id	sid	tid	token	lemma	pos
ejpam-2371	1	1	compile	compile	NOUN
ejpam-2371	1	2	/	/	SYM
ejpam-2371	1	3	output.dvi	output.dvi	NOUN
ejpam-2371	1	4	european	european	ADJ
ejpam-2371	1	5	journal	journal	NOUN
ejpam-2371	1	6	of	of	ADP
ejpam-2371	1	7	pure	pure	ADJ
ejpam-2371	1	8	and	and	CCONJ
ejpam-2371	1	9	applied	apply	VERB
ejpam-2371	1	10	mathematics	mathematic	NOUN
ejpam-2371	1	11	vol	vol	NOUN
ejpam-2371	1	12	.	.	PROPN
ejpam-2371	1	13	8	8	NUM
ejpam-2371	1	14	,	,	PUNCT
ejpam-2371	1	15	no	no	INTJ
ejpam-2371	1	16	.	.	NOUN
ejpam-2371	1	17	4	4	NUM
ejpam-2371	1	18	,	,	PUNCT
ejpam-2371	1	19	2015	2015	NUM
ejpam-2371	1	20	,	,	PUNCT
ejpam-2371	1	21	499	499	NUM
ejpam-2371	1	22	-	-	SYM
ejpam-2371	1	23	501	501	NUM
ejpam-2371	1	24	issn	issn	PROPN
ejpam-2371	1	25	1307	1307	NUM
ejpam-2371	1	26	-	-	SYM
ejpam-2371	1	27	5543	5543	NUM
ejpam-2371	1	28	–	–	PUNCT
ejpam-2371	1	29	www.ejpam.com	www.ejpam.com	X
ejpam-2371	1	30	simpler	simple	ADJ
ejpam-2371	1	31	proof	proof	NOUN
ejpam-2371	1	32	of	of	ADP
ejpam-2371	1	33	the	the	DET
ejpam-2371	1	34	ringrose	ringrose	NOUN
ejpam-2371	1	35	’s	’s	PART
ejpam-2371	1	36	characterization	characterization	NOUN
ejpam-2371	1	37	of	of	ADP
ejpam-2371	1	38	compact	compact	ADJ
ejpam-2371	1	39	operators	operator	NOUN
ejpam-2371	1	40	aydin	aydin	VERB
ejpam-2371	1	41	sh	sh	PROPN
ejpam-2371	1	42	.	.	PROPN
ejpam-2371	1	43	shukurov	shukurov	PROPN
ejpam-2371	1	44	institute	institute	PROPN
ejpam-2371	1	45	of	of	ADP
ejpam-2371	1	46	mathematics	mathematics	PROPN
ejpam-2371	1	47	and	and	CCONJ
ejpam-2371	1	48	mechanics	mechanic	NOUN
ejpam-2371	1	49	,	,	PUNCT
ejpam-2371	1	50	nas	nas	PROPN
ejpam-2371	1	51	of	of	ADP
ejpam-2371	1	52	azerbaijan	azerbaijan	PROPN
ejpam-2371	1	53	,	,	PUNCT
ejpam-2371	1	54	az1141	az1141	ADJ
ejpam-2371	1	55	,	,	PUNCT
ejpam-2371	1	56	b.vahabzade	b.vahabzade	NOUN
ejpam-2371	1	57	9	9	NUM
ejpam-2371	1	58	,	,	PUNCT
ejpam-2371	1	59	baku	baku	PROPN
ejpam-2371	1	60	,	,	PUNCT
ejpam-2371	1	61	azerbaijan	azerbaijan	PROPN
ejpam-2371	1	62	abstract	abstract	NOUN
ejpam-2371	1	63	.	.	PUNCT
ejpam-2371	2	1	the	the	DET
ejpam-2371	2	2	aim	aim	NOUN
ejpam-2371	2	3	of	of	ADP
ejpam-2371	2	4	this	this	DET
ejpam-2371	2	5	note	note	NOUN
ejpam-2371	2	6	is	be	AUX
ejpam-2371	2	7	to	to	PART
ejpam-2371	2	8	give	give	VERB
ejpam-2371	2	9	short	short	ADJ
ejpam-2371	2	10	,	,	PUNCT
ejpam-2371	2	11	simpler	simple	ADJ
ejpam-2371	2	12	and	and	CCONJ
ejpam-2371	2	13	elementary	elementary	ADJ
ejpam-2371	2	14	proof	proof	NOUN
ejpam-2371	2	15	of	of	ADP
ejpam-2371	2	16	one	one	NUM
ejpam-2371	2	17	characterization	characterization	NOUN
ejpam-2371	2	18	of	of	ADP
ejpam-2371	2	19	compact	compact	ADJ
ejpam-2371	2	20	operators	operator	NOUN
ejpam-2371	2	21	via	via	ADP
ejpam-2371	2	22	orthonormal	orthonormal	ADJ
ejpam-2371	2	23	sequences	sequence	NOUN
ejpam-2371	2	24	,	,	PUNCT
ejpam-2371	2	25	which	which	PRON
ejpam-2371	2	26	,	,	PUNCT
ejpam-2371	2	27	hopefully	hopefully	ADV
ejpam-2371	2	28	will	will	AUX
ejpam-2371	2	29	make	make	VERB
ejpam-2371	2	30	this	this	DET
ejpam-2371	2	31	fact	fact	NOUN
ejpam-2371	2	32	more	more	ADV
ejpam-2371	2	33	accessible	accessible	ADJ
ejpam-2371	2	34	to	to	ADP
ejpam-2371	2	35	nonspecialists	nonspecialists	PROPN
ejpam-2371	2	36	and	and	CCONJ
ejpam-2371	2	37	to	to	ADP
ejpam-2371	2	38	a	a	DET
ejpam-2371	2	39	wide	wide	ADJ
ejpam-2371	2	40	audience	audience	NOUN
ejpam-2371	2	41	(	(	PUNCT
ejpam-2371	2	42	especially	especially	ADV
ejpam-2371	2	43	to	to	ADP
ejpam-2371	2	44	students	student	NOUN
ejpam-2371	2	45	)	)	PUNCT
ejpam-2371	2	46	.	.	PUNCT
ejpam-2371	3	1	beside	beside	ADP
ejpam-2371	3	2	this	this	PRON
ejpam-2371	3	3	,	,	PUNCT
ejpam-2371	3	4	the	the	DET
ejpam-2371	3	5	proof	proof	NOUN
ejpam-2371	3	6	given	give	VERB
ejpam-2371	3	7	here	here	ADV
ejpam-2371	3	8	shows	show	VERB
ejpam-2371	3	9	that	that	SCONJ
ejpam-2371	3	10	this	this	DET
ejpam-2371	3	11	fact	fact	NOUN
ejpam-2371	3	12	holds	hold	VERB
ejpam-2371	3	13	true	true	ADJ
ejpam-2371	3	14	for	for	ADP
ejpam-2371	3	15	operator	operator	NOUN
ejpam-2371	3	16	acting	act	VERB
ejpam-2371	3	17	from	from	ADP
ejpam-2371	3	18	hilbert	hilbert	NOUN
ejpam-2371	3	19	space	space	NOUN
ejpam-2371	3	20	to	to	ADP
ejpam-2371	3	21	some	some	DET
ejpam-2371	3	22	banach	banach	NOUN
ejpam-2371	3	23	(	(	PUNCT
ejpam-2371	3	24	not	not	PART
ejpam-2371	3	25	necessarily	necessarily	ADV
ejpam-2371	3	26	hilbert	hilbert	NOUN
ejpam-2371	3	27	)	)	PUNCT
ejpam-2371	3	28	space	space	NOUN
