id	sid	tid	token	lemma	pos
ejpam-6527	1	1	european	european	PROPN
ejpam-6527	1	2	journal	journal	PROPN
ejpam-6527	1	3	of	of	ADP
ejpam-6527	1	4	pure	pure	ADJ
ejpam-6527	1	5	and	and	CCONJ
ejpam-6527	1	6	applied	applied	ADJ
ejpam-6527	1	7	mathematics	mathematic	NOUN
ejpam-6527	1	8	2025	2025	NUM
ejpam-6527	1	9	,	,	PUNCT
ejpam-6527	1	10	vol	vol	NOUN
ejpam-6527	1	11	.	.	PROPN
ejpam-6527	1	12	18	18	NUM
ejpam-6527	1	13	,	,	PUNCT
ejpam-6527	1	14	issue	issue	NOUN
ejpam-6527	1	15	3	3	NUM
ejpam-6527	1	16	,	,	PUNCT
ejpam-6527	1	17	article	article	NOUN
ejpam-6527	1	18	number	number	NOUN
ejpam-6527	1	19	6527	6527	NUM
ejpam-6527	1	20	issn	issn	VERB
ejpam-6527	1	21	1307	1307	NUM
ejpam-6527	1	22	-	-	SYM
ejpam-6527	1	23	5543	5543	NUM
ejpam-6527	1	24	–	–	PUNCT
ejpam-6527	1	25	ejpam.com	ejpam.com	X
ejpam-6527	1	26	published	publish	VERB
ejpam-6527	1	27	by	by	ADP
ejpam-6527	1	28	new	new	PROPN
ejpam-6527	1	29	york	york	PROPN
ejpam-6527	1	30	business	business	PROPN
ejpam-6527	1	31	global	global	ADJ
ejpam-6527	1	32	equivalence	equivalence	NOUN
ejpam-6527	1	33	and	and	CCONJ
ejpam-6527	1	34	stability	stability	NOUN
ejpam-6527	1	35	of	of	ADP
ejpam-6527	1	36	compactness	compactness	NOUN
ejpam-6527	1	37	in	in	ADP
ejpam-6527	1	38	operator	operator	NOUN
ejpam-6527	1	39	spaces	space	NOUN
ejpam-6527	1	40	over	over	ADP
ejpam-6527	1	41	the	the	DET
ejpam-6527	1	42	non	non	ADJ
ejpam-6527	1	43	-	-	ADJ
ejpam-6527	1	44	commutative	commutative	ADJ
ejpam-6527	1	45	torus	torus	NOUN
ejpam-6527	1	46	mortada	mortada	PROPN
ejpam-6527	1	47	s.	s.	PROPN
ejpam-6527	1	48	ali1,∗	ali1,∗	PROPN
ejpam-6527	1	49	,	,	PUNCT
ejpam-6527	1	50	abd	abd	PROPN
ejpam-6527	1	51	elmotaleb	elmotaleb	PROPN
ejpam-6527	1	52	a.	a.	PROPN
ejpam-6527	1	53	m.	m.	PROPN
ejpam-6527	2	1	a.2	a.2	PROPN
ejpam-6527	2	2	,	,	PUNCT
ejpam-6527	2	3	ibtisam	ibtisam	PROPN
ejpam-6527	2	4	m.	m.	NOUN
ejpam-6527	2	5	o.	o.	PROPN
ejpam-6527	2	6	mohammed1	mohammed1	PROPN
ejpam-6527	2	7	1	1	NUM
ejpam-6527	2	8	department	department	NOUN
ejpam-6527	2	9	of	of	ADP
ejpam-6527	2	10	mathematics	mathematic	NOUN
ejpam-6527	2	11	,	,	PUNCT
ejpam-6527	2	12	college	college	NOUN
ejpam-6527	2	13	of	of	ADP
ejpam-6527	2	14	science	science	PROPN
ejpam-6527	2	15	,	,	PUNCT
ejpam-6527	2	16	al	al	PROPN
ejpam-6527	2	17	-	-	PUNCT
ejpam-6527	2	18	baha	baha	PROPN
ejpam-6527	2	19	university	university	PROPN
ejpam-6527	2	20	,	,	PUNCT
ejpam-6527	2	21	p.o	p.o	PROPN
ejpam-6527	2	22	.	.	PROPN
ejpam-6527	2	23	box	box	PROPN
ejpam-6527	2	24	1988	1988	NUM
ejpam-6527	2	25	,	,	PUNCT
ejpam-6527	2	26	ksa	ksa	PROPN
ejpam-6527	2	27	.	.	PROPN
ejpam-6527	2	28	2	2	NUM
ejpam-6527	2	29	department	department	NOUN
ejpam-6527	2	30	of	of	ADP
ejpam-6527	2	31	mathematics	mathematic	NOUN
ejpam-6527	2	32	,	,	PUNCT
ejpam-6527	2	33	college	college	NOUN
ejpam-6527	2	34	of	of	ADP
ejpam-6527	2	35	science	science	NOUN
ejpam-6527	2	36	and	and	CCONJ
ejpam-6527	2	37	humanity	humanity	NOUN
ejpam-6527	2	38	,	,	PUNCT
ejpam-6527	2	39	prince	prince	PROPN
ejpam-6527	2	40	sattam	sattam	PROPN
ejpam-6527	2	41	bin	bin	PROPN
ejpam-6527	2	42	abdulaziz	abdulaziz	PROPN
ejpam-6527	2	43	university	university	PROPN
ejpam-6527	2	44	,	,	PUNCT
ejpam-6527	2	45	sulail	sulail	NOUN
ejpam-6527	2	46	,	,	PUNCT
ejpam-6527	2	47	al	al	PROPN
ejpam-6527	2	48	-	-	PUNCT
ejpam-6527	2	49	kharj	kharj	PROPN
ejpam-6527	2	50	11942	11942	NUM
ejpam-6527	2	51	,	,	PUNCT
ejpam-6527	2	52	ksa	ksa	PROPN
ejpam-6527	2	53	.	.	PROPN
ejpam-6527	2	54	abstract	abstract	PROPN
ejpam-6527	2	55	.	.	PUNCT
ejpam-6527	3	1	we	we	PRON
ejpam-6527	3	2	investigate	investigate	VERB
ejpam-6527	3	3	compactness	compactness	NOUN
ejpam-6527	3	4	in	in	ADP
ejpam-6527	3	5	operator	operator	NOUN
ejpam-6527	3	6	spaces	space	NOUN
ejpam-6527	3	7	over	over	ADP
ejpam-6527	3	8	the	the	DET
ejpam-6527	3	9	non	non	ADJ
ejpam-6527	3	10	-	-	ADJ
ejpam-6527	3	11	commutative	commutative	ADJ
ejpam-6527	3	12	torus	torus	PROPN
ejpam-6527	3	13	aθ	aθ	NOUN
ejpam-6527	3	14	,	,	PUNCT
ejpam-6527	3	15	applying	apply	VERB
ejpam-6527	3	16	the	the	DET
ejpam-6527	3	17	structure	structure	NOUN
ejpam-6527	3	18	of	of	ADP
ejpam-6527	3	19	non	non	ADJ
ejpam-6527	3	20	-	-	ADJ
ejpam-6527	3	21	commutative	commutative	ADJ
ejpam-6527	3	22	c∗-algebras	c∗-algebra	NOUN
ejpam-6527	3	23	as	as	ADV
ejpam-6527	3	24	well	well	ADV
ejpam-6527	3	25	as	as	ADP
ejpam-6527	3	26	compact	compact	ADJ
ejpam-6527	3	27	operators	operator	NOUN
ejpam-6527	3	28	acting	act	VERB
ejpam-6527	3	29	on	on	ADP
ejpam-6527	3	30	hilbert	hilbert	PROPN
ejpam-6527	3	31	aθ	aθ	NOUN
ejpam-6527	3	32	-	-	PUNCT
ejpam-6527	3	33	modules	module	NOUN
ejpam-6527	3	34	,	,	PUNCT
ejpam-6527	3	35	and	and	CCONJ
ejpam-6527	3	36	provide	provide	VERB
ejpam-6527	3	37	a	a	DET
ejpam-6527	3	38	characterization	characterization	NOUN
ejpam-6527	3	39	of	of	ADP
ejpam-6527	3	40	compactness	compactness	NOUN
ejpam-6527	3	41	in	in	ADP
ejpam-6527	3	42	the	the	DET
ejpam-6527	3	43	framework	framework	NOUN
ejpam-6527	3	44	of	of	ADP
ejpam-6527	3	45	operator	operator	NOUN
ejpam-6527	3	46	spaces	space	NOUN
ejpam-6527	3	47	.	.	PUNCT
ejpam-6527	4	1	key	key	ADJ
ejpam-6527	4	2	results	result	NOUN
ejpam-6527	4	3	include	include	VERB
ejpam-6527	4	4	the	the	DET
ejpam-6527	4	5	equivalence	equivalence	NOUN
ejpam-6527	4	6	between	between	ADP
ejpam-6527	4	7	classical	classical	ADJ
ejpam-6527	4	8	and	and	CCONJ
ejpam-6527	4	9	complete	complete	ADJ
ejpam-6527	4	10	compactness	compactness	NOUN
ejpam-6527	4	11	,	,	PUNCT
ejpam-6527	4	12	and	and	CCONJ
ejpam-6527	4	13	the	the	DET
ejpam-6527	4	14	stability	stability	NOUN
ejpam-6527	4	15	of	of	ADP
ejpam-6527	4	16	compactness	compactness	NOUN
ejpam-6527	4	17	under	under	ADP
ejpam-6527	4	18	tensor	tensor	NOUN
ejpam-6527	4	19	products	product	NOUN
ejpam-6527	4	20	.	.	PUNCT
ejpam-6527	5	1	applications	application	NOUN
ejpam-6527	5	2	and	and	CCONJ
ejpam-6527	5	3	examples	example	NOUN
ejpam-6527	5	4	of	of	ADP
ejpam-6527	5	5	compact	compact	ADJ
ejpam-6527	5	6	operators	operator	NOUN
ejpam-6527	5	7	in	in	ADP
ejpam-6527	5	8	operator	operator	NOUN
ejpam-6527	5	9	spaces	space	NOUN
ejpam-6527	5	10	over	over	ADP
ejpam-6527	5	11	the	the	DET
ejpam-6527	5	12	non	non	ADJ
ejpam-6527	5	13	-	-	ADJ
ejpam-6527	5	14	commutative	commutative	ADJ
ejpam-6527	5	15	torus	torus	NOUN
ejpam-6527	5	16	aθ	aθ	NOUN
ejpam-6527	5	17	are	be	AUX
ejpam-6527	5	18	presented	present	VERB
ejpam-6527	5	19	.	.	PUNCT
ejpam-6527	6	1	we	we	PRON
ejpam-6527	6	2	also	also	ADV
ejpam-6527	6	3	discuss	discuss	VERB
ejpam-6527	6	4	limitations	limitation	NOUN
ejpam-6527	6	5	and	and	CCONJ
ejpam-6527	6	6	propose	propose	VERB
ejpam-6527	6	7	future	future	ADJ
ejpam-6527	6	8	research	research	NOUN
ejpam-6527	6	9	directions	direction	NOUN
ejpam-6527	6	10	to	to	PART
ejpam-6527	6	11	extend	extend	VERB
ejpam-6527	6	12	these	these	DET
ejpam-6527	6	13	results	result	NOUN
ejpam-6527	6	14	to	to	ADP
ejpam-6527	6	15	more	more	ADJ
ejpam-6527	6	16	general	general	ADJ
ejpam-6527	6	17	settings	setting	NOUN
ejpam-6527	6	18	.	.	PUNCT
ejpam-6527	7	1	2020	2020	NUM
ejpam-6527	7	2	mathematics	mathematic	NOUN
ejpam-6527	7	3	subject	subject	NOUN
ejpam-6527	7	4	classifications	classification	NOUN
ejpam-6527	7	5	:	:	PUNCT
ejpam-6527	7	6	46l08	46l08	NUM
ejpam-6527	7	7	,	,	PUNCT
ejpam-6527	7	8	47l25	47l25	NUM
ejpam-6527	7	9	,	,	PUNCT
ejpam-6527	7	10	46l87	46l87	NUM
ejpam-6527	7	11	key	key	ADJ
ejpam-6527	7	12	words	word	NOUN
ejpam-6527	7	13	and	and	CCONJ
ejpam-6527	7	14	phrases	phrase	NOUN
ejpam-6527	7	15	:	:	PUNCT
ejpam-6527	7	16	compactness	compactness	NOUN
ejpam-6527	7	17	,	,	PUNCT
ejpam-6527	7	18	operator	operator	NOUN
ejpam-6527	7	19	spaces	space	NOUN
ejpam-6527	7	20	,	,	PUNCT
ejpam-6527	7	21	non	non	ADJ
ejpam-6527	7	22	-	-	ADJ
ejpam-6527	7	23	commutative	commutative	ADJ
ejpam-6527	7	24	torus	torus	NOUN
ejpam-6527	7	25	,	,	PUNCT
ejpam-6527	7	26	hilbert	hilbert	NOUN
ejpam-6527	7	27	modules	module	NOUN
ejpam-6527	7	28	,	,	PUNCT
ejpam-6527	7	29	quantum	quantum	ADJ
ejpam-6527	7	30	metric	metric	ADJ
ejpam-6527	7	31	spaces	space	NOUN
ejpam-6527	7	32	,	,	PUNCT
ejpam-6527	7	33	tensor	tensor	NOUN
ejpam-6527	7	34	products	product	NOUN
ejpam-6527	7	35	1	1	NUM
ejpam-6527	7	36	.	.	PUNCT
ejpam-6527	8	1	introduction	introduction	NOUN
