id	sid	tid	token	lemma	pos
ejpam-749	1	1	6_749_xie.dvi	6_749_xie.dvi	NUM
ejpam-749	1	2	european	european	PROPN
ejpam-749	1	3	journal	journal	PROPN
ejpam-749	1	4	of	of	ADP
ejpam-749	1	5	pure	pure	ADJ
ejpam-749	1	6	and	and	CCONJ
ejpam-749	1	7	applied	apply	VERB
ejpam-749	1	8	mathematics	mathematic	NOUN
ejpam-749	1	9	vol	vol	NOUN
ejpam-749	1	10	.	.	PUNCT
ejpam-749	2	1	3	3	NUM
ejpam-749	2	2	,	,	PUNCT
ejpam-749	2	3	no	no	INTJ
ejpam-749	2	4	.	.	NOUN
ejpam-749	2	5	4	4	NUM
ejpam-749	2	6	,	,	PUNCT
ejpam-749	2	7	2010	2010	NUM
ejpam-749	2	8	,	,	PUNCT
ejpam-749	2	9	678	678	NUM
ejpam-749	2	10	-	-	SYM
ejpam-749	2	11	685	685	NUM
ejpam-749	2	12	issn	issn	PROPN
ejpam-749	2	13	1307	1307	NUM
ejpam-749	2	14	-	-	SYM
ejpam-749	2	15	5543	5543	NUM
ejpam-749	2	16	–	–	PUNCT
ejpam-749	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-749	2	18	fredholmness	fredholmness	NOUN
ejpam-749	2	19	of	of	ADP
ejpam-749	2	20	combinations	combination	NOUN
ejpam-749	2	21	of	of	ADP
ejpam-749	2	22	two	two	NUM
ejpam-749	2	23	idempotents	idempotent	NOUN
ejpam-749	2	24	tao	tao	PROPN
ejpam-749	2	25	xie∗	xie∗	PROPN
ejpam-749	2	26	,	,	PUNCT
ejpam-749	2	27	kezheng	kezheng	PROPN
ejpam-749	2	28	zuo	zuo	PROPN
ejpam-749	2	29	math	math	PROPN
ejpam-749	2	30	department	department	PROPN
ejpam-749	2	31	,	,	PUNCT
ejpam-749	2	32	hubei	hubei	PROPN
ejpam-749	2	33	normal	normal	ADJ
ejpam-749	2	34	university	university	PROPN
ejpam-749	2	35	,	,	PUNCT
ejpam-749	2	36	hubei	hubei	PROPN
ejpam-749	2	37	,	,	PUNCT
ejpam-749	2	38	huangshi	huangshi	NOUN
ejpam-749	2	39	,	,	PUNCT
ejpam-749	2	40	435002	435002	NUM
ejpam-749	2	41	,	,	PUNCT
ejpam-749	2	42	china	china	PROPN
ejpam-749	2	43	abstract	abstract	NOUN
ejpam-749	2	44	.	.	PUNCT
ejpam-749	3	1	if	if	SCONJ
ejpam-749	3	2	p	p	PROPN
ejpam-749	3	3	and	and	CCONJ
ejpam-749	3	4	q	q	NOUN
ejpam-749	3	5	are	be	AUX
ejpam-749	3	6	two	two	NUM
ejpam-749	3	7	idempotents	idempotent	NOUN
ejpam-749	3	8	on	on	ADP
ejpam-749	3	9	a	a	DET
ejpam-749	3	10	hilbert	hilbert	NOUN
ejpam-749	3	11	space	space	NOUN
ejpam-749	3	12	,	,	PUNCT
ejpam-749	3	13	in	in	ADP
ejpam-749	3	14	this	this	DET
ejpam-749	3	15	paper	paper	NOUN
ejpam-749	3	16	,	,	PUNCT
ejpam-749	3	17	we	we	PRON
ejpam-749	3	18	prove	prove	VERB
ejpam-749	3	19	that	that	SCONJ
ejpam-749	3	20	fredholmness	fredholmness	NOUN
ejpam-749	3	21	of	of	ADP
ejpam-749	3	22	ap	ap	PROPN
ejpam-749	3	23	+	+	PUNCT
ejpam-749	3	24	bq−	bq−	PUNCT
ejpam-749	3	25	cpq	cpq	PROPN
ejpam-749	3	26	is	be	AUX
ejpam-749	3	27	independent	independent	ADJ
ejpam-749	3	28	of	of	ADP
ejpam-749	3	29	the	the	DET
ejpam-749	3	30	choice	choice	NOUN
ejpam-749	3	31	of	of	ADP
ejpam-749	3	32	a	a	DET
ejpam-749	3	33	,	,	PUNCT
ejpam-749	3	34	b	b	NOUN
ejpam-749	3	35	,	,	PUNCT
ejpam-749	3	36	c	c	PROPN
ejpam-749	3	37	with	with	ADP
ejpam-749	3	38	ab	ab	PROPN
ejpam-749	3	39	6=	6=	PROPN
ejpam-749	3	40	0	0	NUM
ejpam-749	3	41	.	.	SYM
ejpam-749	4	1	2000	2000	NUM
ejpam-749	4	2	mathematics	mathematic	NOUN
ejpam-749	4	3	subject	subject	NOUN
ejpam-749	4	4	classifications	classification	NOUN
ejpam-749	4	5	:	:	PUNCT
ejpam-749	4	6	15a03	15a03	NUM
ejpam-749	4	7	,	,	PUNCT
ejpam-749	4	8	15a24	15a24	NUM
ejpam-749	4	9	key	key	ADJ
ejpam-749	4	10	words	word	NOUN
ejpam-749	4	11	and	and	CCONJ
ejpam-749	4	12	phrases	phrase	NOUN
ejpam-749	4	13	:	:	PUNCT
ejpam-749	4	14	idempotent	idempotent	ADJ
ejpam-749	4	15	,	,	PUNCT
ejpam-749	4	16	fredholmness	fredholmness	NOUN
ejpam-749	4	17	,	,	PUNCT
ejpam-749	4	18	combinations	combination	NOUN
ejpam-749	4	19	of	of	ADP
ejpam-749	4	20	idempotents	idempotent	NOUN
ejpam-749	4	21	1	1	NUM
ejpam-749	4	22	.	.	PUNCT
ejpam-749	5	1	introduction	introduction	NOUN
ejpam-749	5	2	idempotents	idempotent	NOUN
ejpam-749	5	3	are	be	AUX
ejpam-749	5	4	important	important	ADJ
ejpam-749	5	5	and	and	CCONJ
ejpam-749	5	6	have	have	VERB
ejpam-749	5	7	wide	wide	ADJ
ejpam-749	5	8	applications	application	NOUN
ejpam-749	5	9	in	in	ADP
ejpam-749	5	10	the	the	DET
ejpam-749	5	11	theory	theory	NOUN
ejpam-749	5	12	of	of	ADP
ejpam-749	5	13	linear	linear	PROPN
ejpam-749	5	14	algebra	algebra	NOUN
ejpam-749	5	15	and	and	CCONJ
ejpam-749	5	16	operator	operator	NOUN
ejpam-749	5	17	theorem	theorem	VERB
ejpam-749	5	18	.	.	PUNCT
ejpam-749	6	1	it	it	PRON
ejpam-749	6	2	is	be	AUX
ejpam-749	6	3	shown	show	VERB
ejpam-749	6	4	in	in	ADP
ejpam-749	6	5	[	[	X
ejpam-749	6	6	17	17	NUM
ejpam-749	6	7	]	]	PUNCT
ejpam-749	6	8	that	that	SCONJ
ejpam-749	6	9	every	every	DET
ejpam-749	6	10	n×	n×	NOUN
ejpam-749	6	11	n	n	NOUN
ejpam-749	6	12	matrix	matrix	NOUN
ejpam-749	6	13	over	over	ADP
ejpam-749	6	14	a	a	DET
ejpam-749	6	15	field	field	NOUN
ejpam-749	6	16	of	of	ADP
ejpam-749	6	17	characteristic	characteristic	ADJ
ejpam-749	6	18	zero	zero	NUM
ejpam-749	6	19	is	be	AUX
ejpam-749	6	20	a	a	DET
ejpam-749	6	21	linear	linear	ADJ
ejpam-749	6	22	combination	combination	NOUN
ejpam-749	6	23	of	of	ADP
ejpam-749	6	24	three	three	NUM
ejpam-749	6	25	idempotents	idempotent	NOUN
ejpam-749	6	26	and	and	CCONJ
ejpam-749	6	27	in	in	ADP
ejpam-749	6	28	[	[	X
ejpam-749	6	29	16	16	NUM
ejpam-749	6	30	]	]	PUNCT
ejpam-749	6	31	that	that	SCONJ
ejpam-749	6	32	every	every	DET
ejpam-749	6	33	bounded	bound	VERB
ejpam-749	6	34	linear	linear	ADJ
ejpam-749	6	35	operator	operator	NOUN
ejpam-749	6	36	on	on	ADP
ejpam-749	6	37	a	a	DET
ejpam-749	6	38	complex	complex	ADJ
ejpam-749	6	39	infinite	infinite	ADJ
ejpam-749	6	40	hilbert	hilbert	NOUN
ejpam-749	6	41	space	space	NOUN
ejpam-749	6	42	is	be	AUX
ejpam-749	6	43	a	a	DET
ejpam-749	6	44	sum	sum	NOUN
ejpam-749	6	45	of	of	ADP
ejpam-749	6	46	at	at	ADV
ejpam-749	6	47	most	most	ADV
ejpam-749	6	48	five	five	NUM
ejpam-749	6	49	idempotents	idempotent	NOUN
ejpam-749	6	50	.	.	PUNCT
ejpam-749	7	1	see	see	VERB
ejpam-749	7	2	also	also	ADV
ejpam-749	7	3	[	[	X
ejpam-749	7	4	5],[18],[19	5],[18],[19	NUM
ejpam-749	7	5	]	]	PUNCT
ejpam-749	7	6	.	.	PUNCT
ejpam-749	8	1	let	let	VERB
ejpam-749	8	2	x	x	PRON
ejpam-749	8	3	be	be	AUX
ejpam-749	8	4	a	a	DET
ejpam-749	8	5	banach	banach	NOUN
ejpam-749	8	6	space	space	NOUN
ejpam-749	8	7	,	,	PUNCT
ejpam-749	8	8	and	and	CCONJ
ejpam-749	8	9	p	p	X
ejpam-749	8	10	,	,	PUNCT
ejpam-749	8	11	q	q	ADJ
ejpam-749	8	12	be	be	AUX
ejpam-749	8	13	two	two	NUM
ejpam-749	8	14	idempotent	idempotent	ADJ
ejpam-749	8	15	operators	operator	NOUN
ejpam-749	8	16	on	on	ADP
ejpam-749	8	17	x	x	X
ejpam-749	8	18	.	.	PUNCT
ejpam-749	9	1	many	many	ADJ
ejpam-749	9	2	researchers	researcher	NOUN
ejpam-749	9	3	(	(	PUNCT
ejpam-749	9	4	see	see	VERB
ejpam-749	9	5	[	[	X
ejpam-749	9	6	1]-[15	1]-[15	NUM
ejpam-749	9	7	]	]	PUNCT
ejpam-749	9	8	and	and	CCONJ
ejpam-749	9	9	the	the	DET
ejpam-749	9	10	references	reference	NOUN
ejpam-749	9	11	within	within	ADV
ejpam-749	9	12	)	)	PUNCT
ejpam-749	9	13	have	have	AUX
ejpam-749	9	14	addressed	address	VERB
ejpam-749	9	15	stability	stability	NOUN
ejpam-749	9	16	properties	property	NOUN
ejpam-749	9	17	of	of	ADP
ejpam-749	9	18	the	the	DET
ejpam-749	9	19	linear	linear	ADJ
ejpam-749	9	20	combination	combination	NOUN
ejpam-749	9	21	ap	ap	PROPN
ejpam-749	10	1	+	+	CCONJ
ejpam-749	10	2	bq	bq	INTJ
ejpam-749	10	3	;	;	PUNCT
ejpam-749	10	4	it	it	PRON
ejpam-749	10	5	has	have	AUX
ejpam-749	10	6	been	be	AUX
ejpam-749	10	7	proved	prove	VERB
ejpam-749	10	8	that	that	SCONJ
ejpam-749	10	9	some	some	DET
ejpam-749	10	10	properties	property	NOUN
ejpam-749	10	11	such	such	ADJ
ejpam-749	10	12	as	as	ADP
ejpam-749	10	13	invertibility	invertibility	NOUN
ejpam-749	10	14	,	,	PUNCT
ejpam-749	10	15	nullity	nullity	NOUN
ejpam-749	10	16	,	,	PUNCT
ejpam-749	10	17	fredholmness	fredholmness	NOUN
ejpam-749	10	18	,	,	PUNCT
ejpam-749	10	19	closeness	closeness	NOUN
ejpam-749	10	20	of	of	ADP
ejpam-749	10	21	the	the	DET
ejpam-749	10	22	range	range	NOUN
ejpam-749	10	23	and	and	CCONJ
ejpam-749	10	24	complementarity	complementarity	NOUN
ejpam-749	10	25	of	of	ADP
ejpam-749	10	26	the	the	DET
ejpam-749	10	27	kernel	kernel	NOUN
ejpam-749	10	28	of	of	ADP
ejpam-749	10	29	linear	linear	PROPN
ejpam-749	10	30	combinations	combination	NOUN
ejpam-749	10	31	of	of	ADP
ejpam-749	10	32	p	p	NOUN
ejpam-749	10	33	and	and	CCONJ
ejpam-749	10	34	q	q	NOUN
ejpam-749	10	35	are	be	AUX
ejpam-749	10	36	independent	independent	ADJ
ejpam-749	10	37	of	of	ADP
ejpam-749	10	38	the	the	DET
ejpam-749	10	39	choice	choice	NOUN
ejpam-749	10	40	of	of	ADP
ejpam-749	10	41	coefficients	coefficient	NOUN
ejpam-749	10	42	a	a	PRON
ejpam-749	10	43	and	and	CCONJ
ejpam-749	10	44	b	b	NOUN
ejpam-749	10	45	,	,	PUNCT
ejpam-749	10	46	provided	provide	VERB
ejpam-749	10	47	ab	ab	PROPN
ejpam-749	10	48	6=	6=	ADP
ejpam-749	10	49	0	0	NUM
ejpam-749	10	50	and	and	CCONJ
ejpam-749	10	51	a+	a+	PRON
ejpam-749	10	52	b	b	PROPN
ejpam-749	10	53	6=	6=	NUM
ejpam-749	10	54	0	0	NUM
ejpam-749	10	55	.	.	PUNCT
ejpam-749	11	1	a	a	DET
ejpam-749	11	2	natural	natural	ADJ
ejpam-749	11	3	question	question	NOUN
ejpam-749	11	4	is	be	AUX
ejpam-749	11	5	whether	whether	SCONJ
ejpam-749	11	6	the	the	DET
ejpam-749	11	7	results	result	NOUN
ejpam-749	11	8	above	above	ADV
ejpam-749	11	9	can	can	AUX
ejpam-749	11	10	be	be	AUX
ejpam-749	11	11	extended	extend	VERB
ejpam-749	11	12	to	to	ADP
ejpam-749	11	13	more	more	ADJ
ejpam-749	11	14	general	general	ADJ
ejpam-749	11	15	situations	situation	NOUN
ejpam-749	11	16	.	.	PUNCT
ejpam-749	12	1	in	in	ADP
ejpam-749	12	2	this	this	DET
ejpam-749	12	3	note	note	NOUN
ejpam-749	12	4	we	we	PRON
ejpam-749	12	5	consider	consider	VERB
ejpam-749	12	6	the	the	DET
ejpam-749	12	7	fredholmness	fredholmness	NOUN
ejpam-749	12	8	of	of	ADP
ejpam-749	12	9	some	some	DET
ejpam-749	12	10	special	special	ADJ
ejpam-749	12	11	combinations	combination	NOUN
ejpam-749	12	12	ap	ap	PROPN
ejpam-749	13	1	+	+	PUNCT
ejpam-749	13	2	bq−	bq−	VERB
ejpam-749	13	3	cqp	cqp	ADJ
ejpam-749	13	4	and	and	CCONJ
ejpam-749	13	5	ap	ap	NOUN
ejpam-749	13	6	+	+	CCONJ
ejpam-749	13	7	bq−	bq−	PUNCT
ejpam-749	13	8	cpq−	cpq−	NOUN
ejpam-749	13	9	dqp	dqp	NOUN
ejpam-749	13	10	when	when	SCONJ
ejpam-749	13	11	p	p	X
ejpam-749	13	12	,	,	PUNCT
ejpam-749	13	13	q	q	X
ejpam-749	13	14	are	be	AUX
ejpam-749	13	15	idempotents	idempotent	NOUN
ejpam-749	13	16	.	.	PUNCT
ejpam-749	14	1	we	we	PRON
ejpam-749	14	2	prove	prove	VERB
ejpam-749	14	3	that	that	SCONJ
ejpam-749	14	4	fredholmness	fredholmness	NOUN
ejpam-749	14	5	and	and	CCONJ
ejpam-749	14	6	index	index	NOUN
ejpam-749	14	7	of	of	ADP
ejpam-749	14	8	any	any	DET
ejpam-749	14	9	combinations	combination	NOUN
ejpam-749	14	10	ap	ap	X
ejpam-749	14	11	+	+	PUNCT
ejpam-749	14	12	bq−	bq−	PUNCT
ejpam-749	14	13	cqp	cqp	ADJ
ejpam-749	14	14	are	be	AUX
ejpam-749	14	15	independent	independent	ADJ
ejpam-749	14	16	of	of	ADP
ejpam-749	14	17	the	the	DET
ejpam-749	14	18	choice	choice	NOUN
ejpam-749	14	19	of	of	ADP
ejpam-749	14	20	a	a	DET
ejpam-749	14	21	,	,	PUNCT
ejpam-749	14	22	b	b	NOUN
ejpam-749	14	23	,	,	PUNCT
ejpam-749	14	24	c	c	PROPN
ejpam-749	14	25	with	with	ADP
ejpam-749	14	26	ab	ab	PROPN
ejpam-749	14	27	6=	6=	PROPN
ejpam-749	14	28	0	0	NUM
ejpam-749	14	29	.	.	PUNCT
ejpam-749	15	1	as	as	ADP
ejpam-749	15	2	an	an	DET
ejpam-749	15	3	application	application	NOUN
ejpam-749	15	4	,	,	PUNCT
ejpam-749	15	5	we	we	PRON
ejpam-749	15	6	obtain	obtain	VERB
ejpam-749	15	7	that	that	SCONJ
ejpam-749	15	8	the	the	DET
ejpam-749	15	9	invertibility	invertibility	NOUN
ejpam-749	15	10	of	of	ADP
ejpam-749	15	11	combinations	combination	NOUN
ejpam-749	15	12	ap	ap	PROPN
ejpam-749	15	13	+	+	PUNCT
ejpam-749	15	14	bq−	bq−	NUM
ejpam-749	15	15	cqp	cqp	ADJ
ejpam-749	15	16	are	be	AUX
ejpam-749	15	17	equivalent	equivalent	ADJ
ejpam-749	15	18	to	to	ADP
ejpam-749	15	19	the	the	DET
ejpam-749	15	20	invertibility	invertibility	NOUN
ejpam-749	15	21	of	of	ADP
ejpam-749	15	22	p	p	NOUN
ejpam-749	15	23	+	+	NOUN
ejpam-749	15	24	q	q	NOUN
ejpam-749	15	25	for	for	ADP
ejpam-749	15	26	all	all	DET
ejpam-749	15	27	a	a	DET
ejpam-749	15	28	,	,	PUNCT
ejpam-749	15	29	b	b	NOUN
ejpam-749	15	30	,	,	PUNCT
ejpam-749	15	31	c	c	PROPN
ejpam-749	15	32	∈	∈	PROPN
ejpam-749	15	33	c	c	PROPN
ejpam-749	15	34	with	with	ADP
ejpam-749	15	35	ab	ab	PROPN
ejpam-749	15	36	6=	6=	PROPN
ejpam-749	15	37	0	0	NUM
ejpam-749	15	38	,	,	PUNCT
ejpam-749	15	39	which	which	PRON
ejpam-749	15	40	generalizes	generalize	VERB
ejpam-749	15	41	the	the	DET
ejpam-749	15	42	result	result	NOUN
ejpam-749	15	43	of	of	ADP
ejpam-749	15	44	[	[	X
ejpam-749	15	45	4	4	NUM
ejpam-749	15	46	]	]	PUNCT
ejpam-749	15	47	.	.	PUNCT
ejpam-749	16	1	moreover	moreover	ADV
ejpam-749	16	2	,	,	PUNCT
ejpam-749	16	3	counter	counter	ADJ
ejpam-749	16	4	examples	example	NOUN
ejpam-749	16	5	are	be	AUX
ejpam-749	16	6	shown	show	VERB
ejpam-749	16	7	that	that	SCONJ
ejpam-749	16	8	the	the	DET
ejpam-749	16	9	combination	combination	NOUN
ejpam-749	16	10	ap	ap	NOUN
