejpam-1528	148	2	f	f	PROPN
ejpam-1528	148	3	e	e	PROPN
ejpam-1528	148	4	=	=	SYM
ejpam-1528	148	5	f	f	PROPN
ejpam-1528	148	6	�	�	PROPN
ejpam-1528	148	7	a−	a−	PROPN
ejpam-1528	148	8	f	f	PROPN
ejpam-1528	148	9	�	�	PROPN
ejpam-1528	148	10	n+1	n+1	PROPN
ejpam-1528	148	11	an+1ada	an+1ada	PUNCT
ejpam-1528	148	12	=	=	SYM
ejpam-1528	149	1	f	f	PROPN
ejpam-1528	149	2	.	.	PUNCT
ejpam-1528	150	1	also	also	ADV
ejpam-1528	150	2	f	f	X
ejpam-1528	150	3	e	e	NOUN
ejpam-1528	150	4	=	=	SYM
ejpam-1528	150	5	e	e	X
ejpam-1528	150	6	f	f	X
ejpam-1528	150	7	(	(	PUNCT
ejpam-1528	150	8	e	e	NOUN
ejpam-1528	150	9	=	=	NOUN
ejpam-1528	150	10	aad	aad	PROPN
ejpam-1528	150	11	=	=	PROPN
ejpam-1528	150	12	ada	ada	PROPN
ejpam-1528	150	13	∈	∈	PROPN
ejpam-1528	150	14	σ2(a	σ2(a	PROPN
ejpam-1528	150	15	)	)	PUNCT
ejpam-1528	150	16	)	)	PUNCT
ejpam-1528	151	1	hence	hence	ADV
ejpam-1528	151	2	f	f	PROPN
ejpam-1528	151	3	≤	≤	PROPN
ejpam-1528	151	4	e.	e.	PROPN
ejpam-1528	151	5	x.	x.	PROPN
ejpam-1528	151	6	mary	mary	PROPN
ejpam-1528	151	7	/	/	SYM
ejpam-1528	151	8	eur	eur	PROPN
ejpam-1528	151	9	.	.	PUNCT
ejpam-1528	152	1	j.	j.	PROPN
ejpam-1528	152	2	pure	pure	PROPN
ejpam-1528	152	3	appl	appl	PROPN
ejpam-1528	152	4	.	.	PROPN
ejpam-1528	152	5	math	math	PROPN
ejpam-1528	152	6	,	,	PUNCT
ejpam-1528	152	7	6	6	NUM
ejpam-1528	152	8	(	(	PUNCT
ejpam-1528	152	9	2013	2013	NUM
ejpam-1528	152	10	)	)	PUNCT
ejpam-1528	152	11	,	,	PUNCT
ejpam-1528	152	12	413	413	NUM
ejpam-1528	152	13	-	-	SYM
ejpam-1528	152	14	427	427	NUM
ejpam-1528	152	15	418	418	NUM
ejpam-1528	152	16	3.2	3.2	NUM
ejpam-1528	152	17	.	.	PUNCT
ejpam-1528	153	1	examples	example	NOUN
ejpam-1528	153	2	many	many	ADJ
ejpam-1528	153	3	maximal	maximal	ADJ
ejpam-1528	153	4	inverses	inverse	NOUN
ejpam-1528	153	5	let	let	VERB
ejpam-1528	153	6	s	s	PRON
ejpam-1528	153	7	be	be	AUX
ejpam-1528	153	8	the	the	DET
ejpam-1528	153	9	semigroup	semigroup	NOUN
ejpam-1528	153	10	generated	generate	VERB
ejpam-1528	153	11	by	by	ADP
ejpam-1528	153	12	three	three	NUM
ejpam-1528	153	13	elements	element	NOUN
ejpam-1528	153	14	e	e	NOUN
ejpam-1528	153	15	,	,	PUNCT
ejpam-1528	153	16	f	f	PROPN
ejpam-1528	153	17	,	,	PUNCT
ejpam-1528	153	18	a	a	DET
ejpam-1528	153	19	subject	subject	NOUN
ejpam-1528	153	20	to	to	ADP
ejpam-1528	153	21	the	the	DET
ejpam-1528	153	22	conditions	condition	NOUN
ejpam-1528	153	23	e	e	X
ejpam-1528	153	24	=	=	SYM
ejpam-1528	153	25	e2	e2	PROPN
ejpam-1528	153	26	=	=	SYM
ejpam-1528	153	27	ea	ea	PROPN
ejpam-1528	153	28	=	=	SYM
ejpam-1528	153	29	ae	ae	PROPN
ejpam-1528	153	30	,	,	PUNCT
ejpam-1528	153	31	f	f	PROPN
ejpam-1528	154	1	=	=	SYM
ejpam-1528	154	2	f	f	PROPN
ejpam-1528	154	3	2	2	NUM
ejpam-1528	154	4	=	=	SYM
ejpam-1528	154	5	f	f	PROPN
ejpam-1528	155	1	a	a	NOUN
ejpam-1528	155	2	=	=	X
ejpam-1528	155	3	a	a	DET
ejpam-1528	155	4	f	f	NOUN
ejpam-1528	155	5	and	and	CCONJ
ejpam-1528	156	1	e	e	X
ejpam-1528	156	2	f	f	PROPN
ejpam-1528	156	3	=	=	SYM
ejpam-1528	156	4	f	f	PROPN
ejpam-1528	156	5	e.	e.	PROPN
ejpam-1528	156	6	then	then	ADV
ejpam-1528	156	7	s	s	VERB
ejpam-1528	156	8	is	be	AUX
ejpam-1528	156	9	commutative	commutative	ADJ
ejpam-1528	156	10	,	,	PUNCT
ejpam-1528	156	11	a	a	PRON
ejpam-1528	156	12	is	be	AUX
ejpam-1528	156	13	maximally	maximally	ADV
ejpam-1528	156	14	invertible	invertible	ADJ
ejpam-1528	156	15	but	but	CCONJ
ejpam-1528	156	16	not	not	PART
ejpam-1528	156	17	naturally	naturally	ADV
ejpam-1528	156	18	invertible	invertible	ADJ
ejpam-1528	156	19	,	,	PUNCT
ejpam-1528	156	20	with	with	ADP
ejpam-1528	156	21	two	two	NUM
ejpam-1528	156	22	maximal	maximal	ADJ
ejpam-1528	156	23	inverses	inverse	NOUN
ejpam-1528	156	24	a−e	a−e	NOUN
ejpam-1528	156	25	=	=	SYM
ejpam-1528	156	26	e	e	NOUN
ejpam-1528	156	27	and	and	CCONJ
ejpam-1528	156	28	a−	a−	PROPN
ejpam-1528	156	29	f	f	PROPN
ejpam-1528	157	1	=	=	SYM
ejpam-1528	157	2	f	f	PROPN
ejpam-1528	157	3	.	.	PUNCT
ejpam-1528	158	1	we	we	PRON
ejpam-1528	158	2	consider	consider	VERB
ejpam-1528	158	3	now	now	ADV
ejpam-1528	158	4	a	a	DET
ejpam-1528	158	5	simple	simple	ADJ
ejpam-1528	158	6	variant	variant	NOUN
ejpam-1528	158	7	of	of	ADP
ejpam-1528	158	8	the	the	DET
ejpam-1528	158	9	previous	previous	ADJ
ejpam-1528	158	10	example	example	NOUN
ejpam-1528	158	11	.	.	PUNCT
ejpam-1528	159	1	let	let	VERB
ejpam-1528	159	2	s′	s′	PROPN
ejpam-1528	159	3	be	be	AUX
ejpam-1528	159	4	the	the	DET
ejpam-1528	159	5	semigroup	semigroup	NOUN
ejpam-1528	159	6	generated	generate	VERB
ejpam-1528	159	7	by	by	ADP
ejpam-1528	159	8	three	three	NUM
ejpam-1528	159	9	elements	element	NOUN
ejpam-1528	159	10	e	e	NOUN
ejpam-1528	159	11	,	,	PUNCT
ejpam-1528	159	12	f	f	PROPN
ejpam-1528	159	13	,	,	PUNCT
ejpam-1528	159	14	a	a	DET
ejpam-1528	159	15	subject	subject	NOUN
ejpam-1528	159	16	to	to	ADP
ejpam-1528	159	17	the	the	DET
ejpam-1528	159	18	conditions	condition	NOUN
ejpam-1528	159	19	e	e	X
ejpam-1528	159	20	=	=	SYM
ejpam-1528	159	21	e2	e2	PROPN
ejpam-1528	159	22	=	=	SYM
ejpam-1528	159	23	ea	ea	PROPN
ejpam-1528	159	24	=	=	SYM
ejpam-1528	159	25	ae	ae	PROPN
ejpam-1528	159	26	,	,	PUNCT
ejpam-1528	159	27	f	f	PROPN
ejpam-1528	159	28	=	=	SYM
ejpam-1528	159	29	f	f	PROPN
ejpam-1528	159	30	2	2	NUM
ejpam-1528	159	31	=	=	SYM
ejpam-1528	159	32	f	f	PROPN
ejpam-1528	160	1	a	a	NOUN
ejpam-1528	160	2	=	=	X
ejpam-1528	160	3	a	a	DET
ejpam-1528	160	4	f	f	NOUN
ejpam-1528	160	5	and	and	CCONJ
ejpam-1528	160	6	e	e	X
ejpam-1528	160	7	f	f	PROPN
ejpam-1528	160	8	=	=	SYM
ejpam-1528	160	9	e	e	PROPN
ejpam-1528	160	10	,	,	PUNCT
ejpam-1528	160	11	f	f	PROPN
ejpam-1528	160	12	e	e	PROPN
ejpam-1528	160	13	=	=	PROPN
ejpam-1528	160	14	f	f	PROPN
ejpam-1528	160	15	.	.	PUNCT
ejpam-1528	161	1	then	then	ADV
ejpam-1528	161	2	σ1(a	σ1(a	NUM
ejpam-1528	161	3	)	)	PUNCT
ejpam-1528	161	4	=	=	PRON
ejpam-1528	161	5	{	{	PUNCT
ejpam-1528	161	6	e	e	PROPN
ejpam-1528	161	7	,	,	PUNCT
ejpam-1528	161	8	f	f	PROPN
ejpam-1528	161	9	}	}	PUNCT
ejpam-1528	161	10	but	but	CCONJ
ejpam-1528	161	11	σ2(a	σ2(a	NUM
ejpam-1528	161	12	)	)	PUNCT
ejpam-1528	161	13	is	be	AUX
ejpam-1528	161	14	empty	empty	ADJ
ejpam-1528	161	15	since	since	SCONJ
ejpam-1528	161	16	e	e	PROPN
ejpam-1528	161	17	and	and	CCONJ
ejpam-1528	161	18	f	f	X
ejpam-1528	161	19	do	do	AUX
ejpam-1528	161	20	not	not	PART
ejpam-1528	161	21	commute	commute	VERB
ejpam-1528	161	22	.	.	PUNCT
ejpam-1528	162	1	right	right	ADJ
ejpam-1528	162	2	hereditary	hereditary	ADJ
ejpam-1528	162	3	semigroups	semigroup	NOUN
ejpam-1528	162	4	with	with	ADP
ejpam-1528	162	5	central	central	ADJ
ejpam-1528	162	6	idempotents	idempotent	NOUN
ejpam-1528	162	7	[	[	X
ejpam-1528	162	8	6	6	NUM
ejpam-1528	162	9	]	]	PUNCT
ejpam-1528	162	10	in	in	ADP
ejpam-1528	162	11	this	this	DET
ejpam-1528	162	12	example	example	NOUN
ejpam-1528	162	13	we	we	PRON
ejpam-1528	162	14	notably	notably	ADV
ejpam-1528	162	15	show	show	VERB
ejpam-1528	162	16	that	that	SCONJ
ejpam-1528	162	17	elements	element	NOUN
ejpam-1528	162	18	of	of	ADP
ejpam-1528	162	19	a	a	DET
ejpam-1528	162	20	right	right	ADJ
ejpam-1528	162	21	hereditary	hereditary	ADJ
ejpam-1528	162	22	semigroup	semigroup	NOUN
ejpam-1528	162	23	with	with	ADP
ejpam-1528	162	24	central	central	ADJ
ejpam-1528	162	25	idempotents	idempotent	NOUN
ejpam-1528	162	26	are	be	AUX
ejpam-1528	162	27	naturally	naturally	ADV
ejpam-1528	162	28	invertible	invertible	ADJ
ejpam-1528	162	29	,	,	PUNCT
ejpam-1528	162	30	and	and	CCONJ
ejpam-1528	162	31	describe	describe	VERB
ejpam-1528	162	32	the	the	DET
ejpam-1528	162	33	set	set	NOUN
ejpam-1528	162	34	σ(a	σ(a	PROPN
ejpam-1528	162	35	)	)	PUNCT
ejpam-1528	162	36	.	.	PUNCT
ejpam-1528	163	1	let	let	VERB
ejpam-1528	163	2	s	s	PRON
ejpam-1528	163	3	be	be	AUX
ejpam-1528	163	4	a	a	DET
ejpam-1528	163	5	right	right	ADJ
ejpam-1528	163	6	principal	principal	ADJ
ejpam-1528	163	7	projective	projective	NOUN
ejpam-1528	163	8	(	(	PUNCT
ejpam-1528	163	9	p.p	p.p	PROPN
ejpam-1528	163	10	.	.	PUNCT
ejpam-1528	163	11	)	)	PUNCT
ejpam-1528	164	1	semigroup	semigroup	PROPN
ejpam-1528	164	2	with	with	ADP
ejpam-1528	164	3	central	central	ADJ
ejpam-1528	164	4	idempotents	idempotent	NOUN
ejpam-1528	164	5	as	as	SCONJ
ejpam-1528	164	6	defined	define	VERB
ejpam-1528	164	7	in	in	ADP
ejpam-1528	164	8	[	[	X
ejpam-1528	164	9	6	6	NUM
ejpam-1528	164	10	]	]	PUNCT
ejpam-1528	164	11	.	.	PUNCT
ejpam-1528	165	1	then	then	ADV
ejpam-1528	165	2	e(s	e(s	PROPN
ejpam-1528	165	3	)	)	PUNCT
ejpam-1528	165	4	is	be	AUX
ejpam-1528	165	5	a	a	DET
ejpam-1528	165	6	semilattice	semilattice	NOUN
ejpam-1528	165	7	(	(	PUNCT
ejpam-1528	165	8	for	for	ADP
ejpam-1528	165	9	the	the	DET
ejpam-1528	165	10	natural	natural	ADJ
ejpam-1528	165	11	partial	partial	ADJ
ejpam-1528	165	12	order	order	NOUN
ejpam-1528	165	13	)	)	PUNCT
ejpam-1528	165	14	.	.	PUNCT
ejpam-1528	166	1	for	for	ADP
ejpam-1528	166	2	any	any	DET
ejpam-1528	166	3	e	e	PROPN
ejpam-1528	166	4	∈	∈	PROPN
ejpam-1528	166	5	e(s	e(s	PROPN
ejpam-1528	166	6	)	)	PUNCT
ejpam-1528	166	7	,	,	PUNCT
ejpam-1528	166	8	define	define	VERB
ejpam-1528	166	9	ye	ye	NUM
ejpam-1528	166	10	=	=	SYM
ejpam-1528	166	11	{	{	PUNCT
ejpam-1528	166	12	x	x	PUNCT
ejpam-1528	166	13	∈	∈	PROPN
ejpam-1528	166	14	s	s	NOUN
ejpam-1528	166	15	,	,	PUNCT
ejpam-1528	166	16	xe	xe	PROPN
ejpam-1528	166	17	=	=	PROPN
ejpam-1528	166	18	x	x	PROPN
ejpam-1528	166	19	and	and	CCONJ
ejpam-1528	166	20	xs	xs	PROPN
ejpam-1528	166	21	=	=	PUNCT
ejpam-1528	166	22	x	x	SYM
ejpam-1528	166	23	t	t	NOUN
ejpam-1528	166	24	⇒	⇒	NOUN
ejpam-1528	166	25	es	es	X
ejpam-1528	166	26	=	=	PUNCT
ejpam-1528	166	27	et	et	NOUN
ejpam-1528	166	28	}	}	PUNCT
ejpam-1528	166	29	(	(	PUNCT
ejpam-1528	166	30	that	that	PRON
ejpam-1528	166	31	is	be	AUX
ejpam-1528	166	32	the	the	DET
ejpam-1528	166	33	l	l	NOUN
ejpam-1528	166	34	∗−class	∗−class	NOUN
ejpam-1528	166	35	of	of	ADP
ejpam-1528	166	36	e	e	PROPN
ejpam-1528	166	37	for	for	ADP
ejpam-1528	166	38	the	the	DET
ejpam-1528	166	39	extended	extend	VERB
ejpam-1528	166	40	green	green	NOUN
ejpam-1528	166	41	’s	’s	PART
ejpam-1528	166	42	relation	relation	NOUN
ejpam-1528	166	43	l	l	PROPN
ejpam-1528	166	44	∗	∗	NOUN
ejpam-1528	167	1	[	[	X
ejpam-1528	167	2	7	7	NUM
ejpam-1528	167	3	]	]	NUM
ejpam-1528	167	4	)	)	PUNCT
ejpam-1528	167	5	.	.	PUNCT
ejpam-1528	168	1	then	then	ADV
ejpam-1528	168	2	ye	ye	PRON
ejpam-1528	168	3	is	be	AUX
ejpam-1528	168	4	a	a	DET
ejpam-1528	168	5	cancellative	cancellative	ADJ
ejpam-1528	168	6	monoid	monoid	NOUN
ejpam-1528	168	7	(	(	PUNCT
ejpam-1528	168	8	with	with	ADP
ejpam-1528	168	9	unit	unit	NOUN
ejpam-1528	168	10	e	e	NOUN
ejpam-1528	168	11	)	)	PUNCT
ejpam-1528	168	12	and	and	CCONJ
ejpam-1528	168	13	the	the	DET
ejpam-1528	168	14	structure	structure	NOUN
ejpam-1528	168	15	theorem	theorem	NOUN
ejpam-1528	168	16	of	of	ADP
ejpam-1528	168	17	fountain	fountain	NOUN
ejpam-1528	168	18	says	say	VERB
ejpam-1528	168	19	that	that	SCONJ
ejpam-1528	168	20	s	s	VERB
ejpam-1528	168	21	is	be	AUX
ejpam-1528	168	22	the	the	DET
ejpam-1528	168	23	semilattice	semilattice	NOUN
ejpam-1528	168	24	of	of	ADP
ejpam-1528	168	25	these	these	DET
ejpam-1528	168	26	disjoints	disjoint	NOUN
ejpam-1528	168	27	monoids	monoid	NOUN
ejpam-1528	168	28	.	.	PUNCT
ejpam-1528	169	1	if	if	SCONJ
ejpam-1528	169	2	s	s	NOUN
ejpam-1528	169	3	is	be	AUX
ejpam-1528	169	4	right	right	ADJ
ejpam-1528	169	5	semi	semi	ADJ
ejpam-1528	169	6	-	-	ADJ
ejpam-1528	169	7	hereditary	hereditary	ADJ
ejpam-1528	169	8	then	then	ADV
ejpam-1528	169	9	it	it	PRON
ejpam-1528	169	10	is	be	AUX
ejpam-1528	169	11	right	right	ADJ
ejpam-1528	169	12	p.p	p.p	PROPN
ejpam-1528	169	13	.	.	PROPN
ejpam-1528	169	14	and	and	CCONJ
ejpam-1528	169	15	incomparable	incomparable	ADJ
ejpam-1528	169	16	principal	principal	ADJ
ejpam-1528	169	17	right	right	ADJ
ejpam-1528	169	18	ideals	ideal	NOUN
ejpam-1528	169	19	are	be	AUX
ejpam-1528	169	20	disjoints[3	disjoints[3	PROPN
ejpam-1528	169	21	]	]	PUNCT
ejpam-1528	169	22	.	.	PUNCT
ejpam-1528	170	1	it	it	PRON
ejpam-1528	170	2	follows	follow	VERB
ejpam-1528	170	3	notably	notably	ADV
ejpam-1528	170	4	that	that	SCONJ
ejpam-1528	170	5	e(s	e(s	PROPN
ejpam-1528	170	6	)	)	PUNCT
ejpam-1528	170	7	is	be	AUX
ejpam-1528	170	8	a	a	DET
ejpam-1528	170	9	chain	chain	NOUN
ejpam-1528	170	10	(	(	PUNCT
ejpam-1528	170	11	any	any	DET
ejpam-1528	170	12	two	two	NUM
ejpam-1528	170	13	idempotents	idempotent	NOUN
ejpam-1528	170	14	are	be	AUX
ejpam-1528	170	15	comparable	comparable	ADJ
ejpam-1528	170	16	)	)	PUNCT
ejpam-1528	170	17	,	,	PUNCT
ejpam-1528	170	18	and	and	CCONJ
ejpam-1528	170	19	maximal	maximal	ADJ
ejpam-1528	170	20	invertibility	invertibility	NOUN
ejpam-1528	170	21	implies	imply	VERB
ejpam-1528	170	22	natural	natural	ADJ
ejpam-1528	170	23	invertibility	invertibility	NOUN
ejpam-1528	170	24	.	.	PUNCT
ejpam-1528	171	1	let	let	VERB
ejpam-1528	171	2	now	now	ADV
ejpam-1528	171	3	a	a	DET
ejpam-1528	171	4	∈	∈	NOUN
ejpam-1528	171	5	s.	s.	PROPN
ejpam-1528	171	6	if	if	SCONJ
ejpam-1528	171	7	a	a	PRON
ejpam-1528	171	8	is	be	AUX
ejpam-1528	171	9	regular	regular	ADJ
ejpam-1528	171	10	,	,	PUNCT
ejpam-1528	171	11	then	then	ADV
ejpam-1528	171	12	a	a	PRON
ejpam-1528	171	13	is	be	AUX
ejpam-1528	171	14	group	group	NOUN
ejpam-1528	171	15	invertible	invertible	ADJ
ejpam-1528	171	16	hence	hence	ADV
ejpam-1528	171	17	naturally	naturally	ADV
ejpam-1528	171	18	invertible	invertible	ADJ
ejpam-1528	171	19	.	.	PUNCT
ejpam-1528	172	1	we	we	PRON
ejpam-1528	172	2	assume	assume	VERB
ejpam-1528	172	3	in	in	ADP
ejpam-1528	172	4	the	the	DET
ejpam-1528	172	5	sequel	sequel	NOUN
ejpam-1528	172	6	that	that	SCONJ
ejpam-1528	172	7	a	a	PRON
ejpam-1528	172	8	is	be	AUX
ejpam-1528	172	9	not	not	PART
ejpam-1528	172	10	regular	regular	ADJ
ejpam-1528	172	11	.	.	PUNCT
ejpam-1528	173	1	by	by	ADP
ejpam-1528	173	2	centrality	centrality	NOUN
ejpam-1528	173	3	of	of	ADP
ejpam-1528	173	4	the	the	DET
ejpam-1528	173	5	idempotents	idempotent	NOUN
ejpam-1528	173	6	,	,	PUNCT
ejpam-1528	173	7	σ0(a	σ0(a	NUM
ejpam-1528	173	8	)	)	PUNCT
ejpam-1528	173	9	=	=	SYM
ejpam-1528	173	10	σ1(a	σ1(a	PROPN
ejpam-1528	173	11	)	)	PUNCT
ejpam-1528	173	12	=	=	SYM
ejpam-1528	173	13	σ2(a	σ2(a	PROPN
ejpam-1528	173	14	)	)	PUNCT
ejpam-1528	173	15	=	=	PRON
ejpam-1528	173	16	{	{	PUNCT
ejpam-1528	173	17	e	e	PROPN
ejpam-1528	173	18	∈	∈	PROPN
ejpam-1528	173	19	e(s	e(s	PROPN
ejpam-1528	173	20	)	)	PUNCT
ejpam-1528	173	21	,	,	PUNCT
ejpam-1528	173	22	e	e	NOUN
ejpam-1528	173	23	≤h	≤h	NOUN
ejpam-1528	173	24	a	a	X
ejpam-1528	173	25	}	}	PUNCT
ejpam-1528	173	26	.	.	PUNCT
ejpam-1528	174	1	let	let	VERB
ejpam-1528	174	2	a0	a0	PROPN
ejpam-1528	174	3	∈	∈	PROPN
ejpam-1528	174	4	e(s	e(s	PROPN
ejpam-1528	174	5	)	)	PUNCT
ejpam-1528	174	6	be	be	AUX
ejpam-1528	174	7	the	the	DET
ejpam-1528	174	8	idempotent	idempotent	NOUN
ejpam-1528	174	9	such	such	DET
ejpam-1528	174	10	that	that	SCONJ
ejpam-1528	174	11	a	a	DET
ejpam-1528	174	12	∈	∈	PROPN
ejpam-1528	174	13	ya0	ya0	NOUN
ejpam-1528	174	14	.	.	PUNCT
ejpam-1528	175	1	since	since	SCONJ
ejpam-1528	175	2	aa0	aa0	NOUN
ejpam-1528	175	3	=	=	SYM
ejpam-1528	175	4	a0a	a0a	PROPN
ejpam-1528	175	5	=	=	SYM
ejpam-1528	175	6	a	a	NOUN
ejpam-1528	175	7	,	,	PUNCT
ejpam-1528	175	8	any	any	DET
ejpam-1528	175	9	e	e	NOUN
ejpam-1528	175	10	≤h	≤h	NOUN
ejpam-1528	175	11	a	a	DET
ejpam-1528	175	12	satisfies	satisfie	NOUN
ejpam-1528	175	13	e	e	X
ejpam-1528	175	14	≤	≤	ADJ
ejpam-1528	175	15	a0	a0	NOUN
ejpam-1528	175	16	for	for	ADP
ejpam-1528	175	17	the	the	DET
ejpam-1528	175	18	h	h	NOUN
ejpam-1528	175	19	order	order	NOUN
ejpam-1528	175	20	hence	hence	ADV
ejpam-1528	175	21	the	the	DET
ejpam-1528	175	22	natural	natural	ADJ
ejpam-1528	175	23	partial	partial	ADJ
ejpam-1528	175	24	order	order	NOUN
ejpam-1528	175	25	,	,	PUNCT
ejpam-1528	175	26	and	and	CCONJ
ejpam-1528	175	27	since	since	SCONJ
ejpam-1528	175	28	a	a	PRON
ejpam-1528	175	29	is	be	AUX
ejpam-1528	175	30	not	not	PART
ejpam-1528	175	31	regular	regular	ADJ
ejpam-1528	175	32	,	,	PUNCT
ejpam-1528	175	33	e	e	X
ejpam-1528	175	34	<	<	X
ejpam-1528	175	35	a0	a0	PROPN
ejpam-1528	175	36	.	.	PUNCT
ejpam-1528	176	1	conversely	conversely	ADV
ejpam-1528	176	2	,	,	PUNCT
ejpam-1528	176	3	let	let	VERB
ejpam-1528	176	4	e	e	PRON
ejpam-1528	176	5	<	<	X
ejpam-1528	176	6	a0	a0	PROPN
ejpam-1528	176	7	and	and	CCONJ
ejpam-1528	176	8	assume	assume	VERB
ejpam-1528	176	9	s	s	X
ejpam-1528	176	10	is	be	AUX
ejpam-1528	176	11	semi	semi	ADJ
ejpam-1528	176	12	-	-	ADJ
ejpam-1528	176	13	hereditary	hereditary	ADJ
ejpam-1528	176	14	.	.	PUNCT
ejpam-1528	177	1	from	from	ADP
ejpam-1528	177	2	ae	ae	PROPN
ejpam-1528	177	3	=	=	SYM
ejpam-1528	177	4	ea	ea	PROPN
ejpam-1528	177	5	∈	∈	NOUN
ejpam-1528	177	6	es	es	NOUN
ejpam-1528	177	7	∩	∩	NOUN
ejpam-1528	177	8	as	as	ADP
ejpam-1528	177	9	,	,	PUNCT
ejpam-1528	177	10	es	es	NOUN
ejpam-1528	177	11	and	and	CCONJ
ejpam-1528	177	12	as	as	SCONJ
ejpam-1528	177	13	are	be	AUX
ejpam-1528	177	14	comparable	comparable	ADJ
ejpam-1528	177	15	,	,	PUNCT
ejpam-1528	177	16	and	and	CCONJ
ejpam-1528	177	17	from	from	ADP
ejpam-1528	177	18	e	e	X
ejpam-1528	177	19	<	<	X
ejpam-1528	177	20	a0	a0	PROPN
ejpam-1528	177	21	we	we	PRON
ejpam-1528	177	22	get	get	VERB
ejpam-1528	177	23	es	es	ADP
ejpam-1528	177	24	⊂	⊂	PRON
ejpam-1528	177	25	as	as	ADP
ejpam-1528	177	26	(	(	PUNCT
ejpam-1528	177	27	ae	ae	PROPN
ejpam-1528	177	28	∈	∈	PROPN
ejpam-1528	177	29	ye	ye	PRON
ejpam-1528	177	30	disjoint	disjoint	NOUN
ejpam-1528	177	31	from	from	ADP
ejpam-1528	177	32	ya0	ya0	PROPN
ejpam-1528	177	33	hence	hence	ADV
ejpam-1528	177	34	ae	ae	PROPN
ejpam-1528	177	35	6=	6=	PROPN
ejpam-1528	177	36	a	a	PRON
ejpam-1528	177	37	)	)	PUNCT
ejpam-1528	177	38	.	.	PUNCT
ejpam-1528	178	1	it	it	PRON
ejpam-1528	178	2	follows	follow	VERB
ejpam-1528	178	3	that	that	SCONJ
ejpam-1528	178	4	e	e	PROPN
ejpam-1528	178	5	≤r	≤r	VERB
ejpam-1528	178	6	a	a	PRON
ejpam-1528	178	7	and	and	CCONJ
ejpam-1528	178	8	in	in	ADP
ejpam-1528	178	9	particular	particular	ADJ
ejpam-1528	178	10	ea	ea	NOUN
ejpam-1528	179	1	=	=	SYM
ejpam-1528	179	2	aere	aere	X
ejpam-1528	179	3	is	be	AUX
ejpam-1528	179	4	regular	regular	ADJ
ejpam-1528	179	5	.	.	PUNCT
ejpam-1528	180	1	since	since	SCONJ
ejpam-1528	180	2	for	for	ADP
ejpam-1528	180	3	regular	regular	ADJ
ejpam-1528	180	4	elements	element	NOUN
ejpam-1528	180	5	,	,	PUNCT
ejpam-1528	180	6	the	the	DET
ejpam-1528	180	7	appartenance	appartenance	NOUN
ejpam-1528	180	8	in	in	ADP
ejpam-1528	180	9	ye	ye	PRON
ejpam-1528	180	10	is	be	AUX
ejpam-1528	180	11	simply	simply	ADV
ejpam-1528	180	12	green	green	PROPN
ejpam-1528	180	13	’s	’s	PART
ejpam-1528	180	14	relation	relation	NOUN
ejpam-1528	180	15	l	l	NOUN
ejpam-1528	180	16	,	,	PUNCT
ejpam-1528	180	17	we	we	PRON
ejpam-1528	180	18	get	get	VERB
ejpam-1528	180	19	that	that	PRON
ejpam-1528	180	20	ae	ae	PROPN
ejpam-1528	181	1	=	=	PUNCT
ejpam-1528	182	1	eah	eah	PROPN
ejpam-1528	182	2	e	e	PROPN
ejpam-1528	182	3	and	and	CCONJ
ejpam-1528	182	4	e	e	X
ejpam-1528	182	5	≤h	≤h	NOUN
ejpam-1528	182	6	a.	a.	NOUN
ejpam-1528	182	7	finally	finally	ADV
ejpam-1528	182	8	,	,	PUNCT
ejpam-1528	182	9	we	we	PRON
ejpam-1528	182	10	have	have	AUX
ejpam-1528	182	11	proved	prove	VERB
ejpam-1528	182	12	that	that	SCONJ
ejpam-1528	182	13	σ(a	σ(a	PROPN
ejpam-1528	182	14	)	)	PUNCT
ejpam-1528	182	15	is	be	AUX
ejpam-1528	182	16	the	the	DET
ejpam-1528	182	17	chain	chain	NOUN
ejpam-1528	182	18	of	of	ADP
ejpam-1528	182	19	idempotents	idempotent	NOUN
ejpam-1528	182	20	{	{	PUNCT
ejpam-1528	182	21	e	e	NOUN
ejpam-1528	182	22	∈	∈	PROPN
ejpam-1528	182	23	e(s	e(s	PROPN
ejpam-1528	182	24	)	)	PUNCT
ejpam-1528	182	25	,	,	PUNCT
ejpam-1528	183	1	e	e	X
ejpam-1528	183	2	<	<	X
ejpam-1528	183	3	a0	a0	PROPN
ejpam-1528	183	4	}	}	PUNCT
ejpam-1528	183	5	.	.	PUNCT
ejpam-1528	184	1	if	if	SCONJ
ejpam-1528	184	2	we	we	PRON
ejpam-1528	184	3	finally	finally	ADV
ejpam-1528	184	4	assume	assume	VERB
ejpam-1528	184	5	that	that	SCONJ
ejpam-1528	184	6	s	s	VERB
ejpam-1528	184	7	is	be	AUX
ejpam-1528	184	8	right	right	ADJ
ejpam-1528	184	9	hereditary	hereditary	ADJ
ejpam-1528	184	10	(	(	PUNCT
ejpam-1528	184	11	right	right	ADJ
ejpam-1528	184	12	ideals	ideal	NOUN
ejpam-1528	184	13	are	be	AUX
ejpam-1528	184	14	projective	projective	ADJ
ejpam-1528	184	15	)	)	PUNCT
ejpam-1528	184	16	,	,	PUNCT
ejpam-1528	184	17	then	then	ADV
ejpam-1528	184	18	dorofeeva	dorofeeva	VERB
ejpam-1528	184	19	[	[	X
ejpam-1528	184	20	3	3	X
ejpam-1528	184	21	]	]	PUNCT
ejpam-1528	184	22	showed	show	VERB
ejpam-1528	184	23	that	that	SCONJ
ejpam-1528	184	24	s	s	NOUN
ejpam-1528	184	25	satifisies	satifisie	NOUN
ejpam-1528	184	26	the	the	DET
ejpam-1528	184	27	maximum	maximum	ADJ
ejpam-1528	184	28	condition	condition	NOUN
ejpam-1528	184	29	for	for	ADP
ejpam-1528	184	30	principal	principal	ADJ
ejpam-1528	184	31	right	right	ADJ
ejpam-1528	184	32	ideals	ideal	NOUN
ejpam-1528	184	33	.	.	PUNCT
ejpam-1528	185	1	as	as	ADP
ejpam-1528	185	2	a	a	DET
ejpam-1528	185	3	consequence	consequence	NOUN
ejpam-1528	185	4	,	,	PUNCT
ejpam-1528	185	5	the	the	DET
ejpam-1528	185	6	chain	chain	NOUN
ejpam-1528	185	7	of	of	ADP
ejpam-1528	185	8	idempotents	idempotent	NOUN
ejpam-1528	185	9	{	{	PUNCT
ejpam-1528	185	10	e	e	NOUN
ejpam-1528	185	11	∈	∈	PROPN
ejpam-1528	185	12	e(s	e(s	PROPN
ejpam-1528	185	13	)	)	PUNCT