ejpam-6527	8	2	compactness	compactness	NOUN
ejpam-6527	8	3	plays	play	VERB
ejpam-6527	8	4	a	a	DET
ejpam-6527	8	5	foundational	foundational	ADJ
ejpam-6527	8	6	role	role	NOUN
ejpam-6527	8	7	in	in	ADP
ejpam-6527	8	8	the	the	DET
ejpam-6527	8	9	theory	theory	NOUN
ejpam-6527	8	10	of	of	ADP
ejpam-6527	8	11	operators	operator	NOUN
ejpam-6527	8	12	on	on	ADP
ejpam-6527	8	13	banach	banach	NOUN
ejpam-6527	8	14	and	and	CCONJ
ejpam-6527	8	15	hilbert	hilbert	NOUN
ejpam-6527	8	16	spaces	space	NOUN
ejpam-6527	8	17	,	,	PUNCT
ejpam-6527	8	18	as	as	SCONJ
ejpam-6527	8	19	highlighted	highlight	VERB
ejpam-6527	8	20	in	in	ADP
ejpam-6527	8	21	[	[	X
ejpam-6527	8	22	1	1	NUM
ejpam-6527	8	23	,	,	PUNCT
ejpam-6527	8	24	2	2	NUM
ejpam-6527	8	25	]	]	PUNCT
ejpam-6527	8	26	.	.	PUNCT
ejpam-6527	9	1	such	such	DET
ejpam-6527	9	2	an	an	DET
ejpam-6527	9	3	operator	operator	NOUN
ejpam-6527	9	4	is	be	AUX
ejpam-6527	9	5	called	call	VERB
ejpam-6527	9	6	compact	compact	ADJ
ejpam-6527	9	7	if	if	SCONJ
ejpam-6527	9	8	it	it	PRON
ejpam-6527	9	9	sends	send	VERB
ejpam-6527	9	10	bounded	bounded	ADJ
ejpam-6527	9	11	subsets	subset	NOUN
ejpam-6527	9	12	to	to	ADP
ejpam-6527	9	13	relatively	relatively	ADV
ejpam-6527	9	14	compact	compact	ADJ
ejpam-6527	9	15	subsets	subset	NOUN
ejpam-6527	9	16	,	,	PUNCT
ejpam-6527	9	17	and	and	CCONJ
ejpam-6527	9	18	it	it	PRON
ejpam-6527	9	19	has	have	VERB
ejpam-6527	9	20	significant	significant	ADJ
ejpam-6527	9	21	properties	property	NOUN
ejpam-6527	9	22	in	in	ADP
ejpam-6527	9	23	operator	operator	NOUN
ejpam-6527	9	24	theory	theory	NOUN
ejpam-6527	9	25	,	,	PUNCT
ejpam-6527	9	26	as	as	ADV
ejpam-6527	9	27	well	well	ADV
ejpam-6527	9	28	as	as	ADP
ejpam-6527	9	29	connections	connection	NOUN
ejpam-6527	9	30	to	to	ADP
ejpam-6527	9	31	compactness	compactness	NOUN
ejpam-6527	9	32	in	in	ADP
ejpam-6527	9	33	topological	topological	ADJ
ejpam-6527	9	34	spaces	space	NOUN
ejpam-6527	9	35	,	,	PUNCT
ejpam-6527	9	36	spectral	spectral	ADJ
ejpam-6527	9	37	theory	theory	NOUN
ejpam-6527	9	38	,	,	PUNCT
ejpam-6527	9	39	and	and	CCONJ
ejpam-6527	9	40	even	even	ADV
ejpam-6527	9	41	functional	functional	ADJ
ejpam-6527	9	42	calculus	calculus	NOUN
ejpam-6527	9	43	.	.	PUNCT
ejpam-6527	10	1	while	while	SCONJ
ejpam-6527	10	2	the	the	DET
ejpam-6527	10	3	classical	classical	ADJ
ejpam-6527	10	4	theory	theory	NOUN
ejpam-6527	10	5	of	of	ADP
ejpam-6527	10	6	compact	compact	ADJ
ejpam-6527	10	7	operators	operator	NOUN
ejpam-6527	10	8	focuses	focus	VERB
ejpam-6527	10	9	on	on	ADP
ejpam-6527	10	10	spaces	space	NOUN
ejpam-6527	10	11	of	of	ADP
ejpam-6527	10	12	functions	function	NOUN
ejpam-6527	10	13	and	and	CCONJ
ejpam-6527	10	14	matrices	matrix	NOUN
ejpam-6527	10	15	,	,	PUNCT
ejpam-6527	10	16	the	the	DET
ejpam-6527	10	17	study	study	NOUN
ejpam-6527	10	18	of	of	ADP
ejpam-6527	10	19	non	non	ADJ
ejpam-6527	10	20	-	-	ADJ
ejpam-6527	10	21	commutative	commutative	ADJ
ejpam-6527	10	22	operator	operator	NOUN
ejpam-6527	10	23	algebras	algebra	NOUN
ejpam-6527	10	24	presents	present	VERB
ejpam-6527	10	25	an	an	DET
ejpam-6527	10	26	intriguing	intriguing	ADJ
ejpam-6527	10	27	new	new	ADJ
ejpam-6527	10	28	context	context	NOUN
ejpam-6527	10	29	for	for	ADP
ejpam-6527	10	30	this	this	DET
ejpam-6527	10	31	theory	theory	NOUN
ejpam-6527	10	32	.	.	PUNCT
ejpam-6527	11	1	the	the	DET
ejpam-6527	11	2	non	non	ADJ
ejpam-6527	11	3	-	-	ADJ
ejpam-6527	11	4	commutative	commutative	ADJ
ejpam-6527	11	5	torus	torus	NOUN
ejpam-6527	11	6	represents	represent	VERB
ejpam-6527	11	7	one	one	NUM
ejpam-6527	11	8	of	of	ADP
ejpam-6527	11	9	the	the	DET
ejpam-6527	11	10	simplest	simple	ADJ
ejpam-6527	11	11	and	and	CCONJ
ejpam-6527	11	12	most	most	ADV
ejpam-6527	11	13	studied	study	VERB
ejpam-6527	11	14	examples	example	NOUN
ejpam-6527	11	15	of	of	ADP
ejpam-6527	11	16	a	a	DET
ejpam-6527	11	17	non	non	ADJ
ejpam-6527	11	18	-	-	ADJ
ejpam-6527	11	19	commutative	commutative	ADJ
ejpam-6527	11	20	c∗-algebra[3	c∗-algebra[3	NOUN
ejpam-6527	11	21	,	,	PUNCT
ejpam-6527	11	22	4	4	NUM
ejpam-6527	11	23	]	]	PUNCT
ejpam-6527	11	24	.	.	PUNCT
ejpam-6527	12	1	it	it	PRON
ejpam-6527	12	2	plays	play	VERB
ejpam-6527	12	3	a	a	DET
ejpam-6527	12	4	central	central	ADJ
ejpam-6527	12	5	role	role	NOUN
ejpam-6527	12	6	in	in	ADP
ejpam-6527	12	7	various	various	ADJ
ejpam-6527	12	8	branches	branch	NOUN
ejpam-6527	12	9	of	of	ADP
ejpam-6527	12	10	mathematics	mathematic	NOUN
ejpam-6527	12	11	and	and	CCONJ
ejpam-6527	12	12	theoretical	theoretical	ADJ
ejpam-6527	12	13	physics	physics	NOUN
ejpam-6527	12	14	,	,	PUNCT
ejpam-6527	12	15	ranging	range	VERB
ejpam-6527	12	16	from	from	ADP
ejpam-6527	12	17	quantum	quantum	ADJ
ejpam-6527	12	18	mechanics	mechanic	NOUN
ejpam-6527	12	19	and	and	CCONJ
ejpam-6527	12	20	topological	topological	ADJ
ejpam-6527	12	21	∗corresponding	∗corresponde	VERB
ejpam-6527	12	22	author	author	NOUN
ejpam-6527	12	23	.	.	PUNCT
ejpam-6527	13	1	doi	doi	NOUN
ejpam-6527	13	2	:	:	PUNCT
ejpam-6527	13	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6527	https://doi.org/10.29020/nybg.ejpam.v18i3.6527	PROPN
ejpam-6527	13	4	email	email	NOUN
ejpam-6527	13	5	addresses	address	NOUN
ejpam-6527	13	6	:	:	PUNCT
ejpam-6527	13	7	mortada@bu.edu.sa	mortada@bu.edu.sa	PROPN
ejpam-6527	13	8	(	(	PUNCT
ejpam-6527	13	9	m.	m.	PROPN
ejpam-6527	13	10	s.	s.	PROPN
ejpam-6527	13	11	ali	ali	PROPN
ejpam-6527	13	12	)	)	PUNCT
ejpam-6527	13	13	,	,	PUNCT
ejpam-6527	13	14	aa.alameen@psau.edu.sa	aa.alameen@psau.edu.sa	PROPN
ejpam-6527	13	15	(	(	PUNCT
ejpam-6527	13	16	a.	a.	PROPN
ejpam-6527	13	17	e.	e.	PROPN
ejpam-6527	13	18	a.	a.	PROPN
ejpam-6527	13	19	m.	m.	PROPN
ejpam-6527	13	20	a.	a.	NOUN
ejpam-6527	13	21	elamin	elamin	PROPN
ejpam-6527	13	22	)	)	PUNCT
ejpam-6527	13	23	,	,	PUNCT
ejpam-6527	13	24	a.mahjoub@bu.edu.sa	a.mahjoub@bu.edu.sa	PROPN
ejpam-6527	13	25	(	(	PUNCT
ejpam-6527	13	26	i.	i.	PROPN
ejpam-6527	13	27	m.	m.	PROPN
ejpam-6527	13	28	o.	o.	PROPN
ejpam-6527	13	29	mohammed	mohammed	PROPN
ejpam-6527	13	30	)	)	PUNCT
ejpam-6527	13	31	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6527	14	1	1	1	NUM
ejpam-6527	14	2	copyright	copyright	NOUN
ejpam-6527	14	3	:	:	PUNCT
ejpam-6527	14	4	©	©	PROPN
ejpam-6527	14	5	2025	2025	NUM
ejpam-6527	14	6	the	the	DET
ejpam-6527	14	7	author(s	author(s	NOUN
ejpam-6527	14	8	)	)	PUNCT
ejpam-6527	14	9	.	.	PUNCT
ejpam-6527	15	1	(	(	PUNCT
ejpam-6527	15	2	cc	cc	NOUN
ejpam-6527	15	3	by	by	ADP
ejpam-6527	15	4	-	-	PUNCT
ejpam-6527	15	5	nc	nc	PROPN
ejpam-6527	15	6	4.0	4.0	NUM
ejpam-6527	15	7	)	)	PUNCT
ejpam-6527	15	8	m.	m.	NOUN
ejpam-6527	15	9	s.	s.	PROPN
ejpam-6527	15	10	ali	ali	PROPN
ejpam-6527	15	11	et	et	PROPN
ejpam-6527	15	12	al	al	PROPN
ejpam-6527	15	13	.	.	PUNCT
ejpam-6527	15	14	/	/	SYM
ejpam-6527	15	15	eur	eur	PROPN
ejpam-6527	15	16	.	.	PUNCT
ejpam-6527	16	1	j.	j.	PROPN
ejpam-6527	16	2	pure	pure	PROPN
ejpam-6527	16	3	appl	appl	PROPN
ejpam-6527	16	4	.	.	PROPN
ejpam-6527	16	5	math	math	PROPN
ejpam-6527	16	6	,	,	PUNCT
ejpam-6527	16	7	18	18	NUM
ejpam-6527	16	8	(	(	PUNCT
ejpam-6527	16	9	3	3	NUM
ejpam-6527	16	10	)	)	PUNCT
ejpam-6527	16	11	(	(	PUNCT
ejpam-6527	16	12	2025	2025	NUM
ejpam-6527	16	13	)	)	PUNCT
ejpam-6527	16	14	,	,	PUNCT
ejpam-6527	16	15	6527	6527	NUM
ejpam-6527	16	16	2	2	NUM
ejpam-6527	16	17	of	of	ADP
ejpam-6527	16	18	9	9	NUM
ejpam-6527	16	19	dynamics	dynamic	NOUN
ejpam-6527	16	20	to	to	ADP
ejpam-6527	16	21	non	non	ADJ
ejpam-6527	16	22	-	-	ADJ
ejpam-6527	16	23	commutative	commutative	ADJ
ejpam-6527	16	24	geometric	geometric	ADJ
ejpam-6527	16	25	spaces	space	NOUN
ejpam-6527	16	26	.	.	PUNCT
ejpam-6527	17	1	the	the	DET
ejpam-6527	17	2	non	non	ADJ
ejpam-6527	17	3	-	-	ADJ
ejpam-6527	17	4	commutative	commutative	ADJ
ejpam-6527	17	5	torus	torus	NOUN
ejpam-6527	17	6	aθ	aθ	NOUN
ejpam-6527	17	7	is	be	AUX
ejpam-6527	17	8	defined	define	VERB
ejpam-6527	17	9	as	as	ADP
ejpam-6527	17	10	the	the	DET
ejpam-6527	17	11	algebra	algebra	NOUN
ejpam-6527	17	12	generated	generate	VERB
ejpam-6527	17	13	by	by	ADP
ejpam-6527	17	14	two	two	NUM
ejpam-6527	17	15	elements	element	NOUN
ejpam-6527	17	16	,	,	PUNCT
ejpam-6527	17	17	u	u	NOUN
ejpam-6527	17	18	and	and	CCONJ
ejpam-6527	17	19	v	v	NOUN
ejpam-6527	17	20	,	,	PUNCT
ejpam-6527	17	21	with	with	ADP
ejpam-6527	17	22	the	the	DET