ejpam-749	17	1	+	+	CCONJ
ejpam-749	17	2	bq	bq	PROPN
ejpam-749	17	3	−	−	PROPN
ejpam-749	17	4	cpq	cpq	PROPN
ejpam-749	17	5	−	−	PROPN
ejpam-749	17	6	dqp	dqp	PROPN
ejpam-749	17	7	fails	fail	VERB
ejpam-749	17	8	to	to	PART
ejpam-749	17	9	retain	retain	VERB
ejpam-749	17	10	any	any	DET
ejpam-749	17	11	such	such	ADJ
ejpam-749	17	12	properties	property	NOUN
ejpam-749	17	13	.	.	PUNCT
ejpam-749	18	1	∗corresponding	∗corresponde	VERB
ejpam-749	18	2	author	author	NOUN
ejpam-749	18	3	.	.	PUNCT
ejpam-749	19	1	email	email	NOUN
ejpam-749	19	2	addresses	address	NOUN
ejpam-749	19	3	:	:	PUNCT
ejpam-749	19	4	xietao_1294	xietao_1294	PROPN
ejpam-749	19	5	�	�	PROPN
ejpam-749	19	6	163	163	NUM
ejpam-749	19	7	.	.	PUNCT
ejpam-749	20	1	om	om	PROPN
ejpam-749	20	2	(	(	PUNCT
ejpam-749	20	3	t.	t.	PROPN
ejpam-749	20	4	xie	xie	PROPN
ejpam-749	20	5	)	)	PUNCT
ejpam-749	20	6	,	,	PUNCT
ejpam-749	20	7	xiangzuo28	xiangzuo28	PROPN
ejpam-749	20	8	�	�	PROPN
ejpam-749	20	9	yahoo	yahoo	PROPN
ejpam-749	20	10	.	.	PUNCT
ejpam-749	21	1	n	n	PROPN
ejpam-749	21	2	(	(	PUNCT
ejpam-749	21	3	k.	k.	NOUN
ejpam-749	21	4	zuo	zuo	PROPN
ejpam-749	21	5	)	)	PUNCT
ejpam-749	21	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-749	22	1	678	678	NUM
ejpam-749	22	2	c	c	X
ejpam-749	22	3	©	©	PROPN
ejpam-749	22	4	2010	2010	NUM
ejpam-749	22	5	ejpam	ejpam	NOUN
ejpam-749	22	6	all	all	DET
ejpam-749	22	7	rights	right	NOUN
ejpam-749	22	8	reserved	reserve	VERB
ejpam-749	22	9	.	.	PUNCT
ejpam-749	23	1	t.	t.	PROPN
ejpam-749	23	2	xie	xie	PROPN
ejpam-749	23	3	,	,	PUNCT
ejpam-749	23	4	k.	k.	PROPN
ejpam-749	23	5	zuo	zuo	PROPN
ejpam-749	23	6	/	/	SYM
ejpam-749	23	7	eur	eur	PROPN
ejpam-749	23	8	.	.	PUNCT
ejpam-749	24	1	j.	j.	PROPN
ejpam-749	24	2	pure	pure	PROPN
ejpam-749	24	3	appl	appl	PROPN
ejpam-749	24	4	.	.	PROPN
ejpam-749	24	5	math	math	PROPN
ejpam-749	24	6	,	,	PUNCT
ejpam-749	24	7	3	3	NUM
ejpam-749	24	8	(	(	PUNCT
ejpam-749	24	9	2010	2010	NUM
ejpam-749	24	10	)	)	PUNCT
ejpam-749	24	11	,	,	PUNCT
ejpam-749	24	12	678	678	NUM
ejpam-749	24	13	-	-	SYM
ejpam-749	24	14	685	685	NUM
ejpam-749	24	15	679	679	NUM
ejpam-749	24	16	2	2	NUM
ejpam-749	24	17	.	.	PUNCT
ejpam-749	24	18	preliminaries	preliminary	NOUN
ejpam-749	24	19	leth	leth	PROPN
ejpam-749	24	20	be	be	AUX
ejpam-749	24	21	a	a	DET
ejpam-749	24	22	hilbert	hilbert	NOUN
ejpam-749	24	23	space	space	NOUN
ejpam-749	24	24	,	,	PUNCT
ejpam-749	24	25	and	and	CCONJ
ejpam-749	24	26	let	let	VERB
ejpam-749	24	27	all	all	DET
ejpam-749	24	28	bounded	bound	VERB
ejpam-749	24	29	linear	linear	PROPN
ejpam-749	24	30	operators	operator	NOUN
ejpam-749	24	31	onh	onh	PROPN
ejpam-749	24	32	be	be	AUX
ejpam-749	24	33	denoted	denote	VERB
ejpam-749	24	34	byb(h	byb(h	PROPN
ejpam-749	24	35	)	)	PUNCT
ejpam-749	24	36	.	.	PUNCT
ejpam-749	25	1	an	an	DET
ejpam-749	25	2	operator	operator	NOUN
ejpam-749	25	3	p	p	NOUN
ejpam-749	25	4	∈	∈	PROPN
ejpam-749	25	5	b(h	b(h	PROPN
ejpam-749	25	6	)	)	PUNCT
ejpam-749	25	7	is	be	AUX
ejpam-749	25	8	said	say	VERB
ejpam-749	25	9	to	to	PART
ejpam-749	25	10	be	be	AUX
ejpam-749	25	11	idempotent	idempotent	ADJ
ejpam-749	25	12	if	if	SCONJ
ejpam-749	25	13	p2	p2	PROPN
ejpam-749	25	14	=	=	PUNCT
ejpam-749	26	1	p.	p.	NOUN
ejpam-749	26	2	the	the	DET
ejpam-749	26	3	set	set	NOUN
ejpam-749	26	4	p	p	NOUN
ejpam-749	26	5	of	of	ADP
ejpam-749	26	6	all	all	DET
ejpam-749	26	7	idempotents	idempotent	NOUN
ejpam-749	26	8	in	in	ADP
ejpam-749	26	9	b(h	b(h	PROPN
ejpam-749	26	10	)	)	PUNCT
ejpam-749	26	11	is	be	AUX
ejpam-749	26	12	invariant	invariant	ADJ
ejpam-749	26	13	under	under	ADP
ejpam-749	26	14	similarity	similarity	NOUN
ejpam-749	26	15	;	;	PUNCT
ejpam-749	26	16	that	that	PRON
ejpam-749	26	17	is	is	ADV
ejpam-749	26	18	,	,	PUNCT
ejpam-749	26	19	is	be	AUX
ejpam-749	26	20	p	p	PROPN
ejpam-749	26	21	∈	∈	PROPN
ejpam-749	26	22	p	p	NOUN
ejpam-749	26	23	and	and	CCONJ
ejpam-749	26	24	s	s	NOUN
ejpam-749	26	25	∈	∈	PROPN
ejpam-749	26	26	b(h	b(h	PROPN
ejpam-749	26	27	)	)	PUNCT
ejpam-749	26	28	is	be	AUX
ejpam-749	26	29	an	an	DET
ejpam-749	26	30	invertible	invertible	ADJ
ejpam-749	26	31	operator	operator	NOUN
ejpam-749	26	32	,	,	PUNCT
ejpam-749	26	33	then	then	ADV
ejpam-749	26	34	s−1ps	s−1ps	NOUN
ejpam-749	26	35	is	be	AUX
ejpam-749	26	36	still	still	ADV
ejpam-749	26	37	an	an	DET
ejpam-749	26	38	idempotent	idempotent	NOUN
ejpam-749	26	39	since	since	SCONJ
ejpam-749	26	40	(	(	PUNCT
ejpam-749	26	41	s−1ps)2	s−1ps)2	NOUN
ejpam-749	26	42	=	=	SYM
ejpam-749	26	43	s−1pss−1ps	s−1pss−1ps	ADJ
ejpam-749	26	44	=	=	PUNCT
ejpam-749	26	45	s−1p2s	s−1p2	NOUN
ejpam-749	26	46	=	=	SYM
ejpam-749	26	47	s−1ps	s−1ps	NOUN
ejpam-749	26	48	.	.	PUNCT
ejpam-749	27	1	an	an	DET
ejpam-749	27	2	idempotent	idempotent	NOUN
ejpam-749	27	3	p	p	NOUN
ejpam-749	27	4	is	be	AUX
ejpam-749	27	5	called	call	VERB
ejpam-749	27	6	an	an	DET
ejpam-749	27	7	orthogonal	orthogonal	ADJ
ejpam-749	27	8	projection	projection	NOUN
ejpam-749	27	9	if	if	SCONJ
ejpam-749	27	10	p2	p2	PROPN
ejpam-749	27	11	=	=	SYM
ejpam-749	27	12	p	p	X
ejpam-749	27	13	=	=	SYM
ejpam-749	27	14	p∗	p∗	PROPN
ejpam-749	27	15	,	,	PUNCT
ejpam-749	27	16	where	where	SCONJ
ejpam-749	27	17	p∗	p∗	PROPN
ejpam-749	27	18	is	be	AUX
ejpam-749	27	19	the	the	DET
ejpam-749	27	20	adjoint	adjoint	NOUN
ejpam-749	27	21	of	of	ADP
ejpam-749	27	22	p.	p.	PROPN
ejpam-749	27	23	moreover	moreover	ADV
ejpam-749	27	24	,	,	PUNCT
ejpam-749	27	25	for	for	ADP
ejpam-749	27	26	an	an	DET
ejpam-749	27	27	idempotent	idempotent	NOUN
ejpam-749	27	28	p	p	X
ejpam-749	27	29	∈	∈	PROPN
ejpam-749	27	30	p	p	NOUN
ejpam-749	27	31	,	,	PUNCT
ejpam-749	27	32	there	there	PRON
ejpam-749	27	33	exists	exist	VERB
ejpam-749	27	34	an	an	DET
ejpam-749	27	35	invertible	invertible	ADJ
ejpam-749	27	36	operator	operator	NOUN
ejpam-749	27	37	u	u	PROPN
ejpam-749	27	38	∈	∈	PROPN
ejpam-749	27	39	b(h	b(h	PROPN
ejpam-749	27	40	)	)	PUNCT
ejpam-749	27	41	such	such	ADJ
ejpam-749	27	42	that	that	SCONJ
ejpam-749	27	43	u−1pu	u−1pu	PROPN
ejpam-749	27	44	is	be	AUX
ejpam-749	27	45	an	an	DET
ejpam-749	27	46	orthogonal	orthogonal	ADJ
ejpam-749	27	47	projection	projection	NOUN
ejpam-749	27	48	.	.	PUNCT
ejpam-749	28	1	in	in	ADP
ejpam-749	28	2	fact	fact	NOUN
ejpam-749	28	3	,	,	PUNCT
ejpam-749	28	4	if	if	SCONJ
ejpam-749	28	5	p	p	PROPN
ejpam-749	28	6	∈	∈	PROPN
ejpam-749	28	7	p	p	X
ejpam-749	28	8	,	,	PUNCT
ejpam-749	28	9	then	then	ADV
ejpam-749	28	10	p	p	NOUN
ejpam-749	28	11	can	can	AUX
ejpam-749	28	12	be	be	AUX
ejpam-749	28	13	written	write	VERB
ejpam-749	28	14	in	in	ADP
ejpam-749	28	15	the	the	DET
ejpam-749	28	16	form	form	NOUN
ejpam-749	28	17	of	of	ADP
ejpam-749	28	18	p	p	NOUN
ejpam-749	28	19	=	=	PUNCT
ejpam-749	28	20	�	�	PROPN
ejpam-749	28	21	i	i	PRON
ejpam-749	28	22	p1	p1	VERB
ejpam-749	28	23	0	0	NUM
ejpam-749	28	24	0	0	NUM
ejpam-749	28	25	�	�	PROPN
ejpam-749	28	26	with	with	ADP
ejpam-749	28	27	respect	respect	NOUN
ejpam-749	28	28	to	to	ADP
ejpam-749	28	29	the	the	DET
ejpam-749	28	30	space	space	NOUN
ejpam-749	28	31	decompositionh	decompositionh	NOUN
ejpam-749	29	1	=	=	NOUN
ejpam-749	29	2	r(p)⊕r(p)⊥	r(p)⊕r(p)⊥	ADJ
ejpam-749	29	3	,	,	PUNCT
ejpam-749	29	4	wherer(m	wherer(m	NOUN
ejpam-749	29	5	)	)	PUNCT
ejpam-749	29	6	denotes	denote	VERB
ejpam-749	29	7	the	the	DET
ejpam-749	29	8	range	range	NOUN
ejpam-749	29	9	of	of	ADP
ejpam-749	29	10	the	the	DET
ejpam-749	29	11	operator	operator	NOUN
ejpam-749	29	12	m	m	VERB
ejpam-749	29	13	.	.	PUNCT
ejpam-749	30	1	in	in	ADP
ejpam-749	30	2	this	this	DET
ejpam-749	30	3	case	case	NOUN
ejpam-749	30	4	,	,	PUNCT
ejpam-749	30	5	we	we	PRON
ejpam-749	30	6	have	have	VERB
ejpam-749	30	7	�	�	PROPN
ejpam-749	30	8	i	i	PRON
ejpam-749	30	9	p1	p1	PROPN
ejpam-749	30	10	0	0	NUM
ejpam-749	31	1	i	i	PRON
ejpam-749	31	2	�	�	VERB
ejpam-749	31	3	�	�	PROPN
ejpam-749	31	4	i	i	PRON
ejpam-749	31	5	p1	p1	VERB
ejpam-749	31	6	0	0	NUM
ejpam-749	31	7	0	0	NUM
ejpam-749	31	8	�	�	PROPN
ejpam-749	31	9	�	�	PROPN
ejpam-749	31	10	i	i	PRON
ejpam-749	31	11	−p1	−p1	PRON
ejpam-749	31	12	0	0	PUNCT
ejpam-749	32	1	i	i	PRON
ejpam-749	32	2	�	�	PROPN
ejpam-749	32	3	=	=	SYM
ejpam-749	32	4	�	�	PROPN
ejpam-749	32	5	i	i	NOUN
ejpam-749	32	6	0	0	NUM
ejpam-749	32	7	0	0	SYM
ejpam-749	32	8	0	0	NUM
ejpam-749	32	9	�	�	PROPN
ejpam-749	32	10	,	,	PUNCT
ejpam-749	32	11	where	where	SCONJ
ejpam-749	32	12	ep	ep	PROPN
ejpam-749	32	13	=	=	PROPN
ejpam-749	32	14	�	�	PROPN
ejpam-749	32	15	i	i	PRON
ejpam-749	32	16	−p1	−p1	PRON
ejpam-749	32	17	0	0	PUNCT
ejpam-749	33	1	i	i	PRON
ejpam-749	33	2	�	�	PROPN
ejpam-749	33	3	is	be	AUX
ejpam-749	33	4	invertible	invertible	ADJ
ejpam-749	33	5	and	and	CCONJ
ejpam-749	33	6	ep−1	ep−1	PROPN
ejpam-749	33	7	=	=	SYM
ejpam-749	33	8	�	�	PROPN
ejpam-749	34	1	i	i	PRON
ejpam-749	34	2	p1	p1	VERB
ejpam-749	34	3	0	0	NUM
ejpam-749	35	1	i	i	PRON
ejpam-749	35	2	�	�	PROPN
ejpam-749	35	3	.	.	PUNCT
ejpam-749	36	1	an	an	DET
ejpam-749	36	2	operator	operator	NOUN
ejpam-749	36	3	a	a	DET
ejpam-749	36	4	∈	∈	PROPN
ejpam-749	36	5	b(h	b(h	PROPN
ejpam-749	36	6	)	)	PUNCT
ejpam-749	36	7	is	be	AUX
ejpam-749	36	8	said	say	VERB
ejpam-749	36	9	to	to	PART
ejpam-749	36	10	be	be	AUX
ejpam-749	36	11	positive	positive	ADJ
ejpam-749	36	12	if	if	SCONJ
ejpam-749	36	13	(	(	PUNCT
ejpam-749	36	14	ax	ax	INTJ
ejpam-749	36	15	,	,	PUNCT
ejpam-749	36	16	x	x	X
ejpam-749	36	17	)	)	PUNCT
ejpam-749	36	18	≥	≥	X
ejpam-749	36	19	0	0	NUM
ejpam-749	36	20	for	for	ADP
ejpam-749	36	21	all	all	DET
ejpam-749	36	22	x	x	SYM
ejpam-749	36	23	∈	∈	PROPN
ejpam-749	36	24	h	h	NOUN
ejpam-749	36	25	.	.	PUNCT
ejpam-749	37	1	if	if	SCONJ
ejpam-749	37	2	a	a	PRON
ejpam-749	37	3	is	be	AUX
ejpam-749	37	4	positive	positive	ADJ
ejpam-749	37	5	,	,	PUNCT
ejpam-749	37	6	then	then	ADV
ejpam-749	37	7	a	a	DET
ejpam-749	37	8	1	1	NUM
ejpam-749	37	9	2	2	NUM
ejpam-749	37	10	denotes	denote	NOUN
ejpam-749	37	11	the	the	DET
ejpam-749	37	12	positive	positive	ADJ
ejpam-749	37	13	square	square	ADJ
ejpam-749	37	14	root	root	NOUN
ejpam-749	37	15	of	of	ADP
ejpam-749	37	16	a.	a.	NOUN
ejpam-749	37	17	an	an	DET
ejpam-749	37	18	operator	operator	NOUN
ejpam-749	37	19	t	t	NOUN
ejpam-749	37	20	is	be	AUX
ejpam-749	37	21	fredholm	fredholm	NOUN
ejpam-749	37	22	if	if	SCONJ
ejpam-749	37	23	the	the	DET
ejpam-749	37	24	nullities	nullity	NOUN
ejpam-749	37	25	of	of	ADP
ejpam-749	37	26	t	t	NOUN
ejpam-749	37	27	denoted	denote	VERB
ejpam-749	37	28	by	by	ADP
ejpam-749	37	29	nul(t	nul(t	PROPN
ejpam-749	37	30	)	)	PUNCT
ejpam-749	37	31	and	and	CCONJ
ejpam-749	37	32	t	t	PROPN
ejpam-749	37	33	∗	∗	NOUN
ejpam-749	37	34	are	be	AUX
ejpam-749	37	35	finite	finite	ADJ
ejpam-749	37	36	and	and	CCONJ
ejpam-749	37	37	the	the	DET
ejpam-749	37	38	range	range	NOUN
ejpam-749	37	39	of	of	ADP
ejpam-749	37	40	t	t	PROPN
ejpam-749	37	41	is	be	AUX
ejpam-749	37	42	closed	close	VERB
ejpam-749	37	43	.	.	PUNCT
ejpam-749	38	1	for	for	ADP
ejpam-749	38	2	a	a	DET
ejpam-749	38	3	fredholm	fredholm	NOUN
ejpam-749	38	4	operator	operator	NOUN
ejpam-749	38	5	t	t	NOUN
ejpam-749	38	6	,	,	PUNCT
ejpam-749	38	7	its	its	PRON
ejpam-749	38	8	index	index	NOUN
ejpam-749	38	9	,	,	PUNCT
ejpam-749	38	10	indt	indt	NOUN
ejpam-749	38	11	,	,	PUNCT
ejpam-749	38	12	is	be	AUX
ejpam-749	38	13	by	by	ADP
ejpam-749	38	14	definition	definition	NOUN
ejpam-749	38	15	nul(t	nul(t	PROPN
ejpam-749	38	16	)	)	PUNCT
ejpam-749	38	17	-nul(t	-nul(t	PUNCT
ejpam-749	38	18	∗	∗	NOUN
ejpam-749	38	19	)	)	PUNCT
ejpam-749	38	20	.	.	PUNCT
ejpam-749	39	1	it	it	PRON
ejpam-749	39	2	is	be	AUX
ejpam-749	39	3	know	know	VERB
ejpam-749	39	4	that	that	SCONJ
ejpam-749	39	5	the	the	DET
ejpam-749	39	6	fredholmness	fredholmness	NOUN
ejpam-749	39	7	of	of	ADP
ejpam-749	39	8	t	t	PROPN
ejpam-749	39	9	is	be	AUX
ejpam-749	39	10	preserved	preserve	VERB
ejpam-749	39	11	under	under	ADP
ejpam-749	39	12	compact	compact	ADJ
ejpam-749	39	13	perturbations	perturbation	NOUN
ejpam-749	39	14	and	and	CCONJ
ejpam-749	39	15	is	be	AUX
ejpam-749	39	16	equivalent	equivalent	ADJ
ejpam-749	39	17	to	to	ADP
ejpam-749	39	18	the	the	DET
ejpam-749	39	19	existence	existence	NOUN
ejpam-749	39	20	of	of	ADP
ejpam-749	39	21	an	an	DET
ejpam-749	39	22	operator	operator	NOUN
ejpam-749	39	23	t	t	NOUN
ejpam-749	39	24	′	′	NOUN
ejpam-749	39	25	with	with	ADP
ejpam-749	39	26	t	t	PROPN
ejpam-749	39	27	t	t	NOUN
ejpam-749	40	1	′	′	NUM
ejpam-749	40	2	−	−	PROPN
ejpam-749	41	1	i	i	PRON
ejpam-749	41	2	and	and	CCONJ
ejpam-749	41	3	t	t	PROPN
ejpam-749	41	4	′t	′t	NOUN
ejpam-749	41	5	−	−	PROPN
ejpam-749	42	1	i	i	PRON
ejpam-749	42	2	being	be	AUX
ejpam-749	42	3	compact	compact	ADJ
ejpam-749	42	4	.	.	PUNCT
ejpam-749	43	1	for	for	ADP
ejpam-749	43	2	details	detail	NOUN
ejpam-749	43	3	of	of	ADP
ejpam-749	43	4	fredholmness	fredholmness	NOUN
ejpam-749	43	5	,	,	PUNCT
ejpam-749	43	6	see[3	see[3	ADV
ejpam-749	43	7	]	]	PUNCT