ejpam-1528	185	14	,	,	PUNCT
ejpam-1528	185	15	e	e	PROPN
ejpam-1528	185	16	<	<	X
ejpam-1528	185	17	a0	a0	PROPN
ejpam-1528	185	18	}	}	PUNCT
ejpam-1528	185	19	has	have	VERB
ejpam-1528	185	20	a	a	DET
ejpam-1528	185	21	greatest	great	ADJ
ejpam-1528	185	22	element	element	NOUN
ejpam-1528	185	23	m	m	PROPN
ejpam-1528	185	24	and	and	CCONJ
ejpam-1528	185	25	a	a	PRON
ejpam-1528	185	26	is	be	AUX
ejpam-1528	185	27	naturally	naturally	ADV
ejpam-1528	185	28	invertible	invertible	ADJ
ejpam-1528	185	29	with	with	ADP
ejpam-1528	185	30	inverse	inverse	NOUN
ejpam-1528	185	31	a−m	a−m	NOUN
ejpam-1528	185	32	.	.	PUNCT
ejpam-1528	186	1	x.	x.	PROPN
ejpam-1528	186	2	mary	mary	PROPN
ejpam-1528	186	3	/	/	SYM
ejpam-1528	186	4	eur	eur	PROPN
ejpam-1528	186	5	.	.	PUNCT
ejpam-1528	187	1	j.	j.	PROPN
ejpam-1528	187	2	pure	pure	PROPN
ejpam-1528	187	3	appl	appl	PROPN
ejpam-1528	187	4	.	.	PROPN
ejpam-1528	187	5	math	math	PROPN
ejpam-1528	187	6	,	,	PUNCT
ejpam-1528	187	7	6	6	NUM
ejpam-1528	187	8	(	(	PUNCT
ejpam-1528	187	9	2013	2013	NUM
ejpam-1528	187	10	)	)	PUNCT
ejpam-1528	187	11	,	,	PUNCT
ejpam-1528	187	12	413	413	NUM
ejpam-1528	187	13	-	-	SYM
ejpam-1528	187	14	427	427	NUM
ejpam-1528	187	15	419	419	NUM
ejpam-1528	187	16	4	4	NUM
ejpam-1528	187	17	.	.	PUNCT
ejpam-1528	188	1	the	the	DET
ejpam-1528	188	2	ring	ring	NOUN
ejpam-1528	188	3	case	case	NOUN
ejpam-1528	188	4	4.1	4.1	NUM
ejpam-1528	188	5	.	.	PUNCT
ejpam-1528	189	1	invertibility	invertibility	NOUN
ejpam-1528	189	2	along	along	ADP
ejpam-1528	189	3	an	an	DET
ejpam-1528	189	4	element	element	NOUN
ejpam-1528	189	5	in	in	ADP
ejpam-1528	189	6	a	a	DET
ejpam-1528	189	7	ring	ring	NOUN
ejpam-1528	189	8	in	in	ADP
ejpam-1528	189	9	this	this	DET
ejpam-1528	189	10	section	section	NOUN
ejpam-1528	189	11	,	,	PUNCT
ejpam-1528	189	12	r	r	NOUN
ejpam-1528	189	13	denotes	denote	VERB
ejpam-1528	189	14	a	a	DET
ejpam-1528	189	15	unital	unital	ADJ
ejpam-1528	189	16	ring	ring	NOUN
ejpam-1528	189	17	.	.	PUNCT
ejpam-1528	190	1	in	in	ADP
ejpam-1528	190	2	particular	particular	ADJ
ejpam-1528	190	3	,	,	PUNCT
ejpam-1528	190	4	it	it	PRON
ejpam-1528	190	5	is	be	AUX
ejpam-1528	190	6	a	a	DET
ejpam-1528	190	7	semigroup	semigroup	NOUN
ejpam-1528	190	8	and	and	CCONJ
ejpam-1528	190	9	the	the	DET
ejpam-1528	190	10	previous	previous	ADJ
ejpam-1528	190	11	notations	notation	NOUN
ejpam-1528	190	12	and	and	CCONJ
ejpam-1528	190	13	results	result	NOUN
ejpam-1528	190	14	apply	apply	VERB
ejpam-1528	190	15	.	.	PUNCT
ejpam-1528	191	1	in	in	ADP
ejpam-1528	191	2	[	[	X
ejpam-1528	191	3	19	19	NUM
ejpam-1528	191	4	]	]	PUNCT
ejpam-1528	191	5	,	,	PUNCT
ejpam-1528	191	6	invertibilty	invertibilty	NOUN
ejpam-1528	191	7	along	along	ADP
ejpam-1528	191	8	an	an	DET
ejpam-1528	191	9	element	element	NOUN
ejpam-1528	191	10	is	be	AUX
ejpam-1528	191	11	characterized	characterize	VERB
ejpam-1528	191	12	in	in	ADP
ejpam-1528	191	13	terms	term	NOUN
ejpam-1528	191	14	of	of	ADP
ejpam-1528	191	15	existence	existence	NOUN
ejpam-1528	191	16	of	of	ADP
ejpam-1528	191	17	units	unit	NOUN
ejpam-1528	191	18	.	.	PUNCT
ejpam-1528	192	1	theorem	theorem	NOUN
ejpam-1528	192	2	5	5	NUM
ejpam-1528	192	3	.	.	PUNCT
ejpam-1528	193	1	let	let	VERB
ejpam-1528	193	2	d	d	PRON
ejpam-1528	193	3	be	be	AUX
ejpam-1528	193	4	a	a	DET
ejpam-1528	193	5	regular	regular	ADJ
ejpam-1528	193	6	element	element	NOUN
ejpam-1528	193	7	of	of	ADP
ejpam-1528	193	8	a	a	DET
ejpam-1528	193	9	unital	unital	ADJ
ejpam-1528	193	10	ring	ring	NOUN
ejpam-1528	193	11	r	r	NOUN
ejpam-1528	193	12	,	,	PUNCT
ejpam-1528	193	13	d	d	NOUN
ejpam-1528	193	14	′	′	NUM
ejpam-1528	193	15	∈	∈	PROPN
ejpam-1528	193	16	a(d	a(d	PROPN
ejpam-1528	193	17	)	)	PUNCT
ejpam-1528	193	18	.	.	PUNCT
ejpam-1528	194	1	then	then	ADV
ejpam-1528	194	2	the	the	DET
ejpam-1528	194	3	following	follow	VERB
ejpam-1528	194	4	are	be	AUX
ejpam-1528	194	5	equivalent	equivalent	ADJ
ejpam-1528	194	6	:	:	PUNCT
ejpam-1528	194	7	i	i	PRON
ejpam-1528	194	8	)	)	PUNCT
ejpam-1528	194	9	a−d	a−d	PROPN
ejpam-1528	194	10	exists	exist	VERB
ejpam-1528	194	11	.	.	PUNCT
ejpam-1528	195	1	ii	ii	X
ejpam-1528	195	2	)	)	PUNCT
ejpam-1528	195	3	u=	u=	NOUN
ejpam-1528	195	4	da+	da+	VERB
ejpam-1528	195	5	1−	1−	NUM
ejpam-1528	195	6	dd	dd	NOUN
ejpam-1528	195	7	′	′	NUM
ejpam-1528	195	8	is	be	AUX
ejpam-1528	195	9	a	a	DET
ejpam-1528	195	10	unit	unit	NOUN
ejpam-1528	195	11	.	.	PUNCT
ejpam-1528	196	1	iii	iii	X
ejpam-1528	196	2	)	)	PUNCT
ejpam-1528	196	3	v	v	NOUN
ejpam-1528	196	4	=	=	SYM
ejpam-1528	196	5	ad	ad	NOUN
ejpam-1528	196	6	+	+	CCONJ
ejpam-1528	196	7	1−	1−	NUM
ejpam-1528	197	1	d	d	NOUN
ejpam-1528	197	2	′d	′d	NOUN
ejpam-1528	197	3	is	be	AUX
ejpam-1528	197	4	a	a	DET
ejpam-1528	197	5	unit	unit	NOUN
ejpam-1528	197	6	.	.	PUNCT
ejpam-1528	198	1	in	in	ADP
ejpam-1528	198	2	this	this	DET
ejpam-1528	198	3	case	case	NOUN
ejpam-1528	198	4	,	,	PUNCT
ejpam-1528	198	5	a−d	a−d	NOUN
ejpam-1528	198	6	=	=	X
ejpam-1528	198	7	u−1d	u−1d	NOUN
ejpam-1528	198	8	=	=	SYM
ejpam-1528	198	9	dv−1	dv−1	PROPN
ejpam-1528	198	10	.	.	PUNCT
ejpam-1528	199	1	note	note	VERB
ejpam-1528	199	2	that	that	SCONJ
ejpam-1528	199	3	in	in	ADP
ejpam-1528	199	4	the	the	DET
ejpam-1528	199	5	particular	particular	ADJ
ejpam-1528	199	6	case	case	NOUN
ejpam-1528	199	7	of	of	ADP
ejpam-1528	199	8	invertibility	invertibility	NOUN
ejpam-1528	199	9	along	along	ADP
ejpam-1528	199	10	an	an	DET
ejpam-1528	199	11	idempotent	idempotent	ADJ
ejpam-1528	199	12	e	e	NOUN
ejpam-1528	199	13	,	,	PUNCT
ejpam-1528	199	14	this	this	PRON
ejpam-1528	199	15	reduces	reduce	VERB
ejpam-1528	199	16	to	to	PART
ejpam-1528	199	17	:	:	PUNCT
ejpam-1528	199	18	corollary	corollary	ADJ
ejpam-1528	199	19	2	2	X
ejpam-1528	199	20	.	.	PUNCT
ejpam-1528	200	1	let	let	VERB
ejpam-1528	200	2	e	e	PRON
ejpam-1528	200	3	∈	∈	PROPN
ejpam-1528	200	4	e(r	e(r	X
ejpam-1528	200	5	)	)	PUNCT
ejpam-1528	200	6	be	be	AUX
ejpam-1528	200	7	a	a	DET
ejpam-1528	200	8	idempotent	idempotent	ADJ
ejpam-1528	200	9	element	element	NOUN
ejpam-1528	200	10	of	of	ADP
ejpam-1528	200	11	a	a	DET
ejpam-1528	200	12	unital	unital	ADJ
ejpam-1528	200	13	ring	ring	NOUN
ejpam-1528	200	14	r.	r.	PROPN
ejpam-1528	200	15	then	then	ADV
ejpam-1528	200	16	the	the	DET
ejpam-1528	200	17	following	following	NOUN
ejpam-1528	200	18	are	be	AUX
ejpam-1528	200	19	equivalent	equivalent	ADJ
ejpam-1528	200	20	:	:	PUNCT
ejpam-1528	200	21	i	i	NOUN
ejpam-1528	200	22	)	)	PUNCT
ejpam-1528	200	23	a−e	a−e	NOUN
ejpam-1528	200	24	exists	exist	VERB
ejpam-1528	200	25	.	.	PUNCT
ejpam-1528	201	1	ii	ii	X
ejpam-1528	201	2	)	)	PUNCT
ejpam-1528	201	3	u=	u=	NOUN
ejpam-1528	201	4	ea+	ea+	NOUN
ejpam-1528	201	5	1−	1−	NUM
ejpam-1528	201	6	e	e	NOUN
ejpam-1528	201	7	is	be	AUX
ejpam-1528	201	8	a	a	DET
ejpam-1528	201	9	unit	unit	NOUN
ejpam-1528	201	10	.	.	PUNCT
ejpam-1528	202	1	iii	iii	X
ejpam-1528	202	2	)	)	PUNCT
ejpam-1528	202	3	v	v	NOUN
ejpam-1528	202	4	=	=	SYM
ejpam-1528	202	5	ae+	ae+	NOUN
ejpam-1528	203	1	1−	1−	NUM
ejpam-1528	203	2	e	e	NOUN
ejpam-1528	203	3	is	be	AUX
ejpam-1528	203	4	a	a	DET
ejpam-1528	203	5	unit	unit	NOUN
ejpam-1528	203	6	.	.	PUNCT
ejpam-1528	204	1	in	in	ADP
ejpam-1528	204	2	this	this	DET
ejpam-1528	204	3	case	case	NOUN
ejpam-1528	204	4	,	,	PUNCT
ejpam-1528	204	5	a−e	a−e	NOUN
ejpam-1528	204	6	=	=	SYM
ejpam-1528	204	7	u−1e	u−1e	NOUN
ejpam-1528	204	8	=	=	SYM
ejpam-1528	204	9	ev−1	ev−1	PROPN
ejpam-1528	204	10	.	.	PROPN
ejpam-1528	204	11	corollary	corollary	ADJ
ejpam-1528	204	12	3	3	X
ejpam-1528	204	13	.	.	PUNCT
ejpam-1528	205	1	if	if	SCONJ
ejpam-1528	205	2	ae	ae	PROPN
ejpam-1528	205	3	=	=	SYM
ejpam-1528	205	4	ea	ea	PROPN
ejpam-1528	205	5	,	,	PUNCT
ejpam-1528	205	6	then	then	ADV
ejpam-1528	205	7	e	e	X
ejpam-1528	205	8	≤h	≤h	NOUN
ejpam-1528	205	9	a	a	DET
ejpam-1528	205	10	if	if	NOUN
ejpam-1528	205	11	and	and	CCONJ
ejpam-1528	205	12	only	only	ADV
ejpam-1528	205	13	if	if	SCONJ
ejpam-1528	205	14	u=	u=	ADJ
ejpam-1528	205	15	1	1	NUM
ejpam-1528	205	16	+	+	NUM
ejpam-1528	205	17	ae−	ae−	PUNCT
ejpam-1528	205	18	e	e	NOUN
ejpam-1528	205	19	is	be	AUX
ejpam-1528	205	20	a	a	DET
ejpam-1528	205	21	unit	unit	NOUN
ejpam-1528	205	22	.	.	PUNCT
ejpam-1528	206	1	remark	remark	VERB
ejpam-1528	206	2	that	that	SCONJ
ejpam-1528	206	3	a	a	DET
ejpam-1528	206	4	sufficient	sufficient	ADJ
ejpam-1528	206	5	condition	condition	NOUN
ejpam-1528	206	6	for	for	SCONJ
ejpam-1528	206	7	this	this	PRON
ejpam-1528	206	8	to	to	PART
ejpam-1528	206	9	happen	happen	VERB
ejpam-1528	206	10	is	be	AUX
ejpam-1528	206	11	the	the	DET
ejpam-1528	206	12	following	following	NOUN
ejpam-1528	206	13	:	:	PUNCT
ejpam-1528	206	14	lemma	lemma	PROPN
ejpam-1528	206	15	5	5	X
ejpam-1528	206	16	.	.	PUNCT
ejpam-1528	207	1	if	if	SCONJ
ejpam-1528	207	2	ae	ae	PROPN
ejpam-1528	207	3	=	=	SYM
ejpam-1528	207	4	ea	ea	PROPN
ejpam-1528	207	5	and	and	CCONJ
ejpam-1528	207	6	a+	a+	PUNCT
ejpam-1528	207	7	1−	1−	NUM
ejpam-1528	207	8	e	e	NOUN
ejpam-1528	207	9	is	be	AUX
ejpam-1528	207	10	a	a	DET
ejpam-1528	207	11	unit	unit	NOUN
ejpam-1528	207	12	,	,	PUNCT
ejpam-1528	207	13	then	then	ADV
ejpam-1528	207	14	e	e	X
ejpam-1528	207	15	≤h	≤h	NOUN
ejpam-1528	207	16	a.	a.	NOUN
ejpam-1528	207	17	proof	proof	NOUN
ejpam-1528	207	18	.	.	PUNCT
ejpam-1528	208	1	let	let	VERB
ejpam-1528	208	2	u=	u=	NOUN
ejpam-1528	208	3	a+	a+	PRON
ejpam-1528	208	4	1−	1−	NUM
ejpam-1528	208	5	e.	e.	PROPN
ejpam-1528	208	6	then	then	ADV
ejpam-1528	208	7	ue	ue	PROPN
ejpam-1528	209	1	=	=	SYM
ejpam-1528	209	2	ae	ae	PROPN
ejpam-1528	209	3	=	=	SYM
ejpam-1528	209	4	ea	ea	PROPN
ejpam-1528	209	5	hence	hence	ADV
ejpam-1528	209	6	e	e	NOUN
ejpam-1528	209	7	=	=	NOUN
ejpam-1528	209	8	u−1ea	u−1ea	X
ejpam-1528	209	9	=	=	SYM
ejpam-1528	209	10	au−1e	au−1e	PROPN
ejpam-1528	209	11	.	.	PUNCT
ejpam-1528	210	1	4.2	4.2	NUM
ejpam-1528	210	2	.	.	PUNCT
ejpam-1528	210	3	natural	natural	ADJ
ejpam-1528	210	4	inverse	inverse	NOUN
ejpam-1528	210	5	in	in	ADP
ejpam-1528	210	6	a	a	DET
ejpam-1528	210	7	ring	ring	NOUN
ejpam-1528	210	8	let	let	VERB
ejpam-1528	210	9	r	r	PRON
ejpam-1528	210	10	be	be	AUX
ejpam-1528	210	11	a	a	DET
ejpam-1528	210	12	unital	unital	ADJ
ejpam-1528	210	13	ring	ring	NOUN
ejpam-1528	210	14	,	,	PUNCT
ejpam-1528	210	15	and	and	CCONJ
ejpam-1528	210	16	let	let	VERB
ejpam-1528	210	17	a	a	DET
ejpam-1528	210	18	∈	∈	PROPN
ejpam-1528	210	19	r.	r.	NOUN
ejpam-1528	210	20	then	then	ADV
ejpam-1528	210	21	the	the	DET
ejpam-1528	210	22	semilattice	semilattice	NOUN
ejpam-1528	210	23	σ2(a	σ2(a	NUM
ejpam-1528	210	24	)	)	PUNCT
ejpam-1528	210	25	is	be	AUX
ejpam-1528	210	26	actually	actually	ADV
ejpam-1528	210	27	a	a	DET
ejpam-1528	210	28	distributive	distributive	ADJ
ejpam-1528	210	29	lattice	lattice	NOUN
ejpam-1528	210	30	(	(	PUNCT
ejpam-1528	210	31	with	with	ADP
ejpam-1528	210	32	e∨	e∨	PROPN
ejpam-1528	210	33	f	f	PROPN
ejpam-1528	211	1	=	=	PUNCT
ejpam-1528	211	2	e+	e+	PUNCT
ejpam-1528	211	3	f	f	PROPN
ejpam-1528	211	4	−	−	PROPN
ejpam-1528	211	5	e	e	X
ejpam-1528	211	6	f	f	PROPN
ejpam-1528	211	7	)	)	PUNCT
ejpam-1528	211	8	hence	hence	ADV
ejpam-1528	211	9	a	a	PRON
ejpam-1528	211	10	is	be	AUX
ejpam-1528	211	11	2−maximally	2−maximally	ADV
ejpam-1528	211	12	invertible	invertible	ADJ
ejpam-1528	211	13	if	if	SCONJ
ejpam-1528	211	14	and	and	CCONJ
ejpam-1528	211	15	only	only	ADV
ejpam-1528	211	16	if	if	SCONJ
ejpam-1528	211	17	it	it	PRON
ejpam-1528	211	18	is	be	AUX
ejpam-1528	211	19	naturally	naturally	ADV
ejpam-1528	211	20	invertible	invertible	ADJ
ejpam-1528	211	21	.	.	PUNCT
ejpam-1528	212	1	we	we	PRON
ejpam-1528	212	2	derive	derive	VERB
ejpam-1528	212	3	new	new	ADJ
ejpam-1528	212	4	criterion	criterion	NOUN
ejpam-1528	212	5	for	for	ADP
ejpam-1528	212	6	the	the	DET
ejpam-1528	212	7	natural	natural	ADJ
ejpam-1528	212	8	inverse	inverse	NOUN
ejpam-1528	212	9	to	to	AUX
ejpam-1528	212	10	exists	exist	VERB
ejpam-1528	212	11	.	.	PUNCT
ejpam-1528	213	1	x.	x.	PROPN
ejpam-1528	213	2	mary	mary	PROPN
ejpam-1528	213	3	/	/	SYM
ejpam-1528	213	4	eur	eur	PROPN
ejpam-1528	213	5	.	.	PUNCT
ejpam-1528	214	1	j.	j.	PROPN
ejpam-1528	214	2	pure	pure	PROPN
ejpam-1528	214	3	appl	appl	PROPN
ejpam-1528	214	4	.	.	PROPN
ejpam-1528	214	5	math	math	PROPN
ejpam-1528	214	6	,	,	PUNCT
ejpam-1528	214	7	6	6	NUM
ejpam-1528	214	8	(	(	PUNCT
ejpam-1528	214	9	2013	2013	NUM
ejpam-1528	214	10	)	)	PUNCT
ejpam-1528	214	11	,	,	PUNCT
ejpam-1528	214	12	413	413	NUM
ejpam-1528	214	13	-	-	SYM
ejpam-1528	214	14	427	427	NUM
ejpam-1528	214	15	420	420	NUM
ejpam-1528	214	16	theorem	theorem	NOUN
ejpam-1528	214	17	6	6	NUM
ejpam-1528	214	18	.	.	PUNCT
ejpam-1528	215	1	let	let	VERB
ejpam-1528	215	2	a	a	DET
ejpam-1528	215	3	∈	∈	PROPN
ejpam-1528	215	4	r.	r.	NOUN
ejpam-1528	215	5	then	then	ADV
ejpam-1528	215	6	the	the	DET
ejpam-1528	215	7	following	follow	VERB
ejpam-1528	215	8	are	be	AUX
ejpam-1528	215	9	equivalent	equivalent	ADJ
ejpam-1528	215	10	:	:	PUNCT
ejpam-1528	215	11	i	i	NOUN
ejpam-1528	215	12	)	)	PUNCT
ejpam-1528	215	13	a	a	PRON
ejpam-1528	215	14	is	be	AUX
ejpam-1528	215	15	naturally	naturally	ADV
ejpam-1528	215	16	invertible	invertible	ADJ
ejpam-1528	215	17	with	with	ADP
ejpam-1528	215	18	inverse	inverse	NOUN
ejpam-1528	215	19	a−m	a−m	NOUN
ejpam-1528	215	20	;	;	PUNCT
ejpam-1528	215	21	ii	ii	X
ejpam-1528	215	22	)	)	PUNCT
ejpam-1528	215	23	there	there	PRON
ejpam-1528	215	24	exists	exist	VERB
ejpam-1528	215	25	b	b	PROPN
ejpam-1528	215	26	∈	∈	PROPN
ejpam-1528	215	27	{	{	PUNCT
ejpam-1528	215	28	a}′′	a}′′	PROPN
ejpam-1528	215	29	,	,	PUNCT
ejpam-1528	215	30	bab	bab	PROPN
ejpam-1528	215	31	=	=	SYM
ejpam-1528	215	32	b	b	PROPN
ejpam-1528	215	33	and	and	CCONJ
ejpam-1528	215	34	σ2(a−	σ2(a−	NUM
ejpam-1528	215	35	aba	aba	PROPN
ejpam-1528	215	36	)	)	PUNCT
ejpam-1528	215	37	=	=	PRON
ejpam-1528	216	1	{	{	PUNCT
ejpam-1528	216	2	0	0	NUM
ejpam-1528	216	3	}	}	PUNCT
ejpam-1528	216	4	;	;	PUNCT
ejpam-1528	216	5	iii	iii	X
ejpam-1528	216	6	)	)	PUNCT
ejpam-1528	217	1	a	a	PRON
ejpam-1528	217	2	=	=	PUNCT
ejpam-1528	217	3	x	x	SYM
ejpam-1528	218	1	+	+	NUM
ejpam-1528	218	2	y	y	NOUN
ejpam-1528	218	3	with	with	ADP
ejpam-1528	218	4	x	x	PROPN
ejpam-1528	218	5	∈	∈	PROPN
ejpam-1528	218	6	{	{	PUNCT
ejpam-1528	218	7	a}′′	a}′′	NUM
ejpam-1528	218	8	,	,	PUNCT
ejpam-1528	218	9	x	x	ADJ
ejpam-1528	218	10	#	#	NOUN
ejpam-1528	218	11	exists	exist	VERB
ejpam-1528	218	12	,	,	PUNCT
ejpam-1528	218	13	x	x	X
ejpam-1528	218	14	y	y	NOUN
ejpam-1528	218	15	=	=	SYM
ejpam-1528	218	16	0	0	NUM
ejpam-1528	218	17	and	and	CCONJ
ejpam-1528	218	18	σ2(y	σ2(y	X
ejpam-1528	218	19	)	)	PUNCT
ejpam-1528	218	20	=	=	PRON
ejpam-1528	218	21	{	{	PUNCT
ejpam-1528	218	22	0	0	NUM
ejpam-1528	218	23	}	}	PUNCT
ejpam-1528	218	24	.	.	PUNCT
ejpam-1528	219	1	in	in	ADP
ejpam-1528	219	2	this	this	DET
ejpam-1528	219	3	case	case	NOUN
ejpam-1528	219	4	,	,	PUNCT
ejpam-1528	219	5	a−m	a−m	NOUN
ejpam-1528	219	6	=	=	SYM
ejpam-1528	219	7	b	b	SYM
ejpam-1528	219	8	=	=	SYM
ejpam-1528	219	9	x	x	NOUN
ejpam-1528	219	10	#	#	NOUN
ejpam-1528	219	11	.	.	PUNCT
ejpam-1528	220	1	proof	proof	NOUN
ejpam-1528	220	2	.	.	PUNCT
ejpam-1528	221	1	1)⇒	1)⇒	NUM
ejpam-1528	221	2	2	2	NUM
ejpam-1528	221	3	)	)	PUNCT
ejpam-1528	221	4	assume	assume	VERB
ejpam-1528	221	5	a	a	PRON
ejpam-1528	221	6	is	be	AUX
ejpam-1528	221	7	naturally	naturally	ADV
ejpam-1528	221	8	invertible	invertible	ADJ
ejpam-1528	221	9	with	with	ADP
ejpam-1528	221	10	inverse	inverse	NOUN
ejpam-1528	221	11	b	b	NOUN
ejpam-1528	221	12	=	=	NOUN
ejpam-1528	221	13	a−m	a−m	NOUN
ejpam-1528	221	14	.	.	PUNCT
ejpam-1528	222	1	then	then	ADV
ejpam-1528	222	2	m	m	VERB
ejpam-1528	222	3	=	=	ADJ
ejpam-1528	222	4	ab	ab	PROPN
ejpam-1528	222	5	=	=	SYM
ejpam-1528	222	6	ba	ba	PROPN
ejpam-1528	222	7	.	.	PUNCT
ejpam-1528	223	1	let	let	VERB
ejpam-1528	223	2	e	e	PROPN
ejpam-1528	223	3	∈	∈	PROPN
ejpam-1528	223	4	σ2(a−	σ2(a−	PROPN
ejpam-1528	223	5	aba	aba	PROPN
ejpam-1528	223	6	)	)	PUNCT
ejpam-1528	223	7	.	.	PUNCT
ejpam-1528	224	1	the	the	DET
ejpam-1528	224	2	ca	ca	NOUN
ejpam-1528	224	3	=	=	SYM
ejpam-1528	224	4	ac⇒	ac⇒	X
ejpam-1528	224	5	cb	cb	NOUN
ejpam-1528	224	6	=	=	PUNCT
ejpam-1528	224	7	bc⇒	bc⇒	PROPN
ejpam-1528	224	8	c(a−	c(a−	PROPN
ejpam-1528	224	9	aba	aba	PROPN
ejpam-1528	224	10	)	)	PUNCT
ejpam-1528	225	1	=	=	PUNCT
ejpam-1528	225	2	(	(	PUNCT
ejpam-1528	225	3	a−	a−	PROPN
ejpam-1528	225	4	aba)c⇒	aba)c⇒	X
ejpam-1528	225	5	ec	ec	PROPN
ejpam-1528	225	6	=	=	SYM
ejpam-1528	225	7	ce	ce	PROPN
ejpam-1528	225	8	.	.	PROPN
ejpam-1528	225	9	hence	hence	ADV
ejpam-1528	225	10	e	e	X
ejpam-1528	225	11	∈	∈	PROPN
ejpam-1528	225	12	{	{	PUNCT
ejpam-1528	225	13	a}′′.	a}′′.	ADJ
ejpam-1528	225	14	but	but	CCONJ
ejpam-1528	225	15	also	also	ADV
ejpam-1528	225	16	∃t	∃t	PROPN
ejpam-1528	225	17	,	,	PUNCT
ejpam-1528	225	18	s	s	PART
ejpam-1528	225	19	∈	∈	PROPN
ejpam-1528	225	20	r	r	NOUN
ejpam-1528	225	21	,	,	PUNCT
ejpam-1528	225	22	e	e	NOUN
ejpam-1528	225	23	=	=	PUNCT
ejpam-1528	225	24	a(1−	a(1−	NOUN
ejpam-1528	225	25	ba)t	ba)t	ADV
ejpam-1528	225	26	=	=	SYM
ejpam-1528	225	27	s(1−	s(1−	NOUN
ejpam-1528	225	28	ab)a	ab)a	PROPN
ejpam-1528	225	29	and	and	CCONJ
ejpam-1528	225	30	e	e	X
ejpam-1528	225	31	≤h	≤h	NOUN
ejpam-1528	225	32	a.	a.	NOUN
ejpam-1528	225	33	finally	finally	ADV
ejpam-1528	225	34	,	,	PUNCT
ejpam-1528	225	35	e	e	PROPN
ejpam-1528	225	36	∈	∈	PROPN
ejpam-1528	225	37	σ2(a	σ2(a	NUM
ejpam-1528	225	38	)	)	PUNCT
ejpam-1528	225	39	hence	hence	ADV
ejpam-1528	225	40	e	e	X
ejpam-1528	225	41	≤	≤	NUM
ejpam-1528	225	42	m	m	VERB
ejpam-1528	225	43	,	,	PUNCT
ejpam-1528	225	44	em	em	PRON
ejpam-1528	225	45	=	=	NUM
ejpam-1528	225	46	me	i	PRON
ejpam-1528	226	1	=	=	PUNCT
ejpam-1528	226	2	e.	e.	PROPN
ejpam-1528	226	3	computation	computation	PROPN
ejpam-1528	226	4	give	give	VERB
ejpam-1528	226	5	e	e	X
ejpam-1528	226	6	=	=	SYM
ejpam-1528	226	7	em	em	PROPN
ejpam-1528	226	8	=	=	SYM
ejpam-1528	226	9	s(1−	s(1−	PROPN
ejpam-1528	226	10	ab)aba	ab)aba	PROPN
ejpam-1528	227	1	=	=	PUNCT
ejpam-1528	227	2	0	0	X
ejpam-1528	227	3	.	.	X
ejpam-1528	227	4	2)⇒	2)⇒	NUM
ejpam-1528	227	5	3	3	X
ejpam-1528	227	6	)	)	PUNCT
ejpam-1528	227	7	let	let	VERB
ejpam-1528	227	8	b	b	X
ejpam-1528	227	9	∈	∈	PROPN
ejpam-1528	227	10	{	{	PUNCT
ejpam-1528	227	11	a}′′	a}′′	PROPN
ejpam-1528	227	12	,	,	PUNCT
ejpam-1528	227	13	bab	bab	PROPN
ejpam-1528	227	14	=	=	SYM
ejpam-1528	227	15	b	b	PROPN
ejpam-1528	227	16	and	and	CCONJ
ejpam-1528	227	17	σ(a−	σ(a−	PROPN
ejpam-1528	227	18	aba	aba	PROPN
ejpam-1528	227	19	)	)	PUNCT
ejpam-1528	227	20	=	=	PUNCT
ejpam-1528	228	1	{	{	PUNCT
ejpam-1528	228	2	0	0	NUM
ejpam-1528	228	3	}	}	PUNCT
ejpam-1528	228	4	.	.	PUNCT
ejpam-1528	229	1	then	then	ADV
ejpam-1528	229	2	x	x	X
ejpam-1528	229	3	=	=	VERB
ejpam-1528	229	4	aba	aba	PROPN
ejpam-1528	229	5	and	and	CCONJ
ejpam-1528	229	6	y	y	NOUN
ejpam-1528	229	7	=	=	SYM
ejpam-1528	229	8	a−	a−	PROPN
ejpam-1528	229	9	aba	aba	NOUN
ejpam-1528	229	10	satisfy	satisfy	VERB
ejpam-1528	229	11	the	the	DET
ejpam-1528	229	12	required	require	VERB
ejpam-1528	229	13	relations	relation	NOUN
ejpam-1528	229	14	(	(	PUNCT
ejpam-1528	229	15	x	x	X
ejpam-1528	229	16	#	#	NOUN
ejpam-1528	229	17	=	=	SYM
ejpam-1528	229	18	b	b	NOUN
ejpam-1528	229	19	)	)	PUNCT
ejpam-1528	229	20	.	.	PUNCT
ejpam-1528	230	1	3)⇒	3)⇒	NUM
ejpam-1528	230	2	1	1	NUM
ejpam-1528	230	3	)	)	PUNCT
ejpam-1528	230	4	finally	finally	ADV
ejpam-1528	230	5	,	,	PUNCT
ejpam-1528	230	6	let	let	VERB
ejpam-1528	230	7	a	a	DET
ejpam-1528	230	8	=	=	PUNCT
ejpam-1528	230	9	x+	x+	ADJ
ejpam-1528	230	10	y	y	NOUN
ejpam-1528	230	11	with	with	ADP
ejpam-1528	230	12	x	x	PROPN
ejpam-1528	230	13	∈	∈	PROPN
ejpam-1528	230	14	{	{	PUNCT
ejpam-1528	230	15	a}′′	a}′′	NUM
ejpam-1528	230	16	,	,	PUNCT
ejpam-1528	230	17	x	x	ADJ
ejpam-1528	230	18	#	#	NOUN
ejpam-1528	230	19	exists	exist	VERB
ejpam-1528	230	20	,	,	PUNCT
ejpam-1528	230	21	x	x	X
ejpam-1528	230	22	y	y	NOUN
ejpam-1528	230	23	=	=	SYM
ejpam-1528	230	24	0	0	NUM
ejpam-1528	230	25	and	and	CCONJ
ejpam-1528	230	26	σ(y	σ(y	NOUN
ejpam-1528	230	27	)	)	PUNCT
ejpam-1528	230	28	=	=	PUNCT
ejpam-1528	230	29	{	{	PUNCT
ejpam-1528	230	30	0	0	NUM
ejpam-1528	230	31	}	}	PUNCT
ejpam-1528	230	32	.	.	PUNCT
ejpam-1528	231	1	by	by	ADP
ejpam-1528	231	2	properties	property	NOUN
ejpam-1528	231	3	of	of	ADP
ejpam-1528	231	4	the	the	DET
ejpam-1528	231	5	group	group	NOUN
ejpam-1528	231	6	inverse	inverse	NOUN
ejpam-1528	231	7	,	,	PUNCT
ejpam-1528	231	8	x	x	NOUN
ejpam-1528	231	9	#	#	NOUN
ejpam-1528	231	10	∈	∈	NOUN
ejpam-1528	231	11	{	{	PUNCT
ejpam-1528	231	12	x}′′⇒	x}′′⇒	NOUN
ejpam-1528	231	13	x	x	X
ejpam-1528	231	14	x	x	SYM
ejpam-1528	231	15	#	#	NOUN
ejpam-1528	231	16	∈	∈	NOUN
ejpam-1528	231	17	{	{	PUNCT
ejpam-1528	231	18	a}′′.	a}′′.	NOUN
ejpam-1528	231	19	pose	pose	VERB
ejpam-1528	231	20	m	m	VERB
ejpam-1528	231	21	=	=	PUNCT
ejpam-1528	231	22	x	x	PUNCT
ejpam-1528	231	23	x	x	X
ejpam-1528	231	24	#	#	NOUN
ejpam-1528	231	25	.	.	PUNCT
ejpam-1528	232	1	since	since	SCONJ
ejpam-1528	232	2	x	x	X
ejpam-1528	232	3	=	=	PUNCT
ejpam-1528	232	4	x	x	PUNCT
ejpam-1528	232	5	x	x	X
ejpam-1528	232	6	#	#	NOUN
ejpam-1528	232	7	x	x	X
ejpam-1528	232	8	=	=	PUNCT
ejpam-1528	232	9	x	x	X
ejpam-1528	232	10	x#a	x#a	NOUN
ejpam-1528	232	11	=	=	PUNCT
ejpam-1528	232	12	ax	ax	NOUN
ejpam-1528	232	13	x	x	NOUN
ejpam-1528	232	14	#	#	NOUN
