id	sid	tid	token	lemma	pos
ejpam-4071	1	1	european	european	PROPN
ejpam-4071	1	2	journal	journal	PROPN
ejpam-4071	1	3	of	of	ADP
ejpam-4071	1	4	pure	pure	ADJ
ejpam-4071	1	5	and	and	CCONJ
ejpam-4071	1	6	applied	apply	VERB
ejpam-4071	1	7	mathematics	mathematic	NOUN
ejpam-4071	1	8	vol	vol	NOUN
ejpam-4071	1	9	.	.	PUNCT
ejpam-4071	2	1	14	14	NUM
ejpam-4071	2	2	,	,	PUNCT
ejpam-4071	2	3	no	no	INTJ
ejpam-4071	2	4	.	.	NOUN
ejpam-4071	2	5	4	4	NUM
ejpam-4071	2	6	,	,	PUNCT
ejpam-4071	2	7	2021	2021	NUM
ejpam-4071	2	8	,	,	PUNCT
ejpam-4071	2	9	1237	1237	NUM
ejpam-4071	2	10	-	-	SYM
ejpam-4071	2	11	1248	1248	NUM
ejpam-4071	2	12	issn	issn	PROPN
ejpam-4071	2	13	1307	1307	NUM
ejpam-4071	2	14	-	-	SYM
ejpam-4071	2	15	5543	5543	NUM
ejpam-4071	2	16	–	–	PUNCT
ejpam-4071	2	17	ejpam.com	ejpam.com	X
ejpam-4071	2	18	published	publish	VERB
ejpam-4071	2	19	by	by	ADP
ejpam-4071	2	20	new	new	PROPN
ejpam-4071	2	21	york	york	PROPN
ejpam-4071	2	22	business	business	PROPN
ejpam-4071	2	23	global	global	PROPN
ejpam-4071	2	24	chatterjee	chatterjee	NOUN
ejpam-4071	2	25	and	and	CCONJ
ejpam-4071	2	26	extension	extension	NOUN
ejpam-4071	2	27	of	of	ADP
ejpam-4071	2	28	chatterjee	chatterjee	PROPN
ejpam-4071	2	29	fixed	fix	VERB
ejpam-4071	2	30	point	point	NOUN
ejpam-4071	2	31	theorems	theorem	NOUN
ejpam-4071	2	32	on	on	ADP
ejpam-4071	2	33	operators	operator	NOUN
ejpam-4071	2	34	on	on	ADP
ejpam-4071	2	35	hilbert	hilbert	NOUN
ejpam-4071	2	36	c*-modules	c*-module	NOUN
ejpam-4071	2	37	rashwan	rashwan	PROPN
ejpam-4071	2	38	.	.	PUNCT
ejpam-4071	3	1	a.	a.	PROPN
ejpam-4071	3	2	rashwan1,∗	rashwan1,∗	PROPN
ejpam-4071	3	3	,	,	PUNCT
ejpam-4071	3	4	howida	howida	PROPN
ejpam-4071	3	5	adel	adel	PROPN
ejpam-4071	3	6	alfran2	alfran2	PROPN
ejpam-4071	3	7	,	,	PUNCT
ejpam-4071	3	8	asmaa	asmaa	PROPN
ejpam-4071	3	9	fangary3	fangary3	PROPN
ejpam-4071	3	10	,	,	PUNCT
ejpam-4071	3	11	saleh	saleh	PROPN
ejpam-4071	3	12	omran3	omran3	NOUN
ejpam-4071	3	13	1	1	NUM
ejpam-4071	3	14	department	department	NOUN
ejpam-4071	3	15	of	of	ADP
ejpam-4071	3	16	mathematics	mathematic	NOUN
ejpam-4071	3	17	,	,	PUNCT
ejpam-4071	3	18	faculty	faculty	NOUN
ejpam-4071	3	19	of	of	ADP
ejpam-4071	3	20	science	science	NOUN
ejpam-4071	3	21	,	,	PUNCT
ejpam-4071	3	22	assuit	assuit	PROPN
ejpam-4071	3	23	university	university	NOUN
ejpam-4071	3	24	,	,	PUNCT
ejpam-4071	3	25	assuit	assuit	PROPN
ejpam-4071	3	26	,	,	PUNCT
ejpam-4071	3	27	egypt	egypt	PROPN
ejpam-4071	3	28	2	2	NUM
ejpam-4071	3	29	department	department	NOUN
ejpam-4071	3	30	of	of	ADP
ejpam-4071	3	31	mathematics	mathematics	PROPN
ejpam-4071	3	32	,	,	PUNCT
ejpam-4071	3	33	al	al	PROPN
ejpam-4071	3	34	-	-	PUNCT
ejpam-4071	3	35	leith	leith	PROPN
ejpam-4071	3	36	university	university	PROPN
ejpam-4071	3	37	college	college	NOUN
ejpam-4071	3	38	,	,	PUNCT
ejpam-4071	3	39	umm	umm	INTJ
ejpam-4071	3	40	al	al	PROPN
ejpam-4071	3	41	qura	qura	PROPN
ejpam-4071	3	42	university	university	PROPN
ejpam-4071	3	43	,	,	PUNCT
ejpam-4071	3	44	kingdom	kingdom	NOUN
ejpam-4071	3	45	of	of	ADP
ejpam-4071	3	46	saudi	saudi	PROPN
ejpam-4071	3	47	arabia	arabia	PROPN
ejpam-4071	3	48	3	3	NUM
ejpam-4071	3	49	department	department	NOUN
ejpam-4071	3	50	of	of	ADP
ejpam-4071	3	51	mathematics	mathematic	NOUN
ejpam-4071	3	52	,	,	PUNCT
ejpam-4071	3	53	faculty	faculty	NOUN
ejpam-4071	3	54	of	of	ADP
ejpam-4071	3	55	science	science	NOUN
ejpam-4071	3	56	,	,	PUNCT
ejpam-4071	3	57	south	south	PROPN
ejpam-4071	3	58	valley	valley	PROPN
ejpam-4071	3	59	university	university	PROPN
ejpam-4071	3	60	,	,	PUNCT
ejpam-4071	3	61	qena	qena	PROPN
ejpam-4071	3	62	,	,	PUNCT
ejpam-4071	3	63	egypt	egypt	PROPN
ejpam-4071	3	64	abstract	abstract	PROPN
ejpam-4071	3	65	.	.	PUNCT
ejpam-4071	4	1	in	in	ADP
ejpam-4071	4	2	this	this	DET
ejpam-4071	4	3	paper	paper	NOUN
ejpam-4071	4	4	we	we	PRON
ejpam-4071	4	5	consider	consider	VERB
ejpam-4071	4	6	some	some	DET
ejpam-4071	4	7	fixed	fix	VERB
ejpam-4071	4	8	point	point	NOUN
ejpam-4071	4	9	theorem	theorem	ADJ
ejpam-4071	4	10	(	(	PUNCT
ejpam-4071	4	11	such	such	ADJ
ejpam-4071	4	12	as	as	ADP
ejpam-4071	4	13	chatterjee	chatterjee	NOUN
ejpam-4071	4	14	and	and	CCONJ
ejpam-4071	4	15	extension	extension	NOUN
ejpam-4071	4	16	of	of	ADP
ejpam-4071	4	17	chatterjee	chatterjee	NOUN
ejpam-4071	4	18	)	)	PUNCT
ejpam-4071	4	19	in	in	ADP
ejpam-4071	4	20	operators	operator	NOUN
ejpam-4071	4	21	of	of	ADP
ejpam-4071	4	22	hilbert	hilbert	PROPN
ejpam-4071	4	23	c∗-modules	c∗-modules	PROPN
ejpam-4071	4	24	,	,	PUNCT
ejpam-4071	4	25	based	base	VERB
ejpam-4071	4	26	on	on	ADP
ejpam-4071	4	27	a	a	DET
ejpam-4071	4	28	definition	definition	NOUN
ejpam-4071	4	29	of	of	ADP
ejpam-4071	4	30	valued	value	VERB
ejpam-4071	4	31	operator	operator	NOUN
ejpam-4071	4	32	hilbert	hilbert	NOUN
ejpam-4071	4	33	c*-modules	c*-module	NOUN
ejpam-4071	4	34	normed	normed	ADJ
ejpam-4071	4	35	space	space	NOUN
ejpam-4071	4	36	.	.	PUNCT
ejpam-4071	5	1	also	also	ADV
ejpam-4071	5	2	we	we	PRON
ejpam-4071	5	3	give	give	VERB
ejpam-4071	5	4	some	some	DET
ejpam-4071	5	5	examples	example	NOUN
ejpam-4071	5	6	to	to	PART
ejpam-4071	5	7	clear	clear	VERB
ejpam-4071	5	8	our	our	PRON
ejpam-4071	5	9	definitions	definition	NOUN
ejpam-4071	5	10	.	.	PUNCT
ejpam-4071	6	1	2020	2020	NUM
ejpam-4071	6	2	mathematics	mathematic	NOUN
ejpam-4071	6	3	subject	subject	NOUN
ejpam-4071	6	4	classifications	classification	NOUN
ejpam-4071	6	5	:	:	PUNCT
ejpam-4071	6	6	47h10	47h10	NUM
ejpam-4071	6	7	,	,	PUNCT
ejpam-4071	6	8	46l05	46l05	NUM
ejpam-4071	6	9	,	,	PUNCT
ejpam-4071	6	10	46l08	46l08	NUM
ejpam-4071	6	11	key	key	ADJ
ejpam-4071	6	12	words	word	NOUN
ejpam-4071	6	13	and	and	CCONJ
ejpam-4071	6	14	phrases	phrase	NOUN
ejpam-4071	6	15	:	:	PUNCT
ejpam-4071	6	16	fixed	fix	VERB
ejpam-4071	6	17	point	point	NOUN
ejpam-4071	6	18	theorems	theorem	NOUN
ejpam-4071	6	19	,	,	PUNCT
ejpam-4071	6	20	c∗-algebra	c∗-algebra	NOUN
ejpam-4071	6	21	,	,	PUNCT
ejpam-4071	6	22	operators	operator	NOUN
ejpam-4071	6	23	on	on	ADP
ejpam-4071	6	24	hilbert	hilbert	PROPN
ejpam-4071	6	25	c∗-modules	c∗-modules	PROPN
ejpam-4071	6	26	1	1	NUM
ejpam-4071	6	27	.	.	PUNCT
ejpam-4071	7	1	introduction	introduction	NOUN
ejpam-4071	7	2	hilbert	hilbert	PROPN
ejpam-4071	7	3	c∗-modules	c∗-modules	PROPN
ejpam-4071	7	4	consider	consider	VERB
ejpam-4071	7	5	a	a	DET
ejpam-4071	7	6	mathematical	mathematical	ADJ
ejpam-4071	7	7	objects	object	NOUN
ejpam-4071	7	8	where	where	SCONJ
ejpam-4071	7	9	generalize	generalize	VERB
ejpam-4071	7	10	the	the	DET
ejpam-4071	7	11	notion	notion	NOUN
ejpam-4071	7	12	of	of	ADP
ejpam-4071	7	13	a	a	DET
ejpam-4071	7	14	hilbert	hilbert	NOUN
ejpam-4071	7	15	space	space	NOUN
ejpam-4071	7	16	by	by	ADP
ejpam-4071	7	17	allowing	allow	VERB
ejpam-4071	7	18	the	the	DET
ejpam-4071	7	19	inner	inner	ADJ
ejpam-4071	7	20	product	product	NOUN
ejpam-4071	7	21	to	to	PART
ejpam-4071	7	22	take	take	VERB
ejpam-4071	7	23	values	value	NOUN
ejpam-4071	7	24	in	in	ADP
ejpam-4071	7	25	a	a	DET
ejpam-4071	7	26	(	(	PUNCT
ejpam-4071	7	27	commutative	commutative	ADJ
ejpam-4071	7	28	,	,	PUNCT
ejpam-4071	7	29	unital	unital	ADJ
ejpam-4071	7	30	)	)	PUNCT
ejpam-4071	7	31	c∗-algebra	c∗-algebra	NOUN
ejpam-4071	7	32	rather	rather	ADV
ejpam-4071	7	33	than	than	ADP
ejpam-4071	7	34	in	in	ADP
ejpam-4071	7	35	the	the	DET
ejpam-4071	7	36	field	field	NOUN
ejpam-4071	7	37	of	of	ADP
ejpam-4071	7	38	complex	complex	ADJ
ejpam-4071	7	39	numbers	number	NOUN
ejpam-4071	7	40	.	.	PUNCT
ejpam-4071	8	1	hilbert	hilbert	PROPN
ejpam-4071	8	2	c∗-modules	c∗-modules	PROPN
ejpam-4071	8	3	were	be	AUX
ejpam-4071	8	4	first	first	ADV
ejpam-4071	8	5	introduced	introduce	VERB
ejpam-4071	8	6	in	in	ADP
ejpam-4071	8	7	1953	1953	NUM
ejpam-4071	8	8	by	by	ADP
ejpam-4071	8	9	kaplansky	kaplansky	PROPN
ejpam-4071	8	10	[	[	X
ejpam-4071	8	11	5	5	NUM
ejpam-4071	8	12	]	]	PUNCT
ejpam-4071	8	13	.	.	PUNCT
ejpam-4071	9	1	later	later	ADV
ejpam-4071	9	2	,	,	PUNCT
ejpam-4071	9	3	the	the	DET
ejpam-4071	9	4	theory	theory	NOUN
ejpam-4071	9	5	was	be	AUX
ejpam-4071	9	6	developed	develop	VERB
ejpam-4071	9	7	independently	independently	ADV
ejpam-4071	9	8	by	by	ADP
ejpam-4071	9	9	paschke	paschke	ADJ
ejpam-4071	9	10	[	[	X
ejpam-4071	9	11	12	12	NUM
ejpam-4071	9	12	]	]	PUNCT
ejpam-4071	9	13	and	and	CCONJ
ejpam-4071	9	14	rieffel	rieffel	VERB
ejpam-4071	10	1	[	[	X
ejpam-4071	10	2	16	16	NUM
ejpam-4071	10	3	]	]	PUNCT
ejpam-4071	10	4	where	where	SCONJ
ejpam-4071	10	5	the	the	DET
ejpam-4071	10	6	research	research	NOUN
ejpam-4071	10	7	on	on	ADP
ejpam-4071	10	8	hilbert	hilbert	PROPN
ejpam-4071	10	9	c∗-modules	c∗-modules	PROPN
ejpam-4071	10	10	began	begin	VERB
ejpam-4071	10	11	in	in	ADP
ejpam-4071	10	12	the	the	DET
ejpam-4071	10	13	70,s	70,s	NOUN
ejpam-4071	10	14	in	in	ADP
ejpam-4071	10	15	the	the	DET
ejpam-4071	10	16	work	work	NOUN
ejpam-4071	10	17	of	of	ADP
ejpam-4071	10	18	the	the	DET
ejpam-4071	10	19	induced	induce	VERB
ejpam-4071	10	20	representations	representation	NOUN
ejpam-4071	10	21	of	of	ADP
ejpam-4071	10	22	c∗-algebras	c∗-algebra	NOUN
ejpam-4071	10	23	by	by	ADP
ejpam-4071	10	24	m.	m.	NOUN
ejpam-4071	10	25	a.	a.	NOUN
ejpam-4071	10	26	rieffel	rieffel	PROPN
ejpam-4071	10	27	[	[	X
ejpam-4071	10	28	16	16	NUM
ejpam-4071	10	29	]	]	PUNCT
ejpam-4071	10	30	also	also	ADV
ejpam-4071	10	31	kasparov	kasparov	X
ejpam-4071	11	1	[	[	X
ejpam-4071	11	2	6	6	NUM
ejpam-4071	11	3	]	]	PUNCT
ejpam-4071	11	4	introduced	introduce	VERB
ejpam-4071	11	5	the	the	DET
ejpam-4071	11	6	definition	definition	NOUN
ejpam-4071	11	7	of	of	ADP
ejpam-4071	11	8	kk	kk	PROPN
ejpam-4071	11	9	-	-	NOUN
ejpam-4071	11	10	theory	theory	NOUN
ejpam-4071	11	11	by	by	ADP
ejpam-4071	11	12	using	use	VERB
ejpam-4071	11	13	hilbert	hilbert	PROPN
ejpam-4071	11	14	c∗-modules	c∗-modules	PROPN
ejpam-4071	11	15	c*-algebra	c*-algebra	PROPN
ejpam-4071	11	16	is	be	AUX
ejpam-4071	11	17	a	a	DET
ejpam-4071	11	18	main	main	ADJ
ejpam-4071	11	19	subject	subject	NOUN
ejpam-4071	11	20	in	in	ADP
ejpam-4071	11	21	the	the	DET
ejpam-4071	11	22	functional	functional	ADJ
ejpam-4071	11	23	analysis	analysis	NOUN
ejpam-4071	11	24	and	and	CCONJ
ejpam-4071	11	25	the	the	DET
ejpam-4071	11	26	operator	operator	NOUN
ejpam-4071	11	27	theory	theory	NOUN
ejpam-4071	11	28	which	which	PRON
ejpam-4071	11	29	play	play	VERB
ejpam-4071	11	30	fundamental	fundamental	ADJ
ejpam-4071	11	31	role	role	NOUN
ejpam-4071	11	32	in	in	ADP
ejpam-4071	11	33	noncommutative	noncommutative	ADJ
ejpam-4071	11	34	geometry	geometry	NOUN
ejpam-4071	11	35	and	and	CCONJ
ejpam-4071	11	36	theoretical	theoretical	ADJ
ejpam-4071	11	37	physics	physics	NOUN
ejpam-4071	11	38	,	,	PUNCT
ejpam-4071	11	39	especially	especially	ADV
ejpam-4071	11	40	the	the	DET
ejpam-4071	11	41	quantum	quantum	ADJ
ejpam-4071	11	42	mechanics	mechanic	NOUN
ejpam-4071	11	43	ma	ma	PROPN
ejpam-4071	11	44	and	and	CCONJ
ejpam-4071	11	45	et	et	PROPN
ejpam-4071	11	46	al	al	PROPN
ejpam-4071	11	47	.	.	PUNCT
ejpam-4071	12	1	[	[	X
ejpam-4071	12	2	20	20	NUM
ejpam-4071	12	3	]	]	PUNCT
ejpam-4071	12	4	,	,	PUNCT
ejpam-4071	12	5	introduced	introduce	VERB
ejpam-4071	12	6	the	the	DET
ejpam-4071	12	7	concept	concept	NOUN
ejpam-4071	12	8	of	of	ADP
ejpam-4071	12	9	c∗-algebra	c∗-algebra	PROPN
ejpam-4071	12	10	-	-	PUNCT
ejpam-4071	12	11	valued	value	VERB
ejpam-4071	12	12	metric	metric	ADJ
ejpam-4071	12	13	spaces	space	NOUN
ejpam-4071	12	14	.	.	PUNCT
ejpam-4071	13	1	the	the	DET
ejpam-4071	13	2	main	main	ADJ
ejpam-4071	13	3	idea	idea	NOUN
ejpam-4071	13	4	consists	consist	VERB
ejpam-4071	13	5	in	in	ADP
ejpam-4071	13	6	using	use	VERB
ejpam-4071	13	7	the	the	DET
ejpam-4071	13	8	set	set	NOUN
ejpam-4071	13	9	of	of	ADP
ejpam-4071	13	10	all	all	DET
ejpam-4071	13	11	positive	positive	ADJ
ejpam-4071	13	12	elements	element	NOUN
ejpam-4071	13	13	of	of	ADP
ejpam-4071	13	14	a	a	DET
ejpam-4071	13	15	unital	unital	ADJ
ejpam-4071	13	16	c∗-algebra	c∗-algebra	NOUN
ejpam-4071	13	17	instead	instead	ADV
ejpam-4071	13	18	∗corresponding	∗corresponde	VERB
ejpam-4071	13	19	author	author	NOUN
ejpam-4071	13	20	.	.	PUNCT
ejpam-4071	14	1	doi	doi	NOUN
ejpam-4071	14	2	:	:	PUNCT
ejpam-4071	14	3	https://doi.org/10.29020/nybg.ejpam.v14i4.4071	https://doi.org/10.29020/nybg.ejpam.v14i4.4071	ADJ
ejpam-4071	14	4	email	email	NOUN
ejpam-4071	14	5	addresses	address	NOUN
ejpam-4071	14	6	:	:	PUNCT
ejpam-4071	15	1	rashwan10@gmail.com	rashwan10@gmail.com	X
ejpam-4071	15	2	(	(	PUNCT
ejpam-4071	15	3	r.	r.	PROPN
ejpam-4071	15	4	a.	a.	PROPN
ejpam-4071	15	5	rashwan	rashwan	PROPN
ejpam-4071	15	6	)	)	PUNCT
ejpam-4071	15	7	,	,	PUNCT
ejpam-4071	15	8	hafran@uqu.edu.sa	hafran@uqu.edu.sa	PROPN
ejpam-4071	15	9	(	(	PUNCT
ejpam-4071	15	10	h.	h.	PROPN
ejpam-4071	15	11	adel	adel	PROPN
ejpam-4071	15	12	alfran	alfran	PROPN
ejpam-4071	15	13	)	)	PUNCT
ejpam-4071	15	14	,	,	PUNCT
ejpam-4071	15	15	asmaa.fangary44@yahoo.com	asmaa.fangary44@yahoo.com	X
ejpam-4071	15	16	(	(	PUNCT
ejpam-4071	15	17	a.	a.	NOUN
ejpam-4071	15	18	fangary),salehomran@yahoo.com	fangary),salehomran@yahoo.com	PROPN
ejpam-4071	15	19	(	(	PUNCT
ejpam-4071	15	20	s.	s.	PROPN
ejpam-4071	15	21	omran	omran	PROPN
ejpam-4071	15	22	)	)	PUNCT
ejpam-4071	15	23	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-4071	16	1	1237	1237	NUM
ejpam-4071	17	1	©	©	PROPN
ejpam-4071	17	2	2021	2021	NUM
ejpam-4071	17	3	ejpam	ejpam	VERB
ejpam-4071	17	4	all	all	DET
ejpam-4071	17	5	rights	right	NOUN
ejpam-4071	17	6	reserved	reserve	VERB
ejpam-4071	17	7	.	.	PUNCT
ejpam-4071	18	1	r.	r.	PROPN
ejpam-4071	18	2	a.	a.	PROPN
ejpam-4071	18	3	rashwan	rashwan	PROPN
ejpam-4071	18	4	et	et	PROPN
ejpam-4071	18	5	al	al	PROPN
ejpam-4071	18	6	.	.	PUNCT
ejpam-4071	18	7	/	/	SYM
ejpam-4071	18	8	eur	eur	PROPN
ejpam-4071	18	9	.	.	PUNCT
ejpam-4071	19	1	j.	j.	PROPN
ejpam-4071	19	2	pure	pure	PROPN
ejpam-4071	19	3	appl	appl	PROPN
ejpam-4071	19	4	.	.	PROPN
ejpam-4071	19	5	math	math	PROPN
ejpam-4071	19	6	,	,	PUNCT
ejpam-4071	19	7	14	14	NUM
ejpam-4071	19	8	(	(	PUNCT
ejpam-4071	19	9	4	4	NUM
ejpam-4071	19	10	)	)	PUNCT
ejpam-4071	19	11	(	(	PUNCT
ejpam-4071	19	12	2021	2021	NUM
ejpam-4071	19	13	)	)	PUNCT
ejpam-4071	19	14	,	,	PUNCT
ejpam-4071	19	15	1237	1237	NUM
ejpam-4071	19	16	-	-	SYM
ejpam-4071	19	17	1248	1248	NUM
ejpam-4071	19	18	1238	1238	NUM
ejpam-4071	19	19	of	of	ADP
ejpam-4071	19	20	the	the	DET
ejpam-4071	19	21	set	set	NOUN
ejpam-4071	19	22	of	of	ADP
ejpam-4071	19	23	real	real	ADJ
ejpam-4071	19	24	numbers	number	NOUN
ejpam-4071	19	25	.	.	PUNCT
ejpam-4071	20	1	they	they	PRON
ejpam-4071	20	2	presented	present	VERB
ejpam-4071	20	3	some	some	DET
ejpam-4071	20	4	fixed	fix	VERB
ejpam-4071	20	5	point	point	NOUN
ejpam-4071	20	6	results	result	NOUN
ejpam-4071	20	7	for	for	ADP
ejpam-4071	20	8	mapping	mapping	NOUN
ejpam-4071	20	9	under	under	ADP
ejpam-4071	20	10	contractive	contractive	ADJ
ejpam-4071	20	11	or	or	CCONJ
ejpam-4071	20	12	expansive	expansive	ADJ
ejpam-4071	20	13	conditions	condition	NOUN
ejpam-4071	20	14	in	in	ADP
ejpam-4071	20	15	these	these	DET
ejpam-4071	20	16	spaces	space	NOUN
ejpam-4071	20	17	.	.	PUNCT
ejpam-4071	21	1	later	later	ADV
ejpam-4071	21	2	,	,	PUNCT
ejpam-4071	21	3	ma	ma	PROPN
ejpam-4071	21	4	and	and	CCONJ
ejpam-4071	21	5	et	et	PROPN
ejpam-4071	21	6	al	al	PROPN
ejpam-4071	21	7	.	.	PUNCT
ejpam-4071	22	1	[	[	X
ejpam-4071	22	2	21	21	NUM
ejpam-4071	22	3	]	]	PUNCT
ejpam-4071	22	4	,	,	PUNCT
ejpam-4071	22	5	introduced	introduce	VERB
ejpam-4071	22	6	the	the	DET
ejpam-4071	22	7	concept	concept	NOUN
ejpam-4071	22	8	of	of	ADP
ejpam-4071	22	9	c∗-algebra	c∗-algebra	PROPN
ejpam-4071	22	10	-	-	PUNCT
ejpam-4071	22	11	valued	value	VERB
ejpam-4071	22	12	b	b	NOUN
ejpam-4071	22	13	-	-	PUNCT
ejpam-4071	22	14	metric	metric	ADJ
ejpam-4071	22	15	spaces	space	NOUN
ejpam-4071	22	16	and	and	CCONJ
ejpam-4071	22	17	proved	prove	VERB
ejpam-4071	22	18	some	some	DET
ejpam-4071	22	19	fixed	fix	VERB
ejpam-4071	22	20	point	point	NOUN
ejpam-4071	22	21	theorems	theorem	NOUN
ejpam-4071	22	22	such	such	ADJ
ejpam-4071	22	23	as	as	ADP
ejpam-4071	22	24	banach	banach	NOUN
ejpam-4071	22	25	and	and	CCONJ
ejpam-4071	22	26	kannan	kannan	PROPN
ejpam-4071	22	27	type	type	NOUN
ejpam-4071	22	28	fixed	fix	VERB
ejpam-4071	22	29	point	point	NOUN
ejpam-4071	22	30	theorems.for	theorems.for	ADP
ejpam-4071	22	31	other	other	ADJ
ejpam-4071	22	32	results	result	NOUN
ejpam-4071	22	33	on	on	ADP
ejpam-4071	22	34	c∗-algebravalued	c∗-algebravalue	VERB
ejpam-4071	22	35	b	b	NOUN
ejpam-4071	22	36	-	-	ADJ
ejpam-4071	22	37	metric	metric	ADJ
ejpam-4071	22	38	spaces	space	NOUN
ejpam-4071	22	39	and	and	CCONJ
ejpam-4071	22	40	c∗-algebra	c∗-algebra	NOUN
ejpam-4071	22	41	-	-	PUNCT
ejpam-4071	22	42	valued	value	VERB
ejpam-4071	22	43	-	-	PUNCT
ejpam-4071	22	44	metric	metric	ADJ
ejpam-4071	22	45	spaces	space	NOUN
ejpam-4071	22	46	,	,	PUNCT
ejpam-4071	22	47	see	see	VERB
ejpam-4071	22	48	[	[	X
ejpam-4071	22	49	4	4	NUM
ejpam-4071	22	50	,	,	PUNCT
ejpam-4071	22	51	13	13	NUM
ejpam-4071	22	52	,	,	PUNCT
ejpam-4071	22	53	15	15	NUM
ejpam-4071	22	54	,	,	PUNCT
ejpam-4071	22	55	18	18	NUM
ejpam-4071	22	56	,	,	PUNCT
ejpam-4071	22	57	22	22	NUM
ejpam-4071	22	58	]	]	PUNCT
ejpam-4071	22	59	.	.	PUNCT
ejpam-4071	23	1	an	an	DET
ejpam-4071	23	2	element	element	NOUN
ejpam-4071	23	3	x	x	SYM
ejpam-4071	23	4	∈	∈	PROPN
ejpam-4071	23	5	a	a	PRON
ejpam-4071	23	6	is	be	AUX
ejpam-4071	23	7	a	a	DET
ejpam-4071	23	8	positive	positive	ADJ
ejpam-4071	23	9	element	element	NOUN
ejpam-4071	23	10	,	,	PUNCT
ejpam-4071	23	11	denote	denote	VERB
ejpam-4071	23	12	it	it	PRON
ejpam-4071	23	13	by	by	ADP
ejpam-4071	23	14	x	x	PUNCT
ejpam-4071	23	15	⪰	⪰	NOUN
ejpam-4071	23	16	0	0	NUM
ejpam-4071	23	17	,	,	PUNCT
ejpam-4071	23	18	if	if	SCONJ
ejpam-4071	23	19	x	x	SYM
ejpam-4071	23	20	∈	∈	PROPN
ejpam-4071	23	21	ah	ah	INTJ
ejpam-4071	23	22	and	and	CCONJ
ejpam-4071	23	23	σ(x	σ(x	NOUN
ejpam-4071	23	24	)	)	PUNCT
ejpam-4071	23	25	⊂	⊂	PROPN
ejpam-4071	24	1	[	[	X
ejpam-4071	24	2	0,+∞	0,+∞	X
ejpam-4071	24	3	]	]	X
ejpam-4071	24	4	,	,	PUNCT
ejpam-4071	24	5	where	where	SCONJ
ejpam-4071	24	6	σ(x	σ(x	NOUN
ejpam-4071	24	7	)	)	PUNCT
ejpam-4071	24	8	is	be	AUX
ejpam-4071	24	9	the	the	DET
ejpam-4071	24	10	spectrum	spectrum	NOUN
ejpam-4071	24	11	of	of	ADP
ejpam-4071	24	12	x	x	PUNCT
ejpam-4071	24	13	and	and	CCONJ
ejpam-4071	24	14	ah	ah	INTJ
ejpam-4071	24	15	=	=	SYM
ejpam-4071	24	16	{	{	PUNCT
ejpam-4071	24	17	x	x	PUNCT
ejpam-4071	24	18	∈	∈	PROPN
ejpam-4071	24	19	a	a	PRON
ejpam-4071	24	20	:	:	PUNCT
ejpam-4071	24	21	x∗	x∗	PROPN
ejpam-4071	24	22	=	=	PUNCT
ejpam-4071	24	23	x	x	X
ejpam-4071	24	24	}	}	PUNCT
ejpam-4071	24	25	.	.	PUNCT
ejpam-4071	25	1	using	use	VERB
ejpam-4071	25	2	positive	positive	ADJ
ejpam-4071	25	3	elements	element	NOUN
ejpam-4071	25	4	,	,	PUNCT
ejpam-4071	25	5	one	one	PRON
ejpam-4071	25	6	can	can	AUX
ejpam-4071	25	7	define	define	VERB
ejpam-4071	25	8	a	a	DET
ejpam-4071	25	9	partial	partial	ADJ
ejpam-4071	25	10	ordering	ordering	NOUN
ejpam-4071	25	11	⪯	⪯	NOUN
ejpam-4071	25	12	on	on	ADP
ejpam-4071	25	13	ah	ah	INTJ
ejpam-4071	25	14	as	as	SCONJ
ejpam-4071	25	15	follows	follow	VERB
ejpam-4071	25	16	:	:	PUNCT
ejpam-4071	25	17	x	x	PUNCT
ejpam-4071	25	18	⪯	⪯	NOUN
ejpam-4071	25	19	y	y	PROPN
ejpam-4071	25	20	if	if	SCONJ
ejpam-4071	25	21	and	and	CCONJ
ejpam-4071	25	22	only	only	ADV
ejpam-4071	25	23	if	if	SCONJ
ejpam-4071	25	24	y−x	y−x	NOUN
ejpam-4071	25	25	⪰	⪰	VERB
ejpam-4071	25	26	0	0	NUM
ejpam-4071	25	27	.	.	PUNCT
ejpam-4071	25	28	from	from	ADP
ejpam-4071	25	29	now	now	ADV
ejpam-4071	25	30	on	on	ADV
ejpam-4071	25	31	,	,	PUNCT
ejpam-4071	25	32	by	by	ADP
ejpam-4071	25	33	a+	a+	PUNCT
ejpam-4071	25	34	we	we	PRON
ejpam-4071	25	35	denote	denote	VERB
ejpam-4071	25	36	the	the	DET
ejpam-4071	25	37	set	set	NOUN
ejpam-4071	25	38	{	{	PUNCT
ejpam-4071	25	39	x	x	SYM
ejpam-4071	25	40	∈	∈	PROPN
ejpam-4071	25	41	a	a	PRON
ejpam-4071	25	42	:	:	PUNCT
ejpam-4071	25	43	x	x	PUNCT
ejpam-4071	25	44	⪰	⪰	NOUN
ejpam-4071	25	45	0	0	NUM
ejpam-4071	25	46	}	}	PUNCT
ejpam-4071	25	47	and	and	CCONJ
ejpam-4071	25	48	|x|	|x|	PROPN
ejpam-4071	25	49	=	=	SYM
ejpam-4071	25	50	(	(	PUNCT
ejpam-4071	25	51	x∗x	x∗x	ADJ
ejpam-4071	25	52	)	)	PUNCT
ejpam-4071	25	53	1	1	NUM
ejpam-4071	25	54	2	2	NUM
ejpam-4071	25	55	.	.	X
ejpam-4071	26	1	2	2	X
ejpam-4071	26	2	.	.	NUM
ejpam-4071	26	3	preliminaries	preliminary	NOUN
ejpam-4071	26	4	in	in	ADP
ejpam-4071	26	5	this	this	DET
ejpam-4071	26	6	section	section	NOUN
ejpam-4071	26	7	,	,	PUNCT
ejpam-4071	26	8	we	we	PRON
ejpam-4071	26	9	begin	begin	VERB
ejpam-4071	26	10	with	with	ADP
ejpam-4071	26	11	some	some	DET
ejpam-4071	26	12	basic	basic	ADJ
ejpam-4071	26	13	notations	notation	NOUN
ejpam-4071	26	14	and	and	CCONJ
ejpam-4071	26	15	definition	definition	NOUN
ejpam-4071	26	16	c∗-algebra	c∗-algebra	NOUN
ejpam-4071	26	17	and	and	CCONJ
ejpam-4071	26	18	fixed	fix	VERB
ejpam-4071	26	19	point	point	NOUN
ejpam-4071	26	20	theory	theory	NOUN
ejpam-4071	26	21	that	that	PRON
ejpam-4071	26	22	will	will	AUX
ejpam-4071	26	23	be	be	AUX
ejpam-4071	26	24	very	very	ADV
ejpam-4071	26	25	important	important	ADJ
ejpam-4071	26	26	and	and	CCONJ
ejpam-4071	26	27	useful	useful	ADJ
ejpam-4071	26	28	in	in	ADP
ejpam-4071	26	29	the	the	DET
