id	sid	tid	token	lemma	pos
ejpam-1882	1	1	european	european	PROPN
ejpam-1882	1	2	journal	journal	PROPN
ejpam-1882	1	3	of	of	ADP
ejpam-1882	1	4	pure	pure	ADJ
ejpam-1882	1	5	and	and	CCONJ
ejpam-1882	1	6	applied	apply	VERB
ejpam-1882	1	7	mathematics	mathematic	NOUN
ejpam-1882	1	8	vol	vol	NOUN
ejpam-1882	1	9	.	.	PUNCT
ejpam-1882	2	1	7	7	NUM
ejpam-1882	2	2	,	,	PUNCT
ejpam-1882	2	3	no	no	INTJ
ejpam-1882	2	4	.	.	NOUN
ejpam-1882	2	5	2	2	NUM
ejpam-1882	2	6	,	,	PUNCT
ejpam-1882	2	7	2014	2014	NUM
ejpam-1882	2	8	,	,	PUNCT
ejpam-1882	2	9	129	129	NUM
ejpam-1882	2	10	-	-	SYM
ejpam-1882	2	11	130	130	NUM
ejpam-1882	2	12	issn	issn	PROPN
ejpam-1882	2	13	1307	1307	NUM
ejpam-1882	2	14	-	-	SYM
ejpam-1882	2	15	5543	5543	NUM
ejpam-1882	2	16	–	–	PUNCT
ejpam-1882	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-1882	2	18	the	the	DET
ejpam-1882	2	19	distance	distance	NOUN
ejpam-1882	2	20	from	from	ADP
ejpam-1882	2	21	a	a	DET
ejpam-1882	2	22	point	point	NOUN
ejpam-1882	2	23	to	to	ADP
ejpam-1882	2	24	a	a	DET
ejpam-1882	2	25	compact	compact	ADJ
ejpam-1882	2	26	convex	convex	NOUN
ejpam-1882	2	27	set	set	VERB
ejpam-1882	2	28	m.	m.	NOUN
ejpam-1882	2	29	t.	t.	PROPN
ejpam-1882	2	30	heydari	heydari	PROPN
ejpam-1882	2	31	department	department	PROPN
ejpam-1882	2	32	of	of	ADP
ejpam-1882	2	33	mathematics	mathematics	PROPN
ejpam-1882	2	34	,	,	PUNCT
ejpam-1882	2	35	college	college	NOUN
ejpam-1882	2	36	of	of	ADP
ejpam-1882	2	37	sciences	sciences	PROPN
ejpam-1882	2	38	,	,	PUNCT
ejpam-1882	2	39	yasouj	yasouj	NOUN
ejpam-1882	2	40	university	university	NOUN
ejpam-1882	2	41	,	,	PUNCT
ejpam-1882	2	42	yasouj	yasouj	NOUN
ejpam-1882	2	43	,	,	PUNCT
ejpam-1882	2	44	75914	75914	NUM
ejpam-1882	2	45	,	,	PUNCT
ejpam-1882	2	46	iran	iran	PROPN
ejpam-1882	2	47	abstract	abstract	NOUN
ejpam-1882	2	48	.	.	PUNCT
ejpam-1882	3	1	let	let	VERB
ejpam-1882	3	2	k	k	PRON
ejpam-1882	3	3	be	be	AUX
ejpam-1882	3	4	a	a	DET
ejpam-1882	3	5	compact	compact	ADJ
ejpam-1882	3	6	convex	convex	NOUN
ejpam-1882	3	7	subset	subset	NOUN
ejpam-1882	3	8	of	of	ADP
ejpam-1882	3	9	the	the	DET
ejpam-1882	3	10	plane	plane	NOUN
ejpam-1882	3	11	and	and	CCONJ
ejpam-1882	3	12	λ	λ	PROPN
ejpam-1882	3	13	∈	∈	PROPN
ejpam-1882	3	14	c\k	c\k	PROPN
ejpam-1882	3	15	,	,	PUNCT
ejpam-1882	3	16	then	then	ADV
ejpam-1882	3	17	dist(λ	dist(λ	PROPN
ejpam-1882	3	18	,	,	PUNCT
ejpam-1882	3	19	k	k	NOUN
ejpam-1882	3	20	)	)	PUNCT
ejpam-1882	3	21	=	=	PUNCT
ejpam-1882	3	22	‖(λ−	‖(λ−	NUM
ejpam-1882	3	23	nµ	nµ	ADV
ejpam-1882	3	24	)	)	PUNCT
ejpam-1882	3	25	−1‖−1	−1‖−1	NOUN
ejpam-1882	3	26	,	,	PUNCT
ejpam-1882	3	27	where	where	SCONJ
ejpam-1882	3	28	µ	µ	NOUN
ejpam-1882	3	29	is	be	AUX
ejpam-1882	3	30	the	the	DET
ejpam-1882	3	31	lebesgue	lebesgue	ADJ
ejpam-1882	3	32	measure	measure	NOUN
ejpam-1882	3	33	concentrated	concentrate	VERB
ejpam-1882	3	34	on	on	ADP
ejpam-1882	3	35	k	k	PROPN
ejpam-1882	3	36	and	and	CCONJ
ejpam-1882	3	37	nµ	nµ	ADV
ejpam-1882	3	38	be	be	AUX
ejpam-1882	3	39	the	the	DET
ejpam-1882	3	40	multiplication	multiplication	NOUN