ejpam-6527	17	23	relation	relation	NOUN
ejpam-6527	17	24	uv	uv	NOUN
ejpam-6527	17	25	=	=	PROPN
ejpam-6527	17	26	e2πiθv	e2πiθv	PROPN
ejpam-6527	17	27	u	u	NOUN
ejpam-6527	17	28	,	,	PUNCT
ejpam-6527	17	29	where	where	SCONJ
ejpam-6527	17	30	θ	θ	PROPN
ejpam-6527	17	31	is	be	AUX
ejpam-6527	17	32	a	a	DET
ejpam-6527	17	33	positive	positive	ADJ
ejpam-6527	17	34	angle	angle	NOUN
ejpam-6527	17	35	argument	argument	NOUN
ejpam-6527	17	36	.	.	PUNCT
ejpam-6527	18	1	for	for	ADP
ejpam-6527	18	2	instance	instance	NOUN
ejpam-6527	18	3	,	,	PUNCT
ejpam-6527	18	4	this	this	DET
ejpam-6527	18	5	algebra	algebra	NOUN
ejpam-6527	18	6	possesses	possess	VERB
ejpam-6527	18	7	a	a	DET
ejpam-6527	18	8	rich	rich	ADJ
ejpam-6527	18	9	representation	representation	NOUN
ejpam-6527	18	10	theory	theory	NOUN
ejpam-6527	18	11	and	and	CCONJ
ejpam-6527	18	12	serves	serve	VERB
ejpam-6527	18	13	as	as	ADP
ejpam-6527	18	14	a	a	DET
ejpam-6527	18	15	non	non	ADJ
ejpam-6527	18	16	-	-	ADJ
ejpam-6527	18	17	commutative	commutative	ADJ
ejpam-6527	18	18	generalization	generalization	NOUN
ejpam-6527	18	19	of	of	ADP
ejpam-6527	18	20	the	the	DET
ejpam-6527	18	21	classical	classical	ADJ
ejpam-6527	18	22	two	two	NUM
ejpam-6527	18	23	-	-	PUNCT
ejpam-6527	18	24	torus	torus	NOUN
ejpam-6527	18	25	.	.	PUNCT
ejpam-6527	19	1	in	in	ADP
ejpam-6527	19	2	other	other	ADJ
ejpam-6527	19	3	words	word	NOUN
ejpam-6527	19	4	,	,	PUNCT
ejpam-6527	19	5	the	the	DET
ejpam-6527	19	6	non	non	ADJ
ejpam-6527	19	7	-	-	ADJ
ejpam-6527	19	8	commutative	commutative	ADJ
ejpam-6527	19	9	torus	torus	NOUN
ejpam-6527	19	10	has	have	VERB
ejpam-6527	19	11	a	a	DET
ejpam-6527	19	12	rich	rich	ADJ
ejpam-6527	19	13	history	history	NOUN
ejpam-6527	19	14	,	,	PUNCT
ejpam-6527	19	15	related	relate	VERB
ejpam-6527	19	16	to	to	ADP
ejpam-6527	19	17	studies	study	NOUN
ejpam-6527	19	18	in	in	ADP
ejpam-6527	19	19	spectral	spectral	ADJ
ejpam-6527	19	20	theory	theory	NOUN
ejpam-6527	19	21	and	and	CCONJ
ejpam-6527	19	22	representation	representation	NOUN
ejpam-6527	19	23	theory	theory	NOUN
ejpam-6527	19	24	of	of	ADP
ejpam-6527	19	25	c∗-algebras[5	c∗-algebras[5	NOUN
ejpam-6527	19	26	]	]	PUNCT
ejpam-6527	19	27	.	.	PUNCT
ejpam-6527	20	1	in	in	ADP
ejpam-6527	20	2	this	this	DET
ejpam-6527	20	3	paper	paper	NOUN
ejpam-6527	20	4	,	,	PUNCT
ejpam-6527	20	5	we	we	PRON
ejpam-6527	20	6	study	study	VERB
ejpam-6527	20	7	the	the	DET
ejpam-6527	20	8	compactness	compactness	NOUN
ejpam-6527	20	9	properties	property	NOUN
ejpam-6527	20	10	of	of	ADP
ejpam-6527	20	11	operators	operator	NOUN
ejpam-6527	20	12	on	on	ADP
ejpam-6527	20	13	operator	operator	NOUN
ejpam-6527	20	14	spaces	space	NOUN
ejpam-6527	20	15	related	relate	VERB
ejpam-6527	20	16	to	to	ADP
ejpam-6527	20	17	aθ	aθ	NOUN
ejpam-6527	20	18	.	.	PUNCT
ejpam-6527	21	1	operator	operator	NOUN
ejpam-6527	21	2	spaces	space	NOUN
ejpam-6527	21	3	are	be	AUX
ejpam-6527	21	4	subspaces	subspace	NOUN
ejpam-6527	21	5	of	of	ADP
ejpam-6527	21	6	operator	operator	NOUN
ejpam-6527	21	7	algebras	algebra	NOUN
ejpam-6527	21	8	equipped	equip	VERB
ejpam-6527	21	9	with	with	ADP
ejpam-6527	21	10	a	a	DET
ejpam-6527	21	11	matrix	matrix	NOUN
ejpam-6527	21	12	norm	norm	NOUN
ejpam-6527	21	13	structure	structure	NOUN
ejpam-6527	21	14	that	that	PRON
ejpam-6527	21	15	satisfies	satisfy	VERB
ejpam-6527	21	16	the	the	DET
ejpam-6527	21	17	ruan	ruan	PROPN
ejpam-6527	21	18	axioms[6–8	axioms[6–8	PROPN
ejpam-6527	21	19	]	]	PUNCT
ejpam-6527	21	20	.	.	PUNCT
ejpam-6527	22	1	operator	operator	NOUN
ejpam-6527	22	2	spaces	space	NOUN
ejpam-6527	22	3	provide	provide	VERB
ejpam-6527	22	4	a	a	DET
ejpam-6527	22	5	rigorous	rigorous	ADJ
ejpam-6527	22	6	framework	framework	NOUN
ejpam-6527	22	7	for	for	ADP
ejpam-6527	22	8	analyzing	analyze	VERB
ejpam-6527	22	9	operator	operator	NOUN
ejpam-6527	22	10	behavior	behavior	NOUN
ejpam-6527	22	11	,	,	PUNCT
ejpam-6527	22	12	particularly	particularly	ADV
ejpam-6527	22	13	in	in	ADP
ejpam-6527	22	14	the	the	DET
ejpam-6527	22	15	context	context	NOUN
ejpam-6527	22	16	of	of	ADP
ejpam-6527	22	17	completely	completely	ADV
ejpam-6527	22	18	bounded	bounded	ADJ
ejpam-6527	22	19	maps	map	NOUN
ejpam-6527	22	20	.	.	PUNCT
ejpam-6527	23	1	these	these	DET
ejpam-6527	23	2	spaces	space	NOUN
ejpam-6527	23	3	have	have	AUX
ejpam-6527	23	4	demonstrated	demonstrate	VERB
ejpam-6527	23	5	their	their	PRON
ejpam-6527	23	6	fundamental	fundamental	ADJ
ejpam-6527	23	7	role	role	NOUN
ejpam-6527	23	8	as	as	ADP
ejpam-6527	23	9	a	a	DET
ejpam-6527	23	10	powerful	powerful	ADJ
ejpam-6527	23	11	tool	tool	NOUN
ejpam-6527	23	12	across	across	ADP
ejpam-6527	23	13	various	various	ADJ
ejpam-6527	23	14	disciplines	discipline	NOUN
ejpam-6527	23	15	,	,	PUNCT
ejpam-6527	23	16	including	include	VERB
ejpam-6527	23	17	quantum	quantum	NOUN
ejpam-6527	23	18	computing	computing	NOUN
ejpam-6527	23	19	,	,	PUNCT
ejpam-6527	23	20	harmonic	harmonic	ADJ
ejpam-6527	23	21	analysis	analysis	NOUN
ejpam-6527	23	22	,	,	PUNCT
ejpam-6527	23	23	and	and	CCONJ
ejpam-6527	23	24	operator	operator	NOUN
ejpam-6527	23	25	algebras[9	algebras[9	PROPN
ejpam-6527	23	26	,	,	PUNCT
ejpam-6527	23	27	10	10	NUM
ejpam-6527	23	28	]	]	PUNCT
ejpam-6527	23	29	.	.	PUNCT
ejpam-6527	24	1	compactness	compactness	NOUN
ejpam-6527	24	2	for	for	ADP
ejpam-6527	24	3	operator	operator	NOUN
ejpam-6527	24	4	spaces	space	NOUN
ejpam-6527	24	5	is	be	AUX
ejpam-6527	24	6	of	of	ADP
ejpam-6527	24	7	special	special	ADJ
ejpam-6527	24	8	importance	importance	NOUN
ejpam-6527	24	9	in	in	ADP
ejpam-6527	24	10	the	the	DET
ejpam-6527	24	11	non	non	ADJ
ejpam-6527	24	12	-	-	ADJ
ejpam-6527	24	13	commutative	commutative	ADJ
ejpam-6527	24	14	realm	realm	NOUN
ejpam-6527	24	15	,	,	PUNCT
ejpam-6527	24	16	as	as	SCONJ
ejpam-6527	24	17	it	it	PRON
ejpam-6527	24	18	combines	combine	VERB
ejpam-6527	24	19	classical	classical	ADJ
ejpam-6527	24	20	notions	notion	NOUN
ejpam-6527	24	21	of	of	ADP
ejpam-6527	24	22	compactness	compactness	NOUN
ejpam-6527	24	23	with	with	ADP
ejpam-6527	24	24	the	the	DET
ejpam-6527	24	25	well	well	ADV
ejpam-6527	24	26	-	-	PUNCT
ejpam-6527	24	27	developed	develop	VERB
ejpam-6527	24	28	theory	theory	NOUN
ejpam-6527	24	29	of	of	ADP
ejpam-6527	24	30	completely	completely	ADV
ejpam-6527	24	31	bounded	bounded	ADJ
ejpam-6527	24	32	maps	map	NOUN
ejpam-6527	24	33	.	.	PUNCT
ejpam-6527	25	1	this	this	PRON
ejpam-6527	25	2	provides	provide	VERB
ejpam-6527	25	3	a	a	DET
ejpam-6527	25	4	synthesis	synthesis	NOUN
ejpam-6527	25	5	of	of	ADP
ejpam-6527	25	6	functional	functional	ADJ
ejpam-6527	25	7	analysis	analysis	NOUN
ejpam-6527	25	8	,	,	PUNCT
ejpam-6527	25	9	operator	operator	NOUN
ejpam-6527	25	10	algebras	algebra	NOUN
ejpam-6527	25	11	,	,	PUNCT
ejpam-6527	25	12	and	and	CCONJ
ejpam-6527	25	13	the	the	DET
ejpam-6527	25	14	structure	structure	NOUN
ejpam-6527	25	15	of	of	ADP
ejpam-6527	25	16	the	the	DET
ejpam-6527	25	17	non	non	ADJ
ejpam-6527	25	18	-	-	ADJ
ejpam-6527	25	19	commutative	commutative	ADJ
ejpam-6527	25	20	torus	torus	NOUN
ejpam-6527	25	21	for	for	ADP
ejpam-6527	25	22	compact	compact	ADJ
ejpam-6527	25	23	operators	operator	NOUN
ejpam-6527	25	24	on	on	ADP
ejpam-6527	25	25	operator	operator	NOUN
ejpam-6527	25	26	spaces	space	NOUN
ejpam-6527	25	27	over	over	ADP
ejpam-6527	25	28	aθ[11–13	aθ[11–13	NUM
ejpam-6527	25	29	]	]	PUNCT
ejpam-6527	25	30	.	.	PUNCT
ejpam-6527	26	1	the	the	DET
ejpam-6527	26	2	notion	notion	NOUN
ejpam-6527	26	3	of	of	ADP
ejpam-6527	26	4	compactness	compactness	NOUN
ejpam-6527	26	5	in	in	ADP
ejpam-6527	26	6	operator	operator	NOUN
ejpam-6527	26	7	spaces	space	NOUN
ejpam-6527	26	8	,	,	PUNCT
ejpam-6527	26	9	although	although	SCONJ
ejpam-6527	26	10	distinct	distinct	ADJ
ejpam-6527	26	11	from	from	ADP
ejpam-6527	26	12	its	its	PRON
ejpam-6527	26	13	classical	classical	ADJ
ejpam-6527	26	14	analogue	analogue	NOUN
ejpam-6527	26	15	in	in	ADP
ejpam-6527	26	16	banach	banach	NOUN
ejpam-6527	26	17	spaces	space	NOUN
ejpam-6527	26	18	,	,	PUNCT
ejpam-6527	26	19	serves	serve	VERB
ejpam-6527	26	20	as	as	ADP
ejpam-6527	26	21	a	a	DET
ejpam-6527	26	22	conceptual	conceptual	ADJ
ejpam-6527	26	23	bridge	bridge	NOUN
ejpam-6527	26	24	between	between	ADP
ejpam-6527	26	25	these	these	DET
ejpam-6527	26	26	two	two	NUM