ejpam-4071	26	30	sequal	sequal	ADJ
ejpam-4071	26	31	.	.	PUNCT
ejpam-4071	27	1	definition	definition	NOUN
ejpam-4071	27	2	1	1	NUM
ejpam-4071	27	3	.	.	PUNCT
ejpam-4071	28	1	[	[	X
ejpam-4071	28	2	9	9	NUM
ejpam-4071	28	3	]	]	X
ejpam-4071	28	4	a	a	DET
ejpam-4071	28	5	banach	banach	NOUN
ejpam-4071	28	6	∗-algebra	∗-algebra	NOUN
ejpam-4071	28	7	is	be	AUX
ejpam-4071	28	8	a	a	DET
ejpam-4071	28	9	∗-algebra	∗-algebra	NOUN
ejpam-4071	28	10	a	a	DET
ejpam-4071	28	11	together	together	NOUN
ejpam-4071	28	12	with	with	ADP
ejpam-4071	28	13	a	a	DET
ejpam-4071	28	14	complete	complete	ADJ
ejpam-4071	28	15	submultiplicative	submultiplicative	ADJ
ejpam-4071	28	16	norm	norm	NOUN
ejpam-4071	28	17	such	such	ADJ
ejpam-4071	28	18	that	that	PRON
ejpam-4071	28	19	∥ab∥	∥ab∥	ADJ
ejpam-4071	28	20	≤	≤	NUM
ejpam-4071	28	21	∥a∥∥b∥	∥a∥∥b∥	NOUN
ejpam-4071	28	22	(	(	PUNCT
ejpam-4071	28	23	for	for	ADP
ejpam-4071	28	24	all	all	DET
ejpam-4071	28	25	a	a	PRON
ejpam-4071	28	26	,	,	PUNCT
ejpam-4071	28	27	b	b	X
ejpam-4071	28	28	∈	∈	PROPN
ejpam-4071	28	29	a	a	PRON
ejpam-4071	28	30	)	)	PUNCT
ejpam-4071	28	31	.	.	PUNCT
ejpam-4071	29	1	a	a	DET
ejpam-4071	29	2	c∗algebra	c∗algebra	NOUN
ejpam-4071	29	3	is	be	AUX
ejpam-4071	29	4	a	a	DET
ejpam-4071	29	5	banach	banach	NOUN
ejpam-4071	29	6	∗-algebra	∗-algebra	NOUN
ejpam-4071	29	7	such	such	ADJ
ejpam-4071	29	8	that	that	DET
ejpam-4071	29	9	∥a∗a∥	∥a∗a∥	NOUN
ejpam-4071	29	10	=	=	SYM
ejpam-4071	29	11	∥a∥2	∥a∥2	PROPN
ejpam-4071	29	12	(	(	PUNCT
ejpam-4071	29	13	for	for	ADP
ejpam-4071	29	14	all	all	DET
ejpam-4071	29	15	a	a	DET
ejpam-4071	29	16	∈	∈	NOUN
ejpam-4071	29	17	a	a	NOUN
ejpam-4071	29	18	)	)	PUNCT
ejpam-4071	29	19	.	.	PUNCT
ejpam-4071	30	1	definition	definition	NOUN
ejpam-4071	30	2	2	2	NUM
ejpam-4071	30	3	.	.	PUNCT
ejpam-4071	31	1	[	[	X
ejpam-4071	31	2	9	9	NUM
ejpam-4071	31	3	]	]	X
ejpam-4071	31	4	an	an	DET
ejpam-4071	31	5	element	element	NOUN
ejpam-4071	31	6	a	a	DET
ejpam-4071	31	7	∈	∈	NOUN
ejpam-4071	31	8	a	a	PRON
ejpam-4071	31	9	is	be	AUX
ejpam-4071	31	10	positive	positive	ADJ
ejpam-4071	31	11	element	element	NOUN
ejpam-4071	31	12	,	,	PUNCT
ejpam-4071	31	13	if	if	SCONJ
ejpam-4071	31	14	a	a	DET
ejpam-4071	31	15	=	=	PUNCT
ejpam-4071	31	16	a∗	a∗	NOUN
ejpam-4071	31	17	and	and	CCONJ
ejpam-4071	31	18	σ(a	σ(a	PROPN
ejpam-4071	31	19	)	)	PUNCT
ejpam-4071	31	20	⊆	⊆	NUM
ejpam-4071	31	21	r+	r+	NOUN
ejpam-4071	31	22	,	,	PUNCT
ejpam-4071	31	23	where	where	SCONJ
ejpam-4071	31	24	σ(a	σ(a	PROPN
ejpam-4071	31	25	)	)	PUNCT
ejpam-4071	31	26	is	be	AUX
ejpam-4071	31	27	the	the	DET
ejpam-4071	31	28	spectrum	spectrum	NOUN
ejpam-4071	31	29	of	of	ADP
ejpam-4071	31	30	a	a	PRON
ejpam-4071	31	31	,	,	PUNCT
ejpam-4071	31	32	we	we	PRON
ejpam-4071	31	33	denote	denote	VERB
ejpam-4071	31	34	a+	a+	PUNCT
ejpam-4071	31	35	the	the	DET
ejpam-4071	31	36	set	set	NOUN
ejpam-4071	31	37	of	of	ADP
ejpam-4071	31	38	all	all	DET
ejpam-4071	31	39	positive	positive	ADJ
ejpam-4071	31	40	element	element	NOUN
ejpam-4071	31	41	in	in	ADP
ejpam-4071	31	42	a.	a.	NOUN
ejpam-4071	31	43	definition	definition	NOUN
ejpam-4071	31	44	3	3	NUM
ejpam-4071	31	45	.	.	PUNCT
ejpam-4071	32	1	[	[	X
ejpam-4071	32	2	8	8	NUM
ejpam-4071	32	3	,	,	PUNCT
ejpam-4071	32	4	19	19	NUM
ejpam-4071	32	5	]	]	PUNCT
ejpam-4071	32	6	a	a	DET
ejpam-4071	32	7	pre	pre	ADJ
ejpam-4071	32	8	-	-	ADJ
ejpam-4071	32	9	hilbert	hilbert	ADJ
ejpam-4071	32	10	c∗-module	c∗-module	NOUN
ejpam-4071	32	11	e	e	NOUN
ejpam-4071	32	12	over	over	ADP
ejpam-4071	32	13	a	a	DET
ejpam-4071	32	14	c∗-algebra	c∗-algebra	PROPN
ejpam-4071	32	15	a	a	PRON
ejpam-4071	32	16	,	,	PUNCT
ejpam-4071	32	17	is	be	AUX
ejpam-4071	32	18	a	a	DET
ejpam-4071	32	19	right	right	ADJ
ejpam-4071	32	20	a	a	NOUN
ejpam-4071	32	21	-	-	PUNCT
ejpam-4071	32	22	module	module	NOUN
ejpam-4071	32	23	together	together	ADV
ejpam-4071	32	24	with	with	ADP
ejpam-4071	32	25	an	an	DET
ejpam-4071	32	26	a	a	ADV
ejpam-4071	32	27	-	-	PUNCT
ejpam-4071	32	28	valued	value	VERB
ejpam-4071	32	29	inner	inner	ADJ
ejpam-4071	32	30	product	product	NOUN
ejpam-4071	32	31	<	<	X
ejpam-4071	32	32	.	.	PUNCT
ejpam-4071	32	33	,	,	PUNCT
ejpam-4071	32	34	.	.	PUNCT
ejpam-4071	33	1	>	>	PUNCT
ejpam-4071	33	2	:	:	PUNCT
ejpam-4071	33	3	e	e	X
ejpam-4071	33	4	×	×	NOUN
ejpam-4071	33	5	e	e	NOUN
ejpam-4071	33	6	−→	−→	NOUN
ejpam-4071	33	7	a	a	DET
ejpam-4071	33	8	satisfying	satisfy	VERB
ejpam-4071	33	9	the	the	DET
ejpam-4071	33	10	conditions	condition	NOUN
ejpam-4071	33	11	:	:	PUNCT
ejpam-4071	33	12	(	(	PUNCT
ejpam-4071	33	13	1	1	X
ejpam-4071	33	14	)	)	PUNCT
ejpam-4071	33	15	<	<	X
ejpam-4071	33	16	x	x	X
ejpam-4071	33	17	,	,	PUNCT
ejpam-4071	33	18	x	x	INTJ
ejpam-4071	33	19	>	>	PUNCT
ejpam-4071	33	20	⪰	⪰	NOUN
ejpam-4071	33	21	0	0	NUM
ejpam-4071	33	22	for	for	ADP
ejpam-4071	33	23	all	all	DET
ejpam-4071	33	24	x	x	SYM
ejpam-4071	33	25	∈	∈	PROPN
ejpam-4071	33	26	e	e	NOUN
ejpam-4071	33	27	;	;	PUNCT
ejpam-4071	33	28	(	(	PUNCT
ejpam-4071	33	29	2	2	X
ejpam-4071	33	30	)	)	PUNCT
ejpam-4071	33	31	<	<	X
ejpam-4071	33	32	x	x	X
ejpam-4071	33	33	,	,	PUNCT
ejpam-4071	33	34	x	x	INTJ
ejpam-4071	33	35	>	>	PUNCT
ejpam-4071	33	36	=	=	SYM
ejpam-4071	33	37	0	0	PUNCT
ejpam-4071	33	38	if	if	SCONJ
ejpam-4071	33	39	and	and	CCONJ
ejpam-4071	33	40	only	only	ADV
ejpam-4071	33	41	if	if	SCONJ
ejpam-4071	33	42	x	x	SYM
ejpam-4071	33	43	=	=	SYM
ejpam-4071	33	44	0	0	NUM
ejpam-4071	33	45	;	;	PUNCT
ejpam-4071	33	46	(	(	PUNCT
ejpam-4071	33	47	3	3	X
ejpam-4071	33	48	)	)	PUNCT
ejpam-4071	33	49	<	<	X
ejpam-4071	33	50	x	x	X
ejpam-4071	33	51	,	,	PUNCT
ejpam-4071	33	52	αy	αy	ADP
ejpam-4071	33	53	+	+	CCONJ
ejpam-4071	33	54	βz	βz	PRON
ejpam-4071	33	55	>	>	PUNCT
ejpam-4071	33	56	=	=	NOUN
ejpam-4071	33	57	α	α	X
ejpam-4071	33	58	<	<	X
ejpam-4071	33	59	x	x	X
ejpam-4071	33	60	,	,	PUNCT
ejpam-4071	33	61	y	y	PROPN
ejpam-4071	33	62	>	>	X
ejpam-4071	34	1	+	+	PROPN
ejpam-4071	34	2	β	β	X
ejpam-4071	34	3	<	<	X
ejpam-4071	34	4	x	x	X
ejpam-4071	34	5	,	,	PUNCT
ejpam-4071	34	6	z	z	X
ejpam-4071	34	7	>	>	X
ejpam-4071	34	8	for	for	ADP
ejpam-4071	34	9	all	all	DET
ejpam-4071	34	10	x	x	NOUN
ejpam-4071	34	11	,	,	PUNCT
ejpam-4071	34	12	y	y	PROPN
ejpam-4071	34	13	,	,	PUNCT
ejpam-4071	34	14	z	z	NOUN
ejpam-4071	34	15	∈	∈	PROPN
ejpam-4071	34	16	e	e	X
ejpam-4071	34	17	,	,	PUNCT
ejpam-4071	34	18	α	α	X
ejpam-4071	34	19	,	,	PUNCT
ejpam-4071	34	20	β	β	X
ejpam-4071	34	21	∈	∈	NOUN
ejpam-4071	34	22	c	c	X
ejpam-4071	34	23	;	;	PUNCT
ejpam-4071	34	24	(	(	PUNCT
ejpam-4071	34	25	4	4	X
ejpam-4071	34	26	)	)	PUNCT
ejpam-4071	34	27	<	<	X
ejpam-4071	34	28	x	x	X
ejpam-4071	34	29	,	,	PUNCT
ejpam-4071	34	30	ya	ya	PRON
ejpam-4071	34	31	>	>	PUNCT
ejpam-4071	34	32	=	=	X
ejpam-4071	34	33	<	<	X
ejpam-4071	34	34	x	x	X
ejpam-4071	34	35	,	,	PUNCT
ejpam-4071	34	36	y	y	PROPN
ejpam-4071	34	37	>	>	X
ejpam-4071	34	38	a	a	PRON
ejpam-4071	34	39	for	for	ADP
ejpam-4071	34	40	all	all	DET
ejpam-4071	34	41	x	x	NOUN
ejpam-4071	34	42	,	,	PUNCT
ejpam-4071	34	43	y	y	PROPN
ejpam-4071	34	44	∈	∈	PROPN
ejpam-4071	34	45	e	e	PROPN
ejpam-4071	34	46	,	,	PUNCT
ejpam-4071	34	47	a	a	DET
ejpam-4071	34	48	∈	∈	PROPN
ejpam-4071	34	49	a	a	PRON
ejpam-4071	34	50	;	;	PUNCT
ejpam-4071	34	51	(	(	PUNCT
ejpam-4071	34	52	5	5	NUM
ejpam-4071	34	53	)	)	PUNCT
ejpam-4071	34	54	<	<	X
ejpam-4071	34	55	x	x	X
ejpam-4071	34	56	,	,	PUNCT
ejpam-4071	34	57	y	y	PROPN
ejpam-4071	34	58	>	>	X
ejpam-4071	34	59	∗=	∗=	PROPN
ejpam-4071	34	60	<	<	X
ejpam-4071	34	61	y	y	PROPN
ejpam-4071	34	62	,	,	PUNCT
ejpam-4071	34	63	x	x	X
ejpam-4071	34	64	>	>	X
ejpam-4071	34	65	for	for	ADP
ejpam-4071	34	66	all	all	DET
ejpam-4071	34	67	x	x	NOUN
ejpam-4071	34	68	,	,	PUNCT
ejpam-4071	34	69	y	y	PROPN
ejpam-4071	34	70	∈	∈	PROPN
ejpam-4071	34	71	e.	e.	PROPN
ejpam-4071	34	72	definition	definition	NOUN
ejpam-4071	34	73	4	4	NUM
ejpam-4071	34	74	.	.	PUNCT
ejpam-4071	35	1	[	[	X
ejpam-4071	35	2	8	8	X
ejpam-4071	35	3	]	]	X
ejpam-4071	35	4	the	the	DET
ejpam-4071	35	5	norm	norm	NOUN
ejpam-4071	35	6	of	of	ADP
ejpam-4071	35	7	an	an	DET
ejpam-4071	35	8	element	element	NOUN
ejpam-4071	35	9	e	e	X
ejpam-4071	35	10	∈	∈	NOUN
ejpam-4071	35	11	e	e	NOUN
ejpam-4071	35	12	is	be	AUX
ejpam-4071	35	13	defined	define	VERB
ejpam-4071	35	14	as	as	ADP
ejpam-4071	35	15	∥x∥e	∥x∥e	PROPN
ejpam-4071	35	16	:	:	PUNCT
ejpam-4071	35	17	=	=	NOUN
ejpam-4071	35	18	√	√	ADP
ejpam-4071	35	19	∥	∥	NUM
ejpam-4071	35	20	<	<	X
ejpam-4071	35	21	x	x	X
ejpam-4071	35	22	,	,	PUNCT
ejpam-4071	35	23	x	x	PROPN
ejpam-4071	35	24	>	>	X
ejpam-4071	35	25	∥r	∥r	PROPN
ejpam-4071	35	26	,	,	PUNCT
ejpam-4071	35	27	where	where	SCONJ
ejpam-4071	35	28	∥.∥r	∥.∥r	PROPN
ejpam-4071	35	29	is	be	AUX
ejpam-4071	35	30	the	the	DET
ejpam-4071	35	31	r	r	NOUN
ejpam-4071	35	32	-	-	PUNCT
ejpam-4071	35	33	valued	value	VERB
ejpam-4071	35	34	norm	norm	NOUN
ejpam-4071	35	35	.	.	PUNCT
ejpam-4071	36	1	if	if	SCONJ
ejpam-4071	36	2	a	a	DET
ejpam-4071	36	3	pre	pre	NOUN
ejpam-4071	36	4	-	-	NOUN
ejpam-4071	36	5	hilbert	hilbert	ADJ
ejpam-4071	36	6	a	a	DET
ejpam-4071	36	7	-module	-module	NOUN
ejpam-4071	36	8	is	be	AUX
ejpam-4071	36	9	complete	complete	ADJ
ejpam-4071	36	10	with	with	ADP
ejpam-4071	36	11	respect	respect	NOUN
ejpam-4071	36	12	to	to	ADP
ejpam-4071	36	13	its	its	PRON
ejpam-4071	36	14	norm	norm	NOUN
ejpam-4071	36	15	,	,	PUNCT
ejpam-4071	36	16	it	it	PRON
ejpam-4071	36	17	is	be	AUX
ejpam-4071	36	18	said	say	VERB
ejpam-4071	36	19	to	to	PART
ejpam-4071	36	20	be	be	AUX
ejpam-4071	36	21	a	a	DET
ejpam-4071	36	22	hilbert	hilbert	NOUN
ejpam-4071	36	23	a	a	DET
ejpam-4071	36	24	-module	-module	NOUN
ejpam-4071	36	25	.	.	PUNCT
ejpam-4071	36	26	example	example	NOUN
ejpam-4071	37	1	1	1	NUM
ejpam-4071	37	2	.	.	PUNCT
ejpam-4071	38	1	every	every	DET
ejpam-4071	38	2	c∗-algebra	c∗-algebra	PROPN
ejpam-4071	38	3	a	a	PRON
ejpam-4071	38	4	is	be	AUX
ejpam-4071	38	5	a	a	DET
ejpam-4071	38	6	hilbert	hilbert	NOUN
ejpam-4071	38	7	a	a	DET
ejpam-4071	38	8	-	-	PUNCT
ejpam-4071	38	9	module	module	NOUN
ejpam-4071	38	10	over	over	ADP
ejpam-4071	38	11	itself	itself	PRON
ejpam-4071	38	12	when	when	SCONJ
ejpam-4071	38	13	equipped	equip	VERB
ejpam-4071	38	14	with	with	ADP
ejpam-4071	38	15	the	the	DET
ejpam-4071	38	16	a	a	ADV
ejpam-4071	38	17	-	-	PUNCT
ejpam-4071	38	18	valued	value	VERB
ejpam-4071	38	19	inner	inner	ADJ
ejpam-4071	38	20	product	product	NOUN
ejpam-4071	38	21	given	give	VERB
ejpam-4071	38	22	simply	simply	ADV
ejpam-4071	38	23	by	by	ADP
ejpam-4071	38	24	<	<	X
ejpam-4071	38	25	a	a	PROPN
ejpam-4071	38	26	,	,	PUNCT
ejpam-4071	38	27	b	b	X
ejpam-4071	38	28	>	>	X
ejpam-4071	38	29	=	=	PUNCT
ejpam-4071	38	30	a∗b	a∗b	PROPN
ejpam-4071	38	31	,	,	PUNCT
ejpam-4071	38	32	(	(	PUNCT
ejpam-4071	38	33	a	a	PRON
ejpam-4071	38	34	,	,	PUNCT
ejpam-4071	38	35	b	b	PROPN
ejpam-4071	38	36	∈	∈	PROPN
ejpam-4071	38	37	a	a	PRON
ejpam-4071	38	38	)	)	PUNCT
ejpam-4071	38	39	.	.	PUNCT
ejpam-4071	39	1	definition	definition	NOUN
ejpam-4071	39	2	5	5	NUM
ejpam-4071	39	3	.	.	PUNCT
ejpam-4071	40	1	[	[	X
ejpam-4071	40	2	19	19	NUM
ejpam-4071	40	3	]	]	PUNCT
ejpam-4071	40	4	let	let	VERB
ejpam-4071	40	5	e	e	PRON
ejpam-4071	40	6	be	be	AUX
ejpam-4071	40	7	a	a	DET
ejpam-4071	40	8	hilbert	hilbert	NOUN
ejpam-4071	40	9	a	a	NOUN
ejpam-4071	40	10	-	-	PUNCT
ejpam-4071	40	11	module	module	NOUN
ejpam-4071	40	12	.	.	PUNCT
ejpam-4071	41	1	a	a	DET
ejpam-4071	41	2	map	map	NOUN
ejpam-4071	41	3	t	t	NOUN
ejpam-4071	41	4	:	:	PUNCT
ejpam-4071	41	5	e	e	X
ejpam-4071	41	6	−→	−→	NOUN
ejpam-4071	41	7	e	e	NOUN
ejpam-4071	41	8	is	be	AUX
ejpam-4071	41	9	said	say	VERB
ejpam-4071	41	10	to	to	PART
ejpam-4071	41	11	be	be	AUX
ejpam-4071	41	12	adjointable	adjointable	ADJ
ejpam-4071	41	13	if	if	SCONJ
ejpam-4071	41	14	there	there	PRON
ejpam-4071	41	15	exists	exist	VERB
ejpam-4071	41	16	a	a	DET
ejpam-4071	41	17	map	map	NOUN
ejpam-4071	41	18	t	t	NOUN
ejpam-4071	41	19	∗	∗	NOUN
ejpam-4071	41	20	:	:	PUNCT
ejpam-4071	42	1	e	e	X
ejpam-4071	42	2	−→	−→	NOUN
ejpam-4071	42	3	e	e	NOUN
ejpam-4071	42	4	satisfying	satisfy	VERB
ejpam-4071	42	5	r.	r.	PROPN
ejpam-4071	42	6	a.	a.	PROPN
ejpam-4071	42	7	rashwan	rashwan	PROPN
ejpam-4071	42	8	et	et	PROPN
ejpam-4071	42	9	al	al	PROPN
ejpam-4071	42	10	.	.	PUNCT
ejpam-4071	42	11	/	/	SYM
ejpam-4071	42	12	eur	eur	PROPN
ejpam-4071	42	13	.	.	PUNCT
ejpam-4071	43	1	j.	j.	PROPN
ejpam-4071	43	2	pure	pure	PROPN
ejpam-4071	43	3	appl	appl	PROPN
ejpam-4071	43	4	.	.	PROPN
ejpam-4071	43	5	math	math	PROPN
ejpam-4071	43	6	,	,	PUNCT
ejpam-4071	43	7	14	14	NUM
ejpam-4071	43	8	(	(	PUNCT
ejpam-4071	43	9	4	4	NUM
ejpam-4071	43	10	)	)	PUNCT
ejpam-4071	43	11	(	(	PUNCT
ejpam-4071	43	12	2021	2021	NUM
ejpam-4071	43	13	)	)	PUNCT
ejpam-4071	43	14	,	,	PUNCT
ejpam-4071	43	15	1237	1237	NUM
ejpam-4071	43	16	-	-	SYM
ejpam-4071	43	17	1248	1248	NUM
ejpam-4071	43	18	1239	1239	NUM
ejpam-4071	43	19	<	<	X
ejpam-4071	43	20	x	x	X
ejpam-4071	43	21	,	,	PUNCT
ejpam-4071	43	22	ty	ty	INTJ
ejpam-4071	43	23	>	>	PUNCT
ejpam-4071	43	24	=	=	X
ejpam-4071	43	25	<	<	X
ejpam-4071	43	26	t	t	NOUN
ejpam-4071	43	27	∗x	∗x	NOUN
ejpam-4071	43	28	,	,	PUNCT
ejpam-4071	43	29	y	y	PROPN
ejpam-4071	43	30	>	>	X
ejpam-4071	43	31	for	for	ADP
ejpam-4071	43	32	all	all	DET
ejpam-4071	43	33	x	x	NOUN
ejpam-4071	43	34	,	,	PUNCT
ejpam-4071	43	35	y	y	PROPN
ejpam-4071	43	36	∈	∈	PROPN
ejpam-4071	43	37	e.	e.	PROPN
ejpam-4071	43	38	definition	definition	NOUN
ejpam-4071	43	39	6	6	NUM
ejpam-4071	43	40	.	.	PUNCT
ejpam-4071	44	1	[	[	X
ejpam-4071	44	2	3	3	X
ejpam-4071	44	3	]	]	X
ejpam-4071	44	4	an	an	DET
ejpam-4071	44	5	element	element	NOUN
ejpam-4071	44	6	t	t	PROPN
ejpam-4071	44	7	∈	∈	PROPN
ejpam-4071	44	8	l(e	l(e	NOUN
ejpam-4071	44	9	)	)	PUNCT
ejpam-4071	44	10	is	be	AUX
ejpam-4071	44	11	positive	positive	ADJ
ejpam-4071	44	12	if	if	SCONJ
ejpam-4071	44	13	for	for	SCONJ
ejpam-4071	44	14	every	every	DET
ejpam-4071	44	15	x	x	SYM
ejpam-4071	44	16	∈	∈	PROPN
ejpam-4071	44	17	e	e	NOUN
ejpam-4071	44	18	we	we	PRON
ejpam-4071	44	19	have	have	VERB
ejpam-4071	44	20	<	<	X
ejpam-4071	44	21	tx	tx	PROPN
ejpam-4071	44	22	,	,	PUNCT
ejpam-4071	44	23	x	x	X
ejpam-4071	44	24	>	>	X
ejpam-4071	44	25	a⪰	a⪰	PROPN
ejpam-4071	44	26	0	0	PUNCT
ejpam-4071	45	1	and	and	CCONJ
ejpam-4071	45	2	we	we	PRON
ejpam-4071	45	3	write	write	VERB
ejpam-4071	45	4	it	it	PRON
ejpam-4071	45	5	by	by	ADP
ejpam-4071	45	6	t	t	NOUN
ejpam-4071	45	7	⪰	⪰	NOUN
ejpam-4071	45	8	0	0	PUNCT
ejpam-4071	46	1	and	and	CCONJ
ejpam-4071	46	2	we	we	PRON
ejpam-4071	46	3	denote	denote	VERB
ejpam-4071	46	4	the	the	DET
ejpam-4071	46	5	set	set	NOUN
ejpam-4071	46	6	l(e)+	l(e)+	NOUN
ejpam-4071	46	7	=	=	PUNCT
ejpam-4071	46	8	{	{	PUNCT
ejpam-4071	46	9	t	t	NOUN
ejpam-4071	46	10	∈	∈	PROPN
ejpam-4071	46	11	e	e	X
ejpam-4071	46	12	;	;	PUNCT
ejpam-4071	46	13	t	t	X
ejpam-4071	46	14	⪰	⪰	NOUN
ejpam-4071	46	15	0	0	NUM
ejpam-4071	46	16	}	}	PUNCT
ejpam-4071	46	17	,	,	PUNCT
ejpam-4071	46	18	we	we	PRON
ejpam-4071	46	19	define	define	VERB
ejpam-4071	46	20	a	a	DET
ejpam-4071	46	21	partial	partial	ADJ
ejpam-4071	46	22	ordering	ordering	NOUN
ejpam-4071	46	23	relation	relation	NOUN
ejpam-4071	46	24	on	on	ADP
ejpam-4071	46	25	l(e)+	l(e)+	PROPN
ejpam-4071	46	26	as	as	SCONJ
ejpam-4071	46	27	if	if	SCONJ
ejpam-4071	46	28	t1	t1	PROPN
ejpam-4071	46	29	,	,	PUNCT
ejpam-4071	46	30	t2	t2	NOUN
ejpam-4071	46	31	∈	∈	PROPN
ejpam-4071	46	32	l(e	l(e	NOUN
ejpam-4071	46	33	)	)	PUNCT
ejpam-4071	46	34	,	,	PUNCT
ejpam-4071	46	35	t1	t1	NOUN
ejpam-4071	46	36	⪯l(e	⪯l(e	NOUN
ejpam-4071	46	37	)	)	PUNCT
ejpam-4071	46	38	t2	t2	NOUN
ejpam-4071	46	39	if	if	SCONJ
ejpam-4071	47	1	and	and	CCONJ
ejpam-4071	47	2	only	only	ADV
ejpam-4071	47	3	if	if	SCONJ
ejpam-4071	47	4	t2	t2	PROPN
ejpam-4071	47	5	−	−	PROPN
ejpam-4071	47	6	t1	t1	NOUN
ejpam-4071	47	7	∈	∈	PROPN
ejpam-4071	47	8	l(e)+	l(e)+	PROPN
ejpam-4071	47	9	definition	definition	NOUN
ejpam-4071	47	10	7	7	NUM
ejpam-4071	47	11	.	.	PUNCT
ejpam-4071	48	1	[	[	X
ejpam-4071	48	2	3	3	X
ejpam-4071	48	3	]	]	X
ejpam-4071	48	4	l(e	l(e	NOUN
ejpam-4071	48	5	)	)	PUNCT
ejpam-4071	48	6	=	=	PRON
ejpam-4071	48	7	{	{	PUNCT
ejpam-4071	48	8	t	t	NOUN
ejpam-4071	48	9	:	:	PUNCT
ejpam-4071	48	10	e	e	X
ejpam-4071	48	11	−→	−→	NOUN
ejpam-4071	48	12	e	e	NOUN
ejpam-4071	48	13	}	}	PUNCT
ejpam-4071	48	14	is	be	AUX
ejpam-4071	48	15	the	the	DET
ejpam-4071	48	16	set	set	NOUN
ejpam-4071	48	17	of	of	ADP
ejpam-4071	48	18	all	all	DET
ejpam-4071	48	19	adjiontable	adjiontable	ADJ
ejpam-4071	48	20	linear	linear	NOUN
ejpam-4071	48	21	operators	operator	NOUN
ejpam-4071	48	22	with	with	ADP
ejpam-4071	48	23	∥t∥	∥t∥	PROPN
ejpam-4071	48	24	=	=	SYM
ejpam-4071	48	25	sup{∥tx∥e	sup{∥tx∥e	PROPN
ejpam-4071	48	26	;	;	PUNCT
ejpam-4071	48	27	∥x∥e	∥x∥e	X
ejpam-4071	48	28	≤	≤	ADV
ejpam-4071	48	29	1	1	NUM
ejpam-4071	48	30	}	}	PUNCT
ejpam-4071	48	31	is	be	AUX
ejpam-4071	48	32	a	a	DET
ejpam-4071	48	33	c∗-algebra	c∗-algebra	PROPN
ejpam-4071	48	34	.	.	NOUN
ejpam-4071	48	35	3	3	NUM
ejpam-4071	48	36	.	.	X
ejpam-4071	48	37	main	main	ADJ
ejpam-4071	48	38	results	result	NOUN
ejpam-4071	48	39	definition	definition	NOUN
ejpam-4071	48	40	8	8	NUM
ejpam-4071	48	41	.	.	PUNCT
ejpam-4071	49	1	let	let	VERB
ejpam-4071	49	2	l(e)+	l(e)+	PROPN
ejpam-4071	49	3	be	be	AUX
ejpam-4071	49	4	a	a	DET
ejpam-4071	49	5	subset	subset	NOUN
ejpam-4071	49	6	of	of	ADP
ejpam-4071	49	7	l(e	l(e	NOUN
ejpam-4071	49	8	)	)	PUNCT
ejpam-4071	49	9	.	.	PUNCT
ejpam-4071	50	1	l(e)+	l(e)+	PROPN
ejpam-4071	50	2	is	be	AUX
ejpam-4071	50	3	called	call	VERB
ejpam-4071	50	4	cone	cone	NOUN
ejpam-4071	50	5	of	of	ADP
ejpam-4071	50	6	l(e	l(e	NOUN
ejpam-4071	50	7	)	)	PUNCT
ejpam-4071	51	1	if	if	SCONJ
ejpam-4071	51	2	and	and	CCONJ
ejpam-4071	51	3	only	only	ADV
ejpam-4071	51	4	if	if	SCONJ
ejpam-4071	51	5	:	:	PUNCT
ejpam-4071	51	6	(	(	PUNCT
ejpam-4071	51	7	1	1	X
ejpam-4071	51	8	)	)	PUNCT
ejpam-4071	51	9	l(e)+	l(e)+	NOUN
ejpam-4071	51	10	∩	∩	NOUN
ejpam-4071	51	11	(	(	PUNCT
ejpam-4071	51	12	−l(e)+	−l(e)+	PROPN
ejpam-4071	51	13	)	)	PUNCT
ejpam-4071	51	14	=	=	SYM
ejpam-4071	51	15	{	{	PUNCT
ejpam-4071	51	16	0l(e	0l(e	NOUN
ejpam-4071	51	17	)	)	PUNCT
ejpam-4071	51	18	}	}	PUNCT
ejpam-4071	51	19	,	,	PUNCT
ejpam-4071	51	20	(	(	PUNCT
ejpam-4071	51	21	0l(e	0l(e	NOUN
ejpam-4071	51	22	)	)	PUNCT
ejpam-4071	51	23	is	be	AUX
ejpam-4071	51	24	the	the	DET
ejpam-4071	51	25	zero	zero	NUM
ejpam-4071	51	26	vector	vector	NOUN
ejpam-4071	51	27	)	)	PUNCT
ejpam-4071	51	28	;	;	PUNCT
ejpam-4071	51	29	(	(	PUNCT
ejpam-4071	51	30	2	2	X
ejpam-4071	51	31	)	)	PUNCT
ejpam-4071	51	32	l(e)+	l(e)+	NOUN
ejpam-4071	51	33	is	be	AUX
ejpam-4071	51	34	closed	close	VERB
ejpam-4071	51	35	in	in	ADP
ejpam-4071	51	36	l(e	l(e	NOUN
ejpam-4071	51	37	)	)	PUNCT
ejpam-4071	51	38	;	;	PUNCT
ejpam-4071	51	39	(	(	PUNCT
ejpam-4071	51	40	3	3	X
ejpam-4071	51	41	)	)	PUNCT
ejpam-4071	51	42	ta+	ta+	NOUN
ejpam-4071	51	43	sb	sb	PROPN
ejpam-4071	51	44	∈	∈	PROPN
ejpam-4071	51	45	l(e)+	l(e)+	PROPN
ejpam-4071	51	46	;	;	PUNCT
ejpam-4071	51	47	at	at	ADP
ejpam-4071	51	48	+	+	CCONJ
ejpam-4071	51	49	bs	bs	NOUN
ejpam-4071	51	50	∈	∈	PROPN
ejpam-4071	51	51	l(e)+	l(e)+	PROPN
ejpam-4071	51	52	a	a	PROPN
ejpam-4071	51	53	,	,	PUNCT
ejpam-4071	51	54	b	b	PROPN
ejpam-4071	51	55	∈	∈	PROPN
ejpam-4071	51	56	a	a	PRON
ejpam-4071	51	57	,	,	PUNCT
ejpam-4071	51	58	tλ+	tλ+	PROPN
ejpam-4071	51	59	sβ	sβ	PROPN
ejpam-4071	51	60	∈	∈	PROPN
ejpam-4071	51	61	l(e)+	l(e)+	NOUN
ejpam-4071	51	62	:	:	PUNCT
ejpam-4071	51	63	λ	λ	NOUN
ejpam-4071	51	64	,	,	PUNCT
ejpam-4071	51	65	β	β	X
ejpam-4071	51	66	∈	∈	PROPN
ejpam-4071	51	67	c	c	X
ejpam-4071	51	68	;	;	PUNCT
ejpam-4071	51	69	(	(	PUNCT
ejpam-4071	51	70	4	4	X
ejpam-4071	51	71	)	)	PUNCT
ejpam-4071	51	72	l(e)+	l(e)+	NOUN
ejpam-4071	51	73	·	·	PUNCT
ejpam-4071	51	74	l(e)+	l(e)+	NOUN
ejpam-4071	51	75	⊆	⊆	NUM
ejpam-4071	51	76	l(e)+	l(e)+	PROPN
ejpam-4071	51	77	.	.	PUNCT
ejpam-4071	52	1	definition	definition	NOUN
ejpam-4071	52	2	9	9	NUM
ejpam-4071	52	3	.	.	PUNCT
ejpam-4071	53	1	an	an	DET
ejpam-4071	53	2	l(e)-valued	l(e)-value	VERB
ejpam-4071	53	3	metric	metric	NOUN
ejpam-4071	53	4	on	on	ADP
ejpam-4071	53	5	a	a	DET
ejpam-4071	53	6	set	set	NOUN
ejpam-4071	53	7	x	x	PUNCT
ejpam-4071	53	8	is	be	AUX
ejpam-4071	53	9	a	a	DET
ejpam-4071	53	10	function	function	NOUN
ejpam-4071	53	11	dl(e	dl(e	NUM
ejpam-4071	53	12	)	)	PUNCT
ejpam-4071	53	13	:	:	PUNCT
ejpam-4071	54	1	x×x	x×x	PROPN
ejpam-4071	54	2	−→	−→	NOUN
ejpam-4071	54	3	l(e	l(e	NOUN
ejpam-4071	54	4	)	)	PUNCT
ejpam-4071	54	5	such	such	ADJ
ejpam-4071	54	6	that	that	PRON
ejpam-4071	54	7	for	for	ADP
ejpam-4071	54	8	all	all	DET
ejpam-4071	54	9	x	x	NOUN
ejpam-4071	54	10	,	,	PUNCT
ejpam-4071	54	11	y	y	PROPN
ejpam-4071	54	12	and	and	CCONJ
ejpam-4071	54	13	z	z	PROPN
ejpam-4071	54	14	in	in	ADP
ejpam-4071	54	15	x	x	PUNCT
ejpam-4071	54	16	the	the	DET
ejpam-4071	54	17	following	follow	VERB
ejpam-4071	54	18	conditions	condition	NOUN
ejpam-4071	54	19	are	be	AUX
ejpam-4071	54	20	hold	hold	ADJ
ejpam-4071	54	21	:	:	PUNCT
ejpam-4071	54	22	(	(	PUNCT
ejpam-4071	54	23	1	1	X
ejpam-4071	54	24	)	)	PUNCT
ejpam-4071	54	25	dl(e)(x	dl(e)(x	NOUN
ejpam-4071	54	26	,	,	PUNCT
ejpam-4071	54	27	y	y	NOUN
ejpam-4071	54	28	)	)	PUNCT
ejpam-4071	54	29	⪰	⪰	NOUN
ejpam-4071	54	30	0	0	NUM
ejpam-4071	54	31	;	;	PUNCT
ejpam-4071	54	32	(	(	PUNCT
ejpam-4071	54	33	2	2	X
ejpam-4071	54	34	)	)	PUNCT