ejpam-1882	3	41	operator	operator	NOUN
ejpam-1882	3	42	on	on	ADP
ejpam-1882	3	43	l2(µ	l2(µ	PROPN
ejpam-1882	3	44	)	)	PUNCT
ejpam-1882	3	45	.	.	PUNCT
ejpam-1882	4	1	2010	2010	NUM
ejpam-1882	4	2	mathematics	mathematic	NOUN
ejpam-1882	4	3	subject	subject	NOUN
ejpam-1882	4	4	classifications	classification	NOUN
ejpam-1882	4	5	:	:	PUNCT
ejpam-1882	4	6	47a12	47a12	NUM
ejpam-1882	4	7	,	,	PUNCT
ejpam-1882	4	8	11f23	11f23	NUM
ejpam-1882	4	9	key	key	ADJ
ejpam-1882	4	10	words	word	NOUN
ejpam-1882	4	11	and	and	CCONJ
ejpam-1882	4	12	phrases	phrase	NOUN
ejpam-1882	4	13	:	:	PUNCT
ejpam-1882	4	14	compact	compact	ADJ
ejpam-1882	4	15	convex	convex	NOUN
ejpam-1882	4	16	set	set	NOUN
ejpam-1882	4	17	,	,	PUNCT
ejpam-1882	4	18	distance	distance	NOUN
ejpam-1882	4	19	,	,	PUNCT
ejpam-1882	4	20	numerical	numerical	ADJ
ejpam-1882	4	21	range	range	NOUN
ejpam-1882	4	22	1	1	NUM
ejpam-1882	4	23	.	.	PUNCT
ejpam-1882	4	24	main	main	ADJ
ejpam-1882	4	25	result	result	NOUN
ejpam-1882	4	26	let	let	VERB
ejpam-1882	4	27	k	k	PRON
ejpam-1882	4	28	be	be	AUX
ejpam-1882	4	29	a	a	DET
ejpam-1882	4	30	compact	compact	ADJ
ejpam-1882	4	31	convex	convex	NOUN
ejpam-1882	4	32	subset	subset	NOUN
ejpam-1882	4	33	of	of	ADP
ejpam-1882	4	34	the	the	DET
ejpam-1882	4	35	plane	plane	NOUN
ejpam-1882	4	36	and	and	CCONJ
ejpam-1882	4	37	µ	µ	NOUN
ejpam-1882	4	38	be	be	AUX
ejpam-1882	4	39	the	the	DET
ejpam-1882	4	40	lebesgue	lebesgue	ADJ
ejpam-1882	4	41	measure	measure	NOUN
ejpam-1882	4	42	concentrated	concentrate	VERB
ejpam-1882	4	43	on	on	ADP
ejpam-1882	4	44	k	k	PROPN
ejpam-1882	4	45	,	,	PUNCT
ejpam-1882	4	46	i.e.	i.e.	X
ejpam-1882	4	47	,	,	PUNCT
ejpam-1882	4	48	µ=	µ=	NOUN
ejpam-1882	4	49	m2|k	m2|k	NOUN
ejpam-1882	4	50	.	.	PUNCT
ejpam-1882	5	1	define	define	VERB
ejpam-1882	5	2	nµ	nµ	PRON
ejpam-1882	5	3	on	on	ADP
ejpam-1882	5	4	l2(µ	l2(µ	PROPN
ejpam-1882	5	5	)	)	PUNCT
ejpam-1882	5	6	by	by	ADP
ejpam-1882	5	7	nµ	nµ	PRON
ejpam-1882	5	8	f	f	PROPN
ejpam-1882	5	9	=	=	PROPN
ejpam-1882	5	10	z	z	NOUN
ejpam-1882	5	11	f	f	PROPN
ejpam-1882	5	12	for	for	ADP
ejpam-1882	5	13	each	each	DET
ejpam-1882	5	14	f	f	PROPN
ejpam-1882	5	15	in	in	ADP
ejpam-1882	5	16	l2(µ	l2(µ	PROPN
ejpam-1882	5	17	)	)	PUNCT
ejpam-1882	5	18	.	.	PUNCT
ejpam-1882	6	1	it	it	PRON
ejpam-1882	6	2	is	be	AUX
ejpam-1882	6	3	easy	easy	ADJ
ejpam-1882	6	4	to	to	PART
ejpam-1882	6	5	check	check	VERB
ejpam-1882	6	6	that	that	SCONJ
ejpam-1882	6	7	nµ	nµ	ADV
ejpam-1882	6	8	is	be	AUX
ejpam-1882	6	9	normal	normal	ADJ
ejpam-1882	6	10	.	.	PUNCT
ejpam-1882	7	1	let	let	VERB
ejpam-1882	7	2	s	s	PRON
ejpam-1882	7	3	∈	∈	PROPN
ejpam-1882	7	4	k	k	NOUN
ejpam-1882	7	5	and	and	CCONJ
ejpam-1882	7	6	put	put	VERB
ejpam-1882	7	7	un	un	PROPN
ejpam-1882	7	8	=	=	NOUN
ejpam-1882	7	9	b(s	b(s	PROPN
ejpam-1882	7	10	,	,	PUNCT
ejpam-1882	7	11	1	1	NUM
ejpam-1882	7	12	n	n	CCONJ
ejpam-1882	7	13	)	)	PUNCT
ejpam-1882	7	14	,	,	PUNCT
ejpam-1882	7	15	the	the	DET
ejpam-1882	7	16	disc	disc	NOUN
ejpam-1882	7	17	with	with	ADP
ejpam-1882	7	18	center	center	NOUN