ejpam-749	43	8	,	,	PUNCT
ejpam-749	43	9	chapter	chapter	NOUN
ejpam-749	43	10	xi	xi	PROPN
ejpam-749	43	11	.	.	PUNCT
ejpam-749	44	1	for	for	ADP
ejpam-749	44	2	the	the	DET
ejpam-749	44	3	proof	proof	NOUN
ejpam-749	44	4	of	of	ADP
ejpam-749	44	5	the	the	DET
ejpam-749	44	6	main	main	ADJ
ejpam-749	44	7	theorem	theorem	NOUN
ejpam-749	44	8	we	we	PRON
ejpam-749	44	9	need	need	VERB
ejpam-749	44	10	the	the	DET
ejpam-749	44	11	following	follow	VERB
ejpam-749	44	12	two	two	NUM
ejpam-749	44	13	lemmas	lemma	NOUN
ejpam-749	44	14	which	which	PRON
ejpam-749	44	15	are	be	AUX
ejpam-749	44	16	well	well	ADV
ejpam-749	44	17	known	know	VERB
ejpam-749	44	18	,	,	PUNCT
ejpam-749	44	19	so	so	CCONJ
ejpam-749	44	20	the	the	DET
ejpam-749	44	21	proofs	proof	NOUN
ejpam-749	44	22	are	be	AUX
ejpam-749	44	23	omitted	omit	VERB
ejpam-749	44	24	.	.	PUNCT
ejpam-749	45	1	lemma	lemma	PROPN
ejpam-749	45	2	1	1	NUM
ejpam-749	45	3	(	(	PUNCT
ejpam-749	45	4	[	[	X
ejpam-749	45	5	3	3	NUM
ejpam-749	45	6	]	]	PUNCT
ejpam-749	45	7	)	)	PUNCT
ejpam-749	45	8	.	.	PUNCT
ejpam-749	46	1	let	let	VERB
ejpam-749	46	2	a=	a=	PROPN
ejpam-749	46	3	�	�	PROPN
ejpam-749	46	4	a11	a11	PROPN
ejpam-749	46	5	a12	a12	PROPN
ejpam-749	46	6	a21	a21	PROPN
ejpam-749	46	7	a22	a22	PROPN
ejpam-749	46	8	�	�	PROPN
ejpam-749	46	9	be	be	AUX
ejpam-749	46	10	a	a	DET
ejpam-749	46	11	bounded	bounded	ADJ
ejpam-749	46	12	linear	linear	ADJ
ejpam-749	46	13	operator	operator	NOUN
ejpam-749	46	14	on	on	ADP
ejpam-749	46	15	h	h	PROPN
ejpam-749	46	16	⊕k	⊕k	PROPN
ejpam-749	46	17	.	.	PUNCT
ejpam-749	47	1	then	then	ADV
ejpam-749	47	2	a	a	PRON
ejpam-749	47	3	is	be	AUX
ejpam-749	47	4	a	a	DET
ejpam-749	47	5	positive	positive	ADJ
ejpam-749	47	6	operator	operator	NOUN
ejpam-749	47	7	if	if	SCONJ
ejpam-749	48	1	and	and	CCONJ
ejpam-749	48	2	only	only	ADV
ejpam-749	48	3	if	if	SCONJ
ejpam-749	48	4	a11	a11	PROPN
ejpam-749	48	5	≥	≥	PROPN
ejpam-749	48	6	0	0	NUM
ejpam-749	48	7	,	,	PUNCT
ejpam-749	48	8	a22	a22	PROPN
ejpam-749	48	9	≥	≥	PROPN
ejpam-749	48	10	0	0	NUM
ejpam-749	48	11	,	,	PUNCT
ejpam-749	48	12	a12	a12	NOUN
ejpam-749	48	13	=	=	SYM
ejpam-749	48	14	a∗21	a∗21	PROPN
ejpam-749	48	15	and	and	CCONJ
ejpam-749	48	16	there	there	ADV
ejpam-749	48	17	exists	exist	VERB
ejpam-749	48	18	a	a	DET
ejpam-749	48	19	contraction	contraction	NOUN
ejpam-749	48	20	d	d	NOUN
ejpam-749	48	21	from	from	ADP
ejpam-749	48	22	k	k	PROPN
ejpam-749	48	23	intoh	intoh	ADJ
ejpam-749	48	24	such	such	ADJ
ejpam-749	48	25	that	that	SCONJ
ejpam-749	48	26	a=	a=	PROPN
ejpam-749	48	27			NOUN
ejpam-749	48	28			ADJ
ejpam-749	48	29	a11	a11	PROPN
ejpam-749	48	30	a	a	DET
ejpam-749	48	31	1	1	NUM
ejpam-749	48	32	2	2	NUM
ejpam-749	48	33	11da	11da	NOUN
ejpam-749	48	34	1	1	NUM
ejpam-749	48	35	2	2	NUM
ejpam-749	48	36	22	22	NUM
ejpam-749	48	37	a	a	DET
ejpam-749	48	38	1	1	NUM
ejpam-749	48	39	2	2	NUM
ejpam-749	48	40	22d∗a	22d∗a	NUM
ejpam-749	48	41	1	1	NUM
ejpam-749	48	42	2	2	NUM
ejpam-749	48	43	11	11	NUM
ejpam-749	48	44	a22	a22	PROPN
ejpam-749	48	45			PROPN
ejpam-749	49	1			PROPN
ejpam-749	49	2	.	.	PUNCT
ejpam-749	50	1	lemma	lemma	PROPN
ejpam-749	50	2	2	2	NUM
ejpam-749	50	3	(	(	PUNCT
ejpam-749	50	4	[	[	X
ejpam-749	50	5	3	3	NUM
ejpam-749	50	6	]	]	PUNCT
ejpam-749	50	7	)	)	PUNCT
ejpam-749	50	8	.	.	PUNCT
ejpam-749	51	1	let	let	VERB
ejpam-749	51	2	t	t	PROPN
ejpam-749	51	3	=	=	SYM
ejpam-749	51	4	�	�	PROPN
ejpam-749	51	5	a	a	DET
ejpam-749	51	6	b	b	PROPN
ejpam-749	51	7	c	c	NOUN
ejpam-749	51	8	d	d	X
ejpam-749	51	9	�	�	PROPN
ejpam-749	51	10	be	be	AUX
ejpam-749	51	11	an	an	DET
ejpam-749	51	12	operator	operator	NOUN
ejpam-749	51	13	on	on	ADP
ejpam-749	51	14	h	h	PROPN
ejpam-749	51	15	⊕k	⊕k	PROPN
ejpam-749	51	16	,	,	PUNCT
ejpam-749	51	17	where	where	SCONJ
ejpam-749	51	18	a	a	PRON
ejpam-749	51	19	is	be	AUX
ejpam-749	51	20	fredholm	fredholm	NOUN
ejpam-749	51	21	with	with	ADP
ejpam-749	51	22	a′	a′	PROPN
ejpam-749	51	23	act	act	PROPN
ejpam-749	51	24	onh	onh	PROPN
ejpam-749	51	25	satisfying	satisfy	VERB
ejpam-749	52	1	aa′	aa′	ADV
ejpam-749	53	1	=	=	PUNCT
ejpam-749	53	2	i	i	PRON
ejpam-749	53	3	+	+	CCONJ
ejpam-749	53	4	k1	k1	PROPN
ejpam-749	53	5	and	and	CCONJ
ejpam-749	53	6	a′a=	a′a=	VERB
ejpam-749	53	7	i	i	PRON
ejpam-749	53	8	+	+	CCONJ
ejpam-749	53	9	k2	k2	NOUN
ejpam-749	53	10	for	for	ADP
ejpam-749	53	11	some	some	DET
ejpam-749	53	12	compact	compact	ADJ
ejpam-749	53	13	operators	operator	NOUN
ejpam-749	53	14	k1	k1	NOUN
ejpam-749	53	15	and	and	CCONJ
ejpam-749	53	16	k2	k2	PROPN
ejpam-749	53	17	.	.	PUNCT
ejpam-749	54	1	then	then	ADV
ejpam-749	54	2	t	t	PROPN
ejpam-749	54	3	is	be	AUX
ejpam-749	54	4	fredholm	fredholm	NOUN
ejpam-749	54	5	if	if	SCONJ
ejpam-749	54	6	and	and	CCONJ
ejpam-749	54	7	only	only	ADV
ejpam-749	54	8	if	if	SCONJ
ejpam-749	54	9	d−	d−	PROPN
ejpam-749	54	10	ca′b	ca′b	NOUN
ejpam-749	54	11	is	be	AUX
ejpam-749	54	12	.	.	PUNCT
ejpam-749	55	1	in	in	ADP
ejpam-749	55	2	this	this	DET
ejpam-749	55	3	case	case	NOUN
ejpam-749	55	4	,	,	PUNCT
ejpam-749	55	5	indt	indt	NOUN
ejpam-749	55	6	=	=	NOUN
ejpam-749	55	7	inda+	inda+	X
ejpam-749	55	8	ind(d−	ind(d−	X
ejpam-749	55	9	ca′b	ca′b	PROPN
ejpam-749	55	10	)	)	PUNCT
ejpam-749	55	11	.	.	PUNCT
ejpam-749	56	1	t.	t.	PROPN
ejpam-749	56	2	xie	xie	PROPN
ejpam-749	56	3	,	,	PUNCT
ejpam-749	56	4	k.	k.	PROPN
ejpam-749	56	5	zuo	zuo	PROPN
ejpam-749	56	6	/	/	SYM
ejpam-749	56	7	eur	eur	PROPN
ejpam-749	56	8	.	.	PUNCT
ejpam-749	57	1	j.	j.	PROPN
ejpam-749	57	2	pure	pure	PROPN
ejpam-749	57	3	appl	appl	PROPN
ejpam-749	57	4	.	.	PROPN
ejpam-749	57	5	math	math	PROPN
ejpam-749	57	6	,	,	PUNCT
ejpam-749	57	7	3	3	NUM
ejpam-749	57	8	(	(	PUNCT
ejpam-749	57	9	2010	2010	NUM
ejpam-749	57	10	)	)	PUNCT
ejpam-749	57	11	,	,	PUNCT
ejpam-749	57	12	678	678	NUM
ejpam-749	57	13	-	-	SYM
ejpam-749	57	14	685	685	NUM
ejpam-749	57	15	680	680	NUM
ejpam-749	57	16	3	3	NUM
ejpam-749	57	17	.	.	PUNCT
ejpam-749	57	18	main	main	ADJ
ejpam-749	57	19	results	result	NOUN
ejpam-749	57	20	theorem	theorem	VERB
ejpam-749	57	21	1	1	NUM
ejpam-749	57	22	.	.	PUNCT
ejpam-749	58	1	let	let	VERB
ejpam-749	58	2	p	p	NOUN
ejpam-749	58	3	and	and	CCONJ
ejpam-749	58	4	q	q	PROPN
ejpam-749	58	5	inb(h	inb(h	PROPN
ejpam-749	58	6	)	)	PUNCT
ejpam-749	58	7	be	be	AUX
ejpam-749	58	8	two	two	NUM
ejpam-749	58	9	idempotents	idempotent	NOUN
ejpam-749	58	10	,	,	PUNCT
ejpam-749	59	1	then	then	ADV
ejpam-749	59	2	the	the	DET
ejpam-749	59	3	fredholmness	fredholmness	NOUN
ejpam-749	59	4	of	of	ADP
ejpam-749	59	5	ap+	ap+	PROPN
ejpam-749	59	6	bq−cpq	bq−cpq	PROPN
ejpam-749	59	7	is	be	AUX
ejpam-749	59	8	independent	independent	ADJ
ejpam-749	59	9	of	of	ADP
ejpam-749	59	10	the	the	DET
ejpam-749	59	11	choice	choice	NOUN
ejpam-749	59	12	of	of	ADP
ejpam-749	59	13	a	a	DET
ejpam-749	59	14	,	,	PUNCT
ejpam-749	59	15	b	b	NOUN
ejpam-749	59	16	,	,	PUNCT
ejpam-749	59	17	c	c	PROPN
ejpam-749	59	18	with	with	ADP
ejpam-749	59	19	ab	ab	PROPN
ejpam-749	59	20	6=	6=	ADP
ejpam-749	59	21	0	0	NUM
ejpam-749	59	22	and	and	CCONJ
ejpam-749	59	23	ind(ap	ind(ap	VERB
ejpam-749	59	24	+	+	SYM
ejpam-749	59	25	bq−	bq−	NUM
ejpam-749	59	26	cpq	cpq	NOUN
ejpam-749	59	27	)	)	PUNCT
ejpam-749	60	1	=	=	PUNCT
ejpam-749	60	2	ind(p	ind(p	PROPN
ejpam-749	61	1	+	+	NOUN
ejpam-749	61	2	q	q	NOUN
ejpam-749	61	3	)	)	PUNCT
ejpam-749	61	4	.	.	PUNCT
ejpam-749	62	1	proof	proof	NOUN
ejpam-749	62	2	.	.	PUNCT
ejpam-749	63	1	let	let	VERB
ejpam-749	63	2	p	p	NOUN
ejpam-749	63	3	and	and	CCONJ
ejpam-749	63	4	q	q	NOUN
ejpam-749	63	5	be	be	AUX
ejpam-749	63	6	two	two	NUM
ejpam-749	63	7	idempotents	idempotent	NOUN
ejpam-749	63	8	.	.	PUNCT
ejpam-749	64	1	by	by	ADP
ejpam-749	64	2	the	the	DET
ejpam-749	64	3	discussion	discussion	NOUN
ejpam-749	64	4	above	above	ADP
ejpam-749	64	5	,	,	PUNCT
ejpam-749	64	6	since	since	SCONJ
ejpam-749	64	7	ap	ap	PROPN
ejpam-749	64	8	+	+	PROPN
ejpam-749	64	9	bq−	bq−	PUNCT
ejpam-749	64	10	cpq	cpq	PROPN
ejpam-749	64	11	is	be	AUX
ejpam-749	64	12	fredholm	fredholm	ADJ
ejpam-749	64	13	if	if	SCONJ
ejpam-749	64	14	and	and	CCONJ
ejpam-749	64	15	only	only	ADV
ejpam-749	64	16	if	if	SCONJ
ejpam-749	64	17	as−1ps	as−1ps	PROPN
ejpam-749	64	18	+	+	X
ejpam-749	64	19	bs−1qs	bs−1qs	PROPN
ejpam-749	64	20	−	−	PROPN
ejpam-749	64	21	c(s−1ps)(s−1ps	c(s−1ps)(s−1ps	NUM
ejpam-749	64	22	)	)	PUNCT
ejpam-749	64	23	is	be	AUX
ejpam-749	64	24	fredholm	fredholm	NOUN
ejpam-749	64	25	,	,	PUNCT
ejpam-749	64	26	to	to	PART
ejpam-749	64	27	consider	consider	VERB
ejpam-749	64	28	the	the	DET
ejpam-749	64	29	fredholmness	fredholmness	NOUN
ejpam-749	64	30	of	of	ADP
ejpam-749	64	31	ap	ap	PROPN
ejpam-749	64	32	+	+	PUNCT
ejpam-749	64	33	bq−	bq−	PUNCT
ejpam-749	64	34	cpq	cpq	PROPN
ejpam-749	64	35	,	,	PUNCT
ejpam-749	64	36	without	without	ADP
ejpam-749	64	37	loss	loss	NOUN
ejpam-749	64	38	of	of	ADP
ejpam-749	64	39	generality	generality	NOUN
ejpam-749	64	40	,	,	PUNCT
ejpam-749	64	41	we	we	PRON
ejpam-749	64	42	can	can	AUX
ejpam-749	64	43	assume	assume	VERB
ejpam-749	64	44	that	that	SCONJ
ejpam-749	64	45	one	one	NUM
ejpam-749	64	46	of	of	ADP
ejpam-749	64	47	p	p	NOUN
ejpam-749	64	48	and	and	CCONJ
ejpam-749	64	49	q	q	NOUN
ejpam-749	64	50	is	be	AUX
ejpam-749	64	51	an	an	DET
ejpam-749	64	52	orthogonal	orthogonal	ADJ
ejpam-749	64	53	projection	projection	NOUN
ejpam-749	64	54	.	.	PUNCT
ejpam-749	65	1	for	for	ADP
ejpam-749	65	2	example	example	NOUN
ejpam-749	65	3	,	,	PUNCT
ejpam-749	65	4	assume	assume	VERB
ejpam-749	65	5	that	that	SCONJ
ejpam-749	65	6	q	q	NOUN
ejpam-749	65	7	is	be	AUX
ejpam-749	65	8	an	an	DET
ejpam-749	65	9	orthogonal	orthogonal	ADJ
ejpam-749	65	10	projection	projection	NOUN
ejpam-749	65	11	.	.	PUNCT
ejpam-749	66	1	of	of	ADP
ejpam-749	66	2	course	course	NOUN
ejpam-749	66	3	,	,	PUNCT
ejpam-749	66	4	q	q	PUNCT
ejpam-749	66	5	is	be	AUX
ejpam-749	66	6	a	a	DET
ejpam-749	66	7	positive	positive	ADJ
ejpam-749	66	8	operator	operator	NOUN
ejpam-749	66	9	.	.	PUNCT
ejpam-749	67	1	in	in	ADP
ejpam-749	67	2	this	this	DET
ejpam-749	67	3	case	case	NOUN
ejpam-749	67	4	,	,	PUNCT
ejpam-749	67	5	by	by	ADP
ejpam-749	67	6	lemma	lemma	PROPN
ejpam-749	67	7	1	1	NUM
ejpam-749	67	8	,	,	PUNCT
ejpam-749	67	9	p	p	NOUN
ejpam-749	67	10	and	and	CCONJ
ejpam-749	67	11	q	q	NOUN
ejpam-749	67	12	have	have	VERB
ejpam-749	67	13	the	the	DET
ejpam-749	67	14	following	follow	VERB
ejpam-749	67	15	operator	operator	NOUN
ejpam-749	67	16	matrix	matrix	NOUN
ejpam-749	67	17	forms	form	NOUN
ejpam-749	67	18	:	:	PUNCT
ejpam-749	67	19	p	p	X
ejpam-749	67	20	=	=	PUNCT
ejpam-749	67	21	�	�	PROPN
ejpam-749	67	22	i	i	PRON
ejpam-749	67	23	p1	p1	VERB
ejpam-749	67	24	0	0	NUM
ejpam-749	67	25	0	0	NUM
ejpam-749	67	26	�	�	PROPN
ejpam-749	67	27	and	and	CCONJ
ejpam-749	67	28	q	q	NOUN
ejpam-749	67	29	=	=	NOUN
ejpam-749	67	30			X
ejpam-749	67	31			PROPN
ejpam-749	67	32	q1	q1	PROPN
ejpam-749	67	33	q	q	NOUN
ejpam-749	67	34	1	1	NUM
ejpam-749	67	35	2	2	NUM
ejpam-749	67	36	1	1	NUM
ejpam-749	67	37	dq	dq	NUM
ejpam-749	67	38	1	1	NUM
ejpam-749	67	39	2	2	NUM
ejpam-749	67	40	2	2	NUM
ejpam-749	67	41	q	q	NOUN
ejpam-749	67	42	1	1	NUM
ejpam-749	67	43	2	2	NUM
ejpam-749	67	44	2	2	NUM
ejpam-749	67	45	d∗q	d∗q	NUM
ejpam-749	67	46	1	1	NUM
ejpam-749	67	47	2	2	NUM
ejpam-749	67	48	1	1	NUM
ejpam-749	67	49	q2	q2	NOUN
ejpam-749	67	50			X
ejpam-749	68	1			NOUN
ejpam-749	68	2	with	with	ADP
ejpam-749	68	3	respect	respect	NOUN
ejpam-749	68	4	to	to	ADP
ejpam-749	68	5	the	the	DET
ejpam-749	68	6	space	space	NOUN
ejpam-749	68	7	decomposition	decomposition	NOUN
ejpam-749	68	8	h	h	NOUN
ejpam-749	69	1	=	=	NOUN
ejpam-749	69	2	r(p)⊕r(p)⊥	r(p)⊕r(p)⊥	VERB
ejpam-749	69	3	,	,	PUNCT
ejpam-749	69	4	where	where	SCONJ
ejpam-749	69	5	q1	q1	PROPN
ejpam-749	69	6	and	and	CCONJ
ejpam-749	69	7	q2	q2	NOUN
ejpam-749	69	8	are	be	AUX
ejpam-749	69	9	positive	positive	ADJ
ejpam-749	69	10	operators	operator	NOUN
ejpam-749	69	11	onr(p	onr(p	VERB
ejpam-749	69	12	)	)	PUNCT
ejpam-749	69	13	andr(p)⊥	andr(p)⊥	VERB
ejpam-749	69	14	,	,	PUNCT
ejpam-749	69	15	respectively	respectively	ADV
ejpam-749	69	16	,	,	PUNCT
ejpam-749	69	17	and	and	CCONJ
ejpam-749	69	18	d	d	NOUN
ejpam-749	69	19	is	be	AUX
ejpam-749	69	20	a	a	DET
ejpam-749	69	21	contraction	contraction	NOUN
ejpam-749	69	22	operator	operator	NOUN
ejpam-749	69	23	from	from	ADP
ejpam-749	69	24	r(p)⊥	r(p)⊥	ADJ
ejpam-749	69	25	into	into	ADP
ejpam-749	69	26	r(p	r(p	PROPN
ejpam-749	69	27	)	)	PUNCT
ejpam-749	69	28	.	.	PUNCT
ejpam-749	70	1	furthermore	furthermore	ADV
ejpam-749	70	2	,	,	PUNCT
ejpam-749	70	3	q1	q1	PROPN
ejpam-749	70	4	and	and	CCONJ
ejpam-749	70	5	q2	q2	NOUN
ejpam-749	70	6	have	have	VERB
ejpam-749	70	7	the	the	DET
ejpam-749	70	8	following	follow	VERB
ejpam-749	70	9	operator	operator	NOUN
ejpam-749	70	10	matrix	matrix	NOUN
ejpam-749	70	11	forms	form	NOUN
ejpam-749	70	12	:	:	PUNCT
ejpam-749	70	13	q1	q1	NOUN