ejpam-4071	54	35	dl(e)(x	dl(e)(x	NOUN
ejpam-4071	54	36	,	,	PUNCT
ejpam-4071	54	37	y	y	NOUN
ejpam-4071	54	38	)	)	PUNCT
ejpam-4071	54	39	=	=	SYM
ejpam-4071	54	40	0	0	PUNCT
ejpam-4071	55	1	if	if	SCONJ
ejpam-4071	55	2	and	and	CCONJ
ejpam-4071	55	3	only	only	ADV
ejpam-4071	55	4	if	if	SCONJ
ejpam-4071	55	5	x	x	X
ejpam-4071	55	6	=	=	SYM
ejpam-4071	55	7	y	y	PROPN
ejpam-4071	55	8	;	;	PUNCT
ejpam-4071	55	9	(	(	PUNCT
ejpam-4071	55	10	3	3	X
ejpam-4071	55	11	)	)	PUNCT
ejpam-4071	55	12	dl(e)(x	dl(e)(x	NOUN
ejpam-4071	55	13	,	,	PUNCT
ejpam-4071	55	14	y	y	NOUN
ejpam-4071	55	15	)	)	PUNCT
ejpam-4071	55	16	=	=	SYM
ejpam-4071	55	17	dl(e)(y	dl(e)(y	NUM
ejpam-4071	55	18	,	,	PUNCT
ejpam-4071	55	19	x	x	NOUN
ejpam-4071	55	20	)	)	PUNCT
ejpam-4071	55	21	;	;	PUNCT
ejpam-4071	55	22	(	(	PUNCT
ejpam-4071	55	23	4	4	X
ejpam-4071	55	24	)	)	PUNCT
ejpam-4071	55	25	dl(e)(x	dl(e)(x	NOUN
ejpam-4071	55	26	,	,	PUNCT
ejpam-4071	55	27	y	y	NOUN
ejpam-4071	55	28	)	)	PUNCT
ejpam-4071	55	29	⪯	⪯	NOUN
ejpam-4071	55	30	dl(e)(x	dl(e)(x	NOUN
ejpam-4071	55	31	,	,	PUNCT
ejpam-4071	55	32	z	z	NOUN
ejpam-4071	55	33	)	)	PUNCT
ejpam-4071	55	34	+	+	CCONJ
ejpam-4071	55	35	dl(e)(z	dl(e)(z	PROPN
ejpam-4071	55	36	,	,	PUNCT
ejpam-4071	55	37	y	y	NOUN
ejpam-4071	55	38	)	)	PUNCT
ejpam-4071	55	39	.	.	PUNCT
ejpam-4071	56	1	then	then	ADV
ejpam-4071	56	2	the	the	DET
ejpam-4071	56	3	triple	triple	ADJ
ejpam-4071	56	4	(	(	PUNCT
ejpam-4071	56	5	x	x	NOUN
ejpam-4071	56	6	,	,	PUNCT
ejpam-4071	56	7	l(e	l(e	NOUN
ejpam-4071	56	8	)	)	PUNCT
ejpam-4071	56	9	,	,	PUNCT
ejpam-4071	56	10	dl(e	dl(e	NOUN
ejpam-4071	56	11	)	)	PUNCT
ejpam-4071	56	12	)	)	PUNCT
ejpam-4071	56	13	is	be	AUX
ejpam-4071	56	14	called	call	VERB
ejpam-4071	56	15	an	an	DET
ejpam-4071	56	16	l(e)-valued	l(e)-value	VERB
ejpam-4071	56	17	metric	metric	ADJ
ejpam-4071	56	18	space	space	NOUN
ejpam-4071	56	19	.	.	PUNCT
ejpam-4071	57	1	definition	definition	NOUN
ejpam-4071	57	2	10	10	NUM
ejpam-4071	57	3	.	.	PUNCT
ejpam-4071	58	1	[	[	X
ejpam-4071	58	2	20	20	NUM
ejpam-4071	58	3	]	]	PUNCT
ejpam-4071	58	4	let	let	VERB
ejpam-4071	58	5	x	x	PRON
ejpam-4071	58	6	be	be	AUX
ejpam-4071	58	7	a	a	DET
ejpam-4071	58	8	nonempty	nonempty	ADJ
ejpam-4071	58	9	set	set	VERB
ejpam-4071	58	10	.	.	PUNCT
ejpam-4071	59	1	suppose	suppose	VERB
ejpam-4071	59	2	the	the	DET
ejpam-4071	59	3	mapping	mapping	NOUN
ejpam-4071	59	4	d	d	NOUN
ejpam-4071	59	5	:	:	PUNCT
ejpam-4071	60	1	x	x	SYM
ejpam-4071	60	2	×	×	NOUN
ejpam-4071	60	3	x	x	PUNCT
ejpam-4071	60	4	−→	−→	ADP
ejpam-4071	60	5	a	a	DET
ejpam-4071	60	6	satisfies	satisfie	NOUN
ejpam-4071	60	7	:	:	PUNCT
ejpam-4071	60	8	(	(	PUNCT
ejpam-4071	60	9	1	1	X
ejpam-4071	60	10	)	)	PUNCT
ejpam-4071	60	11	0a	0a	PROPN
ejpam-4071	60	12	⪯	⪯	NOUN
ejpam-4071	60	13	d(x	d(x	PROPN
ejpam-4071	60	14	,	,	PUNCT
ejpam-4071	60	15	y	y	NOUN
ejpam-4071	60	16	)	)	PUNCT
ejpam-4071	60	17	for	for	ADP
ejpam-4071	60	18	all	all	DET
ejpam-4071	60	19	x	x	NOUN
ejpam-4071	60	20	,	,	PUNCT
ejpam-4071	60	21	y	y	PROPN
ejpam-4071	60	22	∈	∈	PROPN
ejpam-4071	60	23	x	x	X
ejpam-4071	60	24	and	and	CCONJ
ejpam-4071	60	25	d(x	d(x	PROPN
ejpam-4071	60	26	,	,	PUNCT
ejpam-4071	60	27	y	y	NOUN
ejpam-4071	60	28	)	)	PUNCT
ejpam-4071	60	29	=	=	SYM
ejpam-4071	60	30	0a	0a	PROPN
ejpam-4071	61	1	if	if	SCONJ
ejpam-4071	61	2	and	and	CCONJ
ejpam-4071	61	3	only	only	ADV
ejpam-4071	61	4	if	if	SCONJ
ejpam-4071	61	5	x	x	X
ejpam-4071	61	6	=	=	SYM
ejpam-4071	61	7	y.	y.	NOUN
ejpam-4071	61	8	(	(	PUNCT
ejpam-4071	61	9	2	2	NUM
ejpam-4071	61	10	)	)	PUNCT
ejpam-4071	61	11	d(x	d(x	PROPN
ejpam-4071	61	12	,	,	PUNCT
ejpam-4071	61	13	y	y	NOUN
ejpam-4071	61	14	)	)	PUNCT
ejpam-4071	61	15	=	=	SYM
ejpam-4071	61	16	d(y	d(y	NOUN
ejpam-4071	61	17	,	,	PUNCT
ejpam-4071	61	18	x	x	NOUN
ejpam-4071	61	19	)	)	PUNCT
ejpam-4071	61	20	for	for	ADP
ejpam-4071	61	21	all	all	DET
ejpam-4071	61	22	x	x	NOUN
ejpam-4071	61	23	,	,	PUNCT
ejpam-4071	61	24	y	y	PROPN
ejpam-4071	61	25	∈	∈	PROPN
ejpam-4071	61	26	x	x	X
ejpam-4071	61	27	.	.	PUNCT
ejpam-4071	62	1	(	(	PUNCT
ejpam-4071	62	2	3	3	X
ejpam-4071	62	3	)	)	PUNCT
ejpam-4071	62	4	d(x	d(x	PROPN
ejpam-4071	62	5	,	,	PUNCT
ejpam-4071	62	6	y	y	NOUN
ejpam-4071	62	7	)	)	PUNCT
ejpam-4071	62	8	⪯	⪯	PROPN
ejpam-4071	62	9	d(x	d(x	PROPN
ejpam-4071	62	10	,	,	PUNCT
ejpam-4071	62	11	z	z	NOUN
ejpam-4071	62	12	)	)	PUNCT
ejpam-4071	63	1	+	+	CCONJ
ejpam-4071	63	2	d(z	d(z	PROPN
ejpam-4071	63	3	,	,	PUNCT
ejpam-4071	63	4	y	y	NOUN
ejpam-4071	63	5	)	)	PUNCT
ejpam-4071	63	6	for	for	ADP
ejpam-4071	63	7	all	all	DET
ejpam-4071	63	8	x	x	NOUN
ejpam-4071	63	9	,	,	PUNCT
ejpam-4071	63	10	y	y	PROPN
ejpam-4071	63	11	,	,	PUNCT
ejpam-4071	63	12	z	z	PROPN
ejpam-4071	63	13	∈	∈	PROPN
ejpam-4071	63	14	x.	x.	NOUN
ejpam-4071	63	15	then	then	ADV
ejpam-4071	63	16	d	d	PROPN
ejpam-4071	63	17	is	be	AUX
ejpam-4071	63	18	called	call	VERB
ejpam-4071	63	19	a	a	DET
ejpam-4071	63	20	c∗-algebra	c∗-algebra	PROPN
ejpam-4071	63	21	-	-	PUNCT
ejpam-4071	63	22	valued	value	VERB
ejpam-4071	63	23	metric	metric	NOUN
ejpam-4071	63	24	on	on	ADP
ejpam-4071	63	25	x	x	PUNCT
ejpam-4071	63	26	and	and	CCONJ
ejpam-4071	63	27	(	(	PUNCT
ejpam-4071	63	28	x	x	X
ejpam-4071	63	29	,	,	PUNCT
ejpam-4071	63	30	a	a	DET
ejpam-4071	63	31	,	,	PUNCT
ejpam-4071	63	32	d	d	NOUN
ejpam-4071	63	33	)	)	PUNCT
ejpam-4071	63	34	is	be	AUX
ejpam-4071	63	35	a	a	DET
ejpam-4071	63	36	c∗-algebra	c∗-algebra	PROPN
ejpam-4071	63	37	-	-	PUNCT
ejpam-4071	63	38	valued	value	VERB
ejpam-4071	63	39	metric	metric	ADJ
ejpam-4071	63	40	space	space	NOUN
ejpam-4071	63	41	.	.	PUNCT
ejpam-4071	64	1	r.	r.	PROPN
ejpam-4071	64	2	a.	a.	PROPN
ejpam-4071	64	3	rashwan	rashwan	PROPN
ejpam-4071	64	4	et	et	PROPN
ejpam-4071	64	5	al	al	PROPN
ejpam-4071	64	6	.	.	PUNCT
ejpam-4071	64	7	/	/	SYM
ejpam-4071	64	8	eur	eur	PROPN
ejpam-4071	64	9	.	.	PUNCT
ejpam-4071	65	1	j.	j.	PROPN
ejpam-4071	65	2	pure	pure	PROPN
ejpam-4071	65	3	appl	appl	PROPN
ejpam-4071	65	4	.	.	PROPN
ejpam-4071	65	5	math	math	PROPN
ejpam-4071	65	6	,	,	PUNCT
ejpam-4071	65	7	14	14	NUM
ejpam-4071	65	8	(	(	PUNCT
ejpam-4071	65	9	4	4	NUM
ejpam-4071	65	10	)	)	PUNCT
ejpam-4071	65	11	(	(	PUNCT
ejpam-4071	65	12	2021	2021	NUM
ejpam-4071	65	13	)	)	PUNCT
ejpam-4071	65	14	,	,	PUNCT
ejpam-4071	65	15	1237	1237	NUM
ejpam-4071	65	16	-	-	SYM
ejpam-4071	65	17	1248	1248	NUM
ejpam-4071	65	18	1240	1240	NUM
ejpam-4071	65	19	definition	definition	NOUN
ejpam-4071	65	20	11	11	NUM
ejpam-4071	65	21	.	.	PUNCT
ejpam-4071	66	1	let	let	VERB
ejpam-4071	66	2	(	(	PUNCT
ejpam-4071	66	3	x	x	NOUN
ejpam-4071	66	4	,	,	PUNCT
ejpam-4071	66	5	l(e	l(e	NOUN
ejpam-4071	66	6	)	)	PUNCT
ejpam-4071	66	7	,	,	PUNCT
ejpam-4071	66	8	dl(e	dl(e	NOUN
ejpam-4071	66	9	)	)	PUNCT
ejpam-4071	66	10	)	)	PUNCT
ejpam-4071	66	11	be	be	AUX
ejpam-4071	66	12	an	an	DET
ejpam-4071	66	13	l(e)valued	l(e)value	VERB
ejpam-4071	66	14	metric	metric	ADJ
ejpam-4071	66	15	spacs	spac	NOUN
ejpam-4071	66	16	.	.	PUNCT
ejpam-4071	67	1	suppose	suppose	VERB
ejpam-4071	67	2	that	that	SCONJ
ejpam-4071	67	3	xn	xn	PROPN
ejpam-4071	68	1	⊂	⊂	PROPN
ejpam-4071	68	2	x	x	X
ejpam-4071	69	1	and	and	CCONJ
ejpam-4071	69	2	x	x	SYM
ejpam-4071	69	3	∈	∈	NOUN
ejpam-4071	69	4	x	x	INTJ
ejpam-4071	69	5	if	if	SCONJ
ejpam-4071	69	6	for	for	ADP
ejpam-4071	69	7	any	any	DET
ejpam-4071	69	8	εl(e	εl(e	NUM
ejpam-4071	69	9	)	)	PUNCT
ejpam-4071	69	10	≻	≻	NOUN
ejpam-4071	69	11	0l(e	0l(e	NOUN
ejpam-4071	69	12	)	)	PUNCT
ejpam-4071	69	13	(	(	PUNCT
ejpam-4071	69	14	where	where	SCONJ
ejpam-4071	69	15	0l(e	0l(e	NOUN
ejpam-4071	69	16	)	)	PUNCT
ejpam-4071	69	17	is	be	AUX
ejpam-4071	69	18	the	the	DET
ejpam-4071	69	19	zero	zero	NUM
ejpam-4071	69	20	element	element	NOUN
ejpam-4071	69	21	in	in	ADP
ejpam-4071	69	22	l(e	l(e	NOUN
ejpam-4071	69	23	)	)	PUNCT
ejpam-4071	69	24	)	)	PUNCT
ejpam-4071	70	1	there	there	PRON
ejpam-4071	70	2	exists	exist	VERB
ejpam-4071	70	3	n	n	PRON
ejpam-4071	70	4	∈	∈	PROPN
ejpam-4071	70	5	n	n	PRON
ejpam-4071	70	6	such	such	ADJ
ejpam-4071	70	7	that	that	PRON
ejpam-4071	70	8	for	for	ADP
ejpam-4071	70	9	all	all	DET
ejpam-4071	70	10	n	n	CCONJ
ejpam-4071	70	11	>	>	PUNCT
ejpam-4071	70	12	n	n	PROPN
ejpam-4071	70	13	,	,	PUNCT
ejpam-4071	70	14	dl(e)(xn	dl(e)(xn	PROPN
ejpam-4071	70	15	,	,	PUNCT
ejpam-4071	70	16	x	x	X
ejpam-4071	70	17	)	)	PUNCT
ejpam-4071	70	18	⪯	⪯	NOUN
ejpam-4071	70	19	εl(e	εl(e	PUNCT
ejpam-4071	70	20	)	)	PUNCT
ejpam-4071	70	21	,	,	PUNCT
ejpam-4071	70	22	then	then	ADV
ejpam-4071	70	23	{	{	PUNCT
ejpam-4071	70	24	xn	xn	X
ejpam-4071	70	25	}	}	PUNCT
ejpam-4071	70	26	is	be	AUX
ejpam-4071	70	27	said	say	VERB
ejpam-4071	70	28	to	to	PART
ejpam-4071	70	29	be	be	AUX
ejpam-4071	70	30	converge	converge	VERB
ejpam-4071	70	31	with	with	ADP
ejpam-4071	70	32	respect	respect	NOUN
ejpam-4071	70	33	to	to	ADP
ejpam-4071	70	34	l(e	l(e	NOUN
ejpam-4071	70	35	)	)	PUNCT
ejpam-4071	70	36	,	,	PUNCT
ejpam-4071	70	37	and	and	CCONJ
ejpam-4071	70	38	{	{	PUNCT
ejpam-4071	70	39	xn	xn	NOUN
ejpam-4071	70	40	}	}	PUNCT
ejpam-4071	70	41	converges	converge	VERB
ejpam-4071	70	42	to	to	ADP
ejpam-4071	70	43	x	x	PUNCT
ejpam-4071	70	44	and	and	CCONJ
ejpam-4071	70	45	x	x	X
ejpam-4071	70	46	is	be	AUX
ejpam-4071	70	47	the	the	DET
ejpam-4071	70	48	limit	limit	NOUN
ejpam-4071	70	49	of	of	ADP
ejpam-4071	70	50	{	{	PUNCT
ejpam-4071	70	51	xn	xn	NUM
ejpam-4071	70	52	}	}	PUNCT
ejpam-4071	70	53	.	.	PUNCT
ejpam-4071	71	1	we	we	PRON
ejpam-4071	71	2	denote	denote	VERB
ejpam-4071	71	3	it	it	PRON
ejpam-4071	71	4	by	by	ADP
ejpam-4071	71	5	limn−→+∞{xn	limn−→+∞{xn	NOUN
ejpam-4071	71	6	}	}	PUNCT
ejpam-4071	71	7	=	=	SYM
ejpam-4071	71	8	x	x	X
ejpam-4071	71	9	.	.	PUNCT
ejpam-4071	72	1	if	if	SCONJ
ejpam-4071	72	2	for	for	ADP
ejpam-4071	72	3	any	any	DET
ejpam-4071	72	4	εl(e	εl(e	NUM
ejpam-4071	72	5	)	)	PUNCT
ejpam-4071	72	6	≻	≻	NOUN
ejpam-4071	72	7	0l(e	0l(e	NOUN
ejpam-4071	72	8	)	)	PUNCT
ejpam-4071	72	9	there	there	PRON
ejpam-4071	72	10	exists	exist	VERB
ejpam-4071	72	11	n	n	PRON
ejpam-4071	72	12	∈	∈	PROPN
ejpam-4071	72	13	n	n	PRON
ejpam-4071	72	14	such	such	ADJ
ejpam-4071	72	15	that	that	PRON
ejpam-4071	72	16	for	for	SCONJ
ejpam-4071	72	17	all	all	DET
ejpam-4071	72	18	n	n	CCONJ
ejpam-4071	72	19	,	,	PUNCT
ejpam-4071	72	20	m	m	VERB
ejpam-4071	72	21	>	>	X
ejpam-4071	72	22	n	n	PROPN
ejpam-4071	72	23	,	,	PUNCT
ejpam-4071	72	24	d(xn	d(xn	PROPN
ejpam-4071	72	25	,	,	PUNCT
ejpam-4071	72	26	xm	xm	PROPN
ejpam-4071	72	27	)	)	PUNCT
ejpam-4071	72	28	⪯	⪯	NOUN
ejpam-4071	72	29	εl(e	εl(e	PUNCT
ejpam-4071	72	30	)	)	PUNCT
ejpam-4071	72	31	,	,	PUNCT
ejpam-4071	72	32	then	then	ADV
ejpam-4071	72	33	{	{	PUNCT
ejpam-4071	72	34	xn	xn	X
ejpam-4071	72	35	}	}	PUNCT
ejpam-4071	72	36	is	be	AUX
ejpam-4071	72	37	said	say	VERB
ejpam-4071	72	38	to	to	PART
ejpam-4071	72	39	be	be	AUX
ejpam-4071	72	40	a	a	DET
ejpam-4071	72	41	cauchy	cauchy	NOUN
ejpam-4071	72	42	with	with	ADP
ejpam-4071	72	43	respect	respect	NOUN
ejpam-4071	72	44	to	to	ADP
ejpam-4071	72	45	l(e	l(e	NOUN
ejpam-4071	72	46	)	)	PUNCT
ejpam-4071	72	47	.	.	PUNCT
ejpam-4071	73	1	we	we	PRON
ejpam-4071	73	2	say	say	VERB
ejpam-4071	73	3	(	(	PUNCT
ejpam-4071	73	4	x	x	NOUN
ejpam-4071	73	5	,	,	PUNCT
ejpam-4071	73	6	l(e	l(e	NOUN
ejpam-4071	73	7	)	)	PUNCT
ejpam-4071	73	8	,	,	PUNCT
ejpam-4071	73	9	dl(e	dl(e	NOUN
ejpam-4071	73	10	)	)	PUNCT
ejpam-4071	73	11	)	)	PUNCT
ejpam-4071	73	12	is	be	AUX
ejpam-4071	73	13	a	a	DET
ejpam-4071	73	14	complete	complete	ADJ
ejpam-4071	73	15	l(e)valued	l(e)value	VERB
ejpam-4071	73	16	metric	metric	ADJ
ejpam-4071	73	17	spacs	spac	NOUN
ejpam-4071	73	18	if	if	SCONJ
ejpam-4071	73	19	every	every	DET
ejpam-4071	73	20	cauchy	cauchy	ADJ
ejpam-4071	73	21	sequence	sequence	NOUN
ejpam-4071	73	22	with	with	ADP
ejpam-4071	73	23	respect	respect	NOUN
ejpam-4071	73	24	to	to	ADP
ejpam-4071	73	25	l(e	l(e	NOUN
ejpam-4071	73	26	)	)	PUNCT
ejpam-4071	73	27	is	be	AUX
ejpam-4071	73	28	convergent	convergent	ADJ
ejpam-4071	73	29	.	.	PUNCT
ejpam-4071	74	1	lemma	lemma	PROPN
ejpam-4071	74	2	1	1	NUM
ejpam-4071	74	3	.	.	PUNCT
ejpam-4071	75	1	a	a	DET
ejpam-4071	75	2	sequence	sequence	NOUN
ejpam-4071	75	3	xn	xn	PUNCT
ejpam-4071	76	1	⊂	⊂	PROPN
ejpam-4071	76	2	x	x	X
ejpam-4071	76	3	is	be	AUX
ejpam-4071	76	4	convergence	convergence	NOUN
ejpam-4071	76	5	if	if	SCONJ
ejpam-4071	76	6	∥xn∥	∥xn∥	PROPN
ejpam-4071	76	7	−→	−→	NOUN
ejpam-4071	76	8	0	0	NUM
ejpam-4071	76	9	forall	forall	VERB
ejpam-4071	76	10	n	n	NOUN
ejpam-4071	76	11	>	>	X
ejpam-4071	76	12	n	n	PRON
ejpam-4071	76	13	such	such	ADJ
ejpam-4071	76	14	that	that	SCONJ
ejpam-4071	76	15	n	n	PROPN
ejpam-4071	76	16	∈	∈	PROPN
ejpam-4071	76	17	n.	n.	NOUN
ejpam-4071	76	18	example	example	NOUN
ejpam-4071	76	19	2	2	X
ejpam-4071	76	20	.	.	PUNCT
ejpam-4071	77	1	let	let	VERB
ejpam-4071	77	2	x	x	SYM
ejpam-4071	77	3	=	=	SYM
ejpam-4071	77	4	a⊕n	a⊕n	PROPN
ejpam-4071	77	5	,	,	PUNCT
ejpam-4071	77	6	e	e	X
ejpam-4071	77	7	=	=	SYM
ejpam-4071	77	8	a⊕n	a⊕n	PROPN
ejpam-4071	77	9	and	and	CCONJ
ejpam-4071	77	10	l(e	l(e	NOUN
ejpam-4071	77	11	)	)	PUNCT
ejpam-4071	77	12	=	=	PRON
ejpam-4071	78	1	{	{	PUNCT
ejpam-4071	78	2	t	t	NOUN
ejpam-4071	78	3	:	:	PUNCT
ejpam-4071	78	4	a⊕n	a⊕n	PROPN
ejpam-4071	78	5	−→	−→	PROPN
ejpam-4071	78	6	a⊕n	a⊕n	PROPN
ejpam-4071	78	7	:	:	PUNCT
ejpam-4071	79	1	t	t	PROPN
ejpam-4071	79	2	(	(	PUNCT
ejpam-4071	79	3	a1	a1	PROPN
ejpam-4071	79	4	,	,	PUNCT
ejpam-4071	79	5	a2	a2	PROPN
ejpam-4071	79	6	,	,	PUNCT
ejpam-4071	79	7	...	...	PUNCT
ejpam-4071	79	8	,	,	PUNCT
ejpam-4071	79	9	an	an	X
ejpam-4071	79	10	)	)	PUNCT
ejpam-4071	79	11	=	=	SYM
ejpam-4071	79	12	(	(	PUNCT
ejpam-4071	79	13	ta1	ta1	PROPN
ejpam-4071	79	14	,	,	PUNCT
ejpam-4071	79	15	ta2	ta2	PROPN
ejpam-4071	79	16	,	,	PUNCT
ejpam-4071	79	17	...	...	PUNCT
ejpam-4071	79	18	,	,	PUNCT
ejpam-4071	79	19	tan	tan	PROPN
ejpam-4071	79	20	)	)	PUNCT
ejpam-4071	79	21	}	}	PUNCT
ejpam-4071	79	22	.	.	PUNCT
ejpam-4071	80	1	define	define	VERB
ejpam-4071	80	2	d((a1	d((a1	PROPN
ejpam-4071	80	3	,	,	PUNCT
ejpam-4071	80	4	a2	a2	PROPN
ejpam-4071	80	5	,	,	PUNCT
ejpam-4071	80	6	...	...	PUNCT
ejpam-4071	80	7	,	,	PUNCT
ejpam-4071	80	8	an	an	PRON
ejpam-4071	80	9	)	)	PUNCT
ejpam-4071	80	10	,	,	PUNCT
ejpam-4071	80	11	(	(	PUNCT
ejpam-4071	80	12	b1	b1	NOUN
ejpam-4071	80	13	,	,	PUNCT
ejpam-4071	80	14	b2	b2	NOUN
ejpam-4071	80	15	,	,	PUNCT
ejpam-4071	80	16	...	...	PUNCT
ejpam-4071	80	17	,	,	PUNCT
ejpam-4071	80	18	bn	bn	NOUN
ejpam-4071	80	19	)	)	PUNCT
ejpam-4071	80	20	)	)	PUNCT
ejpam-4071	81	1	=	=	PRON
ejpam-4071	82	1	(	(	PUNCT
ejpam-4071	82	2	∥ta1	∥ta1	NOUN
ejpam-4071	82	3	−	−	NOUN
ejpam-4071	82	4	tb1∥r	tb1∥r	NOUN
ejpam-4071	82	5	,	,	PUNCT
ejpam-4071	82	6	∥ta2	∥ta2	ADP
ejpam-4071	82	7	−	−	NOUN
ejpam-4071	82	8	tb2∥r	tb2∥r	NOUN
ejpam-4071	82	9	,	,	PUNCT
ejpam-4071	82	10	...	...	PUNCT
ejpam-4071	82	11	,	,	PUNCT
ejpam-4071	82	12	∥tan	∥tan	PROPN
ejpam-4071	82	13	−	−	PROPN
ejpam-4071	82	14	tbn∥r)ia	tbn∥r)ia	PROPN
ejpam-4071	82	15	,	,	PUNCT
ejpam-4071	82	16	where	where	SCONJ
ejpam-4071	82	17	(	(	PUNCT
ejpam-4071	82	18	a1	a1	NOUN
ejpam-4071	82	19	,	,	PUNCT
ejpam-4071	82	20	a2	a2	PROPN
ejpam-4071	82	21	,	,	PUNCT
ejpam-4071	82	22	...	...	PUNCT
ejpam-4071	82	23	,	,	PUNCT
ejpam-4071	82	24	an	an	PRON
ejpam-4071	82	25	)	)	PUNCT
ejpam-4071	82	26	,	,	PUNCT
ejpam-4071	82	27	(	(	PUNCT
ejpam-4071	82	28	b1	b1	NOUN
ejpam-4071	82	29	,	,	PUNCT
ejpam-4071	82	30	b2	b2	NOUN
ejpam-4071	82	31	,	,	PUNCT
ejpam-4071	82	32	...	...	PUNCT
ejpam-4071	82	33	,	,	PUNCT
ejpam-4071	82	34	bn	bn	X
ejpam-4071	82	35	)	)	PUNCT
ejpam-4071	82	36	∈	∈	PROPN
ejpam-4071	82	37	a⊕n	a⊕n	PROPN
ejpam-4071	82	38	and	and	CCONJ
ejpam-4071	82	39	ia	ia	PROPN
ejpam-4071	82	40	is	be	AUX
ejpam-4071	82	41	the	the	DET
ejpam-4071	82	42	identity	identity	NOUN
ejpam-4071	82	43	element	element	NOUN
ejpam-4071	82	44	of	of	ADP
ejpam-4071	82	45	a	a	PRON
ejpam-4071	82	46	.	.	PUNCT
ejpam-4071	83	1	it	it	PRON
ejpam-4071	83	2	is	be	AUX
ejpam-4071	83	3	easy	easy	ADJ
ejpam-4071	83	4	to	to	PART
ejpam-4071	83	5	verify	verify	VERB
ejpam-4071	83	6	that	that	SCONJ
ejpam-4071	83	7	dl(e	dl(e	NOUN
ejpam-4071	83	8	)	)	PUNCT
ejpam-4071	83	9	is	be	AUX
ejpam-4071	83	10	an	an	DET
ejpam-4071	83	11	l(e	l(e	NOUN
ejpam-4071	83	12	)	)	PUNCT
ejpam-4071	83	13	-valued	-value	VERB
ejpam-4071	83	14	metric	metric	ADJ
ejpam-4071	83	15	space	space	NOUN
ejpam-4071	83	16	and	and	CCONJ
ejpam-4071	83	17	(	(	PUNCT
ejpam-4071	83	18	x	x	X
ejpam-4071	83	19	,	,	PUNCT
ejpam-4071	83	20	a⊕n	a⊕n	PROPN
ejpam-4071	83	21	,	,	PUNCT
ejpam-4071	83	22	dl(e	dl(e	NOUN
ejpam-4071	83	23	)	)	PUNCT
ejpam-4071	83	24	)	)	PUNCT
ejpam-4071	84	1	is	be	AUX
ejpam-4071	84	2	a	a	DET
ejpam-4071	84	3	complete	complete	ADJ
ejpam-4071	84	4	l(e	l(e	NOUN
ejpam-4071	84	5	)	)	PUNCT
ejpam-4071	84	6	-valued	-value	VERB
ejpam-4071	84	7	metric	metric	ADJ
ejpam-4071	84	8	space	space	NOUN
ejpam-4071	84	9	,	,	PUNCT
ejpam-4071	84	10	since	since	SCONJ
ejpam-4071	84	11	a	a	PRON
ejpam-4071	84	12	is	be	AUX
ejpam-4071	84	13	complete	complete	ADJ
ejpam-4071	84	14	.	.	PUNCT
ejpam-4071	85	1	definition	definition	NOUN
ejpam-4071	85	2	12	12	NUM
ejpam-4071	85	3	.	.	PUNCT
ejpam-4071	86	1	let	let	VERB
ejpam-4071	86	2	(	(	PUNCT
ejpam-4071	86	3	x	x	NOUN
ejpam-4071	86	4	,	,	PUNCT
ejpam-4071	86	5	l(e	l(e	NOUN
ejpam-4071	86	6	)	)	PUNCT
ejpam-4071	86	7	)	)	PUNCT
ejpam-4071	87	1	is	be	AUX
ejpam-4071	87	2	an	an	DET
ejpam-4071	87	3	l(e)-metric	l(e)-metric	PROPN
ejpam-4071	87	4	space	space	NOUN
ejpam-4071	87	5	,	,	PUNCT
ejpam-4071	87	6	we	we	PRON
ejpam-4071	87	7	define	define	VERB
ejpam-4071	87	8	the	the	DET
ejpam-4071	87	9	open	open	ADJ
ejpam-4071	87	10	ball	ball	NOUN
ejpam-4071	87	11	on	on	ADP
ejpam-4071	87	12	x	x	PROPN
ejpam-4071	87	13	bl(e)(a	bl(e)(a	NOUN
ejpam-4071	87	14	,	,	PUNCT
ejpam-4071	87	15	ϵl(e	ϵl(e	NUM
ejpam-4071	87	16	)	)	PUNCT
ejpam-4071	87	17	)	)	PUNCT
ejpam-4071	88	1	=	=	PRON
ejpam-4071	88	2	{	{	PUNCT
ejpam-4071	88	3	x	x	PUNCT
ejpam-4071	88	4	∈	∈	PROPN
ejpam-4071	88	5	x	x	NOUN
ejpam-4071	88	6	;	;	PUNCT
ejpam-4071	88	7	∥x−	∥x−	NUM
ejpam-4071	88	8	a∥	a∥	VERB
ejpam-4071	88	9	≺	≺	NOUN
ejpam-4071	88	10	ϵl(e	ϵl(e	NUM
ejpam-4071	88	11	)	)	PUNCT
ejpam-4071	88	12	}	}	PUNCT
ejpam-4071	88	13	definition	definition	NOUN
ejpam-4071	88	14	13	13	NUM
ejpam-4071	88	15	.	.	PUNCT
ejpam-4071	88	16	suppose	suppose	VERB
ejpam-4071	88	17	that	that	SCONJ
ejpam-4071	88	18	(	(	PUNCT
ejpam-4071	88	19	x	x	X
ejpam-4071	88	20	,	,	PUNCT
ejpam-4071	88	21	dl(e	dl(e	NUM
ejpam-4071	88	22	)	)	PUNCT
ejpam-4071	88	23	)	)	PUNCT
ejpam-4071	88	24	is	be	AUX
ejpam-4071	88	25	l(e)-metric	l(e)-metric	PROPN
ejpam-4071	88	26	space	space	NOUN
ejpam-4071	88	27	,	,	PUNCT
ejpam-4071	88	28	let	let	VERB
ejpam-4071	88	29	x	x	SYM
ejpam-4071	88	30	∈	∈	PROPN
ejpam-4071	88	31	x	x	X
ejpam-4071	88	32	then	then	ADV
ejpam-4071	88	33	a	a	DET
ejpam-4071	88	34	neighhborhood	neighhborhood	NOUN
ejpam-4071	88	35	of	of	ADP
ejpam-4071	88	36	x	x	PUNCT
ejpam-4071	88	37	is	be	AUX
ejpam-4071	88	38	any	any	DET
ejpam-4071	88	39	set	set	NOUN
ejpam-4071	88	40	containing	contain	VERB
ejpam-4071	88	41	bl(e)(x	bl(e)(x	NOUN
ejpam-4071	88	42	,	,	PUNCT
ejpam-4071	88	43	ϵl(e	ϵl(e	NUM
ejpam-4071	88	44	)	)	PUNCT
ejpam-4071	88	45	)	)	PUNCT
ejpam-4071	88	46	for	for	ADP
ejpam-4071	88	47	some	some	DET
ejpam-4071	88	48	ϵl(e	ϵl(e	NUM
ejpam-4071	88	49	)	)	PUNCT
ejpam-4071	88	50	≻	≻	NOUN
ejpam-4071	88	51	0l(e	0l(e	NOUN
ejpam-4071	88	52	)	)	PUNCT
ejpam-4071	88	53	.	.	PUNCT
ejpam-4071	89	1	definition	definition	NOUN
ejpam-4071	89	2	14	14	NUM
ejpam-4071	89	3	.	.	PUNCT
ejpam-4071	89	4	suppose	suppose	VERB
ejpam-4071	89	5	that	that	SCONJ
ejpam-4071	89	6	(	(	PUNCT
ejpam-4071	89	7	x	x	X
ejpam-4071	89	8	,	,	PUNCT
ejpam-4071	89	9	dl(e	dl(e	NUM
ejpam-4071	89	10	)	)	PUNCT
ejpam-4071	89	11	)	)	PUNCT
ejpam-4071	89	12	is	be	AUX
ejpam-4071	89	13	l(e)-metric	l(e)-metric	PROPN
ejpam-4071	89	14	space	space	NOUN
ejpam-4071	89	15	,	,	PUNCT
ejpam-4071	89	16	a	a	DET
ejpam-4071	89	17	subset	subset	NOUN
ejpam-4071	89	18	u	u	NOUN
ejpam-4071	89	19	⊂	⊂	PROPN
ejpam-4071	89	20	x	x	X
ejpam-4071	89	21	is	be	AUX
ejpam-4071	89	22	open	open	ADJ
ejpam-4071	89	23	if	if	SCONJ
ejpam-4071	89	24	for	for	SCONJ
ejpam-4071	89	25	every	every	DET
ejpam-4071	89	26	x	x	SYM
ejpam-4071	89	27	∈	∈	PROPN
ejpam-4071	89	28	u	u	NOUN
ejpam-4071	89	29	there	there	PRON
ejpam-4071	89	30	exist	exist	VERB
ejpam-4071	89	31	an	an	DET
ejpam-4071	89	32	open	open	ADJ
ejpam-4071	89	33	ball	ball	NOUN
ejpam-4071	89	34	bl(e)(a	bl(e)(a	NOUN
ejpam-4071	89	35	,	,	PUNCT
ejpam-4071	89	36	ϵl(e	ϵl(e	NUM
ejpam-4071	89	37	)	)	PUNCT
ejpam-4071	89	38	)	)	PUNCT
ejpam-4071	89	39	such	such	ADJ
ejpam-4071	89	40	that	that	SCONJ
ejpam-4071	89	41	x	x	SYM
ejpam-4071	89	42	∈	∈	PROPN
ejpam-4071	89	43	bl(e)(x	bl(e)(x	NOUN
ejpam-4071	89	44	,	,	PUNCT
ejpam-4071	89	45	ϵl(e	ϵl(e	NUM
ejpam-4071	89	46	)	)	PUNCT
ejpam-4071	89	47	)	)	PUNCT
ejpam-4071	90	1	⊂	⊂	PROPN
ejpam-4071	90	2	u	u	PROPN
ejpam-4071	90	3	.	.	PUNCT
ejpam-4071	90	4	motivaied	motivaie	VERB
ejpam-4071	90	5	by	by	ADP
ejpam-4071	90	6	the	the	DET
ejpam-4071	90	7	idea	idea	NOUN
ejpam-4071	90	8	in	in	ADP
ejpam-4071	90	9	[	[	X
ejpam-4071	90	10	7],[17],[9	7],[17],[9	NOUN
ejpam-4071	90	11	]	]	PUNCT
ejpam-4071	90	12	,	,	PUNCT
ejpam-4071	90	13	we	we	PRON
ejpam-4071	90	14	give	give	VERB
ejpam-4071	90	15	the	the	DET
