id	sid	tid	token	lemma	pos
ejpam-3054	1	1	european	european	PROPN
ejpam-3054	1	2	journal	journal	PROPN
ejpam-3054	1	3	of	of	ADP
ejpam-3054	1	4	pure	pure	ADJ
ejpam-3054	1	5	and	and	CCONJ
ejpam-3054	1	6	applied	apply	VERB
ejpam-3054	1	7	mathematics	mathematic	NOUN
ejpam-3054	1	8	vol	vol	NOUN
ejpam-3054	1	9	.	.	PROPN
ejpam-3054	2	1	10	10	NUM
ejpam-3054	2	2	,	,	PUNCT
ejpam-3054	2	3	no	no	INTJ
ejpam-3054	2	4	.	.	NOUN
ejpam-3054	2	5	5	5	NUM
ejpam-3054	2	6	,	,	PUNCT
ejpam-3054	2	7	2017	2017	NUM
ejpam-3054	2	8	,	,	PUNCT
ejpam-3054	2	9	1058	1058	NUM
ejpam-3054	2	10	-	-	SYM
ejpam-3054	2	11	1066	1066	NUM
ejpam-3054	2	12	issn	issn	PROPN
ejpam-3054	2	13	1307	1307	NUM
ejpam-3054	2	14	-	-	SYM
ejpam-3054	2	15	5543	5543	NUM
ejpam-3054	2	16	–	–	PUNCT
ejpam-3054	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3054	2	18	published	publish	VERB
ejpam-3054	2	19	by	by	ADP
ejpam-3054	2	20	new	new	PROPN
ejpam-3054	2	21	york	york	PROPN
ejpam-3054	2	22	business	business	PROPN
ejpam-3054	2	23	global	global	PROPN
ejpam-3054	2	24	linear	linear	PROPN
ejpam-3054	2	25	essential	essential	ADJ
ejpam-3054	2	26	spectrum	spectrum	NOUN
ejpam-3054	2	27	compressors	compressor	NOUN
ejpam-3054	2	28	hassan	hassan	PROPN
ejpam-3054	2	29	outouzzalt	outouzzalt	PROPN
ejpam-3054	2	30	department	department	PROPN
ejpam-3054	2	31	of	of	ADP
ejpam-3054	2	32	mathematics	mathematics	PROPN
ejpam-3054	2	33	,	,	PUNCT
ejpam-3054	2	34	fsjes	fsjes	PROPN
ejpam-3054	2	35	,	,	PUNCT
ejpam-3054	2	36	b.p	b.p	PROPN
ejpam-3054	2	37	.	.	PROPN
ejpam-3054	2	38	8658	8658	NUM
ejpam-3054	2	39	poste	poste	PROPN
ejpam-3054	2	40	dakhla	dakhla	PROPN
ejpam-3054	2	41	,	,	PUNCT
ejpam-3054	2	42	université	université	ADJ
ejpam-3054	2	43	ibn	ibn	PROPN
ejpam-3054	2	44	zohr	zohr	NOUN
ejpam-3054	2	45	agadir	agadir	PROPN
ejpam-3054	2	46	,	,	PUNCT
ejpam-3054	2	47	morocco	morocco	PROPN
ejpam-3054	2	48	abstract	abstract	NOUN
ejpam-3054	2	49	.	.	PUNCT
ejpam-3054	3	1	let	let	VERB
ejpam-3054	3	2	a	a	PRON
ejpam-3054	3	3	be	be	AUX
ejpam-3054	3	4	a	a	DET
ejpam-3054	3	5	unital	unital	ADJ
ejpam-3054	3	6	c∗-algebra	c∗-algebra	NOUN
ejpam-3054	3	7	of	of	ADP
ejpam-3054	3	8	real	real	ADJ
ejpam-3054	3	9	rank	rank	NOUN
ejpam-3054	3	10	zero	zero	NUM
ejpam-3054	3	11	and	and	CCONJ
ejpam-3054	3	12	b	b	NOUN
ejpam-3054	3	13	be	be	AUX
ejpam-3054	3	14	a	a	DET
ejpam-3054	3	15	unital	unital	ADJ
ejpam-3054	3	16	semisimple	semisimple	NOUN
ejpam-3054	3	17	complex	complex	ADJ
ejpam-3054	3	18	banach	banach	NOUN
ejpam-3054	3	19	algebra	algebra	NOUN
ejpam-3054	3	20	.	.	PUNCT
ejpam-3054	4	1	we	we	PRON
ejpam-3054	4	2	characterize	characterize	VERB
ejpam-3054	4	3	linear	linear	ADJ
ejpam-3054	4	4	maps	map	NOUN
ejpam-3054	4	5	from	from	ADP
ejpam-3054	4	6	a	a	PRON
ejpam-3054	4	7	onto	onto	ADP
ejpam-3054	4	8	b	b	NOUN
ejpam-3054	4	9	that	that	PRON
ejpam-3054	4	10	compress	compress	VERB
ejpam-3054	4	11	different	different	ADJ
ejpam-3054	4	12	essential	essential	ADJ
ejpam-3054	4	13	spectral	spectral	ADJ
ejpam-3054	4	14	sets	set	NOUN
ejpam-3054	4	15	such	such	ADJ
ejpam-3054	4	16	as	as	ADP
ejpam-3054	4	17	the	the	DET
ejpam-3054	4	18	(	(	PUNCT
ejpam-3054	4	19	left	left	ADJ
ejpam-3054	4	20	,	,	PUNCT
ejpam-3054	4	21	right	right	ADJ
ejpam-3054	4	22	)	)	PUNCT
ejpam-3054	4	23	essential	essential	ADJ
ejpam-3054	4	24	spectrum	spectrum	NOUN
ejpam-3054	4	25	,	,	PUNCT
ejpam-3054	4	26	the	the	DET
ejpam-3054	4	27	semi	semi	ADJ
ejpam-3054	4	28	-	-	ADJ
ejpam-3054	4	29	fredholm	fredholm	ADJ
ejpam-3054	4	30	spectrum	spectrum	NOUN
ejpam-3054	4	31	,	,	PUNCT
ejpam-3054	4	32	and	and	CCONJ
ejpam-3054	4	33	the	the	DET
ejpam-3054	4	34	weyl	weyl	PROPN
ejpam-3054	4	35	spectrum	spectrum	NOUN
ejpam-3054	4	36	.	.	PUNCT
ejpam-3054	5	1	essentially	essentially	ADV
ejpam-3054	5	2	spectrally	spectrally	ADV
ejpam-3054	5	3	bounded	bound	VERB
ejpam-3054	5	4	linear	linear	ADJ
ejpam-3054	5	5	mappings	mapping	NOUN
ejpam-3054	5	6	from	from	ADP
ejpam-3054	5	7	a	a	PRON
ejpam-3054	5	8	onto	onto	NOUN
ejpam-3054	5	9	b	b	NOUN
ejpam-3054	5	10	are	be	AUX
ejpam-3054	5	11	also	also	ADV
ejpam-3054	5	12	characterized	characterize	VERB
ejpam-3054	5	13	.	.	PUNCT
ejpam-3054	6	1	2010	2010	NUM
ejpam-3054	6	2	mathematics	mathematic	NOUN
ejpam-3054	6	3	subject	subject	NOUN
ejpam-3054	6	4	classifications	classification	NOUN
ejpam-3054	6	5	:	:	PUNCT
ejpam-3054	6	6	47b49	47b49	NUM
ejpam-3054	6	7	,	,	PUNCT
ejpam-3054	6	8	47a10	47a10	NUM
ejpam-3054	6	9	,	,	PUNCT
ejpam-3054	6	10	47d25	47d25	NUM
ejpam-3054	6	11	key	key	ADJ
ejpam-3054	6	12	words	word	NOUN
ejpam-3054	6	13	and	and	CCONJ
ejpam-3054	6	14	phrases	phrase	NOUN
ejpam-3054	6	15	:	:	PUNCT
ejpam-3054	6	16	fredholm	fredholm	NOUN
ejpam-3054	6	17	elements	element	NOUN
ejpam-3054	6	18	,	,	PUNCT
ejpam-3054	6	19	essential	essential	ADJ
ejpam-3054	6	20	spectrum	spectrum	NOUN
ejpam-3054	6	21	,	,	PUNCT
ejpam-3054	6	22	weyl	weyl	PROPN
ejpam-3054	6	23	spectrum	spectrum	PROPN
ejpam-3054	6	24	,	,	PUNCT
ejpam-3054	6	25	essential	essential	ADJ
ejpam-3054	6	26	spectral	spectral	ADJ
ejpam-3054	6	27	radius	radius	NOUN
ejpam-3054	6	28	,	,	PUNCT
ejpam-3054	6	29	linear	linear	NOUN
ejpam-3054	6	30	preservers	preserver	NOUN
ejpam-3054	6	31	.	.	PUNCT
ejpam-3054	7	1	1	1	X
ejpam-3054	7	2	.	.	X
ejpam-3054	7	3	introduction	introduction	NOUN
ejpam-3054	7	4	linear	linear	PROPN
ejpam-3054	7	5	preserver	preserver	NOUN
ejpam-3054	7	6	problems	problem	NOUN
ejpam-3054	7	7	is	be	AUX
ejpam-3054	7	8	an	an	DET
ejpam-3054	7	9	active	active	ADJ
ejpam-3054	7	10	research	research	NOUN
ejpam-3054	7	11	area	area	NOUN
ejpam-3054	7	12	in	in	ADP
ejpam-3054	7	13	matrix	matrix	NOUN
ejpam-3054	7	14	and	and	CCONJ
ejpam-3054	7	15	operator	operator	NOUN
ejpam-3054	7	16	theory	theory	NOUN
ejpam-3054	7	17	.	.	PUNCT
ejpam-3054	8	1	these	these	DET
ejpam-3054	8	2	problems	problem	NOUN
ejpam-3054	8	3	involve	involve	VERB
ejpam-3054	8	4	linear	linear	NOUN
ejpam-3054	8	5	or	or	CCONJ
ejpam-3054	8	6	additive	additive	ADJ
ejpam-3054	8	7	maps	map	NOUN
ejpam-3054	8	8	that	that	PRON
ejpam-3054	8	9	leave	leave	VERB
ejpam-3054	8	10	invariant	invariant	ADJ
ejpam-3054	8	11	certain	certain	ADJ
ejpam-3054	8	12	relations	relation	NOUN
ejpam-3054	8	13	,	,	PUNCT
ejpam-3054	8	14	or	or	CCONJ
ejpam-3054	8	15	subsets	subset	NOUN
ejpam-3054	8	16	,	,	PUNCT
ejpam-3054	8	17	or	or	CCONJ
ejpam-3054	8	18	functions	function	NOUN
ejpam-3054	8	19	.	.	PUNCT
ejpam-3054	9	1	over	over	ADP
ejpam-3054	9	2	the	the	DET
ejpam-3054	9	3	past	past	ADJ
ejpam-3054	9	4	decades	decade	NOUN
ejpam-3054	9	5	much	much	ADJ
ejpam-3054	9	6	work	work	NOUN
ejpam-3054	9	7	has	have	AUX
ejpam-3054	9	8	been	be	AUX
ejpam-3054	9	9	done	do	VERB
ejpam-3054	9	10	on	on	ADP
ejpam-3054	9	11	linear	linear	ADJ
ejpam-3054	9	12	preserver	preserver	NOUN
ejpam-3054	9	13	problems	problem	NOUN
ejpam-3054	9	14	on	on	ADP
ejpam-3054	9	15	matrix	matrix	NOUN
ejpam-3054	9	16	or	or	CCONJ
ejpam-3054	9	17	operator	operator	NOUN
ejpam-3054	9	18	spaces	space	NOUN
ejpam-3054	9	19	.	.	PUNCT
ejpam-3054	10	1	often	often	ADV
ejpam-3054	10	2	,	,	PUNCT
ejpam-3054	10	3	the	the	DET
ejpam-3054	10	4	characterization	characterization	NOUN
ejpam-3054	10	5	of	of	ADP
ejpam-3054	10	6	such	such	ADJ
ejpam-3054	10	7	linear	linear	ADJ
ejpam-3054	10	8	preservers	preserver	NOUN
ejpam-3054	10	9	reveal	reveal	VERB
ejpam-3054	10	10	the	the	DET
ejpam-3054	10	11	algebraic	algebraic	ADJ
ejpam-3054	10	12	structures	structure	NOUN
ejpam-3054	10	13	,	,	PUNCT
ejpam-3054	10	14	in	in	ADP
ejpam-3054	10	15	many	many	ADJ
ejpam-3054	10	16	cases	case	NOUN
ejpam-3054	10	17	,	,	PUNCT
ejpam-3054	10	18	they	they	PRON
ejpam-3054	10	19	are	be	AUX
ejpam-3054	10	20	in	in	ADP
ejpam-3054	10	21	fact	fact	NOUN
ejpam-3054	10	22	jordan	jordan	PROPN
ejpam-3054	10	23	homomorphisms	homomorphisms	PROPN
ejpam-3054	10	24	;	;	PUNCT
ejpam-3054	10	25	see	see	VERB
ejpam-3054	10	26	surveys	survey	NOUN
ejpam-3054	10	27	papers	paper	NOUN
ejpam-3054	10	28	[	[	X
ejpam-3054	10	29	3	3	NUM
ejpam-3054	10	30	,	,	PUNCT
ejpam-3054	10	31	12	12	NUM
ejpam-3054	10	32	,	,	PUNCT
ejpam-3054	10	33	14	14	NUM
ejpam-3054	10	34	,	,	PUNCT
ejpam-3054	10	35	16	16	NUM
ejpam-3054	10	36	,	,	PUNCT
ejpam-3054	10	37	19	19	NUM
ejpam-3054	10	38	]	]	PUNCT
ejpam-3054	10	39	and	and	CCONJ
ejpam-3054	10	40	the	the	DET
ejpam-3054	10	41	references	reference	NOUN
ejpam-3054	10	42	therein	therein	ADV
ejpam-3054	10	43	.	.	PUNCT
ejpam-3054	11	1	throughout	throughout	ADP
ejpam-3054	11	2	,	,	PUNCT
ejpam-3054	11	3	a	a	PRON
ejpam-3054	11	4	and	and	CCONJ
ejpam-3054	11	5	b	b	NOUN
ejpam-3054	11	6	will	will	AUX
ejpam-3054	11	7	denote	denote	VERB
ejpam-3054	11	8	infinite	infinite	ADJ
ejpam-3054	11	9	dimensional	dimensional	ADJ
ejpam-3054	11	10	unital	unital	ADJ
ejpam-3054	11	11	semisimple	semisimple	NOUN
ejpam-3054	11	12	banach	banach	NOUN
ejpam-3054	11	13	algebras	algebra	VERB
ejpam-3054	11	14	over	over	ADP
ejpam-3054	11	15	the	the	DET
ejpam-3054	11	16	field	field	NOUN
ejpam-3054	11	17	c	c	NOUN
ejpam-3054	11	18	of	of	ADP
ejpam-3054	11	19	complex	complex	ADJ
ejpam-3054	11	20	number	number	NOUN
ejpam-3054	11	21	,	,	PUNCT
ejpam-3054	11	22	unless	unless	SCONJ
ejpam-3054	11	23	specified	specify	VERB
ejpam-3054	11	24	otherwise	otherwise	ADV
ejpam-3054	11	25	.	.	PUNCT
ejpam-3054	12	1	the	the	DET
ejpam-3054	12	2	unit	unit	NOUN
ejpam-3054	12	3	is	be	AUX
ejpam-3054	12	4	denoted	denote	VERB
ejpam-3054	12	5	by	by	ADP
ejpam-3054	12	6	1	1	NUM
ejpam-3054	12	7	.	.	PUNCT
ejpam-3054	13	1	a	a	DET
ejpam-3054	13	2	linear	linear	ADJ
ejpam-3054	13	3	mapping	mapping	NOUN
ejpam-3054	13	4	ϕ	ϕ	NOUN
ejpam-3054	13	5	:	:	PUNCT
ejpam-3054	13	6	a→	a→	PROPN
ejpam-3054	13	7	b	b	NOUN
ejpam-3054	13	8	is	be	AUX
ejpam-3054	13	9	said	say	VERB
ejpam-3054	13	10	to	to	PART
ejpam-3054	13	11	be	be	AUX
ejpam-3054	13	12	jordan	jordan	PROPN
ejpam-3054	13	13	homomorphism	homomorphism	PROPN
ejpam-3054	13	14	if	if	SCONJ
ejpam-3054	13	15	ϕ(a2	ϕ(a2	NUM
ejpam-3054	13	16	)	)	PUNCT
ejpam-3054	14	1	=	=	PUNCT
ejpam-3054	14	2	ϕ(a)2	ϕ(a)2	PROPN
ejpam-3054	14	3	for	for	ADP
ejpam-3054	14	4	all	all	DET
ejpam-3054	14	5	a	a	DET
ejpam-3054	14	6	∈	∈	PROPN
ejpam-3054	14	7	a	a	PRON
ejpam-3054	14	8	,	,	PUNCT
ejpam-3054	14	9	or	or	CCONJ
ejpam-3054	14	10	equivalently	equivalently	ADV
ejpam-3054	14	11	ϕ(ab+	ϕ(ab+	PROPN
ejpam-3054	14	12	ba	ba	NOUN
ejpam-3054	14	13	)	)	PUNCT
ejpam-3054	14	14	=	=	PUNCT
ejpam-3054	14	15	ϕ(a)ϕ(b	ϕ(a)ϕ(b	ADJ
ejpam-3054	14	16	)	)	PUNCT
ejpam-3054	14	17	+	+	CCONJ
ejpam-3054	14	18	ϕ(b)ϕ(a	ϕ(b)ϕ(a	NOUN
ejpam-3054	14	19	)	)	PUNCT
ejpam-3054	14	20	for	for	ADP
ejpam-3054	14	21	all	all	DET
ejpam-3054	14	22	a	a	DET
ejpam-3054	14	23	,	,	PUNCT
ejpam-3054	14	24	b	b	X
ejpam-3054	14	25	∈	∈	PROPN
ejpam-3054	14	26	a.	a.	NOUN
ejpam-3054	14	27	clearly	clearly	ADV
ejpam-3054	14	28	,	,	PUNCT
ejpam-3054	14	29	every	every	DET
ejpam-3054	14	30	homomorphism	homomorphism	NOUN
ejpam-3054	14	31	and	and	CCONJ
ejpam-3054	14	32	every	every	DET
ejpam-3054	14	33	anti	anti	ADJ
ejpam-3054	14	34	-	-	NOUN
ejpam-3054	14	35	homomorphism	homomorphism	NOUN
ejpam-3054	14	36	is	be	AUX
ejpam-3054	14	37	a	a	DET
ejpam-3054	14	38	jordan	jordan	PROPN
ejpam-3054	14	39	homomorphism	homomorphism	PROPN
ejpam-3054	14	40	.	.	PUNCT
ejpam-3054	15	1	for	for	ADP
ejpam-3054	15	2	further	further	ADJ
ejpam-3054	15	3	properties	property	NOUN
ejpam-3054	15	4	of	of	ADP
ejpam-3054	15	5	jordan	jordan	PROPN
ejpam-3054	15	6	homomorphisms	homomorphisms	PROPN
ejpam-3054	15	7	,	,	PUNCT
ejpam-3054	15	8	we	we	PRON
ejpam-3054	15	9	refer	refer	VERB
ejpam-3054	15	10	the	the	DET
ejpam-3054	15	11	reader	reader	NOUN
ejpam-3054	15	12	to	to	ADP
ejpam-3054	15	13	[	[	X
ejpam-3054	15	14	11	11	NUM
ejpam-3054	15	15	,	,	PUNCT
ejpam-3054	15	16	13	13	NUM
ejpam-3054	15	17	]	]	PUNCT
ejpam-3054	15	18	.	.	PUNCT
ejpam-3054	16	1	the	the	DET
ejpam-3054	16	2	map	map	NOUN
ejpam-3054	16	3	ϕ	ϕ	NOUN
ejpam-3054	16	4	is	be	AUX
ejpam-3054	16	5	said	say	VERB
ejpam-3054	16	6	to	to	PART
ejpam-3054	16	7	be	be	AUX
ejpam-3054	16	8	essentially	essentially	ADV
ejpam-3054	16	9	spectrally	spectrally	ADV
ejpam-3054	16	10	bounded	bound	VERB
ejpam-3054	16	11	if	if	SCONJ
ejpam-3054	16	12	there	there	PRON
ejpam-3054	16	13	exists	exist	VERB
ejpam-3054	16	14	a	a	DET
ejpam-3054	16	15	positive	positive	ADJ
ejpam-3054	16	16	constant	constant	ADJ
ejpam-3054	16	17	m	m	NOUN
ejpam-3054	16	18	such	such	ADJ
ejpam-3054	16	19	that	that	SCONJ
ejpam-3054	16	20	re(ϕ(a	re(ϕ(a	NOUN
ejpam-3054	16	21	)	)	PUNCT
ejpam-3054	16	22	)	)	PUNCT
ejpam-3054	16	23	≤mre(a	≤mre(a	ADJ
ejpam-3054	16	24	)	)	PUNCT
ejpam-3054	16	25	email	email	NOUN
ejpam-3054	16	26	addresses	address	NOUN
ejpam-3054	16	27	:	:	PUNCT
ejpam-3054	16	28	outouzzalt@gmx.com	outouzzalt@gmx.com	X
ejpam-3054	16	29	(	(	PUNCT
ejpam-3054	16	30	h.	h.	PROPN
ejpam-3054	16	31	outouzzalt	outouzzalt	PROPN
ejpam-3054	16	32	)	)	PUNCT
ejpam-3054	16	33	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3054	16	34	1058	1058	NUM
ejpam-3054	16	35	c	c	NOUN
ejpam-3054	16	36	©	©	PROPN
ejpam-3054	16	37	2017	2017	NUM
ejpam-3054	16	38	ejpam	ejpam	VERB
ejpam-3054	16	39	all	all	DET
ejpam-3054	16	40	rights	right	NOUN
ejpam-3054	16	41	reserved	reserve	VERB
ejpam-3054	16	42	.	.	PUNCT
ejpam-3054	17	1	h.	h.	PROPN
ejpam-3054	17	2	outouzzalt	outouzzalt	PROPN
ejpam-3054	17	3	/	/	SYM
ejpam-3054	17	4	eur	eur	PROPN
ejpam-3054	17	5	.	.	PUNCT
ejpam-3054	18	1	j.	j.	PROPN
ejpam-3054	18	2	pure	pure	PROPN
ejpam-3054	18	3	appl	appl	PROPN
ejpam-3054	18	4	.	.	PROPN
ejpam-3054	18	5	math	math	PROPN
ejpam-3054	18	6	,	,	PUNCT
ejpam-3054	18	7	10	10	NUM
ejpam-3054	18	8	(	(	PUNCT
ejpam-3054	18	9	5	5	NUM
ejpam-3054	18	10	)	)	PUNCT
ejpam-3054	18	11	(	(	PUNCT
ejpam-3054	18	12	2017	2017	NUM
ejpam-3054	18	13	)	)	PUNCT
ejpam-3054	18	14	,	,	PUNCT
ejpam-3054	18	15	1058	1058	NUM
ejpam-3054	18	16	-	-	SYM
ejpam-3054	18	17	1066	1066	NUM
ejpam-3054	18	18	1059	1059	NUM
ejpam-3054	18	19	for	for	ADP
ejpam-3054	18	20	all	all	DET
ejpam-3054	18	21	a	a	DET
ejpam-3054	18	22	∈	∈	PROPN
ejpam-3054	18	23	a	a	PRON
ejpam-3054	18	24	,	,	PUNCT
ejpam-3054	18	25	where	where	SCONJ
ejpam-3054	18	26	re	re	X
ejpam-3054	18	27	(	(	PUNCT
ejpam-3054	18	28	.	.	PUNCT
ejpam-3054	18	29	)	)	PUNCT
ejpam-3054	18	30	stands	stand	VERB
ejpam-3054	18	31	for	for	ADP
ejpam-3054	18	32	the	the	DET
ejpam-3054	18	33	essential	essential	ADJ
ejpam-3054	18	34	spectral	spectral	ADJ
ejpam-3054	18	35	radius	radius	NOUN
ejpam-3054	18	36	.	.	PUNCT
ejpam-3054	19	1	in	in	ADP
ejpam-3054	19	2	[	[	X
ejpam-3054	19	3	6	6	NUM
ejpam-3054	19	4	]	]	PUNCT
ejpam-3054	19	5	,	,	PUNCT
ejpam-3054	19	6	the	the	DET
ejpam-3054	19	7	authors	author	NOUN
ejpam-3054	19	8	characterized	characterize	VERB
ejpam-3054	19	9	linear	linear	ADJ
ejpam-3054	19	10	maps	map	NOUN
ejpam-3054	19	11	on	on	ADP
ejpam-3054	19	12	the	the	DET
ejpam-3054	19	13	algebra	algebra	NOUN
ejpam-3054	19	14	l(h	l(h	PROPN
ejpam-3054	19	15	)	)	PUNCT
ejpam-3054	19	16	of	of	ADP
ejpam-3054	19	17	all	all	DET
ejpam-3054	19	18	bounded	bound	VERB
ejpam-3054	19	19	linear	linear	PROPN
ejpam-3054	19	20	operators	operator	NOUN
ejpam-3054	19	21	on	on	ADP
ejpam-3054	19	22	an	an	DET
ejpam-3054	19	23	infinite	infinite	ADJ
ejpam-3054	19	24	dimensional	dimensional	ADJ
ejpam-3054	19	25	hilbert	hilbert	NOUN
ejpam-3054	19	26	space	space	NOUN
ejpam-3054	19	27	h	h	NOUN
ejpam-3054	19	28	that	that	PRON
ejpam-3054	19	29	are	be	AUX
ejpam-3054	19	30	essentially	essentially	ADV
ejpam-3054	19	31	spectrally	spectrally	ADV
ejpam-3054	19	32	bounded	bound	VERB
ejpam-3054	19	33	,	,	PUNCT
ejpam-3054	19	34	extending	extend	VERB
ejpam-3054	19	35	some	some	DET
ejpam-3054	19	36	recent	recent	ADJ
ejpam-3054	19	37	results	result	NOUN
ejpam-3054	19	38	obtained	obtain	VERB
ejpam-3054	19	39	in	in	ADP
ejpam-3054	19	40	[	[	X
ejpam-3054	19	41	5	5	NUM
ejpam-3054	19	42	]	]	PUNCT
ejpam-3054	19	43	concerning	concern	VERB
ejpam-3054	19	44	linear	linear	PROPN
ejpam-3054	19	45	essential	essential	ADJ
ejpam-3054	19	46	spectral	spectral	ADJ
ejpam-3054	19	47	radius	radius	NOUN
ejpam-3054	19	48	(	(	PUNCT
ejpam-3054	19	49	essential	essential	ADJ
ejpam-3054	19	50	spectrum	spectrum	NOUN
ejpam-3054	19	51	)	)	PUNCT
ejpam-3054	19	52	preservers	preserver	NOUN
ejpam-3054	19	53	.	.	PUNCT
ejpam-3054	20	1	they	they	PRON
ejpam-3054	20	2	proved	prove	VERB
ejpam-3054	20	3	that	that	SCONJ
ejpam-3054	20	4	a	a	DET
ejpam-3054	20	5	linear	linear	NOUN
ejpam-3054	20	6	surjective	surjective	NOUN
ejpam-3054	20	7	up	up	ADP
ejpam-3054	20	8	to	to	ADP
ejpam-3054	20	9	compact	compact	ADJ
ejpam-3054	20	10	operators	operator	NOUN
ejpam-3054	20	11	map	map	VERB
ejpam-3054	20	12	from	from	ADP
ejpam-3054	20	13	l(h	l(h	PROPN
ejpam-3054	20	14	)	)	PUNCT
ejpam-3054	20	15	into	into	ADP
ejpam-3054	20	16	itself	itself	PRON
ejpam-3054	20	17	is	be	AUX
ejpam-3054	20	18	essentially	essentially	ADV
ejpam-3054	20	19	spectrally	spectrally	ADV
ejpam-3054	20	20	bounded	bound	VERB
ejpam-3054	20	21	if	if	SCONJ
ejpam-3054	20	22	and	and	CCONJ
ejpam-3054	20	23	only	only	ADV
ejpam-3054	20	24	if	if	SCONJ
ejpam-3054	20	25	it	it	PRON
ejpam-3054	20	26	preserves	preserve	VERB
ejpam-3054	20	27	the	the	DET
ejpam-3054	20	28	ideal	ideal	NOUN
ejpam-3054	20	29	of	of	ADP
ejpam-3054	20	30	compact	compact	ADJ
ejpam-3054	20	31	operators	operator	NOUN
ejpam-3054	20	32	and	and	CCONJ
ejpam-3054	20	33	the	the	DET
ejpam-3054	20	34	induced	induced	ADJ
ejpam-3054	20	35	linear	linear	NOUN
ejpam-3054	20	36	map	map	NOUN
ejpam-3054	20	37	on	on	ADP
ejpam-3054	20	38	the	the	DET
ejpam-3054	20	39	calkin	calkin	ADJ
ejpam-3054	20	40	algebra	algebra	NOUN
ejpam-3054	20	41	is	be	AUX
ejpam-3054	20	42	either	either	CCONJ
ejpam-3054	20	43	a	a	DET
ejpam-3054	20	44	continuous	continuous	ADJ
ejpam-3054	20	45	epimorphism	epimorphism	NOUN
ejpam-3054	20	46	or	or	CCONJ
ejpam-3054	20	47	a	a	DET
ejpam-3054	20	48	continuous	continuous	ADJ
ejpam-3054	20	49	anti	anti	ADJ
ejpam-3054	20	50	-	-	ADJ
ejpam-3054	20	51	epimorphism	epimorphism	NOUN
ejpam-3054	20	52	multiplied	multiply	VERB
ejpam-3054	20	53	by	by	ADP
ejpam-3054	20	54	a	a	DET
ejpam-3054	20	55	nonzero	nonzero	NOUN
ejpam-3054	20	56	scalar	scalar	NOUN
ejpam-3054	20	57	.	.	PUNCT
ejpam-3054	21	1	recently	recently	ADV
ejpam-3054	21	2	,	,	PUNCT
ejpam-3054	21	3	in	in	ADP
ejpam-3054	21	4	[	[	PUNCT
ejpam-3054	21	5	7	7	NUM
ejpam-3054	21	6	]	]	PUNCT
ejpam-3054	21	7	,	,	PUNCT
ejpam-3054	21	8	as	as	ADP
ejpam-3054	21	9	a	a	DET
ejpam-3054	21	10	local	local	ADJ
ejpam-3054	21	11	version	version	NOUN
ejpam-3054	21	12	,	,	PUNCT
ejpam-3054	21	13	the	the	DET
ejpam-3054	21	14	authors	author	NOUN
ejpam-3054	21	15	studied	study	VERB
ejpam-3054	21	16	linear	linear	ADJ
ejpam-3054	21	17	maps	map	NOUN
ejpam-3054	21	18	on	on	ADP
ejpam-3054	21	19	the	the	DET
ejpam-3054	21	20	algebra	algebra	NOUN
ejpam-3054	21	21	l(h	l(h	PROPN
ejpam-3054	21	22	)	)	PUNCT
ejpam-3054	21	23	of	of	ADP