ejpam-6527	26	27	domains	domain	NOUN
ejpam-6527	26	28	.	.	PUNCT
ejpam-6527	27	1	earlier	early	ADJ
ejpam-6527	27	2	studies	study	NOUN
ejpam-6527	27	3	and	and	CCONJ
ejpam-6527	27	4	research	research	NOUN
ejpam-6527	27	5	works	work	NOUN
ejpam-6527	27	6	have	have	AUX
ejpam-6527	27	7	introduced	introduce	VERB
ejpam-6527	27	8	notions	notion	NOUN
ejpam-6527	27	9	of	of	ADP
ejpam-6527	27	10	compactness	compactness	NOUN
ejpam-6527	27	11	in	in	ADP
ejpam-6527	27	12	hilbert	hilbert	PROPN
ejpam-6527	27	13	c∗-modules	c∗-modules	PROPN
ejpam-6527	27	14	,	,	PUNCT
ejpam-6527	27	15	the	the	DET
ejpam-6527	27	16	behavior	behavior	NOUN
ejpam-6527	27	17	of	of	ADP
ejpam-6527	27	18	compact	compact	ADJ
ejpam-6527	27	19	operators	operator	NOUN
ejpam-6527	27	20	,	,	PUNCT
ejpam-6527	27	21	their	their	PRON
ejpam-6527	27	22	uses	use	NOUN
ejpam-6527	27	23	in	in	ADP
ejpam-6527	27	24	geometry	geometry	NOUN
ejpam-6527	27	25	,	,	PUNCT
ejpam-6527	27	26	as	as	ADV
ejpam-6527	27	27	well	well	ADV
ejpam-6527	27	28	as	as	ADP
ejpam-6527	27	29	in	in	ADP
ejpam-6527	27	30	quantum	quantum	NOUN
ejpam-6527	27	31	and	and	CCONJ
ejpam-6527	27	32	non	non	ADJ
ejpam-6527	27	33	-	-	ADJ
ejpam-6527	27	34	commutative	commutative	ADJ
ejpam-6527	27	35	contexts[14–17	contexts[14–17	NOUN
ejpam-6527	27	36	]	]	PUNCT
ejpam-6527	27	37	.	.	PUNCT
ejpam-6527	28	1	however	however	ADV
ejpam-6527	28	2	,	,	PUNCT
ejpam-6527	28	3	previous	previous	ADJ
ejpam-6527	28	4	studies	study	NOUN
ejpam-6527	28	5	have	have	AUX
ejpam-6527	28	6	not	not	PART
ejpam-6527	28	7	systematically	systematically	ADV
ejpam-6527	28	8	explored	explore	VERB
ejpam-6527	28	9	the	the	DET
ejpam-6527	28	10	relationship	relationship	NOUN
ejpam-6527	28	11	between	between	ADP
ejpam-6527	28	12	classical	classical	ADJ
ejpam-6527	28	13	compactness	compactness	NOUN
ejpam-6527	28	14	and	and	CCONJ
ejpam-6527	28	15	complete	complete	ADJ
ejpam-6527	28	16	compactness	compactness	NOUN
ejpam-6527	28	17	within	within	ADP
ejpam-6527	28	18	the	the	DET
ejpam-6527	28	19	context	context	NOUN
ejpam-6527	28	20	of	of	ADP
ejpam-6527	28	21	operator	operator	NOUN
ejpam-6527	28	22	spaces	space	NOUN
ejpam-6527	28	23	over	over	ADP
ejpam-6527	28	24	the	the	DET
ejpam-6527	28	25	non	non	ADJ
ejpam-6527	28	26	-	-	ADJ
ejpam-6527	28	27	commutative	commutative	ADJ
ejpam-6527	28	28	torus	torus	NOUN
ejpam-6527	28	29	.	.	PUNCT
ejpam-6527	29	1	this	this	DET
ejpam-6527	29	2	study	study	NOUN
ejpam-6527	29	3	bridges	bridge	VERB
ejpam-6527	29	4	these	these	DET
ejpam-6527	29	5	two	two	NUM
ejpam-6527	29	6	notions	notion	NOUN
ejpam-6527	29	7	and	and	CCONJ
ejpam-6527	29	8	demonstrates	demonstrate	VERB
ejpam-6527	29	9	the	the	DET
ejpam-6527	29	10	stability	stability	NOUN
ejpam-6527	29	11	of	of	ADP
ejpam-6527	29	12	compactness	compactness	NOUN
ejpam-6527	29	13	under	under	ADP
ejpam-6527	29	14	multi	multi	ADJ
ejpam-6527	29	15	-	-	ADJ
ejpam-6527	29	16	fold	fold	ADJ
ejpam-6527	29	17	tensor	tensor	NOUN
ejpam-6527	29	18	products	product	NOUN
ejpam-6527	29	19	,	,	PUNCT
ejpam-6527	29	20	which	which	PRON
ejpam-6527	29	21	is	be	AUX
ejpam-6527	29	22	an	an	DET
ejpam-6527	29	23	important	important	ADJ
ejpam-6527	29	24	feature	feature	NOUN
ejpam-6527	29	25	describing	describe	VERB
ejpam-6527	29	26	the	the	DET
ejpam-6527	29	27	structure	structure	NOUN
ejpam-6527	29	28	of	of	ADP
ejpam-6527	29	29	non	non	ADJ
ejpam-6527	29	30	-	-	ADJ
ejpam-6527	29	31	commutative	commutative	ADJ
ejpam-6527	29	32	operator	operator	NOUN
ejpam-6527	29	33	spaces	space	NOUN
ejpam-6527	29	34	[	[	X
ejpam-6527	29	35	18–20	18–20	NUM
ejpam-6527	29	36	]	]	PUNCT
ejpam-6527	29	37	.	.	PUNCT
ejpam-6527	30	1	in	in	ADP
ejpam-6527	30	2	addition	addition	NOUN
ejpam-6527	30	3	,	,	PUNCT
ejpam-6527	30	4	we	we	PRON
ejpam-6527	30	5	also	also	ADV
ejpam-6527	30	6	describe	describe	VERB
ejpam-6527	30	7	theoretical	theoretical	ADJ
ejpam-6527	30	8	applications	application	NOUN
ejpam-6527	30	9	that	that	PRON
ejpam-6527	30	10	illustrate	illustrate	VERB
ejpam-6527	30	11	the	the	DET
ejpam-6527	30	12	effect	effect	NOUN
ejpam-6527	30	13	of	of	ADP
ejpam-6527	30	14	compact	compact	ADJ
ejpam-6527	30	15	operators	operator	NOUN
ejpam-6527	30	16	in	in	ADP
ejpam-6527	30	17	quantum	quantum	ADJ
ejpam-6527	30	18	metric	metric	ADJ
ejpam-6527	30	19	spaces	space	NOUN
ejpam-6527	30	20	,	,	PUNCT
ejpam-6527	30	21	thus	thus	ADV
ejpam-6527	30	22	broadening	broaden	VERB
ejpam-6527	30	23	the	the	DET
ejpam-6527	30	24	applied	applied	ADJ
ejpam-6527	30	25	scope	scope	NOUN
ejpam-6527	30	26	of	of	ADP
ejpam-6527	30	27	our	our	PRON
ejpam-6527	30	28	results	result	NOUN
ejpam-6527	30	29	in	in	ADP
ejpam-6527	30	30	comparison	comparison	NOUN
ejpam-6527	30	31	to	to	ADP
ejpam-6527	30	32	previous	previous	ADJ
ejpam-6527	30	33	work	work	NOUN
ejpam-6527	30	34	.	.	PUNCT
ejpam-6527	31	1	hence	hence	ADV
ejpam-6527	31	2	,	,	PUNCT
ejpam-6527	31	3	this	this	DET
ejpam-6527	31	4	study	study	NOUN
ejpam-6527	31	5	makes	make	VERB
ejpam-6527	31	6	a	a	DET
ejpam-6527	31	7	significant	significant	ADJ
ejpam-6527	31	8	contribution	contribution	NOUN
ejpam-6527	31	9	to	to	ADP
ejpam-6527	31	10	the	the	DET
ejpam-6527	31	11	deeper	deep	ADJ
ejpam-6527	31	12	understanding	understanding	NOUN
ejpam-6527	31	13	of	of	ADP
ejpam-6527	31	14	non	non	ADJ
ejpam-6527	31	15	-	-	ADJ
ejpam-6527	31	16	commutative	commutative	ADJ
ejpam-6527	31	17	operator	operator	NOUN
ejpam-6527	31	18	space	space	NOUN
ejpam-6527	31	19	theory	theory	NOUN
ejpam-6527	31	20	and	and	CCONJ
ejpam-6527	31	21	the	the	DET
ejpam-6527	31	22	rising	rise	VERB
ejpam-6527	31	23	opportunities	opportunity	NOUN
ejpam-6527	31	24	for	for	ADP
ejpam-6527	31	25	applications	application	NOUN
ejpam-6527	31	26	in	in	ADP
ejpam-6527	31	27	modern	modern	ADJ
ejpam-6527	31	28	mathematics	mathematic	NOUN
ejpam-6527	31	29	and	and	CCONJ
ejpam-6527	31	30	physics	physics	NOUN
ejpam-6527	31	31	.	.	PUNCT
ejpam-6527	32	1	our	our	PRON
ejpam-6527	32	2	motivation	motivation	NOUN
ejpam-6527	32	3	arises	arise	VERB
ejpam-6527	32	4	from	from	ADP
ejpam-6527	32	5	fundamental	fundamental	ADJ
ejpam-6527	32	6	questions	question	NOUN
ejpam-6527	32	7	in	in	ADP
ejpam-6527	32	8	non	non	ADJ
ejpam-6527	32	9	-	-	ADJ
ejpam-6527	32	10	commutative	commutative	ADJ
ejpam-6527	32	11	geometry	geometry	NOUN
ejpam-6527	32	12	and	and	CCONJ
ejpam-6527	32	13	quantum	quantum	NOUN
ejpam-6527	32	14	theory	theory	NOUN
ejpam-6527	32	15	[	[	X
ejpam-6527	32	16	16	16	NUM
ejpam-6527	32	17	,	,	PUNCT
ejpam-6527	32	18	21	21	NUM
ejpam-6527	32	19	]	]	PUNCT
ejpam-6527	32	20	,	,	PUNCT
ejpam-6527	32	21	which	which	PRON
ejpam-6527	32	22	are	be	AUX
ejpam-6527	32	23	further	far	ADV
ejpam-6527	32	24	explored	explore	VERB
ejpam-6527	32	25	in	in	ADP
ejpam-6527	32	26	the	the	DET
ejpam-6527	32	27	applications	application	NOUN
ejpam-6527	32	28	section	section	NOUN
ejpam-6527	32	29	.	.	PUNCT
ejpam-6527	33	1	we	we	PRON
ejpam-6527	33	2	further	far	ADV
ejpam-6527	33	3	establish	establish	VERB
ejpam-6527	33	4	connections	connection	NOUN
ejpam-6527	33	5	to	to	ADP
ejpam-6527	33	6	quantum	quantum	ADJ
ejpam-6527	33	7	theory	theory	NOUN
ejpam-6527	33	8	,	,	PUNCT
ejpam-6527	33	9	in	in	ADP
ejpam-6527	33	10	which	which	PRON
ejpam-6527	33	11	compactness	compactness	NOUN
ejpam-6527	33	12	plays	play	VERB
ejpam-6527	33	13	a	a	DET
ejpam-6527	33	14	key	key	ADJ
ejpam-6527	33	15	role	role	NOUN
ejpam-6527	33	16	in	in	ADP
ejpam-6527	33	17	determining	determine	VERB
ejpam-6527	33	18	the	the	DET
ejpam-6527	33	19	behavior	behavior	NOUN
ejpam-6527	33	20	of	of	ADP
ejpam-6527	33	21	quantum	quantum	ADJ
ejpam-6527	33	22	channels	channel	NOUN
ejpam-6527	33	23	[	[	X
ejpam-6527	33	24	22	22	NUM
ejpam-6527	33	25	,	,	PUNCT
ejpam-6527	33	26	23	23	NUM
ejpam-6527	33	27	]	]	PUNCT
ejpam-6527	33	28	.	.	PUNCT
ejpam-6527	34	1	our	our	PRON
ejpam-6527	34	2	results	result	NOUN
ejpam-6527	34	3	build	build	VERB
ejpam-6527	34	4	on	on	ADP
ejpam-6527	34	5	what	what	PRON
ejpam-6527	34	6	other	other	ADJ
ejpam-6527	34	7	researchers	researcher	NOUN
ejpam-6527	34	8	have	have	AUX
ejpam-6527	34	9	done	do	VERB
ejpam-6527	34	10	before	before	ADV
ejpam-6527	34	11	and	and	CCONJ
ejpam-6527	34	12	give	give	VERB
ejpam-6527	34	13	us	we	PRON
ejpam-6527	34	14	new	new	ADJ
ejpam-6527	34	15	ways	way	NOUN