ejpam-4071	90	16	following	follow	VERB
ejpam-4071	90	17	definations	defination	NOUN
ejpam-4071	90	18	.	.	PUNCT
ejpam-4071	91	1	definition	definition	NOUN
ejpam-4071	91	2	15	15	NUM
ejpam-4071	91	3	.	.	PUNCT
ejpam-4071	92	1	let	let	VERB
ejpam-4071	92	2	x	x	PRON
ejpam-4071	92	3	be	be	AUX
ejpam-4071	92	4	vector	vector	NOUN
ejpam-4071	92	5	space	space	NOUN
ejpam-4071	92	6	,	,	PUNCT
ejpam-4071	92	7	if	if	SCONJ
ejpam-4071	92	8	the	the	DET
ejpam-4071	92	9	function	function	NOUN
ejpam-4071	92	10	∥.∥l(e	∥.∥l(e	VERB
ejpam-4071	92	11	)	)	PUNCT
ejpam-4071	92	12	:	:	PUNCT
ejpam-4071	93	1	x	x	X
ejpam-4071	93	2	−→	−→	NOUN
ejpam-4071	93	3	l(e	l(e	NOUN
ejpam-4071	93	4	)	)	PUNCT
ejpam-4071	93	5	has	have	AUX
ejpam-4071	93	6	the	the	DET
ejpam-4071	93	7	following	follow	VERB
ejpam-4071	93	8	properties	property	NOUN
ejpam-4071	93	9	:	:	PUNCT
ejpam-4071	93	10	(	(	PUNCT
ejpam-4071	93	11	1	1	X
ejpam-4071	93	12	)	)	PUNCT
ejpam-4071	93	13	∥x∥l(e	∥x∥l(e	NOUN
ejpam-4071	93	14	)	)	PUNCT
ejpam-4071	93	15	⪰	⪰	NOUN
ejpam-4071	93	16	0	0	NUM
ejpam-4071	93	17	i.e	i.e	PRON
ejpam-4071	93	18	∥x∥l(e	∥x∥l(e	NOUN
ejpam-4071	93	19	)	)	PUNCT
ejpam-4071	93	20	is	be	AUX
ejpam-4071	93	21	a	a	DET
ejpam-4071	93	22	positive	positive	ADJ
ejpam-4071	93	23	operator	operator	NOUN
ejpam-4071	93	24	,	,	PUNCT
ejpam-4071	93	25	∥x∥l(e	∥x∥l(e	NOUN
ejpam-4071	93	26	)	)	PUNCT
ejpam-4071	93	27	=	=	SYM
ejpam-4071	93	28	0	0	PUNCT
ejpam-4071	94	1	if	if	SCONJ
ejpam-4071	94	2	and	and	CCONJ
ejpam-4071	94	3	only	only	ADV
ejpam-4071	94	4	if	if	SCONJ
ejpam-4071	94	5	x	x	SYM
ejpam-4071	94	6	=	=	SYM
ejpam-4071	94	7	0	0	NUM
ejpam-4071	94	8	;	;	PUNCT
ejpam-4071	94	9	(	(	PUNCT
ejpam-4071	94	10	2	2	X
ejpam-4071	94	11	)	)	PUNCT
ejpam-4071	94	12	∥λx∥l(e	∥λx∥l(e	NOUN
ejpam-4071	94	13	)	)	PUNCT
ejpam-4071	94	14	=	=	PUNCT
ejpam-4071	94	15	|λ|∥x∥l(e	|λ|∥x∥l(e	PROPN
ejpam-4071	94	16	)	)	PUNCT
ejpam-4071	94	17	;	;	PUNCT
ejpam-4071	94	18	λ	λ	X
ejpam-4071	94	19	∈	∈	PROPN
ejpam-4071	94	20	c	c	X
ejpam-4071	94	21	;	;	PUNCT
ejpam-4071	94	22	(	(	PUNCT
ejpam-4071	94	23	3	3	X
ejpam-4071	94	24	)	)	PUNCT
ejpam-4071	94	25	∥x+	∥x+	PROPN
ejpam-4071	95	1	y∥l(e	y∥l(e	PROPN
ejpam-4071	95	2	)	)	PUNCT
ejpam-4071	95	3	⪯	⪯	NOUN
ejpam-4071	95	4	∥x∥l(e	∥x∥l(e	NOUN
ejpam-4071	95	5	)	)	PUNCT
ejpam-4071	96	1	+	+	NUM
ejpam-4071	96	2	∥y∥l(e	∥y∥l(e	ADJ
ejpam-4071	96	3	)	)	PUNCT
ejpam-4071	96	4	.	.	PUNCT
ejpam-4071	97	1	then	then	ADV
ejpam-4071	97	2	∥.∥	∥.∥	PUNCT
ejpam-4071	97	3	is	be	AUX
ejpam-4071	97	4	said	say	VERB
ejpam-4071	97	5	to	to	PART
ejpam-4071	97	6	be	be	AUX
ejpam-4071	97	7	l(e)-valued	l(e)-value	VERB
ejpam-4071	97	8	norm	norm	NOUN
ejpam-4071	97	9	defined	define	VERB
ejpam-4071	97	10	on	on	ADP
ejpam-4071	97	11	x	x	PRON
ejpam-4071	97	12	,	,	PUNCT
ejpam-4071	97	13	and	and	CCONJ
ejpam-4071	97	14	(	(	PUNCT
ejpam-4071	97	15	x	x	NOUN
ejpam-4071	97	16	,	,	PUNCT
ejpam-4071	97	17	∥.∥	∥.∥	NUM
ejpam-4071	97	18	)	)	PUNCT
ejpam-4071	97	19	is	be	AUX
ejpam-4071	97	20	said	say	VERB
ejpam-4071	97	21	to	to	PART
ejpam-4071	97	22	be	be	AUX
ejpam-4071	97	23	l(e)-valued	l(e)-value	VERB
ejpam-4071	97	24	normed	normed	ADJ
ejpam-4071	97	25	l(e	l(e	NOUN
ejpam-4071	97	26	)	)	PUNCT
ejpam-4071	97	27	space	space	NOUN
ejpam-4071	97	28	.	.	PUNCT
ejpam-4071	98	1	also	also	ADV
ejpam-4071	98	2	we	we	PRON
ejpam-4071	98	3	will	will	AUX
ejpam-4071	98	4	set	set	VERB
ejpam-4071	98	5	the	the	DET
ejpam-4071	98	6	relation	relation	NOUN
ejpam-4071	98	7	between	between	ADP
ejpam-4071	98	8	l(e)-valued	l(e)-value	VERB
ejpam-4071	98	9	metric	metric	ADJ
ejpam-4071	98	10	space	space	NOUN
ejpam-4071	98	11	and	and	CCONJ
ejpam-4071	98	12	l(e)-valued	l(e)-value	VERB
ejpam-4071	98	13	normed	normed	ADJ
ejpam-4071	98	14	space	space	NOUN
ejpam-4071	98	15	as	as	SCONJ
ejpam-4071	98	16	follow	follow	VERB
ejpam-4071	98	17	dl(e)(x	dl(e)(x	NOUN
ejpam-4071	98	18	,	,	PUNCT
ejpam-4071	98	19	y	y	NOUN
ejpam-4071	98	20	)	)	PUNCT
ejpam-4071	98	21	=	=	SYM
ejpam-4071	99	1	∥x−	∥x−	NUM
ejpam-4071	99	2	y∥l(e	y∥l(e	PROPN
ejpam-4071	99	3	)	)	PUNCT
ejpam-4071	99	4	.	.	PUNCT
ejpam-4071	100	1	r.	r.	PROPN
ejpam-4071	100	2	a.	a.	PROPN
ejpam-4071	100	3	rashwan	rashwan	PROPN
ejpam-4071	100	4	et	et	PROPN
ejpam-4071	100	5	al	al	PROPN
ejpam-4071	100	6	.	.	PUNCT
ejpam-4071	100	7	/	/	SYM
ejpam-4071	100	8	eur	eur	PROPN
ejpam-4071	100	9	.	.	PUNCT
ejpam-4071	101	1	j.	j.	PROPN
ejpam-4071	101	2	pure	pure	PROPN
ejpam-4071	101	3	appl	appl	PROPN
ejpam-4071	101	4	.	.	PROPN
ejpam-4071	101	5	math	math	PROPN
ejpam-4071	101	6	,	,	PUNCT
ejpam-4071	101	7	14	14	NUM
ejpam-4071	101	8	(	(	PUNCT
ejpam-4071	101	9	4	4	NUM
ejpam-4071	101	10	)	)	PUNCT
ejpam-4071	101	11	(	(	PUNCT
ejpam-4071	101	12	2021	2021	NUM
ejpam-4071	101	13	)	)	PUNCT
ejpam-4071	101	14	,	,	PUNCT
ejpam-4071	101	15	1237	1237	NUM
ejpam-4071	101	16	-	-	SYM
ejpam-4071	101	17	1248	1248	NUM
ejpam-4071	101	18	1241	1241	NUM
ejpam-4071	101	19	definition	definition	NOUN
ejpam-4071	101	20	16	16	NUM
ejpam-4071	101	21	.	.	PUNCT
ejpam-4071	102	1	let	let	VERB
ejpam-4071	102	2	x	x	PRON
ejpam-4071	102	3	be	be	AUX
ejpam-4071	102	4	a	a	DET
ejpam-4071	102	5	vector	vector	NOUN
ejpam-4071	102	6	space	space	NOUN
ejpam-4071	102	7	over	over	ADP
ejpam-4071	102	8	a	a	DET
ejpam-4071	102	9	field	field	NOUN
ejpam-4071	102	10	(	(	PUNCT
ejpam-4071	102	11	f	f	NOUN
ejpam-4071	102	12	=	=	SYM
ejpam-4071	102	13	c	c	X
ejpam-4071	102	14	,	,	PUNCT
ejpam-4071	102	15	r	r	NOUN
ejpam-4071	102	16	)	)	PUNCT
ejpam-4071	102	17	we	we	PRON
ejpam-4071	102	18	say	say	VERB
ejpam-4071	102	19	that	that	SCONJ
ejpam-4071	102	20	x	x	PRON
ejpam-4071	102	21	is	be	AUX
ejpam-4071	102	22	a	a	DET
ejpam-4071	102	23	right	right	ADJ
ejpam-4071	102	24	l(e)-vector	l(e)-vector	PROPN
ejpam-4071	102	25	space	space	NOUN
ejpam-4071	102	26	if	if	SCONJ
ejpam-4071	102	27	satisfy	satisfy	VERB
ejpam-4071	102	28	:	:	PUNCT
ejpam-4071	102	29	(	(	PUNCT
ejpam-4071	102	30	1	1	X
ejpam-4071	102	31	)	)	PUNCT
ejpam-4071	102	32	(	(	PUNCT
ejpam-4071	102	33	x+	x+	X
ejpam-4071	102	34	y)t	y)t	PUNCT
ejpam-4071	102	35	=	=	PUNCT
ejpam-4071	102	36	xt	xt	X
ejpam-4071	103	1	+	+	CCONJ
ejpam-4071	103	2	yt	yt	INTJ
ejpam-4071	103	3	;	;	PUNCT
ejpam-4071	103	4	(	(	PUNCT
ejpam-4071	103	5	3	3	X
ejpam-4071	103	6	)	)	PUNCT
ejpam-4071	103	7	x(t1	x(t1	PUNCT
ejpam-4071	104	1	+	+	CCONJ
ejpam-4071	104	2	t2	t2	NOUN
ejpam-4071	104	3	)	)	PUNCT
ejpam-4071	104	4	=	=	PUNCT
ejpam-4071	104	5	xt1	xt1	X
ejpam-4071	105	1	+	+	CCONJ
ejpam-4071	105	2	xt2	xt2	PROPN
ejpam-4071	105	3	;	;	PUNCT
ejpam-4071	105	4	(	(	PUNCT
ejpam-4071	105	5	3	3	X
ejpam-4071	105	6	)	)	PUNCT
ejpam-4071	105	7	(	(	PUNCT
ejpam-4071	105	8	xs)t	xs)t	PROPN
ejpam-4071	105	9	=	=	SYM
ejpam-4071	105	10	x(st	x(st	PROPN
ejpam-4071	105	11	)	)	PUNCT
ejpam-4071	105	12	.	.	PUNCT
ejpam-4071	106	1	where	where	SCONJ
ejpam-4071	106	2	x	x	X
ejpam-4071	106	3	,	,	PUNCT
ejpam-4071	106	4	y	y	PROPN
ejpam-4071	106	5	∈	∈	PROPN
ejpam-4071	106	6	x	x	X
ejpam-4071	106	7	and	and	CCONJ
ejpam-4071	106	8	s	s	PROPN
ejpam-4071	106	9	,	,	PUNCT
ejpam-4071	106	10	t	t	PROPN
ejpam-4071	106	11	∈	∈	PROPN
ejpam-4071	106	12	l(e	l(e	NOUN
ejpam-4071	106	13	)	)	PUNCT
ejpam-4071	106	14	.	.	PUNCT
ejpam-4071	107	1	lemma	lemma	PROPN
ejpam-4071	107	2	3.2	3.2	NUM
ejpam-4071	107	3	let	let	VERB
ejpam-4071	107	4	x	x	PRON
ejpam-4071	107	5	be	be	AUX
ejpam-4071	107	6	a	a	DET
ejpam-4071	107	7	right	right	ADJ
ejpam-4071	107	8	l(e)-vector	l(e)-vector	PROPN
ejpam-4071	107	9	space	space	NOUN
ejpam-4071	107	10	then	then	ADV
ejpam-4071	107	11	,	,	PUNCT
ejpam-4071	107	12	∥xt∥l(e	∥xt∥l(e	PROPN
ejpam-4071	107	13	)	)	PUNCT
ejpam-4071	107	14	⪯	⪯	NOUN
ejpam-4071	107	15	∥x∥∥t∥l(e	∥x∥∥t∥l(e	PROPN
ejpam-4071	107	16	)	)	PUNCT
ejpam-4071	107	17	.	.	PUNCT
ejpam-4071	108	1	proof	proof	NOUN
ejpam-4071	108	2	.	.	PUNCT
ejpam-4071	108	3	∥xt∥2	∥xt∥2	X
ejpam-4071	109	1	=	=	SYM
ejpam-4071	109	2	sup∥x∥=1	sup∥x∥=1	PROPN
ejpam-4071	109	3	{	{	PUNCT
ejpam-4071	109	4	<	<	X
ejpam-4071	109	5	xt	xt	PROPN
ejpam-4071	109	6	,	,	PUNCT
ejpam-4071	109	7	xt	xt	X
ejpam-4071	109	8	>	>	X
ejpam-4071	109	9	,	,	PUNCT
ejpam-4071	109	10	x	x	PUNCT
ejpam-4071	109	11	∈	∈	PROPN
ejpam-4071	109	12	e	e	NOUN
ejpam-4071	109	13	}	}	PUNCT
ejpam-4071	109	14	≤	≤	NUM
ejpam-4071	109	15	∥x∥∥t∥l(e	∥x∥∥t∥l(e	PROPN
ejpam-4071	109	16	)	)	PUNCT
ejpam-4071	109	17	.	.	PUNCT
ejpam-4071	110	1	definition	definition	NOUN
ejpam-4071	110	2	17	17	NUM
ejpam-4071	110	3	.	.	PUNCT
ejpam-4071	111	1	let	let	VERB
ejpam-4071	111	2	a	a	DET
ejpam-4071	111	3	be	be	AUX
ejpam-4071	111	4	c∗-algebra	c∗-algebra	NOUN
ejpam-4071	111	5	,	,	PUNCT
ejpam-4071	111	6	and	and	CCONJ
ejpam-4071	111	7	l(e	l(e	NOUN
ejpam-4071	111	8	)	)	PUNCT
ejpam-4071	111	9	be	be	VERB
ejpam-4071	111	10	an	an	DET
ejpam-4071	111	11	l(e)-normed	l(e)-normed	PROPN
ejpam-4071	111	12	spac	spac	PROPN
ejpam-4071	111	13	.	.	PUNCT
ejpam-4071	112	1	we	we	PRON
ejpam-4071	112	2	say	say	VERB
ejpam-4071	112	3	that	that	SCONJ
ejpam-4071	112	4	l(e	l(e	NOUN
ejpam-4071	112	5	)	)	PUNCT
ejpam-4071	112	6	is	be	AUX
ejpam-4071	112	7	right	right	ADJ
ejpam-4071	112	8	a	a	DET
ejpam-4071	112	9	-	-	PUNCT
ejpam-4071	112	10	module	module	NOUN
ejpam-4071	112	11	if	if	SCONJ
ejpam-4071	112	12	the	the	DET
ejpam-4071	112	13	mapping	mapping	NOUN
ejpam-4071	112	14	is	be	AUX
ejpam-4071	112	15	right	right	ADJ
ejpam-4071	112	16	module	module	NOUN
ejpam-4071	112	17	multiplication	multiplication	NOUN
ejpam-4071	112	18	(	(	PUNCT
ejpam-4071	112	19	a	a	PRON
ejpam-4071	112	20	,	,	PUNCT
ejpam-4071	112	21	t	t	NOUN
ejpam-4071	112	22	)	)	PUNCT
ejpam-4071	112	23	7−→	7−→	PROPN
ejpam-4071	112	24	xa	xa	PROPN
ejpam-4071	112	25	of	of	ADP
ejpam-4071	112	26	a×	a×	PROPN
ejpam-4071	112	27	l(e	l(e	NOUN
ejpam-4071	112	28	)	)	PUNCT
ejpam-4071	112	29	−→	−→	NOUN
ejpam-4071	112	30	l(e	l(e	NOUN
ejpam-4071	112	31	)	)	PUNCT
ejpam-4071	112	32	such	such	ADJ
ejpam-4071	112	33	that	that	SCONJ
ejpam-4071	112	34	the	the	DET
ejpam-4071	112	35	following	follow	VERB
ejpam-4071	112	36	axioms	axiom	NOUN
ejpam-4071	112	37	are	be	AUX
ejpam-4071	112	38	satisfied	satisfied	ADJ
ejpam-4071	112	39	:	:	PUNCT
ejpam-4071	112	40	(	(	PUNCT
ejpam-4071	112	41	1	1	X
ejpam-4071	112	42	)	)	PUNCT
ejpam-4071	112	43	for	for	ADP
ejpam-4071	112	44	each	each	DET
ejpam-4071	112	45	fixed	fix	VERB
ejpam-4071	112	46	a	a	DET
ejpam-4071	112	47	∈	∈	PROPN
ejpam-4071	112	48	a	a	DET
ejpam-4071	112	49	the	the	DET
ejpam-4071	112	50	map	map	NOUN
ejpam-4071	112	51	(	(	PUNCT
ejpam-4071	112	52	a	a	PRON
ejpam-4071	112	53	,	,	PUNCT
ejpam-4071	112	54	t	t	NOUN
ejpam-4071	112	55	)	)	PUNCT
ejpam-4071	112	56	−→	−→	NOUN
ejpam-4071	112	57	ta	ta	PROPN
ejpam-4071	112	58	is	be	AUX
ejpam-4071	112	59	linear	linear	ADJ
ejpam-4071	112	60	on	on	ADP
ejpam-4071	112	61	l(e	l(e	NOUN
ejpam-4071	112	62	):	):	PUNCT
ejpam-4071	112	63	t	t	PROPN
ejpam-4071	112	64	∈	∈	PROPN
ejpam-4071	112	65	l(e	l(e	NOUN
ejpam-4071	112	66	)	)	PUNCT
ejpam-4071	112	67	;	;	PUNCT
ejpam-4071	112	68	(	(	PUNCT
ejpam-4071	112	69	2	2	X
ejpam-4071	112	70	)	)	PUNCT
ejpam-4071	112	71	for	for	ADP
ejpam-4071	112	72	each	each	DET
ejpam-4071	112	73	fixed	fix	VERB
ejpam-4071	112	74	t	t	PROPN
ejpam-4071	112	75	∈	∈	PROPN
ejpam-4071	112	76	l(e	l(e	NOUN
ejpam-4071	112	77	)	)	PUNCT
ejpam-4071	112	78	the	the	DET
ejpam-4071	112	79	map	map	NOUN
ejpam-4071	112	80	(	(	PUNCT
ejpam-4071	112	81	a	a	PRON
ejpam-4071	112	82	,	,	PUNCT
ejpam-4071	112	83	t	t	NOUN
ejpam-4071	112	84	)	)	PUNCT
ejpam-4071	112	85	−→	−→	NOUN
ejpam-4071	112	86	ta	ta	PROPN
ejpam-4071	112	87	is	be	AUX
ejpam-4071	112	88	linear	linear	ADJ
ejpam-4071	112	89	on	on	ADP
ejpam-4071	112	90	a	a	PRON
ejpam-4071	112	91	;	;	PUNCT
ejpam-4071	112	92	(	(	PUNCT
ejpam-4071	112	93	3	3	X
ejpam-4071	112	94	)	)	PUNCT
ejpam-4071	112	95	for	for	ADP
ejpam-4071	112	96	all	all	DET
ejpam-4071	112	97	a1	a1	NOUN
ejpam-4071	112	98	,	,	PUNCT
ejpam-4071	112	99	a2	a2	PROPN
ejpam-4071	112	100	∈	∈	PROPN
ejpam-4071	112	101	a	a	PRON
ejpam-4071	112	102	and	and	CCONJ
ejpam-4071	112	103	all	all	PRON
ejpam-4071	112	104	t	t	NOUN
ejpam-4071	112	105	∈	∈	PROPN
ejpam-4071	112	106	l(e	l(e	NOUN
ejpam-4071	112	107	)	)	PUNCT
ejpam-4071	112	108	we	we	PRON
ejpam-4071	112	109	have	have	VERB
ejpam-4071	112	110	that	that	PRON
ejpam-4071	112	111	(	(	PUNCT
ejpam-4071	112	112	ta1)a2	ta1)a2	NUM
ejpam-4071	112	113	=	=	SYM
ejpam-4071	112	114	t	t	PROPN
ejpam-4071	112	115	(	(	PUNCT
ejpam-4071	112	116	a1a2	a1a2	PROPN
ejpam-4071	112	117	)	)	PUNCT
ejpam-4071	112	118	.	.	PUNCT
ejpam-4071	113	1	example	example	NOUN
ejpam-4071	114	1	3	3	NUM
ejpam-4071	114	2	.	.	PUNCT
ejpam-4071	115	1	if	if	SCONJ
ejpam-4071	115	2	we	we	PRON
ejpam-4071	115	3	define	define	VERB
ejpam-4071	115	4	the	the	DET
ejpam-4071	115	5	norm	norm	NOUN
ejpam-4071	115	6	∥x∥l(e	∥x∥l(e	NOUN
ejpam-4071	115	7	)	)	PUNCT
ejpam-4071	115	8	=	=	SYM
ejpam-4071	115	9	∥x∥il(e	∥x∥il(e	NUM
ejpam-4071	115	10	)	)	PUNCT
ejpam-4071	115	11	(	(	PUNCT
ejpam-4071	115	12	where	where	SCONJ
ejpam-4071	115	13	il(e	il(e	NUM
ejpam-4071	115	14	)	)	PUNCT
ejpam-4071	115	15	is	be	AUX
ejpam-4071	115	16	the	the	DET
ejpam-4071	115	17	identity	identity	NOUN
ejpam-4071	115	18	operator	operator	NOUN
ejpam-4071	115	19	of	of	ADP
ejpam-4071	115	20	l(e	l(e	NOUN
ejpam-4071	115	21	)	)	PUNCT
ejpam-4071	115	22	)	)	PUNCT
ejpam-4071	116	1	then	then	ADV
ejpam-4071	116	2	we	we	PRON
ejpam-4071	116	3	have	have	VERB
ejpam-4071	116	4	that	that	DET
ejpam-4071	116	5	l(e	l(e	NOUN
ejpam-4071	116	6	)	)	PUNCT
ejpam-4071	116	7	with	with	ADP
ejpam-4071	116	8	this	this	DET
ejpam-4071	116	9	norm	norm	NOUN
ejpam-4071	116	10	is	be	AUX
ejpam-4071	116	11	l(e)-norm	l(e)-norm	PROPN
ejpam-4071	116	12	.	.	PUNCT
ejpam-4071	117	1	lemma	lemma	PROPN
ejpam-4071	117	2	2	2	NUM
ejpam-4071	117	3	.	.	PUNCT
ejpam-4071	118	1	if	if	SCONJ
ejpam-4071	118	2	t	t	PROPN
ejpam-4071	118	3	is	be	AUX
ejpam-4071	118	4	positive	positive	ADJ
ejpam-4071	118	5	if	if	SCONJ
ejpam-4071	118	6	and	and	CCONJ
ejpam-4071	118	7	only	only	ADV
ejpam-4071	118	8	if	if	SCONJ
ejpam-4071	118	9	t	t	PROPN
ejpam-4071	118	10	∗	∗	NOUN
ejpam-4071	118	11	is	be	AUX
ejpam-4071	118	12	positive	positive	ADJ
ejpam-4071	118	13	.	.	PUNCT
ejpam-4071	119	1	proof	proof	NOUN
ejpam-4071	119	2	.	.	PUNCT
ejpam-4071	120	1	let	let	VERB
ejpam-4071	120	2	∗	∗	NOUN
ejpam-4071	120	3	:	:	PUNCT
ejpam-4071	120	4	a	a	DET
ejpam-4071	120	5	−→	−→	NOUN
ejpam-4071	120	6	a	a	PRON
ejpam-4071	120	7	is	be	AUX
ejpam-4071	120	8	∗-homomorphism	∗-homomorphism	NOUN
ejpam-4071	120	9	.	.	PUNCT
ejpam-4071	121	1	if	if	SCONJ
ejpam-4071	121	2	t	t	PROPN
ejpam-4071	121	3	∗	∗	NOUN
ejpam-4071	121	4	is	be	AUX
ejpam-4071	121	5	positive	positive	ADJ
ejpam-4071	121	6	implies	implie	NOUN
ejpam-4071	121	7	<	<	X
ejpam-4071	121	8	t	t	NOUN
ejpam-4071	121	9	∗x	∗x	NOUN
ejpam-4071	121	10	,	,	PUNCT
ejpam-4071	121	11	x	x	SYM
ejpam-4071	121	12	>	>	X
ejpam-4071	121	13	⪰	⪰	NOUN
ejpam-4071	121	14	0	0	NUM
ejpam-4071	121	15	implies	imply	VERB
ejpam-4071	121	16	<	<	X
ejpam-4071	121	17	x	x	X
ejpam-4071	121	18	,	,	PUNCT
ejpam-4071	121	19	tx	tx	INTJ
ejpam-4071	121	20	>	>	PUNCT
ejpam-4071	121	21	⪰	⪰	NOUN
ejpam-4071	121	22	0	0	NUM
ejpam-4071	121	23	implies	imply	VERB
ejpam-4071	121	24	<	<	X
ejpam-4071	121	25	x	x	X
ejpam-4071	121	26	,	,	PUNCT
ejpam-4071	121	27	tx	tx	PROPN
ejpam-4071	121	28	>	>	X
ejpam-4071	121	29	∗⪰	∗⪰	PROPN
ejpam-4071	121	30	0	0	PUNCT
ejpam-4071	121	31	implies	imply	VERB
ejpam-4071	121	32	<	<	X
ejpam-4071	121	33	tx	tx	PROPN
ejpam-4071	121	34	,	,	PUNCT
ejpam-4071	121	35	x	x	PRON
ejpam-4071	121	36	>	>	PUNCT
ejpam-4071	121	37	⪰	⪰	NOUN
ejpam-4071	121	38	0	0	NUM
ejpam-4071	121	39	implies	imply	VERB
ejpam-4071	121	40	t	t	PROPN
ejpam-4071	121	41	is	be	AUX
ejpam-4071	121	42	positive	positive	ADJ
ejpam-4071	121	43	.	.	PUNCT
ejpam-4071	122	1	⇐	⇐	ADJ
ejpam-4071	122	2	=	=	PRON
ejpam-4071	122	3	if	if	SCONJ
ejpam-4071	122	4	t	t	PROPN
ejpam-4071	122	5	is	be	AUX
ejpam-4071	122	6	positive	positive	ADJ
ejpam-4071	122	7	implies	implie	NOUN
ejpam-4071	122	8	<	<	X
ejpam-4071	122	9	tx	tx	PROPN
ejpam-4071	122	10	,	,	PUNCT
ejpam-4071	122	11	x	x	PRON
ejpam-4071	122	12	>	>	PUNCT
ejpam-4071	122	13	⪰	⪰	NOUN
ejpam-4071	122	14	0	0	NUM
ejpam-4071	122	15	implies	imply	VERB
ejpam-4071	122	16	<	<	X
ejpam-4071	122	17	x	x	X
ejpam-4071	122	18	,	,	PUNCT
ejpam-4071	122	19	t	t	PROPN
ejpam-4071	122	20	∗x	∗x	NOUN
ejpam-4071	122	21	>	>	PUNCT
ejpam-4071	122	22	⪰	⪰	NOUN
ejpam-4071	122	23	0	0	NUM
ejpam-4071	122	24	implies	imply	VERB
ejpam-4071	122	25	<	<	X
ejpam-4071	122	26	x	x	X
ejpam-4071	122	27	,	,	PUNCT
ejpam-4071	122	28	t	t	PROPN
ejpam-4071	122	29	∗x	∗x	PROPN
ejpam-4071	122	30	>	>	PUNCT
ejpam-4071	122	31	∗⪰	∗⪰	PROPN
ejpam-4071	122	32	0	0	PUNCT
ejpam-4071	122	33	implies	imply	VERB
ejpam-4071	122	34	<	<	X
ejpam-4071	122	35	t	t	NOUN
ejpam-4071	122	36	∗x	∗x	NOUN
ejpam-4071	122	37	,	,	PUNCT
ejpam-4071	122	38	x	x	SYM
ejpam-4071	122	39	>	>	X
ejpam-4071	122	40	⪰	⪰	NOUN
ejpam-4071	122	41	0	0	NUM
ejpam-4071	122	42	implies	imply	VERB
ejpam-4071	122	43	t	t	NOUN
ejpam-4071	122	44	∗	∗	NOUN
ejpam-4071	122	45	⪰	⪰	NOUN
ejpam-4071	122	46	0	0	NUM
ejpam-4071	122	47	implies	imply	VERB
ejpam-4071	122	48	t	t	PROPN
ejpam-4071	122	49	∗	∗	NOUN
ejpam-4071	122	50	is	be	AUX
ejpam-4071	122	51	positive	positive	ADJ
ejpam-4071	122	52	.	.	PUNCT
ejpam-4071	123	1	lemma	lemma	PROPN
ejpam-4071	124	1	3	3	X
ejpam-4071	124	2	.	.	PUNCT
ejpam-4071	125	1	if	if	SCONJ
ejpam-4071	125	2	s	s	NOUN
ejpam-4071	125	3	is	be	AUX
ejpam-4071	125	4	positive	positive	ADJ
ejpam-4071	125	5	operator	operator	NOUN
ejpam-4071	125	6	then	then	ADV
ejpam-4071	125	7	for	for	ADP
ejpam-4071	125	8	any	any	DET
ejpam-4071	125	9	operator	operator	NOUN
ejpam-4071	125	10	t	t	NOUN
ejpam-4071	125	11	implies	imply	VERB
ejpam-4071	125	12	t	t	PROPN
ejpam-4071	125	13	∗st	∗st	PROPN
ejpam-4071	125	14	is	be	AUX
ejpam-4071	125	15	positive	positive	ADJ
ejpam-4071	125	16	operator	operator	NOUN
ejpam-4071	125	17	.	.	PUNCT
ejpam-4071	126	1	proof	proof	NOUN
ejpam-4071	126	2	.	.	PUNCT
ejpam-4071	127	1	since	since	SCONJ
ejpam-4071	127	2	s	s	PRON
ejpam-4071	127	3	⪰	⪰	NOUN
ejpam-4071	127	4	0	0	NUM
ejpam-4071	127	5	,	,	PUNCT
ejpam-4071	127	6	we	we	PRON
ejpam-4071	127	7	can	can	AUX
ejpam-4071	127	8	write	write	VERB
ejpam-4071	127	9	s	s	NOUN
ejpam-4071	127	10	=	=	PUNCT
ejpam-4071	127	11	r∗r	r∗r	X
ejpam-4071	127	12	,	,	PUNCT
ejpam-4071	127	13	for	for	ADP
ejpam-4071	127	14	any	any	PRON
ejpam-4071	127	15	r	r	NOUN
ejpam-4071	127	16	∈	∈	PROPN
ejpam-4071	127	17	(	(	PUNCT
ejpam-4071	127	18	le	le	NOUN
ejpam-4071	127	19	)	)	PUNCT
ejpam-4071	127	20	implies	imply	VERB
ejpam-4071	127	21	t	t	PROPN
ejpam-4071	127	22	∗(r∗r)t	∗(r∗r)t	PROPN
ejpam-4071	127	23	=	=	PUNCT
ejpam-4071	128	1	(	(	PUNCT
ejpam-4071	128	2	t	t	PROPN
ejpam-4071	128	3	∗r∗)(rt	∗r∗)(rt	NUM
ejpam-4071	128	4	)	)	PUNCT
ejpam-4071	128	5	=	=	SYM
ejpam-4071	128	6	(	(	PUNCT
ejpam-4071	128	7	rt	rt	PROPN
ejpam-4071	128	8	)	)	PUNCT
ejpam-4071	128	9	∗(rt	∗(rt	NOUN
ejpam-4071	128	10	)	)	PUNCT
ejpam-4071	128	11	⪰	⪰	NOUN
ejpam-4071	128	12	0	0	NUM
ejpam-4071	128	13	definition	definition	NOUN
ejpam-4071	128	14	18	18	NUM
ejpam-4071	128	15	.	.	PUNCT
ejpam-4071	129	1	a	a	DET
ejpam-4071	129	2	sequence	sequence	NOUN
ejpam-4071	129	3	{	{	PUNCT
ejpam-4071	129	4	xn	xn	NOUN
ejpam-4071	129	5	}	}	PUNCT
ejpam-4071	129	6	in	in	ADP
ejpam-4071	129	7	x	x	VERB
ejpam-4071	129	8	is	be	AUX
ejpam-4071	129	9	said	say	VERB
ejpam-4071	129	10	to	to	PART
ejpam-4071	129	11	be	be	AUX
ejpam-4071	129	12	convergent	convergent	ADJ
ejpam-4071	129	13	if	if	SCONJ
ejpam-4071	129	14	for	for	ADP
ejpam-4071	129	15	every	every	DET
ejpam-4071	129	16	ϵ	ϵ	X
ejpam-4071	129	17	>	>	X
ejpam-4071	129	18	0	0	NUM
ejpam-4071	129	19	,	,	PUNCT
ejpam-4071	129	20	there	there	PRON
ejpam-4071	129	21	is	be	VERB
ejpam-4071	129	22	a	a	DET
ejpam-4071	129	23	natural	natural	ADJ
ejpam-4071	129	24	number	number	NOUN
ejpam-4071	129	25	n	n	ADP
ejpam-4071	129	26	such	such	ADJ
ejpam-4071	129	27	that	that	PRON
ejpam-4071	129	28	for	for	ADP
ejpam-4071	129	29	n	n	PRON
ejpam-4071	129	30	>	>	X
ejpam-4071	129	31	n	n	CCONJ
ejpam-4071	129	32	we	we	PRON
ejpam-4071	129	33	have	have	VERB
ejpam-4071	129	34	r.	r.	PROPN
ejpam-4071	129	35	a.	a.	PROPN
ejpam-4071	129	36	rashwan	rashwan	PROPN
ejpam-4071	129	37	et	et	PROPN
ejpam-4071	129	38	al	al	PROPN
ejpam-4071	129	39	.	.	PUNCT
ejpam-4071	129	40	/	/	SYM
ejpam-4071	129	41	eur	eur	PROPN
ejpam-4071	129	42	.	.	PUNCT
ejpam-4071	130	1	j.	j.	PROPN
ejpam-4071	130	2	pure	pure	PROPN
ejpam-4071	130	3	appl	appl	PROPN
ejpam-4071	130	4	.	.	PROPN
ejpam-4071	130	5	math	math	PROPN
ejpam-4071	130	6	,	,	PUNCT
ejpam-4071	130	7	14	14	NUM
ejpam-4071	130	8	(	(	PUNCT
ejpam-4071	130	9	4	4	NUM
ejpam-4071	130	10	)	)	PUNCT
ejpam-4071	130	11	(	(	PUNCT
ejpam-4071	130	12	2021	2021	NUM
ejpam-4071	130	13	)	)	PUNCT
ejpam-4071	130	14	,	,	PUNCT
ejpam-4071	130	15	1237	1237	NUM
ejpam-4071	130	16	-	-	SYM
ejpam-4071	130	17	1248	1248	NUM
ejpam-4071	130	18	1242	1242	NUM
ejpam-4071	130	19	∥xn	∥xn	PROPN
ejpam-4071	130	20	−	−	PROPN
ejpam-4071	130	21	x∥	x∥	PROPN
ejpam-4071	130	22	⪯l(e	⪯l(e	NOUN
ejpam-4071	130	23	)	)	PUNCT
ejpam-4071	130	24	ϵil(e	ϵil(e	NUM
ejpam-4071	130	25	)	)	PUNCT
ejpam-4071	130	26	(	(	PUNCT