ejpam-3054	21	24	all	all	DET
ejpam-3054	21	25	bounded	bound	VERB
ejpam-3054	21	26	linear	linear	PROPN
ejpam-3054	21	27	operators	operator	NOUN
ejpam-3054	21	28	on	on	ADP
ejpam-3054	21	29	an	an	DET
ejpam-3054	21	30	infinite	infinite	ADJ
ejpam-3054	21	31	dimensional	dimensional	ADJ
ejpam-3054	21	32	hilbert	hilbert	NOUN
ejpam-3054	21	33	space	space	NOUN
ejpam-3054	21	34	h	h	NOUN
ejpam-3054	21	35	that	that	PRON
ejpam-3054	21	36	compress	compress	VERB
ejpam-3054	21	37	the	the	DET
ejpam-3054	21	38	local	local	ADJ
ejpam-3054	21	39	spectrum	spectrum	NOUN
ejpam-3054	21	40	and	and	CCONJ
ejpam-3054	21	41	the	the	DET
ejpam-3054	21	42	ones	one	NOUN
ejpam-3054	21	43	that	that	PRON
ejpam-3054	21	44	are	be	AUX
ejpam-3054	21	45	locally	locally	ADV
ejpam-3054	21	46	spectrally	spectrally	ADV
ejpam-3054	21	47	bounded	bound	VERB
ejpam-3054	21	48	.	.	PUNCT
ejpam-3054	22	1	the	the	DET
ejpam-3054	22	2	object	object	NOUN
ejpam-3054	22	3	of	of	ADP
ejpam-3054	22	4	this	this	DET
ejpam-3054	22	5	note	note	NOUN
ejpam-3054	22	6	is	be	AUX
ejpam-3054	22	7	to	to	PART
ejpam-3054	22	8	study	study	VERB
ejpam-3054	22	9	essential	essential	ADJ
ejpam-3054	22	10	spectrum	spectrum	NOUN
ejpam-3054	22	11	compressors	compressor	NOUN
ejpam-3054	22	12	and	and	CCONJ
ejpam-3054	22	13	essentially	essentially	ADV
ejpam-3054	22	14	spectrally	spectrally	ADV
ejpam-3054	22	15	bounded	bound	VERB
ejpam-3054	22	16	linear	linear	ADJ
ejpam-3054	22	17	maps	map	NOUN
ejpam-3054	22	18	between	between	ADP
ejpam-3054	22	19	banach	banach	NOUN
ejpam-3054	22	20	algebras	algebra	NOUN
ejpam-3054	22	21	.	.	PUNCT
ejpam-3054	23	1	the	the	DET
ejpam-3054	23	2	paper	paper	NOUN
ejpam-3054	23	3	is	be	AUX
ejpam-3054	23	4	organized	organize	VERB
ejpam-3054	23	5	as	as	SCONJ
ejpam-3054	23	6	follows	follow	VERB
ejpam-3054	23	7	.	.	PUNCT
ejpam-3054	24	1	in	in	ADP
ejpam-3054	24	2	the	the	DET
ejpam-3054	24	3	next	next	ADJ
ejpam-3054	24	4	section	section	NOUN
ejpam-3054	24	5	,	,	PUNCT
ejpam-3054	24	6	we	we	PRON
ejpam-3054	24	7	characterize	characterize	VERB
ejpam-3054	24	8	essentially	essentially	ADV
ejpam-3054	24	9	spectrally	spectrally	ADV
ejpam-3054	24	10	bounded	bound	VERB
ejpam-3054	24	11	linear	linear	PROPN
ejpam-3054	24	12	maps	map	NOUN
ejpam-3054	24	13	from	from	ADP
ejpam-3054	24	14	a	a	DET
ejpam-3054	24	15	unital	unital	ADJ
ejpam-3054	24	16	purely	purely	ADV
ejpam-3054	24	17	infinite	infinite	ADJ
ejpam-3054	24	18	c∗-algebra	c∗-algebra	NOUN
ejpam-3054	24	19	of	of	ADP
ejpam-3054	24	20	real	real	ADJ
ejpam-3054	24	21	rank	rank	NOUN
ejpam-3054	24	22	zero	zero	NUM
ejpam-3054	24	23	onto	onto	ADP
ejpam-3054	24	24	a	a	DET
ejpam-3054	24	25	unital	unital	ADJ
ejpam-3054	24	26	semisimple	semisimple	NOUN
ejpam-3054	24	27	banach	banach	NOUN
ejpam-3054	24	28	algebra	algebra	NOUN
ejpam-3054	24	29	.	.	PUNCT
ejpam-3054	25	1	in	in	ADP
ejpam-3054	25	2	section	section	NOUN
ejpam-3054	25	3	3	3	NUM
ejpam-3054	25	4	we	we	PRON
ejpam-3054	25	5	describe	describe	VERB
ejpam-3054	25	6	linear	linear	PROPN
ejpam-3054	25	7	maps	map	NOUN
ejpam-3054	25	8	ϕ	ϕ	NOUN
ejpam-3054	25	9	from	from	ADP
ejpam-3054	25	10	a	a	DET
ejpam-3054	25	11	c∗-algebra	c∗-algebra	PROPN
ejpam-3054	25	12	of	of	ADP
ejpam-3054	25	13	real	real	ADJ
ejpam-3054	25	14	rank	rank	NOUN
ejpam-3054	25	15	zero	zero	NUM
ejpam-3054	25	16	onto	onto	ADP
ejpam-3054	25	17	a	a	DET
ejpam-3054	25	18	semisimple	semisimple	NOUN
ejpam-3054	25	19	banach	banach	NOUN
ejpam-3054	25	20	algebra	algebra	NOUN
ejpam-3054	25	21	that	that	PRON
ejpam-3054	25	22	preserve	preserve	VERB
ejpam-3054	25	23	atkinson	atkinson	NOUN
ejpam-3054	25	24	elements	element	NOUN
ejpam-3054	25	25	and	and	CCONJ
ejpam-3054	25	26	the	the	DET
ejpam-3054	25	27	ones	one	NOUN
ejpam-3054	25	28	that	that	PRON
ejpam-3054	25	29	compress	compress	VERB
ejpam-3054	25	30	different	different	ADJ
ejpam-3054	25	31	essential	essential	ADJ
ejpam-3054	25	32	spectral	spectral	ADJ
ejpam-3054	25	33	sets	set	NOUN
ejpam-3054	25	34	such	such	ADJ
ejpam-3054	25	35	as	as	ADP
ejpam-3054	25	36	the	the	DET
ejpam-3054	25	37	(	(	PUNCT
ejpam-3054	25	38	left	left	ADJ
ejpam-3054	25	39	,	,	PUNCT
ejpam-3054	25	40	right	right	ADJ
ejpam-3054	25	41	)	)	PUNCT
ejpam-3054	25	42	essential	essential	ADJ
ejpam-3054	25	43	spectrum	spectrum	NOUN
ejpam-3054	25	44	,	,	PUNCT
ejpam-3054	25	45	the	the	DET
ejpam-3054	25	46	semi	semi	ADJ
ejpam-3054	25	47	-	-	ADJ
ejpam-3054	25	48	fredholm	fredholm	ADJ
ejpam-3054	25	49	spectrum	spectrum	NOUN
ejpam-3054	25	50	.	.	PUNCT
ejpam-3054	26	1	while	while	SCONJ
ejpam-3054	26	2	the	the	DET
ejpam-3054	26	3	last	last	ADJ
ejpam-3054	26	4	section	section	NOUN
ejpam-3054	26	5	is	be	AUX
ejpam-3054	26	6	devoted	devote	VERB
ejpam-3054	26	7	to	to	ADP
ejpam-3054	26	8	the	the	DET
ejpam-3054	26	9	characterization	characterization	NOUN
ejpam-3054	26	10	of	of	ADP
ejpam-3054	26	11	such	such	ADJ
ejpam-3054	26	12	maps	map	NOUN
ejpam-3054	26	13	ϕ	ϕ	PROPN
ejpam-3054	26	14	that	that	PRON
ejpam-3054	26	15	compress	compress	VERB
ejpam-3054	26	16	the	the	DET
ejpam-3054	26	17	weyl	weyl	PROPN
ejpam-3054	26	18	spectrum	spectrum	NOUN
ejpam-3054	26	19	.	.	PUNCT
ejpam-3054	27	1	2	2	X
ejpam-3054	27	2	.	.	X
ejpam-3054	27	3	essentially	essentially	ADV
ejpam-3054	27	4	spectrally	spectrally	ADV
ejpam-3054	27	5	bounded	bound	VERB
ejpam-3054	27	6	linear	linear	PROPN
ejpam-3054	27	7	maps	map	NOUN
ejpam-3054	27	8	first	first	ADV
ejpam-3054	27	9	,	,	PUNCT
ejpam-3054	27	10	let	let	VERB
ejpam-3054	27	11	us	we	PRON
ejpam-3054	27	12	recall	recall	VERB
ejpam-3054	27	13	the	the	DET
ejpam-3054	27	14	following	follow	VERB
ejpam-3054	27	15	useful	useful	ADJ
ejpam-3054	27	16	facts	fact	NOUN
ejpam-3054	27	17	about	about	ADP
ejpam-3054	27	18	fredholm	fredholm	NOUN
ejpam-3054	27	19	theory	theory	NOUN
ejpam-3054	27	20	in	in	ADP
ejpam-3054	27	21	semisimple	semisimple	NOUN
ejpam-3054	27	22	banach	banach	NOUN
ejpam-3054	27	23	algebras	algebra	VERB
ejpam-3054	27	24	that	that	PRON
ejpam-3054	27	25	will	will	AUX
ejpam-3054	27	26	be	be	AUX
ejpam-3054	27	27	often	often	ADV
ejpam-3054	27	28	used	use	VERB
ejpam-3054	27	29	in	in	ADP
ejpam-3054	27	30	the	the	DET
ejpam-3054	27	31	sequel	sequel	NOUN
ejpam-3054	27	32	.	.	PUNCT
ejpam-3054	28	1	let	let	VERB
ejpam-3054	28	2	a	a	PRON
ejpam-3054	28	3	be	be	AUX
ejpam-3054	28	4	a	a	DET
ejpam-3054	28	5	semisimple	semisimple	NOUN
ejpam-3054	28	6	banach	banach	NOUN
ejpam-3054	28	7	algebra	algebra	NOUN
ejpam-3054	28	8	.	.	PUNCT
ejpam-3054	29	1	the	the	DET
ejpam-3054	29	2	socle	socle	NOUN
ejpam-3054	29	3	of	of	ADP
ejpam-3054	29	4	a	a	DET
ejpam-3054	29	5	,	,	PUNCT
ejpam-3054	29	6	soc	soc	NOUN
ejpam-3054	29	7	(	(	PUNCT
ejpam-3054	29	8	a	a	NOUN
ejpam-3054	29	9	)	)	PUNCT
ejpam-3054	29	10	,	,	PUNCT
ejpam-3054	29	11	is	be	AUX
ejpam-3054	29	12	defined	define	VERB
ejpam-3054	29	13	to	to	PART
ejpam-3054	29	14	be	be	AUX
ejpam-3054	29	15	the	the	DET
ejpam-3054	29	16	sum	sum	NOUN
ejpam-3054	29	17	of	of	ADP
ejpam-3054	29	18	all	all	DET
ejpam-3054	29	19	minimal	minimal	ADJ
ejpam-3054	29	20	left	left	ADJ
ejpam-3054	29	21	(	(	PUNCT
ejpam-3054	29	22	or	or	CCONJ
ejpam-3054	29	23	right	right	ADJ
ejpam-3054	29	24	)	)	PUNCT
ejpam-3054	29	25	ideals	ideal	NOUN
ejpam-3054	29	26	of	of	ADP
ejpam-3054	29	27	a.	a.	NOUN
ejpam-3054	29	28	the	the	DET
ejpam-3054	29	29	ideal	ideal	NOUN
ejpam-3054	29	30	of	of	ADP
ejpam-3054	29	31	inessential	inessential	ADJ
ejpam-3054	29	32	elements	element	NOUN
ejpam-3054	29	33	of	of	ADP
ejpam-3054	29	34	a	a	PRON
ejpam-3054	29	35	is	be	AUX
ejpam-3054	29	36	given	give	VERB
ejpam-3054	29	37	by	by	ADP
ejpam-3054	29	38	i(a	i(a	NOUN
ejpam-3054	29	39	)	)	PUNCT
ejpam-3054	29	40	:	:	PUNCT
ejpam-3054	30	1	=	=	SYM
ejpam-3054	30	2	⋂	⋂	PROPN
ejpam-3054	30	3	{	{	PUNCT
ejpam-3054	30	4	p	p	X
ejpam-3054	30	5	:	:	PUNCT
ejpam-3054	30	6	p	p	X
ejpam-3054	30	7	∈	∈	PROPN
ejpam-3054	30	8	πa	πa	ADP
ejpam-3054	30	9	:	:	PUNCT
ejpam-3054	30	10	soc	soc	NOUN
ejpam-3054	30	11	(	(	PUNCT
ejpam-3054	30	12	a	a	X
ejpam-3054	30	13	)	)	PUNCT
ejpam-3054	30	14	⊆	⊆	NUM
ejpam-3054	30	15	p	p	NOUN
ejpam-3054	30	16	}	}	PUNCT
ejpam-3054	30	17	,	,	PUNCT
ejpam-3054	30	18	where	where	SCONJ
ejpam-3054	30	19	πa	πa	ADP
ejpam-3054	30	20	denotes	denote	VERB
ejpam-3054	30	21	the	the	DET
ejpam-3054	30	22	set	set	NOUN
ejpam-3054	30	23	of	of	ADP
ejpam-3054	30	24	all	all	DET
ejpam-3054	30	25	primitive	primitive	ADJ
ejpam-3054	30	26	ideals	ideal	NOUN
ejpam-3054	30	27	of	of	ADP
ejpam-3054	30	28	a.	a.	NOUN
ejpam-3054	31	1	it	it	PRON
ejpam-3054	31	2	is	be	AUX
ejpam-3054	31	3	a	a	DET
ejpam-3054	31	4	closed	closed	ADJ
ejpam-3054	31	5	ideal	ideal	NOUN
ejpam-3054	31	6	of	of	ADP
ejpam-3054	31	7	a.	a.	NOUN
ejpam-3054	31	8	we	we	PRON
ejpam-3054	31	9	call	call	VERB
ejpam-3054	31	10	c(a	c(a	ADV
ejpam-3054	31	11	)	)	PUNCT
ejpam-3054	31	12	:	:	PUNCT
ejpam-3054	32	1	=	=	PUNCT
ejpam-3054	32	2	a	a	DET
ejpam-3054	32	3	/	/	SYM
ejpam-3054	32	4	i(a	i(a	PROPN
ejpam-3054	32	5	)	)	PUNCT
ejpam-3054	32	6	the	the	DET
ejpam-3054	32	7	generalized	generalized	ADJ
ejpam-3054	32	8	calkin	calkin	ADJ
ejpam-3054	32	9	algebra	algebra	NOUN
ejpam-3054	32	10	of	of	ADP
ejpam-3054	32	11	a.	a.	NOUN
ejpam-3054	32	12	it	it	PRON
ejpam-3054	32	13	should	should	AUX
ejpam-3054	32	14	be	be	AUX
ejpam-3054	32	15	noted	note	VERB
ejpam-3054	32	16	that	that	SCONJ
ejpam-3054	32	17	a	a	DET
ejpam-3054	32	18	semisimple	semisimple	NOUN
ejpam-3054	32	19	banach	banach	NOUN
ejpam-3054	32	20	algebra	algebra	NOUN
ejpam-3054	32	21	is	be	AUX
ejpam-3054	32	22	finite	finite	ADJ
ejpam-3054	32	23	dimensional	dimensional	ADJ
ejpam-3054	32	24	if	if	SCONJ
ejpam-3054	33	1	and	and	CCONJ
ejpam-3054	33	2	only	only	ADV
ejpam-3054	33	3	if	if	SCONJ
ejpam-3054	33	4	it	it	PRON
ejpam-3054	33	5	coincides	coincide	VERB
ejpam-3054	33	6	with	with	ADP
ejpam-3054	33	7	its	its	PRON
ejpam-3054	33	8	socle	socle	NOUN
ejpam-3054	33	9	;	;	PUNCT
ejpam-3054	33	10	see	see	VERB
ejpam-3054	33	11	for	for	ADP
ejpam-3054	33	12	instance	instance	NOUN
ejpam-3054	33	13	[	[	X
ejpam-3054	33	14	2	2	NUM
ejpam-3054	33	15	,	,	PUNCT
ejpam-3054	33	16	theorem	theorem	VERB
ejpam-3054	33	17	5.4.2	5.4.2	NUM
ejpam-3054	33	18	]	]	PUNCT
ejpam-3054	33	19	.	.	PUNCT
ejpam-3054	34	1	since	since	SCONJ
ejpam-3054	34	2	our	our	PRON
ejpam-3054	34	3	algebras	algebra	NOUN
ejpam-3054	34	4	are	be	AUX
ejpam-3054	34	5	always	always	ADV
ejpam-3054	34	6	supposed	suppose	VERB
ejpam-3054	34	7	to	to	PART
ejpam-3054	34	8	be	be	AUX
ejpam-3054	34	9	infinite	infinite	ADJ
ejpam-3054	34	10	dimensional	dimensional	ADJ
ejpam-3054	34	11	,	,	PUNCT
ejpam-3054	34	12	the	the	DET
ejpam-3054	34	13	generalized	generalized	ADJ
ejpam-3054	34	14	calkin	calkin	ADJ
ejpam-3054	34	15	algebra	algebra	NOUN
ejpam-3054	34	16	introduced	introduce	VERB
ejpam-3054	34	17	above	above	ADV
ejpam-3054	34	18	is	be	AUX
ejpam-3054	34	19	not	not	PART
ejpam-3054	34	20	trivial	trivial	ADJ
ejpam-3054	34	21	.	.	PUNCT
ejpam-3054	35	1	an	an	DET
ejpam-3054	35	2	element	element	NOUN
ejpam-3054	35	3	a	a	DET
ejpam-3054	35	4	∈	∈	NOUN
ejpam-3054	35	5	a	a	PRON
ejpam-3054	35	6	is	be	AUX
ejpam-3054	35	7	called	call	VERB
ejpam-3054	35	8	left	left	ADJ
ejpam-3054	35	9	semi	semi	ADJ
ejpam-3054	35	10	-	-	NOUN
ejpam-3054	35	11	fredholm	fredholm	ADJ
ejpam-3054	35	12	(	(	PUNCT
ejpam-3054	35	13	resp	resp	NOUN
ejpam-3054	35	14	.	.	PUNCT
ejpam-3054	36	1	right	right	ADJ
ejpam-3054	36	2	semi	semi	ADJ
ejpam-3054	36	3	-	-	NOUN
ejpam-3054	36	4	fredholm	fredholm	ADJ
ejpam-3054	36	5	)	)	PUNCT
ejpam-3054	36	6	if	if	SCONJ
ejpam-3054	36	7	it	it	PRON
ejpam-3054	36	8	is	be	AUX
ejpam-3054	36	9	left	leave	VERB
ejpam-3054	36	10	(	(	PUNCT
ejpam-3054	36	11	resp	resp	NOUN
ejpam-3054	36	12	.	.	PUNCT
ejpam-3054	37	1	right	right	ADJ
ejpam-3054	37	2	)	)	PUNCT
ejpam-3054	37	3	invertible	invertible	ADJ
ejpam-3054	37	4	modulo	modulo	NOUN
ejpam-3054	37	5	soc	soc	NOUN
ejpam-3054	37	6	(	(	PUNCT
ejpam-3054	37	7	a	a	NOUN
ejpam-3054	37	8	)	)	PUNCT
ejpam-3054	37	9	,	,	PUNCT
ejpam-3054	37	10	and	and	CCONJ
ejpam-3054	37	11	is	be	AUX
ejpam-3054	37	12	called	call	VERB
ejpam-3054	37	13	fredholm	fredholm	NOUN
ejpam-3054	37	14	if	if	SCONJ
ejpam-3054	37	15	it	it	PRON
ejpam-3054	37	16	is	be	AUX
ejpam-3054	37	17	invertible	invertible	ADJ
ejpam-3054	37	18	modulo	modulo	NOUN
ejpam-3054	37	19	soc	soc	NOUN
ejpam-3054	37	20	(	(	PUNCT
ejpam-3054	37	21	a	a	NOUN
ejpam-3054	37	22	)	)	PUNCT
ejpam-3054	37	23	.	.	PUNCT
ejpam-3054	38	1	the	the	DET
ejpam-3054	38	2	element	element	NOUN
ejpam-3054	38	3	a	a	PRON
ejpam-3054	38	4	is	be	AUX
ejpam-3054	38	5	said	say	VERB
ejpam-3054	38	6	to	to	PART
ejpam-3054	38	7	be	be	AUX
ejpam-3054	38	8	atkinson	atkinson	NOUN
ejpam-3054	38	9	if	if	SCONJ
ejpam-3054	38	10	it	it	PRON
ejpam-3054	38	11	is	be	AUX
ejpam-3054	38	12	left	leave	VERB
ejpam-3054	38	13	or	or	CCONJ
ejpam-3054	38	14	right	right	ADJ
ejpam-3054	38	15	semi	semi	NOUN
ejpam-3054	38	16	-	-	NOUN
ejpam-3054	38	17	fredholm	fredholm	ADJ
ejpam-3054	38	18	.	.	PUNCT
ejpam-3054	39	1	it	it	PRON
ejpam-3054	39	2	is	be	AUX
ejpam-3054	39	3	known	know	VERB
ejpam-3054	39	4	that	that	SCONJ
ejpam-3054	39	5	left	leave	VERB
ejpam-3054	39	6	(	(	PUNCT
ejpam-3054	39	7	resp	resp	NOUN
ejpam-3054	39	8	.	.	PUNCT
ejpam-3054	40	1	right	right	ADJ
ejpam-3054	40	2	)	)	PUNCT
ejpam-3054	40	3	invertible	invertible	ADJ
ejpam-3054	40	4	modulo	modulo	NOUN
ejpam-3054	40	5	soc	soc	NOUN
ejpam-3054	40	6	(	(	PUNCT
ejpam-3054	40	7	a	a	X
ejpam-3054	40	8	)	)	PUNCT
ejpam-3054	40	9	is	be	AUX
ejpam-3054	40	10	equivalent	equivalent	ADJ
ejpam-3054	40	11	to	to	AUX
ejpam-3054	40	12	left	left	ADJ
ejpam-3054	40	13	(	(	PUNCT
ejpam-3054	40	14	resp	resp	NOUN
ejpam-3054	40	15	.	.	PUNCT
ejpam-3054	41	1	right	right	ADJ
ejpam-3054	41	2	)	)	PUNCT
ejpam-3054	41	3	invertible	invertible	ADJ
ejpam-3054	41	4	modulo	modulo	PROPN
ejpam-3054	41	5	i(a	i(a	PROPN
ejpam-3054	41	6	)	)	PUNCT
ejpam-3054	41	7	.	.	PUNCT
ejpam-3054	42	1	for	for	ADP
ejpam-3054	42	2	every	every	DET
ejpam-3054	42	3	a	a	DET
ejpam-3054	42	4	∈	∈	PROPN
ejpam-3054	42	5	a	a	DET
ejpam-3054	42	6	we	we	PRON
ejpam-3054	42	7	set	set	VERB
ejpam-3054	42	8	σe(a	σe(a	NOUN
ejpam-3054	42	9	)	)	PUNCT
ejpam-3054	42	10	:	:	PUNCT
ejpam-3054	42	11	=	=	SYM
ejpam-3054	42	12	{	{	PUNCT
ejpam-3054	42	13	λ	λ	X
ejpam-3054	42	14	∈	∈	NOUN
ejpam-3054	42	15	c	c	NOUN
ejpam-3054	42	16	:	:	PUNCT
ejpam-3054	42	17	a−	a−	PROPN
ejpam-3054	42	18	λ	λ	PROPN
ejpam-3054	42	19	is	be	AUX
ejpam-3054	42	20	not	not	PART
ejpam-3054	42	21	fredholm	fredholm	NOUN
ejpam-3054	42	22	}	}	PUNCT
ejpam-3054	42	23	,	,	PUNCT
ejpam-3054	42	24	h.	h.	PROPN
ejpam-3054	42	25	outouzzalt	outouzzalt	PROPN
ejpam-3054	42	26	/	/	SYM
ejpam-3054	42	27	eur	eur	PROPN
ejpam-3054	42	28	.	.	PUNCT
ejpam-3054	43	1	j.	j.	PROPN
ejpam-3054	43	2	pure	pure	PROPN
ejpam-3054	43	3	appl	appl	PROPN
ejpam-3054	43	4	.	.	PROPN
ejpam-3054	43	5	math	math	PROPN
ejpam-3054	43	6	,	,	PUNCT
ejpam-3054	43	7	10	10	NUM
ejpam-3054	43	8	(	(	PUNCT
ejpam-3054	43	9	5	5	NUM
ejpam-3054	43	10	)	)	PUNCT
ejpam-3054	43	11	(	(	PUNCT
ejpam-3054	43	12	2017	2017	NUM
ejpam-3054	43	13	)	)	PUNCT
ejpam-3054	43	14	,	,	PUNCT
ejpam-3054	43	15	1058	1058	NUM
ejpam-3054	43	16	-	-	SYM
ejpam-3054	43	17	1066	1066	NUM
ejpam-3054	43	18	1060	1060	NUM
ejpam-3054	43	19	σle(a	σle(a	PROPN
ejpam-3054	43	20	)	)	PUNCT
ejpam-3054	43	21	:	:	PUNCT
ejpam-3054	43	22	=	=	SYM
ejpam-3054	43	23	{	{	PUNCT
ejpam-3054	43	24	λ	λ	X
ejpam-3054	43	25	∈	∈	NOUN
ejpam-3054	43	26	c	c	NOUN
ejpam-3054	43	27	:	:	PUNCT
ejpam-3054	43	28	a−	a−	PROPN
ejpam-3054	43	29	λ	λ	PROPN
ejpam-3054	43	30	is	be	AUX
ejpam-3054	43	31	not	not	PART
ejpam-3054	43	32	left	leave	VERB
ejpam-3054	43	33	semi	semi	ADJ
ejpam-3054	43	34	-	-	NOUN
ejpam-3054	43	35	fredholm	fredholm	ADJ
ejpam-3054	43	36	}	}	PUNCT
ejpam-3054	43	37	,	,	PUNCT
ejpam-3054	43	38	σre(a	σre(a	PROPN
ejpam-3054	43	39	)	)	PUNCT
ejpam-3054	43	40	:	:	PUNCT
ejpam-3054	44	1	=	=	SYM
ejpam-3054	44	2	{	{	PUNCT
ejpam-3054	44	3	λ	λ	X
ejpam-3054	44	4	∈	∈	NOUN
ejpam-3054	44	5	c	c	NOUN
ejpam-3054	44	6	:	:	PUNCT
ejpam-3054	44	7	a−	a−	PROPN
ejpam-3054	44	8	λ	λ	PROPN
ejpam-3054	44	9	is	be	AUX
ejpam-3054	44	10	not	not	PART
ejpam-3054	44	11	right	right	ADJ
ejpam-3054	44	12	semi	semi	ADJ
ejpam-3054	44	13	-	-	NOUN
ejpam-3054	44	14	fredholm	fredholm	ADJ
ejpam-3054	44	15	}	}	PUNCT
ejpam-3054	44	16	,	,	PUNCT
ejpam-3054	44	17	and	and	CCONJ
ejpam-3054	44	18	σsf	σsf	PROPN
ejpam-3054	44	19	(	(	PUNCT
ejpam-3054	44	20	a	a	X
ejpam-3054	44	21	)	)	PUNCT
ejpam-3054	44	22	:	:	PUNCT
ejpam-3054	44	23	=	=	SYM
ejpam-3054	44	24	{	{	PUNCT
ejpam-3054	44	25	λ	λ	X
ejpam-3054	44	26	∈	∈	NOUN
ejpam-3054	44	27	c	c	NOUN
ejpam-3054	44	28	:	:	PUNCT
ejpam-3054	44	29	a−	a−	PROPN
ejpam-3054	44	30	λ	λ	PROPN
ejpam-3054	44	31	is	be	AUX
ejpam-3054	44	32	not	not	PART
ejpam-3054	44	33	atkinson	atkinson	NOUN
ejpam-3054	44	34	}	}	PUNCT
ejpam-3054	44	35	.	.	PUNCT
ejpam-3054	45	1	these	these	PRON
ejpam-3054	45	2	are	be	AUX
ejpam-3054	45	3	called	call	VERB
ejpam-3054	45	4	respectively	respectively	ADV
ejpam-3054	45	5	the	the	DET
ejpam-3054	45	6	essential	essential	ADJ
ejpam-3054	45	7	spectrum	spectrum	NOUN
ejpam-3054	45	8	,	,	PUNCT
ejpam-3054	45	9	the	the	DET
ejpam-3054	45	10	left	left	ADJ
ejpam-3054	45	11	essential	essential	ADJ
ejpam-3054	45	12	spectrum	spectrum	NOUN
ejpam-3054	45	13	,	,	PUNCT
ejpam-3054	45	14	the	the	DET
ejpam-3054	45	15	right	right	ADJ
ejpam-3054	45	16	essential	essential	ADJ
ejpam-3054	45	17	spectrum	spectrum	NOUN
ejpam-3054	45	18	,	,	PUNCT
ejpam-3054	45	19	and	and	CCONJ
ejpam-3054	45	20	the	the	DET
ejpam-3054	45	21	semi	semi	ADJ
ejpam-3054	45	22	-	-	ADJ
ejpam-3054	45	23	fredholm	fredholm	ADJ
ejpam-3054	45	24	spectrum	spectrum	NOUN
ejpam-3054	45	25	of	of	ADP
ejpam-3054	45	26	a.	a.	NOUN
ejpam-3054	45	27	for	for	ADP
ejpam-3054	45	28	an	an	DET
ejpam-3054	45	29	element	element	NOUN
ejpam-3054	45	30	a	a	DET
ejpam-3054	45	31	∈	∈	PROPN
ejpam-3054	45	32	a	a	PRON
ejpam-3054	45	33	,	,	PUNCT
ejpam-3054	45	34	the	the	DET
ejpam-3054	45	35	essential	essential	ADJ
ejpam-3054	45	36	spectral	spectral	ADJ
ejpam-3054	45	37	radius	radius	NOUN
ejpam-3054	45	38	is	be	AUX
ejpam-3054	45	39	defined	define	VERB
ejpam-3054	45	40	by	by	ADP
ejpam-3054	45	41	re(a	re(a	NOUN
ejpam-3054	45	42	)	)	PUNCT
ejpam-3054	45	43	:	:	PUNCT
ejpam-3054	46	1	=	=	NOUN
ejpam-3054	46	2	max{|λ|	max{|λ|	NOUN
ejpam-3054	46	3	:	:	PUNCT
ejpam-3054	46	4	λ	λ	X
ejpam-3054	46	5	∈	∈	NOUN
ejpam-3054	46	6	σe(a	σe(a	NOUN
ejpam-3054	46	7	)	)	PUNCT
ejpam-3054	46	8	}	}	PUNCT
ejpam-3054	46	9	.	.	PUNCT
ejpam-3054	47	1	it	it	PRON
ejpam-3054	47	2	coincides	coincide	VERB
ejpam-3054	47	3	with	with	ADP
ejpam-3054	47	4	the	the	DET
ejpam-3054	47	5	limit	limit	NOUN
ejpam-3054	47	6	of	of	ADP
ejpam-3054	47	7	the	the	DET
ejpam-3054	47	8	convergent	convergent	NOUN
ejpam-3054	47	9	sequence	sequence	NOUN
ejpam-3054	47	10	(	(	PUNCT