ejpam-1882	7	19	at	at	ADP
ejpam-1882	7	20	s	s	PRON
ejpam-1882	7	21	and	and	CCONJ
ejpam-1882	7	22	radius	radius	NOUN
ejpam-1882	7	23	1	1	NUM
ejpam-1882	7	24	n	n	NOUN
ejpam-1882	7	25	,	,	PUNCT
ejpam-1882	7	26	so	so	ADV
ejpam-1882	7	27	µ(un	µ(un	NUM
ejpam-1882	7	28	)	)	PUNCT
ejpam-1882	7	29	6=	6=	ADP
ejpam-1882	7	30	0	0	NUM
ejpam-1882	7	31	.	.	PUNCT
ejpam-1882	8	1	since	since	SCONJ
ejpam-1882	8	2	µ	µ	NOUN
ejpam-1882	8	3	is	be	AUX
ejpam-1882	8	4	regular	regular	ADJ
ejpam-1882	8	5	then	then	ADV
ejpam-1882	8	6	µ(un)<∞.	µ(un)<∞.	INTJ
ejpam-1882	8	7	now	now	ADV
ejpam-1882	8	8	define	define	VERB
ejpam-1882	8	9	fn	fn	NOUN
ejpam-1882	8	10	=	=	SYM
ejpam-1882	8	11	1	1	NUM
ejpam-1882	8	12	p	p	NOUN
ejpam-1882	8	13	µ(un	µ(un	PROPN
ejpam-1882	8	14	)	)	PUNCT
ejpam-1882	8	15	χun	χun	INTJ
ejpam-1882	8	16	,	,	PUNCT
ejpam-1882	8	17	so	so	ADV
ejpam-1882	8	18	‖	‖	ADJ
ejpam-1882	8	19	fn‖2	fn‖2	PROPN
ejpam-1882	8	20	=	=	SYM
ejpam-1882	8	21	1	1	NUM
ejpam-1882	8	22	and	and	CCONJ
ejpam-1882	8	23	‖(nµ	‖(nµ	ADJ
ejpam-1882	8	24	−	−	PROPN
ejpam-1882	8	25	s	s	PART
ejpam-1882	8	26	)	)	PUNCT
ejpam-1882	8	27	fn‖2	fn‖2	ADJ
ejpam-1882	8	28	−→	−→	NOUN
ejpam-1882	8	29	0	0	NUM
ejpam-1882	8	30	,	,	PUNCT
ejpam-1882	8	31	that	that	PRON
ejpam-1882	8	32	is	be	AUX
ejpam-1882	8	33	s	s	PROPN
ejpam-1882	8	34	∈	∈	NOUN
ejpam-1882	8	35	σ(nµ	σ(nµ	NOUN
ejpam-1882	8	36	)	)	PUNCT
ejpam-1882	8	37	.	.	PUNCT
ejpam-1882	9	1	let	let	VERB
ejpam-1882	9	2	s	s	PRON
ejpam-1882	9	3	∈	∈	PROPN
ejpam-1882	9	4	k	k	PROPN
ejpam-1882	9	5	c	c	PROPN
ejpam-1882	9	6	,	,	PUNCT
ejpam-1882	9	7	then	then	ADV
ejpam-1882	9	8	there	there	PRON
ejpam-1882	9	9	is	be	VERB
ejpam-1882	9	10	an	an	DET
ejpam-1882	9	11	open	open	ADJ
ejpam-1882	9	12	set	set	NOUN
ejpam-1882	9	13	u	u	NOUN
ejpam-1882	9	14	with	with	ADP
ejpam-1882	9	15	µ(u	µ(u	NOUN
ejpam-1882	9	16	)	)	PUNCT
ejpam-1882	9	17	=	=	SYM
ejpam-1882	9	18	0	0	NUM
ejpam-1882	9	19	and	and	CCONJ
ejpam-1882	9	20	s	s	PROPN
ejpam-1882	9	21	∈	∈	PROPN
ejpam-1882	9	22	u	u	NOUN
ejpam-1882	9	23	.	.	PUNCT
ejpam-1882	10	1	define	define	VERB
ejpam-1882	10	2	ψ(z	ψ(z	PROPN
ejpam-1882	10	3	)	)	PUNCT
ejpam-1882	10	4	=	=	SYM
ejpam-1882	11	1	¨	¨	NOUN
ejpam-1882	11	2	(	(	PUNCT
ejpam-1882	11	3	s−	s−	PROPN
ejpam-1882	11	4	z)−1	z)−1	NUM
ejpam-1882	11	5	if	if	SCONJ
ejpam-1882	11	6	z	z	NOUN
ejpam-1882	11	7	∈	∈	VERB
ejpam-1882	11	8	u	u	NOUN
ejpam-1882	11	9	c	c	NOUN
ejpam-1882	11	10	;	;	PUNCT
ejpam-1882	11	11	0	0	PUNCT
ejpam-1882	11	12	if	if	SCONJ
ejpam-1882	11	13	z	z	PROPN
ejpam-1882	11	14	∈	∈	PROPN
ejpam-1882	11	15	u	u	NOUN
ejpam-1882	11	16	.	.	PUNCT
ejpam-1882	12	1	there	there	PRON
ejpam-1882	12	2	is	be	VERB
ejpam-1882	12	3	r	r	NOUN
ejpam-1882	12	4	>	>	X
ejpam-1882	12	5	0	0	NUM
ejpam-1882	12	6	such	such	ADJ
ejpam-1882	12	7	that	that	SCONJ
ejpam-1882	12	8	b(s	b(	NOUN
ejpam-1882	12	9	,	,	PUNCT
ejpam-1882	12	10	r	r	NOUN
ejpam-1882	12	11	)	)	PUNCT
ejpam-1882	12	12	⊂	⊂	PROPN
ejpam-1882	12	13	u	u	NOUN
ejpam-1882	12	14	.	.	PUNCT
ejpam-1882	13	1	if	if	SCONJ