ejpam-4071	130	27	where	where	SCONJ
ejpam-4071	130	28	il(e	il(e	NUM
ejpam-4071	130	29	)	)	PUNCT
ejpam-4071	130	30	the	the	DET
ejpam-4071	130	31	identity	identity	NOUN
ejpam-4071	130	32	operator	operator	NOUN
ejpam-4071	130	33	of	of	ADP
ejpam-4071	130	34	l(e	l(e	NOUN
ejpam-4071	130	35	)	)	PUNCT
ejpam-4071	130	36	)	)	PUNCT
ejpam-4071	130	37	.	.	PUNCT
ejpam-4071	131	1	definition	definition	NOUN
ejpam-4071	131	2	19	19	NUM
ejpam-4071	131	3	.	.	PUNCT
ejpam-4071	132	1	a	a	DET
ejpam-4071	132	2	sequence	sequence	NOUN
ejpam-4071	132	3	{	{	PUNCT
ejpam-4071	132	4	xn	xn	NOUN
ejpam-4071	132	5	}	}	PUNCT
ejpam-4071	132	6	in	in	ADP
ejpam-4071	132	7	x	x	VERB
ejpam-4071	132	8	is	be	AUX
ejpam-4071	132	9	said	say	VERB
ejpam-4071	132	10	to	to	PART
ejpam-4071	132	11	be	be	AUX
ejpam-4071	132	12	a	a	DET
ejpam-4071	132	13	cuachy	cuachy	ADJ
ejpam-4071	132	14	sequence	sequence	NOUN
ejpam-4071	132	15	if	if	SCONJ
ejpam-4071	132	16	for	for	ADP
ejpam-4071	132	17	every	every	DET
ejpam-4071	132	18	ϵ	ϵ	X
ejpam-4071	132	19	>	>	X
ejpam-4071	132	20	0	0	NUM
ejpam-4071	132	21	,	,	PUNCT
ejpam-4071	132	22	there	there	PRON
ejpam-4071	132	23	is	be	VERB
ejpam-4071	132	24	a	a	DET
ejpam-4071	132	25	natural	natural	ADJ
ejpam-4071	132	26	number	number	NOUN
ejpam-4071	132	27	n	n	ADP
ejpam-4071	132	28	such	such	ADJ
ejpam-4071	132	29	that	that	PRON
ejpam-4071	132	30	for	for	ADP
ejpam-4071	132	31	n	n	CCONJ
ejpam-4071	132	32	,	,	PUNCT
ejpam-4071	132	33	m	m	VERB
ejpam-4071	132	34	>	>	X
ejpam-4071	133	1	n	n	CCONJ
ejpam-4071	133	2	we	we	PRON
ejpam-4071	133	3	have	have	VERB
ejpam-4071	133	4	∥xn	∥xn	VERB
ejpam-4071	133	5	−	−	PROPN
ejpam-4071	133	6	xm∥	xm∥	PROPN
ejpam-4071	133	7	⪯l(e	⪯l(e	NOUN
ejpam-4071	133	8	)	)	PUNCT
ejpam-4071	133	9	ϵil(e	ϵil(e	NUM
ejpam-4071	133	10	)	)	PUNCT
ejpam-4071	133	11	.	.	PUNCT
ejpam-4071	134	1	lemma	lemma	PROPN
ejpam-4071	134	2	4	4	NUM
ejpam-4071	134	3	.	.	PUNCT
ejpam-4071	135	1	a	a	DET
ejpam-4071	135	2	sequence	sequence	NOUN
ejpam-4071	135	3	{	{	PUNCT
ejpam-4071	135	4	xn	xn	NOUN
ejpam-4071	135	5	}	}	PUNCT
ejpam-4071	135	6	in	in	ADP
ejpam-4071	135	7	x	x	SYM
ejpam-4071	135	8	is	be	AUX
ejpam-4071	135	9	convergence	convergence	NOUN
ejpam-4071	135	10	in	in	ADP
ejpam-4071	135	11	x	x	PUNCT
ejpam-4071	135	12	if	if	SCONJ
ejpam-4071	135	13	∥xn∥r	∥xn∥r	PRON
ejpam-4071	135	14	−→	−→	NOUN
ejpam-4071	135	15	0	0	NUM
ejpam-4071	135	16	at	at	ADP
ejpam-4071	135	17	n	n	ADV
ejpam-4071	135	18	−→	−→	NOUN
ejpam-4071	136	1	+	+	ADJ
ejpam-4071	136	2	∞.	∞.	PROPN
ejpam-4071	136	3	proof	proof	NOUN
ejpam-4071	136	4	.	.	PUNCT
ejpam-4071	137	1	since	since	SCONJ
ejpam-4071	137	2	in	in	ADP
ejpam-4071	137	3	l(e)valued	l(e)value	VERB
ejpam-4071	137	4	metric	metric	ADJ
ejpam-4071	137	5	spacs	spac	NOUN
ejpam-4071	137	6	.	.	PUNCT
ejpam-4071	138	1	we	we	PRON
ejpam-4071	138	2	say	say	VERB
ejpam-4071	138	3	that	that	SCONJ
ejpam-4071	138	4	a	a	DET
ejpam-4071	138	5	sequance	sequance	NOUN
ejpam-4071	138	6	xn	xn	PUNCT
ejpam-4071	139	1	⊂	⊂	PROPN
ejpam-4071	139	2	x	x	X
ejpam-4071	139	3	converges	converge	VERB
ejpam-4071	139	4	to	to	ADP
ejpam-4071	139	5	x	x	PUNCT
ejpam-4071	139	6	∈	∈	PROPN
ejpam-4071	139	7	x	x	INTJ
ejpam-4071	139	8	if	if	SCONJ
ejpam-4071	139	9	for	for	ADP
ejpam-4071	139	10	any	any	DET
ejpam-4071	139	11	εl(e	εl(e	NUM
ejpam-4071	139	12	)	)	PUNCT
ejpam-4071	139	13	≻	≻	NOUN
ejpam-4071	139	14	0l(e	0l(e	NOUN
ejpam-4071	139	15	)	)	PUNCT
ejpam-4071	139	16	(	(	PUNCT
ejpam-4071	139	17	where	where	SCONJ
ejpam-4071	139	18	0l(e	0l(e	NOUN
ejpam-4071	139	19	)	)	PUNCT
ejpam-4071	139	20	is	be	AUX
ejpam-4071	139	21	the	the	DET
ejpam-4071	139	22	zero	zero	NUM
ejpam-4071	139	23	element	element	NOUN
ejpam-4071	139	24	in	in	ADP
ejpam-4071	139	25	l(e	l(e	NOUN
ejpam-4071	139	26	)	)	PUNCT
ejpam-4071	139	27	)	)	PUNCT
ejpam-4071	140	1	there	there	PRON
ejpam-4071	140	2	exists	exist	VERB
ejpam-4071	140	3	n	n	PRON
ejpam-4071	140	4	∈	∈	PROPN
ejpam-4071	140	5	n	n	PRON
ejpam-4071	140	6	such	such	ADJ
ejpam-4071	140	7	that	that	PRON
ejpam-4071	140	8	for	for	ADP
ejpam-4071	140	9	all	all	DET
ejpam-4071	140	10	n	n	CCONJ
ejpam-4071	140	11	>	>	PUNCT
ejpam-4071	140	12	n	n	PROPN
ejpam-4071	140	13	,	,	PUNCT
ejpam-4071	140	14	dl(e)(xn	dl(e)(xn	PROPN
ejpam-4071	140	15	,	,	PUNCT
ejpam-4071	140	16	x	x	X
ejpam-4071	140	17	)	)	PUNCT
ejpam-4071	140	18	⪯	⪯	NOUN
ejpam-4071	140	19	εl(e	εl(e	PUNCT
ejpam-4071	140	20	)	)	PUNCT
ejpam-4071	140	21	,	,	PUNCT
ejpam-4071	140	22	then	then	ADV
ejpam-4071	140	23	this	this	PRON
ejpam-4071	140	24	implies	imply	VERB
ejpam-4071	140	25	∥dl(e)(xn	∥dl(e)(xn	PROPN
ejpam-4071	140	26	,	,	PUNCT
ejpam-4071	140	27	x)∥r	x)∥r	X
ejpam-4071	140	28	<	<	X
ejpam-4071	140	29	e	e	X
ejpam-4071	140	30	,	,	PUNCT
ejpam-4071	140	31	e	e	PROPN
ejpam-4071	140	32	∈	∈	PROPN
ejpam-4071	140	33	r.	r.	PROPN
ejpam-4071	140	34	lemma	lemma	PROPN
ejpam-4071	140	35	5	5	NUM
ejpam-4071	140	36	.	.	PUNCT
ejpam-4071	141	1	[	[	X
ejpam-4071	141	2	2	2	NUM
ejpam-4071	141	3	,	,	PUNCT
ejpam-4071	141	4	9	9	NUM
ejpam-4071	141	5	]	]	PUNCT
ejpam-4071	141	6	suppose	suppose	VERB
ejpam-4071	141	7	that	that	SCONJ
ejpam-4071	141	8	a	a	PRON
ejpam-4071	141	9	is	be	AUX
ejpam-4071	141	10	a	a	DET
ejpam-4071	141	11	unital	unital	ADJ
ejpam-4071	141	12	c∗-algebra	c∗-algebra	NOUN
ejpam-4071	141	13	with	with	ADP
ejpam-4071	141	14	a	a	DET
ejpam-4071	141	15	unit	unit	NOUN
ejpam-4071	141	16	i	i	PRON
ejpam-4071	141	17	:	:	PUNCT
ejpam-4071	141	18	(	(	PUNCT
ejpam-4071	141	19	1	1	X
ejpam-4071	141	20	)	)	PUNCT
ejpam-4071	141	21	for	for	ADP
ejpam-4071	141	22	any	any	DET
ejpam-4071	141	23	x	x	SYM
ejpam-4071	141	24	∈	∈	PROPN
ejpam-4071	141	25	a+	a+	PUNCT
ejpam-4071	141	26	we	we	PRON
ejpam-4071	141	27	have	have	VERB
ejpam-4071	141	28	x	x	PART
ejpam-4071	141	29	⪯	⪯	VERB
ejpam-4071	141	30	i	i	PRON
ejpam-4071	141	31	if	if	SCONJ
ejpam-4071	141	32	and	and	CCONJ
ejpam-4071	141	33	only	only	ADV
ejpam-4071	141	34	if	if	SCONJ
ejpam-4071	141	35	∥x∥	∥x∥	NOUN
ejpam-4071	141	36	≤	≤	NOUN
ejpam-4071	141	37	1	1	NUM
ejpam-4071	141	38	;	;	PUNCT
ejpam-4071	141	39	(	(	PUNCT
ejpam-4071	141	40	2	2	X
ejpam-4071	141	41	)	)	PUNCT
ejpam-4071	141	42	if	if	SCONJ
ejpam-4071	141	43	a	a	DET
ejpam-4071	141	44	∈	∈	PROPN
ejpam-4071	141	45	a+	a+	PUNCT
ejpam-4071	141	46	with	with	ADP
ejpam-4071	141	47	∥a∥	∥a∥	NOUN
ejpam-4071	141	48	<	<	X
ejpam-4071	141	49	1	1	NUM
ejpam-4071	141	50	2	2	NUM
ejpam-4071	141	51	,	,	PUNCT
ejpam-4071	141	52	then	then	ADV
ejpam-4071	141	53	i	i	PRON
ejpam-4071	141	54	−	−	VERB
ejpam-4071	141	55	a	a	PRON
ejpam-4071	141	56	is	be	AUX
ejpam-4071	141	57	invertable	invertable	ADJ
ejpam-4071	141	58	and	and	CCONJ
ejpam-4071	141	59	∥a(i	∥a(i	ADJ
ejpam-4071	141	60	−	−	NOUN
ejpam-4071	141	61	a)−1∥	a)−1∥	NOUN
ejpam-4071	141	62	<	<	X
ejpam-4071	141	63	1	1	NUM
ejpam-4071	141	64	;	;	PUNCT
ejpam-4071	141	65	(	(	PUNCT
ejpam-4071	141	66	3	3	X
ejpam-4071	141	67	)	)	PUNCT
ejpam-4071	141	68	suppose	suppose	VERB
ejpam-4071	141	69	that	that	SCONJ
ejpam-4071	141	70	a	a	X
ejpam-4071	141	71	,	,	PUNCT
ejpam-4071	141	72	b	b	X
ejpam-4071	141	73	∈	∈	PROPN
ejpam-4071	141	74	a	a	DET
ejpam-4071	141	75	with	with	ADP
ejpam-4071	141	76	a	a	PRON
ejpam-4071	141	77	,	,	PUNCT
ejpam-4071	141	78	b	b	NOUN
ejpam-4071	141	79	⪰	⪰	NOUN
ejpam-4071	141	80	0	0	NUM
ejpam-4071	141	81	and	and	CCONJ
ejpam-4071	141	82	ab	ab	PROPN
ejpam-4071	141	83	=	=	SYM
ejpam-4071	141	84	ba	ba	PROPN
ejpam-4071	141	85	,	,	PUNCT
ejpam-4071	141	86	then	then	ADV
ejpam-4071	141	87	ab	ab	PROPN
ejpam-4071	141	88	⪰	⪰	PROPN
ejpam-4071	141	89	0	0	NUM
ejpam-4071	141	90	.	.	PUNCT
ejpam-4071	142	1	(	(	PUNCT
ejpam-4071	142	2	4	4	NUM
ejpam-4071	142	3	)	)	PUNCT
ejpam-4071	142	4	by	by	ADP
ejpam-4071	142	5	á	á	NOUN
ejpam-4071	142	6	we	we	PRON
ejpam-4071	142	7	denote	denote	VERB
ejpam-4071	142	8	the	the	DET
ejpam-4071	142	9	set	set	NOUN
ejpam-4071	142	10	{	{	PUNCT
ejpam-4071	142	11	a	a	DET
ejpam-4071	142	12	∈	∈	PROPN
ejpam-4071	142	13	a	a	PRON
ejpam-4071	142	14	:	:	PUNCT
ejpam-4071	142	15	ab	ab	PROPN
ejpam-4071	142	16	=	=	PUNCT
ejpam-4071	142	17	ba	ba	PROPN
ejpam-4071	142	18	forall	forall	NOUN
ejpam-4071	142	19	b	b	PROPN
ejpam-4071	142	20	∈	∈	PROPN
ejpam-4071	142	21	a	a	PRON
ejpam-4071	142	22	}	}	PUNCT
ejpam-4071	142	23	let	let	VERB
ejpam-4071	142	24	a	a	DET
ejpam-4071	142	25	∈	∈	PROPN
ejpam-4071	142	26	á	á	NOUN
ejpam-4071	142	27	,	,	PUNCT
ejpam-4071	142	28	if	if	SCONJ
ejpam-4071	142	29	b	b	X
ejpam-4071	142	30	,	,	PUNCT
ejpam-4071	142	31	c	c	PROPN
ejpam-4071	142	32	∈	∈	PROPN
ejpam-4071	143	1	a	a	DET
ejpam-4071	143	2	with	with	ADP
ejpam-4071	143	3	b	b	NOUN
ejpam-4071	143	4	⪰	⪰	NOUN
ejpam-4071	143	5	c	c	NOUN
ejpam-4071	143	6	⪰	⪰	NOUN
ejpam-4071	143	7	0	0	PUNCT
ejpam-4071	144	1	(	(	PUNCT
ejpam-4071	144	2	i	i	PRON
ejpam-4071	144	3	−	−	PROPN
ejpam-4071	144	4	a)−1b	a)−1b	PROPN
ejpam-4071	144	5	⪰	⪰	NOUN
ejpam-4071	144	6	(	(	PUNCT
ejpam-4071	144	7	i	i	PRON
ejpam-4071	144	8	−	−	PROPN
ejpam-4071	144	9	a)−1c	a)−1c	PROPN
ejpam-4071	144	10	.	.	PUNCT
ejpam-4071	145	1	definition	definition	NOUN
ejpam-4071	145	2	20	20	NUM
ejpam-4071	145	3	.	.	PUNCT
ejpam-4071	146	1	let	let	VERB
ejpam-4071	146	2	(	(	PUNCT
ejpam-4071	146	3	x	x	NOUN
ejpam-4071	146	4	,	,	PUNCT
ejpam-4071	146	5	l(e	l(e	NOUN
ejpam-4071	146	6	)	)	PUNCT
ejpam-4071	146	7	,	,	PUNCT
ejpam-4071	146	8	∥.∥l(e	∥.∥l(e	NOUN
ejpam-4071	146	9	)	)	PUNCT
ejpam-4071	146	10	)	)	PUNCT
ejpam-4071	146	11	be	be	AUX
ejpam-4071	146	12	an	an	DET
ejpam-4071	146	13	l(e	l(e	NOUN
ejpam-4071	146	14	)	)	PUNCT
ejpam-4071	146	15	normed	normed	ADJ
ejpam-4071	146	16	space	space	NOUN
ejpam-4071	146	17	.	.	PUNCT
ejpam-4071	147	1	we	we	PRON
ejpam-4071	147	2	call	call	VERB
ejpam-4071	147	3	a	a	DET
ejpam-4071	147	4	mapping	mapping	NOUN
ejpam-4071	147	5	t	t	NOUN
ejpam-4071	147	6	:	:	PUNCT
ejpam-4071	147	7	x	x	PUNCT
ejpam-4071	147	8	−→	−→	NOUN
ejpam-4071	147	9	x	x	VERB
ejpam-4071	147	10	is	be	AUX
ejpam-4071	147	11	l(e	l(e	NOUN
ejpam-4071	147	12	)	)	PUNCT
ejpam-4071	147	13	contractive	contractive	ADJ
ejpam-4071	147	14	mapping	mapping	NOUN
ejpam-4071	147	15	on	on	ADP
ejpam-4071	147	16	x	x	SYM
ejpam-4071	147	17	if	if	SCONJ
ejpam-4071	147	18	there	there	PRON
ejpam-4071	147	19	exists	exist	VERB
ejpam-4071	147	20	an	an	DET
ejpam-4071	147	21	m	m	PROPN
ejpam-4071	147	22	∈	∈	PROPN
ejpam-4071	147	23	l(e	l(e	NOUN
ejpam-4071	147	24	)	)	PUNCT
ejpam-4071	147	25	with	with	ADP
ejpam-4071	147	26	∥m∥l(e	∥m∥l(e	NOUN
ejpam-4071	147	27	)	)	PUNCT
ejpam-4071	147	28	≤	≤	NUM
ejpam-4071	147	29	1	1	NUM
ejpam-4071	147	30	such	such	ADJ
ejpam-4071	147	31	that	that	SCONJ
ejpam-4071	147	32	∥tx−	∥tx−	ADP
ejpam-4071	147	33	ty∥l(e	ty∥l(e	ADJ
ejpam-4071	147	34	)	)	PUNCT
ejpam-4071	147	35	⪯m∗∥x−	⪯m∗∥x−	PRON
ejpam-4071	147	36	y∥l(e)m	y∥l(e)m	VERB
ejpam-4071	147	37	forall	forall	PROPN
ejpam-4071	147	38	x	x	X
ejpam-4071	147	39	,	,	PUNCT
ejpam-4071	147	40	y	y	PROPN
ejpam-4071	147	41	∈	∈	PROPN
ejpam-4071	147	42	x.	x.	NOUN
ejpam-4071	147	43	definition	definition	NOUN
ejpam-4071	147	44	21	21	NUM
ejpam-4071	147	45	.	.	PUNCT
ejpam-4071	148	1	an	an	DET
ejpam-4071	148	2	l(e)banach	l(e)banach	NOUN
ejpam-4071	148	3	space	space	NOUN
ejpam-4071	148	4	is	be	AUX
ejpam-4071	148	5	a	a	DET
ejpam-4071	148	6	complete	complete	ADJ
ejpam-4071	148	7	l(e)-normed	l(e)-normed	PROPN
ejpam-4071	148	8	space	space	NOUN
ejpam-4071	148	9	(	(	PUNCT
ejpam-4071	148	10	x	x	NOUN
ejpam-4071	148	11	,	,	PUNCT
ejpam-4071	148	12	∥.∥l(e	∥.∥l(e	NOUN
ejpam-4071	148	13	)	)	PUNCT
ejpam-4071	148	14	)	)	PUNCT
ejpam-4071	148	15	.	.	PUNCT
ejpam-4071	149	1	many	many	ADJ
ejpam-4071	149	2	results	result	NOUN
ejpam-4071	149	3	on	on	ADP
ejpam-4071	149	4	fixed	fix	VERB
ejpam-4071	149	5	point	point	NOUN
ejpam-4071	149	6	theorems	theorem	NOUN
ejpam-4071	149	7	have	have	AUX
ejpam-4071	149	8	been	be	AUX
ejpam-4071	149	9	extended	extend	VERB
ejpam-4071	149	10	from	from	ADP
ejpam-4071	149	11	metric	metric	ADJ
ejpam-4071	149	12	spaces	space	NOUN
ejpam-4071	149	13	to	to	ADP
ejpam-4071	149	14	c∗-algebra	c∗-algebra	PROPN
ejpam-4071	149	15	valued	value	VERB
ejpam-4071	149	16	metric	metric	ADJ
ejpam-4071	149	17	spaces	space	NOUN
ejpam-4071	149	18	with	with	ADP
ejpam-4071	149	19	different	different	ADJ
ejpam-4071	149	20	contraction	contraction	NOUN
ejpam-4071	149	21	conditions	condition	NOUN
ejpam-4071	149	22	(	(	PUNCT
ejpam-4071	149	23	see	see	VERB
ejpam-4071	149	24	for	for	ADP
ejpam-4071	149	25	example	example	NOUN
ejpam-4071	149	26	[	[	X
ejpam-4071	149	27	20],[9],[10],[11],[14	20],[9],[10],[11],[14	NUM
ejpam-4071	149	28	]	]	NOUN
ejpam-4071	149	29	)	)	PUNCT
ejpam-4071	149	30	theorem	theorem	NOUN
ejpam-4071	149	31	1	1	NUM
ejpam-4071	149	32	.	.	PUNCT
ejpam-4071	150	1	(	(	PUNCT
ejpam-4071	150	2	chatterjee	chatterjee	NOUN
ejpam-4071	150	3	type	type	NOUN
ejpam-4071	150	4	theorem	theorem	VERB
ejpam-4071	150	5	[	[	X
ejpam-4071	150	6	1	1	NUM
ejpam-4071	150	7	]	]	PUNCT
ejpam-4071	150	8	)	)	PUNCT
ejpam-4071	150	9	let	let	VERB
ejpam-4071	150	10	(	(	PUNCT
ejpam-4071	150	11	x	x	NOUN
ejpam-4071	150	12	,	,	PUNCT
ejpam-4071	150	13	l(e	l(e	NOUN
ejpam-4071	150	14	)	)	PUNCT
ejpam-4071	150	15	,	,	PUNCT
ejpam-4071	150	16	∥.∥l(e	∥.∥l(e	NOUN
ejpam-4071	150	17	)	)	PUNCT
ejpam-4071	150	18	)	)	PUNCT
ejpam-4071	151	1	be	be	AUX
ejpam-4071	151	2	an	an	DET
ejpam-4071	151	3	l(e	l(e	NOUN
ejpam-4071	151	4	)	)	PUNCT
ejpam-4071	151	5	complete	complete	ADJ
ejpam-4071	151	6	normed	normed	ADJ
ejpam-4071	151	7	space	space	NOUN
ejpam-4071	151	8	and	and	CCONJ
ejpam-4071	151	9	t	t	NOUN
ejpam-4071	151	10	:	:	PUNCT
ejpam-4071	151	11	x	x	PUNCT
ejpam-4071	151	12	−→	−→	NOUN
ejpam-4071	151	13	x	x	VERB
ejpam-4071	151	14	be	be	AUX
ejpam-4071	151	15	a	a	DET
ejpam-4071	151	16	self	self	NOUN
ejpam-4071	151	17	mapping	mapping	NOUN
ejpam-4071	151	18	satisfy	satisfy	VERB
ejpam-4071	151	19	the	the	DET
ejpam-4071	151	20	following	follow	VERB
ejpam-4071	151	21	contraction	contraction	NOUN
ejpam-4071	151	22	condition	condition	NOUN
ejpam-4071	151	23	∥tx−	∥tx−	SCONJ
ejpam-4071	151	24	ty∥	ty∥	NOUN
ejpam-4071	151	25	l(e	l(e	NOUN
ejpam-4071	151	26	)	)	PUNCT
ejpam-4071	151	27	⪯	⪯	NOUN
ejpam-4071	151	28	m	m	VERB
ejpam-4071	151	29	2	2	NUM
ejpam-4071	151	30	[	[	PUNCT
ejpam-4071	151	31	∥tx−	∥tx−	ADP
ejpam-4071	151	32	y∥	y∥	VERB
ejpam-4071	151	33	l(e	l(e	NOUN
ejpam-4071	151	34	)	)	PUNCT
ejpam-4071	152	1	+	+	CCONJ
ejpam-4071	152	2	∥ty	∥ty	VERB
ejpam-4071	152	3	−	−	PROPN
ejpam-4071	152	4	x∥	x∥	NOUN
ejpam-4071	153	1	l(e	l(e	NOUN
ejpam-4071	153	2	)	)	PUNCT
ejpam-4071	154	1	]	]	PUNCT
ejpam-4071	154	2	,	,	PUNCT
ejpam-4071	154	3	where	where	SCONJ
ejpam-4071	154	4	m	m	VERB
ejpam-4071	154	5	∈	∈	PROPN
ejpam-4071	154	6	(	(	PUNCT
ejpam-4071	154	7	l(e))̀+	l(e))̀+	ADV
ejpam-4071	154	8	with	with	ADP
ejpam-4071	154	9	∥m∥l(e	∥m∥l(e	NOUN
ejpam-4071	154	10	)	)	PUNCT
ejpam-4071	154	11	<	<	X
ejpam-4071	154	12	1	1	NUM
ejpam-4071	154	13	,	,	PUNCT
ejpam-4071	154	14	then	then	ADV
ejpam-4071	154	15	t	t	PROPN
ejpam-4071	154	16	has	have	VERB
ejpam-4071	154	17	a	a	DET
ejpam-4071	154	18	unique	unique	ADJ
ejpam-4071	154	19	fixed	fix	VERB
ejpam-4071	154	20	point	point	NOUN
ejpam-4071	154	21	.	.	PUNCT
ejpam-4071	155	1	proof	proof	NOUN
ejpam-4071	155	2	.	.	PUNCT
ejpam-4071	156	1	let	let	VERB
ejpam-4071	156	2	x0	x0	PROPN
ejpam-4071	156	3	∈	∈	PROPN
ejpam-4071	156	4	x	x	PRON
ejpam-4071	156	5	be	be	AUX
ejpam-4071	156	6	arbitrary	arbitrary	ADJ
ejpam-4071	156	7	point	point	NOUN
ejpam-4071	156	8	and	and	CCONJ
ejpam-4071	156	9	construct	construct	VERB
ejpam-4071	156	10	a	a	DET
ejpam-4071	156	11	sequence	sequence	NOUN
ejpam-4071	156	12	{	{	PUNCT
ejpam-4071	156	13	xn}+∞	xn}+∞	PROPN
ejpam-4071	156	14	n=0	n=0	PROPN
ejpam-4071	156	15	⊆	⊆	NUM
ejpam-4071	156	16	x	x	SYM
ejpam-4071	156	17	by	by	ADP
ejpam-4071	156	18	the	the	DET
ejpam-4071	156	19	way	way	NOUN
ejpam-4071	156	20	:	:	PUNCT
ejpam-4071	157	1	x1	x1	PROPN
ejpam-4071	157	2	=	=	SYM
ejpam-4071	157	3	tx0	tx0	PROPN
ejpam-4071	157	4	,	,	PUNCT
ejpam-4071	157	5	x2	x2	PROPN
ejpam-4071	157	6	=	=	SYM
ejpam-4071	157	7	tx1	tx1	PROPN
ejpam-4071	157	8	,	,	PUNCT
ejpam-4071	157	9	.....	.....	PUNCT
ejpam-4071	157	10	,	,	PUNCT
ejpam-4071	157	11	xn+1	xn+1	PROPN
ejpam-4071	157	12	=	=	PUNCT
ejpam-4071	158	1	txn	txn	PROPN
ejpam-4071	158	2	r.	r.	PROPN
ejpam-4071	158	3	a.	a.	PROPN
ejpam-4071	158	4	rashwan	rashwan	PROPN
ejpam-4071	158	5	et	et	PROPN
ejpam-4071	158	6	al	al	PROPN
ejpam-4071	158	7	.	.	PUNCT
ejpam-4071	158	8	/	/	SYM
ejpam-4071	158	9	eur	eur	PROPN
ejpam-4071	158	10	.	.	PUNCT
ejpam-4071	159	1	j.	j.	PROPN
ejpam-4071	159	2	pure	pure	PROPN
ejpam-4071	159	3	appl	appl	PROPN
ejpam-4071	159	4	.	.	PROPN
ejpam-4071	159	5	math	math	PROPN
ejpam-4071	159	6	,	,	PUNCT
ejpam-4071	159	7	14	14	NUM
ejpam-4071	159	8	(	(	PUNCT
ejpam-4071	159	9	4	4	NUM
ejpam-4071	159	10	)	)	PUNCT
ejpam-4071	159	11	(	(	PUNCT
ejpam-4071	159	12	2021	2021	NUM
ejpam-4071	159	13	)	)	PUNCT
ejpam-4071	159	14	,	,	PUNCT
ejpam-4071	159	15	1237	1237	NUM
ejpam-4071	159	16	-	-	SYM
ejpam-4071	159	17	1248	1248	NUM
ejpam-4071	159	18	1243	1243	NUM
ejpam-4071	159	19	∥xn+1	∥xn+1	NOUN
ejpam-4071	159	20	−	−	NOUN
ejpam-4071	159	21	xn∥l(e	xn∥l(e	NOUN
ejpam-4071	159	22	)	)	PUNCT
ejpam-4071	160	1	=	=	SYM
ejpam-4071	160	2	∥txn	∥txn	PRON
ejpam-4071	160	3	−	−	PROPN
ejpam-4071	160	4	txn−1∥l(e	txn−1∥l(e	PROPN
ejpam-4071	160	5	)	)	PUNCT
ejpam-4071	160	6	⪯	⪯	NOUN
ejpam-4071	160	7	m	m	VERB
ejpam-4071	160	8	2	2	NUM
ejpam-4071	160	9	[	[	PUNCT
ejpam-4071	160	10	∥txn	∥txn	NUM
ejpam-4071	160	11	−	−	PROPN
ejpam-4071	160	12	xn−1∥l(e	xn−1∥l(e	PROPN
ejpam-4071	160	13	)	)	PUNCT
ejpam-4071	161	1	+	+	CCONJ
ejpam-4071	161	2	∥txn−1	∥txn−1	VERB
ejpam-4071	161	3	−	−	PROPN
ejpam-4071	161	4	xn∥l(e	xn∥l(e	NOUN
ejpam-4071	161	5	)	)	PUNCT
ejpam-4071	161	6	]	]	PUNCT
ejpam-4071	162	1	=	=	PUNCT
ejpam-4071	162	2	m	m	VERB
ejpam-4071	162	3	2	2	NUM
ejpam-4071	162	4	[	[	PUNCT
ejpam-4071	162	5	∥xn+1	∥xn+1	NOUN
ejpam-4071	162	6	−	−	PROPN
ejpam-4071	162	7	xn−1∥l(e	xn−1∥l(e	PROPN
ejpam-4071	162	8	)	)	PUNCT
ejpam-4071	163	1	+	+	NUM
ejpam-4071	163	2	∥xn	∥xn	PROPN
ejpam-4071	163	3	−	−	NUM
ejpam-4071	163	4	xn∥l(e	xn∥l(e	NOUN
ejpam-4071	163	5	)	)	PUNCT
ejpam-4071	163	6	]	]	PUNCT
ejpam-4071	164	1	⪯	⪯	NOUN
ejpam-4071	164	2	m	m	VERB
ejpam-4071	164	3	2	2	NUM
ejpam-4071	164	4	[	[	PUNCT
ejpam-4071	164	5	∥xn+1	∥xn+1	NOUN
ejpam-4071	164	6	−	−	NOUN
ejpam-4071	164	7	xn∥l(e	xn∥l(e	NOUN
ejpam-4071	164	8	)	)	PUNCT
ejpam-4071	165	1	+	+	NUM
ejpam-4071	165	2	∥xn	∥xn	PROPN
ejpam-4071	165	3	−	−	PROPN
ejpam-4071	165	4	xn−1∥l(e	xn−1∥l(e	PROPN
ejpam-4071	165	5	)	)	PUNCT
ejpam-4071	165	6	]	]	PUNCT
ejpam-4071	166	1	⪯	⪯	VERB
ejpam-4071	166	2	m	m	PROPN
ejpam-4071	166	3	2	2	NUM
ejpam-4071	166	4	∥xn+1	∥xn+1	NOUN
ejpam-4071	166	5	−	−	NOUN
ejpam-4071	166	6	xn∥l(e	xn∥l(e	NOUN
ejpam-4071	166	7	)	)	PUNCT
ejpam-4071	167	1	+	+	CCONJ
ejpam-4071	167	2	m	m	VERB
ejpam-4071	167	3	2	2	NUM
ejpam-4071	167	4	∥xn	∥xn	PROPN
ejpam-4071	167	5	−	−	PROPN
ejpam-4071	167	6	xn−1∥l(e	xn−1∥l(e	PROPN
ejpam-4071	167	7	)	)	PUNCT
ejpam-4071	167	8	.	.	PUNCT
ejpam-4071	168	1	thus	thus	ADV
ejpam-4071	168	2	,	,	PUNCT
ejpam-4071	168	3	(	(	PUNCT
ejpam-4071	168	4	il(e	il(e	X
ejpam-4071	168	5	)	)	PUNCT
ejpam-4071	168	6	−	−	PROPN
ejpam-4071	168	7	m	m	NOUN
ejpam-4071	168	8	2	2	NUM
ejpam-4071	168	9	)	)	PUNCT
ejpam-4071	168	10	∥xn+1	∥xn+1	VERB
ejpam-4071	168	11	−	−	PROPN
ejpam-4071	168	12	xn∥l(e	xn∥l(e	NOUN
ejpam-4071	168	13	)	)	PUNCT
ejpam-4071	168	14	⪯	⪯	PROPN
ejpam-4071	168	15	m	m	PROPN
ejpam-4071	168	16	2	2	NUM
ejpam-4071	168	17	∥xn	∥xn	PROPN
ejpam-4071	168	18	−	−	PROPN
ejpam-4071	168	19	xn−1∥l(e	xn−1∥l(e	PROPN
ejpam-4071	168	20	)	)	PUNCT
ejpam-4071	168	21	.	.	PUNCT
ejpam-4071	169	1	since	since	SCONJ
ejpam-4071	169	2	m	m	PROPN
ejpam-4071	169	3	∈	∈	PROPN
ejpam-4071	169	4	(	(	PUNCT
ejpam-4071	169	5	l(e))̀+	l(e))̀+	ADV
ejpam-4071	169	6	with	with	ADP
ejpam-4071	169	7	∥m	∥m	PROPN
ejpam-4071	169	8	2	2	NUM
ejpam-4071	169	9	∥l(e	∥l(e	NOUN
ejpam-4071	169	10	)	)	PUNCT
ejpam-4071	169	11	⪯	⪯	NOUN
ejpam-4071	169	12	1	1	NUM
ejpam-4071	169	13	2	2	NUM
ejpam-4071	169	14	,	,	PUNCT
ejpam-4071	169	15	one	one	PRON
ejpam-4071	169	16	have	have	VERB
ejpam-4071	169	17	(	(	PUNCT
ejpam-4071	169	18	il(e	il(e	PROPN
ejpam-4071	169	19	)	)	PUNCT
ejpam-4071	169	20	−	−	PROPN
ejpam-4071	170	1	m	m	NOUN
ejpam-4071	170	2	2	2	NUM
ejpam-4071	170	3	)	)	PUNCT
ejpam-4071	170	4	−1	−1	NOUN
ejpam-4071	170	5	∈	∈	NOUN
ejpam-4071	170	6	(	(	PUNCT
ejpam-4071	170	7	l(e))̀+	l(e))̀+	NOUN
ejpam-4071	170	8	,	,	PUNCT
ejpam-4071	170	9	and	and	CCONJ
ejpam-4071	170	10	furthermore	furthermore	ADV
ejpam-4071	170	11	m	m	VERB
ejpam-4071	170	12	2	2	NUM
ejpam-4071	170	13	(	(	PUNCT
ejpam-4071	170	14	il(e	il(e	X
ejpam-4071	170	15	)	)	PUNCT
ejpam-4071	170	16	−	−	PROPN
ejpam-4071	170	17	m	m	NOUN
ejpam-4071	170	18	2	2	NUM
ejpam-4071	170	19	)	)	PUNCT
ejpam-4071	170	20	−1	−1	NOUN
ejpam-4071	170	21	∈	∈	NOUN
ejpam-4071	170	22	(	(	PUNCT
ejpam-4071	170	23	l(e))̀+	l(e))̀+	ADV
ejpam-4071	170	24	with	with	ADP
ejpam-4071	170	25	∥m	∥m	PROPN
ejpam-4071	170	26	2	2	NUM
ejpam-4071	170	27	(	(	PUNCT
ejpam-4071	170	28	il(e	il(e	X
ejpam-4071	170	29	)	)	PUNCT
ejpam-4071	170	30	−	−	PROPN
ejpam-4071	170	31	m	m	NOUN
ejpam-4071	170	32	2	2	NUM