ejpam-749	70	14	=	=	SYM
ejpam-749	70	15			NOUN
ejpam-749	70	16			ADJ
ejpam-749	70	17	0	0	NUM
ejpam-749	70	18	0	0	NUM
ejpam-749	70	19	0	0	NUM
ejpam-749	70	20	0	0	NUM
ejpam-749	71	1	i	i	NOUN
ejpam-749	71	2	0	0	NUM
ejpam-749	71	3	0	0	NUM
ejpam-749	71	4	0	0	NUM
ejpam-749	71	5	q11	q11	NOUN
ejpam-749	71	6			PROPN
ejpam-749	72	1			NOUN
ejpam-749	72	2	,	,	PUNCT
ejpam-749	72	3	q2	q2	NOUN
ejpam-749	72	4	=	=	SYM
ejpam-749	72	5			PROPN
ejpam-749	72	6			ADJ
ejpam-749	72	7	q22	q22	NOUN
ejpam-749	72	8	0	0	NUM
ejpam-749	72	9	0	0	NUM
ejpam-749	72	10	0	0	PUNCT
ejpam-749	73	1	i	i	NOUN
ejpam-749	73	2	0	0	NUM
ejpam-749	73	3	0	0	NUM
ejpam-749	73	4	0	0	NUM
ejpam-749	73	5	0	0	NUM
ejpam-749	73	6			PROPN
ejpam-749	73	7			NOUN
ejpam-749	73	8	respect	respect	NOUN
ejpam-749	73	9	to	to	ADP
ejpam-749	73	10	the	the	DET
ejpam-749	73	11	space	space	NOUN
ejpam-749	73	12	decomposition	decomposition	NOUN
ejpam-749	73	13	r(p	r(p	NOUN
ejpam-749	73	14	)	)	PUNCT
ejpam-749	74	1	=	=	SYM
ejpam-749	74	2	n	n	PRON
ejpam-749	74	3	(	(	PUNCT
ejpam-749	74	4	q1)⊕n	q1)⊕n	PROPN
ejpam-749	74	5	(	(	PUNCT
ejpam-749	74	6	i	i	PRON
ejpam-749	74	7	−q1)⊕	−q1)⊕	NOUN
ejpam-749	74	8	(	(	PUNCT
ejpam-749	74	9	r(p)⊖	r(p)⊖	NOUN
ejpam-749	74	10	(	(	PUNCT
ejpam-749	74	11	n	n	CCONJ
ejpam-749	74	12	(	(	PUNCT
ejpam-749	74	13	q1)⊕n	q1)⊕n	PROPN
ejpam-749	74	14	(	(	PUNCT
ejpam-749	74	15	i	i	NOUN
ejpam-749	74	16	−q1	−q1	PROPN
ejpam-749	74	17	)	)	PUNCT
ejpam-749	74	18	)	)	PUNCT
ejpam-749	74	19	)	)	PUNCT
ejpam-749	75	1	and	and	CCONJ
ejpam-749	75	2	the	the	DET
ejpam-749	75	3	space	space	NOUN
ejpam-749	75	4	decomposition	decomposition	NOUN
ejpam-749	75	5	r(p)⊥	r(p)⊥	PRON
ejpam-749	75	6	=	=	SYM
ejpam-749	75	7	(	(	PUNCT
ejpam-749	75	8	r(p)⊥⊖n	r(p)⊥⊖n	NOUN
ejpam-749	75	9	(	(	PUNCT
ejpam-749	75	10	i	i	PRON
ejpam-749	75	11	−q2))⊕n	−q2))⊕n	VERB
ejpam-749	75	12	(	(	PUNCT
ejpam-749	75	13	i	i	PRON
ejpam-749	75	14	−q2)⊕n	−q2)⊕n	PROPN
ejpam-749	75	15	(	(	PUNCT
ejpam-749	75	16	q2	q2	NOUN
ejpam-749	75	17	)	)	PUNCT
ejpam-749	75	18	,	,	PUNCT
ejpam-749	75	19	respectively	respectively	ADV
ejpam-749	75	20	.	.	PUNCT
ejpam-749	76	1	then	then	ADV
ejpam-749	76	2	denoteh0	denoteh0	NOUN
ejpam-749	77	1	=	=	SYM
ejpam-749	77	2	n	n	X
ejpam-749	77	3	(	(	PUNCT
ejpam-749	77	4	q1),h1	q1),h1	NOUN
ejpam-749	77	5	=	=	SYM
ejpam-749	77	6	n	n	X
ejpam-749	77	7	(	(	PUNCT
ejpam-749	77	8	i−q1),h2	i−q1),h2	NOUN
ejpam-749	77	9	=	=	NOUN
ejpam-749	77	10	r(p)⊖(n	r(p)⊖(n	NOUN
ejpam-749	77	11	(	(	PUNCT
ejpam-749	77	12	q1)⊕n	q1)⊕n	NOUN
ejpam-749	77	13	(	(	PUNCT
ejpam-749	77	14	i−q1	i−q1	NOUN
ejpam-749	77	15	)	)	PUNCT
ejpam-749	77	16	)	)	PUNCT
ejpam-749	77	17	,	,	PUNCT
ejpam-749	77	18	h3	h3	NOUN
ejpam-749	77	19	=	=	SYM
ejpam-749	77	20	r(p	r(p	PROPN
ejpam-749	77	21	)	)	PUNCT
ejpam-749	77	22	⊥	⊥	PROPN
ejpam-749	77	23	⊖n	⊖n	PROPN
ejpam-749	77	24	(	(	PUNCT
ejpam-749	77	25	i	i	PRON
ejpam-749	77	26	−q2	−q2	PROPN
ejpam-749	77	27	)	)	PUNCT
ejpam-749	77	28	and	and	CCONJ
ejpam-749	77	29	h4	h4	PROPN
ejpam-749	77	30	=	=	SYM
ejpam-749	77	31	n	n	PROPN
ejpam-749	77	32	(	(	PUNCT
ejpam-749	77	33	i	i	PRON
ejpam-749	77	34	−q2	−q2	PROPN
ejpam-749	77	35	)	)	PUNCT
ejpam-749	77	36	,	,	PUNCT
ejpam-749	77	37	h5	h5	PROPN
ejpam-749	77	38	=	=	SYM
ejpam-749	77	39	n	n	PROPN
ejpam-749	77	40	(	(	PUNCT
ejpam-749	77	41	q2	q2	NOUN
ejpam-749	77	42	)	)	PUNCT
ejpam-749	77	43	,	,	PUNCT
ejpam-749	77	44	therefore	therefore	ADV
ejpam-749	77	45	p	p	PROPN
ejpam-749	77	46	and	and	CCONJ
ejpam-749	77	47	q	q	NOUN
ejpam-749	77	48	have	have	VERB
ejpam-749	77	49	the	the	DET
ejpam-749	77	50	following	follow	VERB
ejpam-749	77	51	matrix	matrix	NOUN
ejpam-749	77	52	representations	representation	NOUN
ejpam-749	77	53	:	:	PUNCT
ejpam-749	77	54	q	q	NOUN
ejpam-749	77	55	=	=	PUNCT
ejpam-749	77	56			X
ejpam-749	77	57			NOUN
ejpam-749	77	58	0	0	NUM
ejpam-749	77	59	0	0	NUM
ejpam-749	77	60	0	0	NUM
ejpam-749	77	61	0	0	NUM
ejpam-749	77	62	0	0	NUM
ejpam-749	77	63	0	0	NUM
ejpam-749	77	64	0	0	NUM
ejpam-749	78	1	i	i	NOUN
ejpam-749	78	2	0	0	NUM
ejpam-749	78	3	0	0	NUM
ejpam-749	78	4	0	0	NUM
ejpam-749	78	5	0	0	NUM
ejpam-749	78	6	0	0	NUM
ejpam-749	78	7	0	0	NUM
ejpam-749	78	8	q11	q11	NOUN
ejpam-749	78	9	q	q	NOUN
ejpam-749	78	10	1	1	NUM
ejpam-749	78	11	2	2	NUM
ejpam-749	78	12	11d1q	11d1q	NOUN
ejpam-749	78	13	1	1	NUM
ejpam-749	78	14	2	2	NUM
ejpam-749	78	15	22	22	NUM
ejpam-749	78	16	0	0	NUM
ejpam-749	78	17	0	0	NUM
ejpam-749	78	18	0	0	NUM
ejpam-749	78	19	0	0	NUM
ejpam-749	78	20	q	q	NOUN
ejpam-749	78	21	1	1	NUM
ejpam-749	78	22	2	2	NUM
ejpam-749	78	23	22d∗1q	22d∗1q	NUM
ejpam-749	78	24	1	1	NUM
ejpam-749	78	25	2	2	NUM
ejpam-749	78	26	11	11	NUM
ejpam-749	78	27	q22	q22	NOUN
ejpam-749	78	28	0	0	NUM
ejpam-749	78	29	0	0	NUM
ejpam-749	78	30	0	0	NUM
ejpam-749	78	31	0	0	NUM
ejpam-749	78	32	0	0	NUM
ejpam-749	78	33	0	0	NUM
ejpam-749	79	1	i	i	NOUN
ejpam-749	79	2	0	0	NUM
ejpam-749	79	3	0	0	NUM
ejpam-749	79	4	0	0	NUM
ejpam-749	79	5	0	0	NUM
ejpam-749	79	6	0	0	NUM
ejpam-749	79	7	0	0	NUM
ejpam-749	79	8	0	0	NUM
ejpam-749	79	9			PUNCT
ejpam-749	80	1			NOUN
ejpam-749	80	2	and	and	CCONJ
ejpam-749	80	3	p	p	NOUN
ejpam-749	80	4	=	=	NOUN
ejpam-749	80	5			NUM
ejpam-749	81	1			NOUN
ejpam-749	81	2	i	i	NOUN
ejpam-749	81	3	0	0	NUM
ejpam-749	81	4	0	0	NUM
ejpam-749	81	5	p11	p11	NOUN
ejpam-749	81	6	p12	p12	NOUN
ejpam-749	81	7	p13	p13	NOUN
ejpam-749	81	8	0	0	NUM
ejpam-749	82	1	i	i	NOUN
ejpam-749	82	2	0	0	NUM
ejpam-749	82	3	p21	p21	NOUN
ejpam-749	82	4	p22	p22	NOUN
ejpam-749	82	5	p23	p23	NOUN
ejpam-749	82	6	0	0	NUM
ejpam-749	82	7	0	0	NUM
ejpam-749	83	1	i	i	PRON
ejpam-749	83	2	p31	p31	VERB
ejpam-749	83	3	p32	p32	ADJ
ejpam-749	83	4	p33	p33	NOUN
ejpam-749	83	5	0	0	NUM
ejpam-749	83	6	0	0	NUM
ejpam-749	83	7	0	0	NUM
ejpam-749	83	8	0	0	NUM
ejpam-749	83	9	0	0	NUM
ejpam-749	83	10	0	0	NUM
ejpam-749	83	11	0	0	NUM
ejpam-749	83	12	0	0	NUM
ejpam-749	83	13	0	0	NUM
ejpam-749	83	14	0	0	NUM
ejpam-749	83	15	0	0	NUM
ejpam-749	83	16	0	0	NUM
ejpam-749	83	17	0	0	NUM
ejpam-749	83	18	0	0	NUM
ejpam-749	83	19	0	0	NUM
ejpam-749	83	20	0	0	NUM
ejpam-749	83	21	0	0	NUM
ejpam-749	83	22	0	0	NUM
ejpam-749	83	23			PROPN
ejpam-749	84	1			PROPN
ejpam-749	84	2	t.	t.	PROPN
ejpam-749	84	3	xie	xie	PROPN
ejpam-749	84	4	,	,	PUNCT
ejpam-749	84	5	k.	k.	PROPN
ejpam-749	84	6	zuo	zuo	PROPN
ejpam-749	84	7	/	/	SYM
ejpam-749	84	8	eur	eur	PROPN
ejpam-749	84	9	.	.	PUNCT
ejpam-749	85	1	j.	j.	PROPN
ejpam-749	85	2	pure	pure	PROPN
ejpam-749	85	3	appl	appl	PROPN
ejpam-749	85	4	.	.	PROPN
ejpam-749	85	5	math	math	PROPN
ejpam-749	85	6	,	,	PUNCT
ejpam-749	85	7	3	3	NUM
ejpam-749	85	8	(	(	PUNCT
ejpam-749	85	9	2010	2010	NUM
ejpam-749	85	10	)	)	PUNCT
ejpam-749	85	11	,	,	PUNCT
ejpam-749	85	12	678	678	NUM
ejpam-749	85	13	-	-	SYM
ejpam-749	85	14	685	685	NUM
ejpam-749	85	15	681	681	NUM
ejpam-749	85	16	with	with	ADP
ejpam-749	85	17	respect	respect	NOUN
ejpam-749	85	18	to	to	ADP
ejpam-749	85	19	the	the	DET
ejpam-749	85	20	space	space	NOUN
ejpam-749	85	21	decomposition	decomposition	NOUN
ejpam-749	85	22	h	h	NOUN
ejpam-749	85	23	=	=	SYM
ejpam-749	86	1	⊕5	⊕5	PROPN
ejpam-749	86	2	i=0	i=0	PROPN
ejpam-749	86	3	hi	hi	INTJ
ejpam-749	86	4	for	for	ADP
ejpam-749	86	5	some	some	DET
ejpam-749	86	6	contraction	contraction	NOUN
ejpam-749	86	7	d1	d1	ADV
ejpam-749	86	8	from	from	ADP
ejpam-749	86	9	h3	h3	NOUN
ejpam-749	86	10	to	to	ADP
ejpam-749	86	11	h2	h2	NOUN
ejpam-749	86	12	.	.	PUNCT
ejpam-749	87	1	if	if	SCONJ
ejpam-749	87	2	we	we	PRON
ejpam-749	87	3	let	let	VERB
ejpam-749	87	4	q0	q0	PROPN
ejpam-749	87	5	=	=	PUNCT
ejpam-749	87	6			X
ejpam-749	87	7			ADJ
ejpam-749	87	8	q11	q11	NOUN
ejpam-749	87	9	q	q	NOUN
ejpam-749	87	10	1	1	NUM
ejpam-749	87	11	2	2	NUM
ejpam-749	87	12	11	11	NUM
ejpam-749	87	13	d1q	d1q	NOUN
ejpam-749	87	14	1	1	NUM
ejpam-749	87	15	2	2	NUM
ejpam-749	87	16	22	22	NUM
ejpam-749	87	17	q	q	NOUN
ejpam-749	87	18	1	1	NUM
ejpam-749	87	19	2	2	NUM
ejpam-749	87	20	22d∗1q	22d∗1q	NUM
ejpam-749	87	21	1	1	NUM
ejpam-749	87	22	2	2	NUM
ejpam-749	87	23	11	11	NUM
ejpam-749	87	24	q22	q22	NOUN
ejpam-749	87	25			PROPN
ejpam-749	88	1			PROPN
ejpam-749	88	2	,	,	PUNCT
ejpam-749	88	3	then	then	ADV
ejpam-749	88	4	q	q	X
ejpam-749	88	5	being	be	AUX
ejpam-749	88	6	an	an	DET
ejpam-749	88	7	orthogonal	orthogonal	ADJ
ejpam-749	88	8	projection	projection	NOUN
ejpam-749	88	9	implies	imply	VERB
ejpam-749	88	10	that	that	SCONJ
ejpam-749	88	11	q0	q0	PROPN
ejpam-749	88	12	is	be	AUX
ejpam-749	88	13	also	also	ADV
ejpam-749	88	14	an	an	DET
ejpam-749	88	15	orthogonal	orthogonal	ADJ
ejpam-749	88	16	projection	projection	NOUN
ejpam-749	88	17	on	on	ADP
ejpam-749	88	18	h2⊕h3	h2⊕h3	PRON
ejpam-749	88	19	.	.	PUNCT
ejpam-749	89	1	that	that	PRON
ejpam-749	89	2	is	is	ADV
ejpam-749	89	3	,	,	PUNCT
ejpam-749	89	4	q0	q0	PROPN
ejpam-749	89	5	=	=	SYM
ejpam-749	89	6	q2	q2	PROPN
ejpam-749	89	7	0	0	NUM
ejpam-749	89	8	.	.	PUNCT
ejpam-749	90	1	we	we	PRON
ejpam-749	90	2	obtain	obtain	VERB
ejpam-749	90	3			PRON
ejpam-749	90	4			PROPN
ejpam-749	90	5			PROPN
ejpam-749	90	6	q11	q11	NOUN
ejpam-749	90	7	=	=	SYM
ejpam-749	90	8	q2	q2	NOUN
ejpam-749	90	9	11	11	NUM
ejpam-749	91	1	+	+	NOUN
ejpam-749	91	2	q	q	NOUN
ejpam-749	91	3	1	1	NUM
ejpam-749	91	4	2	2	NUM
ejpam-749	91	5	11d1q22d∗1q	11d1q22d∗1q	NUM
ejpam-749	91	6	1	1	NUM
ejpam-749	91	7	2	2	NUM
ejpam-749	91	8	11	11	NUM
ejpam-749	91	9	,	,	PUNCT
ejpam-749	91	10	q	q	NOUN
ejpam-749	91	11	1	1	NUM
ejpam-749	91	12	2	2	NUM
ejpam-749	91	13	11	11	NUM
ejpam-749	91	14	d1q	d1q	NOUN
ejpam-749	91	15	1	1	NUM
ejpam-749	91	16	2	2	NUM
ejpam-749	91	17	22	22	NUM
ejpam-749	91	18	=	=	SYM
ejpam-749	91	19	q	q	NOUN
ejpam-749	91	20	3	3	NUM
ejpam-749	91	21	2	2	NUM
ejpam-749	91	22	11	11	NUM
ejpam-749	91	23	d1q	d1q	NOUN
ejpam-749	91	24	1	1	NUM
ejpam-749	91	25	2	2	NUM
ejpam-749	91	26	22	22	NUM
ejpam-749	91	27	+	+	NOUN
ejpam-749	91	28	q	q	ADJ
ejpam-749	91	29	1	1	NUM
ejpam-749	91	30	2	2	NUM
ejpam-749	91	31	11	11	NUM
ejpam-749	91	32	d1q	d1q	NOUN
ejpam-749	91	33	3	3	NUM
ejpam-749	91	34	2	2	NUM
ejpam-749	91	35	22	22	NUM
ejpam-749	91	36	,	,	PUNCT
ejpam-749	91	37	q	q	NOUN
ejpam-749	91	38	1	1	NUM
ejpam-749	91	39	2	2	NUM
ejpam-749	91	40	22d∗1q	22d∗1q	NUM
ejpam-749	91	41	1	1	NUM
ejpam-749	91	42	2	2	NUM
ejpam-749	91	43	11	11	NUM
ejpam-749	91	44	=	=	SYM
ejpam-749	91	45	q	q	NOUN
ejpam-749	91	46	3	3	NUM
ejpam-749	91	47	2	2	NUM
ejpam-749	91	48	22d∗1q	22d∗1q	NUM
ejpam-749	91	49	1	1	NUM
ejpam-749	91	50	2	2	NUM
ejpam-749	91	51	11	11	NUM
ejpam-749	91	52	+	+	NOUN
ejpam-749	91	53	q	q	NOUN
ejpam-749	91	54	1	1	NUM
ejpam-749	91	55	2	2	NUM
ejpam-749	91	56	22d∗1q	22d∗1q	NUM
ejpam-749	91	57	3	3	NUM
ejpam-749	91	58	2	2	NUM
ejpam-749	91	59	11	11	NUM
ejpam-749	91	60	,	,	PUNCT
ejpam-749	91	61	q22	q22	NOUN
ejpam-749	91	62	=	=	SYM
ejpam-749	91	63	q2	q2	NOUN
ejpam-749	91	64	22	22	NUM
ejpam-749	92	1	+	+	NOUN
ejpam-749	92	2	q	q	NOUN
ejpam-749	92	3	1	1	NUM
ejpam-749	92	4	2	2	NUM
ejpam-749	92	5	22	22	NUM
ejpam-749	92	6	d∗1q11d1q	d∗1q11d1q	NOUN
ejpam-749	92	7	1	1	NUM
ejpam-749	92	8	2	2	NUM
ejpam-749	92	9	22	22	NUM
ejpam-749	92	10	.	.	PUNCT
ejpam-749	93	1	it	it	PRON
ejpam-749	93	2	can	can	AUX
ejpam-749	93	3	be	be	AUX
ejpam-749	93	4	derived	derive	VERB
ejpam-749	93	5	by	by	ADP
ejpam-749	93	6	using	use	VERB
ejpam-749	93	7	the	the	DET
ejpam-749	93	8	injectivity	injectivity	NOUN
ejpam-749	93	9	of	of	ADP
ejpam-749	93	10	q11	q11	NOUN
ejpam-749	93	11	,	,	PUNCT
ejpam-749	93	12	i	i	PRON
ejpam-749	93	13	−q11	−q11	VERB
ejpam-749	93	14	,	,	PUNCT
ejpam-749	93	15	q22	q22	NOUN
ejpam-749	93	16	and	and	CCONJ
ejpam-749	93	17	i	i	PRON
ejpam-749	93	18	−q22	−q22	X
ejpam-749	93	19	that	that	PRON
ejpam-749	93	20			PROPN
ejpam-749	93	21			ADJ
ejpam-749	93	22			NOUN
ejpam-749	93	23	d1d∗1	d1d∗1	NOUN
ejpam-749	94	1	=	=	NOUN
ejpam-749	94	2	i	i	PROPN
ejpam-749	94	3	,	,	PUNCT
ejpam-749	94	4	d∗1d1	d∗1d1	X
ejpam-749	95	1	=	=	NOUN
ejpam-749	95	2	i	i	PRON
ejpam-749	95	3	,	,	PUNCT
ejpam-749	95	4	q22	q22	NOUN
ejpam-749	95	5	=	=	PUNCT
ejpam-749	95	6	d∗1(i	d∗1(i	PROPN
ejpam-749	95	7	−q11)d1	−q11)d1	PROPN
ejpam-749	95	8	.	.	PUNCT
ejpam-749	96	1	(	(	PUNCT
ejpam-749	96	2	1	1	X
ejpam-749	96	3	)	)	PUNCT
ejpam-749	96	4	note	note	NOUN
ejpam-749	96	5	that	that	SCONJ
ejpam-749	96	6	ap	ap	PROPN
ejpam-749	96	7	+	+	PUNCT
ejpam-749	96	8	bq−	bq−	PUNCT
ejpam-749	96	9	cpq	cpq	NOUN
ejpam-749	96	10	=	=	PUNCT
ejpam-749	96	11	(	(	PUNCT
ejpam-749	96	12	2	2	X
ejpam-749	96	13	)	)	PUNCT
ejpam-749	96	14	=	=	SYM
ejpam-749	96	15			PROPN
ejpam-749	96	16			NOUN
ejpam-749	96	17	u11	u11	ADJ
ejpam-749	96	18	0	0	NUM
ejpam-749	96	19	u13	u13	PROPN
ejpam-749	96	20	u14	u14	NOUN
ejpam-749	96	21	u15	u15	NOUN
ejpam-749	96	22	u16	u16	PROPN
ejpam-749	96	23	0	0	PROPN
ejpam-749	96	24	u22	u22	PROPN
ejpam-749	96	25	u23	u23	PROPN
ejpam-749	96	26	u24	u24	PROPN
ejpam-749	96	27	u25	u25	VERB