ejpam-6527	34	16	to	to	PART
ejpam-6527	34	17	think	think	VERB
ejpam-6527	34	18	about	about	ADP
ejpam-6527	34	19	compact	compact	ADJ
ejpam-6527	34	20	operators	operator	NOUN
ejpam-6527	34	21	in	in	ADP
ejpam-6527	34	22	non	non	ADJ
ejpam-6527	34	23	-	-	ADJ
ejpam-6527	34	24	commutative	commutative	ADJ
ejpam-6527	34	25	spaces	space	NOUN
ejpam-6527	34	26	.	.	PUNCT
ejpam-6527	35	1	m.	m.	PROPN
ejpam-6527	35	2	s.	s.	PROPN
ejpam-6527	35	3	ali	ali	PROPN
ejpam-6527	35	4	et	et	PROPN
ejpam-6527	35	5	al	al	PROPN
ejpam-6527	35	6	.	.	PUNCT
ejpam-6527	35	7	/	/	SYM
ejpam-6527	35	8	eur	eur	PROPN
ejpam-6527	35	9	.	.	PUNCT
ejpam-6527	36	1	j.	j.	PROPN
ejpam-6527	36	2	pure	pure	PROPN
ejpam-6527	36	3	appl	appl	PROPN
ejpam-6527	36	4	.	.	PROPN
ejpam-6527	36	5	math	math	PROPN
ejpam-6527	36	6	,	,	PUNCT
ejpam-6527	36	7	18	18	NUM
ejpam-6527	36	8	(	(	PUNCT
ejpam-6527	36	9	3	3	NUM
ejpam-6527	36	10	)	)	PUNCT
ejpam-6527	36	11	(	(	PUNCT
ejpam-6527	36	12	2025	2025	NUM
ejpam-6527	36	13	)	)	PUNCT
ejpam-6527	36	14	,	,	PUNCT
ejpam-6527	36	15	6527	6527	NUM
ejpam-6527	36	16	3	3	NUM
ejpam-6527	36	17	of	of	ADP
ejpam-6527	36	18	9	9	NUM
ejpam-6527	36	19	2	2	NUM
ejpam-6527	36	20	.	.	PUNCT
ejpam-6527	36	21	comparison	comparison	NOUN
ejpam-6527	36	22	with	with	ADP
ejpam-6527	36	23	related	related	ADJ
ejpam-6527	36	24	work	work	NOUN
ejpam-6527	36	25	the	the	DET
ejpam-6527	36	26	concept	concept	NOUN
ejpam-6527	36	27	of	of	ADP
ejpam-6527	36	28	compactness	compactness	NOUN
ejpam-6527	36	29	in	in	ADP
ejpam-6527	36	30	operator	operator	NOUN
ejpam-6527	36	31	algebras	algebra	NOUN
ejpam-6527	36	32	and	and	CCONJ
ejpam-6527	36	33	in	in	ADP
ejpam-6527	36	34	hilbert	hilbert	PROPN
ejpam-6527	36	35	c∗-modules	c∗-modules	PROPN
ejpam-6527	36	36	has	have	AUX
ejpam-6527	36	37	been	be	AUX
ejpam-6527	36	38	investigated	investigate	VERB
ejpam-6527	36	39	in	in	ADP
ejpam-6527	36	40	both	both	CCONJ
ejpam-6527	36	41	classical	classical	ADJ
ejpam-6527	36	42	and	and	CCONJ
ejpam-6527	36	43	non	non	ADJ
ejpam-6527	36	44	-	-	ADJ
ejpam-6527	36	45	commutative	commutative	ADJ
ejpam-6527	36	46	settings	setting	NOUN
ejpam-6527	36	47	.	.	PUNCT
ejpam-6527	37	1	earlier	early	ADJ
ejpam-6527	37	2	work	work	NOUN
ejpam-6527	37	3	(	(	PUNCT
ejpam-6527	37	4	e.g.	e.g.	ADV
ejpam-6527	37	5	,	,	PUNCT
ejpam-6527	37	6	lance[15	lance[15	NOUN
ejpam-6527	37	7	]	]	PUNCT
ejpam-6527	37	8	)	)	PUNCT
ejpam-6527	37	9	developed	develop	VERB
ejpam-6527	37	10	a	a	DET
ejpam-6527	37	11	theory	theory	NOUN
ejpam-6527	37	12	for	for	ADP
ejpam-6527	37	13	compact	compact	ADJ
ejpam-6527	37	14	operators	operator	NOUN
ejpam-6527	37	15	on	on	ADP
ejpam-6527	37	16	hilbert	hilbert	PROPN
ejpam-6527	37	17	c∗-modules	c∗-modules	PROPN
ejpam-6527	37	18	.	.	PUNCT
ejpam-6527	38	1	ruan[8	ruan[8	PROPN
ejpam-6527	38	2	]	]	PUNCT
ejpam-6527	38	3	and	and	CCONJ
ejpam-6527	38	4	pisier[10	pisier[10	NOUN
ejpam-6527	38	5	]	]	PUNCT
ejpam-6527	38	6	generalized	generalize	VERB
ejpam-6527	38	7	these	these	DET
ejpam-6527	38	8	concepts	concept	NOUN
ejpam-6527	38	9	to	to	PART
ejpam-6527	38	10	operator	operator	VERB
ejpam-6527	38	11	spaces	space	NOUN
ejpam-6527	38	12	with	with	ADP
ejpam-6527	38	13	completely	completely	ADV
ejpam-6527	38	14	boundedness	boundedness	ADJ
ejpam-6527	38	15	and	and	CCONJ
ejpam-6527	38	16	matrix	matrix	NOUN
ejpam-6527	38	17	norm	norm	NOUN
ejpam-6527	38	18	structures	structure	NOUN
ejpam-6527	38	19	.	.	PUNCT
ejpam-6527	39	1	moreover	moreover	ADV
ejpam-6527	39	2	,	,	PUNCT
ejpam-6527	39	3	recent	recent	ADJ
ejpam-6527	39	4	developments	development	NOUN
ejpam-6527	39	5	have	have	AUX
ejpam-6527	39	6	introduced	introduce	VERB
ejpam-6527	39	7	refined	refined	ADJ
ejpam-6527	39	8	and	and	CCONJ
ejpam-6527	39	9	innovative	innovative	ADJ
ejpam-6527	39	10	tools	tool	NOUN
ejpam-6527	39	11	that	that	PRON
ejpam-6527	39	12	build	build	VERB
ejpam-6527	39	13	upon	upon	SCONJ
ejpam-6527	39	14	these	these	DET
ejpam-6527	39	15	classical	classical	ADJ
ejpam-6527	39	16	foundations	foundation	NOUN
ejpam-6527	39	17	.	.	PUNCT
ejpam-6527	40	1	junge	junge	NOUN
ejpam-6527	40	2	and	and	CCONJ
ejpam-6527	40	3	sherman	sherman	PROPN
ejpam-6527	41	1	[	[	X
ejpam-6527	41	2	7	7	X
ejpam-6527	41	3	]	]	PUNCT
ejpam-6527	41	4	provide	provide	VERB
ejpam-6527	41	5	an	an	DET
ejpam-6527	41	6	overview	overview	NOUN
ejpam-6527	41	7	of	of	ADP
ejpam-6527	41	8	operator	operator	NOUN
ejpam-6527	41	9	spaces	space	NOUN
ejpam-6527	41	10	in	in	ADP
ejpam-6527	41	11	noncommutative	noncommutative	ADJ
ejpam-6527	41	12	ℓp	ℓp	ADJ
ejpam-6527	41	13	spaces	space	NOUN
ejpam-6527	41	14	,	,	PUNCT
ejpam-6527	41	15	which	which	PRON
ejpam-6527	41	16	builds	build	VERB
ejpam-6527	41	17	on	on	ADP
ejpam-6527	41	18	this	this	DET
ejpam-6527	41	19	more	more	ADV
ejpam-6527	41	20	analytic	analytic	ADJ
ejpam-6527	41	21	foundation	foundation	NOUN
ejpam-6527	41	22	.	.	PUNCT
ejpam-6527	42	1	hiai	hiai	PROPN
ejpam-6527	42	2	and	and	CCONJ
ejpam-6527	42	3	ueda[12	ueda[12	PROPN
ejpam-6527	42	4	]	]	PUNCT
ejpam-6527	42	5	have	have	AUX
ejpam-6527	42	6	explored	explore	VERB
ejpam-6527	42	7	novel	novel	ADJ
ejpam-6527	42	8	aspects	aspect	NOUN
ejpam-6527	42	9	of	of	ADP
ejpam-6527	42	10	non	non	ADJ
ejpam-6527	42	11	-	-	ADJ
ejpam-6527	42	12	commutative	commutative	ADJ
ejpam-6527	42	13	operator	operator	NOUN
ejpam-6527	42	14	theory	theory	NOUN
ejpam-6527	42	15	,	,	PUNCT
ejpam-6527	42	16	particularly	particularly	ADV
ejpam-6527	42	17	concerning	concern	VERB
ejpam-6527	42	18	bounded	bounded	ADJ
ejpam-6527	42	19	and	and	CCONJ
ejpam-6527	42	20	compact	compact	ADJ
ejpam-6527	42	21	maps	map	NOUN
ejpam-6527	42	22	,	,	PUNCT
ejpam-6527	42	23	bringing	bring	VERB
ejpam-6527	42	24	new	new	ADJ
ejpam-6527	42	25	insights	insight	NOUN
ejpam-6527	42	26	into	into	ADP
ejpam-6527	42	27	the	the	DET
ejpam-6527	42	28	structure	structure	NOUN
ejpam-6527	42	29	and	and	CCONJ
ejpam-6527	42	30	behavior	behavior	NOUN
ejpam-6527	42	31	of	of	ADP
ejpam-6527	42	32	such	such	ADJ
ejpam-6527	42	33	mappings	mapping	NOUN
ejpam-6527	42	34	.	.	PUNCT
ejpam-6527	43	1	in	in	ADP
ejpam-6527	43	2	particular	particular	ADJ
ejpam-6527	43	3	,	,	PUNCT
ejpam-6527	43	4	a	a	DET
ejpam-6527	43	5	modern	modern	ADJ
ejpam-6527	43	6	approach	approach	NOUN
ejpam-6527	43	7	to	to	ADP
ejpam-6527	43	8	compact	compact	ADJ
ejpam-6527	43	9	quantum	quantum	NOUN
ejpam-6527	43	10	metric	metric	ADJ
ejpam-6527	43	11	spaces	space	NOUN
ejpam-6527	43	12	was	be	AUX
ejpam-6527	43	13	proposed	propose	VERB
ejpam-6527	43	14	by	by	ADP
ejpam-6527	43	15	latrémolière[23	latrémolière[23	PROPN
ejpam-6527	43	16	]	]	PUNCT
ejpam-6527	43	17	,	,	PUNCT
ejpam-6527	43	18	unifying	unify	VERB
ejpam-6527	43	19	compactness	compactness	NOUN
ejpam-6527	43	20	and	and	CCONJ
ejpam-6527	43	21	geometry	geometry	NOUN
ejpam-6527	43	22	via	via	ADP
ejpam-6527	43	23	quantum	quantum	ADJ
ejpam-6527	43	24	gromov	gromov	NOUN
ejpam-6527	43	25	–	–	PUNCT
ejpam-6527	43	26	hausdorff	hausdorff	NOUN
ejpam-6527	43	27	convergence	convergence	NOUN
ejpam-6527	43	28	.	.	PUNCT
ejpam-6527	44	1	we	we	PRON
ejpam-6527	44	2	contribute	contribute	VERB
ejpam-6527	44	3	to	to	ADP
ejpam-6527	44	4	this	this	DET
ejpam-6527	44	5	framework	framework	NOUN
ejpam-6527	44	6	by	by	ADP
ejpam-6527	44	7	relating	relate	VERB
ejpam-6527	44	8	operator	operator	NOUN
ejpam-6527	44	9	-	-	PUNCT
ejpam-6527	44	10	theoretic	theoretic	NOUN
ejpam-6527	44	11	compactness	compactness	NOUN
ejpam-6527	44	12	specifically	specifically	ADV
ejpam-6527	44	13	through	through	ADP
ejpam-6527	44	14	adjointable	adjointable	ADJ
ejpam-6527	44	15	maps	map	NOUN
ejpam-6527	44	16	and	and	CCONJ
ejpam-6527	44	17	complete	complete	ADJ
ejpam-6527	44	18	compactness	compactness	NOUN
ejpam-6527	44	19	,	,	PUNCT
ejpam-6527	44	20	while	while	SCONJ
ejpam-6527	44	21	also	also	ADV
ejpam-6527	44	22	establishing	establish	VERB
ejpam-6527	44	23	the	the	DET
ejpam-6527	44	24	stability	stability	NOUN
ejpam-6527	44	25	of	of	ADP
ejpam-6527	44	26	these	these	DET
ejpam-6527	44	27	properties	property	NOUN
ejpam-6527	44	28	under	under	ADP
ejpam-6527	44	29	the	the	DET
ejpam-6527	44	30	tensor	tensor	NOUN
ejpam-6527	44	31	product	product	NOUN
ejpam-6527	44	32	operation	operation	NOUN
ejpam-6527	44	33	.	.	PUNCT
ejpam-6527	45	1	similarly	similarly	ADV