ejpam-4071	170	33	)	)	PUNCT
ejpam-4071	170	34	−1∥l(e	−1∥l(e	PROPN
ejpam-4071	170	35	)	)	PUNCT
ejpam-4071	170	36	≤	≤	NUM
ejpam-4071	170	37	1	1	NUM
ejpam-4071	170	38	.	.	PUNCT
ejpam-4071	171	1	therefore	therefore	ADV
ejpam-4071	171	2	,	,	PUNCT
ejpam-4071	171	3	∥xn+1	∥xn+1	VERB
ejpam-4071	171	4	−	−	PROPN
ejpam-4071	171	5	xn∥l(e	xn∥l(e	NOUN
ejpam-4071	171	6	)	)	PUNCT
ejpam-4071	171	7	⪯	⪯	NOUN
ejpam-4071	171	8	(	(	PUNCT
ejpam-4071	171	9	m	m	NOUN
ejpam-4071	171	10	2	2	NUM
ejpam-4071	171	11	il(e)−m	il(e)−m	NOUN
ejpam-4071	171	12	2	2	NUM
ejpam-4071	171	13	)	)	PUNCT
ejpam-4071	171	14	∥xn	∥xn	PROPN
ejpam-4071	171	15	−	−	PROPN
ejpam-4071	171	16	xn−1∥l(e	xn−1∥l(e	PROPN
ejpam-4071	171	17	)	)	PUNCT
ejpam-4071	171	18	⪯	⪯	NOUN
ejpam-4071	171	19	(	(	PUNCT
ejpam-4071	171	20	m	m	NOUN
ejpam-4071	171	21	2	2	NUM
ejpam-4071	171	22	il(e)−m	il(e)−m	NOUN
ejpam-4071	171	23	2	2	NUM
ejpam-4071	171	24	)	)	PUNCT
ejpam-4071	171	25	2∥xn−1	2∥xn−1	NUM
ejpam-4071	171	26	−	−	NUM
ejpam-4071	171	27	xn−2∥l(e	xn−2∥l(e	NUM
ejpam-4071	171	28	)	)	PUNCT
ejpam-4071	171	29	...	...	PUNCT
ejpam-4071	172	1	⪯	⪯	NOUN
ejpam-4071	172	2	(	(	PUNCT
ejpam-4071	172	3	m	m	NOUN
ejpam-4071	172	4	2	2	NUM
ejpam-4071	172	5	il(e)−m	il(e)−m	NOUN
ejpam-4071	172	6	2	2	NUM
ejpam-4071	172	7	)	)	PUNCT
ejpam-4071	172	8	n∥x1	n∥x1	NOUN
ejpam-4071	172	9	−	−	NOUN
ejpam-4071	172	10	x0∥l(e	x0∥l(e	NOUN
ejpam-4071	172	11	)	)	PUNCT
ejpam-4071	172	12	.	.	PUNCT
ejpam-4071	173	1	let	let	VERB
ejpam-4071	173	2	t	t	NOUN
ejpam-4071	173	3	=	=	PUNCT
ejpam-4071	173	4	m	m	VERB
ejpam-4071	173	5	2	2	NUM
ejpam-4071	173	6	(	(	PUNCT
ejpam-4071	173	7	il(e	il(e	X
ejpam-4071	173	8	)	)	PUNCT
ejpam-4071	173	9	−	−	PROPN
ejpam-4071	173	10	m	m	NOUN
ejpam-4071	173	11	2	2	NUM
ejpam-4071	173	12	)	)	PUNCT
ejpam-4071	173	13	−1	−1	NOUN
ejpam-4071	173	14	,	,	PUNCT
ejpam-4071	173	15	b	b	X
ejpam-4071	173	16	=	=	NOUN
ejpam-4071	173	17	∥x1	∥x1	NOUN
ejpam-4071	173	18	−	−	PROPN
ejpam-4071	173	19	x0∥l(e	x0∥l(e	PROPN
ejpam-4071	173	20	)	)	PUNCT
ejpam-4071	173	21	.	.	PUNCT
ejpam-4071	174	1	implies	imply	VERB
ejpam-4071	174	2	∥xn+1	∥xn+1	VERB
ejpam-4071	174	3	−	−	PROPN
ejpam-4071	174	4	xn∥l(e	xn∥l(e	NOUN
ejpam-4071	174	5	)	)	PUNCT
ejpam-4071	174	6	⪯	⪯	PROPN
ejpam-4071	174	7	tnb	tnb	PROPN
ejpam-4071	174	8	for	for	ADP
ejpam-4071	174	9	n+	n+	ADP
ejpam-4071	174	10	1	1	NUM
ejpam-4071	174	11	>	>	PUNCT
ejpam-4071	174	12	m	m	VERB
ejpam-4071	174	13	∥xn+1	∥xn+1	ADJ
ejpam-4071	174	14	−	−	PROPN
ejpam-4071	174	15	xm∥l(e	xm∥l(e	SYM
ejpam-4071	174	16	)	)	PUNCT
ejpam-4071	174	17	⪯	⪯	NOUN
ejpam-4071	174	18	∥xn+1	∥xn+1	VERB
ejpam-4071	174	19	−	−	PROPN
ejpam-4071	174	20	xn∥l(e	xn∥l(e	NOUN
ejpam-4071	174	21	)	)	PUNCT
ejpam-4071	175	1	+	+	NUM
ejpam-4071	175	2	∥xn	∥xn	PROPN
ejpam-4071	175	3	−	−	PROPN
ejpam-4071	175	4	xn−1∥l(e	xn−1∥l(e	PROPN
ejpam-4071	175	5	)	)	PUNCT
ejpam-4071	175	6	+	+	CCONJ
ejpam-4071	175	7	·	·	PUNCT
ejpam-4071	175	8	·	·	PUNCT
ejpam-4071	175	9	·	·	PUNCT
ejpam-4071	175	10	+	+	CCONJ
ejpam-4071	175	11	∥xm+1	∥xm+1	VERB
ejpam-4071	175	12	−	−	PROPN
ejpam-4071	175	13	xm∥l(e	xm∥l(e	SYM
ejpam-4071	175	14	)	)	PUNCT
ejpam-4071	175	15	⪯	⪯	PROPN
ejpam-4071	175	16	tnb	tnb	NOUN
ejpam-4071	175	17	+	+	CCONJ
ejpam-4071	175	18	tn−1b	tn−1b	NUM
ejpam-4071	175	19	+	+	X
ejpam-4071	175	20	·	·	PUNCT
ejpam-4071	175	21	·	·	PUNCT
ejpam-4071	175	22	·	·	PUNCT
ejpam-4071	175	23	+	+	NUM
ejpam-4071	175	24	tmb	tmb	X
ejpam-4071	175	25	⪯	⪯	NOUN
ejpam-4071	175	26	(	(	PUNCT
ejpam-4071	175	27	tn	tn	NOUN
ejpam-4071	175	28	+	+	CCONJ
ejpam-4071	175	29	tn−1	tn−1	PROPN
ejpam-4071	175	30	+	+	CCONJ
ejpam-4071	175	31	·	·	PUNCT
ejpam-4071	175	32	·	·	PUNCT
ejpam-4071	175	33	·	·	PUNCT
ejpam-4071	175	34	+	+	NUM
ejpam-4071	176	1	tm)b	tm)b	PROPN
ejpam-4071	176	2	=	=	SYM
ejpam-4071	176	3	∑n	∑n	PROPN
ejpam-4071	176	4	k	k	NOUN
ejpam-4071	176	5	=	=	NOUN
ejpam-4071	176	6	m	m	PROPN
ejpam-4071	176	7	t	t	NOUN
ejpam-4071	176	8	kb	kb	PROPN
ejpam-4071	176	9	=	=	SYM
ejpam-4071	177	1	∑n	∑n	PROPN
ejpam-4071	177	2	k	k	X
ejpam-4071	178	1	=	=	PROPN
ejpam-4071	178	2	m	m	PROPN
ejpam-4071	178	3	t	t	NOUN
ejpam-4071	178	4	k	k	PROPN
ejpam-4071	178	5	2	2	NUM
ejpam-4071	178	6	t	t	NOUN
ejpam-4071	178	7	k	k	X
ejpam-4071	178	8	2b	2b	NUM
ejpam-4071	178	9	1	1	NUM
ejpam-4071	178	10	2b	2b	NUM
ejpam-4071	178	11	1	1	NUM
ejpam-4071	178	12	2	2	NUM
ejpam-4071	178	13	=	=	SYM
ejpam-4071	178	14	∑n	∑n	PROPN
ejpam-4071	178	15	k	k	NOUN
ejpam-4071	178	16	=	=	NOUN
ejpam-4071	178	17	mb	mb	ADJ
ejpam-4071	178	18	1	1	NUM
ejpam-4071	178	19	2	2	NUM
ejpam-4071	178	20	t	t	NOUN
ejpam-4071	178	21	k	k	NOUN
ejpam-4071	178	22	2	2	NUM
ejpam-4071	178	23	t	t	NOUN
ejpam-4071	178	24	k	k	X
ejpam-4071	178	25	2b	2b	NUM
ejpam-4071	178	26	1	1	NUM
ejpam-4071	178	27	2	2	NUM
ejpam-4071	178	28	=	=	SYM
ejpam-4071	178	29	∑n	∑n	PROPN
ejpam-4071	178	30	k	k	NOUN
ejpam-4071	178	31	=	=	PROPN
ejpam-4071	178	32	m(t	m(t	PROPN
ejpam-4071	178	33	k	k	PROPN
ejpam-4071	178	34	2b	2b	NUM
ejpam-4071	178	35	1	1	NUM
ejpam-4071	178	36	2	2	NUM
ejpam-4071	178	37	)	)	PUNCT
ejpam-4071	178	38	∗(t	∗(t	NOUN
ejpam-4071	178	39	k	k	PROPN
ejpam-4071	178	40	2b	2b	NUM
ejpam-4071	178	41	1	1	NUM
ejpam-4071	178	42	2	2	NUM
ejpam-4071	178	43	)	)	PUNCT
ejpam-4071	178	44	=	=	SYM
ejpam-4071	179	1	∑n	∑n	PROPN
ejpam-4071	179	2	k	k	X
ejpam-4071	179	3	=	=	VERB
ejpam-4071	179	4	m	m	VERB
ejpam-4071	179	5	|t	|t	VERB
ejpam-4071	180	1	k	k	X
ejpam-4071	180	2	2b	2b	NUM
ejpam-4071	180	3	1	1	NUM
ejpam-4071	180	4	2	2	NUM
ejpam-4071	180	5	|2	|2	NUM
ejpam-4071	181	1	r.	r.	PROPN
ejpam-4071	181	2	a.	a.	PROPN
ejpam-4071	181	3	rashwan	rashwan	PROPN
ejpam-4071	181	4	et	et	PROPN
ejpam-4071	181	5	al	al	PROPN
ejpam-4071	181	6	.	.	PUNCT
ejpam-4071	181	7	/	/	SYM
ejpam-4071	181	8	eur	eur	PROPN
ejpam-4071	181	9	.	.	PUNCT
ejpam-4071	182	1	j.	j.	PROPN
ejpam-4071	182	2	pure	pure	PROPN
ejpam-4071	182	3	appl	appl	PROPN
ejpam-4071	182	4	.	.	PROPN
ejpam-4071	182	5	math	math	PROPN
ejpam-4071	182	6	,	,	PUNCT
ejpam-4071	182	7	14	14	NUM
ejpam-4071	182	8	(	(	PUNCT
ejpam-4071	182	9	4	4	NUM
ejpam-4071	182	10	)	)	PUNCT
ejpam-4071	182	11	(	(	PUNCT
ejpam-4071	182	12	2021	2021	NUM
ejpam-4071	182	13	)	)	PUNCT
ejpam-4071	182	14	,	,	PUNCT
ejpam-4071	182	15	1237	1237	NUM
ejpam-4071	182	16	-	-	SYM
ejpam-4071	182	17	1248	1248	NUM
ejpam-4071	182	18	1244	1244	NUM
ejpam-4071	182	19	⪯	⪯	NOUN
ejpam-4071	182	20	∥	∥	NUM
ejpam-4071	183	1	∑n	∑n	PROPN
ejpam-4071	184	1	k	k	NOUN
ejpam-4071	184	2	=	=	NOUN
ejpam-4071	184	3	m	m	VERB
ejpam-4071	184	4	|t	|t	VERB
ejpam-4071	185	1	k	k	X
ejpam-4071	185	2	2b	2b	NUM
ejpam-4071	185	3	1	1	NUM
ejpam-4071	185	4	2	2	NUM
ejpam-4071	185	5	|2∥l(e)il(e	|2∥l(e)il(e	NUM
ejpam-4071	185	6	)	)	PUNCT
ejpam-4071	185	7	⪯	⪯	NOUN
ejpam-4071	185	8	∑n	∑n	PROPN
ejpam-4071	186	1	k	k	PROPN
ejpam-4071	186	2	=	=	PROPN
ejpam-4071	186	3	m	m	PROPN
ejpam-4071	186	4	∥b	∥b	ADJ
ejpam-4071	186	5	1	1	NUM
ejpam-4071	186	6	2	2	NUM
ejpam-4071	186	7	∥2l(e)∥t	∥2l(e)∥t	NOUN
ejpam-4071	186	8	k	k	PROPN
ejpam-4071	186	9	2	2	NUM
ejpam-4071	186	10	∥2l(e)il(e	∥2l(e)il(e	NUM
ejpam-4071	186	11	)	)	PUNCT
ejpam-4071	186	12	=	=	SYM
ejpam-4071	186	13	∥b∥l(e	∥b∥l(e	X
ejpam-4071	186	14	)	)	PUNCT
ejpam-4071	187	1	∑n	∑n	PROPN
ejpam-4071	187	2	k	k	NOUN
ejpam-4071	187	3	=	=	PROPN
ejpam-4071	187	4	m	m	PROPN
ejpam-4071	187	5	∥t∥kl(e)il(e	∥t∥kl(e)il(e	PROPN
ejpam-4071	187	6	)	)	PUNCT
ejpam-4071	187	7	⪯	⪯	NOUN
ejpam-4071	187	8	∥b∥l(e	∥b∥l(e	NUM
ejpam-4071	187	9	)	)	PUNCT
ejpam-4071	187	10	∥t∥m	∥t∥m	NOUN
ejpam-4071	187	11	l(e	l(e	NOUN
ejpam-4071	187	12	)	)	PUNCT
ejpam-4071	187	13	1−∥t∥m	1−∥t∥m	NUM
ejpam-4071	187	14	l(e	l(e	NOUN
ejpam-4071	187	15	)	)	PUNCT
ejpam-4071	187	16	il(e	il(e	X
ejpam-4071	187	17	)	)	PUNCT
ejpam-4071	187	18	−→	−→	NOUN
ejpam-4071	187	19	0l(e)(m	0l(e)(m	NOUN
ejpam-4071	187	20	−→	−→	NOUN
ejpam-4071	187	21	+	+	NOUN
ejpam-4071	187	22	∞	∞	NOUN
ejpam-4071	187	23	)	)	PUNCT
ejpam-4071	187	24	,	,	PUNCT
ejpam-4071	187	25	where	where	SCONJ
ejpam-4071	187	26	il(e	il(e	PUNCT
ejpam-4071	187	27	)	)	PUNCT
ejpam-4071	187	28	the	the	DET
ejpam-4071	187	29	unite	unite	NOUN
ejpam-4071	187	30	element	element	NOUN
ejpam-4071	187	31	in	in	ADP
ejpam-4071	187	32	l(e	l(e	NOUN
ejpam-4071	187	33	)	)	PUNCT
ejpam-4071	187	34	,	,	PUNCT
ejpam-4071	187	35	therefore	therefore	ADV
ejpam-4071	187	36	{	{	PUNCT
ejpam-4071	187	37	xn	xn	X
ejpam-4071	187	38	}	}	PUNCT
ejpam-4071	187	39	is	be	AUX
ejpam-4071	187	40	a	a	DET
ejpam-4071	187	41	cauchy	cauchy	ADJ
ejpam-4071	187	42	sequence	sequence	NOUN
ejpam-4071	187	43	with	with	ADP
ejpam-4071	187	44	respect	respect	NOUN
ejpam-4071	187	45	to	to	ADP
ejpam-4071	187	46	l(e	l(e	NOUN
ejpam-4071	187	47	)	)	PUNCT
ejpam-4071	187	48	.	.	PUNCT
ejpam-4071	188	1	by	by	ADP
ejpam-4071	188	2	the	the	DET
ejpam-4071	188	3	completeness	completeness	NOUN
ejpam-4071	188	4	of(x	of(x	ADP
ejpam-4071	188	5	,	,	PUNCT
ejpam-4071	188	6	l(e	l(e	NOUN
ejpam-4071	188	7	)	)	PUNCT
ejpam-4071	188	8	,	,	PUNCT
ejpam-4071	188	9	∥.∥l(e	∥.∥l(e	NOUN
ejpam-4071	188	10	)	)	PUNCT
ejpam-4071	188	11	)	)	PUNCT
ejpam-4071	188	12	,	,	PUNCT
ejpam-4071	188	13	there	there	PRON
ejpam-4071	188	14	exists	exist	VERB
ejpam-4071	188	15	an	an	DET
ejpam-4071	188	16	x	x	SYM
ejpam-4071	188	17	∈	∈	PROPN
ejpam-4071	188	18	x	x	PUNCT
ejpam-4071	188	19	such	such	ADJ
ejpam-4071	188	20	that	that	DET
ejpam-4071	188	21	limn−→+∞	limn−→+∞	NOUN
ejpam-4071	188	22	xn	xn	PUNCT
ejpam-4071	189	1	=	=	PUNCT
ejpam-4071	189	2	limn−→+∞	limn−→+∞	X
ejpam-4071	190	1	txn−1	txn−1	PROPN
ejpam-4071	191	1	=	=	PUNCT
ejpam-4071	192	1	x.	x.	NOUN
ejpam-4071	193	1	since	since	SCONJ
ejpam-4071	193	2	∥tx−	∥tx−	PRON
ejpam-4071	193	3	x∥l(e	x∥l(e	PROPN
ejpam-4071	193	4	)	)	PUNCT
ejpam-4071	193	5	⪯	⪯	VERB
ejpam-4071	193	6	∥tx−	∥tx−	DET
ejpam-4071	193	7	txn∥l(e	txn∥l(e	NOUN
ejpam-4071	193	8	)	)	PUNCT
ejpam-4071	194	1	+	+	CCONJ
ejpam-4071	194	2	∥txn	∥txn	PRON
ejpam-4071	194	3	−	−	PROPN
ejpam-4071	194	4	x∥l(e	x∥l(e	PROPN
ejpam-4071	194	5	)	)	PUNCT
ejpam-4071	194	6	⪯	⪯	NOUN
ejpam-4071	194	7	m	m	VERB
ejpam-4071	194	8	2	2	NUM
ejpam-4071	194	9	(	(	PUNCT
ejpam-4071	194	10	∥tx−	∥tx−	ADP
ejpam-4071	194	11	xn∥l(e	xn∥l(e	VERB
ejpam-4071	194	12	)	)	PUNCT
ejpam-4071	195	1	+	+	CCONJ
ejpam-4071	195	2	∥txn	∥txn	PRON
ejpam-4071	195	3	−	−	PROPN
ejpam-4071	195	4	x∥l(e	x∥l(e	PROPN
ejpam-4071	195	5	)	)	PUNCT
ejpam-4071	195	6	)	)	PUNCT
ejpam-4071	196	1	+	+	CCONJ
ejpam-4071	196	2	∥txn	∥txn	PRON
ejpam-4071	196	3	−	−	PROPN
ejpam-4071	196	4	x∥l(e	x∥l(e	PROPN
ejpam-4071	196	5	)	)	PUNCT
ejpam-4071	196	6	⪯	⪯	NOUN
ejpam-4071	196	7	m	m	VERB
ejpam-4071	196	8	2	2	NUM
ejpam-4071	196	9	(	(	PUNCT
ejpam-4071	196	10	∥tx−	∥tx−	NOUN
ejpam-4071	196	11	x∥l(e	x∥l(e	PROPN
ejpam-4071	196	12	)	)	PUNCT
ejpam-4071	197	1	+	+	CCONJ
ejpam-4071	197	2	∥x−	∥x−	NUM
ejpam-4071	197	3	xn∥l(e	xn∥l(e	X
ejpam-4071	197	4	)	)	PUNCT
ejpam-4071	198	1	+	+	CCONJ
ejpam-4071	198	2	∥txn	∥txn	PRON
ejpam-4071	198	3	−	−	PROPN
ejpam-4071	198	4	x∥l(e	x∥l(e	PROPN
ejpam-4071	198	5	)	)	PUNCT
ejpam-4071	198	6	)	)	PUNCT
ejpam-4071	199	1	+	+	PUNCT
ejpam-4071	199	2	∥txn	∥txn	PRON
ejpam-4071	199	3	−	−	VERB
ejpam-4071	199	4	x∥l(e	x∥l(e	PROPN
ejpam-4071	199	5	)	)	PUNCT
ejpam-4071	199	6	=	=	PUNCT
ejpam-4071	199	7	m	m	VERB
ejpam-4071	199	8	2	2	NUM
ejpam-4071	199	9	∥tx−	∥tx−	ADP
ejpam-4071	199	10	x∥l(e	x∥l(e	PROPN
ejpam-4071	199	11	)	)	PUNCT
ejpam-4071	200	1	+	+	NUM
ejpam-4071	200	2	m	m	VERB
ejpam-4071	200	3	2	2	NUM
ejpam-4071	200	4	∥x−	∥x−	NUM
ejpam-4071	200	5	xn∥l(e	xn∥l(e	X
ejpam-4071	200	6	)	)	PUNCT
ejpam-4071	201	1	+	+	CCONJ
ejpam-4071	201	2	m	m	PROPN
ejpam-4071	201	3	2	2	NUM
ejpam-4071	201	4	∥txn	∥txn	NOUN
ejpam-4071	201	5	−	−	NOUN
ejpam-4071	201	6	x∥l(e	x∥l(e	PROPN
ejpam-4071	201	7	)	)	PUNCT
ejpam-4071	202	1	+	+	NOUN
ejpam-4071	202	2	∥txn	∥txn	NOUN
ejpam-4071	202	3	−	−	PROPN
ejpam-4071	202	4	x∥l(e	x∥l(e	PROPN
ejpam-4071	202	5	)	)	PUNCT
ejpam-4071	202	6	.	.	PUNCT
ejpam-4071	202	7	implies	imply	VERB
ejpam-4071	202	8	∥tx−x∥l(e	∥tx−x∥l(e	PROPN
ejpam-4071	202	9	)	)	PUNCT
ejpam-4071	202	10	⪯	⪯	NOUN
ejpam-4071	202	11	m	m	VERB
ejpam-4071	202	12	2	2	NUM
ejpam-4071	202	13	il(e)−m	il(e)−m	NOUN
ejpam-4071	202	14	2	2	NUM
ejpam-4071	202	15	∥txn−x∥l(e)+	∥txn−x∥l(e)+	NUM
ejpam-4071	202	16	m	m	NUM
ejpam-4071	202	17	2	2	NUM
ejpam-4071	202	18	il(e)−m	il(e)−m	NOUN
ejpam-4071	202	19	2	2	NUM
ejpam-4071	202	20	∥x−xn∥l(e)+	∥x−xn∥l(e)+	NOUN
ejpam-4071	202	21	1	1	NUM
ejpam-4071	202	22	il(e)−m	il(e)−m	NOUN
ejpam-4071	202	23	2	2	NUM
ejpam-4071	202	24	∥txn−x∥l(e	∥txn−x∥l(e	PROPN
ejpam-4071	202	25	)	)	PUNCT
ejpam-4071	202	26	∥tx−	∥tx−	DET
ejpam-4071	202	27	x∥l(e	x∥l(e	PROPN
ejpam-4071	202	28	)	)	PUNCT
ejpam-4071	202	29	⪯	⪯	NOUN
ejpam-4071	202	30	m	m	VERB
ejpam-4071	202	31	2	2	NUM
ejpam-4071	202	32	il(e)−m	il(e)−m	NOUN
ejpam-4071	202	33	2	2	NUM
ejpam-4071	202	34	∥xn+1	∥xn+1	NOUN
ejpam-4071	202	35	−	−	PROPN
ejpam-4071	202	36	x∥l(e	x∥l(e	PROPN
ejpam-4071	202	37	)	)	PUNCT
ejpam-4071	203	1	+	+	CCONJ
ejpam-4071	203	2	1	1	NUM
ejpam-4071	203	3	il(e)−m	il(e)−m	NOUN
ejpam-4071	203	4	2	2	NUM
ejpam-4071	203	5	∥xn+1	∥xn+1	NOUN
ejpam-4071	203	6	−	−	PROPN
ejpam-4071	203	7	x∥l(e	x∥l(e	PROPN
ejpam-4071	203	8	)	)	PUNCT
ejpam-4071	203	9	−→	−→	NOUN
ejpam-4071	203	10	0(n	0(n	NUM
ejpam-4071	203	11	−→	−→	NOUN
ejpam-4071	203	12	+	+	NOUN
ejpam-4071	203	13	∞	∞	NOUN
ejpam-4071	203	14	)	)	PUNCT
ejpam-4071	203	15	implies	imply	VERB
ejpam-4071	203	16	∥tx−	∥tx−	SCONJ
ejpam-4071	203	17	x∥l(e	x∥l(e	PROPN
ejpam-4071	203	18	)	)	PUNCT
ejpam-4071	203	19	=	=	SYM
ejpam-4071	203	20	0	0	NUM
ejpam-4071	203	21	implies	imply	VERB
ejpam-4071	203	22	tx	tx	PROPN
ejpam-4071	203	23	=	=	PUNCT
ejpam-4071	203	24	x.	x.	NOUN
ejpam-4071	203	25	to	to	PART
ejpam-4071	203	26	prove	prove	VERB
ejpam-4071	203	27	the	the	DET
ejpam-4071	203	28	uniquness	uniquness	NOUN
ejpam-4071	203	29	suppose	suppose	VERB
ejpam-4071	203	30	that	that	SCONJ
ejpam-4071	203	31	y(̸=	y(̸=	PROPN
ejpam-4071	203	32	x	x	NOUN
ejpam-4071	203	33	)	)	PUNCT
ejpam-4071	203	34	is	be	AUX
ejpam-4071	203	35	another	another	DET
ejpam-4071	203	36	fixed	fix	VERB
ejpam-4071	203	37	point	point	NOUN
ejpam-4071	203	38	of	of	ADP
ejpam-4071	203	39	t	t	PROPN
ejpam-4071	203	40	,	,	PUNCT
ejpam-4071	203	41	then	then	ADV
ejpam-4071	203	42	0	0	NUM
ejpam-4071	203	43	⪯	⪯	NOUN
ejpam-4071	203	44	∥x−	∥x−	PROPN
ejpam-4071	203	45	y∥l(e	y∥l(e	PROPN
ejpam-4071	203	46	)	)	PUNCT
ejpam-4071	203	47	=	=	SYM
ejpam-4071	203	48	∥tx−	∥tx−	DET
ejpam-4071	203	49	ty∥l(e	ty∥l(e	ADJ
ejpam-4071	203	50	)	)	PUNCT
ejpam-4071	203	51	⪯	⪯	NOUN
ejpam-4071	203	52	m	m	VERB
ejpam-4071	203	53	2	2	NUM
ejpam-4071	203	54	(	(	PUNCT
ejpam-4071	203	55	∥tx−	∥tx−	NOUN
ejpam-4071	203	56	y∥l(e	y∥l(e	PROPN
ejpam-4071	203	57	)	)	PUNCT
ejpam-4071	204	1	+	+	CCONJ
ejpam-4071	204	2	∥ty	∥ty	VERB
ejpam-4071	204	3	−	−	PROPN
ejpam-4071	204	4	x∥l(e	x∥l(e	PROPN
ejpam-4071	204	5	)	)	PUNCT
ejpam-4071	204	6	)	)	PUNCT
ejpam-4071	204	7	implies	imply	VERB
ejpam-4071	204	8	∥x−	∥x−	PROPN
ejpam-4071	204	9	y∥l(e	y∥l(e	PROPN
ejpam-4071	204	10	)	)	PUNCT
ejpam-4071	204	11	⪯	⪯	NOUN
ejpam-4071	204	12	m	m	VERB
ejpam-4071	204	13	2	2	NUM
ejpam-4071	204	14	il(e)−m	il(e)−m	NOUN
ejpam-4071	204	15	2	2	NUM
ejpam-4071	204	16	∥x−	∥x−	PROPN
ejpam-4071	204	17	y∥l(e	y∥l(e	PROPN
ejpam-4071	204	18	)	)	PUNCT
ejpam-4071	204	19	implies	imply	VERB
ejpam-4071	204	20	∥∥x−	∥∥x−	PROPN
ejpam-4071	204	21	y∥l(e)∥l(e	y∥l(e)∥l(e	NOUN
ejpam-4071	204	22	)	)	PUNCT
ejpam-4071	204	23	⪯	⪯	NOUN
ejpam-4071	204	24	∥	∥	PROPN
ejpam-4071	204	25	m	m	VERB
ejpam-4071	204	26	2	2	NUM
ejpam-4071	204	27	il(e)−m	il(e)−m	NOUN
ejpam-4071	204	28	2	2	NUM
ejpam-4071	204	29	∥l(e)∥∥x−	∥l(e)∥∥x−	NUM
ejpam-4071	204	30	y∥l(e)∥l(e	y∥l(e)∥l(e	NOUN
ejpam-4071	204	31	)	)	PUNCT
ejpam-4071	204	32	≺	≺	VERB
ejpam-4071	204	33	∥∥x−	∥∥x−	PROPN
ejpam-4071	204	34	y∥l(e)∥l(e	y∥l(e)∥l(e	NOUN
ejpam-4071	204	35	)	)	PUNCT
ejpam-4071	204	36	this	this	PRON
ejpam-4071	204	37	means	mean	VERB
ejpam-4071	204	38	that	that	SCONJ
ejpam-4071	204	39	∥x−	∥x−	PROPN
ejpam-4071	204	40	y∥l(e	y∥l(e	PROPN
ejpam-4071	204	41	)	)	PUNCT
ejpam-4071	204	42	=	=	SYM
ejpam-4071	205	1	0	0	NUM
ejpam-4071	205	2	implies	imply	VERB
ejpam-4071	205	3	x	x	PUNCT
ejpam-4071	205	4	=	=	SYM
ejpam-4071	205	5	y	y	PROPN
ejpam-4071	205	6	.	.	PUNCT
ejpam-4071	206	1	therefore	therefore	ADV
ejpam-4071	206	2	the	the	DET
ejpam-4071	206	3	fixed	fix	VERB
ejpam-4071	206	4	point	point	NOUN
ejpam-4071	206	5	is	be	AUX
ejpam-4071	206	6	unique	unique	ADJ
ejpam-4071	206	7	.	.	PUNCT
ejpam-4071	207	1	r.	r.	PROPN
ejpam-4071	207	2	a.	a.	PROPN
ejpam-4071	207	3	rashwan	rashwan	PROPN
ejpam-4071	207	4	et	et	PROPN
ejpam-4071	207	5	al	al	PROPN
ejpam-4071	207	6	.	.	PUNCT
ejpam-4071	207	7	/	/	SYM
ejpam-4071	207	8	eur	eur	PROPN
ejpam-4071	207	9	.	.	PUNCT
ejpam-4071	208	1	j.	j.	PROPN
ejpam-4071	208	2	pure	pure	PROPN
ejpam-4071	208	3	appl	appl	PROPN
ejpam-4071	208	4	.	.	PROPN
ejpam-4071	208	5	math	math	PROPN
ejpam-4071	208	6	,	,	PUNCT
ejpam-4071	208	7	14	14	NUM
ejpam-4071	208	8	(	(	PUNCT
ejpam-4071	208	9	4	4	NUM
ejpam-4071	208	10	)	)	PUNCT
ejpam-4071	208	11	(	(	PUNCT
ejpam-4071	208	12	2021	2021	NUM
ejpam-4071	208	13	)	)	PUNCT
ejpam-4071	208	14	,	,	PUNCT
ejpam-4071	208	15	1237	1237	NUM
ejpam-4071	208	16	-	-	SYM
ejpam-4071	208	17	1248	1248	NUM
ejpam-4071	208	18	1245	1245	NUM
ejpam-4071	208	19	theorem	theorem	NOUN
ejpam-4071	208	20	2	2	NUM
ejpam-4071	208	21	.	.	PUNCT
ejpam-4071	208	22	(	(	PUNCT
ejpam-4071	208	23	extension	extension	NOUN
ejpam-4071	208	24	of	of	ADP
ejpam-4071	208	25	chatterjee	chatterjee	PROPN
ejpam-4071	208	26	type	type	NOUN
ejpam-4071	208	27	theorem	theorem	PROPN
ejpam-4071	208	28	)	)	PUNCT
ejpam-4071	208	29	let	let	VERB
ejpam-4071	208	30	(	(	PUNCT
ejpam-4071	208	31	x	x	NOUN
ejpam-4071	208	32	,	,	PUNCT
ejpam-4071	208	33	l(e	l(e	NOUN
ejpam-4071	208	34	)	)	PUNCT
ejpam-4071	208	35	,	,	PUNCT
ejpam-4071	208	36	∥.∥l(e	∥.∥l(e	NOUN
ejpam-4071	208	37	)	)	PUNCT
ejpam-4071	208	38	)	)	PUNCT
ejpam-4071	209	1	be	be	AUX
ejpam-4071	209	2	an	an	DET
ejpam-4071	209	3	l(e	l(e	NOUN
ejpam-4071	209	4	)	)	PUNCT
ejpam-4071	209	5	complete	complete	ADJ
ejpam-4071	209	6	normed	normed	ADJ
ejpam-4071	209	7	space	space	NOUN
ejpam-4071	209	8	and	and	CCONJ
ejpam-4071	209	9	t	t	NOUN
ejpam-4071	209	10	:	:	PUNCT
ejpam-4071	209	11	x	x	PUNCT
ejpam-4071	209	12	−→	−→	NOUN
ejpam-4071	209	13	x	x	VERB
ejpam-4071	209	14	be	be	AUX
ejpam-4071	209	15	a	a	DET
ejpam-4071	209	16	self	self	NOUN
ejpam-4071	209	17	mapping	mapping	NOUN
ejpam-4071	209	18	satisfy	satisfy	VERB
ejpam-4071	209	19	the	the	DET
ejpam-4071	209	20	following	follow	VERB
ejpam-4071	209	21	contraction	contraction	NOUN
ejpam-4071	209	22	condition	condition	NOUN
ejpam-4071	209	23	∥tx−	∥tx−	ADP
ejpam-4071	209	24	ty∥l(e	ty∥l(e	NOUN
ejpam-4071	209	25	)	)	PUNCT
ejpam-4071	209	26	⪯	⪯	NOUN
ejpam-4071	209	27	m	m	VERB
ejpam-4071	209	28	3	3	NUM
ejpam-4071	209	29	[	[	PUNCT
ejpam-4071	209	30	∥x−	∥x−	PROPN
ejpam-4071	209	31	y∥l(e	y∥l(e	PROPN
ejpam-4071	209	32	)	)	PUNCT
ejpam-4071	210	1	+	+	CCONJ
ejpam-4071	210	2	∥tx−	∥tx−	DET
ejpam-4071	210	3	y∥l(e	y∥l(e	PROPN
ejpam-4071	210	4	)	)	PUNCT
ejpam-4071	210	5	+	+	CCONJ
ejpam-4071	210	6	∥ty	∥ty	VERB
ejpam-4071	210	7	−	−	PROPN
ejpam-4071	210	8	x∥l(e	x∥l(e	PROPN
ejpam-4071	210	9	)	)	PUNCT
ejpam-4071	210	10	]	]	X
ejpam-4071	210	11	,	,	PUNCT
ejpam-4071	210	12	where	where	SCONJ
ejpam-4071	210	13	m	m	VERB
ejpam-4071	210	14	∈	∈	PROPN
ejpam-4071	210	15	(	(	PUNCT
ejpam-4071	210	16	l(e))̀+	l(e))̀+	ADV
ejpam-4071	210	17	with	with	ADP
ejpam-4071	210	18	∥m∥l(e	∥m∥l(e	NOUN
ejpam-4071	210	19	)	)	PUNCT
ejpam-4071	210	20	<	<	X
ejpam-4071	210	21	3	3	NUM
ejpam-4071	210	22	4	4	NUM
ejpam-4071	210	23	,	,	PUNCT
ejpam-4071	210	24	then	then	ADV
ejpam-4071	210	25	t	t	PROPN
ejpam-4071	210	26	has	have	VERB
ejpam-4071	210	27	a	a	DET
ejpam-4071	210	28	unique	unique	ADJ
ejpam-4071	210	29	fixed	fix	VERB
ejpam-4071	210	30	point	point	NOUN
ejpam-4071	210	31	.	.	PUNCT
ejpam-4071	211	1	proof	proof	NOUN
ejpam-4071	211	2	.	.	PUNCT
ejpam-4071	212	1	le	le	X
ejpam-4071	213	1	x0	x0	PROPN
ejpam-4071	213	2	∈	∈	PROPN
ejpam-4071	213	3	x	x	PRON
ejpam-4071	213	4	be	be	AUX
ejpam-4071	213	5	arbitrary	arbitrary	ADJ
ejpam-4071	213	6	point	point	NOUN
ejpam-4071	213	7	and	and	CCONJ
ejpam-4071	213	8	construct	construct	VERB
ejpam-4071	213	9	a	a	DET
ejpam-4071	213	10	sequence	sequence	NOUN
ejpam-4071	213	11	{	{	PUNCT
ejpam-4071	213	12	xn}+∞	xn}+∞	PROPN
ejpam-4071	213	13	n=0	n=0	PROPN
ejpam-4071	213	14	⊆	⊆	NUM
ejpam-4071	213	15	x	x	SYM
ejpam-4071	213	16	by	by	ADP
ejpam-4071	213	17	the	the	DET
ejpam-4071	213	18	way	way	NOUN
ejpam-4071	213	19	:	:	PUNCT
ejpam-4071	213	20	x1	x1	PROPN
ejpam-4071	213	21	=	=	SYM
ejpam-4071	213	22	tx0	tx0	PROPN
ejpam-4071	213	23	,	,	PUNCT
ejpam-4071	213	24	x2	x2	PROPN
ejpam-4071	213	25	=	=	SYM
ejpam-4071	213	26	tx1	tx1	PROPN
ejpam-4071	213	27	,	,	PUNCT
ejpam-4071	213	28	.....	.....	PUNCT
ejpam-4071	213	29	,	,	PUNCT
ejpam-4071	213	30	xn+1	xn+1	PROPN
ejpam-4071	214	1	=	=	SYM
ejpam-4071	214	2	txn	txn	AUX
ejpam-4071	214	3	.	.	PUNCT
ejpam-4071	214	4	∥xn+1	∥xn+1	VERB
ejpam-4071	214	5	−	−	PROPN
ejpam-4071	214	6	xn∥l(e	xn∥l(e	NOUN
ejpam-4071	214	7	)	)	PUNCT
ejpam-4071	215	1	=	=	SYM
ejpam-4071	215	2	∥txn	∥txn	PRON