ejpam-1528	232	15	,	,	PUNCT
ejpam-1528	232	16	m	m	VERB
ejpam-1528	232	17	≤h	≤h	NOUN
ejpam-1528	232	18	a	a	DET
ejpam-1528	232	19	and	and	CCONJ
ejpam-1528	232	20	m	m	PROPN
ejpam-1528	232	21	∈	∈	PROPN
ejpam-1528	232	22	σ2(a	σ2(a	PROPN
ejpam-1528	232	23	)	)	PUNCT
ejpam-1528	232	24	.	.	PUNCT
ejpam-1528	233	1	let	let	VERB
ejpam-1528	233	2	e	e	PRON
ejpam-1528	233	3	∈	∈	PROPN
ejpam-1528	233	4	σ2(a	σ2(a	PROPN
ejpam-1528	233	5	)	)	PUNCT
ejpam-1528	233	6	.	.	PUNCT
ejpam-1528	234	1	then	then	ADV
ejpam-1528	234	2	e	e	X
ejpam-1528	234	3	=	=	PUNCT
ejpam-1528	234	4	a−eae	a−eae	ADV
ejpam-1528	234	5	,	,	PUNCT
ejpam-1528	234	6	and	and	CCONJ
ejpam-1528	234	7	e	e	NOUN
ejpam-1528	234	8	is	be	AUX
ejpam-1528	234	9	in	in	ADP
ejpam-1528	234	10	the	the	DET
ejpam-1528	234	11	bicommutant	bicommutant	NOUN
ejpam-1528	234	12	of	of	ADP
ejpam-1528	234	13	y	y	PROPN
ejpam-1528	234	14	=	=	SYM
ejpam-1528	234	15	a−	a−	PROPN
ejpam-1528	234	16	x	x	X
ejpam-1528	234	17	.	.	PUNCT
ejpam-1528	235	1	then	then	ADV
ejpam-1528	235	2	e−	e−	NUM
ejpam-1528	235	3	em	em	PRON
ejpam-1528	236	1	=	=	PUNCT
ejpam-1528	236	2	e(1−	e(1−	PROPN
ejpam-1528	236	3	x	x	SYM
ejpam-1528	236	4	x	x	NOUN
ejpam-1528	236	5	#	#	NOUN
ejpam-1528	236	6	)	)	PUNCT
ejpam-1528	236	7	=	=	SYM
ejpam-1528	237	1	ea−ea(1−	ea−ea(1−	PROPN
ejpam-1528	237	2	x	x	PUNCT
ejpam-1528	237	3	x	x	X
ejpam-1528	237	4	#	#	NOUN
ejpam-1528	237	5	)	)	PUNCT
ejpam-1528	237	6	=	=	PUNCT
ejpam-1528	237	7	ea−e(x	ea−e(x	PROPN
ejpam-1528	238	1	+	+	CCONJ
ejpam-1528	238	2	y)(1−	y)(1−	PROPN
ejpam-1528	238	3	x	x	SYM
ejpam-1528	238	4	x	x	NOUN
ejpam-1528	238	5	#	#	NOUN
ejpam-1528	238	6	)	)	PUNCT
ejpam-1528	238	7	=	=	SYM
ejpam-1528	238	8	ea−e	ea−e	NOUN
ejpam-1528	238	9	y	y	PROPN
ejpam-1528	238	10	and	and	CCONJ
ejpam-1528	238	11	e−	e−	NUM
ejpam-1528	238	12	em	em	PROPN
ejpam-1528	238	13	∈	∈	PROPN
ejpam-1528	238	14	σ2(y	σ2(y	ADJ
ejpam-1528	238	15	)	)	PUNCT
ejpam-1528	238	16	.	.	PUNCT
ejpam-1528	239	1	by	by	ADP
ejpam-1528	239	2	hypothesis	hypothesis	NOUN
ejpam-1528	239	3	,	,	PUNCT
ejpam-1528	239	4	e−	e−	PROPN
ejpam-1528	239	5	em	em	PRON
ejpam-1528	239	6	=	=	PUNCT
ejpam-1528	239	7	0	0	PUNCT
ejpam-1528	239	8	and	and	CCONJ
ejpam-1528	239	9	e	e	X
ejpam-1528	239	10	≤	≤	NUM
ejpam-1528	239	11	m	m	VERB
ejpam-1528	239	12	,	,	PUNCT
ejpam-1528	239	13	m	m	VERB
ejpam-1528	239	14	is	be	AUX
ejpam-1528	239	15	the	the	DET
ejpam-1528	239	16	greatest	great	ADJ
ejpam-1528	239	17	element	element	NOUN
ejpam-1528	239	18	of	of	ADP
ejpam-1528	239	19	σ2(a	σ2(a	PROPN
ejpam-1528	239	20	)	)	PUNCT
ejpam-1528	239	21	and	and	CCONJ
ejpam-1528	239	22	a	a	PRON
ejpam-1528	239	23	is	be	AUX
ejpam-1528	239	24	naturally	naturally	ADV
ejpam-1528	239	25	invertible	invertible	ADJ
ejpam-1528	239	26	with	with	ADP
ejpam-1528	239	27	inverse	inverse	NOUN
ejpam-1528	239	28	a−x	a−x	NOUN
ejpam-1528	239	29	x	x	SYM
ejpam-1528	239	30	#	#	NOUN
ejpam-1528	239	31	.	.	PUNCT
ejpam-1528	240	1	the	the	DET
ejpam-1528	240	2	unique	unique	ADJ
ejpam-1528	240	3	decomposition	decomposition	NOUN
ejpam-1528	240	4	a	a	DET
ejpam-1528	240	5	=	=	SYM
ejpam-1528	240	6	x	x	SYM
ejpam-1528	240	7	+	+	CCONJ
ejpam-1528	240	8	y	y	NOUN
ejpam-1528	240	9	=	=	PRON
ejpam-1528	240	10	am	be	AUX
ejpam-1528	240	11	+	+	X
ejpam-1528	240	12	(	(	PUNCT
ejpam-1528	240	13	a	a	DET
ejpam-1528	240	14	−	−	NOUN
ejpam-1528	240	15	am	am	NOUN
ejpam-1528	240	16	)	)	PUNCT
ejpam-1528	240	17	=	=	PUNCT
ejpam-1528	240	18	aba	aba	PROPN
ejpam-1528	240	19	+	+	CCONJ
ejpam-1528	240	20	(	(	PUNCT
ejpam-1528	240	21	a	a	DET
ejpam-1528	240	22	−	−	PROPN
ejpam-1528	240	23	aba	aba	PROPN
ejpam-1528	240	24	)	)	PUNCT
ejpam-1528	240	25	as	as	ADP
ejpam-1528	240	26	in	in	ADP
ejpam-1528	240	27	the	the	DET
ejpam-1528	240	28	previous	previous	ADJ
ejpam-1528	240	29	theorem	theorem	NOUN
ejpam-1528	240	30	will	will	AUX
ejpam-1528	240	31	be	be	AUX
ejpam-1528	240	32	called	call	VERB
ejpam-1528	240	33	the	the	DET
ejpam-1528	240	34	natural	natural	ADJ
ejpam-1528	240	35	core	core	NOUN
ejpam-1528	240	36	decomposition	decomposition	NOUN
ejpam-1528	240	37	of	of	ADP
ejpam-1528	240	38	a.	a.	NOUN
ejpam-1528	240	39	4.3	4.3	NUM
ejpam-1528	240	40	.	.	PUNCT
ejpam-1528	241	1	link	link	VERB
ejpam-1528	241	2	with	with	ADP
ejpam-1528	241	3	the	the	DET
ejpam-1528	241	4	koliha	koliha	VERB
ejpam-1528	241	5	-	-	PUNCT
ejpam-1528	241	6	drazin	drazin	NOUN
ejpam-1528	241	7	inverse	inverse	NOUN
ejpam-1528	241	8	we	we	PRON
ejpam-1528	241	9	recall	recall	VERB
ejpam-1528	241	10	the	the	DET
ejpam-1528	241	11	following	follow	VERB
ejpam-1528	241	12	definitions	definition	NOUN
ejpam-1528	241	13	of	of	ADP
ejpam-1528	241	14	quasinilpotency	quasinilpotency	NOUN
ejpam-1528	241	15	and	and	CCONJ
ejpam-1528	241	16	quasipolarity	quasipolarity	NOUN
ejpam-1528	241	17	in	in	ADP
ejpam-1528	241	18	unital	unital	ADJ
ejpam-1528	241	19	rings	ring	NOUN
ejpam-1528	241	20	due	due	ADP
ejpam-1528	241	21	to	to	ADP
ejpam-1528	241	22	r.	r.	PROPN
ejpam-1528	241	23	harte	harte	PROPN
ejpam-1528	242	1	[	[	X
ejpam-1528	242	2	10	10	NUM
ejpam-1528	242	3	]	]	PUNCT
ejpam-1528	242	4	.	.	PUNCT
ejpam-1528	243	1	definition	definition	NOUN
ejpam-1528	243	2	3	3	NUM
ejpam-1528	243	3	.	.	PUNCT
ejpam-1528	244	1	an	an	DET
ejpam-1528	244	2	element	element	NOUN
ejpam-1528	244	3	q	q	NOUN
ejpam-1528	244	4	of	of	ADP
ejpam-1528	244	5	a	a	DET
ejpam-1528	244	6	unital	unital	ADJ
ejpam-1528	244	7	ring	ring	NOUN
ejpam-1528	244	8	r	r	NOUN
ejpam-1528	244	9	is	be	AUX
ejpam-1528	244	10	quasinilpotent	quasinilpotent	NOUN
ejpam-1528	244	11	if	if	SCONJ
ejpam-1528	244	12	∀x	∀x	X
ejpam-1528	244	13	∈	∈	PROPN
ejpam-1528	244	14	{	{	PUNCT
ejpam-1528	244	15	q}′	q}′	NOUN
ejpam-1528	244	16	,	,	PUNCT
ejpam-1528	244	17	1	1	NUM
ejpam-1528	244	18	+	+	NUM
ejpam-1528	244	19	xq	xq	PROPN
ejpam-1528	244	20	∈	∈	PROPN
ejpam-1528	244	21	r−1	r−1	PROPN
ejpam-1528	244	22	,	,	PUNCT
ejpam-1528	244	23	and	and	CCONJ
ejpam-1528	244	24	quasi	quasi	ADJ
ejpam-1528	244	25	-	-	NOUN
ejpam-1528	244	26	quasinilpotent	quasinilpotent	NOUN
ejpam-1528	244	27	if	if	SCONJ
ejpam-1528	244	28	∀x	∀x	X
ejpam-1528	244	29	∈	∈	PROPN
ejpam-1528	244	30	{	{	PUNCT
ejpam-1528	244	31	q}′′	q}′′	NUM
ejpam-1528	244	32	,	,	PUNCT
ejpam-1528	244	33	1	1	NUM
ejpam-1528	244	34	+	+	NUM
ejpam-1528	244	35	xq	xq	PROPN
ejpam-1528	244	36	∈	∈	PROPN
ejpam-1528	244	37	r−1	r−1	PROPN
ejpam-1528	244	38	note	note	VERB
ejpam-1528	244	39	that	that	SCONJ
ejpam-1528	244	40	quasi	quasi	ADJ
ejpam-1528	244	41	-	-	ADJ
ejpam-1528	244	42	quasinilpotent	quasinilpotent	ADJ
ejpam-1528	244	43	elements	element	NOUN
ejpam-1528	244	44	need	need	AUX
ejpam-1528	244	45	not	not	PART
ejpam-1528	244	46	be	be	AUX
ejpam-1528	244	47	quasinilpotent	quasinilpotent	ADJ
ejpam-1528	244	48	in	in	ADP
ejpam-1528	244	49	general	general	ADJ
ejpam-1528	244	50	.	.	PUNCT
ejpam-1528	245	1	the	the	DET
ejpam-1528	245	2	two	two	NUM
ejpam-1528	245	3	notions	notion	NOUN
ejpam-1528	245	4	however	however	ADV
ejpam-1528	245	5	coincide	coincide	VERB
ejpam-1528	245	6	for	for	ADP
ejpam-1528	245	7	banach	banach	NOUN
ejpam-1528	245	8	algebras	algebra	NOUN
ejpam-1528	245	9	.	.	PUNCT
ejpam-1528	246	1	definition	definition	NOUN
ejpam-1528	246	2	4	4	NUM
ejpam-1528	246	3	.	.	PUNCT
ejpam-1528	247	1	an	an	DET
ejpam-1528	247	2	element	element	NOUN
ejpam-1528	247	3	a	a	PRON
ejpam-1528	247	4	of	of	ADP
ejpam-1528	247	5	a	a	DET
ejpam-1528	247	6	unital	unital	ADJ
ejpam-1528	247	7	ring	ring	NOUN
ejpam-1528	247	8	r	r	NOUN
ejpam-1528	247	9	is	be	AUX
ejpam-1528	247	10	quasipolar	quasipolar	ADJ
ejpam-1528	247	11	(	(	PUNCT
ejpam-1528	247	12	resp	resp	NOUN
ejpam-1528	247	13	.	.	PUNCT
ejpam-1528	248	1	quasi	quasi	ADJ
ejpam-1528	248	2	-	-	ADJ
ejpam-1528	248	3	quasipolar	quasipolar	ADJ
ejpam-1528	248	4	)	)	PUNCT
ejpam-1528	248	5	if	if	SCONJ
ejpam-1528	248	6	there	there	PRON
ejpam-1528	248	7	exists	exist	VERB
ejpam-1528	248	8	a	a	DET
ejpam-1528	248	9	idempotent	idempotent	NOUN
ejpam-1528	248	10	(	(	PUNCT
ejpam-1528	248	11	called	call	VERB
ejpam-1528	248	12	spectral	spectral	ADJ
ejpam-1528	248	13	idempotent	idempotent	NOUN
ejpam-1528	248	14	)	)	PUNCT
ejpam-1528	248	15	p	p	NOUN
ejpam-1528	248	16	in	in	ADP
ejpam-1528	248	17	{	{	PUNCT
ejpam-1528	248	18	a}′′	a}′′	NUM
ejpam-1528	248	19	such	such	ADJ
ejpam-1528	248	20	that	that	SCONJ
ejpam-1528	248	21	ap	ap	PROPN
ejpam-1528	248	22	is	be	AUX
ejpam-1528	248	23	quasinilpotent	quasinilpotent	NOUN
ejpam-1528	248	24	(	(	PUNCT
ejpam-1528	248	25	resp	resp	NOUN
ejpam-1528	248	26	.	.	PUNCT
ejpam-1528	249	1	quasi	quasi	ADJ
ejpam-1528	249	2	-	-	NOUN
ejpam-1528	249	3	quasinilpotent	quasinilpotent	NOUN
ejpam-1528	249	4	)	)	PUNCT
ejpam-1528	249	5	and	and	CCONJ
ejpam-1528	249	6	a+	a+	PUNCT
ejpam-1528	249	7	p	p	PROPN
ejpam-1528	249	8	∈	∈	PROPN
ejpam-1528	249	9	r−1	r−1	PROPN
ejpam-1528	249	10	.	.	PUNCT
ejpam-1528	250	1	x.	x.	PROPN
ejpam-1528	250	2	mary	mary	PROPN
ejpam-1528	250	3	/	/	SYM
ejpam-1528	250	4	eur	eur	PROPN
ejpam-1528	250	5	.	.	PUNCT
ejpam-1528	251	1	j.	j.	PROPN
ejpam-1528	251	2	pure	pure	PROPN
ejpam-1528	251	3	appl	appl	PROPN
ejpam-1528	251	4	.	.	PROPN
ejpam-1528	251	5	math	math	PROPN
ejpam-1528	251	6	,	,	PUNCT
ejpam-1528	251	7	6	6	NUM
ejpam-1528	251	8	(	(	PUNCT
ejpam-1528	251	9	2013	2013	NUM
ejpam-1528	251	10	)	)	PUNCT
ejpam-1528	251	11	,	,	PUNCT
ejpam-1528	251	12	413	413	NUM
ejpam-1528	251	13	-	-	SYM
ejpam-1528	251	14	427	427	NUM
ejpam-1528	251	15	421	421	NUM
ejpam-1528	251	16	it	it	PRON
ejpam-1528	251	17	was	be	AUX
ejpam-1528	251	18	remarked	remark	VERB
ejpam-1528	251	19	in	in	ADP
ejpam-1528	251	20	[	[	X
ejpam-1528	251	21	17	17	NUM
ejpam-1528	251	22	]	]	PUNCT
ejpam-1528	251	23	that	that	SCONJ
ejpam-1528	251	24	the	the	DET
ejpam-1528	251	25	last	last	ADJ
ejpam-1528	251	26	condition	condition	NOUN
ejpam-1528	251	27	can	can	AUX
ejpam-1528	251	28	be	be	AUX
ejpam-1528	251	29	replaced	replace	VERB
ejpam-1528	251	30	by	by	ADP
ejpam-1528	251	31	the	the	DET
ejpam-1528	251	32	following	follow	VERB
ejpam-1528	251	33	one	one	NUM
ejpam-1528	251	34	1	1	NUM
ejpam-1528	251	35	−	−	PROPN
ejpam-1528	251	36	p	p	NOUN
ejpam-1528	251	37	≤h	≤h	NOUN
ejpam-1528	251	38	a.	a.	NOUN
ejpam-1528	252	1	this	this	PRON
ejpam-1528	252	2	is	be	AUX
ejpam-1528	252	3	the	the	DET
ejpam-1528	252	4	content	content	NOUN
ejpam-1528	252	5	of	of	ADP
ejpam-1528	252	6	lemma	lemma	PROPN
ejpam-1528	252	7	5	5	NUM
ejpam-1528	252	8	.	.	PUNCT
ejpam-1528	253	1	it	it	PRON
ejpam-1528	253	2	was	be	AUX
ejpam-1528	253	3	proved	prove	VERB
ejpam-1528	253	4	by	by	ADP
ejpam-1528	253	5	j.	j.	PROPN
ejpam-1528	253	6	koliha	koliha	PROPN
ejpam-1528	253	7	and	and	CCONJ
ejpam-1528	253	8	p.	p.	PROPN
ejpam-1528	253	9	patricio	patricio	PROPN
ejpam-1528	253	10	(	(	PUNCT
ejpam-1528	253	11	theorem	theorem	VERB
ejpam-1528	253	12	4.2	4.2	NUM
ejpam-1528	253	13	in	in	ADP
ejpam-1528	253	14	[	[	X
ejpam-1528	253	15	17	17	NUM
ejpam-1528	253	16	]	]	SYM
ejpam-1528	253	17	)	)	PUNCT
ejpam-1528	253	18	that	that	SCONJ
ejpam-1528	253	19	quasipolar	quasipolar	ADJ
ejpam-1528	253	20	elements	element	NOUN
ejpam-1528	253	21	are	be	AUX
ejpam-1528	253	22	exactly	exactly	ADV
ejpam-1528	253	23	the	the	DET
ejpam-1528	253	24	generalized	generalized	ADJ
ejpam-1528	253	25	drazin	drazin	NOUN
ejpam-1528	253	26	invertible	invertible	ADJ
ejpam-1528	253	27	elements	element	NOUN
ejpam-1528	253	28	(	(	PUNCT
ejpam-1528	253	29	also	also	ADV
ejpam-1528	253	30	called	call	VERB
ejpam-1528	253	31	koliha	koliha	ADJ
ejpam-1528	253	32	-	-	PUNCT
ejpam-1528	253	33	drazin	drazin	PROPN
ejpam-1528	253	34	invertible	invertible	ADJ
ejpam-1528	253	35	elements	element	NOUN
ejpam-1528	253	36	):	):	PUNCT
ejpam-1528	253	37	definition	definition	NOUN
ejpam-1528	253	38	5	5	NUM
ejpam-1528	253	39	.	.	PUNCT
ejpam-1528	254	1	an	an	DET
ejpam-1528	254	2	element	element	NOUN
ejpam-1528	254	3	a	a	PRON
ejpam-1528	254	4	of	of	ADP
ejpam-1528	254	5	a	a	DET
ejpam-1528	254	6	unital	unital	ADJ
ejpam-1528	254	7	ring	ring	NOUN
ejpam-1528	254	8	r	r	NOUN
ejpam-1528	254	9	is	be	AUX
ejpam-1528	254	10	generalized	generalize	VERB
ejpam-1528	254	11	drazin	drazin	PROPN
ejpam-1528	254	12	invertible	invertible	ADJ
ejpam-1528	254	13	(	(	PUNCT
ejpam-1528	254	14	resp	resp	NOUN
ejpam-1528	254	15	.	.	PUNCT
ejpam-1528	255	1	quasigeneralized	quasigeneralize	VERB
ejpam-1528	255	2	drazin	drazin	PROPN
ejpam-1528	255	3	invertible	invertible	ADJ
ejpam-1528	255	4	)	)	PUNCT
ejpam-1528	255	5	if	if	SCONJ
ejpam-1528	255	6	there	there	PRON
ejpam-1528	255	7	exists	exist	VERB
ejpam-1528	255	8	b	b	PROPN
ejpam-1528	255	9	in	in	ADP
ejpam-1528	255	10	{	{	PUNCT
ejpam-1528	255	11	a}′′	a}′′	NUM
ejpam-1528	255	12	such	such	ADJ
ejpam-1528	255	13	that	that	PRON
ejpam-1528	255	14	bab	bab	PROPN
ejpam-1528	255	15	=	=	SYM
ejpam-1528	255	16	b	b	PROPN
ejpam-1528	255	17	and	and	CCONJ
ejpam-1528	255	18	a2	a2	PROPN
ejpam-1528	255	19	b	b	PROPN
ejpam-1528	255	20	−	−	PROPN
ejpam-1528	255	21	a	a	PRON
ejpam-1528	255	22	is	be	AUX
ejpam-1528	255	23	quasinilpotent	quasinilpotent	NOUN
ejpam-1528	255	24	(	(	PUNCT
ejpam-1528	255	25	resp	resp	NOUN
ejpam-1528	255	26	.	.	PUNCT
ejpam-1528	256	1	quasi	quasi	ADJ
ejpam-1528	256	2	-	-	NOUN
ejpam-1528	256	3	quasinilpotent	quasinilpotent	ADJ
ejpam-1528	256	4	)	)	PUNCT
ejpam-1528	256	5	.	.	PUNCT
ejpam-1528	257	1	theorem	theorem	VERB
ejpam-1528	257	2	7	7	NUM
ejpam-1528	257	3	.	.	PUNCT
ejpam-1528	258	1	an	an	DET
ejpam-1528	258	2	element	element	NOUN
ejpam-1528	258	3	a	a	PRON
ejpam-1528	258	4	of	of	ADP
ejpam-1528	258	5	a	a	DET
ejpam-1528	258	6	unital	unital	ADJ
ejpam-1528	258	7	ring	ring	NOUN
ejpam-1528	258	8	r	r	NOUN
ejpam-1528	258	9	is	be	AUX
ejpam-1528	258	10	generalized	generalize	VERB
ejpam-1528	258	11	drazin	drazin	PROPN
ejpam-1528	258	12	invertible	invertible	ADJ
ejpam-1528	258	13	(	(	PUNCT
ejpam-1528	258	14	resp	resp	NOUN
ejpam-1528	258	15	.	.	PUNCT
ejpam-1528	259	1	quasigeneralized	quasigeneralize	VERB
ejpam-1528	259	2	drazin	drazin	PROPN
ejpam-1528	259	3	invertible	invertible	ADJ
ejpam-1528	259	4	)	)	PUNCT
ejpam-1528	260	1	if	if	SCONJ
ejpam-1528	260	2	and	and	CCONJ
ejpam-1528	260	3	only	only	ADV
ejpam-1528	260	4	if	if	SCONJ
ejpam-1528	260	5	it	it	PRON
ejpam-1528	260	6	is	be	AUX
ejpam-1528	260	7	quasipolar	quasipolar	ADJ
ejpam-1528	260	8	(	(	PUNCT
ejpam-1528	260	9	resp	resp	NOUN
ejpam-1528	260	10	.	.	PUNCT
ejpam-1528	261	1	quasi	quasi	ADJ
ejpam-1528	261	2	-	-	ADJ
ejpam-1528	261	3	quasipolar	quasipolar	ADJ
ejpam-1528	261	4	)	)	PUNCT
ejpam-1528	261	5	.	.	PUNCT
ejpam-1528	262	1	in	in	ADP
ejpam-1528	262	2	this	this	DET
ejpam-1528	262	3	case	case	NOUN
ejpam-1528	262	4	b	b	X
ejpam-1528	262	5	=	=	SYM
ejpam-1528	262	6	(	(	PUNCT
ejpam-1528	262	7	a+	a+	PUNCT
ejpam-1528	262	8	p)−1(1−	p)−1(1−	NUM
ejpam-1528	262	9	p	p	NOUN
ejpam-1528	262	10	)	)	PUNCT
ejpam-1528	262	11	.	.	PUNCT
ejpam-1528	263	1	next	next	ADJ
ejpam-1528	263	2	theorem	theorem	NOUN
ejpam-1528	263	3	proves	prove	VERB
ejpam-1528	263	4	that	that	SCONJ
ejpam-1528	263	5	the	the	DET
ejpam-1528	263	6	natural	natural	ADJ
ejpam-1528	263	7	inverse	inverse	NOUN
ejpam-1528	263	8	generalizes	generalize	VERB
ejpam-1528	263	9	not	not	PART
ejpam-1528	263	10	only	only	ADV
ejpam-1528	263	11	the	the	DET
ejpam-1528	263	12	drazin	drazin	PROPN
ejpam-1528	263	13	inverse	inverse	NOUN
ejpam-1528	263	14	,	,	PUNCT
ejpam-1528	263	15	but	but	CCONJ
ejpam-1528	263	16	also	also	ADV
ejpam-1528	263	17	the	the	DET
ejpam-1528	263	18	koliha	koliha	VERB
ejpam-1528	263	19	-	-	PUNCT
ejpam-1528	263	20	drazin	drazin	NOUN
ejpam-1528	263	21	inverse	inverse	NOUN
ejpam-1528	263	22	in	in	ADP
ejpam-1528	263	23	a	a	DET
ejpam-1528	263	24	ring	ring	NOUN
ejpam-1528	263	25	:	:	PUNCT
ejpam-1528	263	26	theorem	theorem	NOUN
ejpam-1528	263	27	8	8	NUM
ejpam-1528	263	28	.	.	PUNCT
ejpam-1528	264	1	let	let	VERB
ejpam-1528	264	2	r	r	PRON
ejpam-1528	264	3	be	be	AUX
ejpam-1528	264	4	a	a	DET
ejpam-1528	264	5	unital	unital	ADJ
ejpam-1528	264	6	ring	ring	NOUN
ejpam-1528	264	7	,	,	PUNCT
ejpam-1528	264	8	and	and	CCONJ
ejpam-1528	264	9	a	a	DET
ejpam-1528	264	10	∈	∈	NOUN
ejpam-1528	264	11	r	r	NOUN
ejpam-1528	264	12	be	be	VERB
ejpam-1528	264	13	quasi	quasi	ADJ
ejpam-1528	264	14	-	-	ADJ
ejpam-1528	264	15	quasipolar	quasipolar	ADJ
ejpam-1528	264	16	with	with	ADP
ejpam-1528	264	17	spectral	spectral	ADJ
ejpam-1528	264	18	idempotent	idempotent	NOUN
ejpam-1528	264	19	p	p	NOUN
ejpam-1528	264	20	and	and	CCONJ
ejpam-1528	264	21	quasi	quasi	ADJ
ejpam-1528	264	22	-	-	ADJ
ejpam-1528	264	23	koliha	koliha	ADJ
ejpam-1528	264	24	-	-	PUNCT
ejpam-1528	264	25	drazin	drazin	PROPN
ejpam-1528	264	26	inverse	inverse	PROPN
ejpam-1528	264	27	b.	b.	PROPN
ejpam-1528	265	1	then	then	ADV
ejpam-1528	265	2	a	a	PRON
ejpam-1528	265	3	is	be	AUX
ejpam-1528	265	4	naturally	naturally	ADV
ejpam-1528	265	5	invertible	invertible	ADJ
ejpam-1528	265	6	,	,	PUNCT
ejpam-1528	265	7	m	m	VERB
ejpam-1528	265	8	=	=	SYM
ejpam-1528	265	9	1−	1−	NUM
ejpam-1528	265	10	p	p	NOUN
ejpam-1528	265	11	is	be	AUX
ejpam-1528	265	12	the	the	DET
ejpam-1528	265	13	greatest	great	ADJ
ejpam-1528	265	14	element	element	NOUN
ejpam-1528	265	15	of	of	ADP
ejpam-1528	265	16	σ2(a	σ2(a	PROPN
ejpam-1528	265	17	)	)	PUNCT
ejpam-1528	265	18	and	and	CCONJ
ejpam-1528	265	19	the	the	DET
ejpam-1528	265	20	quasi	quasi	ADJ
ejpam-1528	265	21	-	-	ADJ
ejpam-1528	265	22	generalized	generalized	ADJ
ejpam-1528	265	23	drazin	drazin	PROPN
ejpam-1528	265	24	inverse	inverse	PROPN
ejpam-1528	265	25	b	b	PROPN
ejpam-1528	265	26	is	be	AUX
ejpam-1528	265	27	equal	equal	ADJ
ejpam-1528	265	28	to	to	ADP
ejpam-1528	265	29	a−m	a−m	NOUN
ejpam-1528	265	30	,	,	PUNCT
ejpam-1528	265	31	the	the	DET
ejpam-1528	265	32	natural	natural	ADJ
ejpam-1528	265	33	generalized	generalized	ADJ
ejpam-1528	265	34	inverse	inverse	NOUN
ejpam-1528	265	35	of	of	ADP
ejpam-1528	265	36	a.	a.	NOUN
ejpam-1528	265	37	proof	proof	NOUN
ejpam-1528	265	38	.	.	PUNCT
ejpam-1528	266	1	assume	assume	VERB
ejpam-1528	266	2	a	a	PRON
ejpam-1528	266	3	is	be	AUX
ejpam-1528	266	4	quasi	quasi	ADJ
ejpam-1528	266	5	-	-	ADJ
ejpam-1528	266	6	quasipolar	quasipolar	ADJ
ejpam-1528	266	7	in	in	ADP
ejpam-1528	266	8	the	the	DET
ejpam-1528	266	9	ring	ring	NOUN
ejpam-1528	266	10	sense	sense	NOUN
ejpam-1528	266	11	.	.	PUNCT
ejpam-1528	267	1	then	then	ADV
ejpam-1528	267	2	exists	exist	VERB
ejpam-1528	267	3	spectral	spectral	ADJ
ejpam-1528	267	4	idempotent	idempotent	NOUN
ejpam-1528	267	5	p	p	NOUN
ejpam-1528	267	6	in	in	ADP
ejpam-1528	267	7	{	{	PUNCT
ejpam-1528	267	8	a}′′	a}′′	NUM
ejpam-1528	267	9	such	such	ADJ
ejpam-1528	267	10	that	that	SCONJ
ejpam-1528	267	11	ap	ap	PROPN
ejpam-1528	267	12	is	be	AUX
ejpam-1528	267	13	quasi	quasi	ADJ
ejpam-1528	267	14	-	-	NOUN
ejpam-1528	267	15	quasinilpotent	quasinilpotent	ADJ
ejpam-1528	267	16	and	and	CCONJ
ejpam-1528	267	17	a+	a+	PUNCT
ejpam-1528	267	18	p	p	PROPN
ejpam-1528	267	19	∈	∈	PROPN
ejpam-1528	267	20	r−1	r−1	PROPN
ejpam-1528	267	21	.	.	PUNCT
ejpam-1528	268	1	by	by	ADP
ejpam-1528	268	2	lemma	lemma	PROPN
ejpam-1528	268	3	5	5	NUM
ejpam-1528	268	4	,	,	PUNCT
ejpam-1528	268	5	m	m	VERB
ejpam-1528	268	6	=	=	NOUN
ejpam-1528	268	7	1−	1−	NUM
ejpam-1528	268	8	p	p	NOUN
ejpam-1528	268	9	≤h	≤h	PROPN
ejpam-1528	268	10	a	a	PRON
ejpam-1528	268	11	,	,	PUNCT
ejpam-1528	268	12	hence	hence	ADV
ejpam-1528	268	13	it	it	PRON
ejpam-1528	268	14	is	be	AUX
ejpam-1528	268	15	in	in	ADP
ejpam-1528	268	16	σ2(a	σ2(a	NOUN
ejpam-1528	268	17	)	)	PUNCT
ejpam-1528	268	18	.	.	PUNCT
ejpam-1528	269	1	let	let	VERB
ejpam-1528	269	2	f	f	PROPN
ejpam-1528	269	3	∈	∈	PROPN
ejpam-1528	269	4	σ2(a	σ2(a	PROPN
ejpam-1528	269	5	)	)	PUNCT
ejpam-1528	269	6	.	.	PUNCT
ejpam-1528	270	1	then	then	ADV
ejpam-1528	270	2	exists	exist	VERB
ejpam-1528	270	3	x	x	X
ejpam-1528	270	4	∈	∈	PROPN
ejpam-1528	270	5	s	s	PROPN
ejpam-1528	270	6	,	,	PUNCT
ejpam-1528	270	7	f	f	PROPN
ejpam-1528	270	8	=	=	SYM
ejpam-1528	270	9	xa	xa	PROPN
ejpam-1528	270	10	.	.	PUNCT
ejpam-1528	271	1	by	by	ADP
ejpam-1528	271	2	quasi	quasi	NOUN
ejpam-1528	271	3	-	-	NOUN
ejpam-1528	271	4	quasinilpotency	quasinilpotency	NOUN
ejpam-1528	271	5	,	,	PUNCT
ejpam-1528	271	6	(	(	PUNCT
ejpam-1528	271	7	1−	1−	NUM
ejpam-1528	271	8	f	f	NOUN
ejpam-1528	271	9	p	p	NOUN
ejpam-1528	271	10	)	)	PUNCT
ejpam-1528	271	11	=	=	SYM
ejpam-1528	271	12	(	(	PUNCT
ejpam-1528	271	13	1−	1−	NUM
ejpam-1528	271	14	xap	xap	PROPN
ejpam-1528	271	15	)	)	PUNCT
ejpam-1528	271	16	∈	∈	PROPN
ejpam-1528	271	17	r−1	r−1	PROPN
ejpam-1528	271	18	.	.	PUNCT
ejpam-1528	272	1	but	but	CCONJ
ejpam-1528	272	2	by	by	ADP
ejpam-1528	272	3	commutativity	commutativity	NOUN
ejpam-1528	272	4	of	of	ADP
ejpam-1528	272	5	{	{	PUNCT
ejpam-1528	272	6	a}′′	a}′′	PROPN
ejpam-1528	272	7	and	and	CCONJ
ejpam-1528	272	8	the	the	DET
ejpam-1528	272	9	fact	fact	NOUN
ejpam-1528	272	10	that	that	SCONJ
ejpam-1528	272	11	f	f	X
ejpam-1528	272	12	,	,	PUNCT
ejpam-1528	272	13	p	p	PROPN
ejpam-1528	272	14	∈	∈	PROPN
ejpam-1528	272	15	e(s	e(s	PROPN
ejpam-1528	272	16	)	)	PUNCT
ejpam-1528	272	17	,	,	PUNCT
ejpam-1528	272	18	we	we	PRON
ejpam-1528	272	19	have	have	VERB
ejpam-1528	272	20	(	(	PUNCT
ejpam-1528	272	21	1−	1−	NUM
ejpam-1528	272	22	f	f	X
ejpam-1528	272	23	p)(1	p)(1	PROPN
ejpam-1528	273	1	+	+	CCONJ