ejpam-749	96	28	u26	u26	VERB
ejpam-749	97	1	0	0	NUM
ejpam-749	97	2	0	0	NUM
ejpam-749	97	3	v11	v11	NOUN
ejpam-749	97	4	v12	v12	VERB
ejpam-749	97	5	u35	u35	NUM
ejpam-749	97	6	u36	u36	NOUN
ejpam-749	97	7	0	0	NUM
ejpam-749	97	8	0	0	NUM
ejpam-749	97	9	v21	v21	PROPN
ejpam-749	97	10	v22	v22	NOUN
ejpam-749	97	11	0	0	NUM
ejpam-749	97	12	0	0	NUM
ejpam-749	97	13	0	0	NUM
ejpam-749	97	14	0	0	NUM
ejpam-749	97	15	0	0	NUM
ejpam-749	97	16	0	0	NUM
ejpam-749	97	17	u55	u55	NOUN
ejpam-749	97	18	0	0	NUM
ejpam-749	97	19	0	0	NUM
ejpam-749	97	20	0	0	NUM
ejpam-749	97	21	0	0	NUM
ejpam-749	97	22	0	0	NUM
ejpam-749	97	23	0	0	NUM
ejpam-749	97	24	0	0	NUM
ejpam-749	98	1			PROPN
ejpam-749	99	1			NOUN
ejpam-749	99	2	(	(	PUNCT
ejpam-749	99	3	3	3	NUM
ejpam-749	99	4	)	)	PUNCT
ejpam-749	99	5	with	with	ADP
ejpam-749	99	6	respect	respect	NOUN
ejpam-749	99	7	to	to	ADP
ejpam-749	99	8	the	the	DET
ejpam-749	99	9	space	space	NOUN
ejpam-749	99	10	decomposition	decomposition	NOUN
ejpam-749	99	11	h	h	NOUN
ejpam-749	99	12	=	=	SYM
ejpam-749	99	13	⊕5	⊕5	PROPN
ejpam-749	99	14	i=0hi	i=0hi	NOUN
ejpam-749	99	15	,	,	PUNCT
ejpam-749	99	16	where	where	SCONJ
ejpam-749	99	17	u11	u11	PROPN
ejpam-749	99	18	=	=	NOUN
ejpam-749	99	19	ai	ai	INTJ
ejpam-749	99	20	,	,	PUNCT
ejpam-749	99	21	u13	u13	X
ejpam-749	99	22	=	=	PUNCT
ejpam-749	99	23	−cp11q	−cp11q	NOUN
ejpam-749	99	24	1	1	NUM
ejpam-749	99	25	2	2	NUM
ejpam-749	99	26	22	22	NUM
ejpam-749	99	27	d∗1q	d∗1q	NOUN
ejpam-749	99	28	1	1	NUM
ejpam-749	99	29	2	2	NUM
ejpam-749	99	30	11	11	NUM
ejpam-749	99	31	,	,	PUNCT
ejpam-749	99	32	u14	u14	NOUN
ejpam-749	99	33	=	=	PUNCT
ejpam-749	99	34	ap11	ap11	PROPN
ejpam-749	99	35	−	−	PROPN
ejpam-749	99	36	cp11q22	cp11q22	PROPN
ejpam-749	99	37	,	,	PUNCT
ejpam-749	99	38	u15	u15	NOUN
ejpam-749	99	39	=	=	SYM
ejpam-749	99	40	ap12	ap12	PROPN
ejpam-749	99	41	−	−	PROPN
ejpam-749	99	42	cp12	cp12	PROPN
ejpam-749	99	43	,	,	PUNCT
ejpam-749	99	44	u16	u16	NOUN
ejpam-749	99	45	=	=	SYM
ejpam-749	99	46	ap13	ap13	PROPN
ejpam-749	99	47	,	,	PUNCT
ejpam-749	99	48	u22	u22	PROPN
ejpam-749	99	49	=	=	SYM
ejpam-749	99	50	(	(	PUNCT
ejpam-749	99	51	a+	a+	PUNCT
ejpam-749	99	52	b−	b−	PROPN
ejpam-749	99	53	c)i	c)i	NOUN
ejpam-749	99	54	,	,	PUNCT
ejpam-749	99	55	u23	u23	PROPN
ejpam-749	99	56	=	=	SYM
ejpam-749	100	1	−cp21q	−cp21q	NOUN
ejpam-749	100	2	1	1	NUM
ejpam-749	100	3	2	2	NUM
ejpam-749	100	4	22d∗1q	22d∗1q	NUM
ejpam-749	100	5	1	1	NUM
ejpam-749	100	6	2	2	NUM
ejpam-749	100	7	11	11	NUM
ejpam-749	100	8	,	,	PUNCT
ejpam-749	100	9	u24	u24	NOUN
ejpam-749	100	10	=	=	SYM
ejpam-749	101	1	ap21	ap21	PROPN
ejpam-749	101	2	−	−	PROPN
ejpam-749	101	3	cp21q22	cp21q22	PROPN
ejpam-749	101	4	,	,	PUNCT
ejpam-749	101	5	u25	u25	NOUN
ejpam-749	101	6	=	=	SYM
ejpam-749	101	7	ap22	ap22	PROPN
ejpam-749	101	8	−	−	PROPN
ejpam-749	101	9	cp22	cp22	PROPN
ejpam-749	101	10	,	,	PUNCT
ejpam-749	101	11	u26	u26	NOUN
ejpam-749	101	12	=	=	SYM
ejpam-749	101	13	ap23	ap23	PROPN
ejpam-749	101	14	,	,	PUNCT
ejpam-749	101	15	u35	u35	ADJ
ejpam-749	101	16	=	=	SYM
ejpam-749	101	17	ap32	ap32	PROPN
ejpam-749	101	18	−	−	PROPN
ejpam-749	102	1	cp32	cp32	PROPN
ejpam-749	102	2	,	,	PUNCT
ejpam-749	102	3	u36	u36	ADV
ejpam-749	102	4	=	=	SYM
ejpam-749	102	5	ap33	ap33	PROPN
ejpam-749	102	6	,	,	PUNCT
ejpam-749	102	7	u55	u55	NOUN
ejpam-749	102	8	=	=	SYM
ejpam-749	102	9	bi	bi	NOUN
ejpam-749	102	10	.	.	PUNCT
ejpam-749	103	1	t.	t.	PROPN
ejpam-749	103	2	xie	xie	PROPN
ejpam-749	103	3	,	,	PUNCT
ejpam-749	103	4	k.	k.	PROPN
ejpam-749	103	5	zuo	zuo	PROPN
ejpam-749	103	6	/	/	SYM
ejpam-749	103	7	eur	eur	PROPN
ejpam-749	103	8	.	.	PUNCT
ejpam-749	104	1	j.	j.	PROPN
ejpam-749	104	2	pure	pure	PROPN
ejpam-749	104	3	appl	appl	PROPN
ejpam-749	104	4	.	.	PROPN
ejpam-749	104	5	math	math	PROPN
ejpam-749	104	6	,	,	PUNCT
ejpam-749	104	7	3	3	NUM
ejpam-749	104	8	(	(	PUNCT
ejpam-749	104	9	2010	2010	NUM
ejpam-749	104	10	)	)	PUNCT
ejpam-749	104	11	,	,	PUNCT
ejpam-749	104	12	678	678	NUM
ejpam-749	104	13	-	-	SYM
ejpam-749	104	14	685	685	NUM
ejpam-749	104	15	682	682	NUM
ejpam-749	104	16	and	and	CCONJ
ejpam-749	104	17	v11	v11	NOUN
ejpam-749	104	18	=	=	NOUN
ejpam-749	104	19	ai	ai	PROPN
ejpam-749	104	20	+	+	PROPN
ejpam-749	105	1	bq11	bq11	PROPN
ejpam-749	105	2	−	−	NOUN
ejpam-749	105	3	c(q11	c(q11	NOUN
ejpam-749	105	4	+	+	CCONJ
ejpam-749	105	5	p31q	p31q	NOUN
ejpam-749	105	6	1	1	NUM
ejpam-749	105	7	2	2	NUM
ejpam-749	105	8	22d∗1q	22d∗1q	NUM
ejpam-749	105	9	1	1	NUM
ejpam-749	105	10	2	2	NUM
ejpam-749	105	11	11	11	NUM
ejpam-749	105	12	)	)	PUNCT
ejpam-749	106	1	=	=	VERB
ejpam-749	106	2	ai	ai	VERB
ejpam-749	106	3	+	+	CCONJ
ejpam-749	107	1	bq11	bq11	PROPN
ejpam-749	107	2	−	−	NOUN
ejpam-749	107	3	c(q11	c(q11	NOUN
ejpam-749	108	1	+	+	CCONJ
ejpam-749	108	2	p31d∗1q	p31d∗1q	NOUN
ejpam-749	108	3	1	1	NUM
ejpam-749	108	4	2	2	NUM
ejpam-749	108	5	11(i	11(i	NUM
ejpam-749	108	6	−q11	−q11	NOUN
ejpam-749	108	7	)	)	PUNCT
ejpam-749	108	8	1	1	NUM
ejpam-749	108	9	2	2	NUM
ejpam-749	108	10	)	)	PUNCT
ejpam-749	108	11	,	,	PUNCT
ejpam-749	108	12	v12	v12	VERB
ejpam-749	108	13	=	=	SYM
ejpam-749	108	14	ap31	ap31	PROPN
ejpam-749	108	15	+	+	CCONJ
ejpam-749	108	16	bq	bq	X
ejpam-749	108	17	1	1	NUM
ejpam-749	108	18	2	2	NUM
ejpam-749	108	19	11d1q	11d1q	NOUN
ejpam-749	108	20	1	1	NUM
ejpam-749	108	21	2	2	NUM
ejpam-749	108	22	22	22	NUM
ejpam-749	108	23	−	−	NOUN
ejpam-749	108	24	c(q	c(q	PROPN
ejpam-749	108	25	1	1	NUM
ejpam-749	108	26	2	2	NUM
ejpam-749	108	27	11d1q	11d1q	NUM
ejpam-749	108	28	1	1	NUM
ejpam-749	108	29	2	2	NUM
ejpam-749	108	30	22	22	NUM
ejpam-749	108	31	+	+	CCONJ
ejpam-749	108	32	p31q22	p31q22	ADJ
ejpam-749	108	33	)	)	PUNCT
ejpam-749	108	34	,	,	PUNCT
ejpam-749	108	35	=	=	SYM
ejpam-749	108	36	ap31	ap31	PROPN
ejpam-749	108	37	+	+	CCONJ
ejpam-749	108	38	bq	bq	X
ejpam-749	108	39	1	1	NUM
ejpam-749	108	40	2	2	NUM
ejpam-749	108	41	11(i	11(i	NUM
ejpam-749	108	42	−q11	−q11	NUM
ejpam-749	108	43	)	)	PUNCT
ejpam-749	108	44	1	1	NUM
ejpam-749	108	45	2	2	NUM
ejpam-749	108	46	d1	d1	NOUN
ejpam-749	108	47	−	−	NOUN
ejpam-749	108	48	c(q	c(q	PROPN
ejpam-749	108	49	1	1	NUM
ejpam-749	108	50	2	2	NUM
ejpam-749	108	51	11(i	11(i	NUM
ejpam-749	108	52	−q11	−q11	NOUN
ejpam-749	108	53	)	)	PUNCT
ejpam-749	108	54	1	1	NUM
ejpam-749	108	55	2	2	NUM
ejpam-749	108	56	d1	d1	NOUN
ejpam-749	108	57	+	+	CCONJ
ejpam-749	108	58	p31d∗1(i	p31d∗1(i	NOUN
ejpam-749	108	59	−q11	−q11	NOUN
ejpam-749	108	60	)	)	PUNCT
ejpam-749	108	61	1	1	NUM
ejpam-749	108	62	2	2	NUM
ejpam-749	108	63	d1	d1	NOUN
ejpam-749	108	64	)	)	PUNCT
ejpam-749	108	65	,	,	PUNCT
ejpam-749	108	66	v21	v21	PROPN
ejpam-749	108	67	=	=	SYM
ejpam-749	108	68	bq	bq	NOUN
ejpam-749	108	69	1	1	NUM
ejpam-749	108	70	2	2	NUM
ejpam-749	108	71	22d∗1q	22d∗1q	NUM
ejpam-749	108	72	1	1	NUM
ejpam-749	108	73	2	2	NUM
ejpam-749	108	74	11	11	NUM
ejpam-749	108	75	=	=	SYM
ejpam-749	108	76	bd∗1q	bd∗1q	NOUN
ejpam-749	108	77	1	1	NUM
ejpam-749	108	78	2	2	NUM
ejpam-749	108	79	11(i	11(i	NUM
ejpam-749	108	80	−q11	−q11	NOUN
ejpam-749	108	81	)	)	PUNCT
ejpam-749	108	82	1	1	NUM
ejpam-749	108	83	2	2	NUM
ejpam-749	108	84	,	,	PUNCT
ejpam-749	108	85	v22	v22	NOUN
ejpam-749	108	86	=	=	SYM
ejpam-749	108	87	bq22	bq22	PROPN
ejpam-749	108	88	=	=	SYM
ejpam-749	108	89	bd∗1(i	bd∗1(i	PROPN
ejpam-749	108	90	−q11)d1	−q11)d1	PROPN
ejpam-749	108	91	.	.	PUNCT
ejpam-749	109	1	we	we	PRON
ejpam-749	109	2	claim	claim	VERB
ejpam-749	109	3	that	that	SCONJ
ejpam-749	109	4	ap+	ap+	PROPN
ejpam-749	109	5	bq−	bq−	PUNCT
ejpam-749	109	6	cpq	cpq	PROPN
ejpam-749	109	7	is	be	AUX
ejpam-749	109	8	fredholm	fredholm	ADJ
ejpam-749	109	9	if	if	SCONJ
ejpam-749	109	10	and	and	CCONJ
ejpam-749	109	11	only	only	ADV
ejpam-749	109	12	if	if	SCONJ
ejpam-749	109	13	i−q11	i−q11	PROPN
ejpam-749	109	14	is	be	AUX
ejpam-749	109	15	invertible	invertible	ADJ
ejpam-749	109	16	and	and	CCONJ
ejpam-749	109	17	i−	i−	PROPN
ejpam-749	109	18	p31d∗1(i	p31d∗1(i	NOUN
ejpam-749	109	19	−	−	PROPN
ejpam-749	109	20	p11	p11	NOUN
ejpam-749	109	21	)	)	PUNCT
ejpam-749	109	22	−	−	NOUN
ejpam-749	110	1	1	1	NUM
ejpam-749	110	2	2	2	NUM
ejpam-749	110	3	p	p	NOUN
ejpam-749	110	4	1	1	NUM
ejpam-749	110	5	2	2	NUM
ejpam-749	110	6	11	11	NUM
ejpam-749	110	7	is	be	AUX
ejpam-749	110	8	fredholm	fredholm	NOUN
ejpam-749	110	9	.	.	PUNCT
ejpam-749	111	1	indeed	indeed	ADV
ejpam-749	111	2	,	,	PUNCT
ejpam-749	111	3	if	if	SCONJ
ejpam-749	111	4	ap	ap	PROPN
ejpam-749	111	5	+	+	PROPN
ejpam-749	111	6	bq−	bq−	PROPN
ejpam-749	111	7	cpq	cpq	PROPN
ejpam-749	111	8	is	be	AUX
ejpam-749	111	9	fredholm	fredholm	NOUN
ejpam-749	111	10	,	,	PUNCT
ejpam-749	111	11	then	then	ADV
ejpam-749	111	12	,	,	PUNCT
ejpam-749	111	13	letting	let	VERB
ejpam-749	111	14	a	a	DET
ejpam-749	111	15	be	be	AUX
ejpam-749	111	16	an	an	DET
ejpam-749	111	17	operator	operator	NOUN
ejpam-749	111	18	onh	onh	NOUN
ejpam-749	111	19	such	such	ADJ
ejpam-749	111	20	that	that	SCONJ
ejpam-749	111	21	k	k	PROPN
ejpam-749	112	1	=	=	PRON
ejpam-749	112	2	(	(	PUNCT
ejpam-749	112	3	ap	ap	PROPN
ejpam-749	112	4	+	+	CCONJ
ejpam-749	112	5	bq−	bq−	PUNCT
ejpam-749	112	6	cpq)a−	cpq)a−	NOUN
ejpam-749	112	7	i	i	PRON
ejpam-749	112	8	is	be	AUX
ejpam-749	112	9	compact	compact	ADJ
ejpam-749	112	10	,	,	PUNCT
ejpam-749	112	11	we	we	PRON
ejpam-749	112	12	have	have	AUX
ejpam-749	112	13	,	,	PUNCT
ejpam-749	112	14	with	with	ADP
ejpam-749	112	15	a=	a=	ADJ
ejpam-749	112	16	�	�	PROPN
ejpam-749	112	17	a1	a1	PROPN
ejpam-749	112	18	a2	a2	PROPN
ejpam-749	112	19	a3	a3	PROPN
ejpam-749	112	20	a4	a4	PROPN
ejpam-749	112	21	�	�	PROPN
ejpam-749	112	22	and	and	CCONJ
ejpam-749	112	23	k	k	PROPN
ejpam-749	112	24	=	=	PROPN
ejpam-749	112	25	�	�	PROPN
ejpam-749	112	26	k1	k1	PROPN
ejpam-749	112	27	k2	k2	PROPN
ejpam-749	112	28	k3	k3	VERB
ejpam-749	112	29	k4	k4	PROPN
ejpam-749	112	30	�	�	PROPN
ejpam-749	112	31	onh	onh	PROPN
ejpam-749	112	32	=	=	AUX
ejpam-749	112	33	r(p)⊕r(p)⊥	r(p)⊕r(p)⊥	PROPN
ejpam-749	112	34	,	,	PUNCT
ejpam-749	112	35	�	�	PROPN
ejpam-749	112	36	v11	v11	NOUN
ejpam-749	112	37	v12	v12	VERB
ejpam-749	112	38	v21	v21	PROPN
ejpam-749	112	39	v22	v22	PROPN
ejpam-749	112	40	�	�	PROPN
ejpam-749	112	41	�	�	PROPN
ejpam-749	112	42	a1	a1	PROPN
ejpam-749	112	43	a2	a2	PROPN
ejpam-749	112	44	a3	a3	PROPN
ejpam-749	112	45	a4	a4	PROPN
ejpam-749	112	46	�	�	PROPN
ejpam-749	112	47	=	=	SYM
ejpam-749	112	48	�	�	PROPN
ejpam-749	113	1	i	i	NOUN
ejpam-749	113	2	+	+	CCONJ
ejpam-749	113	3	k1	k1	PROPN
ejpam-749	113	4	k2	k2	NOUN
ejpam-749	113	5	k3	k3	VERB
ejpam-749	113	6	i	i	PRON
ejpam-749	113	7	+	+	CCONJ
ejpam-749	113	8	k4	k4	PROPN
ejpam-749	113	9	�	�	PROPN
ejpam-749	113	10	.	.	PUNCT
ejpam-749	114	1	carrying	carry	VERB
ejpam-749	114	2	out	out	ADP
ejpam-749	114	3	the	the	DET
ejpam-749	114	4	mulitiplication	mulitiplication	NOUN
ejpam-749	114	5	here	here	ADV
ejpam-749	114	6	yields	yield	VERB
ejpam-749	114	7	bq	bq	VERB
ejpam-749	114	8	1	1	NUM
ejpam-749	114	9	2	2	NUM
ejpam-749	114	10	22	22	NUM
ejpam-749	114	11	d∗1q	d∗1q	NOUN
ejpam-749	114	12	1	1	NUM
ejpam-749	114	13	2	2	NUM
ejpam-749	114	14	11	11	NUM
ejpam-749	114	15	a2	a2	NOUN
ejpam-749	114	16	+	+	CCONJ
ejpam-749	114	17	bq22a4	bq22a4	NOUN
ejpam-749	114	18	=	=	SYM
ejpam-749	115	1	i	i	PRON
ejpam-749	115	2	+	+	CCONJ
ejpam-749	115	3	k4	k4	ADJ
ejpam-749	115	4	or	or	CCONJ
ejpam-749	115	5	bq	bq	INTJ
ejpam-749	115	6	1	1	NUM
ejpam-749	115	7	2	2	NUM
ejpam-749	115	8	22(d	22(d	NUM
ejpam-749	115	9	∗	∗	NOUN
ejpam-749	115	10	1q	1q	NUM
ejpam-749	115	11	1	1	NUM
ejpam-749	115	12	2	2	NUM
ejpam-749	115	13	11a2	11a2	NUM
ejpam-749	115	14	+	+	NOUN
ejpam-749	115	15	q	q	NOUN
ejpam-749	115	16	1	1	NUM
ejpam-749	115	17	2	2	NUM
ejpam-749	115	18	22a4	22a4	NUM
ejpam-749	115	19	)	)	PUNCT
ejpam-749	116	1	=	=	PUNCT
ejpam-749	117	1	i	i	PRON
ejpam-749	117	2	+	+	CCONJ
ejpam-749	117	3	k4	k4	ADJ
ejpam-749	117	4	.	.	PUNCT
ejpam-749	118	1	this	this	PRON
ejpam-749	118	2	shows	show	VERB
ejpam-749	118	3	that	that	SCONJ
ejpam-749	118	4	q	q	PROPN
ejpam-749	118	5	1	1	NUM
ejpam-749	118	6	2	2	NUM
ejpam-749	118	7	22	22	NUM
ejpam-749	118	8	is	be	AUX
ejpam-749	118	9	fredholm	fredholm	NOUN
ejpam-749	118	10	and	and	CCONJ
ejpam-749	118	11	hence	hence	ADV
ejpam-749	118	12	so	so	ADV
ejpam-749	118	13	is	be	AUX
ejpam-749	118	14	q22	q22	ADJ
ejpam-749	118	15	.	.	PUNCT
ejpam-749	119	1	therefore	therefore	ADV
ejpam-749	119	2	,	,	PUNCT
ejpam-749	119	3	q22	q22	NOUN
ejpam-749	119	4	is	be	AUX
ejpam-749	119	5	invertible	invertible	ADJ
ejpam-749	119	6	and	and	CCONJ
ejpam-749	119	7	thus	thus	ADV
ejpam-749	119	8	so	so	ADV
ejpam-749	119	9	is	be	AUX
ejpam-749	119	10	i	i	PRON
ejpam-749	119	11	−q11	−q11	NOUN
ejpam-749	119	12	by	by	ADP
ejpam-749	119	13	(	(	PUNCT
ejpam-749	119	14	1	1	NUM
ejpam-749	119	15	)	)	PUNCT
ejpam-749	119	16	.	.	PUNCT
ejpam-749	120	1	the	the	DET
ejpam-749	120	2	fredholmness	fredholmness	NOUN