ejpam-4071	215	3	−	−	PROPN
ejpam-4071	215	4	txn−1∥l(e	txn−1∥l(e	PROPN
ejpam-4071	215	5	)	)	PUNCT
ejpam-4071	215	6	⪯	⪯	NOUN
ejpam-4071	215	7	m	m	VERB
ejpam-4071	215	8	3	3	NUM
ejpam-4071	215	9	[	[	X
ejpam-4071	215	10	∥xn−xn−1∥l(e)+∥txn−xn−1∥l(e)+∥txn−1−xn∥l(e	∥xn−xn−1∥l(e)+∥txn−xn−1∥l(e)+∥txn−1−xn∥l(e	NOUN
ejpam-4071	215	11	)	)	PUNCT
ejpam-4071	215	12	]	]	PUNCT
ejpam-4071	216	1	=	=	PUNCT
ejpam-4071	216	2	m	m	VERB
ejpam-4071	216	3	3	3	NUM
ejpam-4071	217	1	[	[	X
ejpam-4071	217	2	∥xn	∥xn	PRON
ejpam-4071	217	3	−	−	PROPN
ejpam-4071	217	4	xn−1∥l(e	xn−1∥l(e	PROPN
ejpam-4071	217	5	)	)	PUNCT
ejpam-4071	218	1	+	+	CCONJ
ejpam-4071	218	2	∥xn+1	∥xn+1	VERB
ejpam-4071	218	3	−	−	PROPN
ejpam-4071	218	4	xn−1∥l(e	xn−1∥l(e	PROPN
ejpam-4071	218	5	)	)	PUNCT
ejpam-4071	219	1	+	+	NUM
ejpam-4071	219	2	∥xn	∥xn	PROPN
ejpam-4071	219	3	−	−	NUM
ejpam-4071	219	4	xn∥l(e	xn∥l(e	NOUN
ejpam-4071	219	5	)	)	PUNCT
ejpam-4071	219	6	]	]	PUNCT
ejpam-4071	220	1	⪯	⪯	NOUN
ejpam-4071	220	2	m	m	VERB
ejpam-4071	220	3	3	3	NUM
ejpam-4071	221	1	[	[	X
ejpam-4071	221	2	∥xn	∥xn	PRON
ejpam-4071	221	3	−	−	PROPN
ejpam-4071	221	4	xn−1∥l(e	xn−1∥l(e	PROPN
ejpam-4071	221	5	)	)	PUNCT
ejpam-4071	222	1	+	+	CCONJ
ejpam-4071	222	2	∥xn+1	∥xn+1	ADJ
ejpam-4071	222	3	−	−	NOUN
ejpam-4071	222	4	xn∥l(e	xn∥l(e	NOUN
ejpam-4071	222	5	)	)	PUNCT
ejpam-4071	223	1	+	+	NUM
ejpam-4071	223	2	∥xn	∥xn	PROPN
ejpam-4071	223	3	−	−	PROPN
ejpam-4071	223	4	xn−1∥l(e	xn−1∥l(e	PROPN
ejpam-4071	223	5	)	)	PUNCT
ejpam-4071	223	6	]	]	PUNCT
ejpam-4071	224	1	=	=	PUNCT
ejpam-4071	224	2	m	m	VERB
ejpam-4071	224	3	3	3	NUM
ejpam-4071	224	4	[	[	PUNCT
ejpam-4071	224	5	2∥xn	2∥xn	NUM
ejpam-4071	224	6	−	−	PROPN
ejpam-4071	224	7	xn−1∥l(e	xn−1∥l(e	PROPN
ejpam-4071	224	8	)	)	PUNCT
ejpam-4071	225	1	+	+	CCONJ
ejpam-4071	225	2	∥xn+1	∥xn+1	ADJ
ejpam-4071	225	3	−	−	NOUN
ejpam-4071	225	4	xn∥l(e	xn∥l(e	NOUN
ejpam-4071	225	5	)	)	PUNCT
ejpam-4071	225	6	]	]	PUNCT
ejpam-4071	226	1	=	=	PUNCT
ejpam-4071	226	2	2	2	NUM
ejpam-4071	226	3	m	m	NOUN
ejpam-4071	226	4	3	3	NUM
ejpam-4071	226	5	∥xn	∥xn	PROPN
ejpam-4071	226	6	−	−	PROPN
ejpam-4071	226	7	xn−1∥l(e	xn−1∥l(e	PROPN
ejpam-4071	226	8	)	)	PUNCT
ejpam-4071	227	1	+	+	NUM
ejpam-4071	227	2	m	m	VERB
ejpam-4071	227	3	3	3	NUM
ejpam-4071	227	4	∥xn+1	∥xn+1	NOUN
ejpam-4071	227	5	−	−	NOUN
ejpam-4071	227	6	xn∥l(e	xn∥l(e	NOUN
ejpam-4071	227	7	)	)	PUNCT
ejpam-4071	227	8	.	.	PUNCT
ejpam-4071	228	1	thus	thus	ADV
ejpam-4071	228	2	,	,	PUNCT
ejpam-4071	228	3	(	(	PUNCT
ejpam-4071	228	4	il(e	il(e	X
ejpam-4071	228	5	)	)	PUNCT
ejpam-4071	228	6	−	−	PROPN
ejpam-4071	228	7	m	m	NOUN
ejpam-4071	228	8	3	3	NUM
ejpam-4071	228	9	)	)	PUNCT
ejpam-4071	228	10	∥xn+1	∥xn+1	VERB
ejpam-4071	228	11	−	−	PROPN
ejpam-4071	228	12	xn∥l(e	xn∥l(e	NOUN
ejpam-4071	228	13	)	)	PUNCT
ejpam-4071	228	14	⪯	⪯	NOUN
ejpam-4071	228	15	2	2	NUM
ejpam-4071	228	16	m	m	NOUN
ejpam-4071	228	17	3	3	NUM
ejpam-4071	228	18	∥xn	∥xn	PROPN
ejpam-4071	228	19	−	−	PROPN
ejpam-4071	228	20	xn−1∥l(e	xn−1∥l(e	PROPN
ejpam-4071	228	21	)	)	PUNCT
ejpam-4071	228	22	.	.	PUNCT
ejpam-4071	229	1	since	since	SCONJ
ejpam-4071	229	2	m	m	PROPN
ejpam-4071	229	3	∈	∈	PROPN
ejpam-4071	229	4	(	(	PUNCT
ejpam-4071	229	5	l(e))̀+	l(e))̀+	ADV
ejpam-4071	229	6	with	with	ADP
ejpam-4071	229	7	∥m	∥m	PROPN
ejpam-4071	229	8	3	3	NUM
ejpam-4071	229	9	∥l(e	∥l(e	NOUN
ejpam-4071	229	10	)	)	PUNCT
ejpam-4071	229	11	≤	≤	NUM
ejpam-4071	229	12	1	1	NUM
ejpam-4071	229	13	4	4	NUM
ejpam-4071	229	14	,	,	PUNCT
ejpam-4071	229	15	one	one	PRON
ejpam-4071	229	16	have	have	VERB
ejpam-4071	229	17	(	(	PUNCT
ejpam-4071	229	18	il(e	il(e	PROPN
ejpam-4071	229	19	)	)	PUNCT
ejpam-4071	229	20	−	−	PROPN
ejpam-4071	229	21	m	m	NOUN
ejpam-4071	229	22	3	3	NUM
ejpam-4071	229	23	)	)	PUNCT
ejpam-4071	229	24	−1	−1	NOUN
ejpam-4071	229	25	∈	∈	NOUN
ejpam-4071	229	26	(	(	PUNCT
ejpam-4071	229	27	l(e))̀+	l(e))̀+	NOUN
ejpam-4071	229	28	,	,	PUNCT
ejpam-4071	229	29	and	and	CCONJ
ejpam-4071	229	30	furthermore	furthermore	ADV
ejpam-4071	229	31	m	m	VERB
ejpam-4071	229	32	3	3	NUM
ejpam-4071	229	33	(	(	PUNCT
ejpam-4071	229	34	i	i	PRON
ejpam-4071	229	35	−	−	VERB
ejpam-4071	229	36	m	m	VERB
ejpam-4071	229	37	3	3	NUM
ejpam-4071	229	38	)	)	PUNCT
ejpam-4071	229	39	−1	−1	NOUN
ejpam-4071	229	40	∈	∈	NOUN
ejpam-4071	229	41	(	(	PUNCT
ejpam-4071	229	42	l(e))̀+	l(e))̀+	ADV
ejpam-4071	229	43	with	with	ADP
ejpam-4071	229	44	∥m	∥m	PROPN
ejpam-4071	229	45	3	3	NUM
ejpam-4071	229	46	(	(	PUNCT
ejpam-4071	229	47	il(e	il(e	X
ejpam-4071	229	48	)	)	PUNCT
ejpam-4071	229	49	−	−	PROPN
ejpam-4071	229	50	m	m	NOUN
ejpam-4071	229	51	3	3	NUM
ejpam-4071	229	52	)	)	PUNCT
ejpam-4071	229	53	−1∥l(e	−1∥l(e	PROPN
ejpam-4071	229	54	)	)	PUNCT
ejpam-4071	229	55	≤	≤	NUM
ejpam-4071	229	56	1	1	NUM
ejpam-4071	229	57	2	2	NUM
ejpam-4071	229	58	,	,	PUNCT
ejpam-4071	229	59	we	we	PRON
ejpam-4071	229	60	have	have	VERB
ejpam-4071	229	61	that	that	SCONJ
ejpam-4071	229	62	∥2(m3	∥2(m3	ADJ
ejpam-4071	229	63	(	(	PUNCT
ejpam-4071	229	64	il(e	il(e	PROPN
ejpam-4071	229	65	)	)	PUNCT
ejpam-4071	229	66	−	−	PROPN
ejpam-4071	229	67	m	m	NOUN
ejpam-4071	229	68	3	3	NUM
ejpam-4071	229	69	)	)	PUNCT
ejpam-4071	229	70	−1)∥l(e	−1)∥l(e	NOUN
ejpam-4071	229	71	)	)	PUNCT
ejpam-4071	229	72	≤	≤	NUM
ejpam-4071	229	73	1	1	NUM
ejpam-4071	229	74	.	.	PUNCT
ejpam-4071	230	1	therefore	therefore	ADV
ejpam-4071	230	2	,	,	PUNCT
ejpam-4071	230	3	∥xn+1	∥xn+1	VERB
ejpam-4071	230	4	−	−	PROPN
ejpam-4071	230	5	xn∥l(e	xn∥l(e	NOUN
ejpam-4071	230	6	)	)	PUNCT
ejpam-4071	230	7	⪯	⪯	NOUN
ejpam-4071	230	8	2	2	NUM
ejpam-4071	230	9	(	(	PUNCT
ejpam-4071	230	10	m	m	PROPN
ejpam-4071	230	11	3	3	NUM
ejpam-4071	230	12	il(e)−m	il(e)−m	NOUN
ejpam-4071	230	13	3	3	NUM
ejpam-4071	230	14	)	)	PUNCT
ejpam-4071	230	15	∥xn	∥xn	PROPN
ejpam-4071	230	16	−	−	PROPN
ejpam-4071	230	17	xn−1∥l(e	xn−1∥l(e	PROPN
ejpam-4071	230	18	)	)	PUNCT
ejpam-4071	231	1	=	=	PUNCT
ejpam-4071	231	2	t∥xn	t∥xn	NOUN
ejpam-4071	231	3	−	−	PROPN
ejpam-4071	231	4	xn−1∥l(e	xn−1∥l(e	PROPN
ejpam-4071	231	5	)	)	PUNCT
ejpam-4071	231	6	⪯	⪯	NOUN
ejpam-4071	231	7	t2∥xn−1	t2∥xn−1	VERB
ejpam-4071	231	8	−	−	ADP
ejpam-4071	231	9	xn−2∥l(e	xn−2∥l(e	PROPN
ejpam-4071	231	10	)	)	PUNCT
ejpam-4071	231	11	...	...	PUNCT
ejpam-4071	232	1	⪯	⪯	VERB
ejpam-4071	232	2	tn∥x1	tn∥x1	NOUN
ejpam-4071	232	3	−	−	PROPN
ejpam-4071	232	4	x0∥l(e	x0∥l(e	PROPN
ejpam-4071	232	5	)	)	PUNCT
ejpam-4071	232	6	,	,	PUNCT
ejpam-4071	232	7	where	where	SCONJ
ejpam-4071	232	8	t	t	NOUN
ejpam-4071	232	9	=	=	SYM
ejpam-4071	232	10	2(m3	2(m3	NUM
ejpam-4071	232	11	(	(	PUNCT
ejpam-4071	232	12	il(e	il(e	PROPN
ejpam-4071	232	13	)	)	PUNCT
ejpam-4071	232	14	−	−	PROPN
ejpam-4071	232	15	m	m	NOUN
ejpam-4071	232	16	3	3	NUM
ejpam-4071	232	17	)	)	PUNCT
ejpam-4071	232	18	−1	−1	NOUN
ejpam-4071	232	19	)	)	PUNCT
ejpam-4071	232	20	.	.	PUNCT
ejpam-4071	233	1	for	for	ADP
ejpam-4071	233	2	n+	n+	ADP
ejpam-4071	233	3	1	1	NUM
ejpam-4071	233	4	>	>	X
ejpam-4071	233	5	m	m	PROPN
ejpam-4071	233	6	.	.	PUNCT
ejpam-4071	233	7	r.	r.	PROPN
ejpam-4071	233	8	a.	a.	PROPN
ejpam-4071	233	9	rashwan	rashwan	PROPN
ejpam-4071	233	10	et	et	PROPN
ejpam-4071	233	11	al	al	PROPN
ejpam-4071	233	12	.	.	PUNCT
ejpam-4071	233	13	/	/	SYM
ejpam-4071	233	14	eur	eur	PROPN
ejpam-4071	233	15	.	.	PUNCT
ejpam-4071	234	1	j.	j.	PROPN
ejpam-4071	234	2	pure	pure	PROPN
ejpam-4071	234	3	appl	appl	PROPN
ejpam-4071	234	4	.	.	PROPN
ejpam-4071	234	5	math	math	PROPN
ejpam-4071	234	6	,	,	PUNCT
ejpam-4071	234	7	14	14	NUM
ejpam-4071	234	8	(	(	PUNCT
ejpam-4071	234	9	4	4	NUM
ejpam-4071	234	10	)	)	PUNCT
ejpam-4071	234	11	(	(	PUNCT
ejpam-4071	234	12	2021	2021	NUM
ejpam-4071	234	13	)	)	PUNCT
ejpam-4071	234	14	,	,	PUNCT
ejpam-4071	234	15	1237	1237	NUM
ejpam-4071	234	16	-	-	SYM
ejpam-4071	234	17	1248	1248	NUM
ejpam-4071	234	18	1246	1246	NUM
ejpam-4071	234	19	∥xn+1	∥xn+1	NOUN
ejpam-4071	234	20	−	−	PROPN
ejpam-4071	234	21	xm∥l(e	xm∥l(e	SYM
ejpam-4071	234	22	)	)	PUNCT
ejpam-4071	234	23	⪯	⪯	NOUN
ejpam-4071	234	24	∥xn+1	∥xn+1	VERB
ejpam-4071	234	25	−	−	PROPN
ejpam-4071	234	26	xn∥l(e	xn∥l(e	NOUN
ejpam-4071	234	27	)	)	PUNCT
ejpam-4071	235	1	+	+	NUM
ejpam-4071	235	2	∥xn	∥xn	PROPN
ejpam-4071	235	3	−	−	PROPN
ejpam-4071	235	4	xn−1∥l(e	xn−1∥l(e	PROPN
ejpam-4071	235	5	)	)	PUNCT
ejpam-4071	235	6	+	+	CCONJ
ejpam-4071	235	7	·	·	PUNCT
ejpam-4071	235	8	·	·	PUNCT
ejpam-4071	235	9	·	·	PUNCT
ejpam-4071	235	10	+	+	CCONJ
ejpam-4071	235	11	∥xm+1	∥xm+1	VERB
ejpam-4071	235	12	−	−	PROPN
ejpam-4071	235	13	xm∥l(e	xm∥l(e	NOUN
ejpam-4071	235	14	)	)	PUNCT
ejpam-4071	235	15	⪯	⪯	NOUN
ejpam-4071	235	16	(	(	PUNCT
ejpam-4071	235	17	tn	tn	NOUN
ejpam-4071	235	18	+	+	CCONJ
ejpam-4071	235	19	tn−1	tn−1	PROPN
ejpam-4071	235	20	+	+	CCONJ
ejpam-4071	235	21	·	·	PUNCT
ejpam-4071	235	22	·	·	PUNCT
ejpam-4071	235	23	·	·	PUNCT
ejpam-4071	235	24	+	+	NUM
ejpam-4071	235	25	tm)∥x1	tm)∥x1	NOUN
ejpam-4071	235	26	−	−	PROPN
ejpam-4071	235	27	x0∥l(e	x0∥l(e	PROPN
ejpam-4071	235	28	)	)	PUNCT
ejpam-4071	235	29	.	.	PUNCT
ejpam-4071	236	1	let	let	VERB
ejpam-4071	236	2	b	b	NOUN
ejpam-4071	236	3	=	=	NOUN
ejpam-4071	236	4	∥x1	∥x1	NOUN
ejpam-4071	236	5	−	−	PROPN
ejpam-4071	236	6	x0∥l(e	x0∥l(e	PROPN
ejpam-4071	236	7	)	)	PUNCT
ejpam-4071	236	8	⇒	⇒	NOUN
ejpam-4071	236	9	∥xn+1	∥xn+1	VERB
ejpam-4071	236	10	−	−	PROPN
ejpam-4071	236	11	xm∥l(e	xm∥l(e	NOUN
ejpam-4071	236	12	)	)	PUNCT
ejpam-4071	237	1	=	=	SYM
ejpam-4071	238	1	∑n	∑n	NUM
ejpam-4071	238	2	k	k	X
ejpam-4071	238	3	=	=	NOUN
ejpam-4071	238	4	m	m	PROPN
ejpam-4071	238	5	t	t	NOUN
ejpam-4071	238	6	kb	kb	PROPN
ejpam-4071	238	7	=	=	SYM
ejpam-4071	239	1	∑n	∑n	PROPN
ejpam-4071	239	2	k	k	X
ejpam-4071	240	1	=	=	PROPN
ejpam-4071	240	2	m	m	PROPN
ejpam-4071	240	3	t	t	NOUN
ejpam-4071	240	4	k	k	PROPN
ejpam-4071	240	5	2	2	NUM
ejpam-4071	240	6	t	t	NOUN
ejpam-4071	240	7	k	k	X
ejpam-4071	240	8	2b	2b	NUM
ejpam-4071	240	9	1	1	NUM
ejpam-4071	240	10	2b	2b	NUM
ejpam-4071	240	11	1	1	NUM
ejpam-4071	240	12	2	2	NUM
ejpam-4071	240	13	=	=	SYM
ejpam-4071	240	14	∑n	∑n	PROPN
ejpam-4071	240	15	k	k	NOUN
ejpam-4071	240	16	=	=	NOUN
ejpam-4071	240	17	mb	mb	ADJ
ejpam-4071	240	18	1	1	NUM
ejpam-4071	240	19	2	2	NUM
ejpam-4071	240	20	t	t	NOUN
ejpam-4071	240	21	k	k	NOUN
ejpam-4071	240	22	2	2	NUM
ejpam-4071	240	23	t	t	NOUN
ejpam-4071	240	24	k	k	X
ejpam-4071	240	25	2b	2b	NUM
ejpam-4071	240	26	1	1	NUM
ejpam-4071	240	27	2	2	NUM
ejpam-4071	240	28	=	=	SYM
ejpam-4071	240	29	∑n	∑n	PROPN
ejpam-4071	240	30	k	k	NOUN
ejpam-4071	240	31	=	=	PROPN
ejpam-4071	240	32	m(t	m(t	PROPN
ejpam-4071	240	33	k	k	PROPN
ejpam-4071	240	34	2b	2b	NUM
ejpam-4071	240	35	1	1	NUM
ejpam-4071	240	36	2	2	NUM
ejpam-4071	240	37	)	)	PUNCT
ejpam-4071	240	38	∗(t	∗(t	NOUN
ejpam-4071	240	39	k	k	PROPN
ejpam-4071	240	40	2b	2b	NUM
ejpam-4071	240	41	1	1	NUM
ejpam-4071	240	42	2	2	NUM
ejpam-4071	240	43	)	)	PUNCT
ejpam-4071	240	44	=	=	SYM
ejpam-4071	241	1	∑n	∑n	PROPN
ejpam-4071	241	2	k	k	X
ejpam-4071	241	3	=	=	VERB
ejpam-4071	241	4	m	m	VERB
ejpam-4071	241	5	|t	|t	VERB
ejpam-4071	242	1	k	k	X
ejpam-4071	242	2	2b	2b	NUM
ejpam-4071	242	3	1	1	NUM
ejpam-4071	242	4	2	2	NUM
ejpam-4071	242	5	|2	|2	NUM
ejpam-4071	242	6	⪯	⪯	NOUN
ejpam-4071	242	7	∥	∥	X
ejpam-4071	242	8	∑n	∑n	PROPN
ejpam-4071	243	1	k	k	NOUN
ejpam-4071	243	2	=	=	NOUN
ejpam-4071	243	3	m	m	VERB
ejpam-4071	243	4	|t	|t	VERB
ejpam-4071	244	1	k	k	X
ejpam-4071	244	2	2b	2b	NUM
ejpam-4071	244	3	1	1	NUM
ejpam-4071	244	4	2	2	NUM
ejpam-4071	244	5	|2∥l(e)il(e	|2∥l(e)il(e	NUM
ejpam-4071	244	6	)	)	PUNCT
ejpam-4071	244	7	⪯	⪯	NOUN
ejpam-4071	244	8	∑n	∑n	PROPN
ejpam-4071	245	1	k	k	PROPN
ejpam-4071	245	2	=	=	PROPN
ejpam-4071	245	3	m	m	PROPN
ejpam-4071	245	4	∥b	∥b	ADJ
ejpam-4071	245	5	1	1	NUM
ejpam-4071	245	6	2	2	NUM
ejpam-4071	245	7	∥2l(e)∥t	∥2l(e)∥t	NOUN
ejpam-4071	245	8	k	k	PROPN
ejpam-4071	245	9	2	2	NUM
ejpam-4071	245	10	∥2l(e)il(e	∥2l(e)il(e	NUM
ejpam-4071	245	11	)	)	PUNCT
ejpam-4071	245	12	=	=	SYM
ejpam-4071	245	13	∥b∥l(e	∥b∥l(e	X
ejpam-4071	245	14	)	)	PUNCT
ejpam-4071	246	1	∑n	∑n	PROPN
ejpam-4071	246	2	k	k	NOUN
ejpam-4071	246	3	=	=	PROPN
ejpam-4071	246	4	m	m	PROPN
ejpam-4071	246	5	∥t∥kl(e)il(e	∥t∥kl(e)il(e	PROPN
ejpam-4071	246	6	)	)	PUNCT
ejpam-4071	246	7	⪯	⪯	NOUN
ejpam-4071	246	8	∥b∥l(e	∥b∥l(e	NUM
ejpam-4071	246	9	)	)	PUNCT
ejpam-4071	246	10	∥t∥m	∥t∥m	NOUN
ejpam-4071	246	11	l(e	l(e	NOUN
ejpam-4071	246	12	)	)	PUNCT
ejpam-4071	246	13	1−∥t∥m	1−∥t∥m	NUM
ejpam-4071	246	14	l(e	l(e	NOUN
ejpam-4071	246	15	)	)	PUNCT
ejpam-4071	246	16	il(e	il(e	X
ejpam-4071	246	17	)	)	PUNCT
ejpam-4071	246	18	−→	−→	NOUN
ejpam-4071	246	19	0l(e)(m	0l(e)(m	NOUN
ejpam-4071	246	20	−→	−→	NOUN
ejpam-4071	246	21	+	+	NOUN
ejpam-4071	246	22	∞	∞	NOUN
ejpam-4071	246	23	)	)	PUNCT
ejpam-4071	246	24	,	,	PUNCT
ejpam-4071	246	25	where	where	SCONJ
ejpam-4071	246	26	il(e	il(e	PUNCT
ejpam-4071	246	27	)	)	PUNCT
ejpam-4071	246	28	the	the	DET
ejpam-4071	246	29	unite	unite	NOUN
ejpam-4071	246	30	element	element	NOUN
ejpam-4071	246	31	in	in	ADP
ejpam-4071	246	32	l(e	l(e	NOUN
ejpam-4071	246	33	)	)	PUNCT
ejpam-4071	246	34	,	,	PUNCT
ejpam-4071	246	35	therefore	therefore	ADV
ejpam-4071	246	36	{	{	PUNCT
ejpam-4071	246	37	xn	xn	X
ejpam-4071	246	38	}	}	PUNCT
ejpam-4071	246	39	is	be	AUX
ejpam-4071	246	40	a	a	DET
ejpam-4071	246	41	cauchy	cauchy	ADJ
ejpam-4071	246	42	sequence	sequence	NOUN
ejpam-4071	246	43	with	with	ADP
ejpam-4071	246	44	respect	respect	NOUN
ejpam-4071	246	45	to	to	ADP
ejpam-4071	246	46	l(e	l(e	NOUN
ejpam-4071	246	47	)	)	PUNCT
ejpam-4071	246	48	.	.	PUNCT
ejpam-4071	247	1	by	by	ADP
ejpam-4071	247	2	the	the	DET
ejpam-4071	247	3	completeness	completeness	NOUN
ejpam-4071	247	4	of(x	of(x	ADP
ejpam-4071	247	5	,	,	PUNCT
ejpam-4071	247	6	l(e	l(e	NOUN
ejpam-4071	247	7	)	)	PUNCT
ejpam-4071	247	8	,	,	PUNCT
ejpam-4071	247	9	∥.∥l(e	∥.∥l(e	NOUN
ejpam-4071	247	10	)	)	PUNCT
ejpam-4071	247	11	)	)	PUNCT
ejpam-4071	247	12	,	,	PUNCT
ejpam-4071	247	13	there	there	PRON
ejpam-4071	247	14	exists	exist	VERB
ejpam-4071	247	15	an	an	DET
ejpam-4071	247	16	x	x	SYM
ejpam-4071	247	17	∈	∈	PROPN
ejpam-4071	247	18	x	x	PUNCT
ejpam-4071	247	19	such	such	ADJ
ejpam-4071	247	20	that	that	DET
ejpam-4071	247	21	limn−→+∞	limn−→+∞	NOUN
ejpam-4071	247	22	xn	xn	PUNCT
ejpam-4071	248	1	=	=	PUNCT
ejpam-4071	248	2	limn−→+∞	limn−→+∞	X
ejpam-4071	249	1	txn−1	txn−1	PROPN
ejpam-4071	250	1	=	=	PUNCT
ejpam-4071	251	1	x.	x.	NOUN
ejpam-4071	252	1	since	since	SCONJ
ejpam-4071	252	2	∥tx−	∥tx−	PRON
ejpam-4071	252	3	x∥l(e	x∥l(e	PROPN
ejpam-4071	252	4	)	)	PUNCT
ejpam-4071	252	5	⪯	⪯	VERB
ejpam-4071	252	6	∥tx−	∥tx−	DET
ejpam-4071	252	7	txn∥l(e	txn∥l(e	NOUN
ejpam-4071	252	8	)	)	PUNCT
ejpam-4071	253	1	+	+	CCONJ
ejpam-4071	253	2	∥txn	∥txn	PRON
ejpam-4071	253	3	−	−	PROPN
ejpam-4071	253	4	x∥l(e	x∥l(e	PROPN
ejpam-4071	253	5	)	)	PUNCT
ejpam-4071	253	6	⪯	⪯	NOUN
ejpam-4071	253	7	m	m	VERB
ejpam-4071	253	8	3	3	NUM
ejpam-4071	253	9	(	(	PUNCT
ejpam-4071	253	10	∥x−xn∥l(e)+∥tx−xn∥l(e)+∥txn−x∥l(e))+∥txn−x∥l(e	∥x−xn∥l(e)+∥tx−xn∥l(e)+∥txn−x∥l(e))+∥txn−x∥l(e	PROPN
ejpam-4071	253	11	)	)	PUNCT
ejpam-4071	253	12	⪯	⪯	NOUN
ejpam-4071	253	13	m	m	VERB
ejpam-4071	253	14	3	3	NUM
ejpam-4071	253	15	(	(	PUNCT
ejpam-4071	253	16	∥x−xn∥l(e)+∥tx−xn∥l(e)+∥xn+1−x∥l(e))+∥txn−x∥l(e	∥x−xn∥l(e)+∥tx−xn∥l(e)+∥xn+1−x∥l(e))+∥txn−x∥l(e	PROPN
ejpam-4071	253	17	)	)	PUNCT
ejpam-4071	253	18	.	.	PUNCT
ejpam-4071	253	19	implies	imply	VERB
ejpam-4071	253	20	∥tx−x∥l(e	∥tx−x∥l(e	PROPN
ejpam-4071	253	21	)	)	PUNCT
ejpam-4071	253	22	⪯	⪯	NOUN
ejpam-4071	253	23	m	m	VERB
ejpam-4071	253	24	3	3	NUM
ejpam-4071	253	25	il(e)−m	il(e)−m	NOUN
ejpam-4071	253	26	3	3	NUM
ejpam-4071	253	27	(	(	PUNCT
ejpam-4071	253	28	2∥x−xn∥l(e)+∥xn+1−x∥l(e))+	2∥x−xn∥l(e)+∥xn+1−x∥l(e))+	NUM
ejpam-4071	253	29	1	1	NUM
ejpam-4071	253	30	il(e)−m	il(e)−m	NOUN
ejpam-4071	253	31	3	3	NUM
ejpam-4071	253	32	∥xn+1−x∥l(e	∥xn+1−x∥l(e	NOUN
ejpam-4071	253	33	)	)	PUNCT
ejpam-4071	253	34	−→	−→	NOUN
ejpam-4071	253	35	0(at	0(at	NOUN
ejpam-4071	253	36	n	n	PRON
ejpam-4071	253	37	−→	−→	NOUN
ejpam-4071	253	38	+	+	NOUN
ejpam-4071	253	39	∞	∞	NOUN
ejpam-4071	253	40	)	)	PUNCT
ejpam-4071	253	41	.	.	PUNCT
ejpam-4071	254	1	then	then	ADV
ejpam-4071	254	2	this	this	PRON
ejpam-4071	254	3	implies	imply	VERB
ejpam-4071	254	4	that	that	SCONJ
ejpam-4071	254	5	tx	tx	PROPN
ejpam-4071	254	6	=	=	PUNCT
ejpam-4071	254	7	x	x	X
ejpam-4071	254	8	i.e.	i.e.	X
ejpam-4071	254	9	,	,	PUNCT
ejpam-4071	254	10	x	x	PUNCT
ejpam-4071	254	11	is	be	AUX
ejpam-4071	254	12	fixed	fix	VERB
ejpam-4071	254	13	point	point	NOUN
ejpam-4071	254	14	of	of	ADP
ejpam-4071	254	15	t	t	PROPN
ejpam-4071	254	16	.	.	PUNCT
ejpam-4071	255	1	to	to	PART
ejpam-4071	255	2	prove	prove	VERB
ejpam-4071	255	3	the	the	DET
ejpam-4071	255	4	uniquencess	uniquencess	NOUN
ejpam-4071	255	5	suppose	suppose	VERB
ejpam-4071	255	6	that	that	SCONJ
ejpam-4071	255	7	y(̸=	y(̸=	PROPN
ejpam-4071	255	8	x	x	NOUN
ejpam-4071	255	9	)	)	PUNCT
ejpam-4071	255	10	is	be	AUX
ejpam-4071	255	11	another	another	DET
ejpam-4071	255	12	fixed	fix	VERB
ejpam-4071	255	13	point	point	NOUN
ejpam-4071	255	14	of	of	ADP
ejpam-4071	255	15	t	t	PROPN
ejpam-4071	255	16	,	,	PUNCT
ejpam-4071	255	17	then	then	ADV
ejpam-4071	255	18	0	0	NUM
ejpam-4071	255	19	≤	≤	NOUN
ejpam-4071	255	20	∥x−	∥x−	PROPN
ejpam-4071	255	21	y∥l(e	y∥l(e	PROPN
ejpam-4071	255	22	)	)	PUNCT
ejpam-4071	255	23	=	=	SYM
ejpam-4071	255	24	∥tx−	∥tx−	DET
ejpam-4071	255	25	ty∥l(e	ty∥l(e	ADJ
ejpam-4071	255	26	)	)	PUNCT
ejpam-4071	255	27	references	reference	NOUN
ejpam-4071	255	28	1247	1247	NUM
ejpam-4071	255	29	⪯	⪯	NOUN
ejpam-4071	255	30	m	m	VERB
ejpam-4071	255	31	3	3	NUM
ejpam-4071	255	32	(	(	PUNCT
ejpam-4071	255	33	∥x−y∥l(e)+∥tx−y∥l(e)+∥ty−x∥l(e	∥x−y∥l(e)+∥tx−y∥l(e)+∥ty−x∥l(e	NOUN
ejpam-4071	255	34	)	)	PUNCT
ejpam-4071	255	35	)	)	PUNCT
ejpam-4071	255	36	⪯m∥x−	⪯m∥x−	X
ejpam-4071	255	37	y∥l(e	y∥l(e	PROPN
ejpam-4071	255	38	)	)	PUNCT
ejpam-4071	255	39	,	,	PUNCT
ejpam-4071	255	40	implies	imply	VERB
ejpam-4071	255	41	0	0	NUM
ejpam-4071	255	42	≤	≤	NUM
ejpam-4071	255	43	∥∥x−	∥∥x−	NUM
ejpam-4071	255	44	y∥∥l(e	y∥∥l(e	NOUN
ejpam-4071	255	45	)	)	PUNCT
ejpam-4071	255	46	≤	≤	PUNCT
ejpam-4071	255	47	∥m∥x−	∥m∥x−	ADV
ejpam-4071	255	48	y∥∥l(e	y∥∥l(e	NUM
ejpam-4071	255	49	)	)	PUNCT
ejpam-4071	255	50	<	<	X
ejpam-4071	255	51	∥∥x−	∥∥x−	PROPN
ejpam-4071	255	52	y∥∥l(e	y∥∥l(e	NOUN
ejpam-4071	255	53	)	)	PUNCT
ejpam-4071	255	54	this	this	PRON
ejpam-4071	255	55	is	be	AUX
ejpam-4071	255	56	contradiction	contradiction	NOUN
ejpam-4071	255	57	implies	imply	VERB
ejpam-4071	255	58	x	x	NOUN
ejpam-4071	255	59	=	=	PUNCT
ejpam-4071	255	60	y.	y.	NOUN
ejpam-4071	255	61	therefore	therefore	ADV
ejpam-4071	255	62	the	the	DET
ejpam-4071	255	63	fixed	fix	VERB
ejpam-4071	255	64	point	point	NOUN
ejpam-4071	255	65	is	be	AUX
ejpam-4071	255	66	unique	unique	ADJ
ejpam-4071	255	67	.	.	PUNCT
ejpam-4071	256	1	4	4	X
ejpam-4071	256	2	.	.	X
ejpam-4071	256	3	conclusions	conclusion	NOUN
ejpam-4071	256	4	in	in	ADP
ejpam-4071	256	5	this	this	DET
ejpam-4071	256	6	paper	paper	NOUN
ejpam-4071	256	7	,	,	PUNCT
ejpam-4071	256	8	we	we	PRON
ejpam-4071	256	9	introduced	introduce	VERB
ejpam-4071	256	10	the	the	DET
ejpam-4071	256	11	notions	notion	NOUN
ejpam-4071	256	12	of	of	ADP
ejpam-4071	256	13	metric	metric	ADJ
ejpam-4071	256	14	space	space	NOUN
ejpam-4071	256	15	valued	value	VERB
ejpam-4071	256	16	-	-	PUNCT
ejpam-4071	256	17	operator	operator	NOUN
ejpam-4071	256	18	of	of	ADP
ejpam-4071	256	19	hilbert	hilbert	PROPN
ejpam-4071	256	20	c∗-module	c∗-module	PROPN
ejpam-4071	256	21	.	.	PUNCT
ejpam-4071	257	1	we	we	PRON
ejpam-4071	257	2	define	define	VERB
ejpam-4071	257	3	some	some	DET
ejpam-4071	257	4	contraction	contraction	NOUN
ejpam-4071	257	5	mapping	mapping	NOUN
ejpam-4071	257	6	and	and	CCONJ
ejpam-4071	257	7	prove	prove	VERB
ejpam-4071	257	8	some	some	DET
ejpam-4071	257	9	fixed	fix	VERB
ejpam-4071	257	10	point	point	NOUN
ejpam-4071	257	11	theorems	theorem	NOUN
ejpam-4071	257	12	(	(	PUNCT
ejpam-4071	257	13	such	such	ADJ
ejpam-4071	257	14	as	as	ADP
ejpam-4071	257	15	chatterjee	chatterjee	NOUN
ejpam-4071	257	16	and	and	CCONJ
ejpam-4071	257	17	extension	extension	NOUN
ejpam-4071	257	18	of	of	ADP
ejpam-4071	257	19	chatterjee	chatterjee	NOUN
ejpam-4071	257	20	)	)	PUNCT
ejpam-4071	257	21	for	for	ADP
ejpam-4071	257	22	a	a	DET
ejpam-4071	257	23	self	self	NOUN
ejpam-4071	257	24	mappings	mapping	NOUN
ejpam-4071	257	25	t	t	NOUN
ejpam-4071	257	26	on	on	ADP
ejpam-4071	257	27	the	the	DET
ejpam-4071	257	28	banach	banach	NOUN
ejpam-4071	257	29	space	space	NOUN
ejpam-4071	257	30	l(e	l(e	NOUN
ejpam-4071	257	31	)	)	PUNCT
ejpam-4071	257	32	.	.	PUNCT
ejpam-4071	258	1	references	reference	NOUN
ejpam-4071	258	2	[	[	X
ejpam-4071	258	3	1	1	NUM
ejpam-4071	258	4	]	]	X
ejpam-4071	258	5	chatterjee	chatterjee	NOUN
ejpam-4071	258	6	,	,	PUNCT
ejpam-4071	258	7	sk	sk	PROPN
ejpam-4071	258	8	.	.	PUNCT
ejpam-4071	258	9	fixed	fix	VERB
ejpam-4071	258	10	-	-	PUNCT
ejpam-4071	258	11	point	point	NOUN
ejpam-4071	258	12	theorems	theorem	NOUN
ejpam-4071	258	13	.	.	PUNCT
ejpam-4071	259	1	c.	c.	PROPN
ejpam-4071	259	2	r.	r.	PROPN
ejpam-4071	259	3	acad	acad	PROPN
ejpam-4071	259	4	.	.	PUNCT
ejpam-4071	260	1	bulgare	bulgare	PROPN
ejpam-4071	260	2	sci	sci	PROPN
ejpam-4071	260	3	.	.	PROPN
ejpam-4071	260	4	25	25	NUM
ejpam-4071	260	5	,	,	PUNCT