ejpam-2371	3	29	.	.	PUNCT
ejpam-2371	4	1	2010	2010	NUM
ejpam-2371	4	2	mathematics	mathematic	NOUN
ejpam-2371	4	3	subject	subject	NOUN
ejpam-2371	4	4	classifications	classification	NOUN
ejpam-2371	4	5	:	:	PUNCT
ejpam-2371	4	6	46b25	46b25	NUM
ejpam-2371	4	7	,	,	PUNCT
ejpam-2371	4	8	47b07	47b07	NUM
ejpam-2371	4	9	.	.	PUNCT
ejpam-2371	5	1	key	key	ADJ
ejpam-2371	5	2	words	word	NOUN
ejpam-2371	5	3	and	and	CCONJ
ejpam-2371	5	4	phrases	phrase	NOUN
ejpam-2371	5	5	:	:	PUNCT
ejpam-2371	5	6	orthonormal	orthonormal	ADJ
ejpam-2371	5	7	sequence	sequence	NOUN
ejpam-2371	5	8	and	and	CCONJ
ejpam-2371	5	9	orthonormal	orthonormal	ADJ
ejpam-2371	5	10	bases	basis	NOUN
ejpam-2371	5	11	in	in	ADP
ejpam-2371	5	12	hilbert	hilbert	PROPN
ejpam-2371	5	13	space	space	NOUN
ejpam-2371	5	14	,	,	PUNCT
ejpam-2371	5	15	ringrose	ringrose	VERB
ejpam-2371	5	16	’s	’s	PART
ejpam-2371	5	17	characterization	characterization	NOUN
ejpam-2371	5	18	of	of	ADP
ejpam-2371	5	19	compact	compact	ADJ
ejpam-2371	5	20	operators	operator	NOUN
ejpam-2371	5	21	,	,	PUNCT
ejpam-2371	5	22	linear	linear	PROPN
ejpam-2371	5	23	operators	operator	NOUN
ejpam-2371	5	24	,	,	PUNCT
ejpam-2371	5	25	compact	compact	ADJ
ejpam-2371	5	26	operators	operator	NOUN
ejpam-2371	5	27	1	1	NUM
ejpam-2371	5	28	.	.	PUNCT
ejpam-2371	6	1	introduction	introduction	NOUN
ejpam-2371	6	2	the	the	DET
ejpam-2371	6	3	aim	aim	NOUN
ejpam-2371	6	4	of	of	ADP
ejpam-2371	6	5	this	this	DET
ejpam-2371	6	6	note	note	NOUN
ejpam-2371	6	7	is	be	AUX
ejpam-2371	6	8	to	to	PART
ejpam-2371	6	9	give	give	VERB
ejpam-2371	6	10	short	short	ADJ
ejpam-2371	6	11	,	,	PUNCT
ejpam-2371	6	12	simpler	simple	ADJ
ejpam-2371	6	13	and	and	CCONJ
ejpam-2371	6	14	elementary	elementary	ADJ
ejpam-2371	6	15	proof	proof	NOUN
ejpam-2371	6	16	of	of	ADP
ejpam-2371	6	17	the	the	DET
ejpam-2371	6	18	following	follow	VERB
ejpam-2371	6	19	theorem	theorem	NOUN
ejpam-2371	6	20	1	1	NUM
ejpam-2371	6	21	.	.	PUNCT
ejpam-2371	7	1	linear	linear	PROPN
ejpam-2371	7	2	(	(	PUNCT
ejpam-2371	7	3	not	not	PART
ejpam-2371	7	4	necessarily	necessarily	ADV
ejpam-2371	7	5	bounded	bound	VERB
ejpam-2371	7	6	)	)	PUNCT
ejpam-2371	7	7	operator	operator	NOUN
ejpam-2371	7	8	acting	act	VERB
ejpam-2371	7	9	on	on	ADP
ejpam-2371	7	10	a	a	DET
ejpam-2371	7	11	hilbert	hilbert	NOUN
ejpam-2371	7	12	space	space	NOUN
ejpam-2371	7	13	h	h	NOUN
ejpam-2371	7	14	is	be	AUX
ejpam-2371	7	15	compact	compact	ADJ
ejpam-2371	7	16	if	if	SCONJ
ejpam-2371	8	1	and	and	CCONJ
ejpam-2371	8	2	only	only	ADV
ejpam-2371	8	3	if	if	SCONJ
ejpam-2371	8	4	it	it	PRON
ejpam-2371	8	5	satisfies	satisfy	VERB
ejpam-2371	8	6	‖aen‖	‖aen‖	PUNCT
ejpam-2371	8	7	→	→	SYM
ejpam-2371	8	8	0	0	NUM
ejpam-2371	8	9	for	for	ADP
ejpam-2371	8	10	each	each	DET
ejpam-2371	8	11	orthonormal	orthonormal	ADJ
ejpam-2371	8	12	sequence	sequence	NOUN
ejpam-2371	8	13	�	�	X
ejpam-2371	8	14	en	en	X
ejpam-2371	8	15	in	in	ADP
ejpam-2371	8	16	h.	h.	PROPN
ejpam-2371	8	17	the	the	DET
ejpam-2371	8	18	proof	proof	NOUN
ejpam-2371	8	19	of	of	ADP
ejpam-2371	8	20	this	this	DET
ejpam-2371	8	21	theorem	theorem	NOUN
ejpam-2371	8	22	for	for	ADP
ejpam-2371	8	23	bounded	bound	VERB
ejpam-2371	8	24	linear	linear	PROPN
ejpam-2371	8	25	operators	operator	NOUN
ejpam-2371	8	26	can	can	AUX
ejpam-2371	8	27	be	be	AUX
ejpam-2371	8	28	found	find	VERB
ejpam-2371	8	29	in	in	ADP
ejpam-2371	8	30	[	[	X
ejpam-2371	8	31	3	3	NUM
ejpam-2371	8	32	]	]	PUNCT
ejpam-2371	8	33	.	.	PUNCT
ejpam-2371	9	1	it	it	PRON
ejpam-2371	9	2	is	be	AUX
ejpam-2371	9	3	shown	show	VERB
ejpam-2371	9	4	in	in	ADP
ejpam-2371	9	5	[	[	X
ejpam-2371	9	6	2	2	X
ejpam-2371	9	7	]	]	PUNCT
ejpam-2371	9	8	that	that	DET
ejpam-2371	9	9	continuity	continuity	NOUN
ejpam-2371	9	10	assumption	assumption	NOUN
ejpam-2371	9	11	on	on	ADP
ejpam-2371	9	12	a	a	DET
ejpam-2371	9	13	is	be	AUX
ejpam-2371	9	14	superfluous	superfluous	ADJ
ejpam-2371	9	15	.	.	PUNCT
ejpam-2371	10	1	note	note	VERB
ejpam-2371	10	2	that	that	SCONJ
ejpam-2371	10	3	,	,	PUNCT
ejpam-2371	10	4	the	the	DET
ejpam-2371	10	5	following	following	NOUN
ejpam-2371	10	6	,	,	PUNCT
ejpam-2371	10	7	in	in	ADP
ejpam-2371	10	8	some	some	DET
ejpam-2371	10	9	sense	sense	NOUN
ejpam-2371	10	10	more	more	ADV
ejpam-2371	10	11	general	general	ADJ
ejpam-2371	10	12	fact	fact	NOUN
ejpam-2371	10	13	is	be	AUX
ejpam-2371	10	14	also	also	ADV
ejpam-2371	10	15	valid	valid	ADJ
ejpam-2371	10	16	:	:	PUNCT
ejpam-2371	10	17	linear	linear	ADJ
ejpam-2371	10	18	(	(	PUNCT
ejpam-2371	10	19	not	not	PART