ejpam-749	120	3	of	of	ADP
ejpam-749	120	4	ap	ap	PROPN
ejpam-749	120	5	+	+	PUNCT
ejpam-749	120	6	bq−	bq−	PUNCT
ejpam-749	120	7	cpq	cpq	PROPN
ejpam-749	120	8	is	be	AUX
ejpam-749	120	9	equivalent	equivalent	ADJ
ejpam-749	120	10	to	to	ADP
ejpam-749	120	11	that	that	PRON
ejpam-749	120	12	of	of	ADP
ejpam-749	120	13	�	�	PROPN
ejpam-749	120	14	v11	v11	NOUN
ejpam-749	120	15	v12	v12	VERB
ejpam-749	120	16	v21	v21	PROPN
ejpam-749	120	17	v22	v22	PROPN
ejpam-749	120	18	�	�	PROPN
ejpam-749	120	19	by	by	ADP
ejpam-749	120	20	(	(	PUNCT
ejpam-749	120	21	3	3	NUM
ejpam-749	120	22	)	)	PUNCT
ejpam-749	120	23	,	,	PUNCT
ejpam-749	120	24	which	which	PRON
ejpam-749	120	25	is	be	AUX
ejpam-749	120	26	in	in	ADP
ejpam-749	120	27	turn	turn	NOUN
ejpam-749	120	28	equivalent	equivalent	ADJ
ejpam-749	120	29	to	to	ADP
ejpam-749	120	30	that	that	PRON
ejpam-749	120	31	of	of	ADP
ejpam-749	120	32	v11	v11	NOUN
ejpam-749	120	33	−	−	NOUN
ejpam-749	120	34	v12v	v12v	NOUN
ejpam-749	120	35	′22v21	′22v21	NOUN
ejpam-749	120	36	=	=	PUNCT
ejpam-749	120	37	ai	ai	VERB
ejpam-749	120	38	+	+	PROPN
ejpam-749	121	1	bq11	bq11	PROPN
ejpam-749	121	2	−	−	PROPN
ejpam-749	121	3	(	(	PUNCT
ejpam-749	121	4	ap31	ap31	PROPN
ejpam-749	121	5	+	+	CCONJ
ejpam-749	121	6	bq	bq	PROPN
ejpam-749	121	7	1	1	NUM
ejpam-749	121	8	2	2	NUM
ejpam-749	121	9	11d1q	11d1q	NOUN
ejpam-749	121	10	1	1	NUM
ejpam-749	121	11	2	2	NUM
ejpam-749	121	12	22)(bq22	22)(bq22	NUM
ejpam-749	121	13	)	)	PUNCT
ejpam-749	121	14	′(bq	′(bq	NOUN
ejpam-749	121	15	1	1	NUM
ejpam-749	121	16	2	2	NUM
ejpam-749	121	17	22d∗1q	22d∗1q	NUM
ejpam-749	121	18	1	1	NUM
ejpam-749	121	19	2	2	NUM
ejpam-749	121	20	11	11	NUM
ejpam-749	121	21	)	)	PUNCT
ejpam-749	121	22	by	by	ADP
ejpam-749	121	23	lemma	lemma	PROPN
ejpam-749	121	24	2	2	NUM
ejpam-749	121	25	.	.	PUNCT
ejpam-749	122	1	but	but	CCONJ
ejpam-749	122	2	this	this	DET
ejpam-749	122	3	letter	letter	NOUN
ejpam-749	122	4	operator	operator	NOUN
ejpam-749	122	5	is	be	AUX
ejpam-749	122	6	equal	equal	ADJ
ejpam-749	122	7	to	to	PART
ejpam-749	122	8	ai	ai	VERB
ejpam-749	122	9	+	+	PROPN
ejpam-749	123	1	bq11	bq11	PROPN
ejpam-749	123	2	−	−	PROPN
ejpam-749	123	3	(	(	PUNCT
ejpam-749	123	4	ap31	ap31	PROPN
ejpam-749	123	5	+	+	CCONJ
ejpam-749	123	6	bq	bq	PROPN
ejpam-749	123	7	1	1	NUM
ejpam-749	123	8	2	2	NUM
ejpam-749	123	9	11d1d∗1(i	11d1d∗1(i	NUM
ejpam-749	123	10	−q11	−q11	NOUN
ejpam-749	123	11	)	)	PUNCT
ejpam-749	123	12	1	1	NUM
ejpam-749	123	13	2	2	NUM
ejpam-749	123	14	d1)d	d1)d	NOUN
ejpam-749	123	15	∗	∗	NOUN
ejpam-749	123	16	1(i	1(i	NUM
ejpam-749	123	17	−q11	−q11	NOUN
ejpam-749	123	18	)	)	PUNCT
ejpam-749	123	19	−	−	NOUN
ejpam-749	123	20	1	1	NUM
ejpam-749	123	21	2	2	NUM
ejpam-749	123	22	d1d∗1q	d1d∗1q	NOUN
ejpam-749	123	23	1	1	NUM
ejpam-749	123	24	2	2	NUM
ejpam-749	123	25	11	11	NUM
ejpam-749	123	26	,	,	PUNCT
ejpam-749	123	27	t.	t.	PROPN
ejpam-749	123	28	xie	xie	PROPN
ejpam-749	123	29	,	,	PUNCT
ejpam-749	123	30	k.	k.	PROPN
ejpam-749	123	31	zuo	zuo	PROPN
ejpam-749	123	32	/	/	SYM
ejpam-749	123	33	eur	eur	PROPN
ejpam-749	123	34	.	.	PUNCT
ejpam-749	124	1	j.	j.	PROPN
ejpam-749	124	2	pure	pure	PROPN
ejpam-749	124	3	appl	appl	PROPN
ejpam-749	124	4	.	.	PROPN
ejpam-749	124	5	math	math	PROPN
ejpam-749	124	6	,	,	PUNCT
ejpam-749	124	7	3	3	NUM
ejpam-749	124	8	(	(	PUNCT
ejpam-749	124	9	2010	2010	NUM
ejpam-749	124	10	)	)	PUNCT
ejpam-749	124	11	,	,	PUNCT
ejpam-749	124	12	678	678	NUM
ejpam-749	124	13	-	-	SYM
ejpam-749	124	14	685	685	NUM
ejpam-749	124	15	683	683	NUM
ejpam-749	124	16	which	which	PRON
ejpam-749	124	17	can	can	AUX
ejpam-749	124	18	be	be	AUX
ejpam-749	124	19	further	far	ADV
ejpam-749	124	20	simplified	simplify	VERB
ejpam-749	124	21	to	to	PART
ejpam-749	124	22	a(i	a(i	VERB
ejpam-749	124	23	−	−	PROPN
ejpam-749	124	24	p31d∗1(i	p31d∗1(i	NOUN
ejpam-749	124	25	−q11	−q11	NOUN
ejpam-749	124	26	)	)	PUNCT
ejpam-749	124	27	−	−	NOUN
ejpam-749	125	1	1	1	NUM
ejpam-749	125	2	2	2	NUM
ejpam-749	125	3	q	q	NOUN
ejpam-749	125	4	1	1	NUM
ejpam-749	125	5	2	2	NUM
ejpam-749	125	6	11	11	NUM
ejpam-749	125	7	)	)	PUNCT
ejpam-749	125	8	by	by	ADP
ejpam-749	125	9	(	(	PUNCT
ejpam-749	125	10	1	1	NUM
ejpam-749	125	11	)	)	PUNCT
ejpam-749	125	12	.	.	PUNCT
ejpam-749	126	1	this	this	PRON
ejpam-749	126	2	proves	prove	VERB
ejpam-749	126	3	one	one	NUM
ejpam-749	126	4	direction	direction	NOUN
ejpam-749	126	5	.	.	PUNCT
ejpam-749	127	1	for	for	ADP
ejpam-749	127	2	the	the	DET
ejpam-749	127	3	other	other	ADJ
ejpam-749	127	4	,	,	PUNCT
ejpam-749	127	5	if	if	SCONJ
ejpam-749	127	6	i	i	PRON
ejpam-749	127	7	−	−	VERB
ejpam-749	127	8	q11	q11	NOUN
ejpam-749	127	9	is	be	AUX
ejpam-749	127	10	invertible	invertible	ADJ
ejpam-749	127	11	and	and	CCONJ
ejpam-749	127	12	i	i	PRON
ejpam-749	128	1	−	−	PROPN
ejpam-749	128	2	p31d∗1(i	p31d∗1(i	NOUN
ejpam-749	128	3	−	−	PROPN
ejpam-749	128	4	q11	q11	NOUN
ejpam-749	128	5	)	)	PUNCT
ejpam-749	129	1	−	−	NOUN
ejpam-749	129	2	1	1	NUM
ejpam-749	129	3	2	2	NUM
ejpam-749	129	4	q	q	NOUN
ejpam-749	129	5	1	1	NUM
ejpam-749	129	6	2	2	NUM
ejpam-749	129	7	11	11	NUM
ejpam-749	129	8	is	be	AUX
ejpam-749	129	9	fredholm	fredholm	NOUN
ejpam-749	129	10	then	then	ADV
ejpam-749	129	11	we	we	PRON
ejpam-749	129	12	can	can	AUX
ejpam-749	129	13	reverse	reverse	VERB
ejpam-749	129	14	the	the	DET
ejpam-749	129	15	above	above	ADJ
ejpam-749	129	16	arguments	argument	NOUN
ejpam-749	129	17	to	to	PART
ejpam-749	129	18	show	show	VERB
ejpam-749	129	19	that	that	SCONJ
ejpam-749	129	20	ap+	ap+	PROPN
ejpam-749	129	21	bq−	bq−	PUNCT
ejpam-749	129	22	cpq	cpq	PROPN
ejpam-749	129	23	is	be	AUX
ejpam-749	129	24	fredholm	fredholm	NOUN
ejpam-749	129	25	.	.	PUNCT
ejpam-749	130	1	the	the	DET
ejpam-749	130	2	equivalence	equivalence	NOUN
ejpam-749	130	3	of	of	ADP
ejpam-749	130	4	fredholmness	fredholmness	NOUN
ejpam-749	130	5	of	of	ADP
ejpam-749	130	6	ap	ap	PROPN
ejpam-749	130	7	+	+	CCONJ
ejpam-749	130	8	bq	bq	PROPN
ejpam-749	130	9	−	−	PROPN
ejpam-749	130	10	cpq	cpq	PROPN
ejpam-749	130	11	and	and	CCONJ
ejpam-749	130	12	p	p	PROPN
ejpam-749	130	13	+	+	PROPN
ejpam-749	130	14	q	q	NOUN
ejpam-749	130	15	follows	follow	VERB
ejpam-749	130	16	easily	easily	ADV
ejpam-749	130	17	.	.	PUNCT
ejpam-749	131	1	finally	finally	ADV
ejpam-749	131	2	,	,	PUNCT
ejpam-749	131	3	we	we	PRON
ejpam-749	131	4	also	also	ADV
ejpam-749	131	5	have	have	AUX
ejpam-749	131	6	ind(ap	ind(ap	VERB
ejpam-749	131	7	+	+	PUNCT
ejpam-749	131	8	bq−	bq−	PUNCT
ejpam-749	131	9	cpq	cpq	NOUN
ejpam-749	131	10	)	)	PUNCT
ejpam-749	131	11	=	=	SYM
ejpam-749	131	12	ind(i	ind(i	PROPN
ejpam-749	132	1	−	−	PROPN
ejpam-749	132	2	p31d∗1(i	p31d∗1(i	NOUN
ejpam-749	132	3	−q11	−q11	NOUN
ejpam-749	132	4	)	)	PUNCT
ejpam-749	133	1	−	−	NOUN
ejpam-749	134	1	1	1	NUM
ejpam-749	134	2	2	2	NUM
ejpam-749	134	3	q	q	NOUN
ejpam-749	134	4	1	1	NUM
ejpam-749	134	5	2	2	NUM
ejpam-749	134	6	11	11	NUM
ejpam-749	134	7	)	)	PUNCT
ejpam-749	134	8	=	=	PUNCT
ejpam-749	134	9	ind(p	ind(p	PROPN
ejpam-749	135	1	+	+	NOUN
ejpam-749	135	2	q	q	NOUN
ejpam-749	135	3	)	)	PUNCT
ejpam-749	135	4	,	,	PUNCT
ejpam-749	136	1	which	which	PRON
ejpam-749	136	2	complete	complete	VERB
ejpam-749	136	3	the	the	DET
ejpam-749	136	4	proof	proof	NOUN
ejpam-749	137	1	.	.	PUNCT
ejpam-749	138	1	as	as	ADP
ejpam-749	138	2	an	an	DET
ejpam-749	138	3	application	application	NOUN
ejpam-749	138	4	,	,	PUNCT
ejpam-749	138	5	we	we	PRON
ejpam-749	138	6	immediately	immediately	ADV
ejpam-749	138	7	have	have	VERB
ejpam-749	138	8	the	the	DET
ejpam-749	138	9	following	follow	VERB
ejpam-749	138	10	corollary	corollary	NOUN
ejpam-749	138	11	.	.	PUNCT
ejpam-749	139	1	corollary	corollary	ADJ
ejpam-749	139	2	1	1	NUM
ejpam-749	139	3	.	.	PUNCT
ejpam-749	140	1	let	let	VERB
ejpam-749	140	2	p	p	PRON
ejpam-749	140	3	,	,	PUNCT
ejpam-749	140	4	q	q	ADJ
ejpam-749	140	5	be	be	AUX
ejpam-749	140	6	two	two	NUM
ejpam-749	140	7	idempotents	idempotent	NOUN
ejpam-749	140	8	inb(x	inb(x	NUM
ejpam-749	140	9	)	)	PUNCT
ejpam-749	140	10	.	.	PUNCT
ejpam-749	141	1	then	then	ADV
ejpam-749	141	2	(	(	PUNCT
ejpam-749	141	3	i	i	NOUN
ejpam-749	141	4	)	)	PUNCT
ejpam-749	141	5	the	the	DET
ejpam-749	141	6	invertibility	invertibility	NOUN
ejpam-749	141	7	of	of	ADP
ejpam-749	141	8	ap	ap	PROPN
ejpam-749	141	9	+	+	PUNCT
ejpam-749	141	10	bq−	bq−	PUNCT
ejpam-749	141	11	cqp	cqp	ADJ
ejpam-749	141	12	is	be	AUX
ejpam-749	141	13	independent	independent	ADJ
ejpam-749	141	14	of	of	ADP
ejpam-749	141	15	the	the	DET
ejpam-749	141	16	choice	choice	NOUN
ejpam-749	141	17	of	of	ADP
ejpam-749	141	18	a	a	DET
ejpam-749	141	19	,	,	PUNCT
ejpam-749	141	20	b	b	NOUN
ejpam-749	141	21	,	,	PUNCT
ejpam-749	141	22	c	c	PROPN
ejpam-749	141	23	∈	∈	PROPN
ejpam-749	141	24	c	c	PROPN
ejpam-749	141	25	and	and	CCONJ
ejpam-749	141	26	ab	ab	PROPN
ejpam-749	141	27	6=	6=	ADP
ejpam-749	141	28	0	0	NUM
ejpam-749	141	29	.	.	PUNCT
ejpam-749	142	1	(	(	PUNCT
ejpam-749	142	2	ii	ii	NOUN
ejpam-749	142	3	)	)	PUNCT
ejpam-749	142	4	the	the	DET
ejpam-749	142	5	invertibility	invertibility	NOUN
ejpam-749	142	6	of	of	ADP
ejpam-749	142	7	ap+	ap+	ADJ
ejpam-749	142	8	bq−	bq−	NUM
ejpam-749	142	9	cqp	cqp	NOUN
ejpam-749	142	10	is	be	AUX
ejpam-749	142	11	equivalent	equivalent	ADJ
ejpam-749	142	12	to	to	ADP
ejpam-749	142	13	the	the	DET
ejpam-749	142	14	invertibility	invertibility	NOUN
ejpam-749	142	15	of	of	ADP
ejpam-749	142	16	ap+	ap+	ADJ
ejpam-749	142	17	bq	bq	INTJ
ejpam-749	142	18	for	for	ADP
ejpam-749	142	19	all	all	DET
ejpam-749	142	20	choice	choice	NOUN
ejpam-749	142	21	of	of	ADP
ejpam-749	142	22	a	a	DET
ejpam-749	142	23	,	,	PUNCT
ejpam-749	142	24	b	b	NOUN
ejpam-749	142	25	,	,	PUNCT
ejpam-749	142	26	c	c	PROPN
ejpam-749	142	27	∈	∈	PROPN
ejpam-749	142	28	c	c	PROPN
ejpam-749	142	29	and	and	CCONJ
ejpam-749	142	30	ab	ab	PROPN
ejpam-749	142	31	6=	6=	ADP
ejpam-749	142	32	0	0	NUM
ejpam-749	142	33	.	.	PUNCT
ejpam-749	143	1	proof	proof	NOUN
ejpam-749	143	2	.	.	PUNCT
ejpam-749	144	1	(	(	PUNCT
ejpam-749	144	2	i	i	NOUN
ejpam-749	144	3	)	)	PUNCT
ejpam-749	144	4	let	let	VERB
ejpam-749	144	5	a0p	a0p	PROPN
ejpam-749	144	6	+	+	CCONJ
ejpam-749	144	7	b0q−	b0q−	NOUN
ejpam-749	144	8	c0qp	c0qp	PUNCT
ejpam-749	144	9	be	be	AUX
ejpam-749	144	10	invertible	invertible	ADJ
ejpam-749	144	11	for	for	ADP
ejpam-749	144	12	some	some	DET
ejpam-749	144	13	a0	a0	NOUN
ejpam-749	144	14	,	,	PUNCT
ejpam-749	144	15	b0	b0	NOUN
ejpam-749	144	16	,	,	PUNCT
ejpam-749	144	17	c0	c0	PROPN
ejpam-749	144	18	∈	∈	PROPN
ejpam-749	144	19	c	c	PROPN
ejpam-749	144	20	with	with	ADP
ejpam-749	144	21	a0	a0	PROPN
ejpam-749	144	22	b0	b0	PROPN
ejpam-749	144	23	6=	6=	ADP
ejpam-749	144	24	0	0	NUM
ejpam-749	144	25	.	.	PUNCT
ejpam-749	145	1	then	then	ADV
ejpam-749	145	2	a0p	a0p	X
ejpam-749	145	3	+	+	CCONJ
ejpam-749	145	4	b0q−c0qp	b0q−c0qp	NUM
ejpam-749	145	5	is	be	AUX
ejpam-749	145	6	fredholm	fredholm	NOUN
ejpam-749	145	7	with	with	ADP
ejpam-749	145	8	the	the	DET
ejpam-749	145	9	nullity	nullity	NOUN
ejpam-749	145	10	and	and	CCONJ
ejpam-749	145	11	defect	defect	VERB
ejpam-749	145	12	equal	equal	ADJ
ejpam-749	145	13	to	to	ADP
ejpam-749	145	14	zero	zero	NUM
ejpam-749	145	15	.	.	PUNCT
ejpam-749	146	1	by	by	ADP
ejpam-749	146	2	the	the	DET
ejpam-749	146	3	above	above	ADJ
ejpam-749	146	4	theorem	theorem	NOUN
ejpam-749	146	5	,	,	PUNCT
ejpam-749	146	6	ap	ap	PROPN
ejpam-749	146	7	+	+	CCONJ
ejpam-749	146	8	bq−	bq−	PUNCT
ejpam-749	146	9	cqp	cqp	ADJ
ejpam-749	146	10	is	be	AUX
ejpam-749	146	11	invertible	invertible	ADJ
ejpam-749	146	12	for	for	ADP
ejpam-749	146	13	all	all	DET
ejpam-749	146	14	a	a	DET
ejpam-749	146	15	,	,	PUNCT
ejpam-749	146	16	b	b	NOUN
ejpam-749	146	17	,	,	PUNCT
ejpam-749	146	18	c	c	PROPN
ejpam-749	146	19	∈	∈	PROPN
ejpam-749	146	20	c	c	PROPN
ejpam-749	146	21	with	with	ADP
ejpam-749	146	22	ab	ab	PROPN
ejpam-749	146	23	6=	6=	PROPN
ejpam-749	146	24	0	0	NUM
ejpam-749	146	25	.	.	PUNCT
ejpam-749	147	1	(	(	PUNCT
ejpam-749	147	2	ii	ii	NOUN
ejpam-749	147	3	)	)	PUNCT
ejpam-749	147	4	let	let	VERB
ejpam-749	147	5	c	c	NOUN
ejpam-749	147	6	=	=	SYM
ejpam-749	147	7	0	0	NUM
ejpam-749	147	8	,	,	PUNCT
ejpam-749	147	9	then	then	ADV
ejpam-749	147	10	the	the	DET
ejpam-749	147	11	(	(	PUNCT
ejpam-749	147	12	ii	ii	NOUN
ejpam-749	147	13	)	)	PUNCT
ejpam-749	147	14	follows	follow	VERB
ejpam-749	147	15	from	from	ADP
ejpam-749	147	16	(	(	PUNCT
ejpam-749	147	17	i	i	NOUN
ejpam-749	147	18	)	)	PUNCT
ejpam-749	147	19	.	.	PUNCT
ejpam-749	148	1	remark	remark	PROPN
ejpam-749	148	2	1	1	NUM
ejpam-749	148	3	.	.	PUNCT
ejpam-749	149	1	let	let	VERB
ejpam-749	149	2	c	c	NOUN
ejpam-749	149	3	=	=	SYM
ejpam-749	149	4	0	0	NUM
ejpam-749	149	5	,	,	PUNCT
ejpam-749	149	6	we	we	PRON
ejpam-749	149	7	obtain	obtain	VERB
ejpam-749	149	8	the	the	DET
ejpam-749	149	9	theorems	theorem	NOUN
ejpam-749	149	10	of	of	ADP
ejpam-749	149	11	[	[	X