ejpam-1528	273	2	f	f	PROPN
ejpam-1528	273	3	p	p	NOUN
ejpam-1528	273	4	)	)	PUNCT
ejpam-1528	273	5	=	=	SYM
ejpam-1528	274	1	1−	1−	NUM
ejpam-1528	274	2	f	f	X
ejpam-1528	275	1	p.	p.	NOUN
ejpam-1528	275	2	by	by	ADP
ejpam-1528	275	3	invertibility	invertibility	NOUN
ejpam-1528	275	4	,	,	PUNCT
ejpam-1528	275	5	1	1	NUM
ejpam-1528	275	6	+	+	NUM
ejpam-1528	275	7	f	f	X
ejpam-1528	275	8	p	p	NOUN
ejpam-1528	275	9	=	=	NOUN
ejpam-1528	275	10	1	1	NUM
ejpam-1528	276	1	hence	hence	ADV
ejpam-1528	276	2	f	f	X
ejpam-1528	276	3	p	p	X
ejpam-1528	276	4	=	=	NOUN
ejpam-1528	276	5	0	0	NUM
ejpam-1528	276	6	.	.	PUNCT
ejpam-1528	277	1	it	it	PRON
ejpam-1528	277	2	follows	follow	VERB
ejpam-1528	277	3	that	that	SCONJ
ejpam-1528	277	4	f	f	PROPN
ejpam-1528	277	5	m	m	NOUN
ejpam-1528	277	6	=	=	ADJ
ejpam-1528	277	7	f	f	X
ejpam-1528	277	8	(	(	PUNCT
ejpam-1528	277	9	1	1	NUM
ejpam-1528	277	10	−	−	PROPN
ejpam-1528	277	11	p	p	X
ejpam-1528	277	12	)	)	PUNCT
ejpam-1528	277	13	=	=	PUNCT
ejpam-1528	278	1	f	f	X
ejpam-1528	279	1	−	−	NOUN
ejpam-1528	279	2	f	f	X
ejpam-1528	280	1	p	p	X
ejpam-1528	280	2	=	=	PUNCT
ejpam-1528	280	3	f	f	PROPN
ejpam-1528	280	4	and	and	CCONJ
ejpam-1528	280	5	f	f	PROPN
ejpam-1528	280	6	≤	≤	PROPN
ejpam-1528	280	7	m	m	VERB
ejpam-1528	280	8	for	for	ADP
ejpam-1528	280	9	the	the	DET
ejpam-1528	280	10	natural	natural	ADJ
ejpam-1528	280	11	partial	partial	ADJ
ejpam-1528	280	12	order	order	NOUN
ejpam-1528	280	13	.	.	PUNCT
ejpam-1528	281	1	m	m	PROPN
ejpam-1528	281	2	is	be	AUX
ejpam-1528	281	3	the	the	DET
ejpam-1528	281	4	greatest	great	ADJ
ejpam-1528	281	5	element	element	NOUN
ejpam-1528	281	6	of	of	ADP
ejpam-1528	281	7	σ2(a	σ2(a	PROPN
ejpam-1528	281	8	)	)	PUNCT
ejpam-1528	281	9	.	.	PUNCT
ejpam-1528	282	1	now	now	ADV
ejpam-1528	282	2	the	the	DET
ejpam-1528	282	3	generalized	generalized	ADJ
ejpam-1528	282	4	drazin	drazin	PROPN
ejpam-1528	282	5	inverse	inverse	NOUN
ejpam-1528	282	6	of	of	ADP
ejpam-1528	282	7	a	a	DET
ejpam-1528	282	8	b	b	NOUN
ejpam-1528	282	9	=	=	SYM
ejpam-1528	282	10	(	(	PUNCT
ejpam-1528	282	11	a+	a+	PUNCT
ejpam-1528	282	12	p)−1(1−	p)−1(1−	NUM
ejpam-1528	282	13	p	p	NOUN
ejpam-1528	282	14	)	)	PUNCT
ejpam-1528	282	15	is	be	AUX
ejpam-1528	282	16	obviously	obviously	ADV
ejpam-1528	282	17	inh(1−p	inh(1−p	PROPN
ejpam-1528	282	18	)	)	PUNCT
ejpam-1528	282	19	and	and	CCONJ
ejpam-1528	282	20	is	be	AUX
ejpam-1528	282	21	an	an	DET
ejpam-1528	282	22	outer	outer	ADJ
ejpam-1528	282	23	inverse	inverse	NOUN
ejpam-1528	282	24	of	of	ADP
ejpam-1528	282	25	a	a	PRON
ejpam-1528	282	26	by	by	ADP
ejpam-1528	282	27	definition	definition	NOUN
ejpam-1528	282	28	.	.	PUNCT
ejpam-1528	283	1	by	by	ADP
ejpam-1528	283	2	unicity	unicity	NOUN
ejpam-1528	283	3	,	,	PUNCT
ejpam-1528	283	4	it	it	PRON
ejpam-1528	283	5	is	be	AUX
ejpam-1528	283	6	a−m	a−m	NOUN
ejpam-1528	283	7	.	.	PUNCT
ejpam-1528	284	1	if	if	SCONJ
ejpam-1528	284	2	we	we	PRON
ejpam-1528	284	3	require	require	VERB
ejpam-1528	284	4	the	the	DET
ejpam-1528	284	5	element	element	NOUN
ejpam-1528	284	6	a	a	PRON
ejpam-1528	284	7	to	to	PART
ejpam-1528	284	8	be	be	AUX
ejpam-1528	284	9	quasipolar	quasipolar	ADJ
ejpam-1528	284	10	instead	instead	ADV
ejpam-1528	284	11	of	of	ADP
ejpam-1528	284	12	quasi	quasi	ADJ
ejpam-1528	284	13	-	-	ADJ
ejpam-1528	284	14	quasipolar	quasipolar	ADJ
ejpam-1528	284	15	with	with	ADP
ejpam-1528	284	16	koliha	koliha	VERB
ejpam-1528	284	17	-	-	PUNCT
ejpam-1528	284	18	drazin	drazin	PROPN
ejpam-1528	284	19	inverse	inverse	PROPN
ejpam-1528	284	20	b	b	PROPN
ejpam-1528	284	21	,	,	PUNCT
ejpam-1528	284	22	then	then	ADV
ejpam-1528	284	23	the	the	DET
ejpam-1528	284	24	idempotent	idempotent	NOUN
ejpam-1528	284	25	m	m	VERB
ejpam-1528	284	26	=	=	SYM
ejpam-1528	284	27	1−	1−	NUM
ejpam-1528	284	28	p	p	NOUN
ejpam-1528	284	29	is	be	AUX
ejpam-1528	284	30	actually	actually	ADV
ejpam-1528	284	31	the	the	DET
ejpam-1528	284	32	greatest	great	ADJ
ejpam-1528	284	33	element	element	NOUN
ejpam-1528	284	34	σ1(a	σ1(a	NOUN
ejpam-1528	284	35	)	)	PUNCT
ejpam-1528	284	36	and	and	CCONJ
ejpam-1528	284	37	b	b	X
ejpam-1528	284	38	=	=	NOUN
ejpam-1528	284	39	a−m	a−m	NOUN
ejpam-1528	284	40	is	be	AUX
ejpam-1528	284	41	also	also	ADV
ejpam-1528	284	42	the	the	DET
ejpam-1528	284	43	1−natural	1−natural	ADJ
ejpam-1528	284	44	generalized	generalized	ADJ
ejpam-1528	284	45	inverse	inverse	NOUN
ejpam-1528	284	46	of	of	ADP
ejpam-1528	284	47	a.	a.	NOUN
ejpam-1528	284	48	5	5	NUM
ejpam-1528	284	49	.	.	PUNCT
ejpam-1528	285	1	the	the	DET
ejpam-1528	285	2	banach	banach	NOUN
ejpam-1528	285	3	algebra	algebra	NOUN
ejpam-1528	285	4	case	case	NOUN
ejpam-1528	285	5	in	in	ADP
ejpam-1528	285	6	this	this	DET
ejpam-1528	285	7	section	section	NOUN
ejpam-1528	285	8	,	,	PUNCT
ejpam-1528	285	9	a	a	DET
ejpam-1528	285	10	denotes	denote	NOUN
ejpam-1528	285	11	a	a	DET
ejpam-1528	285	12	unital	unital	ADJ
ejpam-1528	285	13	banach	banach	NOUN
ejpam-1528	285	14	algebra	algebra	NOUN
ejpam-1528	285	15	.	.	PUNCT
ejpam-1528	286	1	for	for	ADP
ejpam-1528	286	2	any	any	DET
ejpam-1528	286	3	a	a	DET
ejpam-1528	286	4	∈a	∈a	NOUN
ejpam-1528	286	5	,	,	PUNCT
ejpam-1528	286	6	we	we	PRON
ejpam-1528	286	7	denote	denote	VERB
ejpam-1528	286	8	its	its	PRON
ejpam-1528	286	9	spectrum	spectrum	NOUN
ejpam-1528	286	10	by	by	ADP
ejpam-1528	286	11	σ(a	σ(a	PROPN
ejpam-1528	286	12	)	)	PUNCT
ejpam-1528	286	13	and	and	CCONJ
ejpam-1528	286	14	its	its	PRON
ejpam-1528	286	15	spectral	spectral	ADJ
ejpam-1528	286	16	radius	radius	NOUN
ejpam-1528	286	17	by	by	ADP
ejpam-1528	286	18	r(a	r(a	PROPN
ejpam-1528	286	19	)	)	PUNCT
ejpam-1528	286	20	.	.	PUNCT
ejpam-1528	287	1	recall	recall	VERB
ejpam-1528	287	2	that	that	SCONJ
ejpam-1528	287	3	in	in	ADP
ejpam-1528	287	4	a	a	DET
ejpam-1528	287	5	banach	banach	NOUN
ejpam-1528	287	6	algebra	algebra	NOUN
ejpam-1528	287	7	,	,	PUNCT
ejpam-1528	287	8	an	an	DET
ejpam-1528	287	9	element	element	NOUN
ejpam-1528	287	10	is	be	AUX
ejpam-1528	287	11	quasinilpotent	quasinilpotent	ADJ
ejpam-1528	287	12	if	if	SCONJ
ejpam-1528	287	13	its	its	PRON
ejpam-1528	287	14	spectrum	spectrum	NOUN
ejpam-1528	287	15	reduces	reduce	VERB
ejpam-1528	287	16	to	to	ADP
ejpam-1528	287	17	0	0	NUM
ejpam-1528	287	18	,	,	PUNCT
ejpam-1528	287	19	or	or	CCONJ
ejpam-1528	287	20	equivalently	equivalently	ADV
ejpam-1528	287	21	if	if	SCONJ
ejpam-1528	287	22	its	its	PRON
ejpam-1528	287	23	spectral	spectral	ADJ
ejpam-1528	287	24	radius	radius	NOUN
ejpam-1528	287	25	is	be	AUX
ejpam-1528	287	26	0	0	NUM
ejpam-1528	287	27	,	,	PUNCT
ejpam-1528	287	28	and	and	CCONJ
ejpam-1528	287	29	quasipolar	quasipolar	ADJ
ejpam-1528	287	30	if	if	SCONJ
ejpam-1528	287	31	0	0	NUM
ejpam-1528	287	32	an	an	DET
ejpam-1528	287	33	isolated	isolated	ADJ
ejpam-1528	287	34	point	point	NOUN
ejpam-1528	287	35	of	of	ADP
ejpam-1528	287	36	the	the	DET
ejpam-1528	287	37	spectrum	spectrum	NOUN
ejpam-1528	287	38	.	.	PUNCT
ejpam-1528	288	1	it	it	PRON
ejpam-1528	288	2	is	be	AUX
ejpam-1528	288	3	known	know	VERB
ejpam-1528	288	4	[	[	PUNCT
ejpam-1528	288	5	10	10	NUM
ejpam-1528	288	6	]	]	PUNCT
ejpam-1528	288	7	that	that	SCONJ
ejpam-1528	288	8	these	these	DET
ejpam-1528	288	9	notions	notion	NOUN
ejpam-1528	288	10	coincide	coincide	VERB
ejpam-1528	288	11	with	with	ADP
ejpam-1528	288	12	their	their	PRON
ejpam-1528	288	13	ring	ring	NOUN
ejpam-1528	288	14	counterpart	counterpart	NOUN
ejpam-1528	288	15	,	,	PUNCT
ejpam-1528	288	16	and	and	CCONJ
ejpam-1528	288	17	also	also	ADV
ejpam-1528	288	18	with	with	ADP
ejpam-1528	288	19	the	the	DET
ejpam-1528	288	20	quasi	quasi	ADJ
ejpam-1528	288	21	-	-	ADJ
ejpam-1528	288	22	quasi	quasi	ADJ
ejpam-1528	288	23	notion	notion	NOUN
ejpam-1528	288	24	(	(	PUNCT
ejpam-1528	288	25	for	for	ADP
ejpam-1528	288	26	instance	instance	NOUN
ejpam-1528	288	27	,	,	PUNCT
ejpam-1528	288	28	σ(a	σ(a	PROPN
ejpam-1528	288	29	)	)	PUNCT
ejpam-1528	289	1	=	=	PRON
ejpam-1528	289	2	{	{	PUNCT
ejpam-1528	289	3	0c	0c	NOUN
ejpam-1528	289	4	}	}	PUNCT
ejpam-1528	289	5	if	if	SCONJ
ejpam-1528	289	6	and	and	CCONJ
ejpam-1528	289	7	only	only	ADV
ejpam-1528	289	8	if	if	SCONJ
ejpam-1528	289	9	a	a	PRON
ejpam-1528	289	10	is	be	AUX
ejpam-1528	289	11	quasinilpotent	quasinilpotent	NOUN
ejpam-1528	289	12	in	in	ADP
ejpam-1528	289	13	the	the	DET
ejpam-1528	289	14	ring	ring	NOUN
ejpam-1528	289	15	sense	sense	NOUN
ejpam-1528	289	16	if	if	SCONJ
ejpam-1528	289	17	and	and	CCONJ
ejpam-1528	289	18	only	only	ADV
ejpam-1528	289	19	if	if	SCONJ
ejpam-1528	289	20	a	a	PRON
ejpam-1528	289	21	is	be	AUX
ejpam-1528	289	22	quasi	quasi	ADJ
ejpam-1528	289	23	-	-	NOUN
ejpam-1528	289	24	quasinilpotent	quasinilpotent	ADJ
ejpam-1528	289	25	in	in	ADP
ejpam-1528	289	26	the	the	DET
ejpam-1528	289	27	ring	ring	NOUN
ejpam-1528	289	28	sense	sense	NOUN
ejpam-1528	289	29	)	)	PUNCT
ejpam-1528	289	30	.	.	PUNCT
ejpam-1528	290	1	corollary	corollary	ADJ
ejpam-1528	290	2	4	4	NUM
ejpam-1528	290	3	.	.	PUNCT
ejpam-1528	290	4	let	let	VERB
ejpam-1528	290	5	a	a	DET
ejpam-1528	290	6	∈	∈	PROPN
ejpam-1528	290	7	a	a	PRON
ejpam-1528	290	8	.	.	PUNCT
ejpam-1528	291	1	if	if	SCONJ
ejpam-1528	291	2	0	0	NUM
ejpam-1528	291	3	is	be	AUX
ejpam-1528	291	4	an	an	DET
ejpam-1528	291	5	isolated	isolated	ADJ
ejpam-1528	291	6	point	point	NOUN
ejpam-1528	291	7	of	of	ADP
ejpam-1528	291	8	the	the	DET
ejpam-1528	291	9	spectrum	spectrum	NOUN
ejpam-1528	291	10	of	of	ADP
ejpam-1528	291	11	a	a	PRON
ejpam-1528	291	12	,	,	PUNCT
ejpam-1528	291	13	then	then	ADV
ejpam-1528	291	14	a	a	PRON
ejpam-1528	291	15	is	be	AUX
ejpam-1528	291	16	naturally	naturally	ADV
ejpam-1528	291	17	invertible	invertible	ADJ
ejpam-1528	291	18	.	.	PUNCT
ejpam-1528	292	1	x.	x.	PROPN
ejpam-1528	292	2	mary	mary	PROPN
ejpam-1528	292	3	/	/	SYM
ejpam-1528	292	4	eur	eur	PROPN
ejpam-1528	292	5	.	.	PUNCT
ejpam-1528	293	1	j.	j.	PROPN
ejpam-1528	293	2	pure	pure	PROPN
ejpam-1528	293	3	appl	appl	PROPN
ejpam-1528	293	4	.	.	PROPN
ejpam-1528	293	5	math	math	PROPN
ejpam-1528	293	6	,	,	PUNCT
ejpam-1528	293	7	6	6	NUM
ejpam-1528	293	8	(	(	PUNCT
ejpam-1528	293	9	2013	2013	NUM
ejpam-1528	293	10	)	)	PUNCT
ejpam-1528	293	11	,	,	PUNCT
ejpam-1528	293	12	413	413	NUM
ejpam-1528	293	13	-	-	SYM
ejpam-1528	293	14	427	427	NUM
ejpam-1528	293	15	422	422	NUM
ejpam-1528	293	16	proof	proof	NOUN
ejpam-1528	293	17	.	.	PUNCT
ejpam-1528	294	1	if	if	SCONJ
ejpam-1528	294	2	0	0	NUM
ejpam-1528	294	3	is	be	AUX
ejpam-1528	294	4	an	an	DET
ejpam-1528	294	5	isolated	isolated	ADJ
ejpam-1528	294	6	point	point	NOUN
ejpam-1528	294	7	of	of	ADP
ejpam-1528	294	8	the	the	DET
ejpam-1528	294	9	spectrum	spectrum	NOUN
ejpam-1528	294	10	of	of	ADP
ejpam-1528	294	11	a	a	PRON
ejpam-1528	294	12	,	,	PUNCT
ejpam-1528	294	13	then	then	ADV
ejpam-1528	294	14	a	a	PRON
ejpam-1528	294	15	is	be	AUX
ejpam-1528	294	16	quasi	quasi	ADJ
ejpam-1528	294	17	-	-	ADJ
ejpam-1528	294	18	quasipolar	quasipolar	ADJ
ejpam-1528	294	19	in	in	ADP
ejpam-1528	294	20	the	the	DET
ejpam-1528	294	21	banach	banach	NOUN
ejpam-1528	294	22	sense	sense	NOUN
ejpam-1528	294	23	,	,	PUNCT
ejpam-1528	294	24	hence	hence	ADV
ejpam-1528	294	25	it	it	PRON
ejpam-1528	294	26	is	be	AUX
ejpam-1528	294	27	quasi	quasi	ADJ
ejpam-1528	294	28	-	-	ADJ
ejpam-1528	294	29	quasipolar	quasipolar	ADJ
ejpam-1528	294	30	in	in	ADP
ejpam-1528	294	31	the	the	DET
ejpam-1528	294	32	ring	ring	NOUN
ejpam-1528	294	33	sense	sense	NOUN
ejpam-1528	294	34	.	.	PUNCT
ejpam-1528	295	1	we	we	PRON
ejpam-1528	295	2	then	then	ADV
ejpam-1528	295	3	apply	apply	VERB
ejpam-1528	295	4	theorem	theorem	ADJ
ejpam-1528	295	5	8	8	NUM
ejpam-1528	295	6	.	.	PUNCT
ejpam-1528	296	1	we	we	PRON
ejpam-1528	296	2	now	now	ADV
ejpam-1528	296	3	investigate	investigate	VERB
ejpam-1528	296	4	the	the	DET
ejpam-1528	296	5	link	link	NOUN
ejpam-1528	296	6	between	between	ADP
ejpam-1528	296	7	σi(a	σi(a	PROPN
ejpam-1528	296	8	)	)	PUNCT
ejpam-1528	296	9	,	,	PUNCT
ejpam-1528	296	10	i	i	NOUN
ejpam-1528	296	11	=	=	NOUN
ejpam-1528	296	12	1,2	1,2	NUM
ejpam-1528	296	13	and	and	CCONJ
ejpam-1528	296	14	σ(a	σ(a	NUM
ejpam-1528	296	15	)	)	PUNCT
ejpam-1528	296	16	.	.	PUNCT
ejpam-1528	297	1	theorem	theorem	VERB
ejpam-1528	297	2	9	9	NUM
ejpam-1528	297	3	.	.	PUNCT
ejpam-1528	298	1	leta	leta	PROPN
ejpam-1528	298	2	be	be	AUX
ejpam-1528	298	3	a	a	DET
ejpam-1528	298	4	unital	unital	ADJ
ejpam-1528	298	5	banach	banach	NOUN
ejpam-1528	298	6	algebra	algebra	NOUN
ejpam-1528	298	7	,	,	PUNCT
ejpam-1528	298	8	a	a	DET
ejpam-1528	298	9	∈a	∈a	NOUN
ejpam-1528	298	10	.	.	PUNCT
ejpam-1528	299	1	then	then	ADV
ejpam-1528	299	2	i	i	PRON
ejpam-1528	299	3	)	)	PUNCT
ejpam-1528	299	4	σ(a	σ(a	PROPN
ejpam-1528	299	5	)	)	PUNCT
ejpam-1528	300	1	=	=	PRON
ejpam-1528	300	2	{	{	PUNCT
ejpam-1528	300	3	0c	0c	NOUN
ejpam-1528	300	4	}	}	PUNCT
ejpam-1528	300	5	⇒	⇒	NOUN
ejpam-1528	300	6	σ1(a	σ1(a	PRON
ejpam-1528	300	7	)	)	PUNCT
ejpam-1528	300	8	=	=	PRON
ejpam-1528	300	9	{	{	PUNCT
ejpam-1528	300	10	0	0	NUM
ejpam-1528	300	11	}	}	PUNCT
ejpam-1528	300	12	.	.	PUNCT
ejpam-1528	301	1	ii	ii	X
ejpam-1528	301	2	)	)	PUNCT
ejpam-1528	301	3	σ2(a	σ2(a	PROPN
ejpam-1528	301	4	)	)	PUNCT
ejpam-1528	301	5	=	=	PRON
ejpam-1528	301	6	{	{	PUNCT
ejpam-1528	301	7	0	0	NUM
ejpam-1528	301	8	}	}	PUNCT
ejpam-1528	301	9	⇒	⇒	NOUN
ejpam-1528	301	10	σ(a	σ(a	PROPN
ejpam-1528	301	11	)	)	PUNCT
ejpam-1528	301	12	is	be	AUX
ejpam-1528	301	13	connected	connect	VERB
ejpam-1528	301	14	and	and	CCONJ
ejpam-1528	301	15	contains	contain	VERB
ejpam-1528	301	16	0c	0c	NOUN
ejpam-1528	301	17	.	.	PUNCT
ejpam-1528	302	1	proof	proof	NOUN
ejpam-1528	302	2	.	.	PUNCT
ejpam-1528	303	1	i	i	PRON
ejpam-1528	303	2	)	)	PUNCT
ejpam-1528	303	3	if	if	SCONJ
ejpam-1528	303	4	the	the	DET
ejpam-1528	303	5	spectrum	spectrum	NOUN
ejpam-1528	303	6	of	of	ADP
ejpam-1528	303	7	a	a	DET
ejpam-1528	303	8	reduces	reduce	NOUN
ejpam-1528	303	9	to	to	ADP
ejpam-1528	303	10	0	0	NUM
ejpam-1528	303	11	,	,	PUNCT
ejpam-1528	303	12	the	the	DET
ejpam-1528	303	13	its	its	PRON
ejpam-1528	303	14	spectral	spectral	ADJ
ejpam-1528	303	15	radius	radius	NOUN
ejpam-1528	303	16	is	be	AUX
ejpam-1528	303	17	equal	equal	ADJ
ejpam-1528	303	18	to	to	ADP
ejpam-1528	303	19	0	0	NUM
ejpam-1528	303	20	.	.	PUNCT
ejpam-1528	304	1	let	let	VERB
ejpam-1528	304	2	e	e	X
ejpam-1528	304	3	∈	∈	PROPN
ejpam-1528	304	4	σ1(a	σ1(a	PROPN
ejpam-1528	304	5	)	)	PUNCT
ejpam-1528	304	6	.	.	PUNCT
ejpam-1528	305	1	then	then	ADV
ejpam-1528	305	2	e	e	X
ejpam-1528	305	3	=	=	SYM
ejpam-1528	305	4	aa−e	aa−e	NOUN
ejpam-1528	305	5	=	=	NOUN
ejpam-1528	305	6	a−ea	a−ea	NOUN
ejpam-1528	305	7	.	.	PUNCT
ejpam-1528	306	1	we	we	PRON
ejpam-1528	306	2	get	get	VERB
ejpam-1528	306	3	||e||	||e||	ADJ
ejpam-1528	306	4	1	1	NUM
ejpam-1528	306	5	n	n	NOUN
ejpam-1528	306	6	=	=	SYM
ejpam-1528	306	7	||en||	||en||	VERB
ejpam-1528	306	8	1	1	NUM
ejpam-1528	306	9	n	n	NOUN
ejpam-1528	306	10	=	=	PUNCT
ejpam-1528	306	11	||an(a−e)n||	||an(a−e)n||	VERB
ejpam-1528	306	12	1	1	NUM
ejpam-1528	306	13	n	n	NOUN
ejpam-1528	306	14	≤	≤	NUM
ejpam-1528	306	15	||an||	||an||	ADJ
ejpam-1528	306	16	1	1	NUM
ejpam-1528	306	17	n	n	NOUN
ejpam-1528	306	18	||(a−e)||	||(a−e)||	NUM
ejpam-1528	306	19	→	→	SYM
ejpam-1528	306	20	0	0	NUM
ejpam-1528	306	21	and	and	CCONJ
ejpam-1528	306	22	||e||=	||e||=	NOUN
ejpam-1528	306	23	0	0	NUM
ejpam-1528	306	24	.	.	PUNCT
ejpam-1528	307	1	ii	ii	PROPN
ejpam-1528	307	2	)	)	PUNCT
ejpam-1528	307	3	if	if	SCONJ
ejpam-1528	307	4	a	a	PRON
ejpam-1528	307	5	is	be	AUX
ejpam-1528	307	6	invertible	invertible	ADJ
ejpam-1528	307	7	,	,	PUNCT
ejpam-1528	307	8	then	then	ADV
ejpam-1528	307	9	1	1	NUM
ejpam-1528	307	10	∈	∈	NOUN
ejpam-1528	307	11	σ2(a	σ2(a	NUM
ejpam-1528	307	12	)	)	PUNCT
ejpam-1528	307	13	.	.	PUNCT
ejpam-1528	308	1	hence	hence	ADV
ejpam-1528	308	2	assume	assume	VERB
ejpam-1528	308	3	σ(a	σ(a	PROPN
ejpam-1528	308	4	)	)	PUNCT
ejpam-1528	308	5	contains	contain	VERB
ejpam-1528	308	6	0	0	NUM
ejpam-1528	309	1	but	but	CCONJ
ejpam-1528	309	2	is	be	AUX
ejpam-1528	309	3	not	not	PART
ejpam-1528	309	4	connected	connect	VERB
ejpam-1528	309	5	.	.	PUNCT
ejpam-1528	310	1	then	then	ADV
ejpam-1528	310	2	σ(a	σ(a	PROPN
ejpam-1528	310	3	)	)	PUNCT
ejpam-1528	310	4	=	=	PUNCT
ejpam-1528	310	5	c0∪c1	c0∪c1	NOUN
ejpam-1528	310	6	with	with	ADP
ejpam-1528	310	7	0	0	NUM
ejpam-1528	310	8	∈	∈	PROPN
ejpam-1528	310	9	c0	c0	NOUN
ejpam-1528	310	10	and	and	CCONJ
ejpam-1528	310	11	c0	c0	PROPN
ejpam-1528	310	12	,	,	PUNCT
ejpam-1528	310	13	c1	c1	PROPN
ejpam-1528	310	14	disjoint	disjoint	NOUN
ejpam-1528	310	15	and	and	CCONJ
ejpam-1528	310	16	open	open	VERB
ejpam-1528	310	17	and	and	CCONJ
ejpam-1528	310	18	closed	close	VERB
ejpam-1528	310	19	in	in	ADP
ejpam-1528	310	20	σ(a	σ(a	PROPN
ejpam-1528	310	21	)	)	PUNCT
ejpam-1528	310	22	.	.	PUNCT
ejpam-1528	311	1	then	then	ADV
ejpam-1528	311	2	the	the	DET
ejpam-1528	311	3	holomorphic	holomorphic	ADJ
ejpam-1528	311	4	calculus	calculus	NOUN
ejpam-1528	311	5	for	for	ADP
ejpam-1528	311	6	f	f	PROPN
ejpam-1528	311	7	(	(	PUNCT
ejpam-1528	311	8	z	z	NOUN
ejpam-1528	311	9	)	)	PUNCT
ejpam-1528	311	10	=	=	SYM
ejpam-1528	311	11	1	1	NUM
ejpam-1528	311	12	z	z	NOUN
ejpam-1528	311	13	on	on	ADP
ejpam-1528	311	14	u	u	PRON
ejpam-1528	311	15	open	open	ADJ
ejpam-1528	311	16	set	set	NOUN
ejpam-1528	311	17	containing	contain	VERB
ejpam-1528	311	18	c1	c1	NOUN
ejpam-1528	311	19	and	and	CCONJ
ejpam-1528	311	20	0	0	NUM
ejpam-1528	311	21	outside	outside	ADP
ejpam-1528	311	22	u	u	NOUN
ejpam-1528	311	23	,	,	PUNCT
ejpam-1528	311	24	such	such	ADJ
ejpam-1528	311	25	that	that	SCONJ
ejpam-1528	311	26	u	u	PROPN
ejpam-1528	311	27	contains	contain	VERB
ejpam-1528	311	28	an	an	DET
ejpam-1528	311	29	open	open	ADJ
ejpam-1528	311	30	neighbourhood	neighbourhood	NOUN
ejpam-1528	311	31	of	of	ADP
ejpam-1528	311	32	c0	c0	PROPN
ejpam-1528	311	33	,	,	PUNCT
ejpam-1528	311	34	defines	define	VERB
ejpam-1528	311	35	an	an	DET
ejpam-1528	311	36	element	element	NOUN
ejpam-1528	311	37	x	x	X
ejpam-1528	312	1	=	=	SYM
ejpam-1528	312	2	f	f	X
ejpam-1528	312	3	(	(	PUNCT
ejpam-1528	312	4	a	a	NOUN
ejpam-1528	312	5	)	)	PUNCT
ejpam-1528	312	6	of	of	ADP
ejpam-1528	312	7	{	{	PUNCT
ejpam-1528	312	8	a}′′	a}′′	NUM
ejpam-1528	312	9	such	such	ADJ
ejpam-1528	312	10	that	that	DET
ejpam-1528	312	11	ax	ax	NOUN
ejpam-1528	312	12	=	=	X
ejpam-1528	312	13	xa	xa	PROPN
ejpam-1528	313	1	=	=	SYM
ejpam-1528	313	2	e	e	PROPN
ejpam-1528	313	3	is	be	AUX
ejpam-1528	313	4	idempotent	idempotent	ADJ
ejpam-1528	313	5	and	and	CCONJ
ejpam-1528	313	6	non	non	ADJ
ejpam-1528	313	7	zero	zero	NUM
ejpam-1528	313	8	,	,	PUNCT
ejpam-1528	313	9	and	and	CCONJ
ejpam-1528	313	10	σ2(a	σ2(a	NUM
ejpam-1528	313	11	)	)	PUNCT
ejpam-1528	313	12	does	do	AUX
ejpam-1528	313	13	not	not	PART
ejpam-1528	313	14	reduce	reduce	VERB
ejpam-1528	313	15	to	to	ADP
ejpam-1528	313	16	{	{	PUNCT
ejpam-1528	313	17	0	0	NUM
ejpam-1528	313	18	}	}	PUNCT
ejpam-1528	313	19	.	.	PUNCT
ejpam-1528	314	1	now	now	ADV
ejpam-1528	314	2	,	,	PUNCT
ejpam-1528	314	3	we	we	PRON
ejpam-1528	314	4	consider	consider	VERB
ejpam-1528	314	5	three	three	NUM
ejpam-1528	314	6	different	different	ADJ
ejpam-1528	314	7	(	(	PUNCT
ejpam-1528	314	8	commutative	commutative	ADJ
ejpam-1528	314	9	)	)	PUNCT
ejpam-1528	314	10	banach	banach	NOUN
ejpam-1528	314	11	algebras	algebra	VERB
ejpam-1528	314	12	to	to	PART
ejpam-1528	314	13	show	show	VERB
ejpam-1528	314	14	that	that	SCONJ
ejpam-1528	314	15	we	we	PRON
ejpam-1528	314	16	can	can	AUX
ejpam-1528	314	17	not	not	PART
ejpam-1528	314	18	do	do	VERB
ejpam-1528	314	19	better	well	ADV
ejpam-1528	314	20	in	in	ADP
ejpam-1528	314	21	the	the	DET
ejpam-1528	314	22	theorem	theorem	NOUN
ejpam-1528	314	23	,	,	PUNCT
ejpam-1528	314	24	nor	nor	CCONJ
ejpam-1528	314	25	define	define	VERB
ejpam-1528	314	26	natural	natural	ADJ
ejpam-1528	314	27	invertibility	invertibility	NOUN
ejpam-1528	314	28	in	in	ADP
ejpam-1528	314	29	terms	term	NOUN
ejpam-1528	314	30	of	of	ADP
ejpam-1528	314	31	the	the	DET
ejpam-1528	314	32	spectrum	spectrum	NOUN
ejpam-1528	314	33	.	.	PUNCT
ejpam-1528	315	1	•	•	NUM
ejpam-1528	315	2	consider	consider	VERB
ejpam-1528	315	3	the	the	DET
ejpam-1528	315	4	banach	banach	NOUN
ejpam-1528	315	5	algebra	algebra	NOUN
ejpam-1528	315	6	a	a	DET
ejpam-1528	315	7	=	=	SYM
ejpam-1528	315	8	c0([0,1	c0([0,1	NOUN
ejpam-1528	315	9	]	]	PUNCT
ejpam-1528	315	10	)	)	PUNCT
ejpam-1528	315	11	of	of	ADP
ejpam-1528	315	12	continuous	continuous	ADJ
ejpam-1528	315	13	functions	function	NOUN
ejpam-1528	315	14	on	on	ADP
ejpam-1528	315	15	[	[	X
ejpam-1528	315	16	0	0	NUM
ejpam-1528	315	17	,	,	PUNCT
ejpam-1528	315	18	1	1	NUM
ejpam-1528	315	19	]	]	PUNCT
ejpam-1528	315	20	,	,	PUNCT
ejpam-1528	315	21	and	and	CCONJ
ejpam-1528	315	22	let	let	VERB
ejpam-1528	315	23	a(t	a(t	VERB
ejpam-1528	315	24	)	)	PUNCT
ejpam-1528	316	1	=	=	SYM
ejpam-1528	317	1	t.	t.	NOUN
ejpam-1528	317	2	then	then	ADV
ejpam-1528	317	3	σ(a	σ(a	PROPN
ejpam-1528	317	4	)	)	PUNCT
ejpam-1528	317	5	=	=	PUNCT
ejpam-1528	318	1	[	[	X
ejpam-1528	318	2	0	0	NUM
ejpam-1528	318	3	,	,	PUNCT
ejpam-1528	318	4	1	1	NUM
ejpam-1528	318	5	]	]	PUNCT
ejpam-1528	318	6	and	and	CCONJ
ejpam-1528	318	7	σ(a	σ(a	PROPN
ejpam-1528	318	8	)	)	PUNCT
ejpam-1528	318	9	=	=	PRON
ejpam-1528	318	10	{	{	PUNCT
ejpam-1528	318	11	0	0	NUM
ejpam-1528	318	12	}	}	PUNCT
ejpam-1528	318	13	.	.	PUNCT