ejpam-6527	45	2	,	,	PUNCT
ejpam-6527	45	3	caspers	casper	NOUN
ejpam-6527	45	4	and	and	CCONJ
ejpam-6527	45	5	skalski[22	skalski[22	PROPN
ejpam-6527	45	6	]	]	PUNCT
ejpam-6527	45	7	studied	study	VERB
ejpam-6527	45	8	the	the	DET
ejpam-6527	45	9	behavior	behavior	NOUN
ejpam-6527	45	10	of	of	ADP
ejpam-6527	45	11	compactness	compactness	NOUN
ejpam-6527	45	12	in	in	ADP
ejpam-6527	45	13	quantum	quantum	ADJ
ejpam-6527	45	14	information	information	NOUN
ejpam-6527	45	15	channels	channel	NOUN
ejpam-6527	45	16	,	,	PUNCT
ejpam-6527	45	17	and	and	CCONJ
ejpam-6527	45	18	how	how	SCONJ
ejpam-6527	45	19	this	this	DET
ejpam-6527	45	20	concept	concept	NOUN
ejpam-6527	45	21	can	can	AUX
ejpam-6527	45	22	be	be	AUX
ejpam-6527	45	23	leveraged	leverage	VERB
ejpam-6527	45	24	to	to	PART
ejpam-6527	45	25	maximize	maximize	VERB
ejpam-6527	45	26	the	the	DET
ejpam-6527	45	27	transfer	transfer	NOUN
ejpam-6527	45	28	of	of	ADP
ejpam-6527	45	29	information	information	NOUN
ejpam-6527	45	30	.	.	PUNCT
ejpam-6527	46	1	our	our	PRON
ejpam-6527	46	2	paper	paper	NOUN
ejpam-6527	46	3	builds	build	VERB
ejpam-6527	46	4	on	on	ADP
ejpam-6527	46	5	this	this	DET
ejpam-6527	46	6	foundation	foundation	NOUN
ejpam-6527	46	7	by	by	ADP
ejpam-6527	46	8	providing	provide	VERB
ejpam-6527	46	9	a	a	DET
ejpam-6527	46	10	functional	functional	ADJ
ejpam-6527	46	11	-	-	PUNCT
ejpam-6527	46	12	analytic	analytic	ADJ
ejpam-6527	46	13	perspective	perspective	NOUN
ejpam-6527	46	14	on	on	ADP
ejpam-6527	46	15	compact	compact	ADJ
ejpam-6527	46	16	operators	operator	NOUN
ejpam-6527	46	17	in	in	ADP
ejpam-6527	46	18	operator	operator	NOUN
ejpam-6527	46	19	spaces	space	NOUN
ejpam-6527	46	20	over	over	ADP
ejpam-6527	46	21	the	the	DET
ejpam-6527	46	22	non	non	ADJ
ejpam-6527	46	23	-	-	ADJ
ejpam-6527	46	24	commutative	commutative	ADJ
ejpam-6527	46	25	torus	torus	NOUN
ejpam-6527	46	26	explicitly	explicitly	ADV
ejpam-6527	46	27	highlighting	highlight	VERB
ejpam-6527	46	28	how	how	SCONJ
ejpam-6527	46	29	compact	compact	ADJ
ejpam-6527	46	30	operators	operator	NOUN
ejpam-6527	46	31	act	act	VERB
ejpam-6527	46	32	as	as	ADP
ejpam-6527	46	33	information	information	NOUN
ejpam-6527	46	34	-	-	PUNCT
ejpam-6527	46	35	preserving	preserve	VERB
ejpam-6527	46	36	maps	map	NOUN
ejpam-6527	46	37	.	.	PUNCT
ejpam-6527	47	1	besnard	besnard	NOUN
ejpam-6527	47	2	and	and	CCONJ
ejpam-6527	47	3	latrémolière[3	latrémolière[3	X
ejpam-6527	47	4	]	]	X
ejpam-6527	47	5	focused	focus	VERB
ejpam-6527	47	6	on	on	ADP
ejpam-6527	47	7	convergence	convergence	NOUN
ejpam-6527	47	8	issues	issue	NOUN
ejpam-6527	47	9	in	in	ADP
ejpam-6527	47	10	quantum	quantum	ADJ
ejpam-6527	47	11	metric	metric	ADJ
ejpam-6527	47	12	geometry	geometry	NOUN
ejpam-6527	47	13	,	,	PUNCT
ejpam-6527	47	14	whereas	whereas	SCONJ
ejpam-6527	47	15	our	our	PRON
ejpam-6527	47	16	results	result	NOUN
ejpam-6527	47	17	concentrate	concentrate	VERB
ejpam-6527	47	18	on	on	ADP
ejpam-6527	47	19	functional	functional	ADJ
ejpam-6527	47	20	structures	structure	NOUN
ejpam-6527	47	21	and	and	CCONJ
ejpam-6527	47	22	equivalence	equivalence	NOUN
ejpam-6527	47	23	theorems	theorem	NOUN
ejpam-6527	47	24	for	for	ADP
ejpam-6527	47	25	classical	classical	ADJ
ejpam-6527	47	26	and	and	CCONJ
ejpam-6527	47	27	non	non	ADJ
ejpam-6527	47	28	-	-	ADJ
ejpam-6527	47	29	classical	classical	ADJ
ejpam-6527	47	30	compactness	compactness	NOUN
ejpam-6527	47	31	in	in	ADP
ejpam-6527	47	32	operator	operator	NOUN
ejpam-6527	47	33	spaces	space	NOUN
ejpam-6527	47	34	.	.	PUNCT
ejpam-6527	48	1	therefore	therefore	ADV
ejpam-6527	48	2	,	,	PUNCT
ejpam-6527	48	3	this	this	DET
ejpam-6527	48	4	paper	paper	NOUN
ejpam-6527	48	5	serves	serve	VERB
ejpam-6527	48	6	both	both	PRON
ejpam-6527	48	7	as	as	ADP
ejpam-6527	48	8	a	a	DET
ejpam-6527	48	9	complement	complement	NOUN
ejpam-6527	48	10	and	and	CCONJ
ejpam-6527	48	11	an	an	DET
ejpam-6527	48	12	extension	extension	NOUN
ejpam-6527	48	13	to	to	ADP
ejpam-6527	48	14	the	the	DET
ejpam-6527	48	15	modern	modern	ADJ
ejpam-6527	48	16	literature	literature	NOUN
ejpam-6527	48	17	,	,	PUNCT
ejpam-6527	48	18	offering	offer	VERB
ejpam-6527	48	19	a	a	DET
ejpam-6527	48	20	unified	unified	ADJ
ejpam-6527	48	21	treatment	treatment	NOUN
ejpam-6527	48	22	of	of	ADP
ejpam-6527	48	23	compactness	compactness	NOUN
ejpam-6527	48	24	for	for	ADP
ejpam-6527	48	25	non	non	ADJ
ejpam-6527	48	26	-	-	ADJ
ejpam-6527	48	27	commutative	commutative	ADJ
ejpam-6527	48	28	tori	tori	NOUN
ejpam-6527	48	29	with	with	ADP
ejpam-6527	48	30	broad	broad	ADJ
ejpam-6527	48	31	theoretical	theoretical	ADJ
ejpam-6527	48	32	and	and	CCONJ
ejpam-6527	48	33	applied	applied	ADJ
ejpam-6527	48	34	implications	implication	NOUN
ejpam-6527	48	35	.	.	PUNCT
ejpam-6527	49	1	3	3	X
ejpam-6527	49	2	.	.	X
ejpam-6527	49	3	preliminaries	preliminary	NOUN
ejpam-6527	49	4	in	in	ADP
ejpam-6527	49	5	this	this	DET
ejpam-6527	49	6	section	section	NOUN
ejpam-6527	49	7	,	,	PUNCT
ejpam-6527	49	8	we	we	PRON
ejpam-6527	49	9	review	review	VERB
ejpam-6527	49	10	key	key	ADJ
ejpam-6527	49	11	concepts	concept	NOUN
ejpam-6527	49	12	related	relate	VERB
ejpam-6527	49	13	to	to	ADP
ejpam-6527	49	14	compact	compact	ADJ
ejpam-6527	49	15	operators	operator	NOUN
ejpam-6527	49	16	,	,	PUNCT
ejpam-6527	49	17	hilbert	hilbert	NOUN
ejpam-6527	49	18	aθmodules	aθmodule	NOUN
ejpam-6527	49	19	,	,	PUNCT
ejpam-6527	49	20	compactness	compactness	NOUN
ejpam-6527	49	21	,	,	PUNCT
ejpam-6527	49	22	and	and	CCONJ
ejpam-6527	49	23	complete	complete	ADJ
ejpam-6527	49	24	compactness	compactness	NOUN
ejpam-6527	49	25	.	.	PUNCT
ejpam-6527	50	1	definition	definition	NOUN
ejpam-6527	50	2	1	1	NUM
ejpam-6527	50	3	.	.	PUNCT
ejpam-6527	51	1	compact	compact	ADJ
ejpam-6527	51	2	operators	operator	NOUN
ejpam-6527	51	3	[	[	X
ejpam-6527	51	4	19	19	NUM
ejpam-6527	51	5	]	]	PUNCT
ejpam-6527	51	6	in	in	ADP
ejpam-6527	51	7	hilbert	hilbert	PROPN
ejpam-6527	51	8	c∗-modules	c∗-modules	PROPN
ejpam-6527	51	9	,	,	PUNCT
ejpam-6527	51	10	an	an	DET
ejpam-6527	51	11	operator	operator	NOUN
ejpam-6527	51	12	is	be	AUX
ejpam-6527	51	13	said	say	VERB
ejpam-6527	51	14	to	to	PART
ejpam-6527	51	15	be	be	AUX
ejpam-6527	51	16	compact	compact	ADJ
ejpam-6527	51	17	if	if	SCONJ
ejpam-6527	51	18	it	it	PRON
ejpam-6527	51	19	lies	lie	VERB
ejpam-6527	51	20	in	in	ADP
ejpam-6527	51	21	the	the	DET
ejpam-6527	51	22	norm	norm	NOUN
ejpam-6527	51	23	closure	closure	NOUN
ejpam-6527	51	24	of	of	ADP
ejpam-6527	51	25	operators	operator	NOUN
ejpam-6527	51	26	of	of	ADP
ejpam-6527	51	27	the	the	DET
ejpam-6527	51	28	form	form	NOUN
ejpam-6527	51	29	ξ	ξ	PROPN
ejpam-6527	51	30	7→	7→	NUM
ejpam-6527	51	31	η⟨ζ	η⟨ζ	NUM
ejpam-6527	51	32	,	,	PUNCT
ejpam-6527	51	33	ξ⟩	ξ⟩	NOUN
ejpam-6527	51	34	,	,	PUNCT
ejpam-6527	51	35	where	where	SCONJ
ejpam-6527	51	36	η	η	PROPN
ejpam-6527	51	37	,	,	PUNCT
ejpam-6527	51	38	ζ	ζ	NOUN
ejpam-6527	51	39	are	be	AUX
ejpam-6527	51	40	fixed	fix	VERB
ejpam-6527	51	41	elements	element	NOUN
ejpam-6527	51	42	of	of	ADP
ejpam-6527	51	43	the	the	DET
ejpam-6527	51	44	module	module	NOUN
ejpam-6527	51	45	,	,	PUNCT
ejpam-6527	51	46	and	and	CCONJ
ejpam-6527	51	47	⟨	⟨	NOUN
ejpam-6527	51	48	·	·	NUM
ejpam-6527	51	49	,	,	PUNCT
ejpam-6527	51	50	·	·	PUNCT
ejpam-6527	51	51	⟩	⟩	NOUN
ejpam-6527	51	52	denotes	denote	VERB
ejpam-6527	51	53	the	the	DET
ejpam-6527	51	54	c∗-valued	c∗-value	VERB
ejpam-6527	51	55	inner	inner	ADJ
ejpam-6527	51	56	product	product	NOUN
ejpam-6527	51	57	.	.	PUNCT
ejpam-6527	52	1	definition	definition	NOUN
ejpam-6527	52	2	2	2	NUM
ejpam-6527	52	3	.	.	PUNCT
ejpam-6527	53	1	hilbert	hilbert	PROPN
ejpam-6527	53	2	aθ	aθ	NOUN
ejpam-6527	53	3	-	-	PUNCT
ejpam-6527	53	4	modules	module	NOUN
ejpam-6527	53	5	[	[	X
ejpam-6527	53	6	3	3	NUM
ejpam-6527	53	7	,	,	PUNCT
ejpam-6527	53	8	13	13	NUM
ejpam-6527	53	9	]	]	PUNCT
ejpam-6527	53	10	m.	m.	NOUN
ejpam-6527	53	11	s.	s.	PROPN
ejpam-6527	53	12	ali	ali	PROPN
ejpam-6527	53	13	et	et	PROPN
ejpam-6527	53	14	al	al	PROPN
ejpam-6527	53	15	.	.	PUNCT
ejpam-6527	53	16	/	/	SYM
ejpam-6527	53	17	eur	eur	PROPN
ejpam-6527	53	18	.	.	PUNCT
ejpam-6527	54	1	j.	j.	PROPN
ejpam-6527	54	2	pure	pure	PROPN
ejpam-6527	54	3	appl	appl	PROPN
ejpam-6527	54	4	.	.	PROPN
ejpam-6527	54	5	math	math	PROPN
ejpam-6527	54	6	,	,	PUNCT