ejpam-749	149	12	4	4	NUM
ejpam-749	149	13	]	]	PUNCT
ejpam-749	149	14	and	and	CCONJ
ejpam-749	149	15	[	[	X
ejpam-749	149	16	7	7	NUM
ejpam-749	149	17	]	]	PUNCT
ejpam-749	149	18	.	.	PUNCT
ejpam-749	150	1	as	as	ADP
ejpam-749	150	2	to	to	ADP
ejpam-749	150	3	the	the	DET
ejpam-749	150	4	invertibility	invertibility	NOUN
ejpam-749	150	5	of	of	ADP
ejpam-749	150	6	ap	ap	PROPN
ejpam-749	150	7	+	+	CCONJ
ejpam-749	150	8	bq−	bq−	PUNCT
ejpam-749	150	9	cpq	cpq	PROPN
ejpam-749	150	10	,	,	PUNCT
ejpam-749	150	11	there	there	PRON
ejpam-749	150	12	is	be	VERB
ejpam-749	150	13	an	an	DET
ejpam-749	150	14	natural	natural	ADJ
ejpam-749	150	15	question	question	NOUN
ejpam-749	150	16	that	that	PRON
ejpam-749	150	17	does	do	VERB
ejpam-749	150	18	the	the	DET
ejpam-749	150	19	combination	combination	NOUN
ejpam-749	150	20	ap	ap	NOUN
ejpam-749	151	1	+	+	CCONJ
ejpam-749	151	2	bq	bq	PROPN
ejpam-749	151	3	−	−	PROPN
ejpam-749	151	4	cpq	cpq	PROPN
ejpam-749	151	5	−	−	PROPN
ejpam-749	151	6	dqp	dqp	PROPN
ejpam-749	151	7	retain	retain	VERB
ejpam-749	151	8	the	the	DET
ejpam-749	151	9	invertibility	invertibility	NOUN
ejpam-749	151	10	for	for	ADP
ejpam-749	151	11	any	any	DET
ejpam-749	151	12	ab	ab	PROPN
ejpam-749	151	13	6=	6=	ADP
ejpam-749	151	14	0	0	NUM
ejpam-749	151	15	and	and	CCONJ
ejpam-749	151	16	a	a	DET
ejpam-749	151	17	+	+	NOUN
ejpam-749	151	18	b	b	NOUN
ejpam-749	151	19	=	=	SYM
ejpam-749	151	20	c	c	PROPN
ejpam-749	152	1	+	+	CCONJ
ejpam-749	153	1	d	d	NOUN
ejpam-749	153	2	.	.	PUNCT
ejpam-749	154	1	however	however	ADV
ejpam-749	154	2	,	,	PUNCT
ejpam-749	154	3	there	there	PRON
ejpam-749	154	4	is	be	VERB
ejpam-749	154	5	an	an	DET
ejpam-749	154	6	counterexample	counterexample	NOUN
ejpam-749	154	7	to	to	PART
ejpam-749	154	8	note	note	VERB
ejpam-749	154	9	that	that	SCONJ
ejpam-749	154	10	this	this	PRON
ejpam-749	154	11	is	be	AUX
ejpam-749	154	12	impossible	impossible	ADJ
ejpam-749	154	13	.	.	PUNCT
ejpam-749	155	1	let	let	VERB
ejpam-749	155	2	p	p	NOUN
ejpam-749	155	3	=	=	X
ejpam-749	155	4	�	�	PROPN
ejpam-749	155	5	1	1	NUM
ejpam-749	155	6	0	0	NUM
ejpam-749	155	7	0	0	NUM
ejpam-749	155	8	0	0	NUM
ejpam-749	155	9	�	�	PROPN
ejpam-749	155	10	,	,	PUNCT
ejpam-749	155	11	q	q	NOUN
ejpam-749	155	12	=	=	PUNCT
ejpam-749	155	13	�	�	PROPN
ejpam-749	155	14	2	2	NUM
ejpam-749	155	15	1	1	NUM
ejpam-749	155	16	−2	−2	NOUN
ejpam-749	155	17	1	1	NUM
ejpam-749	155	18	�	�	PROPN
ejpam-749	155	19	,	,	PUNCT
ejpam-749	155	20	then	then	ADV
ejpam-749	155	21	p	p	X
ejpam-749	155	22	,	,	PUNCT
ejpam-749	155	23	q	q	X
ejpam-749	155	24	are	be	AUX
ejpam-749	155	25	idempotent	idempotent	ADJ
ejpam-749	155	26	and	and	CCONJ
ejpam-749	155	27	the	the	DET
ejpam-749	155	28	determinant	determinant	NOUN
ejpam-749	155	29	of	of	ADP
ejpam-749	155	30	ap	ap	PROPN
ejpam-749	155	31	+	+	PUNCT
ejpam-749	155	32	bq−	bq−	PUNCT
ejpam-749	155	33	cpq	cpq	PROPN
ejpam-749	155	34	−	−	PROPN
ejpam-749	155	35	dqp	dqp	PROPN
ejpam-749	155	36	is	be	AUX
ejpam-749	155	37	0	0	NUM
ejpam-749	155	38	when	when	SCONJ
ejpam-749	155	39	a	a	DET
ejpam-749	155	40	=	=	SYM
ejpam-749	155	41	12	12	NUM
ejpam-749	155	42	,	,	PUNCT
ejpam-749	155	43	b	b	NOUN
ejpam-749	155	44	=	=	SYM
ejpam-749	155	45	−5	−5	NOUN
ejpam-749	155	46	,	,	PUNCT
ejpam-749	155	47	c	c	NOUN
ejpam-749	155	48	=	=	SYM
ejpam-749	155	49	10	10	NUM
ejpam-749	155	50	,	,	PUNCT
ejpam-749	155	51	d	d	NOUN
ejpam-749	155	52	=	=	PUNCT
ejpam-749	155	53	−3	−3	ADJ
ejpam-749	155	54	with	with	ADP
ejpam-749	155	55	a+	a+	PRON
ejpam-749	155	56	b	b	X
ejpam-749	155	57	=	=	SYM
ejpam-749	155	58	c	c	PROPN
ejpam-749	156	1	+	+	CCONJ
ejpam-749	156	2	d	d	NOUN
ejpam-749	156	3	,	,	PUNCT
ejpam-749	156	4	and	and	CCONJ
ejpam-749	156	5	is	be	AUX
ejpam-749	156	6	−3	−3	ADJ
ejpam-749	156	7	when	when	SCONJ
ejpam-749	156	8	a	a	DET
ejpam-749	156	9	=	=	SYM
ejpam-749	156	10	1	1	NUM
ejpam-749	156	11	,	,	PUNCT
ejpam-749	156	12	b	b	NOUN
ejpam-749	156	13	=	=	SYM
ejpam-749	156	14	1	1	NUM
ejpam-749	156	15	,	,	PUNCT
ejpam-749	156	16	c	c	NOUN
ejpam-749	156	17	=	=	SYM
ejpam-749	156	18	−1	−1	NOUN
ejpam-749	156	19	,	,	PUNCT
ejpam-749	156	20	d	d	NOUN
ejpam-749	156	21	=	=	PUNCT
ejpam-749	156	22	−1	−1	NOUN
ejpam-749	156	23	with	with	ADP
ejpam-749	156	24	a+	a+	PRON
ejpam-749	156	25	b	b	X
ejpam-749	156	26	=	=	PRON
ejpam-749	156	27	c+	c+	PROPN
ejpam-749	156	28	d	d	X
ejpam-749	156	29	.	.	PUNCT
ejpam-749	157	1	so	so	ADV
ejpam-749	157	2	the	the	DET
ejpam-749	157	3	invertibility	invertibility	NOUN
ejpam-749	157	4	of	of	ADP
ejpam-749	157	5	ap+	ap+	ADJ
ejpam-749	157	6	bq−	bq−	PUNCT
ejpam-749	157	7	cpq−	cpq−	NOUN
ejpam-749	157	8	dqp	dqp	NOUN
ejpam-749	157	9	depending	depend	VERB
ejpam-749	157	10	on	on	ADP
ejpam-749	157	11	the	the	DET
ejpam-749	157	12	choice	choice	NOUN
ejpam-749	157	13	of	of	ADP
ejpam-749	157	14	scalars	scalar	NOUN
ejpam-749	157	15	a	a	DET
ejpam-749	157	16	,	,	PUNCT
ejpam-749	157	17	b	b	NOUN
ejpam-749	157	18	,	,	PUNCT
ejpam-749	157	19	c	c	NOUN
ejpam-749	157	20	,	,	PUNCT
ejpam-749	157	21	d	d	NOUN
ejpam-749	157	22	with	with	ADP
ejpam-749	157	23	a+	a+	PRON
ejpam-749	157	24	b	b	X
ejpam-749	157	25	=	=	PRON
ejpam-749	157	26	c+	c+	PROPN
ejpam-749	157	27	d	d	X
ejpam-749	157	28	.	.	PUNCT
ejpam-749	158	1	therefore	therefore	ADV
ejpam-749	158	2	the	the	DET
ejpam-749	158	3	idea	idea	NOUN
ejpam-749	158	4	of	of	AUX
ejpam-749	158	5	generalize	generalize	VERB
ejpam-749	158	6	the	the	DET
ejpam-749	158	7	invertibility	invertibility	NOUN
ejpam-749	158	8	of	of	ADP
ejpam-749	158	9	ap	ap	PROPN
ejpam-749	159	1	+	+	CCONJ
ejpam-749	159	2	bq	bq	PROPN
ejpam-749	159	3	−	−	PROPN
ejpam-749	159	4	cpq	cpq	PROPN
ejpam-749	159	5	or	or	CCONJ
ejpam-749	159	6	ap	ap	PROPN
ejpam-749	160	1	+	+	CCONJ
ejpam-749	160	2	bq	bq	PROPN
ejpam-749	160	3	−	−	PROPN
ejpam-749	160	4	cqp	cqp	ADJ
ejpam-749	160	5	to	to	ADP
ejpam-749	160	6	the	the	DET
ejpam-749	160	7	invertibility	invertibility	NOUN
ejpam-749	160	8	of	of	ADP
ejpam-749	160	9	ap	ap	PROPN
ejpam-749	160	10	+	+	CCONJ
ejpam-749	161	1	bq	bq	PROPN
ejpam-749	161	2	−	−	PROPN
ejpam-749	161	3	cpq	cpq	PROPN
ejpam-749	161	4	−	−	PROPN
ejpam-749	161	5	dqp	dqp	PROPN
ejpam-749	161	6	or	or	CCONJ
ejpam-749	161	7	more	more	ADV
ejpam-749	161	8	generally	generally	ADV
ejpam-749	161	9	ap	ap	ADJ
ejpam-749	161	10	+	+	CCONJ
ejpam-749	161	11	bq−	bq−	PUNCT
ejpam-749	161	12	cpq−	cpq−	PROPN
ejpam-749	161	13	dqp	dqp	NOUN
ejpam-749	161	14	−	−	PROPN
ejpam-749	161	15	epqp	epqp	NOUN
ejpam-749	161	16	−	−	PROPN
ejpam-749	161	17	f	f	PROPN
ejpam-749	161	18	qpq−	qpq−	PROPN
ejpam-749	161	19	·	·	PUNCT
ejpam-749	161	20	·	·	PUNCT
ejpam-749	161	21	·	·	PUNCT
ejpam-749	161	22	can	can	AUX
ejpam-749	161	23	not	not	PART
ejpam-749	161	24	be	be	AUX
ejpam-749	161	25	achieved	achieve	VERB
ejpam-749	161	26	.	.	PUNCT
ejpam-749	162	1	references	reference	NOUN
ejpam-749	162	2	684	684	NUM
ejpam-749	162	3	references	reference	NOUN
ejpam-749	162	4	[	[	X
ejpam-749	162	5	1	1	NUM
ejpam-749	162	6	]	]	X
ejpam-749	162	7	j.k	j.k	PROPN
ejpam-749	162	8	.	.	PROPN
ejpam-749	162	9	baksalary	baksalary	PROPN
ejpam-749	162	10	and	and	CCONJ
ejpam-749	162	11	o.m	o.m	PROPN
ejpam-749	162	12	.	.	PROPN
ejpam-749	162	13	baksalary	baksalary	PROPN
ejpam-749	162	14	.	.	PUNCT
ejpam-749	163	1	nonsingularity	nonsingularity	NOUN
ejpam-749	163	2	of	of	ADP
ejpam-749	163	3	linear	linear	PROPN
ejpam-749	163	4	combinations	combination	NOUN
ejpam-749	163	5	of	of	ADP
ejpam-749	163	6	idempotent	idempotent	ADJ
ejpam-749	163	7	matrices	matrix	NOUN
ejpam-749	163	8	.	.	PUNCT
ejpam-749	164	1	linear	linear	ADJ
ejpam-749	164	2	algebra	algebra	NOUN
ejpam-749	164	3	and	and	CCONJ
ejpam-749	164	4	its	its	PRON
ejpam-749	164	5	applications	application	NOUN
ejpam-749	164	6	,	,	PUNCT
ejpam-749	164	7	388	388	NUM
ejpam-749	164	8	:	:	PUNCT
ejpam-749	164	9	25	25	NUM
ejpam-749	164	10	-	-	SYM
ejpam-749	164	11	29	29	NUM
ejpam-749	164	12	,	,	PUNCT
ejpam-749	164	13	2004	2004	NUM
ejpam-749	164	14	.	.	PUNCT
ejpam-749	165	1	[	[	X
ejpam-749	165	2	2	2	NUM
ejpam-749	165	3	]	]	X
ejpam-749	165	4	j.k	j.k	PROPN
ejpam-749	165	5	.	.	PROPN
ejpam-749	165	6	baksalary	baksalary	PROPN
ejpam-749	165	7	and	and	CCONJ
ejpam-749	165	8	o.m	o.m	PROPN
ejpam-749	165	9	.	.	PROPN
ejpam-749	165	10	baksalary	baksalary	PROPN
ejpam-749	165	11	.	.	PUNCT
ejpam-749	166	1	idempotency	idempotency	NOUN
ejpam-749	166	2	of	of	ADP
ejpam-749	166	3	linear	linear	ADJ
ejpam-749	166	4	combinations	combination	NOUN
ejpam-749	166	5	of	of	ADP
ejpam-749	166	6	three	three	NUM
ejpam-749	166	7	idempotent	idempotent	ADJ
ejpam-749	166	8	matrices	matrix	NOUN
ejpam-749	166	9	,	,	PUNCT
ejpam-749	166	10	two	two	NUM
ejpam-749	166	11	of	of	ADP
ejpam-749	166	12	which	which	PRON
ejpam-749	166	13	are	be	AUX
ejpam-749	166	14	disjoint	disjoint	ADJ
ejpam-749	166	15	.	.	PUNCT
ejpam-749	167	1	linear	linear	ADJ
ejpam-749	167	2	algebra	algebra	NOUN
ejpam-749	167	3	and	and	CCONJ
ejpam-749	167	4	its	its	PRON
ejpam-749	167	5	applications	application	NOUN
ejpam-749	167	6	388	388	NUM
ejpam-749	167	7	:	:	SYM
ejpam-749	167	8	67	67	NUM
ejpam-749	167	9	-	-	SYM
ejpam-749	167	10	78	78	NUM
ejpam-749	167	11	,	,	PUNCT
ejpam-749	167	12	2004	2004	NUM
ejpam-749	167	13	.	.	PUNCT
ejpam-749	168	1	[	[	X
ejpam-749	168	2	3	3	X
ejpam-749	168	3	]	]	X
ejpam-749	168	4	j.b	j.b	PROPN
ejpam-749	168	5	.	.	PUNCT
ejpam-749	168	6	conway	conway	PROPN
ejpam-749	168	7	.	.	PUNCT
ejpam-749	169	1	a	a	DET
ejpam-749	169	2	course	course	NOUN
ejpam-749	169	3	in	in	ADP
ejpam-749	169	4	functional	functional	ADJ
ejpam-749	169	5	analysis	analysis	NOUN
ejpam-749	169	6	,	,	PUNCT
ejpam-749	169	7	2nd	2nd	ADJ
ejpam-749	169	8	ed	ed	NOUN
ejpam-749	169	9	.	.	PROPN
ejpam-749	169	10	,	,	PUNCT
ejpam-749	169	11	springer	springer	NOUN
ejpam-749	169	12	,	,	PUNCT
ejpam-749	169	13	new	new	PROPN
ejpam-749	169	14	york	york	PROPN
ejpam-749	169	15	,	,	PUNCT
ejpam-749	169	16	1990	1990	NUM
ejpam-749	169	17	.	.	PUNCT
ejpam-749	170	1	[	[	X
ejpam-749	170	2	4	4	X
ejpam-749	170	3	]	]	X
ejpam-749	170	4	h.	h.	PROPN
ejpam-749	170	5	du	du	PROPN
ejpam-749	170	6	,	,	PUNCT
ejpam-749	170	7	x.	x.	NOUN
ejpam-749	170	8	yao	yao	PROPN
ejpam-749	170	9	and	and	CCONJ
ejpam-749	170	10	c.	c.	PROPN
ejpam-749	170	11	deng	deng	PROPN
ejpam-749	170	12	.	.	PUNCT
ejpam-749	171	1	invertibility	invertibility	NOUN
ejpam-749	171	2	of	of	ADP
ejpam-749	171	3	linear	linear	PROPN
ejpam-749	171	4	combinations	combination	NOUN
ejpam-749	171	5	of	of	ADP
ejpam-749	171	6	two	two	NUM
ejpam-749	171	7	idempotents	idempotent	NOUN
ejpam-749	171	8	.	.	PUNCT
ejpam-749	172	1	proceedings	proceeding	NOUN
ejpam-749	172	2	of	of	ADP
ejpam-749	172	3	american	american	PROPN
ejpam-749	172	4	mathematical	mathematical	PROPN
ejpam-749	172	5	society	society	NOUN
ejpam-749	172	6	,	,	PUNCT
ejpam-749	172	7	134	134	NUM
ejpam-749	172	8	:	:	SYM
ejpam-749	172	9	1451	1451	NUM
ejpam-749	172	10	-	-	SYM
ejpam-749	172	11	1457	1457	NUM
ejpam-749	172	12	,	,	PUNCT
ejpam-749	172	13	2006	2006	NUM
ejpam-749	172	14	.	.	PUNCT
ejpam-749	173	1	[	[	X
ejpam-749	173	2	5	5	NUM
ejpam-749	173	3	]	]	X
ejpam-749	173	4	p.a	p.a	PROPN
ejpam-749	173	5	.	.	PUNCT
ejpam-749	173	6	fillmore	fillmore	PROPN
ejpam-749	173	7	.	.	PUNCT
ejpam-749	174	1	on	on	ADP
ejpam-749	174	2	sums	sum	NOUN
ejpam-749	174	3	of	of	ADP
ejpam-749	174	4	projections	projection	NOUN
ejpam-749	174	5	.	.	PUNCT
ejpam-749	175	1	journal	journal	NOUN
ejpam-749	175	2	of	of	ADP
ejpam-749	175	3	functional	functional	ADJ
ejpam-749	175	4	analysis	analysis	NOUN
ejpam-749	175	5	,	,	PUNCT
ejpam-749	175	6	4	4	NUM
ejpam-749	175	7	:	:	SYM
ejpam-749	175	8	146	146	NUM
ejpam-749	175	9	-	-	SYM
ejpam-749	175	10	152	152	NUM
ejpam-749	175	11	,	,	PUNCT
ejpam-749	175	12	1969	1969	NUM
ejpam-749	175	13	.	.	PUNCT
ejpam-749	176	1	[	[	X
ejpam-749	176	2	6	6	NUM
ejpam-749	176	3	]	]	PUNCT
ejpam-749	176	4	j.	j.	PROPN
ejpam-749	176	5	gro	gro	PROPN
ejpam-749	176	6	and	and	CCONJ
ejpam-749	176	7	g.	g.	PROPN
ejpam-749	176	8	trenkler	trenkler	PROPN
ejpam-749	176	9	.	.	PUNCT
ejpam-749	177	1	nonsingularity	nonsingularity	NOUN
ejpam-749	177	2	of	of	ADP
ejpam-749	177	3	the	the	DET
ejpam-749	177	4	difference	difference	NOUN
ejpam-749	177	5	of	of	ADP
ejpam-749	177	6	two	two	NUM
ejpam-749	177	7	oblique	oblique	ADJ
ejpam-749	177	8	projectors	projector	NOUN
ejpam-749	177	9	.	.	PUNCT
ejpam-749	178	1	siam	siam	ADJ
ejpam-749	178	2	j.	j.	PROPN
ejpam-749	178	3	matrix	matrix	PROPN
ejpam-749	178	4	anal	anal	PROPN
ejpam-749	178	5	.	.	PUNCT
ejpam-749	179	1	appl	appl	PROPN
ejpam-749	179	2	.	.	PROPN
ejpam-749	179	3	,	,	PUNCT
ejpam-749	179	4	21	21	NUM
ejpam-749	179	5	:	:	SYM
ejpam-749	179	6	390	390	NUM
ejpam-749	179	7	-	-	SYM
ejpam-749	179	8	395	395	NUM
ejpam-749	179	9	,	,	PUNCT
ejpam-749	179	10	1999	1999	NUM
ejpam-749	179	11	.	.	PUNCT
ejpam-749	180	1	[	[	X