ejpam-1528	319	1	a	a	PRON
ejpam-1528	319	2	is	be	AUX
ejpam-1528	319	3	naturally	naturally	ADV
ejpam-1528	319	4	invertible	invertible	ADJ
ejpam-1528	319	5	with	with	ADP
ejpam-1528	319	6	b	b	NOUN
ejpam-1528	319	7	=	=	SYM
ejpam-1528	319	8	0	0	PROPN
ejpam-1528	319	9	.	.	NOUN
ejpam-1528	319	10	•	•	NUM
ejpam-1528	319	11	consider	consider	VERB
ejpam-1528	319	12	the	the	DET
ejpam-1528	319	13	banach	banach	NOUN
ejpam-1528	319	14	algebraa	algebraa	NOUN
ejpam-1528	319	15	=	=	PUNCT
ejpam-1528	320	1	c0([0,1]∪	c0([0,1]∪	NOUN
ejpam-1528	321	1	[	[	X
ejpam-1528	321	2	2,3	2,3	NUM
ejpam-1528	321	3	]	]	PUNCT
ejpam-1528	321	4	)	)	PUNCT
ejpam-1528	321	5	of	of	ADP
ejpam-1528	321	6	continuous	continuous	ADJ
ejpam-1528	321	7	functions	function	NOUN
ejpam-1528	321	8	on	on	ADP
ejpam-1528	321	9	[	[	X
ejpam-1528	321	10	0	0	NUM
ejpam-1528	321	11	,	,	PUNCT
ejpam-1528	321	12	1]∪[2	1]∪[2	NUM
ejpam-1528	321	13	,	,	PUNCT
ejpam-1528	321	14	3	3	NUM
ejpam-1528	321	15	]	]	PUNCT
ejpam-1528	321	16	,	,	PUNCT
ejpam-1528	321	17	and	and	CCONJ
ejpam-1528	321	18	let	let	VERB
ejpam-1528	321	19	a(t	a(t	VERB
ejpam-1528	321	20	)	)	PUNCT
ejpam-1528	321	21	=	=	SYM
ejpam-1528	321	22	t	t	PROPN
ejpam-1528	321	23	,	,	PUNCT
ejpam-1528	321	24	0≤	0≤	NUM
ejpam-1528	321	25	t	t	NOUN
ejpam-1528	321	26	≤	≤	NUM
ejpam-1528	321	27	1	1	NUM
ejpam-1528	321	28	and	and	CCONJ
ejpam-1528	321	29	a(t	a(t	VERB
ejpam-1528	321	30	)	)	PUNCT
ejpam-1528	321	31	=	=	SYM
ejpam-1528	321	32	t−1	t−1	PROPN
ejpam-1528	321	33	,	,	PUNCT
ejpam-1528	321	34	2≤	2≤	NUM
ejpam-1528	321	35	t	t	PROPN
ejpam-1528	321	36	≤	≤	ADJ
ejpam-1528	321	37	3	3	NUM
ejpam-1528	321	38	.	.	PUNCT
ejpam-1528	322	1	then	then	ADV
ejpam-1528	322	2	σ(a	σ(a	PROPN
ejpam-1528	322	3	)	)	PUNCT
ejpam-1528	322	4	=	=	PUNCT
ejpam-1528	323	1	[	[	X
ejpam-1528	323	2	0	0	NUM
ejpam-1528	323	3	,	,	PUNCT
ejpam-1528	323	4	2	2	NUM
ejpam-1528	323	5	]	]	PUNCT
ejpam-1528	323	6	and	and	CCONJ
ejpam-1528	323	7	σ(a	σ(a	PROPN
ejpam-1528	323	8	)	)	PUNCT
ejpam-1528	323	9	=	=	PRON
ejpam-1528	323	10	{	{	PUNCT
ejpam-1528	323	11	1[2,3	1[2,3	NOUN
ejpam-1528	323	12	]	]	X
ejpam-1528	323	13	}	}	PUNCT
ejpam-1528	323	14	.	.	PUNCT
ejpam-1528	324	1	a	a	PRON
ejpam-1528	324	2	is	be	AUX
ejpam-1528	324	3	naturally	naturally	ADV
ejpam-1528	324	4	invertible	invertible	ADJ
ejpam-1528	324	5	with	with	ADP
ejpam-1528	324	6	b(t	b(t	NOUN
ejpam-1528	324	7	)	)	PUNCT
ejpam-1528	324	8	=	=	SYM
ejpam-1528	325	1	0	0	NUM
ejpam-1528	325	2	,	,	PUNCT
ejpam-1528	325	3	0	0	NUM
ejpam-1528	325	4	≤	≤	NUM
ejpam-1528	325	5	t	t	NOUN
ejpam-1528	325	6	≤	≤	NUM
ejpam-1528	325	7	1	1	NUM
ejpam-1528	325	8	and	and	CCONJ
ejpam-1528	325	9	b(t	b(t	VERB
ejpam-1528	325	10	)	)	PUNCT
ejpam-1528	325	11	=	=	SYM
ejpam-1528	325	12	1	1	NUM
ejpam-1528	325	13	t−1	t−1	NOUN
ejpam-1528	325	14	,	,	PUNCT
ejpam-1528	325	15	2≤	2≤	NUM
ejpam-1528	325	16	t	t	NOUN
ejpam-1528	325	17	≤	≤	ADJ
ejpam-1528	325	18	3	3	NUM
ejpam-1528	325	19	.	.	NOUN
ejpam-1528	325	20	•	•	NUM
ejpam-1528	325	21	consider	consider	VERB
ejpam-1528	325	22	now	now	ADV
ejpam-1528	325	23	the	the	DET
ejpam-1528	325	24	banach	banach	NOUN
ejpam-1528	325	25	algebra	algebra	NOUN
ejpam-1528	325	26	a	a	DET
ejpam-1528	325	27	=	=	PUNCT
ejpam-1528	325	28	l∞([0	l∞([0	PROPN
ejpam-1528	325	29	,	,	PUNCT
ejpam-1528	325	30	1	1	NUM
ejpam-1528	325	31	]	]	PUNCT
ejpam-1528	325	32	)	)	PUNCT
ejpam-1528	325	33	of	of	ADP
ejpam-1528	325	34	essentially	essentially	ADV
ejpam-1528	325	35	bounded	bound	VERB
ejpam-1528	325	36	measurable	measurable	ADJ
ejpam-1528	325	37	functions	function	NOUN
ejpam-1528	325	38	on	on	ADP
ejpam-1528	325	39	[	[	X
ejpam-1528	325	40	0	0	NUM
ejpam-1528	325	41	,	,	PUNCT
ejpam-1528	325	42	1	1	NUM
ejpam-1528	325	43	]	]	PUNCT
ejpam-1528	325	44	,	,	PUNCT
ejpam-1528	325	45	and	and	CCONJ
ejpam-1528	325	46	let	let	VERB
ejpam-1528	325	47	a(t	a(t	VERB
ejpam-1528	325	48	)	)	PUNCT
ejpam-1528	326	1	=	=	SYM
ejpam-1528	327	1	t.	t.	NOUN
ejpam-1528	327	2	then	then	ADV
ejpam-1528	327	3	σ(a	σ(a	PROPN
ejpam-1528	327	4	)	)	PUNCT
ejpam-1528	327	5	=	=	PUNCT
ejpam-1528	328	1	[	[	X
ejpam-1528	328	2	0	0	NUM
ejpam-1528	328	3	,	,	PUNCT
ejpam-1528	328	4	1	1	NUM
ejpam-1528	328	5	]	]	PUNCT
ejpam-1528	328	6	and	and	CCONJ
ejpam-1528	328	7	σ(a	σ(a	PROPN
ejpam-1528	328	8	)	)	PUNCT
ejpam-1528	328	9	=	=	PRON
ejpam-1528	328	10	{	{	PUNCT
ejpam-1528	328	11	1a	1a	NOUN
ejpam-1528	328	12	,	,	PUNCT
ejpam-1528	328	13	∃0	∃0	PROPN
ejpam-1528	328	14	<	<	X
ejpam-1528	328	15	c	c	X
ejpam-1528	328	16	≤	≤	NOUN
ejpam-1528	328	17	1,λ(a∩	1,λ(a∩	PROPN
ejpam-1528	329	1	[	[	X
ejpam-1528	329	2	0	0	NUM
ejpam-1528	329	3	,	,	PUNCT
ejpam-1528	329	4	c	c	NOUN
ejpam-1528	329	5	]	]	X
ejpam-1528	329	6	)	)	PUNCT
ejpam-1528	329	7	=	=	PUNCT
ejpam-1528	330	1	0	0	NUM
ejpam-1528	330	2	}	}	PUNCT
ejpam-1528	330	3	.	.	PUNCT
ejpam-1528	331	1	this	this	DET
ejpam-1528	331	2	set	set	NOUN
ejpam-1528	331	3	admits	admit	VERB
ejpam-1528	331	4	no	no	DET
ejpam-1528	331	5	maximal	maximal	ADJ
ejpam-1528	331	6	element	element	NOUN
ejpam-1528	331	7	,	,	PUNCT
ejpam-1528	331	8	hence	hence	ADV
ejpam-1528	331	9	a(t	a(t	VERB
ejpam-1528	331	10	)	)	PUNCT
ejpam-1528	332	1	=	=	SYM
ejpam-1528	332	2	t	t	NOUN
ejpam-1528	332	3	is	be	AUX
ejpam-1528	332	4	not	not	PART
ejpam-1528	332	5	naturally	naturally	ADV
ejpam-1528	332	6	invertible	invertible	ADJ
ejpam-1528	332	7	.	.	PUNCT
ejpam-1528	333	1	x.	x.	PROPN
ejpam-1528	333	2	mary	mary	PROPN
ejpam-1528	333	3	/	/	SYM
ejpam-1528	333	4	eur	eur	PROPN
ejpam-1528	333	5	.	.	PUNCT
ejpam-1528	334	1	j.	j.	PROPN
ejpam-1528	334	2	pure	pure	PROPN
ejpam-1528	334	3	appl	appl	PROPN
ejpam-1528	334	4	.	.	PROPN
ejpam-1528	334	5	math	math	PROPN
ejpam-1528	334	6	,	,	PUNCT
ejpam-1528	334	7	6	6	NUM
ejpam-1528	334	8	(	(	PUNCT
ejpam-1528	334	9	2013	2013	NUM
ejpam-1528	334	10	)	)	PUNCT
ejpam-1528	334	11	,	,	PUNCT
ejpam-1528	334	12	413	413	NUM
ejpam-1528	334	13	-	-	SYM
ejpam-1528	334	14	427	427	NUM
ejpam-1528	334	15	423	423	NUM
ejpam-1528	334	16	it	it	PRON
ejpam-1528	334	17	appears	appear	VERB
ejpam-1528	334	18	that	that	SCONJ
ejpam-1528	334	19	natural	natural	ADJ
ejpam-1528	334	20	invertibility	invertibility	NOUN
ejpam-1528	334	21	is	be	AUX
ejpam-1528	334	22	strongly	strongly	ADV
ejpam-1528	334	23	linked	link	VERB
ejpam-1528	334	24	with	with	ADP
ejpam-1528	334	25	the	the	DET
ejpam-1528	334	26	nature	nature	NOUN
ejpam-1528	334	27	of	of	ADP
ejpam-1528	334	28	the	the	DET
ejpam-1528	334	29	structure	structure	NOUN
ejpam-1528	334	30	space	space	NOUN
ejpam-1528	334	31	(	(	PUNCT
ejpam-1528	334	32	or	or	CCONJ
ejpam-1528	334	33	spectrum	spectrum	NOUN
ejpam-1528	334	34	)	)	PUNCT
ejpam-1528	334	35	of	of	ADP
ejpam-1528	334	36	the	the	DET
ejpam-1528	334	37	whole	whole	ADJ
ejpam-1528	334	38	commutative	commutative	ADJ
ejpam-1528	334	39	banach	banach	NOUN
ejpam-1528	334	40	algebra	algebra	NOUN
ejpam-1528	334	41	b	b	NOUN
ejpam-1528	334	42	=	=	SYM
ejpam-1528	334	43	{	{	PUNCT
ejpam-1528	334	44	a}′′	a}′′	NUM
ejpam-1528	334	45	,	,	PUNCT
ejpam-1528	334	46	independently	independently	ADV
ejpam-1528	334	47	of	of	ADP
ejpam-1528	334	48	the	the	DET
ejpam-1528	334	49	nature	nature	NOUN
ejpam-1528	334	50	of	of	ADP
ejpam-1528	334	51	the	the	DET
ejpam-1528	334	52	spectrum	spectrum	NOUN
ejpam-1528	334	53	of	of	ADP
ejpam-1528	334	54	the	the	DET
ejpam-1528	334	55	element	element	NOUN
ejpam-1528	334	56	a.	a.	NOUN
ejpam-1528	334	57	obviously	obviously	ADV
ejpam-1528	334	58	,	,	PUNCT
ejpam-1528	334	59	if	if	SCONJ
ejpam-1528	334	60	the	the	DET
ejpam-1528	334	61	spectrum	spectrum	NOUN
ejpam-1528	334	62	of	of	ADP
ejpam-1528	334	63	{	{	PUNCT
ejpam-1528	334	64	a}′′	a}′′	PROPN
ejpam-1528	334	65	is	be	AUX
ejpam-1528	334	66	not	not	PART
ejpam-1528	334	67	connected	connect	VERB
ejpam-1528	334	68	,	,	PUNCT
ejpam-1528	334	69	then	then	ADV
ejpam-1528	334	70	shilov	shilov	VERB
ejpam-1528	334	71	’s	’s	PART
ejpam-1528	334	72	idempotent	idempotent	NOUN
ejpam-1528	334	73	theorem	theorem	NOUN
ejpam-1528	334	74	gives	give	VERB
ejpam-1528	334	75	the	the	DET
ejpam-1528	334	76	existence	existence	NOUN
ejpam-1528	334	77	of	of	ADP
ejpam-1528	334	78	a	a	DET
ejpam-1528	334	79	nontrivial	nontrivial	ADJ
ejpam-1528	334	80	idempotent	idempotent	NOUN
ejpam-1528	334	81	.	.	PUNCT
ejpam-1528	335	1	this	this	DET
ejpam-1528	335	2	idempotent	idempotent	NOUN
ejpam-1528	335	3	needs	need	VERB
ejpam-1528	335	4	not	not	PART
ejpam-1528	335	5	to	to	PART
ejpam-1528	335	6	be	be	AUX
ejpam-1528	335	7	in	in	ADP
ejpam-1528	335	8	σ(a	σ(a	PROPN
ejpam-1528	335	9	)	)	PUNCT
ejpam-1528	335	10	.	.	PUNCT
ejpam-1528	336	1	next	next	ADJ
ejpam-1528	336	2	theorem	theorem	NOUN
ejpam-1528	336	3	uses	use	VERB
ejpam-1528	336	4	the	the	DET
ejpam-1528	336	5	generalized	generalized	ADJ
ejpam-1528	336	6	spectral	spectral	ADJ
ejpam-1528	336	7	theory	theory	NOUN
ejpam-1528	336	8	of	of	ADP
ejpam-1528	336	9	hile	hile	NOUN
ejpam-1528	336	10	and	and	CCONJ
ejpam-1528	336	11	pfaffenberger	pfaffenberger	ADV
ejpam-1528	336	12	[	[	X
ejpam-1528	336	13	14	14	NUM
ejpam-1528	336	14	,	,	PUNCT
ejpam-1528	336	15	15	15	NUM
ejpam-1528	336	16	]	]	PUNCT
ejpam-1528	336	17	and	and	CCONJ
ejpam-1528	336	18	the	the	DET
ejpam-1528	336	19	associated	associated	ADJ
ejpam-1528	336	20	functional	functional	ADJ
ejpam-1528	336	21	calculus	calculus	NOUN
ejpam-1528	336	22	to	to	PART
ejpam-1528	336	23	construct	construct	VERB
ejpam-1528	336	24	elements	element	NOUN
ejpam-1528	336	25	in	in	ADP
ejpam-1528	336	26	σ	σ	PROPN
ejpam-1528	336	27	j(a	j(a	PROPN
ejpam-1528	336	28	)	)	PUNCT
ejpam-1528	336	29	,	,	PUNCT
ejpam-1528	336	30	j	j	PROPN
ejpam-1528	336	31	=	=	SYM
ejpam-1528	336	32	1,2	1,2	NUM
ejpam-1528	336	33	.	.	PUNCT
ejpam-1528	337	1	the	the	DET
ejpam-1528	337	2	construction	construction	NOUN
ejpam-1528	337	3	is	be	AUX
ejpam-1528	337	4	similar	similar	ADJ
ejpam-1528	337	5	to	to	ADP
ejpam-1528	337	6	the	the	DET
ejpam-1528	337	7	case	case	NOUN
ejpam-1528	337	8	of	of	ADP
ejpam-1528	337	9	a	a	DET
ejpam-1528	337	10	disconnected	disconnected	ADJ
ejpam-1528	337	11	spectrum	spectrum	NOUN
ejpam-1528	337	12	,	,	PUNCT
ejpam-1528	337	13	but	but	CCONJ
ejpam-1528	337	14	instead	instead	ADV
ejpam-1528	337	15	of	of	ADP
ejpam-1528	337	16	using	use	VERB
ejpam-1528	337	17	σ(a	σ(a	PROPN
ejpam-1528	337	18	)	)	PUNCT
ejpam-1528	337	19	(	(	PUNCT
ejpam-1528	337	20	that	that	PRON
ejpam-1528	337	21	can	can	AUX
ejpam-1528	337	22	be	be	AUX
ejpam-1528	337	23	connected	connect	VERB
ejpam-1528	337	24	)	)	PUNCT
ejpam-1528	337	25	,	,	PUNCT
ejpam-1528	337	26	we	we	PRON
ejpam-1528	337	27	use	use	VERB
ejpam-1528	337	28	the	the	DET
ejpam-1528	337	29	generalized	generalized	ADJ
ejpam-1528	337	30	spectrum	spectrum	NOUN
ejpam-1528	337	31	of	of	ADP
ejpam-1528	337	32	hile	hile	NOUN
ejpam-1528	337	33	and	and	CCONJ
ejpam-1528	337	34	pfaffenberger	pfaffenberger	ADV
ejpam-1528	337	35	.	.	PUNCT
ejpam-1528	338	1	if	if	SCONJ
ejpam-1528	338	2	a	a	PRON
ejpam-1528	338	3	,	,	PUNCT
ejpam-1528	338	4	q	q	NOUN
ejpam-1528	338	5	∈	∈	PROPN
ejpam-1528	338	6	a	a	PRON
ejpam-1528	338	7	,	,	PUNCT
ejpam-1528	338	8	then	then	ADV
ejpam-1528	338	9	the	the	DET
ejpam-1528	338	10	spectrum	spectrum	NOUN
ejpam-1528	338	11	of	of	ADP
ejpam-1528	338	12	a	a	DET
ejpam-1528	338	13	relative	relative	NOUN
ejpam-1528	338	14	to	to	ADP
ejpam-1528	338	15	q	q	NOUN
ejpam-1528	338	16	,	,	PUNCT
ejpam-1528	338	17	or	or	CCONJ
ejpam-1528	338	18	q−spectrum	q−spectrum	PRON
ejpam-1528	338	19	of	of	ADP
ejpam-1528	338	20	a	a	DET
ejpam-1528	338	21	σq(a	σq(a	NOUN
ejpam-1528	338	22	)	)	PUNCT
ejpam-1528	338	23	,	,	PUNCT
ejpam-1528	338	24	is	be	AUX
ejpam-1528	338	25	the	the	DET
ejpam-1528	338	26	set	set	NOUN
ejpam-1528	338	27	of	of	ADP
ejpam-1528	338	28	points	point	NOUN
ejpam-1528	338	29	z	z	NOUN
ejpam-1528	338	30	such	such	ADJ
ejpam-1528	338	31	that	that	SCONJ
ejpam-1528	338	32	a−	a−	PROPN
ejpam-1528	338	33	z.1−	z.1−	NOUN
ejpam-1528	338	34	z̄q	z̄q	PROPN
ejpam-1528	338	35	is	be	AUX
ejpam-1528	338	36	not	not	PART
ejpam-1528	338	37	invertible	invertible	ADJ
ejpam-1528	338	38	in	in	ADP
ejpam-1528	338	39	a.	a.	NOUN
ejpam-1528	338	40	theorem	theorem	NOUN
ejpam-1528	338	41	10	10	NUM
ejpam-1528	338	42	.	.	PUNCT
ejpam-1528	339	1	let	let	VERB
ejpam-1528	339	2	a	a	PRON
ejpam-1528	339	3	,	,	PUNCT
ejpam-1528	339	4	q	q	NOUN
ejpam-1528	339	5	∈	∈	PROPN
ejpam-1528	339	6	a	a	PRON
ejpam-1528	339	7	,	,	PUNCT
ejpam-1528	339	8	with	with	ADP
ejpam-1528	339	9	σ(a	σ(a	PROPN
ejpam-1528	339	10	)	)	PUNCT
ejpam-1528	339	11	connected	connect	VERB
ejpam-1528	339	12	set	set	NOUN
ejpam-1528	339	13	that	that	PRON
ejpam-1528	339	14	contains	contain	VERB
ejpam-1528	339	15	0	0	PROPN
ejpam-1528	339	16	.	.	PUNCT
ejpam-1528	340	1	assume	assume	VERB
ejpam-1528	340	2	σ(q	σ(q	PROPN
ejpam-1528	340	3	)	)	PUNCT
ejpam-1528	341	1	∩	∩	NOUN
ejpam-1528	341	2	t	t	NOUN
ejpam-1528	341	3	=	=	PUNCT
ejpam-1528	341	4	;	;	PUNCT
ejpam-1528	341	5	,	,	PUNCT
ejpam-1528	341	6	where	where	SCONJ
ejpam-1528	341	7	t	t	PROPN
ejpam-1528	341	8	is	be	AUX
ejpam-1528	341	9	the	the	DET
ejpam-1528	341	10	unit	unit	NOUN
ejpam-1528	341	11	circle	circle	NOUN
ejpam-1528	341	12	,	,	PUNCT
ejpam-1528	341	13	and	and	CCONJ
ejpam-1528	341	14	σq(a	σq(a	NOUN
ejpam-1528	341	15	)	)	PUNCT
ejpam-1528	341	16	is	be	AUX
ejpam-1528	341	17	not	not	PART
ejpam-1528	341	18	connected	connect	VERB
ejpam-1528	341	19	.	.	PUNCT
ejpam-1528	342	1	then	then	ADV
ejpam-1528	342	2	i	i	PRON
ejpam-1528	342	3	)	)	PUNCT
ejpam-1528	342	4	if	if	SCONJ
ejpam-1528	342	5	q	q	X
ejpam-1528	342	6	∈	∈	PROPN
ejpam-1528	342	7	{	{	PUNCT
ejpam-1528	342	8	a}′	a}′	NOUN
ejpam-1528	342	9	,	,	PUNCT
ejpam-1528	342	10	σ1(a	σ1(a	PRON
ejpam-1528	342	11	)	)	PUNCT
ejpam-1528	342	12	is	be	AUX
ejpam-1528	342	13	not	not	PART
ejpam-1528	342	14	empty	empty	ADJ
ejpam-1528	342	15	;	;	PUNCT
ejpam-1528	342	16	ii	ii	X
ejpam-1528	342	17	)	)	PUNCT
ejpam-1528	342	18	if	if	SCONJ
ejpam-1528	342	19	q	q	X
ejpam-1528	342	20	∈	∈	PROPN
ejpam-1528	342	21	{	{	PUNCT
ejpam-1528	342	22	a}′′	a}′′	NUM
ejpam-1528	342	23	,	,	PUNCT
ejpam-1528	342	24	σ2(a	σ2(a	NUM
ejpam-1528	342	25	)	)	PUNCT
ejpam-1528	342	26	is	be	AUX
ejpam-1528	342	27	not	not	PART
ejpam-1528	342	28	empty	empty	ADJ
ejpam-1528	342	29	.	.	PUNCT
ejpam-1528	343	1	proof	proof	NOUN
ejpam-1528	343	2	.	.	PUNCT
ejpam-1528	344	1	this	this	PRON
ejpam-1528	344	2	is	be	AUX
ejpam-1528	344	3	a	a	DET
ejpam-1528	344	4	consequence	consequence	NOUN
ejpam-1528	344	5	of	of	ADP
ejpam-1528	344	6	theorem	theorem	NOUN
ejpam-1528	344	7	12	12	NUM
ejpam-1528	344	8	in	in	ADP
ejpam-1528	344	9	[	[	X
ejpam-1528	344	10	14	14	NUM
ejpam-1528	344	11	]	]	PUNCT
ejpam-1528	344	12	.	.	PUNCT
ejpam-1528	345	1	indeed	indeed	ADV
ejpam-1528	345	2	,	,	PUNCT
ejpam-1528	345	3	since	since	SCONJ
ejpam-1528	345	4	a	a	PRON
ejpam-1528	345	5	is	be	AUX
ejpam-1528	345	6	not	not	PART
ejpam-1528	345	7	invertible	invertible	ADJ
ejpam-1528	345	8	,	,	PUNCT
ejpam-1528	345	9	0	0	NUM
ejpam-1528	345	10	is	be	AUX
ejpam-1528	345	11	in	in	ADP
ejpam-1528	345	12	the	the	DET
ejpam-1528	345	13	q	q	NOUN
ejpam-1528	345	14	spectrum	spectrum	NOUN
ejpam-1528	345	15	of	of	ADP
ejpam-1528	345	16	a.	a.	NOUN
ejpam-1528	345	17	since	since	SCONJ
ejpam-1528	345	18	σq(a	σq(a	NOUN
ejpam-1528	345	19	)	)	PUNCT
ejpam-1528	345	20	is	be	AUX
ejpam-1528	345	21	not	not	PART
ejpam-1528	345	22	connected	connect	VERB
ejpam-1528	345	23	,	,	PUNCT
ejpam-1528	345	24	we	we	PRON
ejpam-1528	345	25	can	can	AUX
ejpam-1528	345	26	find	find	VERB
ejpam-1528	345	27	a	a	DET
ejpam-1528	345	28	closed	closed	ADJ
ejpam-1528	345	29	rectifiable	rectifiable	ADJ
ejpam-1528	345	30	curve	curve	NOUN
ejpam-1528	345	31	γ	γ	NOUN
ejpam-1528	345	32	in	in	ADP
ejpam-1528	345	33	the	the	DET
ejpam-1528	345	34	q	q	X
ejpam-1528	345	35	resolvent	resolvent	NOUN
ejpam-1528	345	36	such	such	ADJ
ejpam-1528	345	37	that	that	SCONJ
ejpam-1528	345	38	0	0	NUM
ejpam-1528	345	39	is	be	AUX
ejpam-1528	345	40	in	in	ADP
ejpam-1528	345	41	its	its	PRON
ejpam-1528	345	42	exterior	exterior	NOUN
ejpam-1528	345	43	and	and	CCONJ
ejpam-1528	345	44	its	its	PRON
ejpam-1528	345	45	interior	interior	NOUN
ejpam-1528	345	46	contains	contain	VERB
ejpam-1528	345	47	elements	element	NOUN
ejpam-1528	345	48	of	of	ADP
ejpam-1528	345	49	σq(a	σq(a	NOUN
ejpam-1528	345	50	)	)	PUNCT
ejpam-1528	345	51	(	(	PUNCT
ejpam-1528	345	52	a	a	DET
ejpam-1528	345	53	component	component	NOUN
ejpam-1528	345	54	of	of	ADP
ejpam-1528	345	55	σq(a	σq(a	NOUN
ejpam-1528	345	56	)	)	PUNCT
ejpam-1528	345	57	that	that	PRON
ejpam-1528	345	58	does	do	AUX
ejpam-1528	345	59	not	not	PART
ejpam-1528	345	60	contains	contain	VERB
ejpam-1528	345	61	0	0	NUM
ejpam-1528	345	62	)	)	PUNCT
ejpam-1528	345	63	.	.	PUNCT
ejpam-1528	346	1	choosing	choose	VERB
ejpam-1528	346	2	z	z	PROPN
ejpam-1528	346	3	=	=	SYM
ejpam-1528	346	4	0	0	NUM
ejpam-1528	346	5	in	in	ADP
ejpam-1528	346	6	equation	equation	NOUN
ejpam-1528	346	7	4.3	4.3	NUM
ejpam-1528	346	8	gives	give	VERB
ejpam-1528	346	9	an	an	DET
ejpam-1528	346	10	idempotent	idempotent	NOUN
ejpam-1528	346	11	p	p	X
ejpam-1528	346	12	≤r	≤r	PROPN
ejpam-1528	346	13	a.	a.	NOUN
ejpam-1528	346	14	the	the	DET
ejpam-1528	346	15	rest	rest	NOUN
ejpam-1528	346	16	follows	follow	VERB
ejpam-1528	346	17	from	from	ADP
ejpam-1528	346	18	commutation	commutation	NOUN
ejpam-1528	346	19	properties	property	NOUN
ejpam-1528	346	20	.	.	PUNCT
ejpam-1528	347	1	6	6	X
ejpam-1528	347	2	.	.	X
ejpam-1528	347	3	operators	operator	NOUN
ejpam-1528	347	4	finally	finally	ADV
ejpam-1528	347	5	,	,	PUNCT
ejpam-1528	347	6	we	we	PRON
ejpam-1528	347	7	apply	apply	VERB
ejpam-1528	347	8	the	the	DET
ejpam-1528	347	9	previous	previous	ADJ
ejpam-1528	347	10	results	result	NOUN
ejpam-1528	347	11	to	to	ADP
ejpam-1528	347	12	the	the	DET
ejpam-1528	347	13	operator	operator	NOUN
ejpam-1528	347	14	algebra	algebra	VERB
ejpam-1528	347	15	a	a	DET
ejpam-1528	347	16	=	=	X
ejpam-1528	347	17	b(x	b(x	NOUN
ejpam-1528	347	18	)	)	PUNCT
ejpam-1528	347	19	of	of	ADP
ejpam-1528	347	20	bounded	bounded	ADJ
ejpam-1528	347	21	operators	operator	NOUN
ejpam-1528	347	22	on	on	ADP
ejpam-1528	347	23	a	a	DET
ejpam-1528	347	24	banach	banach	NOUN
ejpam-1528	347	25	space	space	NOUN
ejpam-1528	347	26	x	x	X
ejpam-1528	347	27	.	.	PUNCT
ejpam-1528	348	1	6.1	6.1	NUM
ejpam-1528	348	2	.	.	PUNCT
ejpam-1528	349	1	local	local	ADJ
ejpam-1528	349	2	spectral	spectral	ADJ
ejpam-1528	349	3	theory	theory	NOUN
ejpam-1528	349	4	in	in	ADP
ejpam-1528	349	5	the	the	DET
ejpam-1528	349	6	operator	operator	NOUN
ejpam-1528	349	7	case	case	NOUN
ejpam-1528	349	8	,	,	PUNCT
ejpam-1528	349	9	we	we	PRON
ejpam-1528	349	10	can	can	AUX
ejpam-1528	349	11	improve	improve	VERB
ejpam-1528	349	12	somehow	somehow	ADV
ejpam-1528	349	13	the	the	DET
ejpam-1528	349	14	results	result	NOUN
ejpam-1528	349	15	of	of	ADP
ejpam-1528	349	16	the	the	DET
ejpam-1528	349	17	previous	previous	ADJ
ejpam-1528	349	18	section	section	NOUN
ejpam-1528	349	19	.	.	PUNCT
ejpam-1528	350	1	let	let	VERB
ejpam-1528	350	2	x	x	PRON
ejpam-1528	350	3	be	be	AUX
ejpam-1528	350	4	a	a	DET
ejpam-1528	350	5	banach	banach	NOUN
ejpam-1528	350	6	space	space	NOUN
ejpam-1528	350	7	and	and	CCONJ
ejpam-1528	350	8	t	t	NOUN
ejpam-1528	350	9	∈	∈	PROPN
ejpam-1528	350	10	b(x	b(x	PROPN
ejpam-1528	350	11	)	)	PUNCT
ejpam-1528	350	12	.	.	PUNCT
ejpam-1528	351	1	t	t	PROPN
ejpam-1528	351	2	(	(	PUNCT
ejpam-1528	351	3	x	x	PROPN
ejpam-1528	351	4	)	)	PUNCT
ejpam-1528	351	5	,	,	PUNCT
ejpam-1528	351	6	or	or	CCONJ
ejpam-1528	351	7	r(t	r(t	NOUN
ejpam-1528	351	8	)	)	PUNCT
ejpam-1528	351	9	denotes	denote	VERB
ejpam-1528	351	10	its	its	PRON
ejpam-1528	351	11	range	range	NOUN
ejpam-1528	351	12	,	,	PUNCT
ejpam-1528	351	13	n(t	n(t	PROPN
ejpam-1528	351	14	)	)	PUNCT
ejpam-1528	351	15	its	its	PRON
ejpam-1528	351	16	kernel	kernel	NOUN
ejpam-1528	351	17	.	.	PUNCT
ejpam-1528	352	1	we	we	PRON
ejpam-1528	352	2	use	use	VERB
ejpam-1528	352	3	ideas	idea	NOUN
ejpam-1528	352	4	from	from	ADP
ejpam-1528	352	5	local	local	ADJ
ejpam-1528	352	6	spectral	spectral	ADJ
ejpam-1528	352	7	theory	theory	NOUN
ejpam-1528	352	8	[	[	X
ejpam-1528	352	9	1	1	NUM
ejpam-1528	352	10	,	,	PUNCT
ejpam-1528	352	11	12	12	NUM
ejpam-1528	352	12	,	,	PUNCT
ejpam-1528	352	13	20	20	NUM
ejpam-1528	352	14	,	,	PUNCT
ejpam-1528	352	15	21	21	NUM
ejpam-1528	352	16	]	]	PUNCT
ejpam-1528	352	17	and	and	CCONJ
ejpam-1528	352	18	define	define	VERB
ejpam-1528	352	19	the	the	DET
ejpam-1528	352	20	following	follow	VERB
ejpam-1528	352	21	sets	set	NOUN
ejpam-1528	352	22	:	:	PUNCT
ejpam-1528	352	23	definition	definition	NOUN
ejpam-1528	352	24	6	6	NUM
ejpam-1528	352	25	.	.	NOUN
ejpam-1528	352	26	•	•	NUM
ejpam-1528	352	27	the	the	DET
ejpam-1528	352	28	hyperrange	hyperrange	NOUN
ejpam-1528	352	29	of	of	ADP
ejpam-1528	352	30	t	t	PROPN
ejpam-1528	352	31	is	be	AUX
ejpam-1528	352	32	the	the	DET
ejpam-1528	352	33	linear	linear	ADJ
ejpam-1528	352	34	space	space	NOUN
ejpam-1528	352	35	t∞(x	t∞(x	NOUN
ejpam-1528	352	36	)	)	PUNCT
ejpam-1528	353	1	=	=	SYM
ejpam-1528	354	1	⋂	⋂	PROPN
ejpam-1528	354	2	n∈n	n∈n	NOUN
ejpam-1528	354	3	t	t	NOUN
ejpam-1528	354	4	n(x	n(x	PROPN
ejpam-1528	354	5	)	)	PUNCT
ejpam-1528	354	6	;	;	PUNCT
ejpam-1528	354	7	•	•	NUM
ejpam-1528	354	8	the	the	DET