ejpam-3054	47	11	‖an‖	‖an‖	PROPN
ejpam-3054	47	12	1	1	NUM
ejpam-3054	47	13	n	n	PROPN
ejpam-3054	47	14	e	e	NOUN
ejpam-3054	47	15	)	)	PUNCT
ejpam-3054	47	16	n≥1	n≥1	NOUN
ejpam-3054	47	17	,	,	PUNCT
ejpam-3054	47	18	where	where	SCONJ
ejpam-3054	47	19	‖a‖e	‖a‖e	PROPN
ejpam-3054	47	20	:	:	PUNCT
ejpam-3054	47	21	=	=	SYM
ejpam-3054	47	22	‖π(a)‖	‖π(a)‖	PUNCT
ejpam-3054	47	23	is	be	AUX
ejpam-3054	47	24	the	the	DET
ejpam-3054	47	25	essential	essential	ADJ
ejpam-3054	47	26	norm	norm	NOUN
ejpam-3054	47	27	of	of	ADP
ejpam-3054	47	28	a	a	PRON
ejpam-3054	47	29	and	and	CCONJ
ejpam-3054	47	30	π	π	PROPN
ejpam-3054	47	31	is	be	AUX
ejpam-3054	47	32	the	the	DET
ejpam-3054	47	33	canonical	canonical	ADJ
ejpam-3054	47	34	projection	projection	NOUN
ejpam-3054	47	35	from	from	ADP
ejpam-3054	47	36	a	a	PRON
ejpam-3054	47	37	onto	onto	ADP
ejpam-3054	47	38	c(a	c(a	PROPN
ejpam-3054	47	39	)	)	PUNCT
ejpam-3054	47	40	.	.	PUNCT
ejpam-3054	48	1	we	we	PRON
ejpam-3054	48	2	refer	refer	VERB
ejpam-3054	48	3	the	the	DET
ejpam-3054	48	4	reader	reader	NOUN
ejpam-3054	48	5	to	to	ADP
ejpam-3054	48	6	[	[	X
ejpam-3054	48	7	17	17	NUM
ejpam-3054	48	8	,	,	PUNCT
ejpam-3054	48	9	18	18	NUM
ejpam-3054	48	10	]	]	PUNCT
ejpam-3054	48	11	and	and	CCONJ
ejpam-3054	48	12	the	the	DET
ejpam-3054	48	13	monographs	monograph	NOUN
ejpam-3054	48	14	[	[	X
ejpam-3054	48	15	1	1	NUM
ejpam-3054	48	16	,	,	PUNCT
ejpam-3054	48	17	4	4	NUM
ejpam-3054	48	18	]	]	PUNCT
ejpam-3054	48	19	for	for	ADP
ejpam-3054	48	20	basic	basic	ADJ
ejpam-3054	48	21	facts	fact	NOUN
ejpam-3054	48	22	concerning	concern	VERB
ejpam-3054	48	23	atkinson	atkinson	NOUN
ejpam-3054	48	24	and	and	CCONJ
ejpam-3054	48	25	fredholm	fredholm	NOUN
ejpam-3054	48	26	theory	theory	NOUN
ejpam-3054	48	27	in	in	ADP
ejpam-3054	48	28	banach	banach	NOUN
ejpam-3054	48	29	algebras	algebra	NOUN
ejpam-3054	48	30	.	.	PUNCT
ejpam-3054	49	1	a	a	DET
ejpam-3054	49	2	linear	linear	PROPN
ejpam-3054	49	3	map	map	NOUN
ejpam-3054	49	4	ϕ	ϕ	NOUN
ejpam-3054	49	5	:	:	PUNCT
ejpam-3054	49	6	a	a	DET
ejpam-3054	49	7	→	→	SYM
ejpam-3054	49	8	b	b	PROPN
ejpam-3054	49	9	is	be	AUX
ejpam-3054	49	10	said	say	VERB
ejpam-3054	49	11	to	to	PART
ejpam-3054	49	12	be	be	AUX
ejpam-3054	49	13	surjective	surjective	ADJ
ejpam-3054	49	14	up	up	ADP
ejpam-3054	49	15	to	to	ADP
ejpam-3054	49	16	inessential	inessential	ADJ
ejpam-3054	49	17	elements	element	NOUN
ejpam-3054	49	18	if	if	SCONJ
ejpam-3054	49	19	b	b	PROPN
ejpam-3054	49	20	=	=	SYM
ejpam-3054	49	21	ϕ(a	ϕ(a	NOUN
ejpam-3054	49	22	)	)	PUNCT
ejpam-3054	50	1	+	+	CCONJ
ejpam-3054	50	2	i(b	i(b	NOUN
ejpam-3054	50	3	)	)	PUNCT
ejpam-3054	50	4	.	.	PUNCT
ejpam-3054	51	1	it	it	PRON
ejpam-3054	51	2	is	be	AUX
ejpam-3054	51	3	called	call	VERB
ejpam-3054	51	4	spectrally	spectrally	ADV
ejpam-3054	51	5	bounded	bound	VERB
ejpam-3054	51	6	if	if	SCONJ
ejpam-3054	51	7	there	there	PRON
ejpam-3054	51	8	exists	exist	VERB
ejpam-3054	51	9	a	a	DET
ejpam-3054	51	10	positive	positive	ADJ
ejpam-3054	51	11	constant	constant	ADJ
ejpam-3054	51	12	m	m	VERB
ejpam-3054	51	13	such	such	ADJ
ejpam-3054	51	14	that	that	SCONJ
ejpam-3054	51	15	r(ϕ(a	r(ϕ(a	NOUN
ejpam-3054	51	16	)	)	PUNCT
ejpam-3054	51	17	)	)	PUNCT
ejpam-3054	51	18	≤	≤	NOUN
ejpam-3054	51	19	mr(a	mr(a	PUNCT
ejpam-3054	51	20	)	)	PUNCT
ejpam-3054	51	21	)	)	PUNCT
ejpam-3054	51	22	for	for	ADP
ejpam-3054	51	23	all	all	DET
ejpam-3054	51	24	a	a	DET
ejpam-3054	51	25	∈	∈	PROPN
ejpam-3054	51	26	a	a	PRON
ejpam-3054	51	27	,	,	PUNCT
ejpam-3054	51	28	where	where	SCONJ
ejpam-3054	51	29	r	r	NOUN
ejpam-3054	51	30	(	(	PUNCT
ejpam-3054	51	31	.	.	PUNCT
ejpam-3054	51	32	)	)	PUNCT
ejpam-3054	51	33	denotes	denote	VERB
ejpam-3054	51	34	the	the	DET
ejpam-3054	51	35	classical	classical	ADJ
ejpam-3054	51	36	spectral	spectral	ADJ
ejpam-3054	51	37	radius	radius	NOUN
ejpam-3054	51	38	.	.	PUNCT
ejpam-3054	52	1	the	the	DET
ejpam-3054	52	2	following	following	NOUN
ejpam-3054	52	3	,	,	PUNCT
ejpam-3054	52	4	quoted	quote	VERB
ejpam-3054	52	5	in	in	ADP
ejpam-3054	52	6	[	[	X
ejpam-3054	52	7	6	6	NUM
ejpam-3054	52	8	]	]	PUNCT
ejpam-3054	52	9	,	,	PUNCT
ejpam-3054	52	10	is	be	AUX
ejpam-3054	52	11	needed	need	VERB
ejpam-3054	52	12	in	in	ADP
ejpam-3054	52	13	what	what	PRON
ejpam-3054	52	14	follows	follow	VERB
ejpam-3054	52	15	.	.	PUNCT
ejpam-3054	53	1	lemma	lemma	PROPN
ejpam-3054	53	2	1	1	X
ejpam-3054	53	3	.	.	PUNCT
ejpam-3054	54	1	let	let	VERB
ejpam-3054	54	2	a	a	DET
ejpam-3054	54	3	be	be	AUX
ejpam-3054	54	4	a	a	DET
ejpam-3054	54	5	unital	unital	ADJ
ejpam-3054	54	6	purely	purely	ADV
ejpam-3054	54	7	infinite	infinite	ADJ
ejpam-3054	54	8	c∗-algebra	c∗-algebra	PROPN
ejpam-3054	54	9	with	with	ADP
ejpam-3054	54	10	real	real	ADJ
ejpam-3054	54	11	rank	rank	NOUN
ejpam-3054	54	12	zero	zero	NUM
ejpam-3054	54	13	and	and	CCONJ
ejpam-3054	54	14	let	let	VERB
ejpam-3054	54	15	b	b	X
ejpam-3054	54	16	be	be	AUX
ejpam-3054	54	17	a	a	DET
ejpam-3054	54	18	unital	unital	ADJ
ejpam-3054	54	19	semi	semi	ADJ
ejpam-3054	54	20	-	-	ADJ
ejpam-3054	54	21	prime	prime	ADJ
ejpam-3054	54	22	banach	banach	NOUN
ejpam-3054	54	23	algebra	algebra	NOUN
ejpam-3054	54	24	.	.	PUNCT
ejpam-3054	55	1	if	if	SCONJ
ejpam-3054	55	2	ϕ	ϕ	NOUN
ejpam-3054	55	3	:	:	PUNCT
ejpam-3054	55	4	a	a	DET
ejpam-3054	55	5	→	→	SYM
ejpam-3054	55	6	b	b	X
ejpam-3054	55	7	be	be	AUX
ejpam-3054	55	8	a	a	DET
ejpam-3054	55	9	surjective	surjective	ADJ
ejpam-3054	55	10	spectrally	spectrally	ADV
ejpam-3054	55	11	bounded	bound	VERB
ejpam-3054	55	12	linear	linear	PROPN
ejpam-3054	55	13	map	map	NOUN
ejpam-3054	55	14	,	,	PUNCT
ejpam-3054	55	15	then	then	ADV
ejpam-3054	55	16	there	there	PRON
ejpam-3054	55	17	exist	exist	VERB
ejpam-3054	55	18	a	a	DET
ejpam-3054	55	19	central	central	ADJ
ejpam-3054	55	20	invertible	invertible	ADJ
ejpam-3054	55	21	element	element	NOUN
ejpam-3054	55	22	c	c	NOUN
ejpam-3054	55	23	,	,	PUNCT
ejpam-3054	55	24	viz	viz	PROPN
ejpam-3054	55	25	.	.	PROPN
ejpam-3054	55	26	,	,	PUNCT
ejpam-3054	55	27	ϕ(1	ϕ(1	PROPN
ejpam-3054	55	28	)	)	PUNCT
ejpam-3054	55	29	,	,	PUNCT
ejpam-3054	55	30	and	and	CCONJ
ejpam-3054	55	31	a	a	DET
ejpam-3054	55	32	jordan	jordan	PROPN
ejpam-3054	55	33	epimorphism	epimorphism	PROPN
ejpam-3054	55	34	j	j	PROPN
ejpam-3054	55	35	:	:	PUNCT
ejpam-3054	55	36	a→	a→	PROPN
ejpam-3054	55	37	b	b	X
ejpam-3054	55	38	such	such	ADJ
ejpam-3054	55	39	that	that	PRON
ejpam-3054	55	40	ϕ(x	ϕ(x	X
ejpam-3054	55	41	)	)	PUNCT
ejpam-3054	55	42	=	=	PUNCT
ejpam-3054	55	43	cj(x	cj(x	X
ejpam-3054	55	44	)	)	PUNCT
ejpam-3054	55	45	for	for	ADP
ejpam-3054	55	46	all	all	DET
ejpam-3054	55	47	x	x	SYM
ejpam-3054	55	48	∈	∈	NOUN
ejpam-3054	55	49	a.	a.	NOUN
ejpam-3054	55	50	proof	proof	NOUN
ejpam-3054	55	51	.	.	PUNCT
ejpam-3054	56	1	see	see	VERB
ejpam-3054	56	2	[	[	X
ejpam-3054	56	3	6	6	NUM
ejpam-3054	56	4	,	,	PUNCT
ejpam-3054	56	5	lemma	lemma	PROPN
ejpam-3054	56	6	2.1	2.1	NUM
ejpam-3054	56	7	]	]	PUNCT
ejpam-3054	56	8	the	the	DET
ejpam-3054	56	9	problem	problem	NOUN
ejpam-3054	56	10	of	of	ADP
ejpam-3054	56	11	characterizing	characterize	VERB
ejpam-3054	56	12	essentially	essentially	ADV
ejpam-3054	56	13	spectrally	spectrally	ADV
ejpam-3054	56	14	bounded	bound	VERB
ejpam-3054	56	15	it	it	PRON
ejpam-3054	56	16	seems	seem	VERB
ejpam-3054	56	17	to	to	PART
ejpam-3054	56	18	be	be	AUX
ejpam-3054	56	19	difficult	difficult	ADJ
ejpam-3054	56	20	even	even	ADV
ejpam-3054	56	21	when	when	SCONJ
ejpam-3054	56	22	a	a	PRON
ejpam-3054	56	23	and	and	CCONJ
ejpam-3054	56	24	b	b	NOUN
ejpam-3054	56	25	are	be	AUX
ejpam-3054	56	26	supposed	suppose	VERB
ejpam-3054	56	27	to	to	PART
ejpam-3054	56	28	be	be	AUX
ejpam-3054	56	29	c∗-algebras	c∗-algebra	NOUN
ejpam-3054	56	30	of	of	ADP
ejpam-3054	56	31	real	real	ADJ
ejpam-3054	56	32	rank	rank	NOUN
ejpam-3054	56	33	zero	zero	NUM
ejpam-3054	56	34	.	.	PUNCT
ejpam-3054	57	1	recall	recall	VERB
ejpam-3054	57	2	that	that	SCONJ
ejpam-3054	57	3	a	a	DET
ejpam-3054	57	4	c∗algebra	c∗algebra	NOUN
ejpam-3054	57	5	a	a	DET
ejpam-3054	57	6	is	is	NOUN
ejpam-3054	57	7	of	of	ADP
ejpam-3054	57	8	real	real	ADJ
ejpam-3054	57	9	rank	rank	NOUN
ejpam-3054	57	10	zero	zero	NUM
ejpam-3054	57	11	if	if	SCONJ
ejpam-3054	57	12	the	the	DET
ejpam-3054	57	13	set	set	NOUN
ejpam-3054	57	14	of	of	ADP
ejpam-3054	57	15	all	all	PRON
ejpam-3054	57	16	finite	finite	ADJ
ejpam-3054	57	17	real	real	ADJ
ejpam-3054	57	18	linear	linear	ADJ
ejpam-3054	57	19	combinations	combination	NOUN
ejpam-3054	57	20	of	of	ADP
ejpam-3054	57	21	orthogonal	orthogonal	ADJ
ejpam-3054	57	22	projections	projection	NOUN
ejpam-3054	57	23	is	be	AUX
ejpam-3054	57	24	dense	dense	ADJ
ejpam-3054	57	25	in	in	ADP
ejpam-3054	57	26	the	the	DET
ejpam-3054	57	27	set	set	NOUN
ejpam-3054	57	28	of	of	ADP
ejpam-3054	57	29	all	all	DET
ejpam-3054	57	30	self	self	NOUN
ejpam-3054	57	31	adjoint	adjoint	NOUN
ejpam-3054	57	32	elements	element	NOUN
ejpam-3054	57	33	of	of	ADP
ejpam-3054	57	34	a	a	PRON
ejpam-3054	57	35	;	;	PUNCT
ejpam-3054	57	36	see	see	VERB
ejpam-3054	57	37	[	[	X
ejpam-3054	57	38	8	8	NUM
ejpam-3054	57	39	]	]	PUNCT
ejpam-3054	57	40	.	.	PUNCT
ejpam-3054	58	1	however	however	ADV
ejpam-3054	58	2	,	,	PUNCT
ejpam-3054	58	3	we	we	PRON
ejpam-3054	58	4	give	give	VERB
ejpam-3054	58	5	a	a	DET
ejpam-3054	58	6	positive	positive	ADJ
ejpam-3054	58	7	answer	answer	NOUN
ejpam-3054	58	8	to	to	ADP
ejpam-3054	58	9	this	this	DET
ejpam-3054	58	10	problem	problem	NOUN
ejpam-3054	58	11	when	when	SCONJ
ejpam-3054	58	12	a	a	PRON
ejpam-3054	58	13	is	be	AUX
ejpam-3054	58	14	a	a	DET
ejpam-3054	58	15	purely	purely	ADV
ejpam-3054	58	16	infinite	infinite	ADJ
ejpam-3054	58	17	c∗-algebra	c∗-algebra	NOUN
ejpam-3054	58	18	of	of	ADP
ejpam-3054	58	19	real	real	ADJ
ejpam-3054	58	20	rank	rank	NOUN
ejpam-3054	58	21	zero	zero	NUM
ejpam-3054	58	22	.	.	PUNCT
ejpam-3054	59	1	a	a	DET
ejpam-3054	59	2	c∗-algebras	c∗-algebra	NOUN
ejpam-3054	59	3	a	a	DET
ejpam-3054	59	4	is	be	AUX
ejpam-3054	59	5	purely	purely	ADV
ejpam-3054	59	6	infinite	infinite	ADJ
ejpam-3054	59	7	if	if	SCONJ
ejpam-3054	59	8	it	it	PRON
ejpam-3054	59	9	has	have	VERB
ejpam-3054	59	10	no	no	DET
ejpam-3054	59	11	characters	character	NOUN
ejpam-3054	59	12	and	and	CCONJ
ejpam-3054	59	13	if	if	SCONJ
ejpam-3054	59	14	,	,	PUNCT
ejpam-3054	59	15	for	for	ADP
ejpam-3054	59	16	every	every	DET
ejpam-3054	59	17	pair	pair	NOUN
ejpam-3054	59	18	of	of	ADP
ejpam-3054	59	19	positive	positive	ADJ
ejpam-3054	59	20	elements	element	NOUN
ejpam-3054	59	21	a	a	PRON
ejpam-3054	59	22	,	,	PUNCT
ejpam-3054	59	23	b	b	NOUN
ejpam-3054	59	24	in	in	ADP
ejpam-3054	59	25	a	a	PRON
ejpam-3054	59	26	with	with	ADP
ejpam-3054	59	27	a	a	DET
ejpam-3054	59	28	∈	∈	PROPN
ejpam-3054	59	29	aba	aba	NOUN
ejpam-3054	59	30	,	,	PUNCT
ejpam-3054	59	31	there	there	PRON
ejpam-3054	59	32	is	be	VERB
ejpam-3054	59	33	a	a	DET
ejpam-3054	59	34	sequence	sequence	NOUN
ejpam-3054	59	35	(	(	PUNCT
ejpam-3054	59	36	xn)n∈n	xn)n∈n	NUM
ejpam-3054	59	37	in	in	ADP
ejpam-3054	59	38	a	a	DET
ejpam-3054	59	39	such	such	ADJ
ejpam-3054	59	40	that	that	SCONJ
ejpam-3054	59	41	a	a	DET
ejpam-3054	59	42	=	=	X
ejpam-3054	59	43	limn	limn	NOUN
ejpam-3054	59	44	x	x	NOUN
ejpam-3054	59	45	∗	∗	NOUN
ejpam-3054	59	46	nbxn	nbxn	NOUN
ejpam-3054	59	47	;	;	PUNCT
ejpam-3054	59	48	see	see	VERB
ejpam-3054	59	49	[	[	X
ejpam-3054	59	50	15	15	NUM
ejpam-3054	59	51	]	]	PUNCT
ejpam-3054	59	52	.	.	PUNCT
ejpam-3054	60	1	the	the	DET
ejpam-3054	60	2	main	main	ADJ
ejpam-3054	60	3	result	result	NOUN
ejpam-3054	60	4	of	of	ADP
ejpam-3054	60	5	this	this	DET
ejpam-3054	60	6	section	section	NOUN
ejpam-3054	60	7	is	be	AUX
ejpam-3054	60	8	the	the	DET
ejpam-3054	60	9	following	following	NOUN
ejpam-3054	60	10	.	.	PUNCT
ejpam-3054	61	1	it	it	PRON
ejpam-3054	61	2	characterizes	characterize	VERB
ejpam-3054	61	3	essentially	essentially	ADV
ejpam-3054	61	4	spectrally	spectrally	ADV
ejpam-3054	61	5	bounded	bound	VERB
ejpam-3054	61	6	linear	linear	ADJ
ejpam-3054	61	7	maps	map	NOUN
ejpam-3054	61	8	.	.	PUNCT
ejpam-3054	62	1	theorem	theorem	NOUN
ejpam-3054	62	2	1	1	NUM
ejpam-3054	62	3	.	.	PUNCT
ejpam-3054	63	1	let	let	VERB
ejpam-3054	63	2	ϕ	ϕ	NOUN
ejpam-3054	63	3	be	be	AUX
ejpam-3054	63	4	a	a	DET
ejpam-3054	63	5	linear	linear	ADJ
ejpam-3054	63	6	surjective	surjective	NOUN
ejpam-3054	63	7	up	up	ADP
ejpam-3054	63	8	to	to	ADP
ejpam-3054	63	9	inessential	inessential	ADJ
ejpam-3054	63	10	elements	element	NOUN
ejpam-3054	63	11	map	map	NOUN
ejpam-3054	63	12	from	from	ADP
ejpam-3054	63	13	a	a	DET
ejpam-3054	63	14	purely	purely	ADV
ejpam-3054	63	15	infinite	infinite	ADJ
ejpam-3054	63	16	c∗-algebras	c∗-algebra	NOUN
ejpam-3054	63	17	with	with	ADP
ejpam-3054	63	18	real	real	ADJ
ejpam-3054	63	19	rank	rank	NOUN
ejpam-3054	63	20	zero	zero	NUM
ejpam-3054	63	21	a	a	PRON
ejpam-3054	63	22	into	into	ADP
ejpam-3054	63	23	semisimple	semisimple	NOUN
ejpam-3054	63	24	a	a	DET
ejpam-3054	63	25	banach	banach	NOUN
ejpam-3054	63	26	algebra	algebra	NOUN
ejpam-3054	63	27	b.	b.	NOUN
ejpam-3054	64	1	if	if	SCONJ
ejpam-3054	64	2	ϕ	ϕ	NOUN
ejpam-3054	64	3	is	be	AUX
ejpam-3054	64	4	essentially	essentially	ADV
ejpam-3054	64	5	spectrally	spectrally	ADV
ejpam-3054	64	6	bounded	bound	VERB
ejpam-3054	64	7	,	,	PUNCT
ejpam-3054	64	8	then	then	ADV
ejpam-3054	64	9	ϕ(i(a	ϕ(i(a	NUM
ejpam-3054	64	10	)	)	PUNCT
ejpam-3054	64	11	)	)	PUNCT
ejpam-3054	65	1	⊆	⊆	NUM
ejpam-3054	65	2	i(b	i(b	NOUN
ejpam-3054	65	3	)	)	PUNCT
ejpam-3054	65	4	h.	h.	PROPN
ejpam-3054	65	5	outouzzalt	outouzzalt	PROPN
ejpam-3054	65	6	/	/	SYM
ejpam-3054	65	7	eur	eur	PROPN
ejpam-3054	65	8	.	.	PUNCT
ejpam-3054	66	1	j.	j.	PROPN
ejpam-3054	66	2	pure	pure	PROPN
ejpam-3054	66	3	appl	appl	PROPN
ejpam-3054	66	4	.	.	PROPN
ejpam-3054	66	5	math	math	PROPN
ejpam-3054	66	6	,	,	PUNCT
ejpam-3054	66	7	10	10	NUM
ejpam-3054	66	8	(	(	PUNCT
ejpam-3054	66	9	5	5	NUM
ejpam-3054	66	10	)	)	PUNCT
ejpam-3054	66	11	(	(	PUNCT
ejpam-3054	66	12	2017	2017	NUM
ejpam-3054	66	13	)	)	PUNCT
ejpam-3054	66	14	,	,	PUNCT
ejpam-3054	66	15	1058	1058	NUM
ejpam-3054	66	16	-	-	SYM
ejpam-3054	66	17	1066	1066	NUM
ejpam-3054	66	18	1061	1061	NUM
ejpam-3054	66	19	and	and	CCONJ
ejpam-3054	66	20	the	the	DET
ejpam-3054	66	21	induced	induced	ADJ
ejpam-3054	66	22	mapping	mapping	NOUN
ejpam-3054	66	23	ϕ̂	ϕ̂	NUM
ejpam-3054	66	24	:	:	PUNCT
ejpam-3054	66	25	c(a)→	c(a)→	PROPN
ejpam-3054	66	26	c(b	c(b	PROPN
ejpam-3054	66	27	)	)	PUNCT
ejpam-3054	66	28	defined	define	VERB
ejpam-3054	66	29	by	by	ADP
ejpam-3054	66	30	ϕ̂(π(a	ϕ̂(π(a	PROPN
ejpam-3054	66	31	)	)	PUNCT
ejpam-3054	66	32	)	)	PUNCT
ejpam-3054	66	33	:	:	PUNCT
ejpam-3054	67	1	=	=	PUNCT
ejpam-3054	67	2	π(ϕ(a	π(ϕ(a	NOUN
ejpam-3054	67	3	)	)	PUNCT
ejpam-3054	67	4	)	)	PUNCT
ejpam-3054	67	5	,	,	PUNCT
ejpam-3054	67	6	(	(	PUNCT
ejpam-3054	67	7	a	a	DET
ejpam-3054	67	8	∈	∈	PROPN
ejpam-3054	67	9	a	a	PRON
ejpam-3054	67	10	)	)	PUNCT
ejpam-3054	67	11	,	,	PUNCT
ejpam-3054	67	12	is	be	AUX
ejpam-3054	67	13	a	a	DET
ejpam-3054	67	14	continuous	continuous	ADJ
ejpam-3054	67	15	jordan	jordan	PROPN
ejpam-3054	67	16	epimorphism	epimorphism	PROPN
ejpam-3054	67	17	multiplied	multiply	VERB
ejpam-3054	67	18	by	by	ADP
ejpam-3054	67	19	an	an	DET
ejpam-3054	67	20	invertible	invertible	ADJ
ejpam-3054	67	21	central	central	ADJ
ejpam-3054	67	22	element	element	NOUN
ejpam-3054	67	23	of	of	ADP
ejpam-3054	67	24	c(b	c(b	PROPN
ejpam-3054	67	25	)	)	PUNCT
ejpam-3054	67	26	.	.	PUNCT
ejpam-3054	68	1	proof	proof	NOUN
ejpam-3054	68	2	.	.	PUNCT
ejpam-3054	69	1	assume	assume	VERB
ejpam-3054	69	2	that	that	SCONJ
ejpam-3054	69	3	there	there	PRON
ejpam-3054	69	4	is	be	VERB
ejpam-3054	69	5	a	a	DET
ejpam-3054	69	6	positive	positive	ADJ
ejpam-3054	69	7	constant	constant	ADJ
ejpam-3054	69	8	m	m	NOUN
ejpam-3054	69	9	such	such	ADJ
ejpam-3054	69	10	that	that	SCONJ
ejpam-3054	69	11	re(ϕ(x	re(ϕ(x	NOUN
ejpam-3054	69	12	)	)	PUNCT
ejpam-3054	69	13	)	)	PUNCT
ejpam-3054	69	14	≤	≤	NUM
ejpam-3054	69	15	mre(x	mre(x	PROPN
ejpam-3054	69	16	)	)	PUNCT
ejpam-3054	69	17	for	for	ADP
ejpam-3054	69	18	all	all	DET
ejpam-3054	69	19	x	x	SYM
ejpam-3054	69	20	∈	∈	NOUN
ejpam-3054	69	21	a.	a.	NOUN
ejpam-3054	69	22	we	we	PRON
ejpam-3054	69	23	first	first	ADV
ejpam-3054	69	24	show	show	VERB
ejpam-3054	69	25	that	that	SCONJ
ejpam-3054	69	26	ϕ	ϕ	PROPN
ejpam-3054	69	27	maps	map	NOUN
ejpam-3054	69	28	i(a	i(a	PROPN
ejpam-3054	69	29	)	)	PUNCT
ejpam-3054	69	30	into	into	ADP
ejpam-3054	69	31	i(b	i(b	PROPN
ejpam-3054	69	32	)	)	PUNCT
ejpam-3054	69	33	.	.	PUNCT
ejpam-3054	70	1	so	so	ADV
ejpam-3054	70	2	pick	pick	VERB
ejpam-3054	70	3	an	an	DET
ejpam-3054	70	4	inessential	inessential	ADJ
ejpam-3054	70	5	element	element	NOUN
ejpam-3054	70	6	a	a	DET
ejpam-3054	70	7	∈	∈	PROPN
ejpam-3054	70	8	i(a	i(a	PROPN
ejpam-3054	70	9	)	)	PUNCT
ejpam-3054	70	10	,	,	PUNCT
ejpam-3054	70	11	and	and	CCONJ
ejpam-3054	70	12	let	let	VERB
ejpam-3054	70	13	us	we	PRON
ejpam-3054	70	14	prove	prove	VERB
ejpam-3054	70	15	that	that	SCONJ
ejpam-3054	70	16	ϕ(a	ϕ(a	NOUN
ejpam-3054	70	17	)	)	PUNCT
ejpam-3054	70	18	is	be	AUX
ejpam-3054	70	19	inessential	inessential	ADJ
ejpam-3054	70	20	as	as	ADV
ejpam-3054	70	21	well	well	ADV
ejpam-3054	70	22	.	.	PUNCT
ejpam-3054	71	1	let	let	VERB
ejpam-3054	71	2	y	y	PRON
ejpam-3054	71	3	be	be	AUX
ejpam-3054	71	4	an	an	DET
ejpam-3054	71	5	arbitrary	arbitrary	ADJ
ejpam-3054	71	6	element	element	NOUN
ejpam-3054	71	7	in	in	ADP
ejpam-3054	71	8	b	b	NOUN
ejpam-3054	71	9	and	and	CCONJ
ejpam-3054	71	10	note	note	VERB
ejpam-3054	71	11	that	that	SCONJ
ejpam-3054	71	12	,	,	PUNCT
ejpam-3054	71	13	since	since	SCONJ
ejpam-3054	71	14	ϕ	ϕ	NOUN
ejpam-3054	71	15	is	be	AUX
ejpam-3054	71	16	surjective	surjective	ADJ
ejpam-3054	71	17	up	up	ADP
ejpam-3054	71	18	to	to	ADP
ejpam-3054	71	19	inessential	inessential	ADJ
ejpam-3054	71	20	elements	element	NOUN
ejpam-3054	71	21	,	,	PUNCT
ejpam-3054	71	22	there	there	PRON
ejpam-3054	71	23	exist	exist	VERB
ejpam-3054	71	24	x	x	PUNCT
ejpam-3054	71	25	∈	∈	PROPN
ejpam-3054	71	26	a	a	DET
ejpam-3054	71	27	and	and	CCONJ
ejpam-3054	71	28	y0	y0	PROPN
ejpam-3054	71	29	∈	∈	PROPN
ejpam-3054	71	30	i(b	i(b	NOUN
ejpam-3054	71	31	)	)	PUNCT
ejpam-3054	71	32	such	such	ADJ
ejpam-3054	71	33	that	that	SCONJ
ejpam-3054	71	34	y	y	PROPN
ejpam-3054	71	35	=	=	PUNCT
ejpam-3054	71	36	ϕ(x	ϕ(x	PROPN
ejpam-3054	71	37	)	)	PUNCT
ejpam-3054	71	38	+	+	X
ejpam-3054	72	1	y0	y0	NOUN
ejpam-3054	72	2	.	.	PUNCT
ejpam-3054	73	1	for	for	ADP
ejpam-3054	73	2	every	every	DET
ejpam-3054	73	3	λ	λ	PROPN
ejpam-3054	73	4	∈	∈	PROPN
ejpam-3054	73	5	c	c	X
ejpam-3054	73	6	,	,	PUNCT
ejpam-3054	73	7	we	we	PRON
ejpam-3054	73	8	have	have	VERB
ejpam-3054	73	9	r(λπ(ϕ(a	r(λπ(ϕ(a	NOUN
ejpam-3054	73	10	)	)	PUNCT
ejpam-3054	73	11	)	)	PUNCT
ejpam-3054	74	1	+	+	CCONJ
ejpam-3054	74	2	π(y	π(y	NOUN
ejpam-3054	74	3	)	)	PUNCT
ejpam-3054	74	4	)	)	PUNCT
ejpam-3054	75	1	=	=	SYM
ejpam-3054	75	2	r(π(λϕ(a	r(π(λϕ(a	NOUN
ejpam-3054	75	3	)	)	PUNCT
ejpam-3054	75	4	+	+	CCONJ
ejpam-3054	75	5	y	y	NOUN