ejpam-1882	13	2	z	z	PROPN
ejpam-1882	13	3	∈	∈	VERB
ejpam-1882	13	4	u	u	NOUN
ejpam-1882	13	5	c	c	NOUN
ejpam-1882	13	6	then	then	ADV
ejpam-1882	13	7	1	1	NUM
ejpam-1882	13	8	|s−z|	|s−z|	SYM
ejpam-1882	13	9	<	<	X
ejpam-1882	13	10	1	1	NUM
ejpam-1882	13	11	r	r	NOUN
ejpam-1882	13	12	.	.	PUNCT
ejpam-1882	14	1	therefore	therefore	ADV
ejpam-1882	14	2	‖ψ‖∞	‖ψ‖∞	PROPN
ejpam-1882	14	3	≤	≤	NUM
ejpam-1882	14	4	1	1	NUM
ejpam-1882	14	5	r	r	NOUN
ejpam-1882	14	6	a.e	a.e	PROPN
ejpam-1882	14	7	.	.	PROPN
ejpam-1882	15	1	and	and	CCONJ
ejpam-1882	15	2	so	so	ADV
ejpam-1882	15	3	ψ	ψ	X
ejpam-1882	15	4	∈	∈	PROPN
ejpam-1882	15	5	l∞(µ	l∞(µ	NOUN
ejpam-1882	15	6	)	)	PUNCT
ejpam-1882	15	7	.	.	PUNCT
ejpam-1882	16	1	define	define	VERB
ejpam-1882	16	2	the	the	DET
ejpam-1882	16	3	operator	operator	NOUN
ejpam-1882	16	4	t	t	PROPN
ejpam-1882	16	5	on	on	ADP
ejpam-1882	16	6	l2(µ	l2(µ	PROPN
ejpam-1882	16	7	)	)	PUNCT
ejpam-1882	16	8	by	by	ADP
ejpam-1882	16	9	t	t	PROPN
ejpam-1882	16	10	(	(	PUNCT
ejpam-1882	16	11	f	f	NOUN
ejpam-1882	16	12	)	)	PUNCT
ejpam-1882	17	1	=	=	NOUN
ejpam-1882	17	2	ψ	ψ	X
ejpam-1882	17	3	f	f	NOUN
ejpam-1882	17	4	,	,	PUNCT
ejpam-1882	17	5	then	then	ADV
ejpam-1882	17	6	we	we	PRON
ejpam-1882	17	7	have	have	VERB
ejpam-1882	17	8	(	(	PUNCT
ejpam-1882	17	9	s−	s−	PROPN
ejpam-1882	17	10	nµ)t	nµ)t	PROPN
ejpam-1882	17	11	=	=	SYM
ejpam-1882	17	12	t	t	PROPN
ejpam-1882	17	13	(	(	PUNCT
ejpam-1882	17	14	s−	s−	PROPN
ejpam-1882	17	15	nµ	nµ	ADV
ejpam-1882	17	16	)	)	PUNCT
ejpam-1882	17	17	=	=	VERB
ejpam-1882	18	1	i	i	PRON
ejpam-1882	18	2	email	email	NOUN
ejpam-1882	18	3	address	address	NOUN
ejpam-1882	18	4	:	:	PUNCT
ejpam-1882	18	5	heydari@yu.ac.ir	heydari@yu.ac.ir	ADJ
ejpam-1882	18	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1882	18	7	129	129	NUM
ejpam-1882	19	1	c	c	X
ejpam-1882	19	2	©	©	PROPN
ejpam-1882	19	3	2014	2014	NUM
ejpam-1882	19	4	ejpam	ejpam	NOUN
ejpam-1882	19	5	all	all	DET
ejpam-1882	19	6	rights	right	NOUN
ejpam-1882	19	7	reserved	reserve	VERB
ejpam-1882	19	8	.	.	PUNCT
ejpam-1882	20	1	references	reference	NOUN
ejpam-1882	20	2	130	130	NUM
ejpam-1882	20	3	a.e	a.e	NOUN
ejpam-1882	20	4	..	..	PUNCT
ejpam-1882	20	5	thus	thus	ADV
ejpam-1882	20	6	s	s	X
ejpam-1882	20	7	is	be	AUX
ejpam-1882	20	8	not	not	PART
ejpam-1882	20	9	in	in	ADP
ejpam-1882	20	10	σ(nµ	σ(nµ	NUM
ejpam-1882	20	11	)	)	PUNCT
ejpam-1882	20	12	and	and	CCONJ
ejpam-1882	20	13	so	so	ADV
ejpam-1882	20	14	σ(nµ	σ(nµ	ADJ
ejpam-1882	20	15	)	)	PUNCT
ejpam-1882	21	1	=	=	SYM
ejpam-1882	21	2	k	k	PROPN
ejpam-1882	21	3	.	.	PUNCT
ejpam-1882	22	1	thus	thus	ADV
ejpam-1882	22	2	for	for	ADP
ejpam-1882	22	3	λ	λ	PROPN
ejpam-1882	22	4	∈	∈	PROPN
ejpam-1882	22	5	c\k	c\k	PROPN
ejpam-1882	22	6	we	we	PRON
ejpam-1882	22	7	have	have	AUX
ejpam-1882	22	8	(	(	PUNCT
ejpam-1882	22	9	see	see	VERB
ejpam-1882	22	10	[	[	X
ejpam-1882	22	11	1	1	NUM
ejpam-1882	22	12	,	,	PUNCT
ejpam-1882	22	13	proposition	proposition	NOUN
ejpam-1882	22	14	3.9	3.9	NUM
ejpam-1882	22	15	p.198	p.198	NOUN
ejpam-1882	22	16	]	]	PUNCT