ejpam-1528	354	9	hyperkernel	hyperkernel	NOUN
ejpam-1528	354	10	of	of	ADP
ejpam-1528	354	11	t	t	PROPN
ejpam-1528	354	12	is	be	AUX
ejpam-1528	354	13	the	the	DET
ejpam-1528	354	14	linear	linear	ADJ
ejpam-1528	354	15	space	space	NOUN
ejpam-1528	354	16	n∞(t	n∞(t	ADJ
ejpam-1528	354	17	)	)	PUNCT
ejpam-1528	355	1	=	=	PUNCT
ejpam-1528	355	2	⋃	⋃	NOUN
ejpam-1528	355	3	n∈n	n∈n	DET
ejpam-1528	355	4	n(t	n(t	PROPN
ejpam-1528	355	5	n	n	CCONJ
ejpam-1528	355	6	)	)	PUNCT
ejpam-1528	355	7	;	;	PUNCT
ejpam-1528	355	8	•	•	ADP
ejpam-1528	355	9	the	the	DET
ejpam-1528	355	10	quasinilpotent	quasinilpotent	NOUN
ejpam-1528	355	11	part	part	NOUN
ejpam-1528	355	12	(	(	PUNCT
ejpam-1528	355	13	or	or	CCONJ
ejpam-1528	355	14	transfinite	transfinite	ADJ
ejpam-1528	355	15	kernel	kernel	NOUN
ejpam-1528	355	16	)	)	PUNCT
ejpam-1528	355	17	of	of	ADP
ejpam-1528	355	18	t	t	PROPN
ejpam-1528	355	19	is	be	AUX
ejpam-1528	355	20	the	the	DET
ejpam-1528	355	21	linear	linear	ADJ
ejpam-1528	355	22	space	space	NOUN
ejpam-1528	355	23	h0(t	h0(t	X
ejpam-1528	355	24	)	)	PUNCT
ejpam-1528	355	25	=	=	SYM
ejpam-1528	356	1	{	{	PUNCT
ejpam-1528	356	2	x	x	SYM
ejpam-1528	356	3	∈	∈	PROPN
ejpam-1528	356	4	x	x	X
ejpam-1528	356	5	,	,	PUNCT
ejpam-1528	356	6	||t	||t	PROPN
ejpam-1528	356	7	n	n	NOUN
ejpam-1528	356	8	x	x	SYM
ejpam-1528	356	9	||	||	ADP
ejpam-1528	356	10	1	1	NUM
ejpam-1528	356	11	n	n	PROPN
ejpam-1528	356	12	→	→	SYM
ejpam-1528	356	13	0	0	NUM
ejpam-1528	356	14	}	}	PUNCT
ejpam-1528	356	15	;	;	PUNCT
ejpam-1528	356	16	•	•	ADP
ejpam-1528	356	17	the	the	DET
ejpam-1528	356	18	algebraic	algebraic	ADJ
ejpam-1528	356	19	core	core	NOUN
ejpam-1528	356	20	c(t	c(t	PROPN
ejpam-1528	356	21	)	)	PUNCT
ejpam-1528	356	22	of	of	ADP
ejpam-1528	356	23	t	t	PROPN
ejpam-1528	356	24	is	be	AUX
ejpam-1528	356	25	the	the	DET
ejpam-1528	356	26	largest	large	ADJ
ejpam-1528	356	27	subspace	subspace	NOUN
ejpam-1528	356	28	such	such	ADJ
ejpam-1528	356	29	that	that	SCONJ
ejpam-1528	356	30	t	t	PROPN
ejpam-1528	356	31	(	(	PUNCT
ejpam-1528	356	32	m	m	NOUN
ejpam-1528	356	33	)	)	PUNCT
ejpam-1528	356	34	=	=	SYM
ejpam-1528	356	35	m	m	PROPN
ejpam-1528	356	36	;	;	PUNCT
ejpam-1528	356	37	x.	x.	PROPN
ejpam-1528	356	38	mary	mary	PROPN
ejpam-1528	356	39	/	/	SYM
ejpam-1528	356	40	eur	eur	PROPN
ejpam-1528	356	41	.	.	PUNCT
ejpam-1528	357	1	j.	j.	PROPN
ejpam-1528	357	2	pure	pure	PROPN
ejpam-1528	357	3	appl	appl	PROPN
ejpam-1528	357	4	.	.	PROPN
ejpam-1528	357	5	math	math	PROPN
ejpam-1528	357	6	,	,	PUNCT
ejpam-1528	357	7	6	6	NUM
ejpam-1528	357	8	(	(	PUNCT
ejpam-1528	357	9	2013	2013	NUM
ejpam-1528	357	10	)	)	PUNCT
ejpam-1528	357	11	,	,	PUNCT
ejpam-1528	357	12	413	413	NUM
ejpam-1528	357	13	-	-	SYM
ejpam-1528	357	14	427	427	NUM
ejpam-1528	357	15	424	424	NUM
ejpam-1528	357	16	•	•	NOUN
ejpam-1528	357	17	the	the	DET
ejpam-1528	357	18	analytic	analytic	ADJ
ejpam-1528	357	19	core	core	NOUN
ejpam-1528	357	20	(	(	PUNCT
ejpam-1528	357	21	or	or	CCONJ
ejpam-1528	357	22	transfinite	transfinite	VERB
ejpam-1528	357	23	range	range	NOUN
ejpam-1528	357	24	)	)	PUNCT
ejpam-1528	357	25	k(t	k(t	PROPN
ejpam-1528	357	26	)	)	PUNCT
ejpam-1528	357	27	of	of	ADP
ejpam-1528	357	28	t	t	PROPN
ejpam-1528	357	29	consists	consist	VERB
ejpam-1528	357	30	of	of	ADP
ejpam-1528	357	31	all	all	DET
ejpam-1528	357	32	vectors	vector	NOUN
ejpam-1528	357	33	x0	x0	PROPN
ejpam-1528	357	34	∈	∈	PROPN
ejpam-1528	357	35	x	x	PUNCT
ejpam-1528	357	36	for	for	ADP
ejpam-1528	357	37	which	which	PRON
ejpam-1528	357	38	there	there	PRON
ejpam-1528	357	39	exist	exist	VERB
ejpam-1528	357	40	a	a	DET
ejpam-1528	357	41	sequence	sequence	NOUN
ejpam-1528	357	42	xn	xn	SYM
ejpam-1528	357	43	∈	∈	PROPN
ejpam-1528	357	44	x	x	PUNCT
ejpam-1528	357	45	such	such	ADJ
ejpam-1528	357	46	that	that	SCONJ
ejpam-1528	357	47	t	t	NOUN
ejpam-1528	357	48	xn	xn	PUNCT
ejpam-1528	358	1	=	=	SYM
ejpam-1528	358	2	xn−1	xn−1	PROPN
ejpam-1528	358	3	and	and	CCONJ
ejpam-1528	358	4	exists	exist	VERB
ejpam-1528	358	5	c	c	PROPN
ejpam-1528	358	6	>	>	X
ejpam-1528	358	7	0	0	PROPN
ejpam-1528	358	8	,	,	PUNCT
ejpam-1528	358	9	||xn||	||xn||	VERB
ejpam-1528	358	10	≤	≤	NOUN
ejpam-1528	358	11	cn||x0||	cn||x0||	PROPN
ejpam-1528	358	12	.	.	PUNCT
ejpam-1528	359	1	the	the	DET
ejpam-1528	359	2	algebraic	algebraic	PROPN
ejpam-1528	359	3	core	core	NOUN
ejpam-1528	359	4	can	can	AUX
ejpam-1528	359	5	also	also	ADV
ejpam-1528	359	6	be	be	AUX
ejpam-1528	359	7	defined	define	VERB
ejpam-1528	359	8	as	as	SCONJ
ejpam-1528	359	9	follows	follow	VERB
ejpam-1528	359	10	:	:	PUNCT
ejpam-1528	359	11	c(t	c(t	PROPN
ejpam-1528	359	12	)	)	PUNCT
ejpam-1528	359	13	consists	consist	VERB
ejpam-1528	359	14	of	of	ADP
ejpam-1528	359	15	all	all	DET
ejpam-1528	359	16	vectors	vector	NOUN
ejpam-1528	359	17	x0	x0	PROPN
ejpam-1528	359	18	∈	∈	PROPN
ejpam-1528	359	19	x	x	PUNCT
ejpam-1528	359	20	for	for	ADP
ejpam-1528	359	21	which	which	PRON
ejpam-1528	359	22	there	there	PRON
ejpam-1528	359	23	exist	exist	VERB
ejpam-1528	359	24	a	a	DET
ejpam-1528	359	25	sequence	sequence	NOUN
ejpam-1528	359	26	xn	xn	SYM
ejpam-1528	359	27	∈	∈	PROPN
ejpam-1528	359	28	x	x	PUNCT
ejpam-1528	360	1	such	such	ADJ
ejpam-1528	360	2	that	that	SCONJ
ejpam-1528	360	3	t	t	NOUN
ejpam-1528	360	4	xn	xn	PUNCT
ejpam-1528	360	5	=	=	SYM
ejpam-1528	360	6	xn−1	xn−1	PROPN
ejpam-1528	360	7	.	.	PUNCT
ejpam-1528	361	1	we	we	PRON
ejpam-1528	361	2	then	then	ADV
ejpam-1528	361	3	have	have	VERB
ejpam-1528	361	4	the	the	DET
ejpam-1528	361	5	following	follow	VERB
ejpam-1528	361	6	inclusions	inclusion	NOUN
ejpam-1528	361	7	:	:	PUNCT
ejpam-1528	361	8	k(t	k(t	NOUN
ejpam-1528	361	9	)	)	PUNCT
ejpam-1528	362	1	⊂	⊂	PROPN
ejpam-1528	362	2	c(t	c(t	PROPN
ejpam-1528	362	3	)	)	PUNCT
ejpam-1528	362	4	⊂	⊂	PROPN
ejpam-1528	362	5	t∞(x	t∞(x	PROPN
ejpam-1528	362	6	)	)	PUNCT
ejpam-1528	362	7	,	,	PUNCT
ejpam-1528	362	8	n∞(t	n∞(t	INTJ
ejpam-1528	362	9	)	)	PUNCT
ejpam-1528	363	1	⊂	⊂	PROPN
ejpam-1528	363	2	h0(t	h0(t	X
ejpam-1528	363	3	)	)	PUNCT
ejpam-1528	363	4	.	.	PUNCT
ejpam-1528	364	1	in	in	ADP
ejpam-1528	364	2	[	[	X
ejpam-1528	364	3	12	12	NUM
ejpam-1528	364	4	]	]	PUNCT
ejpam-1528	364	5	,	,	PUNCT
ejpam-1528	364	6	it	it	PRON
ejpam-1528	364	7	is	be	AUX
ejpam-1528	364	8	proved	prove	VERB
ejpam-1528	364	9	that	that	SCONJ
ejpam-1528	364	10	for	for	ADP
ejpam-1528	364	11	a	a	DET
ejpam-1528	364	12	bounded	bounded	ADJ
ejpam-1528	364	13	operator	operator	NOUN
ejpam-1528	364	14	t	t	NOUN
ejpam-1528	364	15	,	,	PUNCT
ejpam-1528	364	16	the	the	DET
ejpam-1528	364	17	analytic	analytic	ADJ
ejpam-1528	364	18	core	core	NOUN
ejpam-1528	364	19	corresponds	correspond	VERB
ejpam-1528	364	20	to	to	ADP
ejpam-1528	364	21	the	the	DET
ejpam-1528	364	22	holomorphic	holomorphic	ADJ
ejpam-1528	364	23	range	range	NOUN
ejpam-1528	364	24	{	{	PUNCT
ejpam-1528	364	25	limz→0(t	limz→0(t	NOUN
ejpam-1528	364	26	−	−	PROPN
ejpam-1528	364	27	zi	zi	PROPN
ejpam-1528	364	28	)	)	PUNCT
ejpam-1528	364	29	f	f	PROPN
ejpam-1528	364	30	(	(	PUNCT
ejpam-1528	364	31	z	z	NOUN
ejpam-1528	364	32	)	)	PUNCT
ejpam-1528	364	33	,	,	PUNCT
ejpam-1528	364	34	f	f	PROPN
ejpam-1528	364	35	∈	∈	PROPN
ejpam-1528	364	36	holo(0	holo(0	PROPN
ejpam-1528	364	37	,	,	PUNCT
ejpam-1528	364	38	x	x	NOUN
ejpam-1528	364	39	)	)	PUNCT
ejpam-1528	364	40	}	}	PUNCT
ejpam-1528	364	41	,	,	PUNCT
ejpam-1528	364	42	and	and	CCONJ
ejpam-1528	364	43	that	that	SCONJ
ejpam-1528	364	44	the	the	DET
ejpam-1528	364	45	intersection	intersection	NOUN
ejpam-1528	364	46	if	if	SCONJ
ejpam-1528	364	47	the	the	DET
ejpam-1528	364	48	analytic	analytic	ADJ
ejpam-1528	364	49	core	core	NOUN
ejpam-1528	364	50	with	with	ADP
ejpam-1528	364	51	n(t	n(t	PROPN
ejpam-1528	364	52	)	)	PUNCT
ejpam-1528	364	53	is	be	AUX
ejpam-1528	364	54	the	the	DET
ejpam-1528	364	55	holomorphic	holomorphic	ADJ
ejpam-1528	364	56	kernel	kernel	NOUN
ejpam-1528	364	57	of	of	ADP
ejpam-1528	364	58	t	t	PROPN
ejpam-1528	364	59	{	{	PUNCT
ejpam-1528	364	60	g(0	g(0	PROPN
ejpam-1528	364	61	)	)	PUNCT
ejpam-1528	364	62	,	,	PUNCT
ejpam-1528	364	63	(	(	PUNCT
ejpam-1528	364	64	t	t	PROPN
ejpam-1528	364	65	−	−	PROPN
ejpam-1528	364	66	zi)g(z	zi)g(z	NUM
ejpam-1528	364	67	)	)	PUNCT
ejpam-1528	364	68	=	=	PUNCT
ejpam-1528	364	69	0	0	NUM
ejpam-1528	364	70	,	,	PUNCT
ejpam-1528	364	71	g	g	PROPN
ejpam-1528	364	72	∈	∈	PROPN
ejpam-1528	364	73	holo(0	holo(0	NOUN
ejpam-1528	364	74	,	,	PUNCT
ejpam-1528	364	75	x	x	NOUN
ejpam-1528	364	76	)	)	PUNCT
ejpam-1528	364	77	}	}	PUNCT
ejpam-1528	364	78	.	.	PUNCT
ejpam-1528	365	1	we	we	PRON
ejpam-1528	365	2	have	have	VERB
ejpam-1528	365	3	the	the	DET
ejpam-1528	365	4	following	follow	VERB
ejpam-1528	365	5	relations	relation	NOUN
ejpam-1528	365	6	:	:	PUNCT
ejpam-1528	365	7	proposition	proposition	NOUN
ejpam-1528	365	8	3	3	X
ejpam-1528	365	9	.	.	PUNCT
ejpam-1528	366	1	let	let	VERB
ejpam-1528	366	2	p	p	PROPN
ejpam-1528	366	3	∈	∈	PROPN
ejpam-1528	366	4	σ1(t	σ1(t	X
ejpam-1528	366	5	)	)	PUNCT
ejpam-1528	366	6	.	.	PUNCT
ejpam-1528	367	1	then	then	ADV
ejpam-1528	367	2	p(x	p(x	PROPN
ejpam-1528	367	3	)	)	PUNCT
ejpam-1528	367	4	⊂	⊂	PROPN
ejpam-1528	367	5	k(t	k(t	PUNCT
ejpam-1528	367	6	)	)	PUNCT
ejpam-1528	367	7	and	and	CCONJ
ejpam-1528	367	8	h0(t	h0(t	X
ejpam-1528	367	9	)	)	PUNCT
ejpam-1528	367	10	⊂	⊂	PROPN
ejpam-1528	367	11	n(p	n(p	PROPN
ejpam-1528	367	12	)	)	PUNCT
ejpam-1528	367	13	.	.	PUNCT
ejpam-1528	368	1	proof	proof	NOUN
ejpam-1528	368	2	.	.	PUNCT
ejpam-1528	369	1	let	let	VERB
ejpam-1528	369	2	p	p	PRON
ejpam-1528	369	3	∈	∈	PROPN
ejpam-1528	369	4	σ1(t	σ1(t	X
ejpam-1528	369	5	)	)	PUNCT
ejpam-1528	369	6	.	.	PUNCT
ejpam-1528	370	1	then	then	ADV
ejpam-1528	370	2	p	p	X
ejpam-1528	370	3	=	=	X
ejpam-1528	370	4	t	t	PROPN
ejpam-1528	370	5	t−p	t−p	NUM
ejpam-1528	370	6	p	p	NOUN
ejpam-1528	370	7	=	=	X
ejpam-1528	370	8	t	t	NOUN
ejpam-1528	370	9	t−p	t−p	NUM
ejpam-1528	370	10	=	=	SYM
ejpam-1528	370	11	t−p	t−p	NUM
ejpam-1528	370	12	t	t	NOUN
ejpam-1528	370	13	.	.	PUNCT
ejpam-1528	371	1	let	let	VERB
ejpam-1528	371	2	x0	x0	PROPN
ejpam-1528	371	3	∈	∈	PROPN
ejpam-1528	371	4	p(x	p(x	PROPN
ejpam-1528	371	5	)	)	PUNCT
ejpam-1528	371	6	,	,	PUNCT
ejpam-1528	371	7	and	and	CCONJ
ejpam-1528	371	8	for	for	ADP
ejpam-1528	371	9	all	all	DET
ejpam-1528	371	10	n	n	CCONJ
ejpam-1528	371	11	>	>	X
ejpam-1528	371	12	0	0	NUM
ejpam-1528	371	13	,	,	PUNCT
ejpam-1528	371	14	pose	pose	VERB
ejpam-1528	371	15	xn	xn	PROPN
ejpam-1528	372	1	=	=	SYM
ejpam-1528	372	2	(	(	PUNCT
ejpam-1528	372	3	t−p)n	t−p)n	PROPN
ejpam-1528	372	4	x0	x0	PROPN
ejpam-1528	372	5	.	.	PUNCT
ejpam-1528	373	1	then	then	ADV
ejpam-1528	373	2	t	t	X
ejpam-1528	373	3	xn	xn	PROPN
ejpam-1528	374	1	=	=	SYM
ejpam-1528	374	2	t	t	PROPN
ejpam-1528	374	3	(	(	PUNCT
ejpam-1528	374	4	t−p)n	t−p)n	PROPN
ejpam-1528	374	5	x0	x0	PROPN
ejpam-1528	374	6	=	=	PUNCT
ejpam-1528	375	1	p(t−p)n−1	p(t−p)n−1	NUM
ejpam-1528	375	2	x0	x0	PROPN
ejpam-1528	375	3	=	=	PRON
ejpam-1528	375	4	(	(	PUNCT
ejpam-1528	375	5	t	t	NOUN
ejpam-1528	375	6	−p)n−1p	−p)n−1p	NOUN
ejpam-1528	375	7	x0	x0	PROPN
ejpam-1528	375	8	=	=	PRON
ejpam-1528	375	9	(	(	PUNCT
ejpam-1528	375	10	t	t	PROPN
ejpam-1528	375	11	−p)n−1	−p)n−1	X
ejpam-1528	375	12	x0	x0	PROPN
ejpam-1528	375	13	=	=	PUNCT
ejpam-1528	375	14	xn−1	xn−1	PROPN
ejpam-1528	375	15	.	.	PUNCT
ejpam-1528	376	1	also	also	ADV
ejpam-1528	376	2	||xn||	||xn||	VERB
ejpam-1528	376	3	≤	≤	PROPN
ejpam-1528	376	4	||t−p	||t−p	PROPN
ejpam-1528	376	5	||n||x0||	||n||x0||	PROPN
ejpam-1528	376	6	,	,	PUNCT
ejpam-1528	376	7	hence	hence	ADV
ejpam-1528	376	8	x0	x0	PROPN
ejpam-1528	376	9	∈	∈	PROPN
ejpam-1528	376	10	k(t	k(t	PROPN
ejpam-1528	376	11	)	)	PUNCT
ejpam-1528	376	12	.	.	PUNCT
ejpam-1528	377	1	let	let	VERB
ejpam-1528	377	2	now	now	ADV
ejpam-1528	377	3	x	x	X
ejpam-1528	377	4	∈	∈	PROPN
ejpam-1528	377	5	h0(t	h0(t	X
ejpam-1528	377	6	)	)	PUNCT
ejpam-1528	377	7	.	.	PUNCT
ejpam-1528	378	1	then	then	ADV
ejpam-1528	378	2	p(x	p(x	VERB
ejpam-1528	378	3	)	)	PUNCT
ejpam-1528	378	4	=	=	PUNCT
ejpam-1528	378	5	t−p	t−p	NUM
ejpam-1528	378	6	t	t	NOUN
ejpam-1528	378	7	(	(	PUNCT
ejpam-1528	378	8	x	x	NOUN
ejpam-1528	378	9	)	)	PUNCT
ejpam-1528	378	10	=	=	SYM
ejpam-1528	378	11	(	(	PUNCT
ejpam-1528	378	12	t−p)nt	t−p)nt	PUNCT
ejpam-1528	378	13	n(x	n(x	PROPN
ejpam-1528	378	14	)	)	PUNCT
ejpam-1528	378	15	forall	forall	NOUN
ejpam-1528	378	16	n	n	CCONJ
ejpam-1528	378	17	>	>	X
ejpam-1528	378	18	0	0	NUM
ejpam-1528	379	1	and	and	CCONJ
ejpam-1528	379	2	||p(x)||	||p(x)||	NUM
ejpam-1528	379	3	1	1	NUM
ejpam-1528	379	4	n	n	NOUN
ejpam-1528	379	5	≤	≤	X
ejpam-1528	379	6	||(t−p)n||	||(t−p)n||	VERB
ejpam-1528	379	7	1	1	NUM
ejpam-1528	379	8	n	n	DET
ejpam-1528	379	9	||t	||t	NOUN
ejpam-1528	379	10	n(x)||	n(x)||	ADJ
ejpam-1528	379	11	1	1	NUM
ejpam-1528	379	12	n	n	CCONJ
ejpam-1528	379	13	≤	≤	NUM
ejpam-1528	379	14	||(t−p)||||t	||(t−p)||||t	NOUN
ejpam-1528	379	15	n(x)||	n(x)||	NOUN
ejpam-1528	379	16	1	1	NUM
ejpam-1528	379	17	n	n	NOUN
ejpam-1528	379	18	→	→	SYM
ejpam-1528	379	19	0	0	NUM
ejpam-1528	379	20	and	and	CCONJ
ejpam-1528	379	21	p(x	p(x	PROPN
ejpam-1528	379	22	)	)	PUNCT
ejpam-1528	379	23	=	=	SYM
ejpam-1528	379	24	0	0	X
ejpam-1528	379	25	.	.	PUNCT
ejpam-1528	379	26	corollary	corollary	ADJ
ejpam-1528	379	27	5	5	NUM
ejpam-1528	379	28	.	.	PUNCT
ejpam-1528	379	29	k(t	k(t	PUNCT
ejpam-1528	379	30	)	)	PUNCT
ejpam-1528	380	1	=	=	PUNCT
ejpam-1528	380	2	{	{	PUNCT
ejpam-1528	380	3	0	0	NUM
ejpam-1528	380	4	}	}	PUNCT
ejpam-1528	380	5	⇒	⇒	NOUN
ejpam-1528	380	6	σ1(t	σ1(t	X
ejpam-1528	380	7	)	)	PUNCT
ejpam-1528	380	8	=	=	SYM
ejpam-1528	380	9	{	{	PUNCT
ejpam-1528	380	10	0	0	NUM
ejpam-1528	380	11	}	}	PUNCT
ejpam-1528	380	12	;	;	PUNCT
ejpam-1528	380	13	h0(t	h0(t	X
ejpam-1528	380	14	)	)	PUNCT
ejpam-1528	380	15	=	=	PUNCT
ejpam-1528	380	16	x	x	SYM
ejpam-1528	380	17	⇒	⇒	NOUN
ejpam-1528	380	18	σ1(t	σ1(t	X
ejpam-1528	380	19	)	)	PUNCT
ejpam-1528	380	20	=	=	SYM
ejpam-1528	380	21	{	{	PUNCT
ejpam-1528	380	22	0	0	NUM
ejpam-1528	380	23	}	}	PUNCT
ejpam-1528	380	24	.	.	PUNCT
ejpam-1528	381	1	obviously	obviously	ADV
ejpam-1528	381	2	,	,	PUNCT
ejpam-1528	381	3	the	the	DET
ejpam-1528	381	4	existence	existence	NOUN
ejpam-1528	381	5	of	of	ADP
ejpam-1528	381	6	a	a	DET
ejpam-1528	381	7	greatest	great	ADJ
ejpam-1528	381	8	element	element	NOUN
ejpam-1528	381	9	in	in	ADP
ejpam-1528	381	10	σ2(t	σ2(t	PROPN
ejpam-1528	381	11	)	)	PUNCT
ejpam-1528	381	12	is	be	AUX
ejpam-1528	381	13	guaranteed	guarantee	VERB
ejpam-1528	381	14	by	by	ADP
ejpam-1528	381	15	a	a	DET
ejpam-1528	381	16	decomposition	decomposition	NOUN
ejpam-1528	381	17	of	of	ADP
ejpam-1528	381	18	the	the	DET
ejpam-1528	381	19	form	form	NOUN
ejpam-1528	381	20	x	x	PUNCT
ejpam-1528	381	21	=	=	SYM
ejpam-1528	381	22	h0(t	h0(t	X
ejpam-1528	381	23	)	)	PUNCT
ejpam-1528	381	24	⊕k(t	⊕k(t	PROPN
ejpam-1528	381	25	)	)	PUNCT
ejpam-1528	381	26	,	,	PUNCT
ejpam-1528	381	27	with	with	SCONJ
ejpam-1528	381	28	both	both	DET
ejpam-1528	381	29	subspaces	subspace	NOUN
ejpam-1528	381	30	closed	close	VERB
ejpam-1528	381	31	(	(	PUNCT
ejpam-1528	381	32	choose	choose	VERB
ejpam-1528	381	33	p	p	X
ejpam-1528	381	34	the	the	DET
ejpam-1528	381	35	associated	associated	ADJ
ejpam-1528	381	36	projection	projection	NOUN
ejpam-1528	381	37	on	on	ADP
ejpam-1528	381	38	k(t	k(t	PROPN
ejpam-1528	381	39	)	)	PUNCT
ejpam-1528	381	40	)	)	PUNCT
ejpam-1528	381	41	.	.	PUNCT
ejpam-1528	382	1	but	but	CCONJ
ejpam-1528	382	2	such	such	DET
ejpam-1528	382	3	a	a	DET
ejpam-1528	382	4	decomposition	decomposition	NOUN
ejpam-1528	382	5	occurs	occur	VERB
ejpam-1528	382	6	only	only	ADV
ejpam-1528	382	7	for	for	ADP
ejpam-1528	382	8	quasipolar	quasipolar	ADJ
ejpam-1528	382	9	elements	element	NOUN
ejpam-1528	382	10	:	:	PUNCT
ejpam-1528	382	11	theorem	theorem	VERB
ejpam-1528	382	12	11	11	NUM
ejpam-1528	382	13	.	.	PUNCT
ejpam-1528	383	1	[	[	X
ejpam-1528	383	2	21	21	NUM
ejpam-1528	383	3	,	,	PUNCT
ejpam-1528	383	4	theorem	theorem	VERB
ejpam-1528	383	5	1.6	1.6	NUM
ejpam-1528	383	6	]	]	PUNCT
ejpam-1528	383	7	let	let	VERB
ejpam-1528	383	8	t	t	PROPN
ejpam-1528	383	9	∈	∈	PROPN
ejpam-1528	383	10	b(x	b(x	PROPN
ejpam-1528	383	11	)	)	PUNCT
ejpam-1528	383	12	.	.	PUNCT
ejpam-1528	384	1	then	then	ADV
ejpam-1528	384	2	0	0	NUM
ejpam-1528	384	3	is	be	AUX
ejpam-1528	384	4	an	an	DET
ejpam-1528	384	5	isolated	isolated	ADJ
ejpam-1528	384	6	point	point	NOUN
ejpam-1528	384	7	of	of	ADP
ejpam-1528	384	8	the	the	DET
ejpam-1528	384	9	spectrum	spectrum	NOUN
ejpam-1528	384	10	if	if	SCONJ
ejpam-1528	384	11	and	and	CCONJ
ejpam-1528	384	12	only	only	ADV
ejpam-1528	384	13	if	if	SCONJ
ejpam-1528	384	14	h0(t	h0(t	PROPN
ejpam-1528	384	15	)	)	PUNCT
ejpam-1528	384	16	,	,	PUNCT
ejpam-1528	384	17	k(t	k(t	PROPN
ejpam-1528	384	18	)	)	PUNCT
ejpam-1528	384	19	are	be	AUX
ejpam-1528	384	20	closed	closed	ADJ
ejpam-1528	384	21	and	and	CCONJ
ejpam-1528	384	22	x	x	SYM
ejpam-1528	384	23	=	=	SYM
ejpam-1528	384	24	h0(t	h0(t	X
ejpam-1528	384	25	)	)	PUNCT
ejpam-1528	384	26	⊕	⊕	PROPN
ejpam-1528	384	27	k(t	k(t	PROPN
ejpam-1528	384	28	)	)	PUNCT
ejpam-1528	384	29	.	.	PUNCT
ejpam-1528	385	1	theorem	theorem	NOUN
ejpam-1528	385	2	12	12	NUM
ejpam-1528	385	3	.	.	PUNCT
ejpam-1528	386	1	assume	assume	VERB
ejpam-1528	386	2	k(t	k(t	PROPN
ejpam-1528	386	3	)	)	PUNCT
ejpam-1528	387	1	is	be	AUX
ejpam-1528	387	2	closed	close	VERB
ejpam-1528	387	3	and	and	CCONJ
ejpam-1528	387	4	complemented	complement	VERB
ejpam-1528	387	5	with	with	ADP
ejpam-1528	387	6	complement	complement	NOUN
ejpam-1528	387	7	n	n	DET
ejpam-1528	387	8	hyperinvariant	hyperinvariant	NOUN
ejpam-1528	387	9	,	,	PUNCT
ejpam-1528	387	10	and	and	CCONJ
ejpam-1528	387	11	n(t	n(t	PROPN
ejpam-1528	387	12	)	)	PUNCT
ejpam-1528	387	13	∩	∩	PROPN
ejpam-1528	387	14	k(t	k(t	NOUN
ejpam-1528	387	15	)	)	PUNCT
ejpam-1528	388	1	=	=	PUNCT
ejpam-1528	388	2	{	{	PUNCT
ejpam-1528	388	3	0	0	NUM
ejpam-1528	388	4	}	}	PUNCT
ejpam-1528	388	5	.	.	PUNCT
ejpam-1528	389	1	then	then	ADV
ejpam-1528	389	2	t	t	PROPN
ejpam-1528	389	3	is	be	AUX
ejpam-1528	389	4	naturally	naturally	ADV
ejpam-1528	389	5	invertible	invertible	ADJ
ejpam-1528	389	6	with	with	ADP
ejpam-1528	389	7	greatest	great	ADJ
ejpam-1528	389	8	idempotent	idempotent	NOUN
ejpam-1528	389	9	the	the	DET
ejpam-1528	389	10	projection	projection	NOUN
ejpam-1528	389	11	on	on	ADP
ejpam-1528	389	12	k(t	k(t	PROPN
ejpam-1528	389	13	)	)	PUNCT
ejpam-1528	390	1	parallel	parallel	ADJ
ejpam-1528	390	2	to	to	ADP
ejpam-1528	390	3	n.	n.	PROPN
ejpam-1528	390	4	x.	x.	PROPN
ejpam-1528	390	5	mary	mary	PROPN
ejpam-1528	390	6	/	/	SYM
ejpam-1528	390	7	eur	eur	PROPN
ejpam-1528	390	8	.	.	PUNCT
ejpam-1528	391	1	j.	j.	PROPN
ejpam-1528	391	2	pure	pure	PROPN
ejpam-1528	391	3	appl	appl	PROPN
ejpam-1528	391	4	.	.	PROPN
ejpam-1528	391	5	math	math	PROPN
ejpam-1528	391	6	,	,	PUNCT
ejpam-1528	391	7	6	6	NUM
ejpam-1528	391	8	(	(	PUNCT
ejpam-1528	391	9	2013	2013	NUM
ejpam-1528	391	10	)	)	PUNCT
ejpam-1528	391	11	,	,	PUNCT
ejpam-1528	391	12	413	413	NUM
ejpam-1528	391	13	-	-	SYM
ejpam-1528	391	14	427	427	NUM
ejpam-1528	391	15	425	425	NUM
ejpam-1528	391	16	proof	proof	NOUN
ejpam-1528	391	17	.	.	PUNCT
ejpam-1528	392	1	let	let	VERB
ejpam-1528	392	2	x	x	PUNCT
ejpam-1528	392	3	=	=	PUNCT
ejpam-1528	392	4	k(t	k(t	X
ejpam-1528	392	5	)	)	PUNCT
ejpam-1528	393	1	⊕	⊕	PROPN
ejpam-1528	393	2	n	n	PROPN
ejpam-1528	393	3	and	and	CCONJ
ejpam-1528	393	4	m	m	VERB
ejpam-1528	393	5	the	the	DET
ejpam-1528	393	6	idempotent	idempotent	NOUN
ejpam-1528	393	7	of	of	ADP
ejpam-1528	393	8	the	the	DET
ejpam-1528	393	9	theorem	theorem	NOUN
ejpam-1528	393	10	.	.	PUNCT
ejpam-1528	394	1	first	first	ADV
ejpam-1528	394	2	,	,	PUNCT
ejpam-1528	394	3	we	we	PRON
ejpam-1528	394	4	must	must	AUX
ejpam-1528	394	5	prove	prove	VERB
ejpam-1528	394	6	that	that	SCONJ
ejpam-1528	394	7	m	m	VERB
ejpam-1528	394	8	∈	∈	NOUN
ejpam-1528	394	9	σ2(t	σ2(t	PROPN
ejpam-1528	394	10	)	)	PUNCT
ejpam-1528	394	11	.	.	PUNCT
ejpam-1528	395	1	since	since	SCONJ
ejpam-1528	395	2	k(t	k(t	PROPN
ejpam-1528	395	3	)	)	PUNCT
ejpam-1528	395	4	and	and	CCONJ
ejpam-1528	395	5	n	n	PRON
ejpam-1528	395	6	are	be	AUX
ejpam-1528	395	7	hyperinvariant	hyperinvariant	ADJ
ejpam-1528	395	8	,	,	PUNCT
ejpam-1528	395	9	we	we	PRON
ejpam-1528	395	10	only	only	ADV
ejpam-1528	395	11	have	have	VERB
ejpam-1528	395	12	to	to	PART
ejpam-1528	395	13	prove	prove	VERB
ejpam-1528	395	14	that	that	SCONJ
ejpam-1528	395	15	m	m	VERB
ejpam-1528	395	16	≤h	≤h	NOUN
ejpam-1528	395	17	t	t	NOUN
ejpam-1528	395	18	.	.	PUNCT
ejpam-1528	396	1	consider	consider	VERB
ejpam-1528	396	2	t|k(t	t|k(t	PRON
ejpam-1528	396	3	)	)	PUNCT
ejpam-1528	396	4	:	:	PUNCT
ejpam-1528	396	5	k(t	k(t	X
ejpam-1528	396	6	)	)	PUNCT
ejpam-1528	397	1	→	→	PUNCT
ejpam-1528	397	2	k(t	k(t	NOUN
ejpam-1528	397	3	)	)	PUNCT
ejpam-1528	397	4	the	the	DET
ejpam-1528	397	5	restriction	restriction	NOUN
ejpam-1528	397	6	of	of	ADP
ejpam-1528	397	7	t	t	NOUN
ejpam-1528	397	8	to	to	PART
ejpam-1528	397	9	k(t	k(t	PROPN
ejpam-1528	397	10	)	)	PUNCT
ejpam-1528	397	11	.	.	PUNCT
ejpam-1528	398	1	t|k(t	t|k(t	NOUN
ejpam-1528	398	2	)	)	PUNCT
ejpam-1528	398	3	is	be	AUX
ejpam-1528	398	4	well	well	ADV
ejpam-1528	398	5	defined	define	VERB
ejpam-1528	398	6	since	since	SCONJ
ejpam-1528	398	7	t	t	PROPN
ejpam-1528	398	8	(	(	PUNCT
ejpam-1528	398	9	k(t	k(t	PROPN