ejpam-3054	75	6	)	)	PUNCT
ejpam-3054	75	7	)	)	PUNCT
ejpam-3054	76	1	=	=	SYM
ejpam-3054	76	2	re(λϕ(a	re(λϕ(a	NOUN
ejpam-3054	76	3	)	)	PUNCT
ejpam-3054	76	4	+	+	SYM
ejpam-3054	76	5	y	y	X
ejpam-3054	76	6	)	)	PUNCT
ejpam-3054	76	7	=	=	NOUN
ejpam-3054	76	8	re(ϕ(λa+	re(ϕ(λa+	NOUN
ejpam-3054	76	9	x	x	NOUN
ejpam-3054	76	10	)	)	PUNCT
ejpam-3054	76	11	+	+	CCONJ
ejpam-3054	76	12	y0	y0	NOUN
ejpam-3054	76	13	)	)	PUNCT
ejpam-3054	76	14	=	=	SYM
ejpam-3054	76	15	re(ϕ(λa+	re(ϕ(λa+	NOUN
ejpam-3054	76	16	x	x	NOUN
ejpam-3054	76	17	)	)	PUNCT
ejpam-3054	76	18	)	)	PUNCT
ejpam-3054	76	19	≤	≤	NUM
ejpam-3054	76	20	mre(λa+	mre(λa+	PROPN
ejpam-3054	76	21	x	x	X
ejpam-3054	76	22	)	)	PUNCT
ejpam-3054	76	23	=	=	SYM
ejpam-3054	76	24	mre(x	mre(x	PROPN
ejpam-3054	76	25	)	)	PUNCT
ejpam-3054	76	26	=	=	PUNCT
ejpam-3054	76	27	mr(π(x	mr(π(x	NOUN
ejpam-3054	76	28	)	)	PUNCT
ejpam-3054	76	29	)	)	PUNCT
ejpam-3054	76	30	.	.	PUNCT
ejpam-3054	77	1	since	since	SCONJ
ejpam-3054	77	2	λ	λ	PROPN
ejpam-3054	77	3	7→	7→	PROPN
ejpam-3054	77	4	r(λπ(ϕ(a))+π(y	r(λπ(ϕ(a))+π(y	PROPN
ejpam-3054	77	5	)	)	PUNCT
ejpam-3054	77	6	)	)	PUNCT
ejpam-3054	77	7	is	be	AUX
ejpam-3054	77	8	a	a	DET
ejpam-3054	77	9	subharmonic	subharmonic	ADJ
ejpam-3054	77	10	function	function	NOUN
ejpam-3054	77	11	on	on	ADP
ejpam-3054	77	12	c	c	PROPN
ejpam-3054	77	13	,	,	PUNCT
ejpam-3054	77	14	liouville	liouville	PROPN
ejpam-3054	77	15	’s	’s	PART
ejpam-3054	77	16	theorem	theorem	NOUN
ejpam-3054	77	17	implies	imply	VERB
ejpam-3054	77	18	that	that	SCONJ
ejpam-3054	77	19	r(π(ϕ(a	r(π(ϕ(a	NOUN
ejpam-3054	77	20	)	)	PUNCT
ejpam-3054	77	21	)	)	PUNCT
ejpam-3054	78	1	+	+	CCONJ
ejpam-3054	78	2	π(y	π(y	NOUN
ejpam-3054	78	3	)	)	PUNCT
ejpam-3054	78	4	)	)	PUNCT
ejpam-3054	79	1	=	=	SYM
ejpam-3054	79	2	r(π(y	r(π(y	PROPN
ejpam-3054	79	3	)	)	PUNCT
ejpam-3054	79	4	)	)	PUNCT
ejpam-3054	79	5	.	.	PUNCT
ejpam-3054	80	1	as	as	SCONJ
ejpam-3054	80	2	y	y	PROPN
ejpam-3054	80	3	is	be	AUX
ejpam-3054	80	4	arbitrary	arbitrary	ADJ
ejpam-3054	80	5	in	in	ADP
ejpam-3054	80	6	b	b	NUM
ejpam-3054	80	7	,	,	PUNCT
ejpam-3054	80	8	it	it	PRON
ejpam-3054	80	9	follows	follow	VERB
ejpam-3054	80	10	from	from	ADP
ejpam-3054	80	11	semi	semi	ADJ
ejpam-3054	80	12	-	-	NOUN
ejpam-3054	80	13	simplicity	simplicity	NOUN
ejpam-3054	80	14	of	of	ADP
ejpam-3054	80	15	c(b	c(b	PROPN
ejpam-3054	80	16	)	)	PUNCT
ejpam-3054	80	17	and	and	CCONJ
ejpam-3054	80	18	the	the	DET
ejpam-3054	80	19	zemánek	zemánek	NOUN
ejpam-3054	80	20	’s	’s	PART
ejpam-3054	80	21	characterization	characterization	NOUN
ejpam-3054	80	22	of	of	ADP
ejpam-3054	80	23	the	the	DET
ejpam-3054	80	24	radical	radical	ADJ
ejpam-3054	80	25	[	[	X
ejpam-3054	80	26	2	2	NUM
ejpam-3054	80	27	,	,	PUNCT
ejpam-3054	80	28	theorem	theorem	VERB
ejpam-3054	80	29	5.3.1	5.3.1	NUM
ejpam-3054	80	30	]	]	PUNCT
ejpam-3054	80	31	that	that	SCONJ
ejpam-3054	80	32	π(ϕ(a	π(ϕ(a	NOUN
ejpam-3054	80	33	)	)	PUNCT
ejpam-3054	80	34	)	)	PUNCT
ejpam-3054	80	35	=	=	SYM
ejpam-3054	80	36	0	0	NUM
ejpam-3054	80	37	and	and	CCONJ
ejpam-3054	80	38	ϕ(a	ϕ(a	PROPN
ejpam-3054	80	39	)	)	PUNCT
ejpam-3054	80	40	∈	∈	PROPN
ejpam-3054	80	41	i(b	i(b	PROPN
ejpam-3054	80	42	)	)	PUNCT
ejpam-3054	80	43	.	.	PUNCT
ejpam-3054	81	1	therefore	therefore	ADV
ejpam-3054	81	2	ϕ(i(a	ϕ(i(a	NUM
ejpam-3054	81	3	)	)	PUNCT
ejpam-3054	81	4	)	)	PUNCT
ejpam-3054	82	1	⊆	⊆	NUM
ejpam-3054	82	2	i(b	i(b	NOUN
ejpam-3054	82	3	)	)	PUNCT
ejpam-3054	82	4	,	,	PUNCT
ejpam-3054	82	5	and	and	CCONJ
ejpam-3054	82	6	ϕ	ϕ	NOUN
ejpam-3054	82	7	induces	induce	VERB
ejpam-3054	82	8	a	a	DET
ejpam-3054	82	9	linear	linear	ADJ
ejpam-3054	82	10	map	map	NOUN
ejpam-3054	82	11	ϕ̂	ϕ̂	X
ejpam-3054	82	12	:	:	PUNCT
ejpam-3054	82	13	c(a	c(a	ADV
ejpam-3054	82	14	)	)	PUNCT
ejpam-3054	82	15	→	→	PUNCT
ejpam-3054	82	16	c(b	c(b	PROPN
ejpam-3054	82	17	)	)	PUNCT
ejpam-3054	82	18	defined	define	VERB
ejpam-3054	82	19	by	by	ADP
ejpam-3054	82	20	ϕ̂(π(x	ϕ̂(π(x	NOUN
ejpam-3054	82	21	)	)	PUNCT
ejpam-3054	82	22	)	)	PUNCT
ejpam-3054	82	23	:	:	PUNCT
ejpam-3054	83	1	=	=	PUNCT
ejpam-3054	83	2	π(ϕ(x	π(ϕ(x	PROPN
ejpam-3054	83	3	)	)	PUNCT
ejpam-3054	83	4	)	)	PUNCT
ejpam-3054	83	5	for	for	ADP
ejpam-3054	83	6	all	all	DET
ejpam-3054	83	7	x	x	SYM
ejpam-3054	83	8	∈	∈	NOUN
ejpam-3054	83	9	a.	a.	NOUN
ejpam-3054	83	10	the	the	DET
ejpam-3054	83	11	map	map	NOUN
ejpam-3054	83	12	ϕ̂	ϕ̂	PUNCT
ejpam-3054	83	13	is	be	AUX
ejpam-3054	83	14	obviously	obviously	ADV
ejpam-3054	83	15	surjective	surjective	ADJ
ejpam-3054	83	16	and	and	CCONJ
ejpam-3054	83	17	spectrally	spectrally	ADV
ejpam-3054	83	18	bounded	bound	VERB
ejpam-3054	83	19	.	.	PUNCT
ejpam-3054	84	1	note	note	VERB
ejpam-3054	84	2	that	that	SCONJ
ejpam-3054	84	3	,	,	PUNCT
ejpam-3054	84	4	by	by	ADP
ejpam-3054	84	5	[	[	X
ejpam-3054	84	6	15	15	NUM
ejpam-3054	84	7	,	,	PUNCT
ejpam-3054	84	8	proposition	proposition	NOUN
ejpam-3054	84	9	4.3	4.3	NUM
ejpam-3054	84	10	]	]	PUNCT
ejpam-3054	84	11	,	,	PUNCT
ejpam-3054	84	12	the	the	DET
ejpam-3054	84	13	quotient	quotient	NOUN
ejpam-3054	84	14	of	of	ADP
ejpam-3054	84	15	a	a	DET
ejpam-3054	84	16	c∗-algebra	c∗-algebra	PROPN
ejpam-3054	84	17	of	of	ADP
ejpam-3054	84	18	real	real	ADJ
ejpam-3054	84	19	rank	rank	NOUN
ejpam-3054	84	20	zero	zero	NUM
ejpam-3054	84	21	by	by	ADP
ejpam-3054	84	22	a	a	DET
ejpam-3054	84	23	closed	closed	ADJ
ejpam-3054	84	24	ideal	ideal	NOUN
ejpam-3054	84	25	is	be	AUX
ejpam-3054	84	26	a	a	DET
ejpam-3054	84	27	c∗-algebra	c∗-algebra	PROPN
ejpam-3054	84	28	of	of	ADP
ejpam-3054	84	29	real	real	ADJ
ejpam-3054	84	30	rank	rank	NOUN
ejpam-3054	84	31	zero	zero	NUM
ejpam-3054	84	32	and	and	CCONJ
ejpam-3054	84	33	the	the	DET
ejpam-3054	84	34	quotient	quotient	NOUN
ejpam-3054	84	35	of	of	ADP
ejpam-3054	84	36	a	a	DET
ejpam-3054	84	37	purely	purely	ADV
ejpam-3054	84	38	infinite	infinite	ADJ
ejpam-3054	84	39	c∗-algebra	c∗-algebra	NOUN
ejpam-3054	84	40	by	by	ADP
ejpam-3054	84	41	a	a	DET
ejpam-3054	84	42	closed	closed	ADJ
ejpam-3054	84	43	ideal	ideal	NOUN
ejpam-3054	84	44	is	be	AUX
ejpam-3054	84	45	a	a	DET
ejpam-3054	84	46	purely	purely	ADV
ejpam-3054	84	47	infinite	infinite	ADJ
ejpam-3054	84	48	c∗-algebra	c∗-algebra	NOUN
ejpam-3054	84	49	.	.	PUNCT
ejpam-3054	85	1	thus	thus	ADV
ejpam-3054	85	2	,	,	PUNCT
ejpam-3054	85	3	the	the	DET
ejpam-3054	85	4	desired	desire	VERB
ejpam-3054	85	5	conclusion	conclusion	NOUN
ejpam-3054	85	6	follows	follow	VERB
ejpam-3054	85	7	by	by	ADP
ejpam-3054	85	8	applying	apply	VERB
ejpam-3054	85	9	lemma	lemma	PROPN
ejpam-3054	85	10	1	1	NUM
ejpam-3054	85	11	.	.	PUNCT
ejpam-3054	86	1	for	for	ADP
ejpam-3054	86	2	an	an	DET
ejpam-3054	86	3	infinite	infinite	ADJ
ejpam-3054	86	4	-	-	PUNCT
ejpam-3054	86	5	dimensional	dimensional	ADJ
ejpam-3054	86	6	complex	complex	ADJ
ejpam-3054	86	7	hilbert	hilbert	NOUN
ejpam-3054	86	8	spaceh	spaceh	NOUN
ejpam-3054	86	9	,	,	PUNCT
ejpam-3054	86	10	soc	soc	NOUN
ejpam-3054	86	11	(	(	PUNCT
ejpam-3054	86	12	l(h	l(h	PROPN
ejpam-3054	86	13	)	)	PUNCT
ejpam-3054	86	14	)	)	PUNCT
ejpam-3054	87	1	=	=	SYM
ejpam-3054	87	2	f(h	f(h	PROPN
ejpam-3054	87	3	)	)	PUNCT
ejpam-3054	87	4	is	be	AUX
ejpam-3054	87	5	the	the	DET
ejpam-3054	87	6	ideal	ideal	NOUN
ejpam-3054	87	7	of	of	ADP
ejpam-3054	87	8	all	all	DET
ejpam-3054	87	9	finite	finite	PROPN
ejpam-3054	87	10	rank	rank	NOUN
ejpam-3054	87	11	operators	operator	NOUN
ejpam-3054	87	12	on	on	ADP
ejpam-3054	87	13	h	h	PROPN
ejpam-3054	87	14	,	,	PUNCT
ejpam-3054	87	15	i(l(h	i(l(h	PROPN
ejpam-3054	87	16	)	)	PUNCT
ejpam-3054	87	17	)	)	PUNCT
ejpam-3054	88	1	=	=	SYM
ejpam-3054	88	2	k(h	k(h	PROPN
ejpam-3054	88	3	)	)	PUNCT
ejpam-3054	88	4	is	be	AUX
ejpam-3054	88	5	the	the	DET
ejpam-3054	88	6	closed	closed	ADJ
ejpam-3054	88	7	ideal	ideal	NOUN
ejpam-3054	88	8	of	of	ADP
ejpam-3054	88	9	all	all	DET
ejpam-3054	88	10	compact	compact	ADJ
ejpam-3054	88	11	operators	operator	NOUN
ejpam-3054	88	12	on	on	ADP
ejpam-3054	88	13	h	h	NOUN
ejpam-3054	88	14	,	,	PUNCT
ejpam-3054	88	15	and	and	CCONJ
ejpam-3054	88	16	the	the	DET
ejpam-3054	88	17	generalized	generalized	ADJ
ejpam-3054	88	18	calkin	calkin	ADJ
ejpam-3054	88	19	algebra	algebra	PROPN
ejpam-3054	88	20	c(l(h	c(l(h	PROPN
ejpam-3054	88	21	)	)	PUNCT
ejpam-3054	88	22	)	)	PUNCT
ejpam-3054	88	23	coincides	coincide	VERB
ejpam-3054	88	24	with	with	ADP
ejpam-3054	88	25	the	the	DET
ejpam-3054	88	26	usual	usual	ADJ
ejpam-3054	88	27	calkin	calkin	ADJ
ejpam-3054	88	28	algebra	algebra	NOUN
ejpam-3054	88	29	c(h	c(h	NOUN
ejpam-3054	88	30	)	)	PUNCT
ejpam-3054	88	31	=	=	SYM
ejpam-3054	88	32	l(h)/k(h	l(h)/k(h	NOUN
ejpam-3054	88	33	)	)	PUNCT
ejpam-3054	88	34	,	,	PUNCT
ejpam-3054	88	35	and	and	CCONJ
ejpam-3054	88	36	it	it	PRON
ejpam-3054	88	37	is	be	AUX
ejpam-3054	88	38	prime	prime	ADJ
ejpam-3054	88	39	.	.	PUNCT
ejpam-3054	89	1	thus	thus	ADV
ejpam-3054	89	2	,	,	PUNCT
ejpam-3054	89	3	a	a	DET
ejpam-3054	89	4	jordan	jordan	PROPN
ejpam-3054	89	5	homomorphism	homomorphism	PROPN
ejpam-3054	89	6	ϕ̂	ϕ̂	X
ejpam-3054	89	7	:	:	PUNCT
ejpam-3054	89	8	c(h)→	c(h)→	NOUN
ejpam-3054	89	9	c(h	c(h	VERB
ejpam-3054	89	10	)	)	PUNCT
ejpam-3054	89	11	is	be	AUX
ejpam-3054	89	12	either	either	CCONJ
ejpam-3054	89	13	a	a	DET
ejpam-3054	89	14	homomorphism	homomorphism	NOUN
ejpam-3054	89	15	or	or	CCONJ
ejpam-3054	89	16	an	an	DET
ejpam-3054	89	17	anti	anti	NOUN
ejpam-3054	89	18	-	-	NOUN
ejpam-3054	89	19	homomorphism	homomorphism	NOUN
ejpam-3054	89	20	by	by	ADP
ejpam-3054	89	21	[	[	PUNCT
ejpam-3054	89	22	11	11	NUM
ejpam-3054	89	23	]	]	PUNCT
ejpam-3054	89	24	.	.	PUNCT
ejpam-3054	90	1	more	more	ADV
ejpam-3054	90	2	generally	generally	ADV
ejpam-3054	90	3	,	,	PUNCT
ejpam-3054	90	4	if	if	SCONJ
ejpam-3054	90	5	a	a	PRON
ejpam-3054	90	6	is	be	AUX
ejpam-3054	90	7	a	a	DET
ejpam-3054	90	8	c∗-algebra	c∗-algebra	PROPN
ejpam-3054	90	9	,	,	PUNCT
ejpam-3054	90	10	then	then	ADV
ejpam-3054	90	11	soc	soc	NOUN
ejpam-3054	90	12	(	(	PUNCT
ejpam-3054	90	13	a	a	NOUN
ejpam-3054	90	14	)	)	PUNCT
ejpam-3054	90	15	is	be	AUX
ejpam-3054	90	16	the	the	DET
ejpam-3054	90	17	set	set	NOUN
ejpam-3054	90	18	of	of	ADP
ejpam-3054	90	19	all	all	DET
ejpam-3054	90	20	finite	finite	PROPN
ejpam-3054	90	21	rank	rank	NOUN
ejpam-3054	90	22	element	element	NOUN
ejpam-3054	90	23	in	in	ADP
ejpam-3054	90	24	a	a	PRON
ejpam-3054	90	25	,	,	PUNCT
ejpam-3054	90	26	and	and	CCONJ
ejpam-3054	90	27	i(a	i(a	NUM
ejpam-3054	90	28	)	)	PUNCT
ejpam-3054	90	29	=	=	NOUN
ejpam-3054	90	30	soc	soc	NOUN
ejpam-3054	90	31	(	(	PUNCT
ejpam-3054	90	32	a	a	NOUN
ejpam-3054	90	33	)	)	PUNCT
ejpam-3054	90	34	=	=	SYM
ejpam-3054	90	35	k(a	k(a	PROPN
ejpam-3054	90	36	)	)	PUNCT
ejpam-3054	90	37	,	,	PUNCT
ejpam-3054	90	38	the	the	DET
ejpam-3054	90	39	set	set	NOUN
ejpam-3054	90	40	of	of	ADP
ejpam-3054	90	41	all	all	DET
ejpam-3054	90	42	compact	compact	ADJ
ejpam-3054	90	43	elements	element	NOUN
ejpam-3054	90	44	in	in	ADP
ejpam-3054	90	45	a	a	PRON
ejpam-3054	90	46	;	;	PUNCT
ejpam-3054	90	47	see	see	VERB
ejpam-3054	90	48	[	[	X
ejpam-3054	90	49	4	4	NUM
ejpam-3054	90	50	]	]	PUNCT
ejpam-3054	90	51	.	.	PUNCT
ejpam-3054	91	1	recall	recall	VERB
ejpam-3054	91	2	that	that	SCONJ
ejpam-3054	91	3	an	an	DET
ejpam-3054	91	4	element	element	NOUN
ejpam-3054	91	5	x	x	PUNCT
ejpam-3054	91	6	of	of	ADP
ejpam-3054	91	7	a	a	PRON
ejpam-3054	91	8	is	be	AUX
ejpam-3054	91	9	said	say	VERB
ejpam-3054	91	10	to	to	PART
ejpam-3054	91	11	be	be	AUX
ejpam-3054	91	12	finite	finite	ADJ
ejpam-3054	91	13	(	(	PUNCT
ejpam-3054	91	14	resp	resp	NOUN
ejpam-3054	91	15	.	.	PUNCT
ejpam-3054	92	1	compact	compact	ADJ
ejpam-3054	92	2	)	)	PUNCT
ejpam-3054	92	3	in	in	ADP
ejpam-3054	92	4	a	a	DET
ejpam-3054	92	5	if	if	SCONJ
ejpam-3054	92	6	the	the	DET
ejpam-3054	92	7	wedge	wedge	NOUN
ejpam-3054	92	8	operator	operator	NOUN
ejpam-3054	92	9	x∧x	x∧x	PROPN
ejpam-3054	92	10	:	:	PUNCT
ejpam-3054	92	11	a→	a→	PUNCT
ejpam-3054	92	12	a	a	PRON
ejpam-3054	92	13	,	,	PUNCT
ejpam-3054	92	14	given	give	VERB
ejpam-3054	92	15	by	by	ADP
ejpam-3054	92	16	x∧x(a	x∧x(a	NOUN
ejpam-3054	92	17	)	)	PUNCT
ejpam-3054	92	18	=	=	SYM
ejpam-3054	92	19	xax	xax	PROPN
ejpam-3054	92	20	,	,	PUNCT
ejpam-3054	92	21	is	be	AUX
ejpam-3054	92	22	a	a	DET
ejpam-3054	92	23	finite	finite	ADJ
ejpam-3054	92	24	rank	rank	NOUN
ejpam-3054	92	25	(	(	PUNCT
ejpam-3054	92	26	resp	resp	NOUN
ejpam-3054	92	27	.	.	PUNCT
ejpam-3054	93	1	compact	compact	ADJ
ejpam-3054	93	2	)	)	PUNCT
ejpam-3054	93	3	operator	operator	NOUN
ejpam-3054	93	4	on	on	ADP
ejpam-3054	93	5	a.	a.	NOUN
ejpam-3054	93	6	note	note	NOUN
ejpam-3054	93	7	that	that	SCONJ
ejpam-3054	93	8	even	even	ADV
ejpam-3054	93	9	if	if	SCONJ
ejpam-3054	93	10	the	the	DET
ejpam-3054	93	11	c∗-algebra	c∗-algebra	PROPN
ejpam-3054	93	12	a	a	PRON
ejpam-3054	93	13	is	be	AUX
ejpam-3054	93	14	prime	prime	ADJ
ejpam-3054	93	15	,	,	PUNCT
ejpam-3054	93	16	the	the	DET
ejpam-3054	93	17	generalized	generalized	ADJ
ejpam-3054	93	18	calkin	calkin	ADJ
ejpam-3054	93	19	algebra	algebra	NOUN
ejpam-3054	93	20	c(a	c(a	PROPN
ejpam-3054	93	21	)	)	PUNCT
ejpam-3054	93	22	=	=	SYM
ejpam-3054	93	23	a	a	X
ejpam-3054	93	24	/	/	SYM
ejpam-3054	93	25	k(a	k(a	NOUN
ejpam-3054	93	26	)	)	PUNCT
ejpam-3054	93	27	is	be	AUX
ejpam-3054	93	28	not	not	PART
ejpam-3054	93	29	necessary	necessary	ADJ
ejpam-3054	93	30	prime	prime	ADJ
ejpam-3054	93	31	.	.	PUNCT
ejpam-3054	94	1	for	for	ADP
ejpam-3054	94	2	example	example	NOUN
ejpam-3054	94	3	,	,	PUNCT
ejpam-3054	94	4	consider	consider	VERB
ejpam-3054	94	5	a	a	DET
ejpam-3054	94	6	the	the	DET
ejpam-3054	94	7	c∗-algebra	c∗-algebra	PROPN
ejpam-3054	94	8	generated	generate	VERB
ejpam-3054	94	9	by	by	ADP
ejpam-3054	94	10	k(h	k(h	PROPN
ejpam-3054	94	11	)	)	PUNCT
ejpam-3054	94	12	and	and	CCONJ
ejpam-3054	94	13	two	two	NUM
ejpam-3054	94	14	orthogonal	orthogonal	ADJ
ejpam-3054	94	15	infinite	infinite	ADJ
ejpam-3054	94	16	dimensional	dimensional	ADJ
ejpam-3054	94	17	projections	projection	NOUN
ejpam-3054	94	18	on	on	ADP
ejpam-3054	94	19	a	a	DET
ejpam-3054	94	20	hilbert	hilbert	NOUN
ejpam-3054	94	21	space	space	NOUN
ejpam-3054	94	22	h	h	NOUN
ejpam-3054	94	23	,	,	PUNCT
ejpam-3054	94	24	and	and	CCONJ
ejpam-3054	94	25	note	note	VERB
ejpam-3054	94	26	that	that	SCONJ
ejpam-3054	94	27	c(a	c(a	ADV
ejpam-3054	94	28	)	)	PUNCT
ejpam-3054	94	29	∼=	∼=	PROPN
ejpam-3054	94	30	c2	c2	PROPN
ejpam-3054	94	31	is	be	AUX
ejpam-3054	94	32	not	not	PART
ejpam-3054	94	33	prime	prime	ADJ
ejpam-3054	94	34	.	.	PUNCT
ejpam-3054	95	1	however	however	ADV
ejpam-3054	95	2	,	,	PUNCT
ejpam-3054	95	3	when	when	SCONJ
ejpam-3054	95	4	a	a	PRON
ejpam-3054	95	5	is	be	AUX
ejpam-3054	95	6	factor	factor	NOUN
ejpam-3054	95	7	,	,	PUNCT
ejpam-3054	95	8	the	the	DET
ejpam-3054	95	9	ideal	ideal	NOUN
ejpam-3054	95	10	k(a	k(a	PROPN
ejpam-3054	95	11	)	)	PUNCT
ejpam-3054	95	12	is	be	AUX
ejpam-3054	95	13	the	the	DET
ejpam-3054	95	14	largest	large	ADJ
ejpam-3054	95	15	ideal	ideal	NOUN
ejpam-3054	95	16	of	of	ADP
ejpam-3054	95	17	type	type	NOUN
ejpam-3054	95	18	i	i	PROPN
ejpam-3054	95	19	,	,	PUNCT
ejpam-3054	95	20	and	and	CCONJ
ejpam-3054	95	21	c(a	c(a	ADV
ejpam-3054	95	22	)	)	PUNCT
ejpam-3054	95	23	is	be	AUX
ejpam-3054	95	24	a	a	DET
ejpam-3054	95	25	prime	prime	ADJ
ejpam-3054	95	26	c∗-algebra	c∗-algebra	PROPN
ejpam-3054	95	27	.	.	PUNCT
ejpam-3054	95	28	h.	h.	PROPN
ejpam-3054	95	29	outouzzalt	outouzzalt	PROPN
ejpam-3054	95	30	/	/	SYM
ejpam-3054	95	31	eur	eur	PROPN
ejpam-3054	95	32	.	.	PUNCT
ejpam-3054	96	1	j.	j.	PROPN
ejpam-3054	96	2	pure	pure	PROPN
ejpam-3054	96	3	appl	appl	PROPN
ejpam-3054	96	4	.	.	PROPN
ejpam-3054	96	5	math	math	PROPN
ejpam-3054	96	6	,	,	PUNCT
ejpam-3054	96	7	10	10	NUM
ejpam-3054	96	8	(	(	PUNCT
ejpam-3054	96	9	5	5	NUM
ejpam-3054	96	10	)	)	PUNCT
ejpam-3054	96	11	(	(	PUNCT
ejpam-3054	96	12	2017	2017	NUM
ejpam-3054	96	13	)	)	PUNCT
ejpam-3054	96	14	,	,	PUNCT
ejpam-3054	96	15	1058	1058	NUM
ejpam-3054	96	16	-	-	SYM
ejpam-3054	96	17	1066	1066	NUM
ejpam-3054	96	18	1062	1062	NUM
ejpam-3054	96	19	corollary	corollary	ADJ
ejpam-3054	96	20	1	1	NUM
ejpam-3054	96	21	.	.	PUNCT
ejpam-3054	97	1	let	let	VERB
ejpam-3054	97	2	ϕ	ϕ	NOUN
ejpam-3054	97	3	be	be	AUX
ejpam-3054	97	4	a	a	DET
ejpam-3054	97	5	surjective	surjective	ADJ
ejpam-3054	97	6	up	up	ADP
ejpam-3054	97	7	to	to	ADP
ejpam-3054	97	8	inessential	inessential	ADJ
ejpam-3054	97	9	elements	element	NOUN
ejpam-3054	97	10	linear	linear	NOUN
ejpam-3054	97	11	map	map	NOUN
ejpam-3054	97	12	from	from	ADP
ejpam-3054	97	13	a	a	DET
ejpam-3054	97	14	purely	purely	ADV
ejpam-3054	97	15	infinite	infinite	ADJ
ejpam-3054	97	16	c∗-algebra	c∗-algebra	NOUN
ejpam-3054	97	17	a	a	PRON
ejpam-3054	97	18	with	with	ADP
ejpam-3054	97	19	rank	rank	NOUN
ejpam-3054	97	20	real	real	ADJ
ejpam-3054	97	21	zero	zero	NUM
ejpam-3054	97	22	into	into	ADP
ejpam-3054	97	23	a	a	DET
ejpam-3054	97	24	factor	factor	NOUN
ejpam-3054	97	25	b.	b.	NOUN
ejpam-3054	98	1	then	then	ADV
ejpam-3054	98	2	the	the	DET
ejpam-3054	98	3	following	follow	VERB
ejpam-3054	98	4	assertions	assertion	NOUN
ejpam-3054	98	5	are	be	AUX
ejpam-3054	98	6	equivalent	equivalent	ADJ
ejpam-3054	98	7	.	.	PUNCT
ejpam-3054	99	1	(	(	PUNCT
ejpam-3054	99	2	i	i	NOUN
ejpam-3054	99	3	)	)	PUNCT
ejpam-3054	99	4	ϕ	ϕ	PROPN
ejpam-3054	99	5	is	be	AUX
ejpam-3054	99	6	essentially	essentially	ADV
ejpam-3054	99	7	spectrally	spectrally	ADV
ejpam-3054	99	8	bounded	bound	VERB
ejpam-3054	99	9	.	.	PUNCT
ejpam-3054	100	1	(	(	PUNCT
ejpam-3054	100	2	ii	ii	NOUN
ejpam-3054	100	3	)	)	PUNCT
ejpam-3054	100	4	ϕ(i(a	ϕ(i(a	NUM
ejpam-3054	100	5	)	)	PUNCT
ejpam-3054	100	6	)	)	PUNCT
ejpam-3054	101	1	⊆	⊆	NUM
ejpam-3054	101	2	i(b	i(b	NOUN
ejpam-3054	101	3	)	)	PUNCT
ejpam-3054	101	4	and	and	CCONJ
ejpam-3054	101	5	the	the	DET
ejpam-3054	101	6	induced	induced	ADJ
ejpam-3054	101	7	mapping	mapping	NOUN
ejpam-3054	101	8	ϕ̂	ϕ̂	NUM
ejpam-3054	101	9	:	:	PUNCT
ejpam-3054	101	10	c(a	c(a	ADV
ejpam-3054	101	11	)	)	PUNCT
ejpam-3054	101	12	→	→	PUNCT
ejpam-3054	101	13	c(b	c(b	PROPN
ejpam-3054	101	14	)	)	PUNCT
ejpam-3054	101	15	is	be	AUX
ejpam-3054	101	16	either	either	CCONJ
ejpam-3054	101	17	a	a	DET
ejpam-3054	101	18	continuous	continuous	ADJ
ejpam-3054	101	19	epimorphism	epimorphism	NOUN
ejpam-3054	101	20	or	or	CCONJ
ejpam-3054	101	21	a	a	DET
ejpam-3054	101	22	continuous	continuous	ADJ
ejpam-3054	101	23	anti	anti	NOUN
ejpam-3054	101	24	-	-	NOUN
ejpam-3054	101	25	epimorphism	epimorphism	NOUN
ejpam-3054	101	26	up	up	ADP
ejpam-3054	101	27	to	to	ADP
ejpam-3054	101	28	a	a	DET
ejpam-3054	101	29	nonzero	nonzero	NOUN
ejpam-3054	101	30	complex	complex	ADJ
ejpam-3054	101	31	scalar	scalar	NOUN
ejpam-3054	101	32	.	.	PUNCT
ejpam-3054	102	1	proof	proof	NOUN
ejpam-3054	102	2	.	.	PUNCT
ejpam-3054	103	1	we	we	PRON
ejpam-3054	103	2	only	only	ADV
ejpam-3054	103	3	need	need	VERB
ejpam-3054	103	4	to	to	PART
ejpam-3054	103	5	proof	proof	VERB
ejpam-3054	103	6	that	that	SCONJ
ejpam-3054	103	7	(	(	PUNCT
ejpam-3054	103	8	i)⇒(ii	i)⇒(ii	ADV
ejpam-3054	103	9	)	)	PUNCT
ejpam-3054	103	10	as	as	ADP