ejpam-1882	22	17	):	):	PUNCT
ejpam-1882	22	18	‖(λ−	‖(λ−	NUM
ejpam-1882	22	19	nµ	nµ	NOUN
ejpam-1882	22	20	)	)	PUNCT
ejpam-1882	22	21	−1‖−1	−1‖−1	NOUN
ejpam-1882	22	22	≤	≤	NUM
ejpam-1882	22	23	dist(λ	dist(λ	PROPN
ejpam-1882	22	24	,	,	PUNCT
ejpam-1882	22	25	k	k	NOUN
ejpam-1882	22	26	)	)	PUNCT
ejpam-1882	22	27	.	.	PUNCT
ejpam-1882	23	1	(	(	PUNCT
ejpam-1882	23	2	1	1	X
ejpam-1882	23	3	)	)	PUNCT
ejpam-1882	23	4	to	to	PART
ejpam-1882	23	5	prove	prove	VERB
ejpam-1882	23	6	the	the	DET
ejpam-1882	23	7	inverse	inverse	NOUN
ejpam-1882	23	8	inequality	inequality	NOUN
ejpam-1882	23	9	,	,	PUNCT
ejpam-1882	23	10	we	we	PRON
ejpam-1882	23	11	need	need	VERB
ejpam-1882	23	12	to	to	ADP
ejpam-1882	23	13	the	the	DET
ejpam-1882	23	14	following	follow	VERB
ejpam-1882	23	15	concepts	concept	NOUN
ejpam-1882	23	16	which	which	PRON
ejpam-1882	23	17	can	can	AUX
ejpam-1882	23	18	be	be	AUX
ejpam-1882	23	19	found	find	VERB
ejpam-1882	23	20	in	in	ADP
ejpam-1882	23	21	[	[	X
ejpam-1882	23	22	2	2	NUM
ejpam-1882	23	23	]	]	PUNCT
ejpam-1882	23	24	.	.	PUNCT
ejpam-1882	24	1	for	for	ADP
ejpam-1882	24	2	a	a	DET
ejpam-1882	24	3	bounded	bounded	ADJ
ejpam-1882	24	4	linear	linear	ADJ
ejpam-1882	24	5	operator	operator	NOUN
ejpam-1882	24	6	t	t	PROPN
ejpam-1882	24	7	on	on	ADP
ejpam-1882	24	8	a	a	DET
ejpam-1882	24	9	hilbert	hilbert	NOUN
ejpam-1882	24	10	space	space	NOUN
ejpam-1882	24	11	h	h	NOUN
ejpam-1882	24	12	,	,	PUNCT
ejpam-1882	24	13	the	the	DET
ejpam-1882	24	14	numerical	numerical	ADJ
ejpam-1882	24	15	range	range	PROPN
ejpam-1882	24	16	w	w	PROPN
ejpam-1882	24	17	(	(	PUNCT
ejpam-1882	24	18	t	t	PROPN
ejpam-1882	24	19	)	)	PUNCT
ejpam-1882	24	20	is	be	AUX
ejpam-1882	24	21	the	the	DET
ejpam-1882	24	22	image	image	NOUN
ejpam-1882	24	23	of	of	ADP
ejpam-1882	24	24	the	the	DET
ejpam-1882	24	25	unit	unit	NOUN
ejpam-1882	24	26	sphere	sphere	ADV
ejpam-1882	24	27	of	of	ADP
ejpam-1882	24	28	h	h	PROPN
ejpam-1882	24	29	under	under	ADP
ejpam-1882	24	30	the	the	DET
ejpam-1882	24	31	quadratic	quadratic	ADJ
ejpam-1882	24	32	form	form	NOUN
ejpam-1882	24	33	x	x	PUNCT
ejpam-1882	25	1	→	→	SYM
ejpam-1882	25	2	<	<	X
ejpam-1882	25	3	t	t	X
ejpam-1882	25	4	x	x	SYM
ejpam-1882	25	5	,	,	PUNCT
ejpam-1882	25	6	x	x	PROPN
ejpam-1882	25	7	>	>	X
ejpam-1882	25	8	associated	associate	VERB
ejpam-1882	25	9	with	with	ADP
ejpam-1882	25	10	the	the	DET
ejpam-1882	25	11	operator	operator	NOUN
ejpam-1882	25	12	.	.	PUNCT
ejpam-1882	26	1	more	more	ADV
ejpam-1882	26	2	precisely	precisely	ADV
ejpam-1882	26	3	,	,	PUNCT
ejpam-1882	26	4	w	w	PROPN
ejpam-1882	26	5	(	(	PUNCT
ejpam-1882	26	6	t	t	PROPN
ejpam-1882	26	7	)	)	PUNCT
ejpam-1882	26	8	=	=	PUNCT
ejpam-1882	26	9	{	{	PUNCT
ejpam-1882	26	10	<	<	X
ejpam-1882	26	11	t	t	X
ejpam-1882	26	12	x	x	SYM
ejpam-1882	26	13	,	,	PUNCT
ejpam-1882	26	14	x	x	X
ejpam-1882	26	15	>	>	X
ejpam-1882	26	16	:	:	PUNCT
ejpam-1882	26	17	x	x	SYM
ejpam-1882	26	18	∈h	∈h	NOUN
ejpam-1882	26	19	,	,	PUNCT
ejpam-1882	26	20	‖x‖=	‖x‖=	VERB
ejpam-1882	26	21	1	1	NUM
ejpam-1882	26	22	}	}	PUNCT