ejpam-2371	10	20	necessarily	necessarily	ADV
ejpam-2371	10	21	bounded	bound	VERB
ejpam-2371	10	22	)	)	PUNCT
ejpam-2371	10	23	operator	operator	NOUN
ejpam-2371	10	24	acting	act	VERB
ejpam-2371	10	25	on	on	ADP
ejpam-2371	10	26	a	a	DET
ejpam-2371	10	27	hilbert	hilbert	NOUN
ejpam-2371	10	28	space	space	NOUN
ejpam-2371	10	29	h	h	NOUN
ejpam-2371	10	30	is	be	AUX
ejpam-2371	10	31	compact	compact	ADJ
ejpam-2371	10	32	if	if	SCONJ
ejpam-2371	10	33	and	and	CCONJ
ejpam-2371	10	34	only	only	ADV
ejpam-2371	10	35	if	if	SCONJ
ejpam-2371	10	36	it	it	PRON
ejpam-2371	10	37	satisfies	satisfy	VERB
ejpam-2371	10	38	(	(	PUNCT
ejpam-2371	10	39	aen	aen	PROPN
ejpam-2371	10	40	,	,	PUNCT
ejpam-2371	10	41	en)→	en)→	X
ejpam-2371	10	42	0	0	PUNCT
ejpam-2371	10	43	for	for	ADP
ejpam-2371	10	44	each	each	DET
ejpam-2371	10	45	orthonormal	orthonormal	ADJ
ejpam-2371	10	46	sequence	sequence	NOUN
ejpam-2371	10	47	�	�	X
ejpam-2371	10	48	en	en	X
ejpam-2371	10	49	in	in	ADP
ejpam-2371	10	50	h.	h.	PROPN
ejpam-2371	10	51	for	for	ADP
ejpam-2371	10	52	bounded	bounded	ADJ
ejpam-2371	10	53	operator	operator	NOUN
ejpam-2371	10	54	this	this	DET
ejpam-2371	10	55	proposition	proposition	NOUN
ejpam-2371	10	56	can	can	AUX
ejpam-2371	10	57	be	be	AUX
ejpam-2371	10	58	found	find	VERB
ejpam-2371	10	59	in	in	ADP
ejpam-2371	10	60	[	[	X
ejpam-2371	10	61	1	1	NUM
ejpam-2371	10	62	,	,	PUNCT
ejpam-2371	10	63	4	4	NUM
ejpam-2371	10	64	,	,	PUNCT
ejpam-2371	10	65	5	5	NUM
ejpam-2371	10	66	]	]	PUNCT
ejpam-2371	10	67	.	.	PUNCT
ejpam-2371	11	1	it	it	PRON
ejpam-2371	11	2	is	be	AUX
ejpam-2371	11	3	shown	show	VERB
ejpam-2371	11	4	in	in	ADP
ejpam-2371	11	5	[	[	X
ejpam-2371	11	6	2	2	X
ejpam-2371	11	7	]	]	PUNCT
ejpam-2371	11	8	that	that	SCONJ
ejpam-2371	11	9	this	this	DET
ejpam-2371	11	10	fact	fact	NOUN
ejpam-2371	11	11	remains	remain	VERB
ejpam-2371	11	12	valid	valid	ADJ
ejpam-2371	11	13	without	without	ADP
ejpam-2371	11	14	boundedness	boundedness	NOUN
ejpam-2371	11	15	condition	condition	NOUN
ejpam-2371	11	16	.	.	PUNCT
ejpam-2371	12	1	note	note	VERB
ejpam-2371	12	2	that	that	SCONJ
ejpam-2371	12	3	this	this	DET
ejpam-2371	12	4	proposition	proposition	NOUN
ejpam-2371	12	5	can	can	AUX
ejpam-2371	12	6	be	be	AUX
ejpam-2371	12	7	proved	prove	VERB
ejpam-2371	12	8	(	(	PUNCT
ejpam-2371	12	9	which	which	PRON
ejpam-2371	12	10	is	be	AUX
ejpam-2371	12	11	seen	see	VERB
ejpam-2371	12	12	from	from	ADP
ejpam-2371	12	13	the	the	DET
ejpam-2371	12	14	cited	cite	VERB
ejpam-2371	12	15	references	reference	NOUN
ejpam-2371	12	16	)	)	PUNCT
ejpam-2371	12	17	by	by	ADP
ejpam-2371	12	18	reducing	reduce	VERB
ejpam-2371	12	19	it	it	PRON
ejpam-2371	12	20	to	to	ADP
ejpam-2371	12	21	the	the	DET
ejpam-2371	12	22	above	above	ADJ
ejpam-2371	12	23	theorem	theorem	PROPN
ejpam-2371	12	24	.	.	PUNCT
ejpam-2371	13	1	note	note	VERB
ejpam-2371	13	2	that	that	SCONJ
ejpam-2371	13	3	the	the	DET
ejpam-2371	13	4	proof	proof	NOUN
ejpam-2371	13	5	of	of	ADP
ejpam-2371	13	6	the	the	DET
ejpam-2371	13	7	theorem	theorem	NOUN
ejpam-2371	13	8	given	give	VERB
ejpam-2371	13	9	below	below	ADP
ejpam-2371	13	10	shows	show	VERB
ejpam-2371	13	11	that	that	SCONJ
ejpam-2371	13	12	the	the	DET
ejpam-2371	13	13	proposition	proposition	NOUN
ejpam-2371	13	14	of	of	ADP
ejpam-2371	13	15	this	this	DET
ejpam-2371	13	16	theorem	theorem	NOUN
ejpam-2371	13	17	is	be	AUX
ejpam-2371	13	18	also	also	ADV
ejpam-2371	13	19	true	true	ADJ
ejpam-2371	13	20	for	for	ADP
ejpam-2371	13	21	an	an	DET
ejpam-2371	13	22	operator	operator	NOUN
ejpam-2371	13	23	,	,	PUNCT
ejpam-2371	13	24	acting	act	VERB
ejpam-2371	13	25	from	from	ADP
ejpam-2371	13	26	a	a	DET
ejpam-2371	13	27	hilbert	hilbert	NOUN
ejpam-2371	13	28	space	space	NOUN
ejpam-2371	13	29	to	to	ADP
ejpam-2371	13	30	some	some	DET
ejpam-2371	13	31	banach	banach	NOUN
ejpam-2371	13	32	space	space	NOUN
ejpam-2371	13	33	.	.	PUNCT
ejpam-2371	14	1	hopefully	hopefully	ADV
ejpam-2371	14	2	the	the	DET
ejpam-2371	14	3	exposition	exposition	NOUN
ejpam-2371	14	4	given	give	VERB
ejpam-2371	14	5	in	in	ADP
ejpam-2371	14	6	this	this	DET
ejpam-2371	14	7	short	short	ADJ
ejpam-2371	14	8	note	note	NOUN
ejpam-2371	14	9	will	will	AUX
ejpam-2371	14	10	make	make	VERB
ejpam-2371	14	11	the	the	DET
ejpam-2371	14	12	theorem	theorem	NOUN
ejpam-2371	14	13	and	and	CCONJ
ejpam-2371	14	14	its	its	PRON
ejpam-2371	14	15	generalization	generalization	NOUN
ejpam-2371	14	16	(	(	PUNCT
ejpam-2371	14	17	mentioned	mention	VERB
ejpam-2371	14	18	above	above	ADV