ejpam-3054	103	11	(	(	PUNCT
ejpam-3054	103	12	ii)⇒(i	ii)⇒(i	NOUN
ejpam-3054	103	13	)	)	PUNCT
ejpam-3054	103	14	follows	follow	VERB
ejpam-3054	103	15	easily	easily	ADV
ejpam-3054	103	16	.	.	PUNCT
ejpam-3054	104	1	if	if	SCONJ
ejpam-3054	104	2	ϕ	ϕ	NOUN
ejpam-3054	104	3	is	be	AUX
ejpam-3054	104	4	essentially	essentially	ADV
ejpam-3054	104	5	spectrally	spectrally	ADV
ejpam-3054	104	6	bounded	bound	VERB
ejpam-3054	104	7	then	then	ADV
ejpam-3054	104	8	,	,	PUNCT
ejpam-3054	104	9	by	by	ADP
ejpam-3054	104	10	theorem	theorem	NOUN
ejpam-3054	104	11	1	1	NUM
ejpam-3054	104	12	and	and	CCONJ
ejpam-3054	104	13	the	the	DET
ejpam-3054	104	14	fact	fact	NOUN
ejpam-3054	104	15	that	that	SCONJ
ejpam-3054	104	16	the	the	DET
ejpam-3054	104	17	center	center	NOUN
ejpam-3054	104	18	of	of	ADP
ejpam-3054	104	19	c(b	c(b	PROPN
ejpam-3054	104	20	)	)	PUNCT
ejpam-3054	104	21	is	be	AUX
ejpam-3054	104	22	trivial	trivial	ADJ
ejpam-3054	104	23	,	,	PUNCT
ejpam-3054	104	24	we	we	PRON
ejpam-3054	104	25	infer	infer	VERB
ejpam-3054	104	26	that	that	SCONJ
ejpam-3054	104	27	ϕ̂	ϕ̂	PUNCT
ejpam-3054	104	28	is	be	AUX
ejpam-3054	104	29	a	a	DET
ejpam-3054	104	30	continuous	continuous	ADJ
ejpam-3054	104	31	jordan	jordan	PROPN
ejpam-3054	104	32	epimorphism	epimorphism	PROPN
ejpam-3054	104	33	multiplied	multiply	VERB
ejpam-3054	104	34	by	by	ADP
ejpam-3054	104	35	a	a	DET
ejpam-3054	104	36	nonzero	nonzero	NOUN
ejpam-3054	104	37	complex	complex	ADJ
ejpam-3054	104	38	number	number	NOUN
ejpam-3054	104	39	c.	c.	NOUN
ejpam-3054	104	40	as	as	SCONJ
ejpam-3054	104	41	the	the	DET
ejpam-3054	104	42	algebra	algebra	NOUN
ejpam-3054	104	43	c(b	c(b	PROPN
ejpam-3054	104	44	)	)	PUNCT
ejpam-3054	104	45	is	be	AUX
ejpam-3054	104	46	prime	prime	ADJ
ejpam-3054	104	47	,	,	PUNCT
ejpam-3054	104	48	then	then	ADV
ejpam-3054	104	49	by	by	ADP
ejpam-3054	104	50	[	[	PUNCT
ejpam-3054	104	51	11	11	NUM
ejpam-3054	104	52	]	]	PUNCT
ejpam-3054	104	53	the	the	DET
ejpam-3054	104	54	map	map	NOUN
ejpam-3054	104	55	ϕ̂	ϕ̂	X
ejpam-3054	104	56	is	be	AUX
ejpam-3054	104	57	,	,	PUNCT
ejpam-3054	104	58	in	in	ADP
ejpam-3054	104	59	fact	fact	NOUN
ejpam-3054	104	60	,	,	PUNCT
ejpam-3054	104	61	either	either	CCONJ
ejpam-3054	104	62	an	an	DET
ejpam-3054	104	63	epimorphism	epimorphism	NOUN
ejpam-3054	104	64	or	or	CCONJ
ejpam-3054	104	65	an	an	DET
ejpam-3054	104	66	anti	anti	ADJ
ejpam-3054	104	67	-	-	ADJ
ejpam-3054	104	68	epimorphism	epimorphism	NOUN
ejpam-3054	104	69	multiplied	multiply	VERB
ejpam-3054	104	70	by	by	ADP
ejpam-3054	104	71	c.	c.	PROPN
ejpam-3054	104	72	3	3	NUM
ejpam-3054	104	73	.	.	PUNCT
ejpam-3054	105	1	atkinson	atkinson	PROPN
ejpam-3054	105	2	elements	element	NOUN
ejpam-3054	105	3	preserving	preserve	VERB
ejpam-3054	105	4	linear	linear	PROPN
ejpam-3054	105	5	maps	map	NOUN
ejpam-3054	105	6	recall	recall	VERB
ejpam-3054	105	7	that	that	SCONJ
ejpam-3054	105	8	a	a	DET
ejpam-3054	105	9	linear	linear	NOUN
ejpam-3054	105	10	map	map	NOUN
ejpam-3054	105	11	ϕ	ϕ	NOUN
ejpam-3054	105	12	from	from	ADP
ejpam-3054	105	13	a	a	PRON
ejpam-3054	105	14	into	into	ADP
ejpam-3054	105	15	b	b	NOUN
ejpam-3054	105	16	is	be	AUX
ejpam-3054	105	17	said	say	VERB
ejpam-3054	105	18	to	to	PART
ejpam-3054	105	19	preserve	preserve	VERB
ejpam-3054	105	20	fredholm	fredholm	NOUN
ejpam-3054	105	21	elements	element	NOUN
ejpam-3054	105	22	(	(	PUNCT
ejpam-3054	105	23	resp	resp	NOUN
ejpam-3054	105	24	.	.	PUNCT
ejpam-3054	106	1	preserve	preserve	VERB
ejpam-3054	106	2	fredholm	fredholm	NOUN
ejpam-3054	106	3	elements	element	NOUN
ejpam-3054	106	4	in	in	ADP
ejpam-3054	106	5	both	both	DET
ejpam-3054	106	6	directions	direction	NOUN
ejpam-3054	106	7	)	)	PUNCT
ejpam-3054	106	8	if	if	SCONJ
ejpam-3054	106	9	ϕ(a	ϕ(a	NOUN
ejpam-3054	106	10	)	)	PUNCT
ejpam-3054	106	11	is	be	AUX
ejpam-3054	106	12	a	a	DET
ejpam-3054	106	13	fredholm	fredholm	NOUN
ejpam-3054	106	14	element	element	NOUN
ejpam-3054	106	15	whenever	whenever	SCONJ
ejpam-3054	106	16	(	(	PUNCT
ejpam-3054	106	17	resp	resp	NOUN
ejpam-3054	106	18	.	.	PUNCT
ejpam-3054	107	1	if	if	SCONJ
ejpam-3054	107	2	and	and	CCONJ
ejpam-3054	107	3	only	only	ADV
ejpam-3054	107	4	if	if	SCONJ
ejpam-3054	107	5	)	)	PUNCT
ejpam-3054	107	6	a	a	PRON
ejpam-3054	107	7	is	be	AUX
ejpam-3054	107	8	.	.	PUNCT
ejpam-3054	108	1	the	the	DET
ejpam-3054	108	2	map	map	NOUN
ejpam-3054	108	3	ϕ	ϕ	NOUN
ejpam-3054	108	4	is	be	AUX
ejpam-3054	108	5	said	say	VERB
ejpam-3054	108	6	to	to	PART
ejpam-3054	108	7	compress	compress	VERB
ejpam-3054	108	8	the	the	DET
ejpam-3054	108	9	essential	essential	ADJ
ejpam-3054	108	10	spectrum	spectrum	NOUN
ejpam-3054	108	11	if	if	SCONJ
ejpam-3054	108	12	σe(ϕ(a	σe(ϕ(a	NOUN
ejpam-3054	108	13	)	)	PUNCT
ejpam-3054	108	14	)	)	PUNCT
ejpam-3054	109	1	⊆	⊆	NUM
ejpam-3054	109	2	σe(a	σe(a	NOUN
ejpam-3054	109	3	)	)	PUNCT
ejpam-3054	109	4	for	for	ADP
ejpam-3054	109	5	all	all	DET
ejpam-3054	109	6	a	a	DET
ejpam-3054	109	7	∈	∈	NOUN
ejpam-3054	109	8	a.	a.	NOUN
ejpam-3054	109	9	in	in	ADP
ejpam-3054	109	10	a	a	DET
ejpam-3054	109	11	similar	similar	ADJ
ejpam-3054	109	12	way	way	NOUN
ejpam-3054	109	13	,	,	PUNCT
ejpam-3054	109	14	we	we	PRON
ejpam-3054	109	15	define	define	VERB
ejpam-3054	109	16	linear	linear	ADJ
ejpam-3054	109	17	maps	map	NOUN
ejpam-3054	109	18	compressing	compress	VERB
ejpam-3054	109	19	different	different	ADJ
ejpam-3054	109	20	essential	essential	ADJ
ejpam-3054	109	21	spectra	spectra	NOUN
ejpam-3054	109	22	or	or	CCONJ
ejpam-3054	109	23	preserving	preserve	VERB
ejpam-3054	109	24	left	left	ADJ
ejpam-3054	109	25	semi	semi	ADJ
ejpam-3054	109	26	-	-	ADJ
ejpam-3054	109	27	fredholm	fredholm	ADJ
ejpam-3054	109	28	elements	element	NOUN
ejpam-3054	109	29	,	,	PUNCT
ejpam-3054	109	30	right	right	ADJ
ejpam-3054	109	31	semi	semi	ADJ
ejpam-3054	109	32	-	-	ADJ
ejpam-3054	109	33	fredholm	fredholm	ADJ
ejpam-3054	109	34	elements	element	NOUN
ejpam-3054	109	35	,	,	PUNCT
ejpam-3054	109	36	and	and	CCONJ
ejpam-3054	109	37	atkinson	atkinson	PROPN
ejpam-3054	109	38	elements	element	NOUN
ejpam-3054	109	39	.	.	PUNCT
ejpam-3054	110	1	the	the	DET
ejpam-3054	110	2	following	following	NOUN
ejpam-3054	110	3	describes	describe	VERB
ejpam-3054	110	4	linear	linear	PROPN
ejpam-3054	110	5	mapping	mapping	NOUN
ejpam-3054	110	6	preserving	preserve	VERB
ejpam-3054	110	7	atkinson	atkinson	NOUN
ejpam-3054	110	8	elements	element	NOUN
ejpam-3054	110	9	.	.	PUNCT
ejpam-3054	111	1	theorem	theorem	NOUN
ejpam-3054	111	2	2	2	NUM
ejpam-3054	111	3	.	.	PUNCT
ejpam-3054	112	1	let	let	VERB
ejpam-3054	112	2	a	a	DET
ejpam-3054	112	3	be	be	AUX
ejpam-3054	112	4	a	a	DET
ejpam-3054	112	5	c∗-algebra	c∗-algebra	PROPN
ejpam-3054	112	6	with	with	ADP
ejpam-3054	112	7	real	real	ADJ
ejpam-3054	112	8	rank	rank	NOUN
ejpam-3054	112	9	zero	zero	NUM
ejpam-3054	112	10	and	and	CCONJ
ejpam-3054	112	11	b	b	NOUN
ejpam-3054	112	12	be	be	AUX
ejpam-3054	112	13	a	a	DET
ejpam-3054	112	14	semisimple	semisimple	NOUN
ejpam-3054	112	15	banach	banach	NOUN
ejpam-3054	112	16	algebra	algebra	NOUN
ejpam-3054	112	17	.	.	PUNCT
ejpam-3054	113	1	let	let	VERB
ejpam-3054	113	2	ϕ	ϕ	NOUN
ejpam-3054	113	3	:	:	PUNCT
ejpam-3054	113	4	a→	a→	PROPN
ejpam-3054	113	5	b	b	X
ejpam-3054	113	6	be	be	AUX
ejpam-3054	113	7	a	a	DET
ejpam-3054	113	8	surjective	surjective	ADJ
ejpam-3054	113	9	up	up	ADP
ejpam-3054	113	10	to	to	ADP
ejpam-3054	113	11	inessential	inessential	ADJ
ejpam-3054	113	12	elements	element	NOUN
ejpam-3054	113	13	linear	linear	PROPN
ejpam-3054	113	14	map	map	NOUN
ejpam-3054	113	15	,	,	PUNCT
ejpam-3054	113	16	and	and	CCONJ
ejpam-3054	113	17	consider	consider	VERB
ejpam-3054	113	18	the	the	DET
ejpam-3054	113	19	following	follow	VERB
ejpam-3054	113	20	statements	statement	NOUN
ejpam-3054	113	21	.	.	PUNCT
ejpam-3054	114	1	(	(	PUNCT
ejpam-3054	114	2	i	i	NOUN
ejpam-3054	114	3	)	)	PUNCT
ejpam-3054	114	4	ϕ	ϕ	PROPN
ejpam-3054	114	5	preserves	preserve	VERB
ejpam-3054	114	6	fredholm	fredholm	NOUN
ejpam-3054	114	7	elements	element	NOUN
ejpam-3054	114	8	.	.	PUNCT
ejpam-3054	115	1	(	(	PUNCT
ejpam-3054	115	2	ii	ii	NOUN
ejpam-3054	115	3	)	)	PUNCT
ejpam-3054	115	4	ϕ(1	ϕ(1	PROPN
ejpam-3054	115	5	)	)	PUNCT
ejpam-3054	115	6	is	be	AUX
ejpam-3054	115	7	a	a	DET
ejpam-3054	115	8	fredholm	fredholm	NOUN
ejpam-3054	115	9	element	element	NOUN
ejpam-3054	115	10	and	and	CCONJ
ejpam-3054	115	11	ϕ	ϕ	NOUN
ejpam-3054	115	12	preserves	preserve	NOUN
ejpam-3054	115	13	left	leave	VERB
ejpam-3054	115	14	fredholm	fredholm	NOUN
ejpam-3054	115	15	elements	element	NOUN
ejpam-3054	115	16	.	.	PUNCT
ejpam-3054	116	1	(	(	PUNCT
ejpam-3054	116	2	iii	iii	X
ejpam-3054	116	3	)	)	PUNCT
ejpam-3054	116	4	ϕ(1	ϕ(1	PROPN
ejpam-3054	116	5	)	)	PUNCT
ejpam-3054	116	6	is	be	AUX
ejpam-3054	116	7	a	a	DET
ejpam-3054	116	8	fredholm	fredholm	NOUN
ejpam-3054	116	9	element	element	NOUN
ejpam-3054	116	10	and	and	CCONJ
ejpam-3054	116	11	ϕ	ϕ	NOUN
ejpam-3054	116	12	preserves	preserve	VERB
ejpam-3054	116	13	right	right	ADJ
ejpam-3054	116	14	fredholm	fredholm	NOUN
ejpam-3054	116	15	elements	element	NOUN
ejpam-3054	116	16	.	.	PUNCT
ejpam-3054	117	1	(	(	PUNCT
ejpam-3054	117	2	iv	iv	X
ejpam-3054	117	3	)	)	PUNCT
ejpam-3054	117	4	ϕ(1	ϕ(1	PROPN
ejpam-3054	117	5	)	)	PUNCT
ejpam-3054	117	6	is	be	AUX
ejpam-3054	117	7	a	a	DET
ejpam-3054	117	8	fredholm	fredholm	NOUN
ejpam-3054	117	9	element	element	NOUN
ejpam-3054	117	10	and	and	CCONJ
ejpam-3054	117	11	ϕ	ϕ	NOUN
ejpam-3054	117	12	preserves	preserve	NOUN
ejpam-3054	117	13	atkinson	atkinson	PROPN
ejpam-3054	117	14	elements	element	NOUN
ejpam-3054	117	15	.	.	PUNCT
ejpam-3054	118	1	if	if	SCONJ
ejpam-3054	118	2	any	any	PRON
ejpam-3054	118	3	of	of	ADP
ejpam-3054	118	4	these	these	DET
ejpam-3054	118	5	statements	statement	NOUN
ejpam-3054	118	6	holds	hold	VERB
ejpam-3054	118	7	,	,	PUNCT
ejpam-3054	118	8	then	then	ADV
ejpam-3054	118	9	ϕ(i(a	ϕ(i(a	NUM
ejpam-3054	118	10	)	)	PUNCT
ejpam-3054	118	11	)	)	PUNCT
ejpam-3054	119	1	⊆	⊆	NUM
ejpam-3054	119	2	i(b	i(b	NOUN
ejpam-3054	119	3	)	)	PUNCT
ejpam-3054	119	4	and	and	CCONJ
ejpam-3054	119	5	the	the	DET
ejpam-3054	119	6	induced	induced	ADJ
ejpam-3054	119	7	mapping	mapping	NOUN
ejpam-3054	119	8	ϕ̂	ϕ̂	NUM
ejpam-3054	119	9	:	:	PUNCT
ejpam-3054	119	10	c(a	c(a	ADV
ejpam-3054	119	11	)	)	PUNCT
ejpam-3054	119	12	→	→	PUNCT
ejpam-3054	119	13	c(b	c(b	PROPN
ejpam-3054	119	14	)	)	PUNCT
ejpam-3054	119	15	is	be	AUX
ejpam-3054	119	16	a	a	DET
ejpam-3054	119	17	continuous	continuous	ADJ
ejpam-3054	119	18	jordan	jordan	PROPN
ejpam-3054	119	19	epimorphism	epimorphism	PROPN
ejpam-3054	119	20	multiplied	multiply	VERB
ejpam-3054	119	21	by	by	ADP
ejpam-3054	119	22	an	an	DET
ejpam-3054	119	23	invertible	invertible	ADJ
ejpam-3054	119	24	element	element	NOUN
ejpam-3054	119	25	in	in	ADP
ejpam-3054	119	26	c(b	c(b	PROPN
ejpam-3054	119	27	)	)	PUNCT
ejpam-3054	119	28	.	.	PUNCT
ejpam-3054	120	1	proof	proof	NOUN
ejpam-3054	120	2	.	.	PUNCT
ejpam-3054	121	1	note	note	VERB
ejpam-3054	121	2	that	that	SCONJ
ejpam-3054	121	3	,	,	PUNCT
ejpam-3054	121	4	if	if	SCONJ
ejpam-3054	121	5	any	any	DET
ejpam-3054	121	6	one	one	NUM
ejpam-3054	121	7	of	of	ADP
ejpam-3054	121	8	these	these	DET
ejpam-3054	121	9	statements	statement	NOUN
ejpam-3054	121	10	holds	hold	VERB
ejpam-3054	121	11	then	then	ADV
ejpam-3054	121	12	ϕ(1	ϕ(1	PROPN
ejpam-3054	121	13	)	)	PUNCT
ejpam-3054	121	14	is	be	AUX
ejpam-3054	121	15	a	a	DET
ejpam-3054	121	16	fredholm	fredholm	NOUN
ejpam-3054	121	17	element	element	NOUN
ejpam-3054	121	18	and	and	CCONJ
ejpam-3054	121	19	so	so	ADV
ejpam-3054	121	20	there	there	PRON
ejpam-3054	121	21	exist	exist	VERB
ejpam-3054	121	22	b	b	PROPN
ejpam-3054	121	23	∈	∈	PROPN
ejpam-3054	121	24	b	b	PROPN
ejpam-3054	121	25	and	and	CCONJ
ejpam-3054	121	26	j	j	PROPN
ejpam-3054	121	27	,	,	PUNCT
ejpam-3054	121	28	j′	j′	PROPN
ejpam-3054	121	29	∈	∈	PROPN
ejpam-3054	121	30	i(b	i(b	PROPN
ejpam-3054	121	31	)	)	PUNCT
ejpam-3054	121	32	such	such	ADJ
ejpam-3054	121	33	that	that	DET
ejpam-3054	121	34	bϕ(1	bϕ(1	NOUN
ejpam-3054	121	35	)	)	PUNCT
ejpam-3054	121	36	=	=	SYM
ejpam-3054	121	37	1−	1−	NUM
ejpam-3054	121	38	j	j	PROPN
ejpam-3054	121	39	and	and	CCONJ
ejpam-3054	121	40	ϕ(1)b	ϕ(1)b	PROPN
ejpam-3054	121	41	=	=	SYM
ejpam-3054	121	42	1−	1−	NUM
ejpam-3054	121	43	j′.	j′.	PROPN
ejpam-3054	121	44	h.	h.	PROPN
ejpam-3054	121	45	outouzzalt	outouzzalt	PROPN
ejpam-3054	121	46	/	/	SYM
ejpam-3054	121	47	eur	eur	PROPN
ejpam-3054	121	48	.	.	PUNCT
ejpam-3054	122	1	j.	j.	PROPN
ejpam-3054	122	2	pure	pure	PROPN
ejpam-3054	122	3	appl	appl	PROPN
ejpam-3054	122	4	.	.	PROPN
ejpam-3054	122	5	math	math	PROPN
ejpam-3054	122	6	,	,	PUNCT
ejpam-3054	122	7	10	10	NUM
ejpam-3054	122	8	(	(	PUNCT
ejpam-3054	122	9	5	5	NUM
ejpam-3054	122	10	)	)	PUNCT
ejpam-3054	122	11	(	(	PUNCT
ejpam-3054	122	12	2017	2017	NUM
ejpam-3054	122	13	)	)	PUNCT
ejpam-3054	122	14	,	,	PUNCT
ejpam-3054	122	15	1058	1058	NUM
ejpam-3054	122	16	-	-	SYM
ejpam-3054	122	17	1066	1066	NUM
ejpam-3054	122	18	1063	1063	NUM
ejpam-3054	122	19	for	for	ADP
ejpam-3054	122	20	every	every	DET
ejpam-3054	122	21	a	a	DET
ejpam-3054	122	22	∈	∈	PROPN
ejpam-3054	122	23	a	a	PRON
ejpam-3054	122	24	,	,	PUNCT
ejpam-3054	122	25	set	set	ADJ
ejpam-3054	122	26	ψ(a	ψ(a	PROPN
ejpam-3054	122	27	)	)	PUNCT
ejpam-3054	122	28	=	=	SYM
ejpam-3054	122	29	bϕ(a	bϕ(a	NOUN
ejpam-3054	122	30	)	)	PUNCT
ejpam-3054	122	31	.	.	PUNCT
ejpam-3054	123	1	the	the	DET
ejpam-3054	123	2	equality	equality	NOUN
ejpam-3054	123	3	bϕ(1	bϕ(1	NOUN
ejpam-3054	123	4	)	)	PUNCT
ejpam-3054	123	5	=	=	SYM
ejpam-3054	123	6	1−	1−	NUM
ejpam-3054	123	7	j	j	PROPN
ejpam-3054	123	8	implies	imply	VERB
ejpam-3054	123	9	that	that	SCONJ
ejpam-3054	123	10	ψ	ψ	SYM
ejpam-3054	123	11	compresses	compress	VERB
ejpam-3054	123	12	one	one	NUM
ejpam-3054	123	13	of	of	ADP
ejpam-3054	123	14	the	the	DET
ejpam-3054	123	15	essential	essential	ADJ
ejpam-3054	123	16	spectral	spectral	ADJ
ejpam-3054	123	17	sets	set	NOUN
ejpam-3054	123	18	σe	σe	PROPN
ejpam-3054	123	19	(	(	PUNCT
ejpam-3054	123	20	.	.	PUNCT
ejpam-3054	123	21	)	)	PUNCT
ejpam-3054	123	22	,	,	PUNCT
ejpam-3054	123	23	σle	σle	PROPN
ejpam-3054	123	24	(	(	PUNCT
ejpam-3054	123	25	.	.	PUNCT
ejpam-3054	123	26	)	)	PUNCT
ejpam-3054	123	27	,	,	PUNCT
ejpam-3054	123	28	σre	σre	PROPN
ejpam-3054	123	29	(	(	PUNCT
ejpam-3054	123	30	.	.	PUNCT
ejpam-3054	123	31	)	)	PUNCT
ejpam-3054	123	32	,	,	PUNCT
ejpam-3054	123	33	or	or	CCONJ
ejpam-3054	123	34	σsf	σsf	NOUN
ejpam-3054	123	35	(	(	PUNCT
ejpam-3054	123	36	.	.	PUNCT
ejpam-3054	123	37	)	)	PUNCT
ejpam-3054	123	38	;	;	PUNCT
ejpam-3054	123	39	and	and	CCONJ
ejpam-3054	123	40	so	so	ADV
ejpam-3054	123	41	it	it	PRON
ejpam-3054	123	42	is	be	AUX
ejpam-3054	123	43	essentially	essentially	ADV
ejpam-3054	123	44	spectrally	spectrally	ADV
ejpam-3054	123	45	bounded	bound	VERB
ejpam-3054	123	46	linear	linear	ADJ
ejpam-3054	123	47	map	map	NOUN
ejpam-3054	123	48	since	since	SCONJ
ejpam-3054	123	49	each	each	PRON
ejpam-3054	123	50	of	of	ADP
ejpam-3054	123	51	them	they	PRON
ejpam-3054	123	52	contains	contain	VERB
ejpam-3054	123	53	the	the	DET
ejpam-3054	123	54	boundary	boundary	NOUN
ejpam-3054	123	55	of	of	ADP
ejpam-3054	123	56	the	the	DET
ejpam-3054	123	57	essential	essential	ADJ
ejpam-3054	123	58	spectrum	spectrum	NOUN
ejpam-3054	123	59	.	.	PUNCT
ejpam-3054	124	1	the	the	DET
ejpam-3054	124	2	same	same	ADJ
ejpam-3054	124	3	argument	argument	NOUN
ejpam-3054	124	4	as	as	ADP
ejpam-3054	124	5	in	in	ADP
ejpam-3054	124	6	the	the	DET
ejpam-3054	124	7	proof	proof	NOUN
ejpam-3054	124	8	of	of	ADP
ejpam-3054	124	9	theorem	theorem	ADJ
ejpam-3054	124	10	1	1	NUM
ejpam-3054	124	11	entails	entail	VERB
ejpam-3054	124	12	that	that	SCONJ
ejpam-3054	124	13	ψ(i(a	ψ(i(a	NOUN
ejpam-3054	124	14	)	)	PUNCT
ejpam-3054	124	15	)	)	PUNCT
ejpam-3054	125	1	⊆	⊆	NUM
ejpam-3054	125	2	i(b	i(b	NOUN
ejpam-3054	125	3	)	)	PUNCT
ejpam-3054	125	4	;	;	PUNCT
ejpam-3054	125	5	which	which	PRON
ejpam-3054	125	6	implies	imply	VERB
ejpam-3054	125	7	that	that	SCONJ
ejpam-3054	125	8	ϕ(i(a	ϕ(i(a	PROPN
ejpam-3054	125	9	)	)	PUNCT
ejpam-3054	125	10	)	)	PUNCT
ejpam-3054	126	1	⊆	⊆	NUM
ejpam-3054	126	2	i(b	i(b	NOUN
ejpam-3054	126	3	)	)	PUNCT
ejpam-3054	126	4	since	since	SCONJ
ejpam-3054	126	5	bϕ(i	bϕ(i	NUM
ejpam-3054	126	6	)	)	PUNCT
ejpam-3054	126	7	=	=	SYM
ejpam-3054	126	8	ψ(i	ψ(i	NOUN
ejpam-3054	126	9	)	)	PUNCT
ejpam-3054	126	10	∈	∈	PROPN
ejpam-3054	126	11	i(b	i(b	NOUN
ejpam-3054	126	12	)	)	PUNCT
ejpam-3054	126	13	and	and	CCONJ
ejpam-3054	126	14	ϕ(i	ϕ(i	NUM
ejpam-3054	126	15	)	)	PUNCT
ejpam-3054	126	16	=	=	PUNCT
ejpam-3054	126	17	(	(	PUNCT
ejpam-3054	126	18	ϕ(1)b+	ϕ(1)b+	PROPN
ejpam-3054	126	19	j′)ϕ(i	j′)ϕ(i	PROPN
ejpam-3054	126	20	)	)	PUNCT
ejpam-3054	126	21	=	=	PUNCT
ejpam-3054	126	22	ϕ(1)bϕ(i	ϕ(1)bϕ(i	NOUN
ejpam-3054	126	23	)	)	PUNCT
ejpam-3054	126	24	+	+	NUM
ejpam-3054	126	25	j′ϕ(i	j′ϕ(i	PROPN
ejpam-3054	126	26	)	)	PUNCT
ejpam-3054	126	27	∈	∈	PROPN
ejpam-3054	126	28	j	j	PROPN
ejpam-3054	126	29	for	for	ADP
ejpam-3054	126	30	all	all	PRON
ejpam-3054	126	31	i	i	PRON
ejpam-3054	126	32	∈	∈	PROPN
ejpam-3054	126	33	i(a	i(a	PROPN
ejpam-3054	126	34	)	)	PUNCT
ejpam-3054	126	35	.	.	PUNCT
ejpam-3054	127	1	as	as	ADP
ejpam-3054	127	2	,	,	PUNCT
ejpam-3054	127	3	by	by	ADP
ejpam-3054	127	4	[	[	PUNCT
ejpam-3054	127	5	9	9	NUM
ejpam-3054	127	6	,	,	PUNCT
ejpam-3054	127	7	corollary	corollary	ADJ
ejpam-3054	127	8	3.2	3.2	NUM
ejpam-3054	127	9	]	]	PUNCT
ejpam-3054	127	10	,	,	PUNCT
ejpam-3054	127	11	the	the	DET
ejpam-3054	127	12	induced	induced	ADJ
ejpam-3054	127	13	map	map	NOUN
ejpam-3054	127	14	ψ̂	ψ̂	ADP
ejpam-3054	127	15	is	be	AUX
ejpam-3054	127	16	a	a	DET
ejpam-3054	127	17	jordan	jordan	PROPN
ejpam-3054	127	18	epimorphism	epimorphism	NOUN
ejpam-3054	127	19	;	;	PUNCT
ejpam-3054	127	20	the	the	DET
ejpam-3054	127	21	proof	proof	NOUN
ejpam-3054	127	22	is	be	AUX
ejpam-3054	127	23	therefore	therefore	ADV
ejpam-3054	127	24	complete	complete	ADJ
ejpam-3054	127	25	.	.	PUNCT
ejpam-3054	128	1	as	as	ADP
ejpam-3054	128	2	a	a	DET
ejpam-3054	128	3	consequences	consequence	NOUN
ejpam-3054	128	4	,	,	PUNCT
ejpam-3054	128	5	we	we	PRON
ejpam-3054	128	6	describe	describe	VERB
ejpam-3054	128	7	linear	linear	NOUN
ejpam-3054	128	8	mapping	mapping	NOUN
ejpam-3054	128	9	compressing	compress	VERB
ejpam-3054	128	10	certain	certain	ADJ
ejpam-3054	128	11	essential	essential	ADJ
ejpam-3054	128	12	spectral	spectral	ADJ
ejpam-3054	128	13	sets	set	NOUN
ejpam-3054	128	14	.	.	PUNCT
ejpam-3054	129	1	theorem	theorem	NOUN
ejpam-3054	129	2	3	3	X
ejpam-3054	129	3	.	.	PUNCT
ejpam-3054	130	1	let	let	VERB
ejpam-3054	130	2	a	a	DET
ejpam-3054	130	3	be	be	AUX
ejpam-3054	130	4	a	a	DET
ejpam-3054	130	5	c∗-algebra	c∗-algebra	PROPN
ejpam-3054	130	6	with	with	ADP
ejpam-3054	130	7	real	real	ADJ
ejpam-3054	130	8	rank	rank	NOUN
ejpam-3054	130	9	zero	zero	NUM
ejpam-3054	130	10	and	and	CCONJ
ejpam-3054	130	11	b	b	NOUN
ejpam-3054	130	12	be	be	AUX