ejpam-749	180	2	7	7	X
ejpam-749	180	3	]	]	X
ejpam-749	180	4	h.l	h.l	PROPN
ejpam-749	180	5	.	.	PROPN
ejpam-749	180	6	gau	gau	PROPN
ejpam-749	180	7	and	and	CCONJ
ejpam-749	180	8	p.y	p.y	PROPN
ejpam-749	180	9	.	.	PROPN
ejpam-749	180	10	wu	wu	PROPN
ejpam-749	180	11	.	.	PUNCT
ejpam-749	181	1	fredholmness	fredholmness	PROPN
ejpam-749	181	2	of	of	ADP
ejpam-749	181	3	linear	linear	PROPN
ejpam-749	181	4	combinations	combination	NOUN
ejpam-749	181	5	of	of	ADP
ejpam-749	181	6	two	two	NUM
ejpam-749	181	7	idempotents	idempotent	NOUN
ejpam-749	181	8	.	.	PUNCT
ejpam-749	182	1	integral	integral	ADJ
ejpam-749	182	2	equations	equation	NOUN
ejpam-749	182	3	and	and	CCONJ
ejpam-749	182	4	opertor	opertor	PROPN
ejpam-749	182	5	theory	theory	NOUN
ejpam-749	182	6	,	,	PUNCT
ejpam-749	182	7	59	59	NUM
ejpam-749	182	8	:	:	SYM
ejpam-749	182	9	579	579	NUM
ejpam-749	182	10	-	-	SYM
ejpam-749	182	11	583	583	NUM
ejpam-749	182	12	,	,	PUNCT
ejpam-749	182	13	2007	2007	NUM
ejpam-749	182	14	.	.	PUNCT
ejpam-749	183	1	[	[	X
ejpam-749	183	2	8	8	NUM
ejpam-749	183	3	]	]	X
ejpam-749	183	4	h.l	h.l	PROPN
ejpam-749	183	5	.	.	PROPN
ejpam-749	183	6	gau	gau	PROPN
ejpam-749	183	7	,	,	PUNCT
ejpam-749	183	8	c.j	c.j	PROPN
ejpam-749	183	9	.	.	PROPN
ejpam-749	183	10	wang	wang	PROPN
ejpam-749	183	11	and	and	CCONJ
ejpam-749	183	12	n.c	n.c	PROPN
ejpam-749	183	13	.	.	PROPN
ejpam-749	183	14	wong	wong	PROPN
ejpam-749	183	15	.	.	PUNCT
ejpam-749	183	16	invertibility	invertibility	PROPN
ejpam-749	183	17	and	and	CCONJ
ejpam-749	183	18	fredholmness	fredholmness	NOUN
ejpam-749	183	19	of	of	ADP
ejpam-749	183	20	linear	linear	PROPN
ejpam-749	183	21	combinations	combination	NOUN
ejpam-749	183	22	of	of	ADP
ejpam-749	183	23	quadratic	quadratic	ADJ
ejpam-749	183	24	,	,	PUNCT
ejpam-749	183	25	k	k	ADJ
ejpam-749	183	26	-	-	NOUN
ejpam-749	183	27	potent	potent	ADJ
ejpam-749	183	28	and	and	CCONJ
ejpam-749	183	29	nilpotent	nilpotent	ADJ
ejpam-749	183	30	operators	operator	NOUN
ejpam-749	183	31	.	.	PUNCT
ejpam-749	184	1	operators	operator	NOUN
ejpam-749	184	2	and	and	CCONJ
ejpam-749	184	3	matrices	matrix	NOUN
ejpam-749	184	4	,	,	PUNCT
ejpam-749	184	5	2	2	NUM
ejpam-749	184	6	:	:	SYM
ejpam-749	184	7	193	193	NUM
ejpam-749	184	8	-	-	SYM
ejpam-749	184	9	199	199	NUM
ejpam-749	184	10	,	,	PUNCT
ejpam-749	184	11	2008	2008	NUM
ejpam-749	184	12	.	.	PUNCT
ejpam-749	185	1	[	[	X
ejpam-749	185	2	9	9	NUM
ejpam-749	185	3	]	]	PUNCT
ejpam-749	185	4	r.	r.	PROPN
ejpam-749	185	5	harte	harte	PROPN
ejpam-749	185	6	,	,	PUNCT
ejpam-749	185	7	invertibility	invertibility	NOUN
ejpam-749	185	8	and	and	CCONJ
ejpam-749	185	9	singularity	singularity	NOUN
ejpam-749	185	10	for	for	ADP
ejpam-749	185	11	bounded	bounded	ADJ
ejpam-749	185	12	linear	linear	PROPN
ejpam-749	185	13	operators	operators	PROPN
ejpam-749	185	14	,	,	PUNCT
ejpam-749	185	15	marcel	marcel	PROPN
ejpam-749	185	16	dekker	dekker	PROPN
ejpam-749	185	17	,	,	PUNCT
ejpam-749	185	18	new	new	PROPN
ejpam-749	185	19	york	york	PROPN
ejpam-749	185	20	and	and	CCONJ
ejpam-749	185	21	basel	basel	PROPN
ejpam-749	185	22	,	,	PUNCT
ejpam-749	185	23	1988	1988	NUM
ejpam-749	185	24	.	.	PUNCT
ejpam-749	186	1	[	[	X
ejpam-749	186	2	10	10	NUM
ejpam-749	186	3	]	]	X
ejpam-749	186	4	j.j	j.j	PROPN
ejpam-749	186	5	.	.	PROPN
ejpam-749	186	6	koliha	koliha	PROPN
ejpam-749	186	7	and	and	CCONJ
ejpam-749	186	8	v.	v.	ADP
ejpam-749	186	9	rakočević.	rakočević.	ADJ
ejpam-749	186	10	invertibility	invertibility	NOUN
ejpam-749	186	11	of	of	ADP
ejpam-749	186	12	the	the	DET
ejpam-749	186	13	sum	sum	NOUN
ejpam-749	186	14	of	of	ADP
ejpam-749	186	15	idempotents	idempotent	NOUN
ejpam-749	186	16	.	.	PUNCT
ejpam-749	187	1	linear	linear	ADJ
ejpam-749	187	2	and	and	CCONJ
ejpam-749	187	3	multilinear	multilinear	PROPN
ejpam-749	187	4	algebra	algebra	NOUN
ejpam-749	187	5	,	,	PUNCT
ejpam-749	187	6	50	50	NUM
ejpam-749	187	7	:	:	SYM
ejpam-749	187	8	285	285	NUM
ejpam-749	187	9	-	-	SYM
ejpam-749	187	10	292	292	NUM
ejpam-749	187	11	,	,	PUNCT
ejpam-749	187	12	2002	2002	NUM
ejpam-749	187	13	.	.	PUNCT
ejpam-749	188	1	[	[	X
ejpam-749	188	2	11	11	NUM
ejpam-749	188	3	]	]	X
ejpam-749	188	4	j.j	j.j	PROPN
ejpam-749	188	5	.	.	PROPN
ejpam-749	188	6	koliha	koliha	PROPN
ejpam-749	188	7	and	and	CCONJ
ejpam-749	188	8	v.	v.	ADP
ejpam-749	188	9	rakočević.	rakočević.	ADJ
ejpam-749	188	10	invertibility	invertibility	NOUN
ejpam-749	188	11	of	of	ADP
ejpam-749	188	12	the	the	DET
ejpam-749	188	13	difference	difference	NOUN
ejpam-749	188	14	of	of	ADP
ejpam-749	188	15	idempotents	idempotent	NOUN
ejpam-749	188	16	.	.	PUNCT
ejpam-749	189	1	linear	linear	ADJ
ejpam-749	189	2	and	and	CCONJ
ejpam-749	189	3	multilinear	multilinear	PROPN
ejpam-749	189	4	algebra	algebra	NOUN
ejpam-749	189	5	,	,	PUNCT
ejpam-749	189	6	51	51	NUM
ejpam-749	189	7	:	:	SYM
ejpam-749	189	8	97	97	NUM
ejpam-749	189	9	-	-	SYM
ejpam-749	189	10	110	110	NUM
ejpam-749	189	11	,	,	PUNCT
ejpam-749	189	12	2003	2003	NUM
ejpam-749	189	13	.	.	PUNCT
ejpam-749	190	1	[	[	X
ejpam-749	190	2	12	12	NUM
ejpam-749	190	3	]	]	X
ejpam-749	190	4	j.j	j.j	PROPN
ejpam-749	190	5	.	.	PROPN
ejpam-749	190	6	koliha	koliha	PROPN
ejpam-749	190	7	and	and	CCONJ
ejpam-749	190	8	v.	v.	ADP
ejpam-749	190	9	rakočević.	rakočević.	X
ejpam-749	190	10	i.straškraba	i.straškraba	PROPN
ejpam-749	190	11	.	.	PUNCT
ejpam-749	191	1	the	the	DET
ejpam-749	191	2	difference	difference	NOUN
ejpam-749	191	3	and	and	CCONJ
ejpam-749	191	4	sum	sum	NOUN
ejpam-749	191	5	of	of	ADP
ejpam-749	191	6	projectors	projector	NOUN
ejpam-749	191	7	.	.	PUNCT
ejpam-749	192	1	linear	linear	ADJ
ejpam-749	192	2	algebra	algebra	PROPN
ejpam-749	192	3	appl	appl	NOUN
ejpam-749	192	4	.	.	PUNCT
ejpam-749	192	5	,	,	PUNCT
ejpam-749	192	6	388	388	NUM
ejpam-749	192	7	:	:	PUNCT
ejpam-749	192	8	279	279	NUM
ejpam-749	192	9	-	-	SYM
ejpam-749	192	10	288	288	NUM
ejpam-749	192	11	,	,	PUNCT
ejpam-749	192	12	2004	2004	NUM
ejpam-749	192	13	.	.	PUNCT
ejpam-749	193	1	[	[	X
ejpam-749	193	2	13	13	NUM
ejpam-749	193	3	]	]	X
ejpam-749	193	4	j.j	j.j	PROPN
ejpam-749	193	5	.	.	PROPN
ejpam-749	193	6	koliha	koliha	PROPN
ejpam-749	193	7	and	and	CCONJ
ejpam-749	193	8	v.	v.	ADP
ejpam-749	193	9	rakočević.	rakočević.	ADJ
ejpam-749	193	10	fredholm	fredholm	NOUN
ejpam-749	193	11	properties	property	NOUN
ejpam-749	193	12	of	of	ADP
ejpam-749	193	13	the	the	DET
ejpam-749	193	14	difference	difference	NOUN
ejpam-749	193	15	of	of	ADP
ejpam-749	193	16	orthogonal	orthogonal	ADJ
ejpam-749	193	17	projections	projection	NOUN
ejpam-749	193	18	in	in	ADP
ejpam-749	193	19	a	a	DET
ejpam-749	193	20	hilbert	hilbert	NOUN
ejpam-749	193	21	space	space	NOUN
ejpam-749	193	22	.	.	PUNCT
ejpam-749	194	1	integr	integr	PROPN
ejpam-749	194	2	.	.	PUNCT
ejpam-749	195	1	equ	equ	PROPN
ejpam-749	195	2	.	.	PUNCT
ejpam-749	195	3	oper	oper	PROPN
ejpam-749	195	4	.	.	PROPN
ejpam-749	195	5	theory	theory	NOUN
ejpam-749	195	6	,	,	PUNCT
ejpam-749	195	7	52	52	NUM
ejpam-749	195	8	:	:	SYM
ejpam-749	195	9	125	125	NUM
ejpam-749	195	10	-	-	SYM
ejpam-749	195	11	134	134	NUM
ejpam-749	195	12	,	,	PUNCT
ejpam-749	195	13	2005	2005	NUM
ejpam-749	195	14	.	.	PUNCT
ejpam-749	196	1	[	[	X
ejpam-749	196	2	14	14	NUM
ejpam-749	196	3	]	]	X
ejpam-749	196	4	j.j	j.j	PROPN
ejpam-749	196	5	.	.	PROPN
ejpam-749	196	6	koliha	koliha	PROPN
ejpam-749	196	7	and	and	CCONJ
ejpam-749	196	8	v.	v.	ADP
ejpam-749	196	9	rakočević.	rakočević.	X
ejpam-749	196	10	the	the	DET
ejpam-749	196	11	nullity	nullity	NOUN
ejpam-749	196	12	and	and	CCONJ
ejpam-749	196	13	rank	rank	NOUN
ejpam-749	196	14	of	of	ADP
ejpam-749	196	15	linear	linear	PROPN
ejpam-749	196	16	combinations	combination	NOUN
ejpam-749	196	17	of	of	ADP
ejpam-749	196	18	idempotent	idempotent	ADJ
ejpam-749	196	19	matrices	matrix	NOUN
ejpam-749	196	20	.	.	PUNCT
ejpam-749	197	1	linear	linear	ADJ
ejpam-749	197	2	algebra	algebra	PROPN
ejpam-749	197	3	appl	appl	NOUN
ejpam-749	197	4	.	.	PUNCT
ejpam-749	197	5	,	,	PUNCT
ejpam-749	197	6	418	418	NUM
ejpam-749	197	7	:	:	PUNCT
ejpam-749	197	8	11	11	NUM
ejpam-749	197	9	-	-	SYM
ejpam-749	197	10	14	14	NUM
ejpam-749	197	11	,	,	PUNCT
ejpam-749	197	12	2006	2006	NUM
ejpam-749	197	13	.	.	PUNCT
ejpam-749	198	1	[	[	X
ejpam-749	198	2	15	15	NUM
ejpam-749	198	3	]	]	X
ejpam-749	198	4	j.j	j.j	PROPN
ejpam-749	198	5	.	.	PROPN
ejpam-749	198	6	koliha	koliha	PROPN
ejpam-749	198	7	and	and	CCONJ
ejpam-749	198	8	v.	v.	ADP
ejpam-749	198	9	rakočevićs	rakočevićs	PROPN
ejpam-749	198	10	.	.	PROPN
ejpam-749	198	11	stability	stability	NOUN
ejpam-749	198	12	theorems	theorem	VERB
ejpam-749	198	13	for	for	ADP
ejpam-749	198	14	linear	linear	ADJ
ejpam-749	198	15	combinations	combination	NOUN
ejpam-749	198	16	of	of	ADP
ejpam-749	198	17	idempotents	idempotent	NOUN
ejpam-749	198	18	.	.	PUNCT
ejpam-749	199	1	integr	integr	PROPN
ejpam-749	199	2	.	.	PUNCT
ejpam-749	200	1	equ	equ	PROPN
ejpam-749	200	2	.	.	PUNCT
ejpam-749	200	3	oper	oper	PROPN
ejpam-749	200	4	.	.	PROPN
ejpam-749	200	5	theory	theory	NOUN
ejpam-749	200	6	,	,	PUNCT
ejpam-749	200	7	58	58	NUM
ejpam-749	200	8	:	:	PUNCT
ejpam-749	200	9	597	597	NUM
ejpam-749	200	10	-	-	SYM
ejpam-749	200	11	601	601	NUM
ejpam-749	200	12	,	,	PUNCT
ejpam-749	200	13	2007	2007	NUM
ejpam-749	200	14	.	.	PUNCT
ejpam-749	201	1	[	[	X
ejpam-749	201	2	16	16	NUM
ejpam-749	201	3	]	]	X
ejpam-749	201	4	c.	c.	PROPN
ejpam-749	201	5	pearcy	pearcy	PROPN
ejpam-749	201	6	and	and	CCONJ
ejpam-749	201	7	d.	d.	PROPN
ejpam-749	201	8	topping	topping	NOUN
ejpam-749	201	9	.	.	PUNCT
ejpam-749	202	1	sums	sum	NOUN
ejpam-749	202	2	of	of	ADP
ejpam-749	202	3	small	small	ADJ
ejpam-749	202	4	numbers	number	NOUN
ejpam-749	202	5	of	of	ADP
ejpam-749	202	6	idempotents	idempotent	NOUN
ejpam-749	202	7	.	.	PUNCT
ejpam-749	203	1	michigan	michigan	PROPN
ejpam-749	203	2	journal	journal	PROPN
ejpam-749	203	3	of	of	ADP
ejpam-749	203	4	mathematics	mathematics	PROPN
ejpam-749	203	5	,	,	PUNCT
ejpam-749	203	6	14(4	14(4	NUM
ejpam-749	203	7	):	):	PUNCT
ejpam-749	203	8	453	453	NUM
ejpam-749	203	9	-	-	SYM
ejpam-749	203	10	465	465	NUM
ejpam-749	203	11	,	,	PUNCT
ejpam-749	203	12	1967	1967	NUM
ejpam-749	203	13	.	.	PUNCT
ejpam-749	204	1	references	reference	NOUN
ejpam-749	204	2	685	685	NUM
ejpam-749	204	3	[	[	X
ejpam-749	204	4	17	17	NUM
ejpam-749	204	5	]	]	X
ejpam-749	204	6	v.	v.	CCONJ
ejpam-749	204	7	rabanovic	rabanovic	VERB
ejpam-749	204	8	.	.	PUNCT
ejpam-749	205	1	every	every	DET
ejpam-749	205	2	matrix	matrix	NOUN
ejpam-749	205	3	is	be	AUX
ejpam-749	205	4	a	a	DET
ejpam-749	205	5	linear	linear	ADJ
ejpam-749	205	6	combination	combination	NOUN
ejpam-749	205	7	of	of	ADP
ejpam-749	205	8	three	three	NUM
ejpam-749	205	9	idempotents	idempotent	NOUN
ejpam-749	205	10	.	.	PUNCT
ejpam-749	206	1	linear	linear	ADJ
ejpam-749	206	2	algebra	algebra	NOUN
ejpam-749	206	3	and	and	CCONJ
ejpam-749	206	4	its	its	PRON
ejpam-749	206	5	applications	application	NOUN
ejpam-749	206	6	,	,	PUNCT
ejpam-749	206	7	390	390	NUM
ejpam-749	206	8	:	:	SYM
ejpam-749	206	9	137	137	NUM
ejpam-749	206	10	-	-	SYM
ejpam-749	206	11	143	143	NUM
ejpam-749	206	12	,	,	PUNCT
ejpam-749	206	13	2004	2004	NUM
ejpam-749	206	14	.	.	PUNCT
ejpam-749	207	1	[	[	X
ejpam-749	207	2	18	18	NUM
ejpam-749	207	3	]	]	X
ejpam-749	207	4	p.y	p.y	PROPN
ejpam-749	207	5	.	.	PROPN
ejpam-749	207	6	wu	wu	PROPN
ejpam-749	207	7	.	.	PUNCT
ejpam-749	208	1	sums	sum	NOUN
ejpam-749	208	2	of	of	ADP
ejpam-749	208	3	idempotent	idempotent	ADJ
ejpam-749	208	4	matrices	matrix	NOUN
ejpam-749	208	5	.	.	PUNCT
ejpam-749	209	1	linear	linear	ADJ
ejpam-749	209	2	algebra	algebra	NOUN
ejpam-749	209	3	and	and	CCONJ
ejpam-749	209	4	its	its	PRON
ejpam-749	209	5	applications	application	NOUN
ejpam-749	209	6	,	,	PUNCT
ejpam-749	209	7	142	142	NUM
ejpam-749	209	8	:	:	SYM
ejpam-749	209	9	43	43	NUM
ejpam-749	209	10	-	-	SYM
ejpam-749	209	11	54	54	NUM
ejpam-749	209	12	,	,	PUNCT
ejpam-749	209	13	1990	1990	NUM
ejpam-749	209	14	.	.	PUNCT
ejpam-749	210	1	[	[	X
ejpam-749	210	2	19	19	NUM
ejpam-749	210	3	]	]	X
ejpam-749	210	4	p.y	p.y	PROPN
ejpam-749	210	5	.	.	PROPN
ejpam-749	210	6	wu	wu	PROPN
ejpam-749	210	7	.	.	PUNCT
ejpam-749	211	1	additive	additive	ADJ
ejpam-749	211	2	combinations	combination	NOUN
ejpam-749	211	3	of	of	ADP
ejpam-749	211	4	special	special	ADJ
ejpam-749	211	5	operations	operation	NOUN
ejpam-749	211	6	.	.	PUNCT
ejpam-749	212	1	functional	functional	ADJ
ejpam-749	212	2	analysis	analysis	NOUN
ejpam-749	212	3	and	and	CCONJ
ejpam-749	212	4	operator	operator	NOUN
ejpam-749	212	5	theorem	theorem	VERB
ejpam-749	212	6	,	,	PUNCT
ejpam-749	212	7	30	30	NUM
ejpam-749	212	8	:	:	PUNCT
ejpam-749	212	9	337	337	NUM
ejpam-749	212	10	-	-	SYM
ejpam-749	212	11	361	361	NUM
ejpam-749	212	12	,	,	PUNCT
ejpam-749	212	13	1994	1994	NUM
ejpam-749	212	14	.	.	PUNCT