ejpam-2371	14	19	)	)	PUNCT
ejpam-2371	14	20	more	more	ADV
ejpam-2371	14	21	accessible	accessible	ADJ
ejpam-2371	14	22	to	to	ADP
ejpam-2371	14	23	a	a	DET
ejpam-2371	14	24	wide	wide	ADJ
ejpam-2371	14	25	audience	audience	NOUN
ejpam-2371	14	26	(	(	PUNCT
ejpam-2371	14	27	especially	especially	ADV
ejpam-2371	14	28	to	to	ADP
ejpam-2371	14	29	students	student	NOUN
ejpam-2371	14	30	)	)	PUNCT
ejpam-2371	14	31	.	.	PUNCT
ejpam-2371	15	1	email	email	NOUN
ejpam-2371	15	2	address	address	NOUN
ejpam-2371	15	3	:	:	PUNCT
ejpam-2371	15	4	ashshukurov@gmail.com	ashshukurov@gmail.com	X
ejpam-2371	15	5	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2371	16	1	499	499	NUM
ejpam-2371	16	2	c	c	NOUN
ejpam-2371	16	3	©	©	PROPN
ejpam-2371	16	4	2015	2015	NUM
ejpam-2371	16	5	ejpam	ejpam	NOUN
ejpam-2371	16	6	all	all	DET
ejpam-2371	16	7	rights	right	NOUN
ejpam-2371	16	8	reserved	reserve	VERB
ejpam-2371	16	9	.	.	PUNCT
ejpam-2371	17	1	a.	a.	PROPN
ejpam-2371	17	2	shukurov	shukurov	PROPN
ejpam-2371	17	3	/	/	SYM
ejpam-2371	17	4	eur	eur	PROPN
ejpam-2371	17	5	.	.	PUNCT
ejpam-2371	18	1	j.	j.	PROPN
ejpam-2371	18	2	pure	pure	PROPN
ejpam-2371	18	3	appl	appl	PROPN
ejpam-2371	18	4	.	.	PROPN
ejpam-2371	18	5	math	math	PROPN
ejpam-2371	18	6	,	,	PUNCT
ejpam-2371	18	7	8	8	NUM
ejpam-2371	18	8	(	(	PUNCT
ejpam-2371	18	9	2015	2015	NUM
ejpam-2371	18	10	)	)	PUNCT
ejpam-2371	18	11	,	,	PUNCT
ejpam-2371	18	12	499	499	NUM
ejpam-2371	18	13	-	-	SYM
ejpam-2371	18	14	501	501	NUM
ejpam-2371	18	15	500	500	NUM
ejpam-2371	18	16	2	2	NUM
ejpam-2371	18	17	.	.	PUNCT
ejpam-2371	18	18	main	main	ADJ
ejpam-2371	18	19	result	result	NOUN
ejpam-2371	18	20	and	and	CCONJ
ejpam-2371	18	21	its	its	PRON
ejpam-2371	18	22	proof	proof	NOUN
ejpam-2371	18	23	theorem	theorem	VERB
ejpam-2371	18	24	2	2	NUM
ejpam-2371	18	25	.	.	PUNCT
ejpam-2371	19	1	linear	linear	PROPN
ejpam-2371	19	2	(	(	PUNCT
ejpam-2371	19	3	not	not	PART
ejpam-2371	19	4	necessarily	necessarily	ADV
ejpam-2371	19	5	bounded	bound	VERB
ejpam-2371	19	6	)	)	PUNCT
ejpam-2371	19	7	operator	operator	NOUN
ejpam-2371	19	8	acting	act	VERB
ejpam-2371	19	9	from	from	ADP
ejpam-2371	19	10	a	a	DET
ejpam-2371	19	11	hilbert	hilbert	NOUN
ejpam-2371	19	12	space	space	NOUN
ejpam-2371	19	13	h	h	NOUN
ejpam-2371	19	14	to	to	ADP
ejpam-2371	19	15	some	some	DET
ejpam-2371	19	16	banach	banach	NOUN
ejpam-2371	19	17	space	space	NOUN
ejpam-2371	19	18	is	be	AUX
ejpam-2371	19	19	compact	compact	ADJ
ejpam-2371	19	20	if	if	SCONJ
ejpam-2371	20	1	and	and	CCONJ
ejpam-2371	20	2	only	only	ADV
ejpam-2371	20	3	if	if	SCONJ
ejpam-2371	20	4	it	it	PRON
ejpam-2371	20	5	satisfies	satisfy	VERB
ejpam-2371	20	6	‖aen‖	‖aen‖	PUNCT
ejpam-2371	20	7	→	→	SYM
ejpam-2371	20	8	0	0	NUM
ejpam-2371	20	9	for	for	ADP
ejpam-2371	20	10	each	each	DET
ejpam-2371	20	11	orthonormal	orthonormal	ADJ
ejpam-2371	20	12	sequence	sequence	NOUN
ejpam-2371	20	13	�	�	X
ejpam-2371	20	14	en	en	X
ejpam-2371	20	15	in	in	ADP
ejpam-2371	20	16	h.	h.	PROPN
ejpam-2371	20	17	proof	proof	NOUN
ejpam-2371	20	18	.	.	PUNCT
ejpam-2371	21	1	one	one	PRON
ejpam-2371	21	2	has	have	VERB
ejpam-2371	21	3	to	to	PART
ejpam-2371	21	4	prove	prove	VERB
ejpam-2371	21	5	only	only	ADV
ejpam-2371	21	6	sufficiency	sufficiency	NOUN
ejpam-2371	21	7	of	of	ADP
ejpam-2371	21	8	the	the	DET
ejpam-2371	21	9	above	above	ADJ
ejpam-2371	21	10	condition	condition	NOUN
ejpam-2371	21	11	.	.	PUNCT
ejpam-2371	22	1	the	the	DET
ejpam-2371	22	2	reverse	reverse	ADJ
ejpam-2371	22	3	implication	implication	NOUN
ejpam-2371	22	4	is	be	AUX
ejpam-2371	22	5	obvious	obvious	ADJ
ejpam-2371	22	6	(	(	PUNCT
ejpam-2371	22	7	it	it	PRON
ejpam-2371	22	8	is	be	AUX
ejpam-2371	22	9	a	a	DET
ejpam-2371	22	10	well	well	ADV
ejpam-2371	22	11	-	-	PUNCT
ejpam-2371	22	12	known	know	VERB
ejpam-2371	22	13	fact	fact	NOUN
ejpam-2371	22	14	from	from	ADP
ejpam-2371	22	15	almost	almost	ADV
ejpam-2371	22	16	all	all	DET
ejpam-2371	22	17	university	university	NOUN
ejpam-2371	22	18	textbooks	textbook	NOUN
ejpam-2371	22	19	on	on	ADP
ejpam-2371	22	20	functional	functional	ADJ
ejpam-2371	22	21	analysis	analysis	NOUN
ejpam-2371	22	22	,	,	PUNCT
ejpam-2371	22	23	which	which	PRON
ejpam-2371	22	24	states	state	VERB
ejpam-2371	22	25	that	that	SCONJ
ejpam-2371	22	26	compact	compact	ADJ
ejpam-2371	22	27	operator	operator	NOUN
ejpam-2371	22	28	takes	take	VERB
ejpam-2371	22	29	weakly	weakly	ADJ
ejpam-2371	22	30	convergent	convergent	ADJ
ejpam-2371	22	31	sequence	sequence	NOUN
ejpam-2371	22	32	to	to	PART