ejpam-3054	130	13	a	a	DET
ejpam-3054	130	14	semisimple	semisimple	NOUN
ejpam-3054	130	15	banach	banach	NOUN
ejpam-3054	130	16	algebra	algebra	NOUN
ejpam-3054	130	17	.	.	PUNCT
ejpam-3054	131	1	let	let	VERB
ejpam-3054	131	2	ϕ	ϕ	NOUN
ejpam-3054	131	3	:	:	PUNCT
ejpam-3054	131	4	a→	a→	PROPN
ejpam-3054	131	5	b	b	X
ejpam-3054	131	6	be	be	AUX
ejpam-3054	131	7	a	a	DET
ejpam-3054	131	8	surjective	surjective	ADJ
ejpam-3054	131	9	up	up	ADP
ejpam-3054	131	10	to	to	ADP
ejpam-3054	131	11	inessential	inessential	ADJ
ejpam-3054	131	12	elements	element	NOUN
ejpam-3054	131	13	linear	linear	PROPN
ejpam-3054	131	14	map	map	NOUN
ejpam-3054	131	15	,	,	PUNCT
ejpam-3054	131	16	and	and	CCONJ
ejpam-3054	131	17	consider	consider	VERB
ejpam-3054	131	18	the	the	DET
ejpam-3054	131	19	following	follow	VERB
ejpam-3054	131	20	statements	statement	NOUN
ejpam-3054	131	21	.	.	PUNCT
ejpam-3054	132	1	(	(	PUNCT
ejpam-3054	132	2	i	i	NOUN
ejpam-3054	132	3	)	)	PUNCT
ejpam-3054	132	4	ϕ	ϕ	PROPN
ejpam-3054	132	5	compresses	compress	VERB
ejpam-3054	132	6	the	the	DET
ejpam-3054	132	7	essential	essential	ADJ
ejpam-3054	132	8	spectrum	spectrum	NOUN
ejpam-3054	132	9	.	.	PUNCT
ejpam-3054	133	1	(	(	PUNCT
ejpam-3054	133	2	ii	ii	X
ejpam-3054	133	3	)	)	PUNCT
ejpam-3054	133	4	ϕ	ϕ	PROPN
ejpam-3054	133	5	compresses	compress	VERB
ejpam-3054	133	6	the	the	DET
ejpam-3054	133	7	left	left	ADJ
ejpam-3054	133	8	essential	essential	ADJ
ejpam-3054	133	9	spectrum	spectrum	NOUN
ejpam-3054	133	10	.	.	PUNCT
ejpam-3054	134	1	(	(	PUNCT
ejpam-3054	134	2	iii	iii	X
ejpam-3054	134	3	)	)	PUNCT
ejpam-3054	134	4	ϕ	ϕ	NOUN
ejpam-3054	134	5	compresses	compress	VERB
ejpam-3054	134	6	the	the	DET
ejpam-3054	134	7	right	right	ADJ
ejpam-3054	134	8	essential	essential	ADJ
ejpam-3054	134	9	spectrum	spectrum	NOUN
ejpam-3054	134	10	.	.	PUNCT
ejpam-3054	135	1	(	(	PUNCT
ejpam-3054	135	2	iv	iv	X
ejpam-3054	135	3	)	)	PUNCT
ejpam-3054	135	4	ϕ	ϕ	NOUN
ejpam-3054	135	5	compresses	compress	VERB
ejpam-3054	135	6	the	the	DET
ejpam-3054	135	7	semi	semi	ADJ
ejpam-3054	135	8	-	-	ADJ
ejpam-3054	135	9	fredholm	fredholm	ADJ
ejpam-3054	135	10	spectrum	spectrum	NOUN
ejpam-3054	135	11	.	.	PUNCT
ejpam-3054	136	1	if	if	SCONJ
ejpam-3054	136	2	any	any	PRON
ejpam-3054	136	3	of	of	ADP
ejpam-3054	136	4	these	these	DET
ejpam-3054	136	5	statements	statement	NOUN
ejpam-3054	136	6	holds	hold	VERB
ejpam-3054	136	7	,	,	PUNCT
ejpam-3054	136	8	then	then	ADV
ejpam-3054	136	9	ϕ(i(a	ϕ(i(a	NUM
ejpam-3054	136	10	)	)	PUNCT
ejpam-3054	136	11	)	)	PUNCT
ejpam-3054	137	1	⊆	⊆	NUM
ejpam-3054	137	2	i(b	i(b	NOUN
ejpam-3054	137	3	)	)	PUNCT
ejpam-3054	137	4	and	and	CCONJ
ejpam-3054	137	5	the	the	DET
ejpam-3054	137	6	induced	induced	ADJ
ejpam-3054	137	7	mapping	mapping	NOUN
ejpam-3054	137	8	ϕ̂	ϕ̂	NUM
ejpam-3054	137	9	:	:	PUNCT
ejpam-3054	137	10	c(a)→	c(a)→	X
ejpam-3054	137	11	c(b	c(b	PROPN
ejpam-3054	137	12	)	)	PUNCT
ejpam-3054	137	13	is	be	AUX
ejpam-3054	137	14	a	a	DET
ejpam-3054	137	15	continuous	continuous	ADJ
ejpam-3054	137	16	jordan	jordan	PROPN
ejpam-3054	137	17	epimorphism	epimorphism	PROPN
ejpam-3054	137	18	multiplied	multiply	VERB
ejpam-3054	137	19	by	by	ADP
ejpam-3054	137	20	a	a	DET
ejpam-3054	137	21	central	central	ADJ
ejpam-3054	137	22	invertible	invertible	ADJ
ejpam-3054	137	23	element	element	NOUN
ejpam-3054	137	24	in	in	ADP
ejpam-3054	137	25	c(b	c(b	PROPN
ejpam-3054	137	26	)	)	PUNCT
ejpam-3054	137	27	.	.	PUNCT
ejpam-3054	138	1	proof	proof	NOUN
ejpam-3054	138	2	.	.	PUNCT
ejpam-3054	139	1	it	it	PRON
ejpam-3054	139	2	is	be	AUX
ejpam-3054	139	3	a	a	DET
ejpam-3054	139	4	direct	direct	ADJ
ejpam-3054	139	5	consequence	consequence	NOUN
ejpam-3054	139	6	of	of	ADP
ejpam-3054	139	7	the	the	DET
ejpam-3054	139	8	above	above	ADJ
ejpam-3054	139	9	theorem	theorem	NOUN
ejpam-3054	139	10	.	.	PUNCT
ejpam-3054	140	1	one	one	NUM
ejpam-3054	140	2	get	get	VERB
ejpam-3054	140	3	the	the	DET
ejpam-3054	140	4	followings	following	NOUN
ejpam-3054	140	5	two	two	NUM
ejpam-3054	140	6	corollaries	corollary	NOUN
ejpam-3054	140	7	.	.	PUNCT
ejpam-3054	141	1	corollary	corollary	ADJ
ejpam-3054	141	2	2	2	NUM
ejpam-3054	141	3	.	.	PUNCT
ejpam-3054	142	1	let	let	VERB
ejpam-3054	142	2	a	a	DET
ejpam-3054	142	3	be	be	AUX
ejpam-3054	142	4	a	a	DET
ejpam-3054	142	5	c∗-algebra	c∗-algebra	PROPN
ejpam-3054	142	6	with	with	ADP
ejpam-3054	142	7	real	real	ADJ
ejpam-3054	142	8	rank	rank	NOUN
ejpam-3054	142	9	zero	zero	NUM
ejpam-3054	142	10	and	and	CCONJ
ejpam-3054	142	11	let	let	VERB
ejpam-3054	142	12	b	b	X
ejpam-3054	142	13	be	be	AUX
ejpam-3054	142	14	a	a	DET
ejpam-3054	142	15	factor	factor	NOUN
ejpam-3054	142	16	.	.	PUNCT
ejpam-3054	143	1	a	a	DET
ejpam-3054	143	2	surjective	surjective	ADJ
ejpam-3054	143	3	up	up	ADP
ejpam-3054	143	4	to	to	ADP
ejpam-3054	143	5	inessential	inessential	ADJ
ejpam-3054	143	6	elements	element	NOUN
ejpam-3054	143	7	linear	linear	PROPN
ejpam-3054	143	8	map	map	VERB
ejpam-3054	143	9	ϕ	ϕ	NOUN
ejpam-3054	143	10	:	:	PUNCT
ejpam-3054	143	11	a	a	DET
ejpam-3054	143	12	→	→	SYM
ejpam-3054	143	13	b	b	NOUN
ejpam-3054	143	14	compresses	compress	VERB
ejpam-3054	143	15	the	the	DET
ejpam-3054	143	16	essential	essential	ADJ
ejpam-3054	143	17	spectrum	spectrum	NOUN
ejpam-3054	143	18	(	(	PUNCT
ejpam-3054	143	19	the	the	DET
ejpam-3054	143	20	semi	semi	ADJ
ejpam-3054	143	21	-	-	ADJ
ejpam-3054	143	22	fredholm	fredholm	ADJ
ejpam-3054	143	23	spectrum	spectrum	NOUN
ejpam-3054	143	24	)	)	PUNCT
ejpam-3054	143	25	if	if	SCONJ
ejpam-3054	143	26	and	and	CCONJ
ejpam-3054	143	27	only	only	ADV
ejpam-3054	143	28	if	if	SCONJ
ejpam-3054	143	29	ϕ(i(a	ϕ(i(a	NUM
ejpam-3054	143	30	)	)	PUNCT
ejpam-3054	143	31	)	)	PUNCT
ejpam-3054	144	1	⊆	⊆	NUM
ejpam-3054	144	2	i(b	i(b	NOUN
ejpam-3054	144	3	)	)	PUNCT
ejpam-3054	144	4	,	,	PUNCT
ejpam-3054	144	5	and	and	CCONJ
ejpam-3054	144	6	the	the	DET
ejpam-3054	144	7	induced	induced	ADJ
ejpam-3054	144	8	mapping	mapping	NOUN
ejpam-3054	144	9	ϕ̂	ϕ̂	NUM
ejpam-3054	144	10	:	:	PUNCT
ejpam-3054	144	11	c(a)→	c(a)→	X
ejpam-3054	144	12	c(b	c(b	PROPN
ejpam-3054	144	13	)	)	PUNCT
ejpam-3054	144	14	is	be	AUX
ejpam-3054	144	15	either	either	CCONJ
ejpam-3054	144	16	a	a	DET
ejpam-3054	144	17	continuous	continuous	ADJ
ejpam-3054	144	18	epimorphism	epimorphism	NOUN
ejpam-3054	144	19	or	or	CCONJ
ejpam-3054	144	20	a	a	DET
ejpam-3054	144	21	continuous	continuous	ADJ
ejpam-3054	144	22	anti	anti	NOUN
ejpam-3054	144	23	-	-	NOUN
ejpam-3054	144	24	epimorphism	epimorphism	NOUN
ejpam-3054	144	25	.	.	PUNCT
ejpam-3054	145	1	proof	proof	NOUN
ejpam-3054	145	2	.	.	PUNCT
ejpam-3054	146	1	checking	check	VERB
ejpam-3054	146	2	the	the	DET
ejpam-3054	146	3	“	"	PUNCT
ejpam-3054	146	4	if	if	SCONJ
ejpam-3054	146	5	”	"	PUNCT
ejpam-3054	146	6	part	part	NOUN
ejpam-3054	146	7	is	be	AUX
ejpam-3054	146	8	straightforward	straightforward	ADJ
ejpam-3054	146	9	.	.	PUNCT
ejpam-3054	147	1	so	so	ADV
ejpam-3054	147	2	,	,	PUNCT
ejpam-3054	147	3	assume	assume	VERB
ejpam-3054	147	4	that	that	SCONJ
ejpam-3054	147	5	φ	φ	PROPN
ejpam-3054	147	6	compresses	compress	VERB
ejpam-3054	147	7	the	the	DET
ejpam-3054	147	8	essential	essential	ADJ
ejpam-3054	147	9	spectrum	spectrum	NOUN
ejpam-3054	147	10	,	,	PUNCT
ejpam-3054	147	11	and	and	CCONJ
ejpam-3054	147	12	let	let	VERB
ejpam-3054	147	13	us	we	PRON
ejpam-3054	147	14	establish	establish	VERB
ejpam-3054	147	15	the	the	DET
ejpam-3054	147	16	“	"	PUNCT
ejpam-3054	147	17	only	only	ADV
ejpam-3054	147	18	if	if	SCONJ
ejpam-3054	147	19	part	part	NOUN
ejpam-3054	147	20	”	"	PUNCT
ejpam-3054	147	21	.	.	PUNCT
ejpam-3054	148	1	note	note	VERB
ejpam-3054	148	2	that	that	SCONJ
ejpam-3054	148	3	,	,	PUNCT
ejpam-3054	148	4	by	by	ADP
ejpam-3054	148	5	the	the	DET
ejpam-3054	148	6	above	above	ADJ
ejpam-3054	148	7	theorem	theorem	NOUN
ejpam-3054	148	8	together	together	ADV
ejpam-3054	148	9	with	with	ADP
ejpam-3054	148	10	the	the	DET
ejpam-3054	148	11	same	same	ADJ
ejpam-3054	148	12	argument	argument	NOUN
ejpam-3054	148	13	as	as	ADP
ejpam-3054	148	14	in	in	ADP
ejpam-3054	148	15	the	the	DET
ejpam-3054	148	16	proof	proof	NOUN
ejpam-3054	148	17	of	of	ADP
ejpam-3054	148	18	corollary	corollary	ADJ
ejpam-3054	148	19	1	1	NUM
ejpam-3054	148	20	,	,	PUNCT
ejpam-3054	148	21	ϕ(i(a	ϕ(i(a	NUM
ejpam-3054	148	22	)	)	PUNCT
ejpam-3054	148	23	)	)	PUNCT
ejpam-3054	149	1	⊆	⊆	NUM
ejpam-3054	149	2	i(b	i(b	NOUN
ejpam-3054	149	3	)	)	PUNCT
ejpam-3054	149	4	,	,	PUNCT
ejpam-3054	149	5	and	and	CCONJ
ejpam-3054	149	6	the	the	DET
ejpam-3054	149	7	induced	induced	ADJ
ejpam-3054	149	8	map	map	NOUN
ejpam-3054	149	9	ϕ̂	ϕ̂	X
ejpam-3054	149	10	:	:	PUNCT
ejpam-3054	149	11	c(a	c(a	ADV
ejpam-3054	149	12	)	)	PUNCT
ejpam-3054	149	13	→	→	PUNCT
ejpam-3054	149	14	c(b	c(b	PROPN
ejpam-3054	149	15	)	)	PUNCT
ejpam-3054	149	16	is	be	AUX
ejpam-3054	149	17	either	either	CCONJ
ejpam-3054	149	18	a	a	DET
ejpam-3054	149	19	continuous	continuous	ADJ
ejpam-3054	149	20	epimorphism	epimorphism	NOUN
ejpam-3054	149	21	or	or	CCONJ
ejpam-3054	149	22	a	a	DET
ejpam-3054	149	23	continuous	continuous	ADJ
ejpam-3054	149	24	antiepimorphism	antiepimorphism	NOUN
ejpam-3054	149	25	multiplied	multiply	VERB
ejpam-3054	149	26	by	by	ADP
ejpam-3054	149	27	a	a	DET
ejpam-3054	149	28	nonzero	nonzero	PROPN
ejpam-3054	149	29	scalar	scalar	ADJ
ejpam-3054	149	30	c.	c.	PROPN
ejpam-3054	149	31	obviously	obviously	ADV
ejpam-3054	149	32	c	c	VERB
ejpam-3054	149	33	=	=	NOUN
ejpam-3054	149	34	1	1	NUM
ejpam-3054	149	35	because	because	SCONJ
ejpam-3054	149	36	{	{	PUNCT
ejpam-3054	149	37	c	c	NOUN
ejpam-3054	149	38	}	}	PUNCT
ejpam-3054	149	39	=	=	SYM
ejpam-3054	149	40	σe(ϕ(1	σe(ϕ(1	NUM
ejpam-3054	149	41	)	)	PUNCT
ejpam-3054	149	42	)	)	PUNCT
ejpam-3054	150	1	⊂	⊂	PROPN
ejpam-3054	150	2	σe(1	σe(1	X
ejpam-3054	150	3	)	)	PUNCT
ejpam-3054	150	4	=	=	PUNCT
ejpam-3054	150	5	{	{	PUNCT
ejpam-3054	150	6	1	1	NUM
ejpam-3054	150	7	}	}	PUNCT
ejpam-3054	150	8	.	.	PUNCT
ejpam-3054	151	1	the	the	DET
ejpam-3054	151	2	case	case	NOUN
ejpam-3054	151	3	when	when	SCONJ
ejpam-3054	151	4	ϕ	ϕ	PROPN
ejpam-3054	151	5	compresses	compress	VERB
ejpam-3054	151	6	the	the	DET
ejpam-3054	151	7	semi	semi	ADJ
ejpam-3054	151	8	-	-	ADJ
ejpam-3054	151	9	fredholm	fredholm	ADJ
ejpam-3054	151	10	spectrum	spectrum	NOUN
ejpam-3054	151	11	is	be	AUX
ejpam-3054	151	12	dealt	deal	VERB
ejpam-3054	151	13	with	with	ADP
ejpam-3054	151	14	similarly	similarly	ADV
ejpam-3054	151	15	.	.	PUNCT
ejpam-3054	152	1	h.	h.	PROPN
ejpam-3054	152	2	outouzzalt	outouzzalt	PROPN
ejpam-3054	152	3	/	/	SYM
ejpam-3054	152	4	eur	eur	PROPN
ejpam-3054	152	5	.	.	PUNCT
ejpam-3054	153	1	j.	j.	PROPN
ejpam-3054	153	2	pure	pure	PROPN
ejpam-3054	153	3	appl	appl	PROPN
ejpam-3054	153	4	.	.	PROPN
ejpam-3054	153	5	math	math	PROPN
ejpam-3054	153	6	,	,	PUNCT
ejpam-3054	153	7	10	10	NUM
ejpam-3054	153	8	(	(	PUNCT
ejpam-3054	153	9	5	5	NUM
ejpam-3054	153	10	)	)	PUNCT
ejpam-3054	153	11	(	(	PUNCT
ejpam-3054	153	12	2017	2017	NUM
ejpam-3054	153	13	)	)	PUNCT
ejpam-3054	153	14	,	,	PUNCT
ejpam-3054	153	15	1058	1058	NUM
ejpam-3054	153	16	-	-	SYM
ejpam-3054	153	17	1066	1066	NUM
ejpam-3054	153	18	1064	1064	NUM
ejpam-3054	153	19	corollary	corollary	NOUN
ejpam-3054	153	20	3	3	NUM
ejpam-3054	153	21	.	.	PUNCT
ejpam-3054	154	1	let	let	VERB
ejpam-3054	154	2	ϕ	ϕ	NOUN
ejpam-3054	154	3	be	be	AUX
ejpam-3054	154	4	a	a	DET
ejpam-3054	154	5	surjective	surjective	ADJ
ejpam-3054	154	6	up	up	ADP
ejpam-3054	154	7	to	to	ADP
ejpam-3054	154	8	inessential	inessential	ADJ
ejpam-3054	154	9	elements	element	NOUN
ejpam-3054	154	10	linear	linear	NOUN
ejpam-3054	154	11	map	map	NOUN
ejpam-3054	154	12	from	from	ADP
ejpam-3054	154	13	a	a	DET
ejpam-3054	154	14	c∗-algebra	c∗-algebra	PROPN
ejpam-3054	154	15	a	a	PRON
ejpam-3054	154	16	with	with	ADP
ejpam-3054	154	17	real	real	ADJ
ejpam-3054	154	18	rank	rank	NOUN
ejpam-3054	154	19	zero	zero	NUM
ejpam-3054	154	20	into	into	ADP
ejpam-3054	154	21	a	a	DET
ejpam-3054	154	22	factor	factor	NOUN
ejpam-3054	154	23	b.	b.	NOUN
ejpam-3054	155	1	if	if	SCONJ
ejpam-3054	155	2	a	a	PRON
ejpam-3054	155	3	contains	contain	VERB
ejpam-3054	155	4	a	a	DET
ejpam-3054	155	5	semi	semi	ADJ
ejpam-3054	155	6	-	-	ADJ
ejpam-3054	155	7	fredholm	fredholm	ADJ
ejpam-3054	155	8	element	element	NOUN
ejpam-3054	155	9	a	a	DET
ejpam-3054	155	10	such	such	ADJ
ejpam-3054	155	11	that	that	SCONJ
ejpam-3054	155	12	ϕ(a	ϕ(a	NOUN
ejpam-3054	155	13	)	)	PUNCT
ejpam-3054	155	14	is	be	AUX
ejpam-3054	155	15	not	not	PART
ejpam-3054	155	16	fredholm	fredholm	NOUN
ejpam-3054	155	17	,	,	PUNCT
ejpam-3054	155	18	then	then	ADV
ejpam-3054	155	19	ϕ	ϕ	PROPN
ejpam-3054	155	20	compresses	compress	VERB
ejpam-3054	155	21	the	the	DET
ejpam-3054	155	22	left	left	ADJ
ejpam-3054	155	23	essential	essential	ADJ
ejpam-3054	155	24	spectrum	spectrum	NOUN
ejpam-3054	155	25	(	(	PUNCT
ejpam-3054	155	26	the	the	DET
ejpam-3054	155	27	right	right	ADJ
ejpam-3054	155	28	essential	essential	ADJ
ejpam-3054	155	29	spectrum	spectrum	NOUN
ejpam-3054	155	30	)	)	PUNCT
ejpam-3054	155	31	if	if	SCONJ
ejpam-3054	155	32	and	and	CCONJ
ejpam-3054	155	33	only	only	ADV
ejpam-3054	155	34	if	if	SCONJ
ejpam-3054	155	35	ϕ(i(a	ϕ(i(a	NUM
ejpam-3054	155	36	)	)	PUNCT
ejpam-3054	155	37	)	)	PUNCT
ejpam-3054	156	1	⊆	⊆	NUM
ejpam-3054	156	2	i(b	i(b	NOUN
ejpam-3054	156	3	)	)	PUNCT
ejpam-3054	156	4	,	,	PUNCT
ejpam-3054	156	5	and	and	CCONJ
ejpam-3054	156	6	the	the	DET
ejpam-3054	156	7	induced	induced	ADJ
ejpam-3054	156	8	mapping	mapping	NOUN
ejpam-3054	156	9	ϕ̂	ϕ̂	NUM
ejpam-3054	156	10	:	:	PUNCT
ejpam-3054	156	11	c(a)→	c(a)→	X
ejpam-3054	156	12	c(b	c(b	PROPN
ejpam-3054	156	13	)	)	PUNCT
ejpam-3054	156	14	is	be	AUX
ejpam-3054	156	15	an	an	DET
ejpam-3054	156	16	continuous	continuous	ADJ
ejpam-3054	156	17	epimorphism	epimorphism	NOUN
ejpam-3054	156	18	.	.	PUNCT
ejpam-3054	157	1	proof	proof	NOUN
ejpam-3054	157	2	.	.	PUNCT
ejpam-3054	158	1	by	by	ADP
ejpam-3054	158	2	similar	similar	ADJ
ejpam-3054	158	3	arguments	argument	NOUN
ejpam-3054	158	4	in	in	ADP
ejpam-3054	158	5	the	the	DET
ejpam-3054	158	6	proof	proof	NOUN
ejpam-3054	158	7	of	of	ADP
ejpam-3054	158	8	the	the	DET
ejpam-3054	158	9	above	above	ADJ
ejpam-3054	158	10	corollary	corollary	NOUN
ejpam-3054	158	11	,	,	PUNCT
ejpam-3054	158	12	we	we	PRON
ejpam-3054	158	13	only	only	ADV
ejpam-3054	158	14	have	have	VERB
ejpam-3054	158	15	to	to	PART
ejpam-3054	158	16	show	show	VERB
ejpam-3054	158	17	that	that	SCONJ
ejpam-3054	158	18	ϕ̂	ϕ̂	PROPN
ejpam-3054	158	19	can	can	AUX
ejpam-3054	158	20	not	not	PART
ejpam-3054	158	21	be	be	AUX
ejpam-3054	158	22	an	an	DET
ejpam-3054	158	23	anti	anti	ADJ
ejpam-3054	158	24	-	-	NOUN
ejpam-3054	158	25	epimorphism	epimorphism	NOUN
ejpam-3054	158	26	.	.	PUNCT
ejpam-3054	159	1	so	so	ADV
ejpam-3054	159	2	,	,	PUNCT
ejpam-3054	159	3	assume	assume	VERB
ejpam-3054	159	4	that	that	SCONJ
ejpam-3054	159	5	φ	φ	PROPN
ejpam-3054	159	6	compresses	compress	VERB
ejpam-3054	159	7	the	the	DET
ejpam-3054	159	8	left	left	ADJ
ejpam-3054	159	9	essential	essential	ADJ
ejpam-3054	159	10	spectrum	spectrum	NOUN
ejpam-3054	159	11	,	,	PUNCT
ejpam-3054	159	12	and	and	CCONJ
ejpam-3054	159	13	suppose	suppose	VERB
ejpam-3054	159	14	to	to	ADP
ejpam-3054	159	15	the	the	DET
ejpam-3054	159	16	contrary	contrary	NOUN
ejpam-3054	159	17	that	that	SCONJ
ejpam-3054	159	18	ϕ̂	ϕ̂	PUNCT
ejpam-3054	159	19	is	be	AUX
ejpam-3054	159	20	an	an	DET
ejpam-3054	159	21	anti	anti	NOUN
ejpam-3054	159	22	-	-	NOUN
ejpam-3054	159	23	epimorphism	epimorphism	NOUN
ejpam-3054	159	24	.	.	PUNCT
ejpam-3054	160	1	if	if	SCONJ
ejpam-3054	160	2	the	the	DET
ejpam-3054	160	3	element	element	NOUN
ejpam-3054	160	4	a	a	PRON
ejpam-3054	160	5	is	be	AUX
ejpam-3054	160	6	left	leave	VERB
ejpam-3054	160	7	semi	semi	ADJ
ejpam-3054	160	8	-	-	NOUN
ejpam-3054	160	9	fredholm	fredholm	ADJ
ejpam-3054	160	10	,	,	PUNCT
ejpam-3054	160	11	then	then	ADV
ejpam-3054	160	12	ϕ(a	ϕ(a	NOUN
ejpam-3054	160	13	)	)	PUNCT
ejpam-3054	160	14	is	be	AUX
ejpam-3054	160	15	also	also	ADV
ejpam-3054	160	16	left	leave	VERB
ejpam-3054	160	17	semi	semi	ADJ
ejpam-3054	160	18	-	-	NOUN
ejpam-3054	160	19	fredholm	fredholm	ADJ
ejpam-3054	160	20	,	,	PUNCT
ejpam-3054	160	21	and	and	CCONJ
ejpam-3054	160	22	there	there	PRON
ejpam-3054	160	23	exists	exist	VERB
ejpam-3054	160	24	b	b	PROPN
ejpam-3054	160	25	∈	∈	PROPN
ejpam-3054	160	26	a	a	DET
ejpam-3054	160	27	such	such	ADJ
ejpam-3054	160	28	that	that	SCONJ
ejpam-3054	160	29	π(b)π(a	π(b)π(a	NOUN
ejpam-3054	160	30	)	)	PUNCT
ejpam-3054	160	31	=	=	SYM
ejpam-3054	160	32	π(1	π(1	NOUN
ejpam-3054	160	33	)	)	PUNCT
ejpam-3054	160	34	.	.	PUNCT
ejpam-3054	161	1	thus	thus	ADV
ejpam-3054	161	2	,	,	PUNCT
ejpam-3054	161	3	π(1	π(1	PROPN
ejpam-3054	161	4	)	)	PUNCT
ejpam-3054	161	5	=	=	SYM
ejpam-3054	161	6	ϕ̂(π(b)π(a	ϕ̂(π(b)π(a	NOUN
ejpam-3054	161	7	)	)	PUNCT
ejpam-3054	161	8	)	)	PUNCT
ejpam-3054	162	1	=	=	SYM
ejpam-3054	162	2	ϕ̂(π(a))ϕ̂(π(b	ϕ̂(π(a))ϕ̂(π(b	ADJ
ejpam-3054	162	3	)	)	PUNCT
ejpam-3054	162	4	)	)	PUNCT
ejpam-3054	163	1	which	which	PRON
ejpam-3054	163	2	show	show	VERB
ejpam-3054	163	3	that	that	SCONJ
ejpam-3054	163	4	ϕ(a	ϕ(a	NOUN
ejpam-3054	163	5	)	)	PUNCT
ejpam-3054	163	6	is	be	AUX
ejpam-3054	163	7	right	right	ADJ
ejpam-3054	163	8	semi	semi	ADJ
ejpam-3054	163	9	-	-	NOUN
ejpam-3054	163	10	fredholm	fredholm	ADJ
ejpam-3054	163	11	.	.	PUNCT
ejpam-3054	164	1	this	this	PRON
ejpam-3054	164	2	implies	imply	VERB
ejpam-3054	164	3	that	that	SCONJ
ejpam-3054	164	4	ϕ(a	ϕ(a	NOUN
ejpam-3054	164	5	)	)	PUNCT
ejpam-3054	164	6	is	be	AUX
ejpam-3054	164	7	fredholm	fredholm	NOUN
ejpam-3054	164	8	,	,	PUNCT
ejpam-3054	164	9	which	which	PRON
ejpam-3054	164	10	is	be	AUX
ejpam-3054	164	11	a	a	DET
ejpam-3054	164	12	contradiction	contradiction	NOUN
ejpam-3054	164	13	.	.	PUNCT
ejpam-3054	165	1	by	by	ADP
ejpam-3054	165	2	similarity	similarity	NOUN
ejpam-3054	165	3	,	,	PUNCT
ejpam-3054	165	4	in	in	ADP
ejpam-3054	165	5	the	the	DET
ejpam-3054	165	6	case	case	NOUN
ejpam-3054	165	7	when	when	SCONJ
ejpam-3054	165	8	a	a	PRON
ejpam-3054	165	9	is	be	AUX
ejpam-3054	165	10	right	right	ADJ
ejpam-3054	165	11	semi	semi	ADJ
ejpam-3054	165	12	-	-	ADJ
ejpam-3054	165	13	fredholm	fredholm	ADJ
ejpam-3054	165	14	we	we	PRON
ejpam-3054	165	15	get	get	VERB
ejpam-3054	165	16	a	a	DET
ejpam-3054	165	17	contradiction	contradiction	NOUN
ejpam-3054	165	18	too	too	ADV
ejpam-3054	165	19	.	.	PUNCT
ejpam-3054	166	1	similar	similar	ADJ
ejpam-3054	166	2	arguments	argument	NOUN
ejpam-3054	166	3	yield	yield	VERB
ejpam-3054	166	4	that	that	PRON
ejpam-3054	166	5	ϕ̂	ϕ̂	PUNCT
ejpam-3054	166	6	can	can	AUX
ejpam-3054	166	7	not	not	PART
ejpam-3054	166	8	be	be	AUX
ejpam-3054	166	9	an	an	DET
ejpam-3054	166	10	anti	anti	NOUN
ejpam-3054	166	11	-	-	NOUN
ejpam-3054	166	12	epimorphism	epimorphism	NOUN
ejpam-3054	166	13	in	in	ADP
ejpam-3054	166	14	the	the	DET
ejpam-3054	166	15	case	case	NOUN
ejpam-3054	166	16	when	when	SCONJ
ejpam-3054	166	17	ϕ	ϕ	PROPN