ejpam-1528	398	10	)	)	PUNCT
ejpam-1528	398	11	)	)	PUNCT
ejpam-1528	399	1	⊂	⊂	PROPN
ejpam-1528	399	2	k(t	k(t	X
ejpam-1528	399	3	)	)	PUNCT
ejpam-1528	399	4	,	,	PUNCT
ejpam-1528	399	5	and	and	CCONJ
ejpam-1528	399	6	surjective	surjective	VERB
ejpam-1528	399	7	since	since	SCONJ
ejpam-1528	399	8	t	t	PROPN
ejpam-1528	399	9	(	(	PUNCT
ejpam-1528	399	10	k(t	k(t	PROPN
ejpam-1528	399	11	)	)	PUNCT
ejpam-1528	399	12	)	)	PUNCT
ejpam-1528	400	1	=	=	PUNCT
ejpam-1528	400	2	k(t	k(t	NOUN
ejpam-1528	400	3	)	)	PUNCT
ejpam-1528	400	4	.	.	PUNCT
ejpam-1528	401	1	but	but	CCONJ
ejpam-1528	401	2	from	from	ADP
ejpam-1528	401	3	the	the	DET
ejpam-1528	401	4	hypothesis	hypothesis	NOUN
ejpam-1528	401	5	n(t	n(t	PROPN
ejpam-1528	401	6	)	)	PUNCT
ejpam-1528	401	7	⊂	⊂	PROPN
ejpam-1528	402	1	n	n	CCONJ
ejpam-1528	402	2	it	it	PRON
ejpam-1528	402	3	is	be	AUX
ejpam-1528	402	4	also	also	ADV
ejpam-1528	402	5	injective	injective	ADJ
ejpam-1528	402	6	,	,	PUNCT
ejpam-1528	402	7	hence	hence	ADV
ejpam-1528	402	8	invertible	invertible	ADJ
ejpam-1528	402	9	and	and	CCONJ
ejpam-1528	402	10	exists	exist	VERB
ejpam-1528	402	11	s	s	PART
ejpam-1528	402	12	bounded	bounded	ADJ
ejpam-1528	402	13	operator	operator	NOUN
ejpam-1528	402	14	,	,	PUNCT
ejpam-1528	402	15	ts	ts	ADP
ejpam-1528	402	16	=	=	PROPN
ejpam-1528	402	17	st	st	PROPN
ejpam-1528	403	1	=	=	NOUN
ejpam-1528	403	2	m	m	PROPN
ejpam-1528	403	3	.	.	PUNCT
ejpam-1528	404	1	let	let	VERB
ejpam-1528	404	2	now	now	ADV
ejpam-1528	404	3	p	p	X
ejpam-1528	404	4	be	be	AUX
ejpam-1528	404	5	and	and	CCONJ
ejpam-1528	404	6	idempotent	idempotent	ADJ
ejpam-1528	404	7	in	in	ADP
ejpam-1528	404	8	σ2(t	σ2(t	PROPN
ejpam-1528	404	9	)	)	PUNCT
ejpam-1528	404	10	.	.	PUNCT
ejpam-1528	405	1	then	then	ADV
ejpam-1528	405	2	p(x	p(x	PROPN
ejpam-1528	405	3	)	)	PUNCT
ejpam-1528	405	4	⊂	⊂	PROPN
ejpam-1528	405	5	k(t	k(t	PUNCT
ejpam-1528	405	6	)	)	PUNCT
ejpam-1528	405	7	from	from	ADP
ejpam-1528	405	8	proposition	proposition	NOUN
ejpam-1528	405	9	3	3	NUM
ejpam-1528	405	10	,	,	PUNCT
ejpam-1528	405	11	hence	hence	ADV
ejpam-1528	405	12	p(x	p(x	PROPN
ejpam-1528	405	13	)	)	PUNCT
ejpam-1528	405	14	⊂	⊂	PROPN
ejpam-1528	405	15	m(x	m(x	PROPN
ejpam-1528	405	16	)	)	PUNCT
ejpam-1528	405	17	.	.	PUNCT
ejpam-1528	406	1	it	it	PRON
ejpam-1528	406	2	follows	follow	VERB
ejpam-1528	406	3	that	that	DET
ejpam-1528	406	4	pm	pm	NOUN
ejpam-1528	406	5	p	p	NOUN
ejpam-1528	406	6	=	=	PUNCT
ejpam-1528	406	7	p	p	NOUN
ejpam-1528	406	8	and	and	CCONJ
ejpam-1528	406	9	by	by	ADP
ejpam-1528	406	10	commutation	commutation	NOUN
ejpam-1528	406	11	(	(	PUNCT
ejpam-1528	406	12	σ2(t	σ2(t	PROPN
ejpam-1528	406	13	)	)	PUNCT
ejpam-1528	406	14	is	be	AUX
ejpam-1528	406	15	a	a	DET
ejpam-1528	406	16	commutative	commutative	ADJ
ejpam-1528	406	17	semigroup	semigroup	NOUN
ejpam-1528	406	18	)	)	PUNCT
ejpam-1528	406	19	,	,	PUNCT
ejpam-1528	406	20	pm	pm	NOUN
ejpam-1528	406	21	=	=	PUNCT
ejpam-1528	406	22	m	m	VERB
ejpam-1528	406	23	p	p	NOUN
ejpam-1528	406	24	=	=	PUNCT
ejpam-1528	406	25	pm	pm	NOUN
ejpam-1528	406	26	p	p	NOUN
ejpam-1528	406	27	=	=	PROPN
ejpam-1528	406	28	p	p	PROPN
ejpam-1528	406	29	and	and	CCONJ
ejpam-1528	406	30	m	m	PROPN
ejpam-1528	406	31	is	be	AUX
ejpam-1528	406	32	the	the	DET
ejpam-1528	406	33	greatest	great	ADJ
ejpam-1528	406	34	element	element	NOUN
ejpam-1528	406	35	of	of	ADP
ejpam-1528	406	36	σ2(t	σ2(t	PROPN
ejpam-1528	406	37	)	)	PUNCT
ejpam-1528	406	38	.	.	PUNCT
ejpam-1528	407	1	by	by	ADP
ejpam-1528	407	2	the	the	DET
ejpam-1528	407	3	results	result	NOUN
ejpam-1528	407	4	of	of	ADP
ejpam-1528	407	5	harte	harte	PROPN
ejpam-1528	407	6	[	[	X
ejpam-1528	407	7	12	12	NUM
ejpam-1528	407	8	]	]	PUNCT
ejpam-1528	407	9	,	,	PUNCT
ejpam-1528	407	10	n(t	n(t	NOUN
ejpam-1528	407	11	)	)	PUNCT
ejpam-1528	407	12	∩k(t	∩k(t	NOUN
ejpam-1528	407	13	)	)	PUNCT
ejpam-1528	407	14	is	be	AUX
ejpam-1528	407	15	the	the	DET
ejpam-1528	407	16	holomorphic	holomorphic	ADJ
ejpam-1528	407	17	kernel	kernel	NOUN
ejpam-1528	407	18	of	of	ADP
ejpam-1528	407	19	t	t	PROPN
ejpam-1528	407	20	,	,	PUNCT
ejpam-1528	407	21	and	and	CCONJ
ejpam-1528	407	22	it	it	PRON
ejpam-1528	407	23	reduces	reduce	VERB
ejpam-1528	407	24	to	to	ADP
ejpam-1528	407	25	0	0	NUM
ejpam-1528	407	26	precisely	precisely	ADV
ejpam-1528	407	27	when	when	SCONJ
ejpam-1528	407	28	t	t	PROPN
ejpam-1528	407	29	has	have	VERB
ejpam-1528	407	30	the	the	DET
ejpam-1528	407	31	single	single	ADJ
ejpam-1528	407	32	valued	value	VERB
ejpam-1528	407	33	extension	extension	NOUN
ejpam-1528	407	34	property	property	NOUN
ejpam-1528	407	35	(	(	PUNCT
ejpam-1528	407	36	svep	svep	NOUN
ejpam-1528	407	37	)	)	PUNCT
ejpam-1528	407	38	at	at	ADP
ejpam-1528	407	39	0	0	NUM
ejpam-1528	407	40	(	(	PUNCT
ejpam-1528	407	41	theorem	theorem	NOUN
ejpam-1528	407	42	9	9	NUM
ejpam-1528	407	43	p.	p.	NOUN
ejpam-1528	407	44	180	180	NUM
ejpam-1528	407	45	)	)	PUNCT
ejpam-1528	407	46	.	.	PUNCT
ejpam-1528	408	1	we	we	PRON
ejpam-1528	408	2	get	get	VERB
ejpam-1528	408	3	the	the	DET
ejpam-1528	408	4	following	follow	VERB
ejpam-1528	408	5	corollary	corollary	NOUN
ejpam-1528	408	6	.	.	PUNCT
ejpam-1528	409	1	corollary	corollary	ADJ
ejpam-1528	409	2	6	6	NUM
ejpam-1528	409	3	.	.	PUNCT
ejpam-1528	410	1	let	let	VERB
ejpam-1528	410	2	t	t	PROPN
ejpam-1528	410	3	be	be	AUX
ejpam-1528	410	4	a	a	DET
ejpam-1528	410	5	bounded	bounded	ADJ
ejpam-1528	410	6	operator	operator	NOUN
ejpam-1528	410	7	on	on	ADP
ejpam-1528	410	8	x	x	PUNCT
ejpam-1528	410	9	with	with	ADP
ejpam-1528	410	10	the	the	DET
ejpam-1528	410	11	svep	svep	NOUN
ejpam-1528	410	12	at	at	ADP
ejpam-1528	410	13	0	0	NUM
ejpam-1528	410	14	.	.	PUNCT
ejpam-1528	411	1	if	if	SCONJ
ejpam-1528	411	2	k(t	k(t	PROPN
ejpam-1528	411	3	)	)	PUNCT
ejpam-1528	411	4	is	be	AUX
ejpam-1528	411	5	closed	close	VERB
ejpam-1528	411	6	and	and	CCONJ
ejpam-1528	411	7	hyperinvariantly	hyperinvariantly	ADV
ejpam-1528	411	8	complemented	complement	VERB
ejpam-1528	411	9	,	,	PUNCT
ejpam-1528	411	10	then	then	ADV
ejpam-1528	411	11	t	t	PROPN
ejpam-1528	411	12	is	be	AUX
ejpam-1528	411	13	naturally	naturally	ADV
ejpam-1528	411	14	invertible	invertible	ADJ
ejpam-1528	411	15	.	.	PUNCT
ejpam-1528	412	1	as	as	ADP
ejpam-1528	412	2	a	a	DET
ejpam-1528	412	3	final	final	ADJ
ejpam-1528	412	4	result	result	NOUN
ejpam-1528	412	5	,	,	PUNCT
ejpam-1528	412	6	we	we	PRON
ejpam-1528	412	7	investigate	investigate	VERB
ejpam-1528	412	8	the	the	DET
ejpam-1528	412	9	range	range	NOUN
ejpam-1528	412	10	of	of	ADP
ejpam-1528	412	11	the	the	DET
ejpam-1528	412	12	core	core	NOUN
ejpam-1528	412	13	of	of	ADP
ejpam-1528	412	14	a	a	DET
ejpam-1528	412	15	naturally	naturally	ADV
ejpam-1528	412	16	invertible	invertible	ADJ
ejpam-1528	412	17	element	element	NOUN
ejpam-1528	412	18	:	:	PUNCT
ejpam-1528	412	19	proposition	proposition	NOUN
ejpam-1528	412	20	4	4	NUM
ejpam-1528	412	21	.	.	PUNCT
ejpam-1528	413	1	let	let	VERB
ejpam-1528	413	2	t	t	PROPN
ejpam-1528	413	3	be	be	AUX
ejpam-1528	413	4	naturally	naturally	ADV
ejpam-1528	413	5	invertible	invertible	ADJ
ejpam-1528	413	6	with	with	ADP
ejpam-1528	413	7	natural	natural	ADJ
ejpam-1528	413	8	inverse	inverse	NOUN
ejpam-1528	413	9	b	b	PROPN
ejpam-1528	413	10	,	,	PUNCT
ejpam-1528	413	11	greatest	great	ADJ
ejpam-1528	413	12	idempotent	idempotent	NOUN
ejpam-1528	414	1	m	m	NOUN
ejpam-1528	414	2	=	=	PROPN
ejpam-1528	414	3	t	t	PROPN
ejpam-1528	414	4	b	b	PROPN
ejpam-1528	414	5	=	=	SYM
ejpam-1528	414	6	bt	bt	PROPN
ejpam-1528	414	7	and	and	CCONJ
ejpam-1528	414	8	core	core	PROPN
ejpam-1528	414	9	t	t	PROPN
ejpam-1528	414	10	m	m	PROPN
ejpam-1528	414	11	=	=	PROPN
ejpam-1528	414	12	t	t	PROPN
ejpam-1528	414	13	bt	bt	PROPN
ejpam-1528	414	14	.	.	PUNCT
ejpam-1528	415	1	then	then	ADV
ejpam-1528	415	2	kν(t	kν(t	NOUN
ejpam-1528	415	3	)	)	PUNCT
ejpam-1528	416	1	=	=	SYM
ejpam-1528	416	2	t	t	PROPN
ejpam-1528	416	3	m(x	m(x	PROPN
ejpam-1528	416	4	)	)	PUNCT
ejpam-1528	416	5	is	be	AUX
ejpam-1528	416	6	a	a	DET
ejpam-1528	416	7	closed	closed	ADJ
ejpam-1528	416	8	,	,	PUNCT
ejpam-1528	416	9	hyperinvariant	hyperinvariant	NOUN
ejpam-1528	416	10	,	,	PUNCT
ejpam-1528	416	11	complemented	complement	VERB
ejpam-1528	416	12	(	(	PUNCT
ejpam-1528	416	13	with	with	ADP
ejpam-1528	416	14	hyperinvariant	hyperinvariant	PROPN
ejpam-1528	416	15	complement	complement	PROPN
ejpam-1528	416	16	)	)	PUNCT
ejpam-1528	416	17	subspace	subspace	NOUN
ejpam-1528	416	18	of	of	ADP
ejpam-1528	416	19	the	the	DET
ejpam-1528	416	20	analytic	analytic	ADJ
ejpam-1528	416	21	core	core	NOUN
ejpam-1528	416	22	k(t	k(t	PROPN
ejpam-1528	416	23	)	)	PUNCT
ejpam-1528	416	24	,	,	PUNCT
ejpam-1528	416	25	and	and	CCONJ
ejpam-1528	416	26	t	t	PROPN
ejpam-1528	416	27	kν(t	kν(t	PUNCT
ejpam-1528	416	28	)	)	PUNCT
ejpam-1528	417	1	=	=	SYM
ejpam-1528	417	2	kν(t	kν(t	NOUN
ejpam-1528	417	3	)	)	PUNCT
ejpam-1528	417	4	.	.	PUNCT
ejpam-1528	418	1	proof	proof	NOUN
ejpam-1528	418	2	.	.	PUNCT
ejpam-1528	419	1	by	by	ADP
ejpam-1528	419	2	commutation	commutation	NOUN
ejpam-1528	419	3	,	,	PUNCT
ejpam-1528	419	4	t	t	PROPN
ejpam-1528	419	5	m(x	m(x	PROPN
ejpam-1528	419	6	)	)	PUNCT
ejpam-1528	419	7	⊂	⊂	PROPN
ejpam-1528	419	8	m(x	m(x	PROPN
ejpam-1528	419	9	)	)	PUNCT
ejpam-1528	419	10	.	.	PUNCT
ejpam-1528	420	1	but	but	CCONJ
ejpam-1528	420	2	also	also	ADV
ejpam-1528	420	3	m(x	m(x	NOUN
ejpam-1528	420	4	)	)	PUNCT
ejpam-1528	421	1	=	=	PUNCT
ejpam-1528	421	2	m2(x	m2(x	PROPN
ejpam-1528	421	3	)	)	PUNCT
ejpam-1528	422	1	=	=	SYM
ejpam-1528	422	2	bt	bt	X
ejpam-1528	422	3	m(x	m(x	PROPN
ejpam-1528	422	4	)	)	PUNCT
ejpam-1528	423	1	⊂	⊂	PROPN
ejpam-1528	423	2	t	t	PROPN
ejpam-1528	423	3	m(x	m(x	PROPN
ejpam-1528	423	4	)	)	PUNCT
ejpam-1528	423	5	and	and	CCONJ
ejpam-1528	423	6	the	the	DET
ejpam-1528	423	7	two	two	NUM
ejpam-1528	423	8	subspaces	subspace	NOUN
ejpam-1528	423	9	are	be	AUX
ejpam-1528	423	10	equal	equal	ADJ
ejpam-1528	423	11	.	.	PUNCT
ejpam-1528	424	1	the	the	DET
ejpam-1528	424	2	other	other	ADJ
ejpam-1528	424	3	properties	property	NOUN
ejpam-1528	424	4	follow	follow	VERB
ejpam-1528	424	5	.	.	PUNCT
ejpam-1528	425	1	6.2	6.2	NUM
ejpam-1528	425	2	.	.	PUNCT
ejpam-1528	425	3	miscellanous	miscellanous	ADJ
ejpam-1528	425	4	in	in	ADP
ejpam-1528	425	5	this	this	DET
ejpam-1528	425	6	last	last	ADJ
ejpam-1528	425	7	section	section	NOUN
ejpam-1528	425	8	we	we	PRON
ejpam-1528	425	9	give	give	VERB
ejpam-1528	425	10	examples	example	NOUN
ejpam-1528	425	11	and	and	CCONJ
ejpam-1528	425	12	results	result	NOUN
ejpam-1528	425	13	relative	relative	ADJ
ejpam-1528	425	14	to	to	ADP
ejpam-1528	425	15	natural	natural	ADJ
ejpam-1528	425	16	invertiblity	invertiblity	NOUN
ejpam-1528	425	17	.	.	PUNCT
ejpam-1528	426	1	the	the	DET
ejpam-1528	426	2	shift	shift	NOUN
ejpam-1528	426	3	operator	operator	NOUN
ejpam-1528	426	4	let	let	VERB
ejpam-1528	426	5	s	s	PRON
ejpam-1528	426	6	be	be	AUX
ejpam-1528	426	7	the	the	DET
ejpam-1528	426	8	shift	shift	NOUN
ejpam-1528	426	9	operator	operator	NOUN
ejpam-1528	426	10	on	on	ADP
ejpam-1528	426	11	l2(n	l2(n	NOUN
ejpam-1528	426	12	)	)	PUNCT
ejpam-1528	426	13	.	.	PUNCT
ejpam-1528	427	1	then	then	ADV
ejpam-1528	427	2	s	s	VERB
ejpam-1528	427	3	is	be	AUX
ejpam-1528	427	4	not	not	PART
ejpam-1528	427	5	quasinilpotent	quasinilpotent	ADJ
ejpam-1528	427	6	,	,	PUNCT
ejpam-1528	427	7	but	but	CCONJ
ejpam-1528	427	8	its	its	PRON
ejpam-1528	427	9	hyperrange	hyperrange	NOUN
ejpam-1528	427	10	reduces	reduce	VERB
ejpam-1528	427	11	to	to	ADP
ejpam-1528	427	12	0	0	NUM
ejpam-1528	427	13	.	.	PUNCT
ejpam-1528	428	1	as	as	ADP
ejpam-1528	428	2	a	a	DET
ejpam-1528	428	3	consequence	consequence	NOUN
ejpam-1528	428	4	,	,	PUNCT
ejpam-1528	428	5	σ1(s	σ1(s	X
ejpam-1528	428	6	)	)	PUNCT
ejpam-1528	428	7	=	=	SYM
ejpam-1528	428	8	{	{	PUNCT
ejpam-1528	428	9	0	0	NUM
ejpam-1528	428	10	}	}	PUNCT
ejpam-1528	428	11	.	.	PUNCT
ejpam-1528	429	1	the	the	DET
ejpam-1528	429	2	spectrum	spectrum	NOUN
ejpam-1528	429	3	of	of	ADP
ejpam-1528	429	4	s	s	PROPN
ejpam-1528	429	5	is	be	AUX
ejpam-1528	429	6	the	the	DET
ejpam-1528	429	7	unit	unit	NOUN
ejpam-1528	429	8	disk	disk	NOUN
ejpam-1528	429	9	.	.	PUNCT
ejpam-1528	430	1	6.2.1	6.2.1	NOUN
ejpam-1528	430	2	.	.	PUNCT
ejpam-1528	431	1	strongly	strongly	ADV
ejpam-1528	431	2	irreducible	irreducible	ADJ
ejpam-1528	431	3	operators	operator	NOUN
ejpam-1528	431	4	in	in	ADP
ejpam-1528	431	5	1972	1972	NUM
ejpam-1528	431	6	,	,	PUNCT
ejpam-1528	431	7	f.	f.	PROPN
ejpam-1528	431	8	gilfeather	gilfeather	NOUN
ejpam-1528	432	1	[	[	X
ejpam-1528	432	2	8	8	NUM
ejpam-1528	432	3	]	]	PUNCT
ejpam-1528	432	4	introduced	introduce	VERB
ejpam-1528	432	5	the	the	DET
ejpam-1528	432	6	concept	concept	NOUN
ejpam-1528	432	7	of	of	ADP
ejpam-1528	432	8	strongly	strongly	ADV
ejpam-1528	432	9	irreducible	irreducible	ADJ
ejpam-1528	432	10	operator	operator	NOUN
ejpam-1528	432	11	.	.	PUNCT
ejpam-1528	433	1	a	a	DET
ejpam-1528	433	2	bounded	bounded	ADJ
ejpam-1528	433	3	linear	linear	ADJ
ejpam-1528	433	4	operator	operator	NOUN
ejpam-1528	433	5	t	t	NOUN
ejpam-1528	433	6	is	be	AUX
ejpam-1528	433	7	said	say	VERB
ejpam-1528	433	8	to	to	PART
ejpam-1528	433	9	be	be	AUX
ejpam-1528	433	10	strongly	strongly	ADV
ejpam-1528	433	11	irreducible	irreducible	ADJ
ejpam-1528	433	12	,	,	PUNCT
ejpam-1528	433	13	if	if	SCONJ
ejpam-1528	433	14	there	there	PRON
ejpam-1528	433	15	exists	exist	VERB
ejpam-1528	433	16	no	no	DET
ejpam-1528	433	17	non	non	ADJ
ejpam-1528	433	18	-	-	ADJ
ejpam-1528	433	19	trivial	trivial	ADJ
ejpam-1528	433	20	idempotent	idempotent	NOUN
ejpam-1528	433	21	p	p	NOUN
ejpam-1528	433	22	in	in	ADP
ejpam-1528	433	23	the	the	DET
ejpam-1528	433	24	commutant	commutant	NOUN
ejpam-1528	433	25	of	of	ADP
ejpam-1528	433	26	t	t	PROPN
ejpam-1528	433	27	.	.	PUNCT
ejpam-1528	434	1	this	this	DET
ejpam-1528	434	2	concept	concept	NOUN
ejpam-1528	434	3	actually	actually	ADV
ejpam-1528	434	4	coincides	coincide	VERB
ejpam-1528	434	5	with	with	ADP
ejpam-1528	434	6	the	the	DET
ejpam-1528	434	7	concept	concept	NOUN
ejpam-1528	434	8	of	of	ADP
ejpam-1528	434	9	banach	banach	ADV
ejpam-1528	434	10	irreducible	irreducible	ADJ
ejpam-1528	434	11	operator	operator	NOUN
ejpam-1528	434	12	(	(	PUNCT
ejpam-1528	434	13	a	a	DET
ejpam-1528	434	14	bounded	bounded	ADJ
ejpam-1528	434	15	linear	linear	ADJ
ejpam-1528	434	16	operator	operator	NOUN
ejpam-1528	434	17	t	t	NOUN
ejpam-1528	434	18	is	be	AUX
ejpam-1528	434	19	said	say	VERB
ejpam-1528	434	20	to	to	PART
ejpam-1528	434	21	be	be	AUX
ejpam-1528	434	22	banach	banach	ADV
ejpam-1528	434	23	irreducible	irreducible	ADJ
ejpam-1528	434	24	,	,	PUNCT
ejpam-1528	434	25	if	if	SCONJ
ejpam-1528	434	26	t	t	PROPN
ejpam-1528	434	27	can	can	AUX
ejpam-1528	434	28	not	not	PART
ejpam-1528	434	29	be	be	AUX
ejpam-1528	434	30	written	write	VERB
ejpam-1528	434	31	as	as	ADP
ejpam-1528	434	32	a	a	DET
ejpam-1528	434	33	direct	direct	ADJ
ejpam-1528	434	34	sum	sum	NOUN
ejpam-1528	434	35	of	of	ADP
ejpam-1528	434	36	two	two	NUM
ejpam-1528	434	37	bounded	bounded	ADJ
ejpam-1528	434	38	linear	linear	PROPN
ejpam-1528	434	39	operators	operator	NOUN
ejpam-1528	434	40	)	)	PUNCT
ejpam-1528	434	41	.	.	PUNCT
ejpam-1528	435	1	it	it	PRON
ejpam-1528	435	2	is	be	AUX
ejpam-1528	435	3	clear	clear	ADJ
ejpam-1528	435	4	that	that	SCONJ
ejpam-1528	435	5	strongly	strongly	ADV
ejpam-1528	435	6	irreducible	irreducible	ADJ
ejpam-1528	435	7	operators	operator	NOUN
ejpam-1528	435	8	satisfy	satisfy	VERB
ejpam-1528	435	9	σ1(t	σ1(t	PUNCT
ejpam-1528	435	10	)	)	PUNCT
ejpam-1528	435	11	=	=	SYM
ejpam-1528	435	12	{	{	PUNCT
ejpam-1528	435	13	0	0	NUM
ejpam-1528	435	14	}	}	PUNCT
ejpam-1528	435	15	.	.	PUNCT
ejpam-1528	436	1	also	also	ADV
ejpam-1528	436	2	,	,	PUNCT
ejpam-1528	436	3	the	the	DET
ejpam-1528	436	4	following	follow	VERB
ejpam-1528	436	5	spectral	spectral	ADJ
ejpam-1528	436	6	result	result	NOUN
ejpam-1528	436	7	is	be	AUX
ejpam-1528	436	8	due	due	ADJ
ejpam-1528	436	9	to	to	ADP
ejpam-1528	436	10	herrero	herrero	PROPN
ejpam-1528	436	11	and	and	CCONJ
ejpam-1528	436	12	jiang	jiang	PROPN
ejpam-1528	437	1	[	[	X
ejpam-1528	437	2	13	13	NUM
ejpam-1528	437	3	]	]	NUM
ejpam-1528	437	4	:	:	PUNCT
ejpam-1528	437	5	theorem	theorem	VERB
ejpam-1528	437	6	13	13	NUM
ejpam-1528	437	7	.	.	PUNCT
ejpam-1528	438	1	σ(t	σ(t	PROPN
ejpam-1528	438	2	)	)	PUNCT
ejpam-1528	438	3	is	be	AUX
ejpam-1528	438	4	connected	connect	VERB
ejpam-1528	438	5	if	if	SCONJ
ejpam-1528	438	6	and	and	CCONJ
ejpam-1528	438	7	only	only	ADV
ejpam-1528	438	8	if	if	SCONJ
ejpam-1528	438	9	t	t	PROPN
ejpam-1528	438	10	is	be	AUX
ejpam-1528	438	11	in	in	ADP
ejpam-1528	438	12	the	the	DET
ejpam-1528	438	13	norm	norm	NOUN
ejpam-1528	438	14	closure	closure	NOUN
ejpam-1528	438	15	of	of	ADP
ejpam-1528	438	16	strongly	strongly	ADV
ejpam-1528	438	17	irreducible	irreducible	ADJ
ejpam-1528	438	18	operators	operator	NOUN
ejpam-1528	438	19	.	.	PUNCT
ejpam-1528	439	1	references	reference	NOUN
ejpam-1528	439	2	426	426	NUM
ejpam-1528	439	3	6.2.2	6.2.2	NUM
ejpam-1528	439	4	.	.	PUNCT
ejpam-1528	440	1	rosenblum	rosenblum	PROPN
ejpam-1528	440	2	’s	’s	PART
ejpam-1528	440	3	corollary	corollary	ADJ
ejpam-1528	440	4	,	,	PUNCT
ejpam-1528	440	5	commutant	commutant	ADJ
ejpam-1528	440	6	and	and	CCONJ
ejpam-1528	440	7	bicommutant	bicommutant	NOUN
ejpam-1528	440	8	let	let	AUX
ejpam-1528	440	9	t	t	PROPN
ejpam-1528	440	10	=	=	SYM
ejpam-1528	440	11	�	�	PROPN
ejpam-1528	440	12	x	x	SYM
ejpam-1528	440	13	0	0	NUM
ejpam-1528	440	14	0	0	NUM
ejpam-1528	440	15	y	y	PROPN
ejpam-1528	440	16	�	�	PROPN
ejpam-1528	440	17	be	be	AUX
ejpam-1528	440	18	the	the	DET
ejpam-1528	440	19	a	a	DET
ejpam-1528	440	20	decomposition	decomposition	NOUN
ejpam-1528	440	21	of	of	ADP
ejpam-1528	440	22	t	t	PROPN
ejpam-1528	440	23	with	with	ADP
ejpam-1528	440	24	x	x	SYM
ejpam-1528	440	25	invertible	invertible	ADJ
ejpam-1528	440	26	and	and	CCONJ
ejpam-1528	440	27	m	m	NOUN
ejpam-1528	440	28	=	=	ADJ
ejpam-1528	440	29	�	�	PROPN
ejpam-1528	440	30	x	x	PUNCT
ejpam-1528	441	1	x−1	x−1	NOUN
ejpam-1528	441	2	0	0	NUM
ejpam-1528	441	3	0	0	SYM
ejpam-1528	441	4	0	0	NUM
ejpam-1528	441	5	�	�	PROPN
ejpam-1528	441	6	the	the	DET
ejpam-1528	441	7	greatest	great	ADJ
ejpam-1528	441	8	element	element	NOUN
ejpam-1528	441	9	of	of	ADP
ejpam-1528	441	10	σ1(t	σ1(t	PROPN
ejpam-1528	441	11	)	)	PUNCT
ejpam-1528	441	12	.	.	PUNCT
ejpam-1528	442	1	if	if	SCONJ
ejpam-1528	442	2	σ(x	σ(x	PROPN
ejpam-1528	442	3	)	)	PUNCT
ejpam-1528	442	4	∩	∩	NOUN
ejpam-1528	442	5	σ(y	σ(y	PROPN
ejpam-1528	442	6	)	)	PUNCT
ejpam-1528	443	1	=	=	PUNCT
ejpam-1528	443	2	{	{	PUNCT
ejpam-1528	443	3	0	0	NUM
ejpam-1528	443	4	}	}	PUNCT
ejpam-1528	443	5	,	,	PUNCT
ejpam-1528	443	6	then	then	ADV
ejpam-1528	443	7	by	by	ADP
ejpam-1528	443	8	rosenblum	rosenblum	PROPN
ejpam-1528	443	9	’s	’s	PART
ejpam-1528	443	10	corollary	corollary	NOUN
ejpam-1528	443	11	(	(	PUNCT
ejpam-1528	443	12	see	see	VERB
ejpam-1528	443	13	[	[	X
ejpam-1528	443	14	23	23	NUM
ejpam-1528	443	15	]	]	NUM
ejpam-1528	443	16	)	)	PUNCT
ejpam-1528	443	17	,	,	PUNCT
ejpam-1528	443	18	�	�	PROPN
ejpam-1528	443	19	x	x	SYM
ejpam-1528	443	20	0	0	NUM
ejpam-1528	443	21	0	0	SYM
ejpam-1528	443	22	0	0	NUM
ejpam-1528	443	23	�	�	PROPN
ejpam-1528	443	24	,	,	PUNCT
ejpam-1528	443	25	�	�	PROPN
ejpam-1528	443	26	0	0	NUM
ejpam-1528	443	27	0	0	NUM
ejpam-1528	443	28	0	0	NUM
ejpam-1528	444	1	y	y	PROPN
ejpam-1528	444	2	�	�	PROPN
ejpam-1528	444	3	∈	∈	PROPN
ejpam-1528	444	4	{	{	PUNCT
ejpam-1528	444	5	t}′′	t}′′	PROPN
ejpam-1528	444	6	and	and	CCONJ
ejpam-1528	444	7	t	t	PROPN
ejpam-1528	444	8	=	=	SYM
ejpam-1528	444	9	�	�	PROPN
ejpam-1528	444	10	x	x	SYM
ejpam-1528	444	11	0	0	NUM
ejpam-1528	444	12	0	0	NUM
ejpam-1528	444	13	0	0	NUM
ejpam-1528	444	14	�	�	PROPN
ejpam-1528	444	15	+	+	CCONJ
ejpam-1528	444	16	�	�	PROPN
ejpam-1528	444	17	0	0	NUM
ejpam-1528	444	18	0	0	NUM
ejpam-1528	444	19	0	0	NUM
ejpam-1528	444	20	y	y	PROPN
ejpam-1528	444	21	�	�	PROPN
ejpam-1528	444	22	is	be	AUX
ejpam-1528	444	23	the	the	DET
ejpam-1528	444	24	natural	natural	ADJ
ejpam-1528	444	25	core	core	NOUN
ejpam-1528	444	26	decomposition	decomposition	NOUN
ejpam-1528	444	27	of	of	ADP
ejpam-1528	444	28	t	t	PROPN
ejpam-1528	444	29	,	,	PUNCT
ejpam-1528	444	30	with	with	ADP
ejpam-1528	444	31	m	m	PROPN
ejpam-1528	444	32	=	=	SYM
ejpam-1528	444	33	�	�	PROPN
ejpam-1528	444	34	x	x	PUNCT
ejpam-1528	444	35	x−1	x−1	NOUN
ejpam-1528	444	36	0	0	NUM
ejpam-1528	444	37	0	0	SYM
ejpam-1528	444	38	0	0	NUM
ejpam-1528	444	39	�	�	PROPN
ejpam-1528	444	40	the	the	DET
ejpam-1528	444	41	greatest	great	ADJ
ejpam-1528	444	42	element	element	NOUN
ejpam-1528	444	43	of	of	ADP
ejpam-1528	444	44	σ2(t	σ2(t	PROPN
ejpam-1528	444	45	)	)	PUNCT
ejpam-1528	444	46	.	.	PUNCT
ejpam-1528	445	1	this	this	PRON
ejpam-1528	445	2	is	be	AUX
ejpam-1528	445	3	the	the	DET
ejpam-1528	445	4	case	case	NOUN
ejpam-1528	445	5	for	for	ADP
ejpam-1528	445	6	instance	instance	NOUN
ejpam-1528	445	7	when	when	SCONJ
ejpam-1528	445	8	y	y	PROPN
ejpam-1528	445	9	is	be	AUX
ejpam-1528	445	10	quasinilpotent	quasinilpotent	NOUN
ejpam-1528	445	11	.	.	PUNCT
ejpam-1528	446	1	references	reference	NOUN
ejpam-1528	446	2	[	[	X
ejpam-1528	446	3	1	1	X
ejpam-1528	446	4	]	]	PUNCT
ejpam-1528	446	5	p.	p.	NOUN
ejpam-1528	446	6	aiena	aiena	PROPN
ejpam-1528	446	7	.	.	PUNCT