ejpam-1882	26	23	thus	thus	ADV
ejpam-1882	26	24	the	the	DET
ejpam-1882	26	25	numerical	numerical	ADJ
ejpam-1882	26	26	range	range	NOUN
ejpam-1882	26	27	of	of	ADP
ejpam-1882	26	28	an	an	DET
ejpam-1882	26	29	operator	operator	NOUN
ejpam-1882	26	30	,	,	PUNCT
ejpam-1882	26	31	like	like	ADP
ejpam-1882	26	32	the	the	DET
ejpam-1882	26	33	spectrum	spectrum	NOUN
ejpam-1882	26	34	,	,	PUNCT
ejpam-1882	26	35	is	be	AUX
ejpam-1882	26	36	a	a	DET
ejpam-1882	26	37	subset	subset	NOUN
ejpam-1882	26	38	of	of	ADP
ejpam-1882	26	39	the	the	DET
ejpam-1882	26	40	complex	complex	ADJ
ejpam-1882	26	41	plane	plane	NOUN
ejpam-1882	26	42	whose	whose	DET
ejpam-1882	26	43	geometrical	geometrical	ADJ
ejpam-1882	26	44	properties	property	NOUN
ejpam-1882	26	45	should	should	AUX
ejpam-1882	26	46	say	say	VERB
ejpam-1882	26	47	something	something	PRON
ejpam-1882	26	48	about	about	ADP
ejpam-1882	26	49	the	the	DET
ejpam-1882	26	50	operator	operator	NOUN
ejpam-1882	26	51	.	.	PUNCT
ejpam-1882	27	1	one	one	NUM
ejpam-1882	27	2	of	of	ADP
ejpam-1882	27	3	the	the	DET
ejpam-1882	27	4	most	most	ADV
ejpam-1882	27	5	fundamental	fundamental	ADJ
ejpam-1882	27	6	properties	property	NOUN
ejpam-1882	27	7	of	of	ADP
ejpam-1882	27	8	the	the	DET
ejpam-1882	27	9	numerical	numerical	ADJ
ejpam-1882	27	10	range	range	NOUN
ejpam-1882	27	11	is	be	AUX
ejpam-1882	27	12	its	its	PRON
ejpam-1882	27	13	convexity	convexity	NOUN
ejpam-1882	27	14	,	,	PUNCT
ejpam-1882	27	15	stated	state	VERB
ejpam-1882	27	16	by	by	ADP
ejpam-1882	27	17	the	the	DET
ejpam-1882	27	18	famous	famous	ADJ
ejpam-1882	27	19	toeplitz	toeplitz	NOUN
ejpam-1882	27	20	-	-	PUNCT
ejpam-1882	27	21	hausdorff	hausdorff	NOUN
ejpam-1882	27	22	theorem	theorem	NOUN
ejpam-1882	27	23	.	.	PUNCT
ejpam-1882	28	1	other	other	ADJ
ejpam-1882	28	2	important	important	ADJ
ejpam-1882	28	3	property	property	NOUN
ejpam-1882	28	4	of	of	ADP
ejpam-1882	28	5	w	w	PROPN
ejpam-1882	28	6	(	(	PUNCT
ejpam-1882	28	7	t	t	PROPN
ejpam-1882	28	8	)	)	PUNCT
ejpam-1882	28	9	is	be	AUX
ejpam-1882	28	10	that	that	SCONJ
ejpam-1882	28	11	its	its	PRON
ejpam-1882	28	12	closure	closure	NOUN
ejpam-1882	28	13	contains	contain	VERB
ejpam-1882	28	14	the	the	DET
ejpam-1882	28	15	spectrum	spectrum	NOUN
ejpam-1882	28	16	of	of	ADP
ejpam-1882	28	17	the	the	DET
ejpam-1882	28	18	operator	operator	NOUN
ejpam-1882	28	19	.	.	PUNCT
ejpam-1882	29	1	w	w	PROPN
ejpam-1882	29	2	(	(	PUNCT
ejpam-1882	29	3	t	t	PROPN
ejpam-1882	29	4	)	)	PUNCT
ejpam-1882	29	5	is	be	AUX
ejpam-1882	29	6	a	a	DET
ejpam-1882	29	7	connected	connect	VERB
ejpam-1882	29	8	set	set	NOUN
ejpam-1882	29	9	and	and	CCONJ
ejpam-1882	29	10	for	for	ADP
ejpam-1882	29	11	normal	normal	ADJ
ejpam-1882	29	12	operator	operator	NOUN
ejpam-1882	29	13	n	n	NOUN
ejpam-1882	29	14	,	,	PUNCT
ejpam-1882	29	15	w	w	PROPN
ejpam-1882	29	16	(	(	PUNCT
ejpam-1882	29	17	n	n	CCONJ
ejpam-1882	29	18	)	)	PUNCT
ejpam-1882	29	19	=	=	SYM
ejpam-1882	29	20	co(σ(n	co(σ(n	X
ejpam-1882	29	21	)	)	PUNCT
ejpam-1882	29	22	)	)	PUNCT