ejpam-3054	166	18	compresses	compress	VERB
ejpam-3054	166	19	the	the	DET
ejpam-3054	166	20	right	right	ADJ
ejpam-3054	166	21	semi	semi	ADJ
ejpam-3054	166	22	-	-	ADJ
ejpam-3054	166	23	fredholm	fredholm	ADJ
ejpam-3054	166	24	spectrum	spectrum	NOUN
ejpam-3054	166	25	;	;	PUNCT
ejpam-3054	166	26	and	and	CCONJ
ejpam-3054	166	27	the	the	DET
ejpam-3054	166	28	proof	proof	NOUN
ejpam-3054	166	29	is	be	AUX
ejpam-3054	166	30	complete	complete	ADJ
ejpam-3054	166	31	.	.	PUNCT
ejpam-3054	167	1	4	4	X
ejpam-3054	167	2	.	.	X
ejpam-3054	167	3	linear	linear	PROPN
ejpam-3054	167	4	weyl	weyl	PROPN
ejpam-3054	167	5	spectrum	spectrum	NOUN
ejpam-3054	167	6	compressors	compressor	NOUN
ejpam-3054	167	7	now	now	ADV
ejpam-3054	167	8	,	,	PUNCT
ejpam-3054	167	9	let	let	VERB
ejpam-3054	167	10	us	we	PRON
ejpam-3054	167	11	recall	recall	VERB
ejpam-3054	167	12	the	the	DET
ejpam-3054	167	13	following	follow	VERB
ejpam-3054	167	14	useful	useful	ADJ
ejpam-3054	167	15	facts	fact	NOUN
ejpam-3054	167	16	about	about	ADP
ejpam-3054	167	17	index	index	NOUN
ejpam-3054	167	18	theory	theory	NOUN
ejpam-3054	167	19	in	in	ADP
ejpam-3054	167	20	primitive	primitive	ADJ
ejpam-3054	167	21	banach	banach	NOUN
ejpam-3054	167	22	algebra	algebra	NOUN
ejpam-3054	167	23	that	that	PRON
ejpam-3054	167	24	we	we	PRON
ejpam-3054	167	25	will	will	AUX
ejpam-3054	167	26	need	need	VERB
ejpam-3054	167	27	in	in	ADP
ejpam-3054	167	28	the	the	DET
ejpam-3054	167	29	sequel	sequel	NOUN
ejpam-3054	167	30	.	.	PUNCT
ejpam-3054	168	1	in	in	ADP
ejpam-3054	168	2	what	what	PRON
ejpam-3054	168	3	follows	follow	VERB
ejpam-3054	168	4	and	and	CCONJ
ejpam-3054	168	5	unless	unless	SCONJ
ejpam-3054	168	6	otherwise	otherwise	ADV
ejpam-3054	168	7	specified	specify	VERB
ejpam-3054	168	8	,	,	PUNCT
ejpam-3054	168	9	we	we	PRON
ejpam-3054	168	10	assume	assume	VERB
ejpam-3054	168	11	that	that	SCONJ
ejpam-3054	168	12	a	a	PRON
ejpam-3054	168	13	is	be	AUX
ejpam-3054	168	14	a	a	DET
ejpam-3054	168	15	primitive	primitive	ADJ
ejpam-3054	168	16	banach	banach	NOUN
ejpam-3054	168	17	algebra	algebra	NOUN
ejpam-3054	168	18	with	with	ADP
ejpam-3054	168	19	nontrivial	nontrivial	ADJ
ejpam-3054	168	20	socle	socle	NOUN
ejpam-3054	168	21	.	.	PUNCT
ejpam-3054	169	1	fix	fix	NOUN
ejpam-3054	169	2	e	e	NOUN
ejpam-3054	169	3	∈	∈	PROPN
ejpam-3054	169	4	a	a	DET
ejpam-3054	169	5	a	a	DET
ejpam-3054	169	6	minimal	minimal	ADJ
ejpam-3054	169	7	idempotent	idempotent	NOUN
ejpam-3054	169	8	(	(	PUNCT
ejpam-3054	169	9	such	such	DET
ejpam-3054	169	10	an	an	DET
ejpam-3054	169	11	element	element	NOUN
ejpam-3054	169	12	exists	exist	VERB
ejpam-3054	169	13	if	if	SCONJ
ejpam-3054	169	14	and	and	CCONJ
ejpam-3054	169	15	only	only	ADV
ejpam-3054	169	16	if	if	SCONJ
ejpam-3054	169	17	soc	soc	NOUN
ejpam-3054	169	18	(	(	PUNCT
ejpam-3054	169	19	a	a	NOUN
ejpam-3054	169	20	)	)	PUNCT
ejpam-3054	169	21	6=	6=	ADP
ejpam-3054	169	22	0	0	NUM
ejpam-3054	169	23	)	)	PUNCT
ejpam-3054	169	24	,	,	PUNCT
ejpam-3054	169	25	and	and	CCONJ
ejpam-3054	169	26	let	let	VERB
ejpam-3054	169	27	ρ	ρ	NOUN
ejpam-3054	169	28	:	:	PUNCT
ejpam-3054	169	29	a→	a→	PROPN
ejpam-3054	169	30	l(ae	l(ae	NOUN
ejpam-3054	169	31	)	)	PUNCT
ejpam-3054	169	32	,	,	PUNCT
ejpam-3054	169	33	defined	define	VERB
ejpam-3054	169	34	as	as	ADP
ejpam-3054	169	35	ρ(a)(x	ρ(a)(x	NUM
ejpam-3054	169	36	)	)	PUNCT
ejpam-3054	169	37	:	:	PUNCT
ejpam-3054	170	1	=	=	SYM
ejpam-3054	170	2	ax	ax	NOUN
ejpam-3054	170	3	(	(	PUNCT
ejpam-3054	170	4	x	x	PROPN
ejpam-3054	170	5	∈	∈	PROPN
ejpam-3054	170	6	ae	ae	PROPN
ejpam-3054	170	7	)	)	PUNCT
ejpam-3054	170	8	,	,	PUNCT
ejpam-3054	170	9	denote	denote	VERB
ejpam-3054	170	10	the	the	DET
ejpam-3054	170	11	left	left	ADJ
ejpam-3054	170	12	regular	regular	ADJ
ejpam-3054	170	13	representation	representation	NOUN
ejpam-3054	170	14	of	of	ADP
ejpam-3054	170	15	a	a	PRON
ejpam-3054	170	16	on	on	ADP
ejpam-3054	170	17	the	the	DET
ejpam-3054	170	18	banach	banach	NOUN
ejpam-3054	170	19	space	space	NOUN
ejpam-3054	170	20	ae	ae	PROPN
ejpam-3054	170	21	.	.	PUNCT
ejpam-3054	171	1	for	for	ADP
ejpam-3054	171	2	an	an	DET
ejpam-3054	171	3	element	element	NOUN
ejpam-3054	171	4	a	a	DET
ejpam-3054	171	5	∈	∈	PROPN
ejpam-3054	171	6	a	a	PRON
ejpam-3054	171	7	,	,	PUNCT
ejpam-3054	171	8	we	we	PRON
ejpam-3054	171	9	denote	denote	VERB
ejpam-3054	171	10	as	as	ADP
ejpam-3054	171	11	usual	usual	ADJ
ejpam-3054	171	12	the	the	DET
ejpam-3054	171	13	index	index	NOUN
ejpam-3054	171	14	of	of	ADP
ejpam-3054	171	15	a	a	PRON
ejpam-3054	171	16	by	by	ADP
ejpam-3054	171	17	ind	ind	NOUN
ejpam-3054	171	18	(	(	PUNCT
ejpam-3054	171	19	a	a	NOUN
ejpam-3054	171	20	)	)	PUNCT
ejpam-3054	171	21	:	:	PUNCT
ejpam-3054	172	1	=	=	PUNCT
ejpam-3054	172	2	dim(ker(ρ(a))−	dim(ker(ρ(a))−	NOUN
ejpam-3054	172	3	codim	codim	NOUN
ejpam-3054	172	4	(	(	PUNCT
ejpam-3054	172	5	ρ(a)(ae	ρ(a)(ae	PROPN
ejpam-3054	172	6	)	)	PUNCT
ejpam-3054	172	7	)	)	PUNCT
ejpam-3054	172	8	.	.	PUNCT
ejpam-3054	173	1	it	it	PRON
ejpam-3054	173	2	is	be	AUX
ejpam-3054	173	3	well	well	ADV
ejpam-3054	173	4	known	know	VERB
ejpam-3054	173	5	that	that	SCONJ
ejpam-3054	173	6	ind	ind	NOUN
ejpam-3054	173	7	(	(	PUNCT
ejpam-3054	173	8	a	a	NOUN
ejpam-3054	173	9	)	)	PUNCT
ejpam-3054	173	10	is	be	AUX
ejpam-3054	173	11	independent	independent	ADJ
ejpam-3054	173	12	of	of	ADP
ejpam-3054	173	13	the	the	DET
ejpam-3054	173	14	choice	choice	NOUN
ejpam-3054	173	15	of	of	ADP
ejpam-3054	173	16	e	e	NOUN
ejpam-3054	173	17	;	;	PUNCT
ejpam-3054	173	18	see	see	VERB
ejpam-3054	173	19	for	for	ADP
ejpam-3054	173	20	instance	instance	NOUN
ejpam-3054	173	21	[	[	X
ejpam-3054	173	22	4	4	NUM
ejpam-3054	173	23	]	]	PUNCT
ejpam-3054	173	24	.	.	PUNCT
ejpam-3054	174	1	the	the	DET
ejpam-3054	174	2	element	element	NOUN
ejpam-3054	174	3	a	a	PRON
ejpam-3054	174	4	is	be	AUX
ejpam-3054	174	5	said	say	VERB
ejpam-3054	174	6	to	to	PART
ejpam-3054	174	7	be	be	AUX
ejpam-3054	174	8	weyl	weyl	VERB
ejpam-3054	174	9	element	element	NOUN
ejpam-3054	174	10	if	if	SCONJ
ejpam-3054	174	11	it	it	PRON
ejpam-3054	174	12	is	be	AUX
ejpam-3054	174	13	fredholm	fredholm	NOUN
ejpam-3054	174	14	with	with	ADP
ejpam-3054	174	15	index	index	NOUN
ejpam-3054	174	16	zero	zero	NUM
ejpam-3054	174	17	.	.	PUNCT
ejpam-3054	175	1	the	the	DET
ejpam-3054	175	2	weyl	weyl	PROPN
ejpam-3054	175	3	spectrum	spectrum	NOUN
ejpam-3054	175	4	of	of	ADP
ejpam-3054	175	5	a	a	PRON
ejpam-3054	175	6	is	be	AUX
ejpam-3054	175	7	given	give	VERB
ejpam-3054	175	8	by	by	ADP
ejpam-3054	175	9	w	w	PROPN
ejpam-3054	175	10	(	(	PUNCT
ejpam-3054	175	11	a	a	NOUN
ejpam-3054	175	12	)	)	PUNCT
ejpam-3054	175	13	:	:	PUNCT
ejpam-3054	175	14	=	=	SYM
ejpam-3054	175	15	{	{	PUNCT
ejpam-3054	175	16	λ	λ	X
ejpam-3054	175	17	∈	∈	NOUN
ejpam-3054	175	18	c	c	NOUN
ejpam-3054	175	19	:	:	PUNCT
ejpam-3054	175	20	a−	a−	PROPN
ejpam-3054	175	21	λ	λ	PROPN
ejpam-3054	175	22	is	be	AUX
ejpam-3054	175	23	not	not	PART
ejpam-3054	175	24	weyl	weyl	VERB
ejpam-3054	175	25	}	}	PUNCT
ejpam-3054	175	26	,	,	PUNCT
ejpam-3054	175	27	and	and	CCONJ
ejpam-3054	175	28	it	it	PRON
ejpam-3054	175	29	coincides	coincide	VERB
ejpam-3054	175	30	with	with	ADP
ejpam-3054	175	31	⋂	⋂	PROPN
ejpam-3054	175	32	{	{	PUNCT
ejpam-3054	175	33	σ(a+	σ(a+	PROPN
ejpam-3054	175	34	b	b	NOUN
ejpam-3054	175	35	)	)	PUNCT
ejpam-3054	175	36	:	:	PUNCT
ejpam-3054	175	37	b	b	X
ejpam-3054	175	38	∈	∈	PROPN
ejpam-3054	175	39	i(a	i(a	PROPN
ejpam-3054	175	40	)	)	PUNCT
ejpam-3054	175	41	}	}	PUNCT
ejpam-3054	175	42	;	;	PUNCT
ejpam-3054	175	43	see	see	VERB
ejpam-3054	175	44	[	[	X
ejpam-3054	175	45	4	4	NUM
ejpam-3054	175	46	]	]	PUNCT
ejpam-3054	175	47	.	.	PUNCT
ejpam-3054	176	1	note	note	VERB
ejpam-3054	176	2	that	that	SCONJ
ejpam-3054	176	3	,	,	PUNCT
ejpam-3054	176	4	for	for	ADP
ejpam-3054	176	5	the	the	DET
ejpam-3054	176	6	algebra	algebra	NOUN
ejpam-3054	176	7	l(h	l(h	PROPN
ejpam-3054	176	8	)	)	PUNCT
ejpam-3054	176	9	of	of	ADP
ejpam-3054	176	10	all	all	DET
ejpam-3054	176	11	bounded	bound	VERB
ejpam-3054	176	12	linear	linear	PROPN
ejpam-3054	176	13	operators	operator	NOUN
ejpam-3054	176	14	on	on	ADP
ejpam-3054	176	15	an	an	DET
ejpam-3054	176	16	infinite	infinite	ADJ
ejpam-3054	176	17	dimensional	dimensional	ADJ
ejpam-3054	176	18	complex	complex	ADJ
ejpam-3054	176	19	hilbert	hilbert	NOUN
ejpam-3054	176	20	space	space	NOUN
ejpam-3054	176	21	h	h	NOUN
ejpam-3054	176	22	,	,	PUNCT
ejpam-3054	176	23	the	the	DET
ejpam-3054	176	24	set	set	NOUN
ejpam-3054	176	25	of	of	ADP
ejpam-3054	176	26	all	all	DET
ejpam-3054	176	27	fredholm	fredholm	NOUN
ejpam-3054	176	28	operators	operator	NOUN
ejpam-3054	176	29	strictly	strictly	ADV
ejpam-3054	176	30	contains	contain	VERB
ejpam-3054	176	31	the	the	DET
ejpam-3054	176	32	set	set	NOUN
ejpam-3054	176	33	of	of	ADP
ejpam-3054	176	34	fredholm	fredholm	NOUN
ejpam-3054	176	35	operators	operator	NOUN
ejpam-3054	176	36	of	of	ADP
ejpam-3054	176	37	zero	zero	NUM
ejpam-3054	176	38	index	index	NOUN
ejpam-3054	176	39	,	,	PUNCT
ejpam-3054	176	40	but	but	CCONJ
ejpam-3054	176	41	there	there	PRON
ejpam-3054	176	42	exist	exist	VERB
ejpam-3054	176	43	infinite	infinite	ADJ
ejpam-3054	176	44	dimensional	dimensional	ADJ
ejpam-3054	176	45	banach	banach	NOUN
ejpam-3054	176	46	spaces	space	NOUN
ejpam-3054	176	47	references	reference	NOUN
ejpam-3054	176	48	1065	1065	NUM
ejpam-3054	176	49	for	for	ADP
ejpam-3054	176	50	which	which	PRON
ejpam-3054	176	51	every	every	DET
ejpam-3054	176	52	fredholm	fredholm	NOUN
ejpam-3054	176	53	operator	operator	NOUN
ejpam-3054	176	54	has	have	VERB
ejpam-3054	176	55	index	index	NOUN
ejpam-3054	176	56	zero	zero	NUM
ejpam-3054	176	57	;	;	PUNCT
ejpam-3054	176	58	see	see	VERB
ejpam-3054	176	59	[	[	X
ejpam-3054	176	60	10	10	NUM
ejpam-3054	176	61	]	]	PUNCT
ejpam-3054	176	62	.	.	PUNCT
ejpam-3054	177	1	in	in	ADP
ejpam-3054	177	2	the	the	DET
ejpam-3054	177	3	remainder	remainder	NOUN
ejpam-3054	177	4	of	of	ADP
ejpam-3054	177	5	this	this	DET
ejpam-3054	177	6	paper	paper	NOUN
ejpam-3054	177	7	we	we	PRON
ejpam-3054	177	8	will	will	AUX
ejpam-3054	177	9	assume	assume	VERB
ejpam-3054	177	10	that	that	SCONJ
ejpam-3054	177	11	our	our	PRON
ejpam-3054	177	12	primitive	primitive	ADJ
ejpam-3054	177	13	banach	banach	NOUN
ejpam-3054	177	14	algebras	algebra	NOUN
ejpam-3054	177	15	have	have	VERB
ejpam-3054	177	16	non	non	ADJ
ejpam-3054	177	17	-	-	ADJ
ejpam-3054	177	18	trivial	trivial	ADJ
ejpam-3054	177	19	index	index	NOUN
ejpam-3054	177	20	function	function	NOUN
ejpam-3054	177	21	.	.	PUNCT
ejpam-3054	178	1	the	the	DET
ejpam-3054	178	2	following	following	ADJ
ejpam-3054	178	3	result	result	NOUN
ejpam-3054	178	4	describe	describe	VERB
ejpam-3054	178	5	linear	linear	PROPN
ejpam-3054	178	6	maps	map	NOUN
ejpam-3054	178	7	ϕ	ϕ	NOUN
ejpam-3054	178	8	from	from	ADP
ejpam-3054	178	9	a	a	DET
ejpam-3054	178	10	purely	purely	ADV
ejpam-3054	178	11	infinite	infinite	ADJ
ejpam-3054	178	12	c∗-algebra	c∗-algebra	NOUN
ejpam-3054	178	13	with	with	ADP
ejpam-3054	178	14	real	real	ADJ
ejpam-3054	178	15	rank	rank	NOUN
ejpam-3054	178	16	zero	zero	NUM
ejpam-3054	178	17	onto	onto	ADP
ejpam-3054	178	18	a	a	DET
ejpam-3054	178	19	semisimple	semisimple	NOUN
ejpam-3054	178	20	banach	banach	NOUN
ejpam-3054	178	21	algebras	algebra	VERB
ejpam-3054	178	22	that	that	SCONJ
ejpam-3054	178	23	compress	compress	VERB
ejpam-3054	178	24	the	the	DET
ejpam-3054	178	25	weyl	weyl	PROPN
ejpam-3054	178	26	spectrum	spectrum	NOUN
ejpam-3054	178	27	(	(	PUNCT
ejpam-3054	178	28	i.e.	i.e.	X
ejpam-3054	178	29	,	,	PUNCT
ejpam-3054	178	30	w	w	X
ejpam-3054	178	31	(	(	PUNCT
ejpam-3054	178	32	ϕ(a	ϕ(a	NOUN
ejpam-3054	178	33	)	)	PUNCT
ejpam-3054	178	34	)	)	PUNCT
ejpam-3054	178	35	⊆w	⊆w	NOUN
ejpam-3054	178	36	(	(	PUNCT
ejpam-3054	178	37	a	a	NOUN
ejpam-3054	178	38	)	)	PUNCT
ejpam-3054	178	39	for	for	ADP
ejpam-3054	178	40	all	all	DET
ejpam-3054	178	41	a	a	DET
ejpam-3054	178	42	∈	∈	PROPN
ejpam-3054	178	43	a	a	PRON
ejpam-3054	178	44	)	)	PUNCT
ejpam-3054	178	45	.	.	PUNCT
ejpam-3054	179	1	theorem	theorem	ADJ
ejpam-3054	179	2	4	4	NUM
ejpam-3054	179	3	.	.	PUNCT
ejpam-3054	180	1	let	let	VERB
ejpam-3054	180	2	ϕ	ϕ	NOUN
ejpam-3054	180	3	be	be	AUX
ejpam-3054	180	4	a	a	DET
ejpam-3054	180	5	linear	linear	ADJ
ejpam-3054	180	6	surjective	surjective	NOUN
ejpam-3054	180	7	up	up	ADP
ejpam-3054	180	8	to	to	ADP
ejpam-3054	180	9	inessential	inessential	ADJ
ejpam-3054	180	10	elements	element	NOUN
ejpam-3054	180	11	map	map	NOUN
ejpam-3054	180	12	from	from	ADP
ejpam-3054	180	13	a	a	DET
ejpam-3054	180	14	purely	purely	ADV
ejpam-3054	180	15	infinite	infinite	ADJ
ejpam-3054	180	16	c∗-algebras	c∗-algebra	NOUN
ejpam-3054	180	17	a	a	PRON
ejpam-3054	180	18	with	with	ADP
ejpam-3054	180	19	real	real	ADJ
ejpam-3054	180	20	rank	rank	NOUN
ejpam-3054	180	21	zero	zero	NUM
ejpam-3054	180	22	into	into	ADP
ejpam-3054	180	23	a	a	DET
ejpam-3054	180	24	primitive	primitive	ADJ
ejpam-3054	180	25	banach	banach	NOUN
ejpam-3054	180	26	algebra	algebra	NOUN
ejpam-3054	180	27	b.	b.	NOUN
ejpam-3054	181	1	if	if	SCONJ
ejpam-3054	181	2	ϕ	ϕ	PROPN
ejpam-3054	181	3	compresses	compress	VERB
ejpam-3054	181	4	the	the	DET
ejpam-3054	181	5	weyl	weyl	PROPN
ejpam-3054	181	6	spectrum	spectrum	NOUN
ejpam-3054	181	7	,	,	PUNCT
ejpam-3054	181	8	then	then	ADV
ejpam-3054	181	9	ϕ(i(a	ϕ(i(a	NUM
ejpam-3054	181	10	)	)	PUNCT
ejpam-3054	181	11	)	)	PUNCT
ejpam-3054	182	1	⊆	⊆	NUM
ejpam-3054	182	2	i(b	i(b	NOUN
ejpam-3054	182	3	)	)	PUNCT
ejpam-3054	182	4	and	and	CCONJ
ejpam-3054	182	5	the	the	DET
ejpam-3054	182	6	induced	induced	ADJ
ejpam-3054	182	7	mapping	mapping	NOUN
ejpam-3054	182	8	ϕ̂	ϕ̂	NUM
ejpam-3054	182	9	:	:	PUNCT
ejpam-3054	182	10	c(a	c(a	ADV
ejpam-3054	182	11	)	)	PUNCT
ejpam-3054	182	12	→	→	PUNCT
ejpam-3054	182	13	c(b	c(b	PROPN
ejpam-3054	182	14	)	)	PUNCT
ejpam-3054	182	15	is	be	AUX
ejpam-3054	182	16	a	a	DET
ejpam-3054	182	17	jordan	jordan	PROPN
ejpam-3054	182	18	epimorphism	epimorphism	PROPN
ejpam-3054	182	19	multiplied	multiply	VERB
ejpam-3054	182	20	by	by	ADP
ejpam-3054	182	21	an	an	DET
ejpam-3054	182	22	invertible	invertible	ADJ
ejpam-3054	182	23	central	central	ADJ
ejpam-3054	182	24	element	element	NOUN
ejpam-3054	182	25	of	of	ADP
ejpam-3054	182	26	c(b	c(b	PROPN
ejpam-3054	182	27	)	)	PUNCT
ejpam-3054	182	28	.	.	PUNCT
ejpam-3054	183	1	proof	proof	NOUN
ejpam-3054	183	2	.	.	PUNCT
ejpam-3054	184	1	denote	denote	VERB
ejpam-3054	184	2	by	by	ADP
ejpam-3054	184	3	ηk	ηk	PROPN
ejpam-3054	184	4	the	the	DET
ejpam-3054	184	5	polynomial	polynomial	ADJ
ejpam-3054	184	6	convex	convex	NOUN
ejpam-3054	184	7	hull	hull	NOUN
ejpam-3054	184	8	of	of	ADP
ejpam-3054	184	9	a	a	DET
ejpam-3054	184	10	compact	compact	ADJ
ejpam-3054	184	11	subset	subset	NOUN
ejpam-3054	184	12	k	k	PROPN
ejpam-3054	184	13	of	of	ADP
ejpam-3054	184	14	c.	c.	PROPN
ejpam-3054	184	15	since	since	SCONJ
ejpam-3054	184	16	ηw	ηw	PROPN
ejpam-3054	184	17	(	(	PUNCT
ejpam-3054	184	18	x	x	NOUN
ejpam-3054	184	19	)	)	PUNCT
ejpam-3054	184	20	=	=	SYM
ejpam-3054	184	21	ησe(x	ησe(x	PROPN
ejpam-3054	184	22	)	)	PUNCT
ejpam-3054	184	23	for	for	ADP
ejpam-3054	184	24	all	all	DET
ejpam-3054	184	25	x	x	SYM
ejpam-3054	184	26	∈	∈	PROPN
ejpam-3054	184	27	a	a	PRON
ejpam-3054	184	28	(	(	PUNCT
ejpam-3054	184	29	see	see	VERB
ejpam-3054	184	30	[	[	X
ejpam-3054	184	31	17	17	NUM
ejpam-3054	184	32	,	,	PUNCT
ejpam-3054	184	33	corollary	corollary	ADJ
ejpam-3054	184	34	6.21	6.21	NUM
ejpam-3054	184	35	]	]	PUNCT
ejpam-3054	184	36	)	)	PUNCT
ejpam-3054	184	37	,	,	PUNCT
ejpam-3054	184	38	it	it	PRON
ejpam-3054	184	39	follows	follow	VERB
ejpam-3054	184	40	that	that	SCONJ
ejpam-3054	184	41	the	the	DET
ejpam-3054	184	42	map	map	NOUN
ejpam-3054	184	43	ϕ	ϕ	NOUN
ejpam-3054	184	44	is	be	AUX
ejpam-3054	184	45	essentially	essentially	ADV
ejpam-3054	184	46	spectrally	spectrally	ADV
ejpam-3054	184	47	bounded	bound	VERB
ejpam-3054	184	48	;	;	PUNCT
ejpam-3054	184	49	and	and	CCONJ
ejpam-3054	184	50	the	the	DET
ejpam-3054	184	51	desired	desire	VERB
ejpam-3054	184	52	conclusion	conclusion	NOUN
ejpam-3054	184	53	follows	follow	VERB
ejpam-3054	184	54	from	from	ADP
ejpam-3054	184	55	theorem	theorem	ADJ
ejpam-3054	184	56	1	1	NUM
ejpam-3054	184	57	.	.	PUNCT
ejpam-3054	184	58	recall	recall	VERB
ejpam-3054	184	59	that	that	SCONJ
ejpam-3054	184	60	a	a	DET
ejpam-3054	184	61	weyl	weyl	VERB
ejpam-3054	184	62	operator	operator	NOUN
ejpam-3054	184	63	on	on	ADP
ejpam-3054	184	64	a	a	DET
ejpam-3054	184	65	complex	complex	ADJ
ejpam-3054	184	66	hilbert	hilbert	NOUN
ejpam-3054	184	67	space	space	NOUN
ejpam-3054	184	68	is	be	AUX
ejpam-3054	184	69	a	a	DET
ejpam-3054	184	70	fredholm	fredholm	NOUN
ejpam-3054	184	71	operator	operator	NOUN
ejpam-3054	184	72	with	with	ADP
ejpam-3054	184	73	zero	zero	NUM
ejpam-3054	184	74	index	index	NOUN
ejpam-3054	184	75	.	.	PUNCT
ejpam-3054	185	1	as	as	ADP
ejpam-3054	185	2	consequence	consequence	NOUN
ejpam-3054	185	3	of	of	ADP
ejpam-3054	185	4	the	the	DET
ejpam-3054	185	5	above	above	ADJ
ejpam-3054	185	6	theorem	theorem	NOUN
ejpam-3054	185	7	,	,	PUNCT
ejpam-3054	185	8	one	one	PRON
ejpam-3054	185	9	gets	get	VERB
ejpam-3054	185	10	the	the	DET
ejpam-3054	185	11	following	follow	VERB
ejpam-3054	185	12	result	result	NOUN
ejpam-3054	185	13	.	.	PUNCT
ejpam-3054	186	1	corollary	corollary	ADJ
ejpam-3054	186	2	4	4	NUM
ejpam-3054	186	3	.	.	PUNCT
ejpam-3054	187	1	let	let	VERB
ejpam-3054	187	2	h	h	NOUN
ejpam-3054	187	3	and	and	CCONJ
ejpam-3054	187	4	h′	h′	PROPN
ejpam-3054	187	5	be	be	AUX
ejpam-3054	187	6	infinite	infinite	ADJ
ejpam-3054	187	7	dimensional	dimensional	ADJ
ejpam-3054	187	8	complex	complex	ADJ
ejpam-3054	187	9	hilbert	hilbert	NOUN
ejpam-3054	187	10	spaces	space	NOUN
ejpam-3054	187	11	and	and	CCONJ
ejpam-3054	187	12	let	let	VERB
ejpam-3054	187	13	ϕ	ϕ	NOUN
ejpam-3054	187	14	:	:	PUNCT
ejpam-3054	187	15	l(h	l(h	PROPN
ejpam-3054	187	16	)	)	PUNCT
ejpam-3054	187	17	→	→	SYM
ejpam-3054	187	18	l(h′	l(h′	PROPN
ejpam-3054	187	19	)	)	PUNCT
ejpam-3054	187	20	be	be	AUX
ejpam-3054	187	21	a	a	DET
ejpam-3054	187	22	surjective	surjective	ADJ
ejpam-3054	187	23	up	up	ADP
ejpam-3054	187	24	to	to	ADP
ejpam-3054	187	25	compact	compact	ADJ
ejpam-3054	187	26	operators	operator	NOUN
ejpam-3054	187	27	linear	linear	PROPN
ejpam-3054	187	28	map	map	NOUN
ejpam-3054	187	29	.	.	PUNCT
ejpam-3054	188	1	if	if	SCONJ
ejpam-3054	188	2	ϕ	ϕ	PROPN
ejpam-3054	188	3	compresses	compress	VERB
ejpam-3054	188	4	the	the	DET
ejpam-3054	188	5	weyl	weyl	PROPN
ejpam-3054	188	6	spectrum	spectrum	NOUN
ejpam-3054	188	7	,	,	PUNCT
ejpam-3054	188	8	then	then	ADV
ejpam-3054	188	9	ϕ(k(h	ϕ(k(h	PROPN
ejpam-3054	188	10	)	)	PUNCT
ejpam-3054	188	11	)	)	PUNCT
ejpam-3054	189	1	⊆	⊆	NUM
ejpam-3054	189	2	k(h′	k(h′	PROPN
ejpam-3054	189	3	)	)	PUNCT
ejpam-3054	189	4	and	and	CCONJ
ejpam-3054	189	5	the	the	DET
ejpam-3054	189	6	induced	induced	ADJ
ejpam-3054	189	7	mapping	mapping	NOUN
ejpam-3054	189	8	ϕ̂	ϕ̂	NUM