ejpam-6527	54	7	18	18	NUM
ejpam-6527	54	8	(	(	PUNCT
ejpam-6527	54	9	3	3	NUM
ejpam-6527	54	10	)	)	PUNCT
ejpam-6527	54	11	(	(	PUNCT
ejpam-6527	54	12	2025	2025	NUM
ejpam-6527	54	13	)	)	PUNCT
ejpam-6527	54	14	,	,	PUNCT
ejpam-6527	54	15	6527	6527	NUM
ejpam-6527	54	16	4	4	NUM
ejpam-6527	54	17	of	of	ADP
ejpam-6527	54	18	9	9	NUM
ejpam-6527	54	19	a	a	DET
ejpam-6527	54	20	hilbert	hilbert	NOUN
ejpam-6527	54	21	aθ	aθ	NOUN
ejpam-6527	54	22	-	-	PUNCT
ejpam-6527	54	23	module	module	NOUN
ejpam-6527	54	24	is	be	AUX
ejpam-6527	54	25	a	a	DET
ejpam-6527	54	26	right	right	ADJ
ejpam-6527	54	27	aθ	aθ	NOUN
ejpam-6527	54	28	-	-	PUNCT
ejpam-6527	54	29	module	module	NOUN
ejpam-6527	54	30	equipped	equip	VERB
ejpam-6527	54	31	with	with	ADP
ejpam-6527	54	32	an	an	DET
ejpam-6527	54	33	aθ	aθ	ADV
ejpam-6527	54	34	-	-	PUNCT
ejpam-6527	54	35	valued	value	VERB
ejpam-6527	54	36	inner	inner	ADJ
ejpam-6527	54	37	product	product	NOUN
ejpam-6527	54	38	⟨	⟨	VERB
ejpam-6527	54	39	·	·	PUNCT
ejpam-6527	54	40	,	,	PUNCT
ejpam-6527	54	41	·	·	PUNCT
ejpam-6527	54	42	⟩	⟩	NOUN
ejpam-6527	54	43	:	:	PUNCT
ejpam-6527	54	44	e	e	X
ejpam-6527	54	45	×	×	NOUN
ejpam-6527	54	46	e	e	PROPN
ejpam-6527	54	47	→	→	SYM
ejpam-6527	54	48	aθ	aθ	NOUN
ejpam-6527	54	49	,	,	PUNCT
ejpam-6527	54	50	which	which	PRON
ejpam-6527	54	51	is	be	AUX
ejpam-6527	54	52	positive	positive	ADJ
ejpam-6527	54	53	-	-	PUNCT
ejpam-6527	54	54	definite	definite	ADJ
ejpam-6527	54	55	and	and	CCONJ
ejpam-6527	54	56	complete	complete	ADJ
ejpam-6527	54	57	with	with	ADP
ejpam-6527	54	58	respect	respect	NOUN
ejpam-6527	54	59	to	to	ADP
ejpam-6527	54	60	the	the	DET
ejpam-6527	54	61	norm	norm	NOUN
ejpam-6527	54	62	induced	induce	VERB
ejpam-6527	54	63	by	by	ADP
ejpam-6527	54	64	this	this	DET
ejpam-6527	54	65	inner	inner	ADJ
ejpam-6527	54	66	product	product	NOUN
ejpam-6527	54	67	.	.	PUNCT
ejpam-6527	55	1	definition	definition	NOUN
ejpam-6527	55	2	3	3	NUM
ejpam-6527	55	3	.	.	PUNCT
ejpam-6527	55	4	compactness	compactness	NOUN
ejpam-6527	56	1	[	[	X
ejpam-6527	56	2	15	15	NUM
ejpam-6527	56	3	]	]	X
ejpam-6527	56	4	an	an	DET
ejpam-6527	56	5	operator	operator	NOUN
ejpam-6527	56	6	t	t	NOUN
ejpam-6527	56	7	:	:	PUNCT
ejpam-6527	56	8	e	e	X
ejpam-6527	56	9	→	→	SYM
ejpam-6527	56	10	e	e	X
ejpam-6527	56	11	on	on	ADP
ejpam-6527	56	12	a	a	DET
ejpam-6527	56	13	hilbert	hilbert	NOUN
ejpam-6527	56	14	aθ	aθ	NOUN
ejpam-6527	56	15	-	-	PUNCT
ejpam-6527	56	16	module	module	NOUN
ejpam-6527	56	17	e	e	NOUN
ejpam-6527	56	18	is	be	AUX
ejpam-6527	56	19	said	say	VERB
ejpam-6527	56	20	to	to	PART
ejpam-6527	56	21	be	be	AUX
ejpam-6527	56	22	compact	compact	ADJ
ejpam-6527	56	23	if	if	SCONJ
ejpam-6527	56	24	it	it	PRON
ejpam-6527	56	25	can	can	AUX
ejpam-6527	56	26	be	be	AUX
ejpam-6527	56	27	represented	represent	VERB
ejpam-6527	56	28	as	as	ADP
ejpam-6527	56	29	the	the	DET
ejpam-6527	56	30	norm	norm	NOUN
ejpam-6527	56	31	limit	limit	NOUN
ejpam-6527	56	32	of	of	ADP
ejpam-6527	56	33	finite	finite	ADJ
ejpam-6527	56	34	-	-	ADJ
ejpam-6527	56	35	rank	rank	ADJ
ejpam-6527	56	36	operators	operator	NOUN
ejpam-6527	56	37	:	:	PUNCT
ejpam-6527	56	38	tk(ξ	tk(ξ	ADV
ejpam-6527	56	39	)	)	PUNCT
ejpam-6527	56	40	=	=	PUNCT
ejpam-6527	56	41	nk∑	nk∑	PROPN
ejpam-6527	56	42	i=1	i=1	PROPN
ejpam-6527	56	43	η	η	PROPN
ejpam-6527	56	44	(	(	PUNCT
ejpam-6527	56	45	k	k	NOUN
ejpam-6527	56	46	)	)	PUNCT
ejpam-6527	56	47	i	i	PRON
ejpam-6527	56	48	·	·	PUNCT
ejpam-6527	56	49	⟨ζ(k)i	⟨ζ(k)i	PROPN
ejpam-6527	56	50	,	,	PUNCT
ejpam-6527	56	51	ξ⟩	ξ⟩	PROPN
ejpam-6527	56	52	,	,	PUNCT
ejpam-6527	56	53	where	where	SCONJ
ejpam-6527	56	54	η	η	PROPN
ejpam-6527	56	55	(	(	PUNCT
ejpam-6527	56	56	k	k	NOUN
ejpam-6527	56	57	)	)	PUNCT
ejpam-6527	56	58	i	i	PRON
ejpam-6527	56	59	,	,	PUNCT
ejpam-6527	56	60	ζ	ζ	PROPN
ejpam-6527	56	61	(	(	PUNCT
ejpam-6527	56	62	k	k	NOUN
ejpam-6527	56	63	)	)	PUNCT
ejpam-6527	56	64	i	i	PRON
ejpam-6527	56	65	∈	∈	PROPN
ejpam-6527	56	66	e	e	NOUN
ejpam-6527	56	67	,	,	PUNCT
ejpam-6527	56	68	with	with	ADP
ejpam-6527	56	69	order	order	NOUN
ejpam-6527	56	70	k	k	PROPN
ejpam-6527	56	71	∈	∈	PROPN
ejpam-6527	56	72	n	n	PROPN
ejpam-6527	56	73	and	and	CCONJ
ejpam-6527	56	74	lim	lim	PROPN
ejpam-6527	57	1	k→∞	k→∞	NOUN
ejpam-6527	57	2	∥t	∥t	PROPN
ejpam-6527	57	3	−	−	PROPN
ejpam-6527	58	1	tk∥	tk∥	NOUN
ejpam-6527	59	1	=	=	NOUN
ejpam-6527	60	1	0	0	PROPN
ejpam-6527	60	2	.	.	PUNCT
ejpam-6527	61	1	definition	definition	NOUN
ejpam-6527	61	2	4	4	NUM
ejpam-6527	61	3	.	.	PUNCT
ejpam-6527	61	4	complete	complete	ADJ
ejpam-6527	61	5	compactness	compactness	NOUN
ejpam-6527	61	6	[	[	X
ejpam-6527	61	7	18	18	NUM
ejpam-6527	61	8	,	,	PUNCT
ejpam-6527	61	9	20	20	NUM
ejpam-6527	61	10	,	,	PUNCT
ejpam-6527	61	11	22	22	NUM
ejpam-6527	61	12	]	]	PUNCT
ejpam-6527	61	13	let	let	VERB
ejpam-6527	61	14	t	t	NOUN
ejpam-6527	61	15	:	:	PUNCT
ejpam-6527	61	16	e	e	X
ejpam-6527	61	17	→	→	PUNCT
ejpam-6527	61	18	e	e	AUX
ejpam-6527	61	19	be	be	AUX
ejpam-6527	61	20	an	an	DET
ejpam-6527	61	21	adjointable	adjointable	ADJ
ejpam-6527	61	22	operator	operator	NOUN
ejpam-6527	61	23	on	on	ADP
ejpam-6527	61	24	a	a	DET
ejpam-6527	61	25	hilbert	hilbert	NOUN
ejpam-6527	61	26	aθ	aθ	NOUN
ejpam-6527	61	27	-	-	PUNCT
ejpam-6527	61	28	module	module	NOUN
ejpam-6527	61	29	e.	e.	NOUN
ejpam-6527	61	30	the	the	DET
ejpam-6527	61	31	operator	operator	NOUN
ejpam-6527	61	32	t	t	PROPN
ejpam-6527	61	33	is	be	AUX
ejpam-6527	61	34	said	say	VERB
ejpam-6527	61	35	to	to	PART
ejpam-6527	61	36	be	be	AUX
ejpam-6527	61	37	completely	completely	ADV
ejpam-6527	61	38	compact	compact	ADJ
ejpam-6527	61	39	if	if	SCONJ
ejpam-6527	61	40	its	its	PRON
ejpam-6527	61	41	matrix	matrix	NOUN
ejpam-6527	61	42	amplifications	amplification	VERB
ejpam-6527	61	43	tn	tn	NOUN
ejpam-6527	62	1	:	:	PUNCT
ejpam-6527	62	2	=	=	PUNCT
ejpam-6527	62	3	in	in	ADP
ejpam-6527	62	4	⊗	⊗	PROPN
ejpam-6527	62	5	t	t	PROPN
ejpam-6527	62	6	:	:	PUNCT
ejpam-6527	62	7	mn(e	mn(e	X
ejpam-6527	62	8	)	)	PUNCT
ejpam-6527	62	9	→	→	SYM
ejpam-6527	62	10	mn(e	mn(e	NOUN
ejpam-6527	62	11	)	)	PUNCT
ejpam-6527	62	12	are	be	AUX
ejpam-6527	62	13	compact	compact	ADJ
ejpam-6527	62	14	for	for	ADP
ejpam-6527	62	15	all	all	DET
ejpam-6527	62	16	n	n	PRON
ejpam-6527	62	17	∈	∈	PROPN
ejpam-6527	62	18	n.	n.	NOUN
ejpam-6527	62	19	definition	definition	NOUN
ejpam-6527	62	20	5	5	NUM
ejpam-6527	62	21	.	.	PUNCT
ejpam-6527	62	22	stability	stability	NOUN
ejpam-6527	62	23	under	under	ADP
ejpam-6527	62	24	tensor	tensor	NOUN
ejpam-6527	62	25	products[19	products[19	NOUN
ejpam-6527	62	26	,	,	PUNCT
ejpam-6527	62	27	20	20	NUM
ejpam-6527	62	28	]	]	PUNCT
ejpam-6527	62	29	let	let	VERB
ejpam-6527	62	30	t	t	PROPN
ejpam-6527	62	31	,	,	PUNCT
ejpam-6527	62	32	s	s	AUX
ejpam-6527	62	33	be	be	AUX
ejpam-6527	62	34	compact	compact	ADJ
ejpam-6527	62	35	adjointable	adjointable	NOUN
ejpam-6527	62	36	operators	operator	NOUN
ejpam-6527	62	37	on	on	ADP
ejpam-6527	62	38	hilbert	hilbert	PROPN
ejpam-6527	62	39	aθ	aθ	NOUN
ejpam-6527	62	40	-	-	PUNCT
ejpam-6527	62	41	modules	module	NOUN
ejpam-6527	62	42	e	e	NOUN
ejpam-6527	62	43	,	,	PUNCT
ejpam-6527	62	44	f	f	PROPN
ejpam-6527	62	45	respectively	respectively	ADV
ejpam-6527	62	46	.	.	PUNCT
ejpam-6527	63	1	then	then	ADV
ejpam-6527	63	2	the	the	DET
ejpam-6527	63	3	tensor	tensor	NOUN
ejpam-6527	63	4	product	product	NOUN
ejpam-6527	63	5	operator	operator	NOUN
ejpam-6527	63	6	t	t	PROPN
ejpam-6527	63	7	⊗	⊗	PROPN
ejpam-6527	63	8	s	s	PART
ejpam-6527	63	9	:	:	PUNCT
ejpam-6527	63	10	e	e	PROPN
ejpam-6527	63	11	⊗	⊗	PROPN
ejpam-6527	63	12	f	f	PROPN
ejpam-6527	63	13	→	→	PUNCT
ejpam-6527	63	14	e	e	PROPN
ejpam-6527	63	15	⊗	⊗	PROPN
ejpam-6527	63	16	f	f	PROPN
ejpam-6527	63	17	is	be	AUX
ejpam-6527	63	18	also	also	ADV
ejpam-6527	63	19	compact	compact	ADJ
ejpam-6527	63	20	.	.	PUNCT
ejpam-6527	64	1	definition	definition	NOUN
ejpam-6527	64	2	6	6	NUM
ejpam-6527	64	3	.	.	PUNCT
ejpam-6527	64	4	completely	completely	ADV
ejpam-6527	64	5	bounded	bound	VERB
ejpam-6527	64	6	[	[	X
ejpam-6527	64	7	10	10	NUM
ejpam-6527	64	8	]	]	PUNCT
ejpam-6527	64	9	let	let	VERB
ejpam-6527	64	10	t	t	NOUN
ejpam-6527	64	11	:	:	PUNCT
ejpam-6527	64	12	e	e	X
ejpam-6527	64	13	→	→	PUNCT
ejpam-6527	64	14	f	f	X
ejpam-6527	64	15	be	be	AUX
ejpam-6527	64	16	a	a	DET
ejpam-6527	64	17	compact	compact	ADJ