ejpam-1882	29	23	,	,	PUNCT
ejpam-1882	29	24	(	(	PUNCT
ejpam-1882	29	25	2	2	X
ejpam-1882	29	26	)	)	PUNCT
ejpam-1882	29	27	where	where	SCONJ
ejpam-1882	29	28	σ(n	σ(n	NOUN
ejpam-1882	29	29	)	)	PUNCT
ejpam-1882	29	30	is	be	AUX
ejpam-1882	29	31	the	the	DET
ejpam-1882	29	32	spectrum	spectrum	NOUN
ejpam-1882	29	33	of	of	ADP
ejpam-1882	29	34	n	n	PROPN
ejpam-1882	29	35	.	.	PUNCT
ejpam-1882	30	1	also	also	ADV
ejpam-1882	30	2	we	we	PRON
ejpam-1882	30	3	need	need	VERB
ejpam-1882	30	4	to	to	ADP
ejpam-1882	30	5	the	the	DET
ejpam-1882	30	6	following	following	ADJ
ejpam-1882	30	7	theorem	theorem	NOUN
ejpam-1882	30	8	which	which	PRON
ejpam-1882	30	9	can	can	AUX
ejpam-1882	30	10	be	be	AUX
ejpam-1882	30	11	found	find	VERB
ejpam-1882	30	12	in	in	ADP
ejpam-1882	30	13	[	[	X
ejpam-1882	30	14	3	3	NUM
ejpam-1882	30	15	]	]	PUNCT
ejpam-1882	30	16	.	.	PUNCT
ejpam-1882	31	1	theorem	theorem	NOUN
ejpam-1882	31	2	1	1	X
ejpam-1882	31	3	.	.	PUNCT
ejpam-1882	32	1	let	let	VERB
ejpam-1882	32	2	t	t	PROPN
ejpam-1882	32	3	be	be	AUX
ejpam-1882	32	4	a	a	DET
ejpam-1882	32	5	bounded	bounded	ADJ
ejpam-1882	32	6	linear	linear	ADJ
ejpam-1882	32	7	operator	operator	NOUN
ejpam-1882	32	8	t	t	PROPN
ejpam-1882	32	9	on	on	ADP
ejpam-1882	32	10	a	a	DET
ejpam-1882	32	11	hilbert	hilbert	NOUN
ejpam-1882	32	12	space	space	NOUN
ejpam-1882	32	13	h	h	NOUN
ejpam-1882	32	14	and	and	CCONJ
ejpam-1882	32	15	λ	λ	PROPN
ejpam-1882	32	16	outside	outside	ADP
ejpam-1882	32	17	w	w	PROPN
ejpam-1882	32	18	(	(	PUNCT
ejpam-1882	32	19	t	t	PROPN
ejpam-1882	32	20	)	)	PUNCT
ejpam-1882	32	21	.	.	PUNCT
ejpam-1882	33	1	then	then	ADV
ejpam-1882	33	2	dist(λ	dist(λ	PROPN
ejpam-1882	33	3	,	,	PUNCT
ejpam-1882	33	4	w	w	PROPN
ejpam-1882	33	5	(	(	PUNCT
ejpam-1882	33	6	t	t	NOUN
ejpam-1882	33	7	)	)	PUNCT
ejpam-1882	33	8	)	)	PUNCT
ejpam-1882	33	9	≤	≤	NOUN
ejpam-1882	34	1	‖(λ−	‖(λ−	NUM
ejpam-1882	34	2	t	t	NOUN
ejpam-1882	34	3	)	)	PUNCT
ejpam-1882	34	4	−1‖−1	−1‖−1	NOUN
ejpam-1882	34	5	.	.	PUNCT
ejpam-1882	35	1	(	(	PUNCT
ejpam-1882	35	2	3	3	X
ejpam-1882	35	3	)	)	PUNCT
ejpam-1882	35	4	for	for	ADP
ejpam-1882	35	5	the	the	DET
ejpam-1882	35	6	operator	operator	NOUN
ejpam-1882	35	7	nµ	nµ	ADV
ejpam-1882	35	8	as	as	ADV
ejpam-1882	35	9	defined	define	VERB
ejpam-1882	35	10	in	in	ADP
ejpam-1882	35	11	the	the	DET
ejpam-1882	35	12	first	first	ADJ
ejpam-1882	35	13	paragraph	paragraph	NOUN
ejpam-1882	35	14	,	,	PUNCT
ejpam-1882	35	15	we	we	PRON
ejpam-1882	35	16	have	have	VERB
ejpam-1882	35	17	w	w	PROPN
ejpam-1882	35	18	(	(	PUNCT
ejpam-1882	35	19	nµ	nµ	NOUN
ejpam-1882	35	20	)	)	PUNCT
ejpam-1882	35	21	=	=	SYM
ejpam-1882	36	1	k	k	PROPN
ejpam-1882	36	2	and	and	CCONJ
ejpam-1882	36	3	the	the	DET
ejpam-1882	36	4	above	above	ADJ
ejpam-1882	36	5	theorem	theorem	NOUN
ejpam-1882	36	6	implies	imply	VERB
ejpam-1882	36	7	that	that	SCONJ
ejpam-1882	36	8	:	:	PUNCT
ejpam-1882	36	9	dist(λ	dist(λ	X
ejpam-1882	36	10	,	,	PUNCT
ejpam-1882	36	11	k)≤	k)≤	PRON
ejpam-1882	36	12	‖(λ−	‖(λ−	NUM
ejpam-1882	36	13	nµ	nµ	NOUN
ejpam-1882	36	14	)	)	PUNCT