ejpam-3054	189	9	:	:	PUNCT
ejpam-3054	190	1	c(h	c(h	VERB
ejpam-3054	190	2	)	)	PUNCT
ejpam-3054	190	3	→	→	SYM
ejpam-3054	190	4	c(h′	c(h′	NUM
ejpam-3054	190	5	)	)	PUNCT
ejpam-3054	190	6	is	be	AUX
ejpam-3054	190	7	either	either	CCONJ
ejpam-3054	190	8	a	a	DET
ejpam-3054	190	9	continuous	continuous	ADJ
ejpam-3054	190	10	epimorphism	epimorphism	NOUN
ejpam-3054	190	11	or	or	CCONJ
ejpam-3054	190	12	a	a	DET
ejpam-3054	190	13	continuous	continuous	ADJ
ejpam-3054	190	14	anti	anti	NOUN
ejpam-3054	190	15	-	-	NOUN
ejpam-3054	190	16	epimorphism	epimorphism	NOUN
ejpam-3054	190	17	.	.	PUNCT
ejpam-3054	191	1	aknowledgements	aknowledgement	VERB
ejpam-3054	191	2	the	the	DET
ejpam-3054	191	3	author	author	NOUN
ejpam-3054	191	4	thanks	thank	NOUN
ejpam-3054	191	5	the	the	DET
ejpam-3054	191	6	referee	referee	NOUN
ejpam-3054	191	7	for	for	ADP
ejpam-3054	191	8	their	their	PRON
ejpam-3054	191	9	useful	useful	ADJ
ejpam-3054	191	10	comments	comment	NOUN
ejpam-3054	191	11	and	and	CCONJ
ejpam-3054	191	12	valuable	valuable	ADJ
ejpam-3054	191	13	suggestions	suggestion	NOUN
ejpam-3054	191	14	leading	lead	VERB
ejpam-3054	191	15	to	to	ADP
ejpam-3054	191	16	improvements	improvement	NOUN
ejpam-3054	191	17	in	in	ADP
ejpam-3054	191	18	the	the	DET
ejpam-3054	191	19	manuscript	manuscript	NOUN
ejpam-3054	191	20	.	.	PUNCT
ejpam-3054	192	1	references	reference	NOUN
ejpam-3054	192	2	[	[	X
ejpam-3054	192	3	1	1	X
ejpam-3054	192	4	]	]	PUNCT
ejpam-3054	192	5	p.	p.	NOUN
ejpam-3054	192	6	aiena	aiena	PROPN
ejpam-3054	192	7	.	.	PUNCT
ejpam-3054	193	1	fredholm	fredholm	NOUN
ejpam-3054	193	2	and	and	CCONJ
ejpam-3054	193	3	local	local	ADJ
ejpam-3054	193	4	spectral	spectral	ADJ
ejpam-3054	193	5	theory	theory	NOUN
ejpam-3054	193	6	,	,	PUNCT
ejpam-3054	193	7	with	with	ADP
ejpam-3054	193	8	applications	application	NOUN
ejpam-3054	193	9	to	to	ADP
ejpam-3054	193	10	multipliers	multiplier	NOUN
ejpam-3054	193	11	.	.	PUNCT
ejpam-3054	194	1	kluwer	kluwer	NOUN
ejpam-3054	194	2	academic	academic	ADJ
ejpam-3054	194	3	publishers	publisher	NOUN
ejpam-3054	194	4	,	,	PUNCT
ejpam-3054	194	5	2004	2004	NUM
ejpam-3054	194	6	.	.	PUNCT
ejpam-3054	195	1	[	[	X
ejpam-3054	195	2	2	2	NUM
ejpam-3054	195	3	]	]	X
ejpam-3054	195	4	b.	b.	PROPN
ejpam-3054	195	5	aupetit	aupetit	PROPN
ejpam-3054	195	6	.	.	PUNCT
ejpam-3054	196	1	a	a	DET
ejpam-3054	196	2	primer	primer	NOUN
ejpam-3054	196	3	on	on	ADP
ejpam-3054	196	4	spectral	spectral	ADJ
ejpam-3054	196	5	theory	theory	NOUN
ejpam-3054	196	6	.	.	PUNCT
ejpam-3054	197	1	springer	springer	NOUN
ejpam-3054	197	2	-	-	PUNCT
ejpam-3054	197	3	verlag	verlag	PROPN
ejpam-3054	197	4	,	,	PUNCT
ejpam-3054	197	5	new	new	PROPN
ejpam-3054	197	6	york	york	PROPN
ejpam-3054	197	7	,	,	PUNCT
ejpam-3054	197	8	1991	1991	NUM
ejpam-3054	197	9	.	.	PUNCT
ejpam-3054	198	1	[	[	X
ejpam-3054	198	2	3	3	X
ejpam-3054	198	3	]	]	X
ejpam-3054	198	4	b.	b.	PROPN
ejpam-3054	198	5	aupetit	aupetit	PROPN
ejpam-3054	198	6	.	.	PUNCT
ejpam-3054	199	1	spectrum	spectrum	NOUN
ejpam-3054	199	2	-	-	PUNCT
ejpam-3054	199	3	preserving	preserve	VERB
ejpam-3054	199	4	linear	linear	NOUN
ejpam-3054	199	5	map	map	NOUN
ejpam-3054	199	6	between	between	ADP
ejpam-3054	199	7	banach	banach	NOUN
ejpam-3054	199	8	algebra	algebra	NOUN
ejpam-3054	199	9	or	or	CCONJ
ejpam-3054	199	10	jordanbanach	jordanbanach	NOUN
ejpam-3054	199	11	algebra	algebra	PROPN
ejpam-3054	199	12	.	.	PUNCT
ejpam-3054	200	1	j.	j.	PROPN
ejpam-3054	200	2	london	london	PROPN
ejpam-3054	200	3	math	math	PROPN
ejpam-3054	200	4	.	.	PUNCT
ejpam-3054	201	1	soc	soc	PROPN
ejpam-3054	201	2	.	.	PUNCT
ejpam-3054	201	3	,	,	PUNCT
ejpam-3054	202	1	62(3):917	62(3):917	NUM
ejpam-3054	202	2	-	-	SYM
ejpam-3054	202	3	924	924	NUM
ejpam-3054	202	4	,	,	PUNCT
ejpam-3054	202	5	2000	2000	NUM
ejpam-3054	202	6	.	.	PUNCT
ejpam-3054	203	1	references	reference	NOUN
ejpam-3054	203	2	1066	1066	NUM
ejpam-3054	203	3	[	[	X
ejpam-3054	203	4	4	4	NUM
ejpam-3054	203	5	]	]	PUNCT
ejpam-3054	203	6	b.	b.	PROPN
ejpam-3054	203	7	a.	a.	PROPN
ejpam-3054	203	8	barnes	barnes	PROPN
ejpam-3054	203	9	,	,	PUNCT
ejpam-3054	203	10	g.	g.	PROPN
ejpam-3054	203	11	j.	j.	PROPN
ejpam-3054	203	12	murphy	murphy	PROPN
ejpam-3054	203	13	,	,	PUNCT
ejpam-3054	203	14	m.	m.	PROPN
ejpam-3054	203	15	r.	r.	PROPN
ejpam-3054	203	16	f.	f.	PROPN
ejpam-3054	203	17	smyth	smyth	PROPN
ejpam-3054	203	18	,	,	PUNCT
ejpam-3054	203	19	and	and	CCONJ
ejpam-3054	203	20	t.	t.	PROPN
ejpam-3054	203	21	t.	t.	PROPN
ejpam-3054	203	22	west	west	PROPN
ejpam-3054	203	23	.	.	PUNCT
ejpam-3054	204	1	riesz	riesz	VERB
ejpam-3054	204	2	and	and	CCONJ
ejpam-3054	204	3	fredholm	fredholm	NOUN
ejpam-3054	204	4	theory	theory	NOUN
ejpam-3054	204	5	in	in	ADP
ejpam-3054	204	6	banach	banach	NOUN
ejpam-3054	204	7	algebra	algebra	NOUN
ejpam-3054	204	8	.	.	PUNCT
ejpam-3054	205	1	pitman	pitman	NOUN
ejpam-3054	205	2	,	,	PUNCT
ejpam-3054	205	3	london	london	PROPN
ejpam-3054	205	4	,	,	PUNCT
ejpam-3054	205	5	1982	1982	NUM
ejpam-3054	205	6	.	.	PUNCT
ejpam-3054	206	1	[	[	X
ejpam-3054	206	2	5	5	NUM
ejpam-3054	206	3	]	]	PUNCT
ejpam-3054	206	4	m.	m.	NOUN
ejpam-3054	206	5	bendaoud	bendaoud	NOUN
ejpam-3054	206	6	,	,	PUNCT
ejpam-3054	206	7	a.	a.	NOUN
ejpam-3054	206	8	bourhim	bourhim	NOUN
ejpam-3054	206	9	,	,	PUNCT
ejpam-3054	206	10	and	and	CCONJ
ejpam-3054	206	11	m.	m.	NOUN
ejpam-3054	206	12	sarih	sarih	NOUN
ejpam-3054	206	13	.	.	PUNCT
ejpam-3054	207	1	linear	linear	PROPN
ejpam-3054	207	2	maps	map	NOUN
ejpam-3054	207	3	preserving	preserve	VERB
ejpam-3054	207	4	the	the	DET
ejpam-3054	207	5	essential	essential	ADJ
ejpam-3054	207	6	spectral	spectral	ADJ
ejpam-3054	207	7	radius	radius	NOUN
ejpam-3054	207	8	.	.	PUNCT
ejpam-3054	208	1	linear	linear	PROPN
ejpam-3054	208	2	algebra	algebra	PROPN
ejpam-3054	208	3	appl	appl	NOUN
ejpam-3054	208	4	.	.	PUNCT
ejpam-3054	208	5	,	,	PUNCT
ejpam-3054	209	1	428:1041	428:1041	NOUN
ejpam-3054	209	2	-	-	SYM
ejpam-3054	209	3	1045	1045	NUM
ejpam-3054	209	4	,	,	PUNCT
ejpam-3054	209	5	2008	2008	NUM
ejpam-3054	209	6	.	.	PUNCT
ejpam-3054	210	1	[	[	X
ejpam-3054	210	2	6	6	NUM
ejpam-3054	210	3	]	]	PUNCT
ejpam-3054	210	4	m.	m.	NOUN
ejpam-3054	210	5	bendaoud	bendaoud	NOUN
ejpam-3054	210	6	and	and	CCONJ
ejpam-3054	210	7	a.	a.	NOUN
ejpam-3054	210	8	bourhim	bourhim	NOUN
ejpam-3054	210	9	.	.	PUNCT
ejpam-3054	211	1	essentially	essentially	ADV
ejpam-3054	211	2	spectrally	spectrally	ADV
ejpam-3054	211	3	bounded	bound	VERB
ejpam-3054	211	4	linear	linear	ADJ
ejpam-3054	211	5	maps	map	NOUN
ejpam-3054	211	6	.	.	PUNCT
ejpam-3054	212	1	proc	proc	NOUN
ejpam-3054	212	2	.	.	PUNCT
ejpam-3054	213	1	amer	amer	PROPN
ejpam-3054	213	2	.	.	PUNCT
ejpam-3054	213	3	math	math	PROPN
ejpam-3054	213	4	.	.	PUNCT
ejpam-3054	214	1	soc	soc	PROPN
ejpam-3054	214	2	.	.	PUNCT
ejpam-3054	214	3	,	,	PUNCT
ejpam-3054	214	4	137(10):3329–3334	137(10):3329–3334	NUM
ejpam-3054	214	5	,	,	PUNCT
ejpam-3054	214	6	2009	2009	NUM
ejpam-3054	214	7	.	.	PUNCT
ejpam-3054	215	1	[	[	X
ejpam-3054	215	2	7	7	X
ejpam-3054	215	3	]	]	PUNCT
ejpam-3054	215	4	m.	m.	NOUN
ejpam-3054	215	5	bendaoud	bendaoud	NOUN
ejpam-3054	215	6	and	and	CCONJ
ejpam-3054	215	7	m.	m.	NOUN
ejpam-3054	215	8	sarih	sarih	NOUN
ejpam-3054	215	9	.	.	PUNCT
ejpam-3054	216	1	locally	locally	ADV
ejpam-3054	216	2	spectrally	spectrally	ADV
ejpam-3054	216	3	bounded	bound	VERB
ejpam-3054	216	4	linear	linear	ADJ
ejpam-3054	216	5	maps	map	NOUN
ejpam-3054	216	6	.	.	PUNCT
ejpam-3054	217	1	math	math	NOUN
ejpam-3054	217	2	.	.	PUNCT
ejpam-3054	218	1	bohem	bohem	PROPN
ejpam-3054	218	2	,	,	PUNCT
ejpam-3054	218	3	136(1):81–89	136(1):81–89	NUM
ejpam-3054	218	4	,	,	PUNCT
ejpam-3054	218	5	2011	2011	NUM
ejpam-3054	218	6	.	.	PUNCT
ejpam-3054	219	1	[	[	X
ejpam-3054	219	2	8	8	NUM
ejpam-3054	219	3	]	]	X
ejpam-3054	219	4	l.	l.	PROPN
ejpam-3054	219	5	g.	g.	PROPN
ejpam-3054	219	6	brown	brown	PROPN
ejpam-3054	219	7	and	and	CCONJ
ejpam-3054	219	8	g.	g.	PROPN
ejpam-3054	219	9	k.	k.	PROPN
ejpam-3054	219	10	pedersen	pedersen	PROPN
ejpam-3054	219	11	.	.	PUNCT
ejpam-3054	220	1	c∗-algebras	c∗-algebra	NOUN
ejpam-3054	220	2	of	of	ADP
ejpam-3054	220	3	rank	rank	ADJ
ejpam-3054	220	4	real	real	ADJ
ejpam-3054	220	5	zero	zero	NUM
ejpam-3054	220	6	.	.	PUNCT
ejpam-3054	221	1	j.	j.	PROPN
ejpam-3054	221	2	funct	funct	PROPN
ejpam-3054	221	3	.	.	PUNCT
ejpam-3054	222	1	anal	anal	PROPN
ejpam-3054	222	2	.	.	PUNCT
ejpam-3054	222	3	,	,	PUNCT
ejpam-3054	222	4	99:131	99:131	NUM
ejpam-3054	222	5	-	-	SYM
ejpam-3054	222	6	149	149	NUM
ejpam-3054	222	7	,	,	PUNCT
ejpam-3054	222	8	1991	1991	NUM
ejpam-3054	222	9	.	.	PUNCT
ejpam-3054	223	1	[	[	X
ejpam-3054	223	2	9	9	NUM
ejpam-3054	223	3	]	]	X
ejpam-3054	223	4	j.	j.	PROPN
ejpam-3054	223	5	cui	cui	PROPN
ejpam-3054	223	6	and	and	CCONJ
ejpam-3054	223	7	j.	j.	PROPN
ejpam-3054	223	8	hou	hou	PROPN
ejpam-3054	223	9	.	.	PUNCT
ejpam-3054	224	1	linear	linear	PROPN
ejpam-3054	224	2	maps	map	NOUN
ejpam-3054	224	3	between	between	ADP
ejpam-3054	224	4	banach	banach	NOUN
ejpam-3054	224	5	algebras	algebras	PROPN
ejpam-3054	224	6	compressing	compress	VERB
ejpam-3054	224	7	certains	certain	NOUN
ejpam-3054	224	8	spectral	spectral	ADJ
ejpam-3054	224	9	functions	function	NOUN
ejpam-3054	224	10	.	.	PUNCT
ejpam-3054	225	1	rocky	rocky	ADJ
ejpam-3054	225	2	mountain	mountain	PROPN
ejpam-3054	225	3	j.	j.	PROPN
ejpam-3054	225	4	math	math	PROPN
ejpam-3054	225	5	.	.	PUNCT
ejpam-3054	226	1	soc	soc	PROPN
ejpam-3054	226	2	.	.	PUNCT
ejpam-3054	226	3	,	,	PUNCT
ejpam-3054	226	4	34(2):565	34(2):565	PROPN
ejpam-3054	226	5	-	-	SYM
ejpam-3054	226	6	584	584	NUM
ejpam-3054	226	7	,	,	PUNCT
ejpam-3054	226	8	2004	2004	NUM
ejpam-3054	226	9	.	.	PUNCT
ejpam-3054	227	1	[	[	X
ejpam-3054	227	2	10	10	NUM
ejpam-3054	227	3	]	]	X
ejpam-3054	227	4	w.	w.	PROPN
ejpam-3054	227	5	t.	t.	PROPN
ejpam-3054	227	6	gowers	gowers	PROPN
ejpam-3054	227	7	and	and	CCONJ
ejpam-3054	227	8	b.	b.	PROPN
ejpam-3054	227	9	maurey	maurey	PROPN
ejpam-3054	227	10	.	.	PUNCT
ejpam-3054	228	1	the	the	DET
ejpam-3054	228	2	unconditional	unconditional	ADJ
ejpam-3054	228	3	basic	basic	ADJ
ejpam-3054	228	4	sequence	sequence	NOUN
ejpam-3054	228	5	problem	problem	NOUN
ejpam-3054	228	6	.	.	PUNCT
ejpam-3054	229	1	j.	j.	PROPN
ejpam-3054	229	2	amer	amer	PROPN
ejpam-3054	229	3	.	.	PROPN
ejpam-3054	229	4	math	math	PROPN
ejpam-3054	229	5	.	.	PUNCT
ejpam-3054	230	1	soc	soc	PROPN
ejpam-3054	230	2	.	.	PUNCT
ejpam-3054	230	3	,	,	PUNCT
ejpam-3054	230	4	6:851	6:851	X
ejpam-3054	230	5	-	-	SYM
ejpam-3054	230	6	874	874	NUM
ejpam-3054	230	7	,	,	PUNCT
ejpam-3054	230	8	1993	1993	NUM
ejpam-3054	230	9	.	.	PUNCT
ejpam-3054	231	1	[	[	X
ejpam-3054	231	2	11	11	NUM
ejpam-3054	231	3	]	]	PUNCT
ejpam-3054	231	4	i.	i.	PROPN
ejpam-3054	231	5	n.	n.	PROPN
ejpam-3054	231	6	herstein	herstein	PROPN
ejpam-3054	231	7	.	.	PUNCT
ejpam-3054	232	1	jordan	jordan	PROPN
ejpam-3054	232	2	homomorphisms	homomorphisms	PROPN
ejpam-3054	232	3	.	.	PUNCT
ejpam-3054	233	1	trans	trans	PROPN
ejpam-3054	233	2	.	.	PUNCT
ejpam-3054	234	1	amer	amer	PROPN
ejpam-3054	234	2	.	.	PUNCT
ejpam-3054	234	3	math	math	PROPN
ejpam-3054	234	4	.	.	PUNCT
ejpam-3054	235	1	soc	soc	PROPN
ejpam-3054	235	2	.	.	PUNCT
ejpam-3054	235	3	,	,	PUNCT
ejpam-3054	235	4	81(2):331	81(2):331	NUM
ejpam-3054	235	5	-	-	SYM
ejpam-3054	235	6	341	341	NUM
ejpam-3054	235	7	,	,	PUNCT
ejpam-3054	235	8	1956	1956	NUM
ejpam-3054	235	9	.	.	PUNCT
ejpam-3054	236	1	[	[	X
ejpam-3054	236	2	12	12	NUM
ejpam-3054	236	3	]	]	X
ejpam-3054	236	4	j	j	PROPN
ejpam-3054	236	5	.c	.c	PROPN
ejpam-3054	236	6	.	.	PUNCT
ejpam-3054	237	1	hou	hou	PROPN
ejpam-3054	237	2	.	.	PUNCT
ejpam-3054	237	3	rank	rank	PROPN
ejpam-3054	237	4	preserving	preserve	VERB
ejpam-3054	237	5	linear	linear	NOUN
ejpam-3054	237	6	maps	map	NOUN
ejpam-3054	237	7	on	on	ADP
ejpam-3054	237	8	b(x	b(x	NOUN
ejpam-3054	237	9	)	)	PUNCT
ejpam-3054	237	10	.	.	PUNCT
ejpam-3054	238	1	sci	sci	PROPN
ejpam-3054	238	2	.	.	PUNCT
ejpam-3054	239	1	china	china	PROPN
ejpam-3054	239	2	ser	ser	PROPN
ejpam-3054	239	3	.	.	PUNCT
ejpam-3054	240	1	32(8):929	32(8):929	NOUN
ejpam-3054	240	2	-	-	SYM
ejpam-3054	240	3	940	940	NUM
ejpam-3054	240	4	,	,	PUNCT
ejpam-3054	240	5	1989	1989	NUM
ejpam-3054	240	6	.	.	PUNCT
ejpam-3054	241	1	[	[	X
ejpam-3054	241	2	13	13	NUM
ejpam-3054	241	3	]	]	X
ejpam-3054	241	4	n.	n.	PROPN
ejpam-3054	241	5	jacobson	jacobson	PROPN
ejpam-3054	241	6	and	and	CCONJ
ejpam-3054	241	7	c.	c.	PROPN
ejpam-3054	241	8	e.	e.	PROPN
ejpam-3054	241	9	rickart	rickart	PROPN
ejpam-3054	241	10	.	.	PUNCT
ejpam-3054	242	1	jordan	jordan	PROPN
ejpam-3054	242	2	homomorphism	homomorphism	PROPN
ejpam-3054	242	3	of	of	ADP
ejpam-3054	242	4	rings	ring	NOUN
ejpam-3054	242	5	.	.	PUNCT
ejpam-3054	243	1	trans	trans	PROPN
ejpam-3054	243	2	.	.	PUNCT
ejpam-3054	244	1	amer	amer	PROPN
ejpam-3054	244	2	.	.	PUNCT
ejpam-3054	244	3	math	math	PROPN
ejpam-3054	244	4	.	.	PUNCT
ejpam-3054	245	1	soc	soc	PROPN
ejpam-3054	245	2	.	.	PUNCT
ejpam-3054	245	3	,	,	PUNCT
ejpam-3054	245	4	69:749	69:749	NUM
ejpam-3054	245	5	-	-	SYM
ejpam-3054	245	6	502	502	NUM
ejpam-3054	245	7	,	,	PUNCT
ejpam-3054	245	8	1950	1950	NUM
ejpam-3054	245	9	.	.	PUNCT
ejpam-3054	246	1	[	[	X
ejpam-3054	246	2	14	14	NUM
ejpam-3054	246	3	]	]	PUNCT
ejpam-3054	246	4	a.	a.	NOUN
ejpam-3054	246	5	jafarian	jafarian	NOUN
ejpam-3054	246	6	and	and	CCONJ
ejpam-3054	246	7	a.	a.	PROPN
ejpam-3054	246	8	r.	r.	PROPN
ejpam-3054	246	9	sourour	sourour	PROPN
ejpam-3054	246	10	.	.	PUNCT
ejpam-3054	247	1	spectrum	spectrum	NOUN
ejpam-3054	247	2	preserving	preserve	VERB
ejpam-3054	247	3	linear	linear	ADJ
ejpam-3054	247	4	maps	map	NOUN
ejpam-3054	247	5	.	.	PUNCT
ejpam-3054	248	1	j.	j.	PROPN
ejpam-3054	248	2	funct	funct	PROPN
ejpam-3054	248	3	.	.	PUNCT
ejpam-3054	249	1	anal	anal	PROPN
ejpam-3054	249	2	.	.	PROPN
ejpam-3054	249	3	,	,	PUNCT
ejpam-3054	249	4	66(2):255	66(2):255	NOUN
ejpam-3054	249	5	-	-	SYM
ejpam-3054	249	6	261	261	NUM
ejpam-3054	249	7	,	,	PUNCT
ejpam-3054	249	8	1986	1986	NUM
ejpam-3054	249	9	.	.	PUNCT
ejpam-3054	250	1	[	[	X
ejpam-3054	250	2	15	15	NUM
ejpam-3054	250	3	]	]	X
ejpam-3054	250	4	e.	e.	PROPN
ejpam-3054	250	5	kirchberg	kirchberg	PROPN
ejpam-3054	250	6	and	and	CCONJ
ejpam-3054	250	7	m.	m.	NOUN
ejpam-3054	250	8	rørdam	rørdam	PROPN
ejpam-3054	250	9	.	.	PUNCT
ejpam-3054	251	1	non	non	ADJ
ejpam-3054	251	2	-	-	ADJ
ejpam-3054	251	3	simple	simple	ADJ
ejpam-3054	251	4	purely	purely	ADV
ejpam-3054	251	5	infinite	infinite	ADJ
ejpam-3054	251	6	c∗-algebras	c∗-algebra	NOUN
ejpam-3054	251	7	.	.	PROPN
ejpam-3054	251	8	amer	amer	PROPN
ejpam-3054	251	9	.	.	PUNCT
ejpam-3054	252	1	j.	j.	PROPN
ejpam-3054	252	2	math	math	PROPN
ejpam-3054	252	3	.	.	PUNCT
ejpam-3054	252	4	,	,	PUNCT
ejpam-3054	252	5	122(3	122(3	NUM
ejpam-3054	252	6	):	):	PUNCT
ejpam-3054	252	7	637	637	NUM
ejpam-3054	252	8	-	-	SYM
ejpam-3054	252	9	666	666	NUM
ejpam-3054	252	10	,	,	PUNCT
ejpam-3054	252	11	2000	2000	NUM
ejpam-3054	252	12	.	.	PUNCT
ejpam-3054	253	1	[	[	X
ejpam-3054	253	2	16	16	NUM
ejpam-3054	253	3	]	]	X
ejpam-3054	253	4	c.	c.	PROPN
ejpam-3054	253	5	k.	k.	PROPN
ejpam-3054	253	6	li	li	PROPN
ejpam-3054	253	7	and	and	CCONJ
ejpam-3054	253	8	n.	n.	PROPN
ejpam-3054	253	9	k.	k.	PROPN
ejpam-3054	253	10	tsing	tsing	PROPN
ejpam-3054	253	11	.	.	PUNCT
ejpam-3054	254	1	linear	linear	PROPN
ejpam-3054	254	2	preserver	preserver	NOUN
ejpam-3054	254	3	problems	problem	NOUN
ejpam-3054	254	4	:	:	PUNCT
ejpam-3054	254	5	a	a	DET
ejpam-3054	254	6	bref	bref	ADJ
ejpam-3054	254	7	introduction	introduction	NOUN
ejpam-3054	254	8	and	and	CCONJ
ejpam-3054	254	9	some	some	DET
ejpam-3054	254	10	special	special	ADJ
ejpam-3054	254	11	thechniques	thechnique	NOUN
ejpam-3054	254	12	.	.	PUNCT
ejpam-3054	255	1	linear	linear	ADJ
ejpam-3054	255	2	algebra	algebra	PROPN
ejpam-3054	255	3	appl	appl	NOUN
ejpam-3054	255	4	.	.	PROPN
ejpam-3054	256	1	,	,	PUNCT
ejpam-3054	256	2	162/164:217	162/164:217	NUM
ejpam-3054	256	3	-	-	SYM
ejpam-3054	256	4	235	235	NUM
ejpam-3054	256	5	,	,	PUNCT
ejpam-3054	256	6	1992	1992	NUM
ejpam-3054	256	7	.	.	PUNCT
ejpam-3054	257	1	[	[	X
ejpam-3054	257	2	17	17	NUM
ejpam-3054	257	3	]	]	PUNCT
ejpam-3054	257	4	j.	j.	PROPN
ejpam-3054	257	5	w.	w.	PROPN
ejpam-3054	257	6	rowell	rowell	PROPN
ejpam-3054	257	7	.	.	PUNCT
ejpam-3054	257	8	unilateral	unilateral	ADJ
ejpam-3054	257	9	fredholm	fredholm	NOUN
ejpam-3054	257	10	theory	theory	NOUN
ejpam-3054	257	11	and	and	CCONJ
ejpam-3054	257	12	unilateral	unilateral	ADJ
ejpam-3054	257	13	spectra	spectra	NOUN
ejpam-3054	257	14	.	.	PUNCT
ejpam-3054	257	15	proc	proc	PROPN
ejpam-3054	257	16	.	.	PUNCT
ejpam-3054	258	1	roy	roy	PROPN
ejpam-3054	258	2	.	.	PROPN
ejpam-3054	258	3	irish	irish	PROPN
ejpam-3054	258	4	.	.	PUNCT
ejpam-3054	259	1	acad	acad	PROPN
ejpam-3054	259	2	.	.	PROPN
ejpam-3054	259	3	,	,	PUNCT
ejpam-3054	259	4	84(1)69	84(1)69	NUM
ejpam-3054	259	5	-	-	SYM
ejpam-3054	259	6	85	85	NUM
ejpam-3054	259	7	,	,	PUNCT
ejpam-3054	259	8	1984	1984	NUM
ejpam-3054	259	9	.	.	PUNCT
ejpam-3054	260	1	[	[	X
ejpam-3054	260	2	18	18	NUM
ejpam-3054	260	3	]	]	PUNCT
ejpam-3054	260	4	c.	c.	NOUN
ejpam-3054	260	5	schmoger	schmoger	PROPN
ejpam-3054	260	6	.	.	PUNCT
ejpam-3054	261	1	atkinson	atkinson	PROPN
ejpam-3054	261	2	theory	theory	PROPN
ejpam-3054	261	3	and	and	CCONJ
ejpam-3054	261	4	holomorphic	holomorphic	ADJ
ejpam-3054	261	5	functions	function	NOUN
ejpam-3054	261	6	in	in	ADP
ejpam-3054	261	7	banach	banach	NOUN
ejpam-3054	261	8	algebras	algebra	NOUN
ejpam-3054	261	9	.	.	PUNCT
ejpam-3054	262	1	proc	proc	PROPN
ejpam-3054	262	2	.	.	PUNCT
ejpam-3054	263	1	roy	roy	PROPN
ejpam-3054	263	2	.	.	PROPN
ejpam-3054	263	3	irish	irish	PROPN
ejpam-3054	263	4	.	.	PUNCT
ejpam-3054	264	1	acad	acad	PROPN
ejpam-3054	264	2	.	.	PROPN
ejpam-3054	264	3	,	,	PUNCT
ejpam-3054	264	4	91(1):113	91(1):113	NUM
ejpam-3054	264	5	-	-	SYM
ejpam-3054	264	6	127	127	NUM
ejpam-3054	264	7	,	,	PUNCT
ejpam-3054	264	8	1991	1991	NUM
ejpam-3054	264	9	.	.	PUNCT
ejpam-3054	265	1	[	[	X
ejpam-3054	265	2	19	19	NUM
ejpam-3054	265	3	]	]	PUNCT
ejpam-3054	265	4	a.	a.	PROPN
ejpam-3054	265	5	r.	r.	PROPN
ejpam-3054	265	6	sourour	sourour	PROPN
ejpam-3054	265	7	.	.	PUNCT
ejpam-3054	266	1	inversibility	inversibility	NOUN
ejpam-3054	266	2	preserving	preserve	VERB
ejpam-3054	266	3	linear	linear	ADJ
ejpam-3054	266	4	maps	map	NOUN
ejpam-3054	266	5	on	on	ADP
ejpam-3054	266	6	l(x	l(x	PROPN
ejpam-3054	266	7	)	)	PUNCT
ejpam-3054	266	8	.	.	PUNCT
ejpam-3054	267	1	trans	trans	PROPN
ejpam-3054	267	2	.	.	PUNCT
ejpam-3054	268	1	amer	amer	PROPN
ejpam-3054	268	2	.	.	PUNCT
ejpam-3054	268	3	math	math	PROPN
ejpam-3054	268	4	.	.	PUNCT
ejpam-3054	269	1	soc	soc	PROPN
ejpam-3054	269	2	.	.	PUNCT
ejpam-3054	269	3	,	,	PUNCT
ejpam-3054	269	4	348(1):13	348(1):13	PROPN
ejpam-3054	269	5	-	-	SYM
ejpam-3054	269	6	30	30	NUM
ejpam-3054	269	7	,	,	PUNCT
ejpam-3054	269	8	1996	1996	NUM
ejpam-3054	269	9	.	.	PUNCT