ejpam-1528	447	1	fredholm	fredholm	NOUN
ejpam-1528	447	2	and	and	CCONJ
ejpam-1528	447	3	local	local	ADJ
ejpam-1528	447	4	spectral	spectral	ADJ
ejpam-1528	447	5	theory	theory	NOUN
ejpam-1528	447	6	,	,	PUNCT
ejpam-1528	447	7	with	with	ADP
ejpam-1528	447	8	applications	application	NOUN
ejpam-1528	447	9	to	to	ADP
ejpam-1528	447	10	multipliers	multiplier	NOUN
ejpam-1528	447	11	,	,	PUNCT
ejpam-1528	447	12	kluwer	kluwer	NOUN
ejpam-1528	447	13	academic	academic	ADJ
ejpam-1528	447	14	publishers	publisher	NOUN
ejpam-1528	447	15	,	,	PUNCT
ejpam-1528	447	16	boston	boston	PROPN
ejpam-1528	447	17	,	,	PUNCT
ejpam-1528	447	18	uus	uus	PROPN
ejpam-1528	447	19	.	.	PROPN
ejpam-1528	447	20	2004	2004	NUM
ejpam-1528	448	1	[	[	X
ejpam-1528	448	2	2	2	NUM
ejpam-1528	448	3	]	]	PUNCT
ejpam-1528	448	4	a.	a.	PROPN
ejpam-1528	448	5	b.	b.	PROPN
ejpam-1528	448	6	israel	israel	PROPN
ejpam-1528	448	7	and	and	CCONJ
ejpam-1528	448	8	t.n.e	t.n.e	PROPN
ejpam-1528	448	9	.	.	PUNCT
ejpam-1528	449	1	greville	greville	NOUN
ejpam-1528	449	2	.	.	PUNCT
ejpam-1528	450	1	generalized	generalized	ADJ
ejpam-1528	450	2	inverses	inverse	NOUN
ejpam-1528	450	3	,	,	PUNCT
ejpam-1528	450	4	theory	theory	NOUN
ejpam-1528	450	5	and	and	CCONJ
ejpam-1528	450	6	applications	application	NOUN
ejpam-1528	450	7	,	,	PUNCT
ejpam-1528	450	8	2nd	2nd	PROPN
ejpam-1528	450	9	edition	edition	NOUN
ejpam-1528	450	10	,	,	PUNCT
ejpam-1528	450	11	springer	springer	NOUN
ejpam-1528	450	12	2003	2003	NUM
ejpam-1528	450	13	.	.	PUNCT
ejpam-1528	451	1	[	[	X
ejpam-1528	451	2	3	3	X
ejpam-1528	451	3	]	]	PUNCT
ejpam-1528	451	4	m.	m.	NOUN
ejpam-1528	451	5	p.	p.	PROPN
ejpam-1528	451	6	dorofeeva	dorofeeva	PROPN
ejpam-1528	451	7	.	.	PUNCT
ejpam-1528	452	1	hereditary	hereditary	ADJ
ejpam-1528	452	2	and	and	CCONJ
ejpam-1528	452	3	semi	semi	ADJ
ejpam-1528	452	4	-	-	ADJ
ejpam-1528	452	5	hereditary	hereditary	ADJ
ejpam-1528	452	6	monoids	monoid	NOUN
ejpam-1528	452	7	,	,	PUNCT
ejpam-1528	452	8	semigroup	semigroup	PROPN
ejpam-1528	452	9	forum	forum	PROPN
ejpam-1528	452	10	4	4	NUM
ejpam-1528	452	11	,	,	PUNCT
ejpam-1528	452	12	301–311	301–311	NUM
ejpam-1528	452	13	.	.	PUNCT
ejpam-1528	452	14	1972	1972	NUM
ejpam-1528	452	15	.	.	PUNCT
ejpam-1528	453	1	[	[	X
ejpam-1528	453	2	4	4	NUM
ejpam-1528	453	3	]	]	X
ejpam-1528	453	4	m.p	m.p	PROPN
ejpam-1528	453	5	.	.	PROPN
ejpam-1528	453	6	drazin	drazin	PROPN
ejpam-1528	453	7	.	.	PUNCT
ejpam-1528	454	1	pseudo	pseudo	NOUN
ejpam-1528	454	2	-	-	NOUN
ejpam-1528	454	3	inverses	inverse	NOUN
ejpam-1528	454	4	in	in	ADP
ejpam-1528	454	5	associative	associative	ADJ
ejpam-1528	454	6	rings	ring	NOUN
ejpam-1528	454	7	and	and	CCONJ
ejpam-1528	454	8	semigroups	semigroup	NOUN
ejpam-1528	454	9	,	,	PUNCT
ejpam-1528	454	10	american	american	PROPN
ejpam-1528	454	11	mathematical	mathematical	PROPN
ejpam-1528	454	12	monthly	monthly	ADJ
ejpam-1528	454	13	65	65	NUM
ejpam-1528	454	14	,	,	PUNCT
ejpam-1528	454	15	no	no	INTJ
ejpam-1528	454	16	.	.	NOUN
ejpam-1528	454	17	7	7	NUM
ejpam-1528	454	18	,	,	PUNCT
ejpam-1528	454	19	506–514	506–514	NUM
ejpam-1528	454	20	.	.	NOUN
ejpam-1528	454	21	1958	1958	NUM
ejpam-1528	455	1	[	[	X
ejpam-1528	455	2	5	5	NUM
ejpam-1528	455	3	]	]	X
ejpam-1528	455	4	m.p	m.p	PROPN
ejpam-1528	455	5	.	.	PROPN
ejpam-1528	455	6	drazin	drazin	PROPN
ejpam-1528	455	7	.	.	PUNCT
ejpam-1528	456	1	a	a	DET
ejpam-1528	456	2	class	class	NOUN
ejpam-1528	456	3	of	of	ADP
ejpam-1528	456	4	outer	outer	ADJ
ejpam-1528	456	5	generalized	generalize	VERB
ejpam-1528	456	6	inverses	inverse	NOUN
ejpam-1528	456	7	,	,	PUNCT
ejpam-1528	456	8	linear	linear	ADJ
ejpam-1528	456	9	algebra	algebra	NOUN
ejpam-1528	456	10	and	and	CCONJ
ejpam-1528	456	11	its	its	PRON
ejpam-1528	456	12	applications	application	NOUN
ejpam-1528	456	13	436	436	NUM
ejpam-1528	456	14	,	,	PUNCT
ejpam-1528	456	15	no	no	INTJ
ejpam-1528	456	16	.	.	NOUN
ejpam-1528	456	17	7	7	NUM
ejpam-1528	456	18	,	,	PUNCT
ejpam-1528	456	19	1909–1923	1909–1923	NUM
ejpam-1528	456	20	2012	2012	NUM
ejpam-1528	456	21	.	.	PUNCT
ejpam-1528	457	1	[	[	X
ejpam-1528	457	2	6	6	NUM
ejpam-1528	457	3	]	]	PUNCT
ejpam-1528	457	4	j.	j.	PROPN
ejpam-1528	457	5	fountain	fountain	PROPN
ejpam-1528	457	6	.	.	PUNCT
ejpam-1528	458	1	right	right	INTJ
ejpam-1528	458	2	pp	pp	ADV
ejpam-1528	458	3	monoids	monoid	NOUN
ejpam-1528	458	4	with	with	ADP
ejpam-1528	458	5	central	central	ADJ
ejpam-1528	458	6	idempotents	idempotent	NOUN
ejpam-1528	458	7	,	,	PUNCT
ejpam-1528	458	8	semigroup	semigroup	PROPN
ejpam-1528	458	9	forum	forum	PROPN
ejpam-1528	458	10	13	13	NUM
ejpam-1528	458	11	,	,	PUNCT
ejpam-1528	458	12	no	no	INTJ
ejpam-1528	458	13	.	.	NOUN
ejpam-1528	458	14	3	3	NUM
ejpam-1528	458	15	,	,	PUNCT
ejpam-1528	458	16	229–237	229–237	NUM
ejpam-1528	458	17	.	.	PUNCT
ejpam-1528	458	18	1977	1977	NUM
ejpam-1528	458	19	.	.	PUNCT
ejpam-1528	459	1	[	[	X
ejpam-1528	459	2	7	7	X
ejpam-1528	459	3	]	]	X
ejpam-1528	459	4	j.	j.	PROPN
ejpam-1528	459	5	fountain	fountain	PROPN
ejpam-1528	459	6	.	.	PUNCT
ejpam-1528	460	1	abundant	abundant	ADJ
ejpam-1528	460	2	semigroups	semigroup	NOUN
ejpam-1528	460	3	,	,	PUNCT
ejpam-1528	460	4	proceedings	proceeding	NOUN
ejpam-1528	460	5	of	of	ADP
ejpam-1528	460	6	the	the	DET
ejpam-1528	460	7	london	london	PROPN
ejpam-1528	460	8	mathematical	mathematical	ADJ
ejpam-1528	460	9	society	society	NOUN
ejpam-1528	460	10	3	3	NUM
ejpam-1528	460	11	,	,	PUNCT
ejpam-1528	460	12	no	no	INTJ
ejpam-1528	460	13	.	.	NOUN
ejpam-1528	460	14	1	1	NUM
ejpam-1528	460	15	,	,	PUNCT
ejpam-1528	460	16	103–129	103–129	NUM
ejpam-1528	460	17	.	.	PUNCT
ejpam-1528	460	18	1982	1982	NUM
ejpam-1528	460	19	.	.	PUNCT
ejpam-1528	461	1	[	[	X
ejpam-1528	461	2	8	8	NUM
ejpam-1528	461	3	]	]	X
ejpam-1528	461	4	f.	f.	PROPN
ejpam-1528	461	5	gilfeather	gilfeather	PROPN
ejpam-1528	461	6	.	.	PUNCT
ejpam-1528	462	1	strong	strong	ADJ
ejpam-1528	462	2	reducibility	reducibility	NOUN
ejpam-1528	462	3	of	of	ADP
ejpam-1528	462	4	operators	operator	NOUN
ejpam-1528	462	5	,	,	PUNCT
ejpam-1528	462	6	indiana	indiana	PROPN
ejpam-1528	462	7	university	university	PROPN
ejpam-1528	462	8	mathematics	mathematics	PROPN
ejpam-1528	462	9	journal	journal	PROPN
ejpam-1528	462	10	22	22	NUM
ejpam-1528	462	11	,	,	PUNCT
ejpam-1528	462	12	393–397	393–397	NUM
ejpam-1528	462	13	.	.	NOUN
ejpam-1528	462	14	1972	1972	NUM
ejpam-1528	462	15	.	.	PUNCT
ejpam-1528	463	1	[	[	X
ejpam-1528	463	2	9	9	NUM
ejpam-1528	463	3	]	]	X
ejpam-1528	463	4	j.a	j.a	PROPN
ejpam-1528	463	5	.	.	PROPN
ejpam-1528	463	6	green	green	PROPN
ejpam-1528	463	7	.	.	PUNCT
ejpam-1528	464	1	on	on	ADP
ejpam-1528	464	2	the	the	DET
ejpam-1528	464	3	structure	structure	NOUN
ejpam-1528	464	4	of	of	ADP
ejpam-1528	464	5	semigroups	semigroup	NOUN
ejpam-1528	464	6	,	,	PUNCT
ejpam-1528	464	7	annals	annal	NOUN
ejpam-1528	464	8	of	of	ADP
ejpam-1528	464	9	mathematics	mathematic	NOUN
ejpam-1528	464	10	54	54	NUM
ejpam-1528	464	11	,	,	PUNCT
ejpam-1528	464	12	no	no	INTJ
ejpam-1528	464	13	.	.	NOUN
ejpam-1528	464	14	1	1	NUM
ejpam-1528	464	15	,	,	PUNCT
ejpam-1528	464	16	163–172	163–172	NUM
ejpam-1528	464	17	.	.	PUNCT
ejpam-1528	464	18	1951	1951	NUM
ejpam-1528	464	19	.	.	PUNCT
ejpam-1528	465	1	[	[	X
ejpam-1528	465	2	10	10	NUM
ejpam-1528	465	3	]	]	X
ejpam-1528	465	4	r.	r.	PROPN
ejpam-1528	465	5	harte	harte	PROPN
ejpam-1528	465	6	.	.	PUNCT
ejpam-1528	466	1	on	on	ADP
ejpam-1528	466	2	quasinilpotents	quasinilpotent	NOUN
ejpam-1528	466	3	in	in	ADP
ejpam-1528	466	4	rings	ring	NOUN
ejpam-1528	466	5	,	,	PUNCT
ejpam-1528	466	6	panamerican	panamerican	PROPN
ejpam-1528	466	7	mathematical	mathematical	ADJ
ejpam-1528	466	8	journal	journal	PROPN
ejpam-1528	466	9	1	1	NUM
ejpam-1528	466	10	,	,	PUNCT
ejpam-1528	466	11	10–16	10–16	NUM
ejpam-1528	466	12	.	.	NOUN
ejpam-1528	466	13	1991	1991	NUM
ejpam-1528	466	14	.	.	PUNCT
ejpam-1528	467	1	[	[	X
ejpam-1528	467	2	11	11	NUM
ejpam-1528	467	3	]	]	X
ejpam-1528	467	4	d.	d.	PROPN
ejpam-1528	467	5	kitson	kitson	PROPN
ejpam-1528	467	6	and	and	CCONJ
ejpam-1528	467	7	r.	r.	PROPN
ejpam-1528	467	8	harte	harte	PROPN
ejpam-1528	467	9	.	.	PUNCT
ejpam-1528	468	1	on	on	ADP
ejpam-1528	468	2	browder	browder	PROPN
ejpam-1528	468	3	tuples	tuples	PROPN
ejpam-1528	468	4	,	,	PUNCT
ejpam-1528	468	5	acta	acta	PROPN
ejpam-1528	468	6	scientiarum	scientiarum	PROPN
ejpam-1528	468	7	mathematicarum	mathematicarum	PROPN
ejpam-1528	468	8	75	75	NUM
ejpam-1528	468	9	,	,	PUNCT
ejpam-1528	468	10	no	no	INTJ
ejpam-1528	468	11	.	.	PUNCT
ejpam-1528	468	12	3–4	3–4	NUM
ejpam-1528	468	13	,	,	PUNCT
ejpam-1528	468	14	665–677	665–677	NUM
ejpam-1528	468	15	.	.	PUNCT
ejpam-1528	468	16	2009	2009	NUM
ejpam-1528	468	17	.	.	PUNCT
ejpam-1528	469	1	references	reference	NOUN
ejpam-1528	469	2	427	427	NUM
ejpam-1528	470	1	[	[	X
ejpam-1528	470	2	12	12	NUM
ejpam-1528	470	3	]	]	PUNCT
ejpam-1528	470	4	r.	r.	PROPN
ejpam-1528	470	5	harte	harte	PROPN
ejpam-1528	470	6	.	.	PUNCT
ejpam-1528	471	1	on	on	ADP
ejpam-1528	471	2	local	local	ADJ
ejpam-1528	471	3	spectral	spectral	ADJ
ejpam-1528	471	4	theory	theory	NOUN
ejpam-1528	471	5	,	,	PUNCT
ejpam-1528	471	6	recent	recent	ADJ
ejpam-1528	471	7	advances	advance	NOUN
ejpam-1528	471	8	in	in	ADP
ejpam-1528	471	9	operator	operator	NOUN
ejpam-1528	471	10	theory	theory	NOUN
ejpam-1528	471	11	and	and	CCONJ
ejpam-1528	471	12	applications	application	NOUN
ejpam-1528	471	13	175–183	175–183	NUM
ejpam-1528	471	14	,	,	PUNCT
ejpam-1528	471	15	operator	operator	NOUN
ejpam-1528	471	16	theory	theory	NOUN
ejpam-1528	471	17	:	:	PUNCT
ejpam-1528	471	18	advances	advance	NOUN
ejpam-1528	471	19	and	and	CCONJ
ejpam-1528	471	20	applications	application	NOUN
ejpam-1528	471	21	,	,	PUNCT
ejpam-1528	471	22	187	187	NUM
ejpam-1528	471	23	,	,	PUNCT
ejpam-1528	471	24	birkhäuser	birkhäuser	NOUN
ejpam-1528	471	25	,	,	PUNCT
ejpam-1528	471	26	basel	basel	PROPN
ejpam-1528	471	27	,	,	PUNCT
ejpam-1528	471	28	2009	2009	NUM
ejpam-1528	471	29	.	.	PUNCT
ejpam-1528	472	1	[	[	X
ejpam-1528	472	2	13	13	NUM
ejpam-1528	472	3	]	]	X
ejpam-1528	472	4	d.a	d.a	PROPN
ejpam-1528	472	5	.	.	PROPN
ejpam-1528	472	6	herrero	herrero	PROPN
ejpam-1528	472	7	and	and	CCONJ
ejpam-1528	472	8	c.l	c.l	PROPN
ejpam-1528	472	9	.	.	PROPN
ejpam-1528	472	10	jiang	jiang	PROPN
ejpam-1528	472	11	.	.	PUNCT
ejpam-1528	473	1	limits	limit	NOUN
ejpam-1528	473	2	of	of	ADP
ejpam-1528	473	3	strongly	strongly	ADV
ejpam-1528	473	4	irreducible	irreducible	ADJ
ejpam-1528	473	5	operators	operator	NOUN
ejpam-1528	473	6	,	,	PUNCT
ejpam-1528	473	7	and	and	CCONJ
ejpam-1528	473	8	the	the	DET
ejpam-1528	473	9	riesz	riesz	PROPN
ejpam-1528	473	10	decomposition	decomposition	NOUN
ejpam-1528	473	11	theorem	theorem	NOUN
ejpam-1528	473	12	,	,	PUNCT
ejpam-1528	473	13	michigan	michigan	PROPN
ejpam-1528	473	14	mathematical	mathematical	PROPN
ejpam-1528	473	15	journal	journal	PROPN
ejpam-1528	473	16	37	37	NUM
ejpam-1528	473	17	,	,	PUNCT
ejpam-1528	473	18	no	no	INTJ
ejpam-1528	473	19	.	.	NOUN
ejpam-1528	473	20	2	2	NUM
ejpam-1528	473	21	,	,	PUNCT
ejpam-1528	473	22	283–291	283–291	NUM
ejpam-1528	473	23	.	.	PUNCT
ejpam-1528	473	24	1990	1990	NUM
ejpam-1528	473	25	.	.	PUNCT
ejpam-1528	474	1	[	[	X
ejpam-1528	474	2	14	14	NUM
ejpam-1528	474	3	]	]	X
ejpam-1528	474	4	g.	g.	PROPN
ejpam-1528	474	5	n.	n.	PROPN
ejpam-1528	474	6	hile	hile	PROPN
ejpam-1528	474	7	and	and	CCONJ
ejpam-1528	474	8	w.	w.	PROPN
ejpam-1528	474	9	e.	e.	PROPN
ejpam-1528	474	10	pfaffenberger	pfaffenberger	PROPN
ejpam-1528	474	11	.	.	PUNCT
ejpam-1528	475	1	generalized	generalized	ADJ
ejpam-1528	475	2	spectral	spectral	ADJ
ejpam-1528	475	3	theory	theory	NOUN
ejpam-1528	475	4	in	in	ADP
ejpam-1528	475	5	complex	complex	ADJ
ejpam-1528	475	6	banach	banach	NOUN
ejpam-1528	475	7	algebras	algebra	NOUN
ejpam-1528	475	8	,	,	PUNCT
ejpam-1528	475	9	canadian	canadian	ADJ
ejpam-1528	475	10	journal	journal	NOUN
ejpam-1528	475	11	of	of	ADP
ejpam-1528	475	12	mathematics	mathematics	PROPN
ejpam-1528	475	13	37	37	NUM
ejpam-1528	475	14	,	,	PUNCT
ejpam-1528	475	15	no	no	INTJ
ejpam-1528	475	16	.	.	NOUN
ejpam-1528	475	17	6	6	NUM
ejpam-1528	475	18	,	,	PUNCT
ejpam-1528	475	19	1211–1236	1211–1236	NUM
ejpam-1528	475	20	.	.	PUNCT
ejpam-1528	475	21	1985	1985	NUM
ejpam-1528	475	22	.	.	PUNCT
ejpam-1528	476	1	[	[	X
ejpam-1528	476	2	15	15	NUM
ejpam-1528	476	3	]	]	X
ejpam-1528	476	4	g.	g.	PROPN
ejpam-1528	476	5	n.	n.	PROPN
ejpam-1528	476	6	hile	hile	PROPN
ejpam-1528	476	7	and	and	CCONJ
ejpam-1528	476	8	w.	w.	PROPN
ejpam-1528	476	9	e.	e.	PROPN
ejpam-1528	476	10	pfaffenberger	pfaffenberger	PROPN
ejpam-1528	476	11	.	.	PUNCT
ejpam-1528	477	1	idempotents	idempotent	NOUN
ejpam-1528	477	2	in	in	ADP
ejpam-1528	477	3	complex	complex	ADJ
ejpam-1528	477	4	banach	banach	NOUN
ejpam-1528	477	5	algebras	algebra	NOUN
ejpam-1528	477	6	,	,	PUNCT
ejpam-1528	477	7	canadian	canadian	ADJ
ejpam-1528	477	8	journal	journal	NOUN
ejpam-1528	477	9	of	of	ADP
ejpam-1528	477	10	mathematics	mathematics	PROPN
ejpam-1528	477	11	39	39	NUM
ejpam-1528	477	12	no	no	NOUN
ejpam-1528	477	13	.	.	NOUN
ejpam-1528	478	1	3	3	NUM
ejpam-1528	478	2	,	,	PUNCT
ejpam-1528	478	3	625–630	625–630	NUM
ejpam-1528	478	4	.	.	PUNCT
ejpam-1528	479	1	1987	1987	NUM
ejpam-1528	479	2	.	.	PUNCT
ejpam-1528	480	1	[	[	X
ejpam-1528	480	2	16	16	NUM
ejpam-1528	480	3	]	]	X
ejpam-1528	480	4	j.j	j.j	PROPN
ejpam-1528	480	5	.	.	PROPN
ejpam-1528	480	6	koliha	koliha	PROPN
ejpam-1528	480	7	.	.	PUNCT
ejpam-1528	481	1	a	a	DET
ejpam-1528	481	2	generalized	generalized	ADJ
ejpam-1528	481	3	drazin	drazin	NOUN
ejpam-1528	481	4	inverse	inverse	NOUN
ejpam-1528	481	5	,	,	PUNCT
ejpam-1528	481	6	glasgow	glasgow	PROPN
ejpam-1528	481	7	mathematical	mathematical	ADJ
ejpam-1528	481	8	journal	journal	PROPN
ejpam-1528	481	9	38	38	NUM
ejpam-1528	481	10	,	,	PUNCT
ejpam-1528	481	11	no	no	INTJ
ejpam-1528	481	12	.	.	NOUN
ejpam-1528	481	13	3	3	NUM
ejpam-1528	481	14	,	,	PUNCT
ejpam-1528	481	15	367	367	NUM
ejpam-1528	481	16	–	–	PUNCT
ejpam-1528	481	17	381	381	NUM
ejpam-1528	481	18	.	.	NUM
ejpam-1528	481	19	1996	1996	NUM
ejpam-1528	481	20	.	.	PUNCT
ejpam-1528	482	1	[	[	X
ejpam-1528	482	2	17	17	NUM
ejpam-1528	482	3	]	]	X
ejpam-1528	482	4	j.j	j.j	PROPN
ejpam-1528	482	5	.	.	PROPN
ejpam-1528	482	6	koliha	koliha	PROPN
ejpam-1528	482	7	and	and	CCONJ
ejpam-1528	482	8	p.	p.	PROPN
ejpam-1528	482	9	patricio	patricio	PROPN
ejpam-1528	482	10	.	.	PUNCT
ejpam-1528	483	1	elements	element	NOUN
ejpam-1528	483	2	of	of	ADP
ejpam-1528	483	3	rings	ring	NOUN
ejpam-1528	483	4	with	with	ADP
ejpam-1528	483	5	equal	equal	ADJ
ejpam-1528	483	6	spectral	spectral	ADJ
ejpam-1528	483	7	idempotents	idempotent	NOUN
ejpam-1528	483	8	,	,	PUNCT
ejpam-1528	483	9	journal	journal	NOUN
ejpam-1528	483	10	of	of	ADP
ejpam-1528	483	11	the	the	DET
ejpam-1528	483	12	australian	australian	ADJ
ejpam-1528	483	13	mathematical	mathematical	ADJ
ejpam-1528	483	14	society	society	NOUN
ejpam-1528	483	15	72	72	NUM
ejpam-1528	483	16	,	,	PUNCT
ejpam-1528	483	17	137–152	137–152	NUM
ejpam-1528	483	18	.	.	PUNCT
ejpam-1528	483	19	2002	2002	NUM
ejpam-1528	483	20	.	.	PUNCT
ejpam-1528	484	1	[	[	X
ejpam-1528	484	2	18	18	NUM
ejpam-1528	484	3	]	]	PUNCT
ejpam-1528	484	4	x.	x.	NOUN
ejpam-1528	484	5	mary	mary	PROPN
ejpam-1528	484	6	.	.	PUNCT
ejpam-1528	485	1	on	on	ADP
ejpam-1528	485	2	generalized	generalize	VERB
ejpam-1528	485	3	inverses	inverse	NOUN
ejpam-1528	485	4	and	and	CCONJ
ejpam-1528	485	5	green	green	PROPN
ejpam-1528	485	6	’s	’s	PART
ejpam-1528	485	7	relations	relation	NOUN
ejpam-1528	485	8	,	,	PUNCT
ejpam-1528	485	9	linear	linear	ADJ
ejpam-1528	485	10	algebra	algebra	NOUN
ejpam-1528	485	11	and	and	CCONJ
ejpam-1528	485	12	its	its	PRON
ejpam-1528	485	13	applications	application	NOUN
ejpam-1528	485	14	434	434	NUM
ejpam-1528	485	15	,	,	PUNCT
ejpam-1528	485	16	no	no	INTJ
ejpam-1528	485	17	.	.	NOUN
ejpam-1528	485	18	8	8	NUM
ejpam-1528	485	19	,	,	PUNCT
ejpam-1528	485	20	1836–1844	1836–1844	NUM
ejpam-1528	485	21	.	.	PUNCT
ejpam-1528	485	22	2011	2011	NUM
ejpam-1528	485	23	.	.	PUNCT
ejpam-1528	486	1	[	[	X
ejpam-1528	486	2	19	19	NUM
ejpam-1528	486	3	]	]	PUNCT
ejpam-1528	486	4	x.	x.	NOUN
ejpam-1528	486	5	mary	mary	PROPN
ejpam-1528	486	6	and	and	CCONJ
ejpam-1528	486	7	p.	p.	PROPN
ejpam-1528	486	8	patricio	patricio	PROPN
ejpam-1528	486	9	.	.	PUNCT
ejpam-1528	487	1	generalized	generalized	ADJ
ejpam-1528	487	2	invertibilty	invertibilty	NOUN
ejpam-1528	487	3	moduloh	moduloh	PROPN
ejpam-1528	487	4	in	in	ADP
ejpam-1528	487	5	semigroups	semigroup	NOUN
ejpam-1528	487	6	and	and	CCONJ
ejpam-1528	487	7	rings	ring	NOUN
ejpam-1528	487	8	,	,	PUNCT
ejpam-1528	487	9	linear	linear	PROPN
ejpam-1528	487	10	multilinear	multilinear	PROPN
ejpam-1528	487	11	algebra	algebra	PROPN
ejpam-1528	487	12	61	61	NUM
ejpam-1528	487	13	,	,	PUNCT
ejpam-1528	487	14	no	no	INTJ
ejpam-1528	487	15	.	.	NOUN
ejpam-1528	487	16	8	8	NUM
ejpam-1528	487	17	,	,	PUNCT
ejpam-1528	487	18	1130–1135	1130–1135	NUM
ejpam-1528	487	19	.	.	PUNCT
ejpam-1528	487	20	2013	2013	NUM
ejpam-1528	487	21	.	.	PUNCT
ejpam-1528	488	1	[	[	X
ejpam-1528	488	2	20	20	NUM
ejpam-1528	488	3	]	]	PUNCT
ejpam-1528	488	4	m.	m.	NOUN
ejpam-1528	488	5	gonzalez	gonzalez	PROPN
ejpam-1528	488	6	,	,	PUNCT
ejpam-1528	488	7	m.	m.	NOUN
ejpam-1528	488	8	mbekhta	mbekhta	PROPN
ejpam-1528	488	9	,	,	PUNCT
ejpam-1528	488	10	and	and	CCONJ
ejpam-1528	488	11	m.	m.	NOUN
ejpam-1528	488	12	oudghiri	oudghiri	NOUN
ejpam-1528	488	13	.	.	PUNCT
ejpam-1528	489	1	on	on	ADP
ejpam-1528	489	2	the	the	DET
ejpam-1528	489	3	isolated	isolated	ADJ
ejpam-1528	489	4	points	point	NOUN
ejpam-1528	489	5	of	of	ADP
ejpam-1528	489	6	the	the	DET
ejpam-1528	489	7	surjective	surjective	ADJ
ejpam-1528	489	8	spectrum	spectrum	NOUN
ejpam-1528	489	9	of	of	ADP
ejpam-1528	489	10	a	a	DET
ejpam-1528	489	11	bounded	bounded	ADJ
ejpam-1528	489	12	operator	operator	NOUN
ejpam-1528	489	13	,	,	PUNCT
ejpam-1528	489	14	proceedings	proceeding	NOUN
ejpam-1528	489	15	of	of	ADP
ejpam-1528	489	16	the	the	DET
ejpam-1528	489	17	american	american	PROPN
ejpam-1528	489	18	mathematical	mathematical	PROPN
ejpam-1528	489	19	society	society	NOUN
ejpam-1528	489	20	136	136	NUM
ejpam-1528	489	21	,	,	PUNCT
ejpam-1528	489	22	no	no	INTJ
ejpam-1528	489	23	.	.	NOUN
ejpam-1528	489	24	10	10	NUM
ejpam-1528	489	25	,	,	PUNCT
ejpam-1528	489	26	3521–3528	3521–3528	NUM
ejpam-1528	489	27	.	.	PUNCT
ejpam-1528	489	28	2008	2008	NUM
ejpam-1528	489	29	.	.	PUNCT
ejpam-1528	490	1	[	[	X
ejpam-1528	490	2	21	21	NUM
ejpam-1528	490	3	]	]	PUNCT
ejpam-1528	490	4	m.	m.	NOUN
ejpam-1528	490	5	mbekhta	mbekhta	PROPN
ejpam-1528	490	6	.	.	PUNCT
ejpam-1528	491	1	généralisation	généralisation	PROPN
ejpam-1528	491	2	de	de	PROPN
ejpam-1528	491	3	la	la	PROPN
ejpam-1528	491	4	décomposition	décomposition	PROPN
ejpam-1528	491	5	de	de	PROPN
ejpam-1528	491	6	kato	kato	PROPN
ejpam-1528	491	7	aux	aux	PROPN
ejpam-1528	491	8	opérateurs	opérateur	VERB
ejpam-1528	491	9	paranormaux	paranormaux	PROPN
ejpam-1528	491	10	et	et	PROPN
ejpam-1528	491	11	spectraux	spectraux	NOUN
ejpam-1528	491	12	,	,	PUNCT
ejpam-1528	491	13	glasgow	glasgow	PROPN
ejpam-1528	491	14	mathematical	mathematical	ADJ
ejpam-1528	491	15	journal	journal	NOUN
ejpam-1528	491	16	29	29	NUM
ejpam-1528	491	17	,	,	PUNCT
ejpam-1528	491	18	no	no	INTJ
ejpam-1528	491	19	.	.	NOUN
ejpam-1528	491	20	2	2	NUM
ejpam-1528	491	21	,	,	PUNCT
ejpam-1528	491	22	159–175	159–175	NUM
ejpam-1528	491	23	.	.	PUNCT
ejpam-1528	491	24	1987	1987	NUM
ejpam-1528	491	25	.	.	PUNCT
ejpam-1528	492	1	[	[	X
ejpam-1528	492	2	22	22	NUM
ejpam-1528	492	3	]	]	X
ejpam-1528	492	4	d.d	d.d	PROPN
ejpam-1528	492	5	.	.	PROPN
ejpam-1528	492	6	miller	miller	PROPN
ejpam-1528	492	7	and	and	CCONJ
ejpam-1528	492	8	a.h	a.h	PROPN
ejpam-1528	492	9	.	.	PROPN
ejpam-1528	492	10	clifford	clifford	PROPN
ejpam-1528	492	11	.	.	PUNCT
ejpam-1528	492	12	regulard	regulard	NOUN
ejpam-1528	492	13	-	-	PUNCT
ejpam-1528	492	14	classes	class	NOUN
ejpam-1528	492	15	in	in	ADP
ejpam-1528	492	16	semigroups	semigroup	NOUN
ejpam-1528	492	17	,	,	PUNCT
ejpam-1528	492	18	transactions	transaction	NOUN
ejpam-1528	492	19	of	of	ADP
ejpam-1528	492	20	the	the	DET
ejpam-1528	492	21	american	american	PROPN
ejpam-1528	492	22	mathematical	mathematical	PROPN
ejpam-1528	492	23	society	society	PROPN
ejpam-1528	492	24	82	82	NUM
ejpam-1528	492	25	,	,	PUNCT
ejpam-1528	492	26	no	no	INTJ
ejpam-1528	492	27	.	.	NOUN
ejpam-1528	492	28	1	1	NUM
ejpam-1528	492	29	,	,	PUNCT
ejpam-1528	492	30	270–280	270–280	NUM
ejpam-1528	492	31	.	.	PUNCT
ejpam-1528	493	1	1956	1956	NUM
ejpam-1528	494	1	[	[	X
ejpam-1528	494	2	23	23	NUM
ejpam-1528	494	3	]	]	X
ejpam-1528	494	4	h.	h.	PROPN
ejpam-1528	494	5	radjavi	radjavi	VERB
ejpam-1528	494	6	and	and	CCONJ
ejpam-1528	494	7	p.	p.	NOUN
ejpam-1528	494	8	rosenthal	rosenthal	PROPN
ejpam-1528	494	9	.	.	PUNCT
ejpam-1528	495	1	invariants	invariants	PROPN
ejpam-1528	495	2	subspaces	subspace	NOUN
ejpam-1528	495	3	,	,	PUNCT
ejpam-1528	495	4	springer	springer	NOUN
ejpam-1528	495	5	-	-	PUNCT
ejpam-1528	495	6	verlag	verlag	PROPN
ejpam-1528	495	7	,	,	PUNCT
ejpam-1528	495	8	berlin	berlin	PROPN
ejpam-1528	495	9	,	,	PUNCT
ejpam-1528	495	10	1973	1973	NUM
ejpam-1528	495	11	.	.	PUNCT