ejpam-2371	22	33	convergent	convergent	VERB
ejpam-2371	22	34	one	one	NUM
ejpam-2371	22	35	)	)	PUNCT
ejpam-2371	22	36	.	.	PUNCT
ejpam-2371	23	1	let	let	VERB
ejpam-2371	23	2	b	b	X
ejpam-2371	23	3	be	be	AUX
ejpam-2371	23	4	a	a	DET
ejpam-2371	23	5	unit	unit	NOUN
ejpam-2371	23	6	ball	ball	NOUN
ejpam-2371	23	7	of	of	ADP
ejpam-2371	23	8	the	the	DET
ejpam-2371	23	9	space	space	NOUN
ejpam-2371	23	10	h	h	NOUN
ejpam-2371	23	11	:	:	PUNCT
ejpam-2371	23	12	b	b	X
ejpam-2371	23	13	=	=	SYM
ejpam-2371	23	14	{	{	PUNCT
ejpam-2371	23	15	x	x	X
ejpam-2371	23	16	:	:	PUNCT
ejpam-2371	23	17	‖x‖	‖x‖	VERB
ejpam-2371	23	18	≤	≤	NUM
ejpam-2371	23	19	1	1	NUM
ejpam-2371	23	20	}	}	PUNCT
ejpam-2371	23	21	.	.	PUNCT
ejpam-2371	24	1	to	to	PART
ejpam-2371	24	2	prove	prove	VERB
ejpam-2371	24	3	the	the	DET
ejpam-2371	24	4	theorem	theorem	NOUN
ejpam-2371	24	5	it	it	PRON
ejpam-2371	24	6	suffices	suffice	VERB
ejpam-2371	24	7	to	to	PART
ejpam-2371	24	8	show	show	VERB
ejpam-2371	24	9	that	that	SCONJ
ejpam-2371	24	10	a(b	a(b	PROPN
ejpam-2371	24	11	)	)	PUNCT
ejpam-2371	24	12	is	be	AUX
ejpam-2371	24	13	compact	compact	ADJ
ejpam-2371	24	14	.	.	PUNCT
ejpam-2371	25	1	assume	assume	VERB
ejpam-2371	25	2	the	the	DET
ejpam-2371	25	3	contrary	contrary	NOUN
ejpam-2371	25	4	:	:	PUNCT
ejpam-2371	25	5	a(b	a(b	ADJ
ejpam-2371	25	6	)	)	PUNCT
ejpam-2371	25	7	is	be	AUX
ejpam-2371	25	8	not	not	PART
ejpam-2371	25	9	compact	compact	ADJ
ejpam-2371	25	10	.	.	PUNCT
ejpam-2371	26	1	by	by	ADP
ejpam-2371	26	2	hausdorff	hausdorff	NOUN
ejpam-2371	26	3	criterion	criterion	NOUN
ejpam-2371	26	4	there	there	PRON
ejpam-2371	26	5	exists	exist	VERB
ejpam-2371	26	6	such	such	DET
ejpam-2371	26	7	an	an	DET
ejpam-2371	26	8	ε0	ε0	PROPN
ejpam-2371	26	9	>	>	X
ejpam-2371	26	10	0	0	PUNCT
ejpam-2371	27	1	that	that	SCONJ
ejpam-2371	27	2	there	there	PRON
ejpam-2371	27	3	is	be	VERB
ejpam-2371	27	4	not	not	PART
ejpam-2371	27	5	any	any	DET
ejpam-2371	27	6	compact	compact	ADJ
ejpam-2371	27	7	ε0	ε0	NOUN
ejpam-2371	27	8	-	-	PUNCT
ejpam-2371	27	9	net	net	NOUN
ejpam-2371	27	10	for	for	ADP
ejpam-2371	27	11	a(b	a(b	PROPN
ejpam-2371	27	12	)	)	PUNCT
ejpam-2371	28	1	.	.	PUNCT
ejpam-2371	29	1	then	then	ADV
ejpam-2371	29	2	there	there	PRON
ejpam-2371	29	3	exists	exist	VERB
ejpam-2371	29	4	x1	x1	PROPN
ejpam-2371	29	5	∈	∈	PROPN
ejpam-2371	29	6	b	b	PROPN
ejpam-2371	29	7	such	such	ADJ
ejpam-2371	29	8	that	that	SCONJ
ejpam-2371	29	9	‖ax1‖	‖ax1‖	PROPN
ejpam-2371	29	10	≥	≥	PROPN
ejpam-2371	29	11	ε0	ε0	PROPN
ejpam-2371	29	12	(	(	PUNCT
ejpam-2371	29	13	otherwise	otherwise	ADV
ejpam-2371	29	14	0	0	NUM
ejpam-2371	29	15	is	be	AUX
ejpam-2371	29	16	ε0	ε0	NOUN
ejpam-2371	29	17	-	-	PUNCT
ejpam-2371	29	18	net	net	NOUN
ejpam-2371	29	19	for	for	ADP
ejpam-2371	29	20	a(b	a(b	PROPN
ejpam-2371	29	21	)	)	PUNCT
ejpam-2371	29	22	)	)	PUNCT
ejpam-2371	29	23	.	.	PUNCT
ejpam-2371	30	1	without	without	ADP
ejpam-2371	30	2	loss	loss	NOUN
ejpam-2371	30	3	of	of	ADP
ejpam-2371	30	4	generality	generality	NOUN
ejpam-2371	30	5	we	we	PRON
ejpam-2371	30	6	can	can	AUX
ejpam-2371	30	7	take	take	VERB
ejpam-2371	30	8	‖x1‖	‖x1‖	NOUN
ejpam-2371	30	9	=	=	SYM
ejpam-2371	31	1	1	1	X
ejpam-2371	31	2	.	.	X
ejpam-2371	32	1	if	if	SCONJ
ejpam-2371	32	2	the	the	DET
ejpam-2371	32	3	elements	element	NOUN
ejpam-2371	32	4	x1	x1	PROPN
ejpam-2371	32	5	,	,	PUNCT
ejpam-2371	32	6	x2	x2	PROPN
ejpam-2371	32	7	,	,	PUNCT
ejpam-2371	32	8	.	.	PUNCT
ejpam-2371	32	9	.	.	PUNCT
ejpam-2371	33	1	.	.	PUNCT
ejpam-2371	34	1	,	,	PUNCT
ejpam-2371	34	2	xn	xn	PROPN
ejpam-2371	34	3	are	be	AUX
ejpam-2371	34	4	already	already	ADV
ejpam-2371	34	5	chosen	choose	VERB
ejpam-2371	34	6	,	,	PUNCT
ejpam-2371	34	7	then	then	ADV
ejpam-2371	34	8	(	(	PUNCT
ejpam-2371	34	9	n+1)th	n+1)th	PROPN
ejpam-2371	34	10	element	element	NOUN
ejpam-2371	34	11	is	be	AUX
ejpam-2371	34	12	determined	determine	VERB
ejpam-2371	34	13	as	as	SCONJ
ejpam-2371	34	14	follows	follow	VERB
ejpam-2371	34	15	:	:	PUNCT
ejpam-2371	34	16	every	every	DET
ejpam-2371	34	17	element	element	NOUN
ejpam-2371	34	18	x	x	SYM
ejpam-2371	34	19	∈	∈	PROPN
ejpam-2371	34	20	b	b	NOUN
ejpam-2371	34	21	can	can	AUX
ejpam-2371	34	22	be	be	AUX
ejpam-2371	34	23	represented	represent	VERB
ejpam-2371	34	24	in	in	ADP
ejpam-2371	34	25	the	the	DET
ejpam-2371	34	26	form	form	NOUN
ejpam-2371	34	27	x	x	PUNCT
ejpam-2371	34	28	=	=	SYM
ejpam-2371	34	29	α1	α1	PROPN
ejpam-2371	34	30	x1	x1	PROPN
ejpam-2371	35	1	+	+	ADJ
ejpam-2371	35	2	α2	α2	ADJ
ejpam-2371	35	3	x2	x2	INTJ