ejpam-1882	36	15	−1‖−1	−1‖−1	NOUN
ejpam-1882	36	16	.	.	PUNCT
ejpam-1882	37	1	(	(	PUNCT
ejpam-1882	37	2	4	4	X
ejpam-1882	37	3	)	)	PUNCT
ejpam-1882	37	4	now	now	ADV
ejpam-1882	37	5	the	the	DET
ejpam-1882	37	6	result	result	NOUN
ejpam-1882	37	7	follows	follow	VERB
ejpam-1882	37	8	from	from	ADP
ejpam-1882	37	9	(	(	PUNCT
ejpam-1882	37	10	1	1	NUM
ejpam-1882	37	11	)	)	PUNCT
ejpam-1882	37	12	and	and	CCONJ
ejpam-1882	37	13	(	(	PUNCT
ejpam-1882	37	14	4	4	NUM
ejpam-1882	37	15	)	)	PUNCT
ejpam-1882	37	16	.	.	PUNCT
ejpam-1882	38	1	references	reference	NOUN
ejpam-1882	38	2	[	[	X
ejpam-1882	38	3	1	1	X
ejpam-1882	38	4	]	]	PUNCT
ejpam-1882	38	5	j.	j.	PROPN
ejpam-1882	38	6	b.	b.	PROPN
ejpam-1882	38	7	conway	conway	PROPN
ejpam-1882	38	8	,	,	PUNCT
ejpam-1882	38	9	a	a	DET
ejpam-1882	38	10	course	course	NOUN
ejpam-1882	38	11	in	in	ADP
ejpam-1882	38	12	functional	functional	ADJ
ejpam-1882	38	13	analysis	analysis	NOUN
ejpam-1882	38	14	,	,	PUNCT
ejpam-1882	38	15	second	second	ADJ
ejpam-1882	38	16	ed	ed	NOUN
ejpam-1882	38	17	.	.	PROPN
ejpam-1882	38	18	,	,	PUNCT
ejpam-1882	38	19	springer	springer	NOUN
ejpam-1882	38	20	-	-	PUNCT
ejpam-1882	38	21	verlag	verlag	PROPN
ejpam-1882	38	22	,	,	PUNCT
ejpam-1882	38	23	new	new	PROPN
ejpam-1882	38	24	york	york	PROPN
ejpam-1882	38	25	,	,	PUNCT
ejpam-1882	38	26	1985	1985	NUM
ejpam-1882	38	27	.	.	PUNCT
ejpam-1882	39	1	[	[	X
ejpam-1882	39	2	2	2	X
ejpam-1882	39	3	]	]	PUNCT
ejpam-1882	39	4	p.	p.	PROPN
ejpam-1882	39	5	r.	r.	PROPN
ejpam-1882	39	6	halmos	halmos	PROPN
ejpam-1882	39	7	.	.	PUNCT
ejpam-1882	40	1	a	a	DET
ejpam-1882	40	2	hilbert	hilbert	PROPN
ejpam-1882	40	3	space	space	NOUN
ejpam-1882	40	4	problem	problem	NOUN
ejpam-1882	40	5	book	book	NOUN
ejpam-1882	40	6	,	,	PUNCT
ejpam-1882	40	7	second	second	ADJ
ejpam-1882	40	8	edition	edition	NOUN
ejpam-1882	40	9	,	,	PUNCT
ejpam-1882	40	10	springer	springer	NOUN
ejpam-1882	40	11	,	,	PUNCT
ejpam-1882	40	12	new	new	PROPN
ejpam-1882	40	13	york	york	PROPN
ejpam-1882	40	14	,	,	PUNCT
ejpam-1882	40	15	1982	1982	NUM
ejpam-1882	40	16	.	.	PUNCT
ejpam-1882	41	1	[	[	X
ejpam-1882	41	2	3	3	X
ejpam-1882	41	3	]	]	X
ejpam-1882	41	4	f.	f.	PROPN
ejpam-1882	41	5	j.	j.	PROPN
ejpam-1882	41	6	narcowich	narcowich	PROPN
ejpam-1882	41	7	.	.	PUNCT
ejpam-1882	42	1	analytic	analytic	ADJ
ejpam-1882	42	2	properties	property	NOUN
ejpam-1882	42	3	of	of	ADP
ejpam-1882	42	4	the	the	DET
ejpam-1882	42	5	boundary	boundary	NOUN
ejpam-1882	42	6	of	of	ADP
ejpam-1882	42	7	the	the	DET
ejpam-1882	42	8	numerical	numerical	ADJ
ejpam-1882	42	9	range	range	NOUN
ejpam-1882	42	10	,	,	PUNCT
ejpam-1882	42	11	indiana	indiana	PROPN
ejpam-1882	42	12	university	university	PROPN
ejpam-1882	42	13	mathematics	mathematics	PROPN
ejpam-1882	42	14	journal	journal	NOUN
ejpam-1882	42	15	,	,	PUNCT
ejpam-1882	42	16	29	29	NUM
ejpam-1882	42	17	,	,	PUNCT
ejpam-1882	42	18	67	67	NUM
ejpam-1882	42	19	-	-	SYM
ejpam-1882	42	20	77	77	NUM
ejpam-1882	42	21	.	.	PUNCT
ejpam-1882	42	22	1980	1980	NUM
ejpam-1882	42	23	.	.	PUNCT