ejpam-4071	260	6	727	727	NUM
ejpam-4071	260	7	-	-	SYM
ejpam-4071	260	8	730	730	NUM
ejpam-4071	260	9	(	(	PUNCT
ejpam-4071	260	10	1972	1972	NUM
ejpam-4071	260	11	)	)	PUNCT
ejpam-4071	260	12	.	.	PUNCT
ejpam-4071	261	1	[	[	X
ejpam-4071	261	2	2	2	NUM
ejpam-4071	261	3	]	]	X
ejpam-4071	261	4	douglas	douglas	PROPN
ejpam-4071	261	5	,	,	PUNCT
ejpam-4071	261	6	rg	rg	PROPN
ejpam-4071	261	7	.	.	PROPN
ejpam-4071	261	8	banach	banach	PROPN
ejpam-4071	261	9	algebra	algebra	NOUN
ejpam-4071	261	10	techniques	technique	NOUN
ejpam-4071	261	11	in	in	ADP
ejpam-4071	261	12	operator	operator	NOUN
ejpam-4071	261	13	theory	theory	NOUN
ejpam-4071	261	14	.	.	PUNCT
ejpam-4071	262	1	springer	springer	NOUN
ejpam-4071	262	2	,	,	PUNCT
ejpam-4071	262	3	berlin	berlin	PROPN
ejpam-4071	262	4	(	(	PUNCT
ejpam-4071	262	5	1998	1998	NUM
ejpam-4071	262	6	)	)	PUNCT
ejpam-4071	262	7	.	.	PUNCT
ejpam-4071	263	1	[	[	X
ejpam-4071	263	2	3	3	X
ejpam-4071	263	3	]	]	X
ejpam-4071	263	4	gilbert	gilbert	PROPN
ejpam-4071	263	5	helmberg	helmberg	PROPN
ejpam-4071	263	6	.	.	PUNCT
ejpam-4071	264	1	introduction	introduction	NOUN
ejpam-4071	264	2	to	to	ADP
ejpam-4071	264	3	spectral	spectral	ADJ
ejpam-4071	264	4	theory	theory	NOUN
ejpam-4071	264	5	in	in	ADP
ejpam-4071	264	6	hilbert	hilbert	NOUN
ejpam-4071	264	7	space	space	NOUN
ejpam-4071	264	8	.	.	PUNCT
ejpam-4071	265	1	technological	technological	ADJ
ejpam-4071	265	2	university	university	NOUN
ejpam-4071	265	3	eindhoven	eindhoven	NOUN
ejpam-4071	265	4	.	.	PUNCT
ejpam-4071	266	1	[	[	X
ejpam-4071	266	2	4	4	X
ejpam-4071	266	3	]	]	X
ejpam-4071	266	4	kadelburg	kadelburg	PROPN
ejpam-4071	266	5	et	et	PROPN
ejpam-4071	266	6	al	al	PROPN
ejpam-4071	266	7	,	,	PUNCT
ejpam-4071	266	8	z	z	X
ejpam-4071	266	9	.	.	PUNCT
ejpam-4071	267	1	remarks	remark	NOUN
ejpam-4071	267	2	on	on	ADP
ejpam-4071	267	3	the	the	DET
ejpam-4071	267	4	paper	paper	NOUN
ejpam-4071	267	5	”	"	PUNCT
ejpam-4071	267	6	fixed	fix	VERB
ejpam-4071	267	7	point	point	NOUN
ejpam-4071	267	8	theorems	theorem	NOUN
ejpam-4071	267	9	for	for	ADP
ejpam-4071	267	10	cyclic	cyclic	ADJ
ejpam-4071	267	11	contractions	contraction	NOUN
ejpam-4071	267	12	in	in	ADP
ejpam-4071	267	13	c*-algebra	c*-algebra	PROPN
ejpam-4071	267	14	-	-	PUNCT
ejpam-4071	267	15	valued	value	VERB
ejpam-4071	267	16	b	b	NOUN
ejpam-4071	267	17	-	-	PUNCT
ejpam-4071	267	18	metric	metric	ADJ
ejpam-4071	267	19	spaces	space	NOUN
ejpam-4071	267	20	.	.	PUNCT
ejpam-4071	268	1	adv	adv	PROPN
ejpam-4071	268	2	.	.	PUNCT
ejpam-4071	268	3	oper	oper	PROPN
ejpam-4071	268	4	.	.	PUNCT
ejpam-4071	268	5	theory	theory	NOUN
ejpam-4071	268	6	.	.	PUNCT
ejpam-4071	269	1	no	no	INTJ
ejpam-4071	269	2	.	.	NOUN
ejpam-4071	269	3	1	1	NUM
ejpam-4071	269	4	,	,	PUNCT
ejpam-4071	269	5	93	93	NUM
ejpam-4071	269	6	-	-	SYM
ejpam-4071	269	7	104,1	104,1	NUM
ejpam-4071	269	8	(	(	PUNCT
ejpam-4071	269	9	2016	2016	NUM
ejpam-4071	269	10	)	)	PUNCT
ejpam-4071	269	11	.	.	PUNCT
ejpam-4071	270	1	[	[	X
ejpam-4071	270	2	5	5	NUM
ejpam-4071	270	3	]	]	X
ejpam-4071	270	4	kaplansky	kaplansky	PROPN
ejpam-4071	270	5	,	,	PUNCT
ejpam-4071	270	6	i.	i.	NOUN
ejpam-4071	270	7	modules	module	NOUN
ejpam-4071	270	8	over	over	ADP
ejpam-4071	270	9	operator	operator	NOUN
ejpam-4071	270	10	algebras	algebra	NOUN
ejpam-4071	270	11	.	.	PUNCT
ejpam-4071	271	1	amer	amer	PROPN
ejpam-4071	271	2	j.	j.	PROPN
ejpam-4071	271	3	math	math	PROPN
ejpam-4071	271	4	.	.	PUNCT
ejpam-4071	271	5	,	,	PUNCT
ejpam-4071	271	6	75	75	NUM
ejpam-4071	271	7	,	,	PUNCT
ejpam-4071	271	8	839	839	NUM
ejpam-4071	271	9	-	-	NUM
ejpam-4071	271	10	858	858	NUM
ejpam-4071	271	11	,	,	PUNCT
ejpam-4071	271	12	(	(	PUNCT
ejpam-4071	271	13	1953	1953	NUM
ejpam-4071	271	14	)	)	PUNCT
ejpam-4071	271	15	.	.	PUNCT
ejpam-4071	272	1	[	[	X
ejpam-4071	272	2	6	6	NUM
ejpam-4071	272	3	]	]	X
ejpam-4071	272	4	kasparov	kasparov	PROPN
ejpam-4071	272	5	,	,	PUNCT
ejpam-4071	272	6	g.g	g.g	PROPN
ejpam-4071	272	7	.	.	PROPN
ejpam-4071	272	8	hilbert	hilbert	PROPN
ejpam-4071	272	9	c∗-modules	c∗-modules	PROPN
ejpam-4071	272	10	.	.	PUNCT
ejpam-4071	273	1	theorems	theorem	NOUN
ejpam-4071	273	2	of	of	ADP
ejpam-4071	273	3	stinespring	stinespring	NOUN
ejpam-4071	273	4	and	and	CCONJ
ejpam-4071	273	5	voiculescu	voiculescu	NOUN
ejpam-4071	273	6	,	,	PUNCT
ejpam-4071	273	7	j.	j.	PROPN
ejpam-4071	273	8	operator	operator	PROPN
ejpam-4071	273	9	theory	theory	NOUN
ejpam-4071	273	10	4	4	NUM
ejpam-4071	273	11	,	,	PUNCT
ejpam-4071	273	12	133	133	NUM
ejpam-4071	273	13	-	-	PUNCT
ejpam-4071	273	14	150,(1980	150,(1980	NUM
ejpam-4071	273	15	)	)	PUNCT
ejpam-4071	273	16	.	.	PUNCT
ejpam-4071	274	1	[	[	X
ejpam-4071	274	2	7	7	NUM
ejpam-4071	274	3	]	]	X
ejpam-4071	274	4	karapınar	karapınar	NOUN
ejpam-4071	274	5	,	,	PUNCT
ejpam-4071	274	6	e.	e.	PROPN
ejpam-4071	274	7	fixed	fix	VERB
ejpam-4071	274	8	point	point	NOUN
ejpam-4071	274	9	theorems	theorem	NOUN
ejpam-4071	274	10	in	in	ADP
ejpam-4071	274	11	cone	cone	NOUN
ejpam-4071	274	12	banach	banach	NOUN
ejpam-4071	274	13	spaces	space	VERB
ejpam-4071	274	14	.	.	PUNCT
ejpam-4071	275	1	fixed	fix	VERB
ejpam-4071	275	2	point	point	NOUN
ejpam-4071	275	3	theory	theory	NOUN
ejpam-4071	275	4	appl	appl	NOUN
ejpam-4071	275	5	.	.	PUNCT
ejpam-4071	276	1	2009	2009	NUM
ejpam-4071	276	2	article	article	NOUN
ejpam-4071	276	3	i	i	PROPN
ejpam-4071	276	4	d	d	PROPN
ejpam-4071	276	5	609281	609281	NUM
ejpam-4071	276	6	,	,	PUNCT
ejpam-4071	276	7	9	9	NUM
ejpam-4071	276	8	pages	page	NOUN
ejpam-4071	276	9	,	,	PUNCT
ejpam-4071	276	10	2009	2009	NUM
ejpam-4071	276	11	,	,	PUNCT
ejpam-4071	276	12	doi:10.1155/2009/609281	doi:10.1155/2009/609281	ADP
ejpam-4071	276	13	[	[	PUNCT
ejpam-4071	276	14	8	8	NUM
ejpam-4071	276	15	]	]	PUNCT
ejpam-4071	276	16	lance	lance	NOUN
ejpam-4071	276	17	,	,	PUNCT
ejpam-4071	276	18	e.	e.	PROPN
ejpam-4071	276	19	c.	c.	PROPN
ejpam-4071	276	20	hilbert	hilbert	PROPN
ejpam-4071	276	21	c∗-modules	c∗-modules	PROPN
ejpam-4071	276	22	.	.	PUNCT
ejpam-4071	277	1	a	a	DET
ejpam-4071	277	2	toolkit	toolkit	NOUN
ejpam-4071	277	3	for	for	ADP
ejpam-4071	277	4	operator	operator	NOUN
ejpam-4071	277	5	algebraists	algebraist	NOUN
ejpam-4071	277	6	.	.	PUNCT
ejpam-4071	278	1	cambridge	cambridge	PROPN
ejpam-4071	278	2	,	,	PUNCT
ejpam-4071	278	3	england	england	PROPN
ejpam-4071	278	4	:	:	PUNCT
ejpam-4071	278	5	cambridge	cambridge	PROPN
ejpam-4071	278	6	university	university	PROPN
ejpam-4071	278	7	press	press	NOUN
ejpam-4071	278	8	,	,	PUNCT
ejpam-4071	278	9	1995	1995	NUM
ejpam-4071	278	10	.	.	PUNCT
ejpam-4071	279	1	[	[	X
ejpam-4071	279	2	9	9	NUM
ejpam-4071	279	3	]	]	X
ejpam-4071	279	4	murphy	murphy	NOUN
ejpam-4071	279	5	,	,	PUNCT
ejpam-4071	279	6	g.	g.	PROPN
ejpam-4071	279	7	j.	j.	PROPN
ejpam-4071	279	8	c∗-algebras	c∗-algebras	PROPN
ejpam-4071	279	9	and	and	CCONJ
ejpam-4071	279	10	operator	operator	NOUN
ejpam-4071	279	11	theory	theory	NOUN
ejpam-4071	279	12	.	.	PUNCT
ejpam-4071	280	1	academic	academic	ADJ
ejpam-4071	280	2	press	press	NOUN
ejpam-4071	280	3	,	,	PUNCT
ejpam-4071	280	4	1990	1990	NUM
ejpam-4071	280	5	.	.	PUNCT
ejpam-4071	281	1	[	[	X
ejpam-4071	281	2	10	10	NUM
ejpam-4071	281	3	]	]	X
ejpam-4071	281	4	mustafa	mustafa	PROPN
ejpam-4071	281	5	,	,	PUNCT
ejpam-4071	281	6	r.	r.	PROPN
ejpam-4071	281	7	omran	omran	PROPN
ejpam-4071	281	8	,	,	PUNCT
ejpam-4071	281	9	s.	s.	PROPN
ejpam-4071	281	10	ngoc	ngoc	PROPN
ejpam-4071	281	11	,	,	PUNCT
ejpam-4071	281	12	qn	qn	PROPN
ejpam-4071	281	13	.	.	PROPN
ejpam-4071	281	14	fixed	fix	VERB
ejpam-4071	281	15	point	point	NOUN
ejpam-4071	281	16	theory	theory	NOUN
ejpam-4071	281	17	using	use	VERB
ejpam-4071	281	18	ψ	ψ	ADP
ejpam-4071	281	19	contractive	contractive	ADJ
ejpam-4071	281	20	mapping	mapping	NOUN
ejpam-4071	281	21	in	in	ADP
ejpam-4071	281	22	c∗-algebra	c∗-algebra	PROPN
ejpam-4071	281	23	valued	value	VERB
ejpam-4071	281	24	b	b	NOUN
ejpam-4071	281	25	-	-	PUNCT
ejpam-4071	281	26	metric	metric	ADJ
ejpam-4071	281	27	space	space	NOUN
ejpam-4071	281	28	.	.	PUNCT
ejpam-4071	282	1	mathematics	mathematic	NOUN
ejpam-4071	282	2	,	,	PUNCT
ejpam-4071	282	3	9	9	NUM
ejpam-4071	282	4	,	,	PUNCT
ejpam-4071	282	5	92,(2021	92,(2021	NUM
ejpam-4071	282	6	)	)	PUNCT
ejpam-4071	282	7	.	.	PUNCT
ejpam-4071	283	1	references	reference	NOUN
ejpam-4071	283	2	1248	1248	NUM
ejpam-4071	283	3	[	[	X
ejpam-4071	283	4	11	11	NUM
ejpam-4071	283	5	]	]	SYM
ejpam-4071	283	6	özer	özer	NOUN
ejpam-4071	283	7	,	,	PUNCT
ejpam-4071	283	8	ö.	ö.	PROPN
ejpam-4071	283	9	omran	omran	NOUN
ejpam-4071	283	10	,	,	PUNCT
ejpam-4071	283	11	s.	s.	PROPN
ejpam-4071	283	12	common	common	ADJ
ejpam-4071	283	13	fixed	fix	VERB
ejpam-4071	283	14	point	point	NOUN
ejpam-4071	283	15	in	in	ADP
ejpam-4071	283	16	c∗-algebra	c∗-algebra	PROPN
ejpam-4071	283	17	b	b	X
ejpam-4071	283	18	-	-	PUNCT
ejpam-4071	283	19	valued	value	VERB
ejpam-4071	283	20	metric	metric	ADJ
ejpam-4071	283	21	space	space	NOUN
ejpam-4071	283	22	.	.	PUNCT
ejpam-4071	284	1	aip	aip	PROPN
ejpam-4071	284	2	conference	conference	NOUN
ejpam-4071	284	3	proceedings	proceeding	NOUN
ejpam-4071	284	4	1773	1773	NUM
ejpam-4071	284	5	(	(	PUNCT
ejpam-4071	284	6	1	1	NUM
ejpam-4071	284	7	)	)	PUNCT
ejpam-4071	284	8	050005(2016	050005(2016	NUM
ejpam-4071	284	9	)	)	PUNCT
ejpam-4071	284	10	.	.	PUNCT
ejpam-4071	285	1	[	[	X
ejpam-4071	285	2	12	12	NUM
ejpam-4071	285	3	]	]	X
ejpam-4071	285	4	paschke	paschke	PROPN
ejpam-4071	285	5	,	,	PUNCT
ejpam-4071	285	6	w.	w.	PROPN
ejpam-4071	285	7	l.	l.	PROPN
ejpam-4071	285	8	inner	inner	ADJ
ejpam-4071	285	9	product	product	NOUN
ejpam-4071	285	10	modules	module	NOUN
ejpam-4071	285	11	over	over	ADP
ejpam-4071	285	12	b∗-algebras	b∗-algebra	NOUN
ejpam-4071	285	13	.	.	PUNCT
ejpam-4071	286	1	trans	trans	PROPN
ejpam-4071	286	2	amer	amer	PROPN
ejpam-4071	286	3	.	.	PUNCT
ejpam-4071	286	4	math	math	PROPN
ejpam-4071	286	5	.	.	PUNCT
ejpam-4071	287	1	soc.182	soc.182	PROPN
ejpam-4071	287	2	,	,	PUNCT
ejpam-4071	287	3	443	443	NUM
ejpam-4071	287	4	-	-	NUM
ejpam-4071	287	5	468,(1973	468,(1973	NUM
ejpam-4071	287	6	)	)	PUNCT
ejpam-4071	287	7	.	.	PUNCT
ejpam-4071	288	1	[	[	X
ejpam-4071	288	2	13	13	NUM
ejpam-4071	288	3	]	]	SYM
ejpam-4071	288	4	priyobarta	priyobarta	NOUN
ejpam-4071	288	5	et	et	PROPN
ejpam-4071	288	6	al	al	PROPN
ejpam-4071	288	7	,	,	PUNCT
ejpam-4071	288	8	n.	n.	PROPN
ejpam-4071	288	9	fixed	fix	VERB
ejpam-4071	288	10	point	point	NOUN
ejpam-4071	288	11	theorems	theorem	NOUN
ejpam-4071	288	12	on	on	ADP
ejpam-4071	288	13	parametric	parametric	ADJ
ejpam-4071	288	14	a	a	PRON
ejpam-4071	288	15	-	-	PUNCT
ejpam-4071	288	16	metric	metric	ADJ
ejpam-4071	288	17	space	space	NOUN
ejpam-4071	288	18	,	,	PUNCT
ejpam-4071	288	19	american	american	ADJ
ejpam-4071	288	20	journal	journal	PROPN
ejpam-4071	288	21	of	of	ADP
ejpam-4071	288	22	applied	apply	VERB
ejpam-4071	288	23	mathematics	mathematic	NOUN
ejpam-4071	288	24	and	and	CCONJ
ejpam-4071	288	25	statistics	statistic	NOUN
ejpam-4071	288	26	,	,	PUNCT
ejpam-4071	288	27	vol.6	vol.6	PROPN
ejpam-4071	288	28	,	,	PUNCT
ejpam-4071	288	29	no	no	INTJ
ejpam-4071	288	30	.	.	NOUN
ejpam-4071	288	31	1	1	NUM
ejpam-4071	288	32	,	,	PUNCT
ejpam-4071	288	33	1	1	NUM
ejpam-4071	288	34	-	-	SYM
ejpam-4071	288	35	5	5	NUM
ejpam-4071	288	36	,	,	PUNCT
ejpam-4071	288	37	2018	2018	NUM
ejpam-4071	288	38	.	.	PUNCT
ejpam-4071	289	1	[	[	X
ejpam-4071	289	2	14	14	NUM
ejpam-4071	289	3	]	]	PUNCT
ejpam-4071	289	4	qiaoling	qiaoling	NOUN
ejpam-4071	289	5	,	,	PUNCT
ejpam-4071	289	6	x.	x.	NOUN
ejpam-4071	289	7	lining	lining	PROPN
ejpam-4071	289	8	,	,	PUNCT
ejpam-4071	289	9	j.	j.	PROPN
ejpam-4071	289	10	zhenhua	zhenhua	PROPN
ejpam-4071	289	11	,	,	PUNCT
ejpam-4071	289	12	ma	ma	PROPN
ejpam-4071	289	13	.	.	PROPN
ejpam-4071	289	14	common	common	ADJ
ejpam-4071	289	15	fixed	fix	VERB
ejpam-4071	289	16	point	point	NOUN
ejpam-4071	289	17	theorems	theorem	NOUN
ejpam-4071	289	18	in	in	ADP
ejpam-4071	289	19	c∗-algebravalued	c∗-algebravalue	VERB
ejpam-4071	289	20	metric	metric	ADJ
ejpam-4071	289	21	spaces[j	spaces[j	NOUN
ejpam-4071	289	22	]	]	PUNCT
ejpam-4071	289	23	.	.	PUNCT
ejpam-4071	290	1	journal	journal	PROPN
ejpam-4071	290	2	of	of	ADP
ejpam-4071	290	3	hubei	hubei	PROPN
ejpam-4071	290	4	normal	normal	ADJ
ejpam-4071	290	5	university(natural	university(natural	ADJ
ejpam-4071	290	6	science	science	NOUN
ejpam-4071	290	7	)	)	PUNCT
ejpam-4071	290	8	,	,	PUNCT
ejpam-4071	290	9	2015	2015	NUM
ejpam-4071	290	10	.	.	PUNCT
ejpam-4071	291	1	[	[	X
ejpam-4071	291	2	15	15	NUM
ejpam-4071	291	3	]	]	PUNCT
ejpam-4071	291	4	radenović	radenović	NOUN
ejpam-4071	291	5	et	et	PROPN
ejpam-4071	291	6	al	al	PROPN
ejpam-4071	291	7	,	,	PUNCT
ejpam-4071	291	8	s.	s.	PROPN
ejpam-4071	291	9	coupled	couple	VERB
ejpam-4071	291	10	fixed	fix	VERB
ejpam-4071	291	11	point	point	NOUN
ejpam-4071	291	12	theorems	theorem	NOUN
ejpam-4071	291	13	in	in	ADP
ejpam-4071	291	14	c*-algebra	c*-algebra	PROPN
ejpam-4071	291	15	-	-	PUNCT
ejpam-4071	291	16	valued	value	VERB
ejpam-4071	291	17	b	b	NOUN
ejpam-4071	291	18	-	-	PUNCT
ejpam-4071	291	19	metric	metric	ADJ
ejpam-4071	291	20	spaces	space	NOUN
ejpam-4071	291	21	.	.	PUNCT
ejpam-4071	292	1	scientific	scientific	ADJ
ejpam-4071	292	2	publications	publication	NOUN
ejpam-4071	292	3	of	of	ADP
ejpam-4071	292	4	the	the	DET
ejpam-4071	292	5	state	state	PROPN
ejpam-4071	292	6	university	university	PROPN
ejpam-4071	292	7	of	of	ADP
ejpam-4071	292	8	novi	novi	PROPN
ejpam-4071	292	9	pazar	pazar	PROPN
ejpam-4071	292	10	,	,	PUNCT
ejpam-4071	292	11	ser	ser	NOUN
ejpam-4071	292	12	.	.	PUNCT
ejpam-4071	293	1	a	a	DET
ejpam-4071	293	2	:	:	PUNCT
ejpam-4071	293	3	appl	appl	PROPN
ejpam-4071	293	4	.	.	PROPN
ejpam-4071	293	5	math	math	PROPN
ejpam-4071	293	6	.	.	PUNCT
ejpam-4071	294	1	inform	inform	NOUN
ejpam-4071	294	2	.	.	PUNCT
ejpam-4071	295	1	and	and	CCONJ
ejpam-4071	295	2	mech	mech	NOUN
ejpam-4071	295	3	.	.	PUNCT
ejpam-4071	296	1	vol	vol	NOUN
ejpam-4071	296	2	.	.	PUNCT
ejpam-4071	296	3	9,81	9,81	NOUN
ejpam-4071	296	4	-	-	PUNCT
ejpam-4071	296	5	90,1	90,1	NOUN
ejpam-4071	296	6	(	(	PUNCT
ejpam-4071	296	7	2017	2017	NUM
ejpam-4071	296	8	)	)	PUNCT
ejpam-4071	296	9	.	.	PUNCT
ejpam-4071	297	1	[	[	X
ejpam-4071	297	2	16	16	NUM
ejpam-4071	297	3	]	]	SYM
ejpam-4071	297	4	rieffel	rieffel	NOUN
ejpam-4071	297	5	,	,	PUNCT
ejpam-4071	297	6	m.	m.	NOUN
ejpam-4071	297	7	a.	a.	NOUN
ejpam-4071	297	8	induced	induce	VERB
ejpam-4071	297	9	representations	representation	NOUN
ejpam-4071	297	10	of	of	ADP
ejpam-4071	297	11	c∗-algebras	c∗-algebra	NOUN
ejpam-4071	297	12	.	.	PUNCT
ejpam-4071	298	1	adv	adv	PROPN
ejpam-4071	298	2	in	in	ADP
ejpam-4071	298	3	math	math	NOUN
ejpam-4071	298	4	.	.	PUNCT
ejpam-4071	299	1	,13(2	,13(2	PROPN
ejpam-4071	299	2	)	)	PUNCT
ejpam-4071	299	3	,	,	PUNCT
ejpam-4071	300	1	176257,(1974	176257,(1974	NUM
ejpam-4071	300	2	)	)	PUNCT
ejpam-4071	300	3	.	.	PUNCT
ejpam-4071	301	1	[	[	X
ejpam-4071	301	2	17	17	NUM
ejpam-4071	301	3	]	]	PUNCT
ejpam-4071	301	4	turkoglu	turkoglu	PROPN
ejpam-4071	301	5	,	,	PUNCT
ejpam-4071	301	6	d.	d.	PROPN
ejpam-4071	301	7	abuloha	abuloha	PROPN
ejpam-4071	301	8	,	,	PUNCT
ejpam-4071	301	9	m.	m.	NOUN
ejpam-4071	301	10	and	and	CCONJ
ejpam-4071	301	11	abdeljawad	abdeljawad	NOUN
ejpam-4071	301	12	,	,	PUNCT
ejpam-4071	301	13	t.	t.	PUNCT
ejpam-4071	301	14	some	some	DET
ejpam-4071	301	15	theorems	theorem	NOUN
ejpam-4071	301	16	and	and	CCONJ
ejpam-4071	301	17	examples	example	NOUN
ejpam-4071	301	18	of	of	ADP
ejpam-4071	301	19	cone	cone	NOUN
ejpam-4071	301	20	banach	banach	NOUN
ejpam-4071	301	21	spaces	space	VERB
ejpam-4071	301	22	.	.	PUNCT
ejpam-4071	302	1	j.	j.	PROPN
ejpam-4071	302	2	comput	comput	PROPN
ejpam-4071	302	3	.	.	PUNCT
ejpam-4071	303	1	anal	anal	PROPN
ejpam-4071	303	2	.	.	PUNCT
ejpam-4071	303	3	appl	appl	PROPN
ejpam-4071	303	4	.	.	PROPN
ejpam-4071	304	1	12	12	NUM
ejpam-4071	304	2	4	4	NUM
ejpam-4071	304	3	,	,	PUNCT
ejpam-4071	304	4	739	739	NUM
ejpam-4071	304	5	-	-	SYM
ejpam-4071	304	6	753	753	NUM
ejpam-4071	304	7	,	,	PUNCT
ejpam-4071	304	8	(	(	PUNCT
ejpam-4071	304	9	2010	2010	NUM
ejpam-4071	304	10	)	)	PUNCT
ejpam-4071	304	11	.	.	PUNCT
ejpam-4071	305	1	[	[	X
ejpam-4071	305	2	18	18	NUM
ejpam-4071	305	3	]	]	X
ejpam-4071	305	4	vesna	vesna	PROPN
ejpam-4071	305	5	todorčević	todorčević	PROPN
ejpam-4071	305	6	,	,	PUNCT
ejpam-4071	305	7	harmonic	harmonic	VERB
ejpam-4071	305	8	quasiconformmal	quasiconformmal	ADJ
ejpam-4071	305	9	mappings	mapping	NOUN
ejpam-4071	305	10	and	and	CCONJ
ejpam-4071	305	11	hyperbolic	hyperbolic	ADJ
ejpam-4071	305	12	type	type	NOUN
ejpam-4071	305	13	metrics	metric	NOUN
ejpam-4071	305	14	,	,	PUNCT
ejpam-4071	305	15	springer	springer	NOUN
ejpam-4071	305	16	nature	nature	PROPN
ejpam-4071	305	17	switzerland	switzerland	PROPN
ejpam-4071	305	18	ag	ag	PROPN
ejpam-4071	305	19	2019	2019	NUM
ejpam-4071	305	20	.	.	PUNCT
ejpam-4071	306	1	[	[	X
ejpam-4071	306	2	19	19	NUM
ejpam-4071	306	3	]	]	PUNCT
ejpam-4071	306	4	wegge	wegge	NOUN
ejpam-4071	306	5	-	-	PUNCT
ejpam-4071	306	6	olsen	olsen	NOUN
ejpam-4071	306	7	,	,	PUNCT
ejpam-4071	306	8	n.	n.	PROPN
ejpam-4071	306	9	e.	e.	PROPN
ejpam-4071	306	10	k	k	PROPN
ejpam-4071	306	11	-	-	NOUN
ejpam-4071	306	12	theory	theory	NOUN
ejpam-4071	306	13	and	and	CCONJ
ejpam-4071	306	14	c∗-algebras	c∗-algebra	NOUN
ejpam-4071	306	15	.	.	PUNCT
ejpam-4071	306	16	a	a	DET
ejpam-4071	306	17	friendly	friendly	ADJ
ejpam-4071	306	18	approach	approach	NOUN
ejpam-4071	306	19	.	.	PUNCT
ejpam-4071	307	1	oxford	oxford	PROPN
ejpam-4071	307	2	,	,	PUNCT
ejpam-4071	307	3	england	england	PROPN
ejpam-4071	307	4	:	:	PUNCT
ejpam-4071	307	5	oxford	oxford	PROPN
ejpam-4071	307	6	university	university	PROPN
ejpam-4071	307	7	press	press	NOUN
ejpam-4071	307	8	,	,	PUNCT
ejpam-4071	307	9	1993	1993	NUM
ejpam-4071	307	10	.	.	PUNCT
ejpam-4071	308	1	[	[	X
ejpam-4071	308	2	20	20	NUM
ejpam-4071	308	3	]	]	X
ejpam-4071	308	4	zhenhua	zhenhua	PROPN
ejpam-4071	308	5	,	,	PUNCT
ejpam-4071	308	6	ma	ma	PROPN
ejpam-4071	308	7	.	.	PROPN
ejpam-4071	308	8	lining	lining	PROPN
ejpam-4071	308	9	,	,	PUNCT
ejpam-4071	308	10	j.	j.	PROPN
ejpam-4071	308	11	hongkai	hongkai	PROPN
ejpam-4071	308	12	,	,	PUNCT
ejpam-4071	308	13	s.	s.	PROPN
ejpam-4071	308	14	c∗-algebras	c∗-algebras	PROPN
ejpam-4071	308	15	-	-	PUNCT
ejpam-4071	308	16	valued	value	VERB
ejpam-4071	308	17	metric	metric	ADJ
ejpam-4071	308	18	spaces	space	NOUN
ejpam-4071	308	19	and	and	CCONJ
ejpam-4071	308	20	related	relate	VERB
ejpam-4071	308	21	fixed	fix	VERB
ejpam-4071	308	22	point	point	NOUN
ejpam-4071	308	23	theorems	theorem	NOUN
ejpam-4071	308	24	.	.	PUNCT
ejpam-4071	308	25	fixed	fix	VERB
ejpam-4071	308	26	point	point	NOUN
ejpam-4071	308	27	theory	theory	NOUN
ejpam-4071	308	28	appl	appl	PROPN
ejpam-4071	308	29	.	.	PROPN
ejpam-4071	308	30	2014	2014	NUM
ejpam-4071	308	31	,	,	PUNCT
ejpam-4071	308	32	206	206	NUM
ejpam-4071	308	33	(	(	PUNCT
ejpam-4071	308	34	2014	2014	NUM
ejpam-4071	308	35	)	)	PUNCT
ejpam-4071	308	36	.	.	PUNCT
ejpam-4071	309	1	[	[	X
ejpam-4071	309	2	21	21	NUM
ejpam-4071	309	3	]	]	X
ejpam-4071	309	4	zhenhua	zhenhua	PROPN
ejpam-4071	309	5	,	,	PUNCT
ejpam-4071	309	6	ma	ma	PROPN
ejpam-4071	309	7	.	.	PROPN
ejpam-4071	309	8	lining	lining	PROPN
ejpam-4071	309	9	,	,	PUNCT
ejpam-4071	309	10	j.	j.	PROPN
ejpam-4071	309	11	c∗-algebras	c∗-algebras	PROPN
ejpam-4071	309	12	-	-	PUNCT
ejpam-4071	309	13	valued	value	VERB
ejpam-4071	309	14	b	b	NOUN
ejpam-4071	309	15	-	-	PUNCT
ejpam-4071	309	16	metric	metric	ADJ
ejpam-4071	309	17	spaces	space	NOUN
ejpam-4071	309	18	and	and	CCONJ
ejpam-4071	309	19	related	relate	VERB
ejpam-4071	309	20	fixed	fix	VERB
ejpam-4071	309	21	point	point	NOUN
ejpam-4071	309	22	theorems	theorem	NOUN
ejpam-4071	309	23	.	.	PUNCT
ejpam-4071	309	24	fixed	fix	VERB
ejpam-4071	309	25	point	point	NOUN
ejpam-4071	309	26	theory	theory	NOUN
ejpam-4071	309	27	appl.1,1	appl.1,1	NOUN
ejpam-4071	309	28	-	-	PUNCT
ejpam-4071	309	29	12	12	NUM
ejpam-4071	309	30	,	,	PUNCT
ejpam-4071	309	31	(	(	PUNCT
ejpam-4071	309	32	2015	2015	NUM
ejpam-4071	309	33	)	)	PUNCT
ejpam-4071	309	34	.	.	PUNCT
ejpam-4071	310	1	[	[	X
ejpam-4071	310	2	22	22	NUM
ejpam-4071	310	3	]	]	PUNCT
ejpam-4071	310	4	zoran	zoran	PROPN
ejpam-4071	310	5	kadelburg	kadelburg	PROPN
ejpam-4071	310	6	,	,	PUNCT
ejpam-4071	310	7	stojan	stojan	ADP
ejpam-4071	310	8	radenović	radenović	ADJ
ejpam-4071	310	9	,	,	PUNCT
ejpam-4071	310	10	critical	critical	ADJ
ejpam-4071	310	11	remarks	remark	NOUN
ejpam-4071	310	12	on	on	ADP
ejpam-4071	310	13	some	some	DET
ejpam-4071	310	14	recent	recent	ADJ
ejpam-4071	310	15	fixed	fix	VERB
ejpam-4071	310	16	points	point	NOUN
ejpam-4071	310	17	results	result	NOUN
ejpam-4071	310	18	in	in	ADP
ejpam-4071	310	19	c*-algebra	c*-algebra	PROPN
ejpam-4071	310	20	-	-	PUNCT
ejpam-4071	310	21	valued	value	VERB
ejpam-4071	310	22	metric	metric	ADJ
ejpam-4071	310	23	spaces	space	NOUN
ejpam-4071	310	24	,	,	PUNCT
ejpam-4071	310	25	fixed	fix	VERB
ejpam-4071	310	26	point	point	NOUN
ejpam-4071	310	27	theory	theory	NOUN
ejpam-4071	310	28	appl	appl	PROPN
ejpam-4071	310	29	.	.	PUNCT
ejpam-4071	311	1	(	(	PUNCT
ejpam-4071	311	2	2016	2016	NUM
ejpam-4071	311	3	)	)	PUNCT
ejpam-4071	311	4	2016:53	2016:53	NUM
ejpam-4071	311	5	.	.	PUNCT