ejpam-2371	36	1	+	+	CCONJ
ejpam-2371	36	2	.	.	PUNCT
ejpam-2371	36	3	.	.	PUNCT
ejpam-2371	37	1	.+αn	.+αn	PUNCT
ejpam-2371	37	2	xn	xn	PUNCT
ejpam-2371	38	1	+	+	NOUN
ejpam-2371	38	2	ψ(x	ψ(x	NOUN
ejpam-2371	38	3	)	)	PUNCT
ejpam-2371	38	4	,	,	PUNCT
ejpam-2371	38	5	where	where	SCONJ
ejpam-2371	38	6	|αk|	|αk|	ADJ
ejpam-2371	38	7	≤	≤	NUM
ejpam-2371	38	8	1	1	NUM
ejpam-2371	38	9	,	,	PUNCT
ejpam-2371	38	10	for	for	ADP
ejpam-2371	38	11	all	all	PRON
ejpam-2371	38	12	k	k	NOUN
ejpam-2371	38	13	=	=	SYM
ejpam-2371	38	14	1,2	1,2	NUM
ejpam-2371	38	15	,	,	PUNCT
ejpam-2371	38	16	.	.	PUNCT
ejpam-2371	38	17	.	.	PUNCT
ejpam-2371	38	18	.	.	PUNCT
ejpam-2371	39	1	,	,	PUNCT
ejpam-2371	39	2	n	n	PROPN
ejpam-2371	39	3	and	and	CCONJ
ejpam-2371	39	4	ψ(x	ψ(x	NUM
ejpam-2371	39	5	)	)	PUNCT
ejpam-2371	39	6	is	be	AUX
ejpam-2371	39	7	perpendicular	perpendicular	ADJ
ejpam-2371	39	8	to	to	ADP
ejpam-2371	39	9	x1	x1	PROPN
ejpam-2371	39	10	,	,	PUNCT
ejpam-2371	39	11	x2	x2	PROPN
ejpam-2371	39	12	,	,	PUNCT
ejpam-2371	39	13	.	.	PUNCT
ejpam-2371	39	14	.	.	PUNCT
ejpam-2371	40	1	.	.	PUNCT
ejpam-2371	41	1	,	,	PUNCT
ejpam-2371	41	2	xn	xn	X
ejpam-2371	41	3	.	.	PUNCT
ejpam-2371	42	1	the	the	DET
ejpam-2371	42	2	set	set	NOUN
ejpam-2371	42	3	an	an	DET
ejpam-2371	42	4	=	=	SYM
ejpam-2371	42	5	�	�	PROPN
ejpam-2371	42	6	α1ax1	α1ax1	NOUN
ejpam-2371	42	7	+	+	NOUN
ejpam-2371	42	8	α2ax2	α2ax2	NOUN
ejpam-2371	42	9	+	+	PUNCT
ejpam-2371	42	10	.	.	PUNCT
ejpam-2371	42	11	.	.	PUNCT
ejpam-2371	43	1	.+αnaxn	.+αnaxn	PUNCT
ejpam-2371	43	2	:	:	PUNCT
ejpam-2371	44	1	|αk|	|αk|	ADJ
ejpam-2371	44	2	≤	≤	NUM
ejpam-2371	44	3	1	1	NUM
ejpam-2371	44	4	,	,	PUNCT
ejpam-2371	44	5	k	k	NOUN
ejpam-2371	44	6	=	=	SYM
ejpam-2371	44	7	1,2	1,2	NUM
ejpam-2371	44	8	,	,	PUNCT
ejpam-2371	44	9	.	.	PUNCT
ejpam-2371	44	10	.	.	PUNCT
ejpam-2371	44	11	.	.	PUNCT
ejpam-2371	45	1	,	,	PUNCT
ejpam-2371	45	2	n	n	PRON
ejpam-2371	45	3	is	be	AUX
ejpam-2371	45	4	compact(since	compact(since	NOUN
ejpam-2371	45	5	it	it	PRON
ejpam-2371	45	6	is	be	AUX
ejpam-2371	45	7	bounded	bound	VERB
ejpam-2371	45	8	subset	subset	NOUN
ejpam-2371	45	9	of	of	ADP
ejpam-2371	45	10	finite	finite	ADJ
ejpam-2371	45	11	dimensional	dimensional	ADJ
ejpam-2371	45	12	subspace	subspace	NOUN
ejpam-2371	45	13	)	)	PUNCT
ejpam-2371	45	14	.	.	PUNCT
ejpam-2371	46	1	therefore	therefore	ADV
ejpam-2371	46	2	there	there	PRON
ejpam-2371	46	3	exists	exist	VERB
ejpam-2371	46	4	ξn+1	ξn+1	PROPN
ejpam-2371	46	5	∈	∈	NOUN
ejpam-2371	46	6	b	b	NOUN
ejpam-2371	46	7	such	such	ADJ
ejpam-2371	46	8	that	that	SCONJ
ejpam-2371	46	9	‖aψ(ξn+1)‖	‖aψ(ξn+1)‖	PROPN
ejpam-2371	46	10	≥	≥	NOUN
ejpam-2371	46	11	ε0	ε0	NOUN
ejpam-2371	46	12	;	;	PUNCT
ejpam-2371	46	13	otherwise	otherwise	ADV
ejpam-2371	46	14	the	the	DET
ejpam-2371	46	15	relation	relation	NOUN
ejpam-2371	46	16	‖ax	‖ax	CCONJ
ejpam-2371	46	17	−	−	PROPN
ejpam-2371	46	18	(	(	PUNCT
ejpam-2371	46	19	α1ax1	α1ax1	NOUN
ejpam-2371	46	20	+	+	NOUN
ejpam-2371	46	21	α2ax2	α2ax2	NOUN
ejpam-2371	46	22	+	+	PUNCT
ejpam-2371	46	23	.	.	PUNCT
ejpam-2371	46	24	.	.	PUNCT
ejpam-2371	47	1	.+αnaxn)‖=	.+αnaxn)‖=	PUNCT
ejpam-2371	48	1	‖aψ(x)‖	‖aψ(x)‖	NUM
ejpam-2371	48	2	<	<	X
ejpam-2371	48	3	ε0	ε0	PROPN
ejpam-2371	48	4	would	would	AUX
ejpam-2371	48	5	show	show	VERB
ejpam-2371	48	6	that	that	SCONJ
ejpam-2371	48	7	the	the	DET
ejpam-2371	48	8	compact	compact	ADJ
ejpam-2371	48	9	set	set	VERB
ejpam-2371	48	10	an	an	PRON
ejpam-2371	48	11	is	be	AUX
ejpam-2371	48	12	ε0	ε0	NOUN
ejpam-2371	48	13	-	-	PUNCT
ejpam-2371	48	14	net	net	NOUN
ejpam-2371	48	15	of	of	ADP
ejpam-2371	48	16	a(b	a(b	PROPN
ejpam-2371	48	17	)	)	PUNCT
ejpam-2371	48	18	that	that	PRON
ejpam-2371	48	19	contradicts	contradict	VERB
ejpam-2371	48	20	the	the	DET
ejpam-2371	48	21	definition	definition	NOUN
ejpam-2371	48	22	of	of	ADP
ejpam-2371	48	23	ε0	ε0	PROPN
ejpam-2371	48	24	.	.	PUNCT
ejpam-2371	49	1	define	define	VERB
ejpam-2371	49	2	xn+1	xn+1	PROPN
ejpam-2371	49	3	to	to	PART
ejpam-2371	49	4	be	be	AUX
ejpam-2371	49	5	ψ(ξn+1	ψ(ξn+1	NOUN
ejpam-2371	49	6	)	)	PUNCT
ejpam-2371	49	7	‖ψ(ξn+1)‖	‖ψ(ξn+1)‖	NOUN
ejpam-2371	49	8	:	:	PUNCT
ejpam-2371	49	9	xn+1	xn+1	X
ejpam-2371	49	10	=	=	SYM
ejpam-2371	49	11	ψ(ξn+1	ψ(ξn+1	NOUN
ejpam-2371	49	12	)	)	PUNCT
ejpam-2371	49	13	‖ψ(ξn+1)‖	‖ψ(ξn+1)‖	NOUN
ejpam-2371	49	14	.	.	PUNCT
ejpam-2371	50	1	so	so	ADV
ejpam-2371	50	2	,	,	PUNCT
ejpam-2371	50	3	there	there	PRON
ejpam-2371	50	4	exists	exist	VERB
ejpam-2371	50	5	orthonormal	orthonormal	ADJ
ejpam-2371	50	6	sequence	sequence	NOUN
ejpam-2371	50	7	x1	x1	PROPN
ejpam-2371	50	8	,	,	PUNCT
ejpam-2371	50	9	x2	x2	PROPN
ejpam-2371	50	10	,	,	PUNCT
ejpam-2371	50	11	.	.	PUNCT
ejpam-2371	50	12	.	.	PUNCT
ejpam-2371	51	1	.	.	PUNCT
ejpam-2371	52	1	,	,	PUNCT
ejpam-2371	52	2	xn	xn	PUNCT
ejpam-2371	52	3	such	such	ADJ
ejpam-2371	52	4	that	that	DET
ejpam-2371	52	5	‖axn‖	‖axn‖	NOUN
ejpam-2371	52	6	≥	≥	NOUN
ejpam-2371	52	7	ε0	ε0	PROPN
ejpam-2371	52	8	,	,	PUNCT
ejpam-2371	52	9	for	for	ADP
ejpam-2371	52	10	all	all	DET
ejpam-2371	52	11	n	n	PRON
ejpam-2371	52	12	∈	∈	PROPN
ejpam-2371	52	13	n.	n.	NOUN
ejpam-2371	52	14	contradiction	contradiction	NOUN
ejpam-2371	52	15	.	.	PUNCT
ejpam-2371	53	1	the	the	DET
ejpam-2371	53	2	theorem	theorem	NOUN
ejpam-2371	53	3	is	be	AUX
ejpam-2371	53	4	proved	prove	VERB
ejpam-2371	53	5	.	.	PUNCT
ejpam-2371	54	1	remark	remark	PROPN
ejpam-2371	54	2	1	1	NUM
ejpam-2371	54	3	.	.	PUNCT
ejpam-2371	55	1	since	since	SCONJ
ejpam-2371	55	2	every	every	DET
ejpam-2371	55	3	orthonormal	orthonormal	ADJ
ejpam-2371	55	4	sequence	sequence	NOUN
ejpam-2371	55	5	of	of	ADP
ejpam-2371	55	6	a	a	DET
ejpam-2371	55	7	separable	separable	ADJ
ejpam-2371	55	8	hilbert	hilbert	NOUN
ejpam-2371	55	9	space	space	NOUN
ejpam-2371	55	10	can	can	AUX
ejpam-2371	55	11	be	be	AUX
ejpam-2371	55	12	made	make	VERB
ejpam-2371	55	13	an	an	DET
ejpam-2371	55	14	orthonormal	orthonormal	ADJ
ejpam-2371	55	15	basis	basis	NOUN
ejpam-2371	55	16	by	by	ADP
ejpam-2371	55	17	adding	add	VERB
ejpam-2371	55	18	new	new	ADJ
ejpam-2371	55	19	elements	element	NOUN
ejpam-2371	55	20	,	,	PUNCT
ejpam-2371	55	21	it	it	PRON
ejpam-2371	55	22	is	be	AUX
ejpam-2371	55	23	easy	easy	ADJ
ejpam-2371	55	24	to	to	PART
ejpam-2371	55	25	see	see	VERB
ejpam-2371	55	26	that	that	SCONJ
ejpam-2371	55	27	the	the	DET
ejpam-2371	55	28	following	follow	VERB
ejpam-2371	55	29	equivalent	equivalent	ADJ
ejpam-2371	55	30	formulations	formulation	NOUN
ejpam-2371	55	31	of	of	ADP
ejpam-2371	55	32	the	the	DET
ejpam-2371	55	33	above	above	ADJ
ejpam-2371	55	34	theorems	theorem	NOUN
ejpam-2371	55	35	holds	hold	VERB
ejpam-2371	55	36	:	:	PUNCT
ejpam-2371	55	37	proposition	proposition	NOUN
ejpam-2371	55	38	1	1	NUM
ejpam-2371	55	39	.	.	PUNCT
ejpam-2371	56	1	linear	linear	PROPN
ejpam-2371	56	2	(	(	PUNCT
ejpam-2371	56	3	not	not	PART
ejpam-2371	56	4	necessarily	necessarily	ADV
ejpam-2371	56	5	bounded	bound	VERB
ejpam-2371	56	6	)	)	PUNCT
ejpam-2371	56	7	operator	operator	NOUN
ejpam-2371	56	8	acting	act	VERB
ejpam-2371	56	9	from	from	ADP
ejpam-2371	56	10	a	a	DET
ejpam-2371	56	11	separable	separable	ADJ
ejpam-2371	56	12	hilbert	hilbert	NOUN
ejpam-2371	56	13	space	space	NOUN
ejpam-2371	56	14	h	h	NOUN
ejpam-2371	56	15	to	to	ADP
ejpam-2371	56	16	a	a	DET
ejpam-2371	56	17	banach	banach	NOUN
ejpam-2371	56	18	space	space	NOUN
ejpam-2371	56	19	b	b	NOUN
ejpam-2371	56	20	is	be	AUX
ejpam-2371	56	21	compact	compact	ADJ
ejpam-2371	56	22	if	if	SCONJ
ejpam-2371	56	23	and	and	CCONJ
ejpam-2371	56	24	only	only	ADV
ejpam-2371	56	25	if	if	SCONJ
ejpam-2371	56	26	it	it	PRON
ejpam-2371	56	27	satisfies	satisfy	VERB
ejpam-2371	56	28	‖aen‖	‖aen‖	PUNCT
ejpam-2371	56	29	→	→	SYM
ejpam-2371	56	30	0	0	NUM
ejpam-2371	56	31	for	for	ADP
ejpam-2371	56	32	each	each	DET
ejpam-2371	56	33	orthonormal	orthonormal	ADJ
ejpam-2371	56	34	basis	basis	NOUN
ejpam-2371	56	35	�	�	NOUN
ejpam-2371	56	36	en	en	X
ejpam-2371	56	37	in	in	ADP
ejpam-2371	56	38	h.	h.	PROPN
ejpam-2371	56	39	acknowledgements	acknowledgement	NOUN
ejpam-2371	56	40	the	the	DET
ejpam-2371	56	41	author	author	NOUN
ejpam-2371	56	42	is	be	AUX
ejpam-2371	56	43	grateful	grateful	ADJ
ejpam-2371	56	44	to	to	PART
ejpam-2371	56	45	prof	prof	VERB
ejpam-2371	56	46	.	.	PUNCT
ejpam-2371	57	1	s.s	s.s	PROPN
ejpam-2371	57	2	.	.	PROPN
ejpam-2371	57	3	mirzoev	mirzoev	NOUN
ejpam-2371	57	4	for	for	ADP
ejpam-2371	57	5	drawing	draw	VERB
ejpam-2371	57	6	his	his	PRON
ejpam-2371	57	7	attention	attention	NOUN
ejpam-2371	57	8	to	to	ADP
ejpam-2371	57	9	this	this	DET
ejpam-2371	57	10	question	question	NOUN
ejpam-2371	57	11	.	.	PUNCT
ejpam-2371	58	1	he	he	PRON
ejpam-2371	58	2	thanks	thank	NOUN
ejpam-2371	58	3	also	also	ADV
ejpam-2371	58	4	to	to	ADP
ejpam-2371	58	5	i.	i.	PROPN
ejpam-2371	58	6	gahramanov	gahramanov	PROPN
ejpam-2371	58	7	for	for	ADP
ejpam-2371	58	8	his	his	PRON
ejpam-2371	58	9	help	help	NOUN
ejpam-2371	58	10	in	in	ADP
ejpam-2371	58	11	finding	find	VERB
ejpam-2371	58	12	first	first	ADJ
ejpam-2371	58	13	reference	reference	NOUN
ejpam-2371	58	14	,	,	PUNCT
ejpam-2371	58	15	and	and	CCONJ
ejpam-2371	58	16	a.a.huseynli	a.a.huseynli	VERB
ejpam-2371	58	17	for	for	ADP
ejpam-2371	58	18	discussions	discussion	NOUN
ejpam-2371	58	19	.	.	PUNCT
ejpam-2371	59	1	references	reference	NOUN
ejpam-2371	59	2	501	501	NUM
ejpam-2371	59	3	references	reference	NOUN
ejpam-2371	59	4	[	[	X
ejpam-2371	59	5	1	1	NUM
ejpam-2371	59	6	]	]	PUNCT
ejpam-2371	59	7	j.	j.	PROPN
ejpam-2371	59	8	h.	h.	PROPN
ejpam-2371	59	9	anderson	anderson	PROPN
ejpam-2371	59	10	and	and	CCONJ
ejpam-2371	59	11	j.	j.	PROPN
ejpam-2371	59	12	g.	g.	PROPN
ejpam-2371	59	13	stampfli	stampfli	PROPN
ejpam-2371	59	14	.	.	PUNCT
ejpam-2371	60	1	commutators	commutator	NOUN
ejpam-2371	60	2	and	and	CCONJ
ejpam-2371	60	3	compressions	compression	NOUN
ejpam-2371	60	4	,	,	PUNCT
ejpam-2371	60	5	israel	israel	PROPN
ejpam-2371	60	6	journal	journal	PROPN
ejpam-2371	60	7	of	of	ADP
ejpam-2371	60	8	mathematics	mathematic	NOUN
ejpam-2371	60	9	,	,	PUNCT
ejpam-2371	60	10	10	10	NUM
ejpam-2371	60	11	,	,	PUNCT
ejpam-2371	60	12	433	433	NUM
ejpam-2371	60	13	-	-	SYM
ejpam-2371	60	14	441	441	NUM
ejpam-2371	60	15	.	.	NUM
ejpam-2371	60	16	1971	1971	NUM
ejpam-2371	60	17	.	.	PUNCT
ejpam-2371	61	1	[	[	X
ejpam-2371	61	2	2	2	X
ejpam-2371	61	3	]	]	X
ejpam-2371	61	4	d.	d.	PROPN
ejpam-2371	61	5	bakic	bakic	PROPN
ejpam-2371	61	6	and	and	CCONJ
ejpam-2371	61	7	b.	b.	PROPN
ejpam-2371	61	8	guljas	guljas	PROPN
ejpam-2371	61	9	.	.	PUNCT
ejpam-2371	62	1	which	which	PRON
ejpam-2371	62	2	operators	operator	NOUN
ejpam-2371	62	3	approximately	approximately	ADV
ejpam-2371	62	4	annihilate	annihilate	VERB
ejpam-2371	62	5	orthonormal	orthonormal	ADJ
ejpam-2371	62	6	bases	basis	NOUN
ejpam-2371	62	7	?	?	PUNCT
ejpam-2371	62	8	,	,	PUNCT
ejpam-2371	62	9	acta	acta	PROPN
ejpam-2371	62	10	scientiarum	scientiarum	PROPN
ejpam-2371	62	11	mathematicarum	mathematicarum	PROPN
ejpam-2371	62	12	(	(	PUNCT
ejpam-2371	62	13	szeged	szeged	PROPN
ejpam-2371	62	14	)	)	PUNCT
ejpam-2371	62	15	64	64	NUM
ejpam-2371	62	16	,	,	PUNCT
ejpam-2371	62	17	601	601	NUM
ejpam-2371	62	18	-	-	NUM
ejpam-2371	62	19	607	607	NUM
ejpam-2371	62	20	.	.	PUNCT
ejpam-2371	62	21	1998	1998	NUM
ejpam-2371	62	22	.	.	PUNCT
ejpam-2371	63	1	[	[	X
ejpam-2371	63	2	3	3	X
ejpam-2371	63	3	]	]	X
ejpam-2371	63	4	p.	p.	NOUN
ejpam-2371	63	5	a.	a.	NOUN
ejpam-2371	63	6	fillmore	fillmore	PROPN
ejpam-2371	63	7	and	and	CCONJ
ejpam-2371	63	8	j.	j.	PROPN
ejpam-2371	63	9	p.	p.	PROPN
ejpam-2371	63	10	williams	williams	PROPN
ejpam-2371	63	11	.	.	PUNCT
ejpam-2371	64	1	on	on	ADP
ejpam-2371	64	2	operator	operator	NOUN
ejpam-2371	64	3	ranges	range	NOUN
ejpam-2371	64	4	,	,	PUNCT
ejpam-2371	64	5	advances	advance	NOUN
ejpam-2371	64	6	in	in	ADP
ejpam-2371	64	7	mathematics	mathematic	NOUN
ejpam-2371	64	8	7	7	NUM
ejpam-2371	64	9	,	,	PUNCT
ejpam-2371	64	10	254	254	NUM
ejpam-2371	64	11	-	-	SYM
ejpam-2371	64	12	281	281	NUM
ejpam-2371	64	13	.	.	PUNCT
ejpam-2371	64	14	1971	1971	NUM
ejpam-2371	64	15	.	.	PUNCT
ejpam-2371	65	1	[	[	X
ejpam-2371	65	2	4	4	X
ejpam-2371	65	3	]	]	PUNCT
ejpam-2371	65	4	k.	k.	NOUN
ejpam-2371	65	5	muroi	muroi	PROPN
ejpam-2371	65	6	and	and	CCONJ
ejpam-2371	65	7	k.tamaki	k.tamaki	NOUN
ejpam-2371	65	8	.	.	PUNCT
ejpam-2371	66	1	on	on	ADP
ejpam-2371	66	2	ringrose	ringrose	PROPN
ejpam-2371	66	3	’s	’s	PART
ejpam-2371	66	4	characterization	characterization	NOUN
ejpam-2371	66	5	of	of	ADP
ejpam-2371	66	6	compact	compact	ADJ
ejpam-2371	66	7	operators	operator	NOUN
ejpam-2371	66	8	,	,	PUNCT
ejpam-2371	66	9	mathematica	mathematica	PROPN
ejpam-2371	66	10	japonica	japonica	PROPN
ejpam-2371	66	11	19	19	NUM
ejpam-2371	66	12	,	,	PUNCT
ejpam-2371	66	13	259	259	NUM
ejpam-2371	66	14	-	-	SYM
ejpam-2371	66	15	261	261	NUM
ejpam-2371	66	16	.	.	PUNCT
ejpam-2371	66	17	1974	1974	NUM
ejpam-2371	66	18	.	.	PUNCT
ejpam-2371	67	1	[	[	X
ejpam-2371	67	2	5	5	X
ejpam-2371	67	3	]	]	PUNCT
ejpam-2371	67	4	j.	j.	PROPN
ejpam-2371	67	5	r.	r.	PROPN
ejpam-2371	67	6	ringrose	ringrose	PROPN
ejpam-2371	67	7	.	.	PUNCT
ejpam-2371	68	1	compact	compact	ADJ
ejpam-2371	68	2	non	non	ADJ
ejpam-2371	68	3	-	-	ADJ
ejpam-2371	68	4	selfadjoint	selfadjoint	ADJ
ejpam-2371	68	5	operators	operator	NOUN
ejpam-2371	68	6	,	,	PUNCT
ejpam-2371	68	7	van	van	PROPN
ejpam-2371	68	8	nostrand	nostrand	PROPN
ejpam-2371	68	9	,	,	PUNCT
ejpam-2371	68	10	princeton	princeton	PROPN
ejpam-2371	68	11	,	,	PUNCT
ejpam-2371	68	12	1971	1971	NUM
ejpam-2371	68	13	.	.	PUNCT