ejpam-6527	64	18	linear	linear	NOUN
ejpam-6527	64	19	-	-	PUNCT
ejpam-6527	64	20	transformation	transformation	NOUN
ejpam-6527	64	21	between	between	ADP
ejpam-6527	64	22	operator	operator	NOUN
ejpam-6527	64	23	spaces	space	NOUN
ejpam-6527	64	24	e	e	NOUN
ejpam-6527	64	25	and	and	CCONJ
ejpam-6527	64	26	f	f	PROPN
ejpam-6527	64	27	.	.	PUNCT
ejpam-6527	65	1	the	the	DET
ejpam-6527	65	2	operator	operator	NOUN
ejpam-6527	65	3	t	t	PROPN
ejpam-6527	65	4	is	be	AUX
ejpam-6527	65	5	said	say	VERB
ejpam-6527	65	6	to	to	PART
ejpam-6527	65	7	be	be	AUX
ejpam-6527	65	8	completely	completely	ADV
ejpam-6527	65	9	bounded	bound	VERB
ejpam-6527	65	10	if	if	SCONJ
ejpam-6527	65	11	the	the	DET
ejpam-6527	65	12	sequence	sequence	NOUN
ejpam-6527	65	13	of	of	ADP
ejpam-6527	65	14	amplifications	amplification	NOUN
ejpam-6527	65	15	tn	tn	PROPN
ejpam-6527	65	16	:	:	PUNCT
ejpam-6527	65	17	mn(e	mn(e	X
ejpam-6527	65	18	)	)	PUNCT
ejpam-6527	65	19	→	→	SYM
ejpam-6527	65	20	mn(f	mn(f	NUM
ejpam-6527	65	21	)	)	PUNCT
ejpam-6527	65	22	is	be	AUX
ejpam-6527	65	23	uniformly	uniformly	ADV
ejpam-6527	65	24	bounded	bound	VERB
ejpam-6527	65	25	,	,	PUNCT
ejpam-6527	65	26	that	that	ADV
ejpam-6527	65	27	is	is	ADV
ejpam-6527	65	28	,	,	PUNCT
ejpam-6527	65	29	∥t∥cb	∥t∥cb	NUM
ejpam-6527	65	30	:	:	PUNCT
ejpam-6527	65	31	=	=	NUM
ejpam-6527	65	32	sup	sup	NUM
ejpam-6527	65	33	n∈n	n∈n	ADV
ejpam-6527	65	34	∥tn∥	∥tn∥	NUM
ejpam-6527	65	35	<	<	X
ejpam-6527	65	36	∞	∞	PROPN
ejpam-6527	65	37	,	,	PUNCT
ejpam-6527	65	38	where	where	SCONJ
ejpam-6527	65	39	tn	tn	PROPN
ejpam-6527	65	40	denotes	denote	VERB
ejpam-6527	65	41	the	the	DET
ejpam-6527	65	42	matrix	matrix	NOUN
ejpam-6527	65	43	amplification	amplification	NOUN
ejpam-6527	65	44	of	of	ADP
ejpam-6527	65	45	t	t	PROPN
ejpam-6527	65	46	acting	act	VERB
ejpam-6527	65	47	on	on	ADP
ejpam-6527	65	48	mn(e	mn(e	NOUN
ejpam-6527	65	49	)	)	PUNCT
ejpam-6527	65	50	.	.	PUNCT
ejpam-6527	66	1	m.	m.	PROPN
ejpam-6527	66	2	s.	s.	PROPN
ejpam-6527	66	3	ali	ali	PROPN
ejpam-6527	66	4	et	et	PROPN
ejpam-6527	66	5	al	al	PROPN
ejpam-6527	66	6	.	.	PUNCT
ejpam-6527	66	7	/	/	SYM
ejpam-6527	66	8	eur	eur	PROPN
ejpam-6527	66	9	.	.	PUNCT
ejpam-6527	67	1	j.	j.	PROPN
ejpam-6527	67	2	pure	pure	PROPN
ejpam-6527	67	3	appl	appl	PROPN
ejpam-6527	67	4	.	.	PROPN
ejpam-6527	67	5	math	math	PROPN
ejpam-6527	67	6	,	,	PUNCT
ejpam-6527	67	7	18	18	NUM
ejpam-6527	67	8	(	(	PUNCT
ejpam-6527	67	9	3	3	NUM
ejpam-6527	67	10	)	)	PUNCT
ejpam-6527	67	11	(	(	PUNCT
ejpam-6527	67	12	2025	2025	NUM
ejpam-6527	67	13	)	)	PUNCT
ejpam-6527	67	14	,	,	PUNCT
ejpam-6527	67	15	6527	6527	NUM
ejpam-6527	67	16	5	5	NUM
ejpam-6527	67	17	of	of	ADP
ejpam-6527	67	18	9	9	NUM
ejpam-6527	67	19	4	4	NUM
ejpam-6527	67	20	.	.	PUNCT
ejpam-6527	67	21	main	main	ADJ
ejpam-6527	67	22	results	result	NOUN
ejpam-6527	67	23	and	and	CCONJ
ejpam-6527	67	24	applications	application	NOUN
ejpam-6527	67	25	4.1	4.1	NUM
ejpam-6527	67	26	.	.	PUNCT
ejpam-6527	68	1	main	main	ADJ
ejpam-6527	68	2	results	result	NOUN
ejpam-6527	68	3	in	in	ADP
ejpam-6527	68	4	this	this	DET
ejpam-6527	68	5	subsection	subsection	NOUN
ejpam-6527	68	6	,	,	PUNCT
ejpam-6527	68	7	we	we	PRON
ejpam-6527	68	8	will	will	AUX
ejpam-6527	68	9	prove	prove	VERB
ejpam-6527	68	10	our	our	PRON
ejpam-6527	68	11	main	main	ADJ
ejpam-6527	68	12	theorems	theorem	NOUN
ejpam-6527	68	13	on	on	ADP
ejpam-6527	68	14	compactness	compactness	NOUN
ejpam-6527	68	15	in	in	ADP
ejpam-6527	68	16	operator	operator	NOUN
ejpam-6527	68	17	spaces	space	NOUN
ejpam-6527	68	18	over	over	ADP
ejpam-6527	68	19	aθ	aθ	NOUN
ejpam-6527	68	20	.	.	PUNCT
ejpam-6527	69	1	theorem	theorem	NOUN
ejpam-6527	69	2	1	1	NUM
ejpam-6527	69	3	.	.	PUNCT
ejpam-6527	70	1	an	an	DET
ejpam-6527	70	2	operator	operator	NOUN
ejpam-6527	70	3	t	t	NOUN
ejpam-6527	70	4	is	be	AUX
ejpam-6527	70	5	compact	compact	ADJ
ejpam-6527	70	6	if	if	SCONJ
ejpam-6527	71	1	and	and	CCONJ
ejpam-6527	71	2	only	only	ADV
ejpam-6527	71	3	if	if	SCONJ
ejpam-6527	71	4	it	it	PRON
ejpam-6527	71	5	is	be	AUX
ejpam-6527	71	6	completely	completely	ADV
ejpam-6527	71	7	compact	compact	ADJ
ejpam-6527	71	8	in	in	ADP
ejpam-6527	71	9	the	the	DET
ejpam-6527	71	10	operator	operator	NOUN
ejpam-6527	71	11	space	space	NOUN
ejpam-6527	71	12	sense	sense	NOUN
ejpam-6527	71	13	,	,	PUNCT
ejpam-6527	71	14	provided	provide	VERB
ejpam-6527	71	15	that	that	SCONJ
ejpam-6527	71	16	t	t	PROPN
ejpam-6527	71	17	is	be	AUX
ejpam-6527	71	18	an	an	DET
ejpam-6527	71	19	adjointable	adjointable	ADJ
ejpam-6527	71	20	operator	operator	NOUN
ejpam-6527	71	21	.	.	PUNCT
ejpam-6527	72	1	proof	proof	NOUN
ejpam-6527	72	2	.	.	PUNCT
ejpam-6527	73	1	let	let	AUX
ejpam-6527	73	2	t	t	PROPN
ejpam-6527	73	3	∈	∈	PROPN
ejpam-6527	73	4	l(e	l(e	NOUN
ejpam-6527	73	5	)	)	PUNCT
ejpam-6527	73	6	be	be	AUX
ejpam-6527	73	7	adjointable	adjointable	ADJ
ejpam-6527	73	8	.	.	PUNCT
ejpam-6527	74	1	if	if	SCONJ
ejpam-6527	74	2	t	t	PROPN
ejpam-6527	74	3	is	be	AUX
ejpam-6527	74	4	compact	compact	ADJ
ejpam-6527	74	5	,	,	PUNCT
ejpam-6527	74	6	then	then	ADV
ejpam-6527	74	7	by	by	ADP
ejpam-6527	74	8	definition	definition	NOUN
ejpam-6527	74	9	,	,	PUNCT
ejpam-6527	74	10	there	there	PRON
ejpam-6527	74	11	exists	exist	VERB
ejpam-6527	74	12	a	a	DET
ejpam-6527	74	13	sequence	sequence	NOUN
ejpam-6527	74	14	of	of	ADP
ejpam-6527	74	15	finite	finite	ADJ
ejpam-6527	74	16	-	-	ADJ
ejpam-6527	74	17	rank	rank	ADJ
ejpam-6527	74	18	operators	operator	NOUN
ejpam-6527	74	19	{	{	PUNCT
ejpam-6527	74	20	tk	tk	PROPN
ejpam-6527	74	21	}	}	PUNCT
ejpam-6527	75	1	such	such	ADJ
ejpam-6527	75	2	that	that	SCONJ
ejpam-6527	75	3	lim	lim	PROPN
ejpam-6527	75	4	k→∞	k→∞	NOUN
ejpam-6527	75	5	∥t	∥t	PROPN
ejpam-6527	75	6	−	−	PROPN
ejpam-6527	76	1	tk∥	tk∥	NOUN
ejpam-6527	76	2	=	=	NOUN
ejpam-6527	76	3	0	0	NUM
ejpam-6527	76	4	,	,	PUNCT
ejpam-6527	76	5	where	where	SCONJ
ejpam-6527	76	6	each	each	DET
ejpam-6527	76	7	tk	tk	PROPN
ejpam-6527	76	8	is	be	AUX
ejpam-6527	76	9	of	of	ADP
ejpam-6527	76	10	the	the	DET
ejpam-6527	76	11	form	form	NOUN
ejpam-6527	76	12	tk(ξ	tk(ξ	PUNCT
ejpam-6527	76	13	)	)	PUNCT
ejpam-6527	77	1	=	=	PUNCT
ejpam-6527	77	2	nk∑	nk∑	PROPN
ejpam-6527	77	3	i=1	i=1	PROPN
ejpam-6527	77	4	η	η	PROPN
ejpam-6527	77	5	(	(	PUNCT
ejpam-6527	77	6	k	k	NOUN
ejpam-6527	77	7	)	)	PUNCT
ejpam-6527	77	8	i	i	PRON
ejpam-6527	77	9	·	·	PUNCT
ejpam-6527	77	10	⟨ζ(k)i	⟨ζ(k)i	PROPN
ejpam-6527	77	11	,	,	PUNCT
ejpam-6527	77	12	ξ⟩	ξ⟩	PROPN
ejpam-6527	77	13	,	,	PUNCT
ejpam-6527	77	14	with	with	ADP
ejpam-6527	77	15	η	η	PROPN
ejpam-6527	77	16	(	(	PUNCT
ejpam-6527	77	17	k	k	NOUN
ejpam-6527	77	18	)	)	PUNCT
ejpam-6527	77	19	i	i	PRON
ejpam-6527	77	20	,	,	PUNCT
ejpam-6527	77	21	ζ	ζ	PROPN
ejpam-6527	77	22	(	(	PUNCT
ejpam-6527	77	23	k	k	NOUN
ejpam-6527	77	24	)	)	PUNCT
ejpam-6527	78	1	i	i	PRON
ejpam-6527	78	2	∈	∈	PROPN
ejpam-6527	78	3	e.	e.	PROPN
ejpam-6527	78	4	for	for	ADP
ejpam-6527	78	5	each	each	DET
ejpam-6527	78	6	n	n	PRON
ejpam-6527	78	7	∈	∈	PROPN
ejpam-6527	78	8	n	n	CCONJ
ejpam-6527	78	9	,	,	PUNCT
ejpam-6527	78	10	consider	consider	VERB
ejpam-6527	78	11	the	the	DET
ejpam-6527	78	12	matrix	matrix	NOUN
ejpam-6527	78	13	amplification	amplification	NOUN
ejpam-6527	78	14	tn	tn	NOUN
ejpam-6527	79	1	:	:	PUNCT
ejpam-6527	79	2	=	=	PUNCT
ejpam-6527	79	3	in	in	ADP
ejpam-6527	79	4	⊗	⊗	PROPN
ejpam-6527	79	5	t	t	PROPN
ejpam-6527	79	6	:	:	PUNCT
ejpam-6527	79	7	mn(e	mn(e	X
ejpam-6527	79	8	)	)	PUNCT
ejpam-6527	79	9	→	→	SYM
ejpam-6527	79	10	mn(e	mn(e	NOUN
ejpam-6527	79	11	)	)	PUNCT
ejpam-6527	79	12	.	.	PUNCT
ejpam-6527	80	1	since	since	SCONJ
ejpam-6527	80	2	matrix	matrix	NOUN
ejpam-6527	80	3	norms	norm	NOUN
ejpam-6527	80	4	in	in	ADP
ejpam-6527	80	5	operator	operator	NOUN
ejpam-6527	80	6	spaces	space	NOUN
ejpam-6527	80	7	are	be	AUX
ejpam-6527	80	8	defined	define	VERB
ejpam-6527	80	9	via	via	ADP
ejpam-6527	80	10	ruan	ruan	PROPN
ejpam-6527	80	11	’s	’s	PART
ejpam-6527	80	12	axioms	axiom	NOUN
ejpam-6527	80	13	,	,	PUNCT
ejpam-6527	80	14	the	the	DET
ejpam-6527	80	15	compactness	compactness	NOUN
ejpam-6527	80	16	of	of	ADP
ejpam-6527	80	17	t	t	PROPN
ejpam-6527	80	18	implies	imply	VERB
ejpam-6527	80	19	that	that	SCONJ
ejpam-6527	80	20	the	the	DET
ejpam-6527	80	21	sequence	sequence	NOUN
ejpam-6527	80	22	tn	tn	PROPN
ejpam-6527	80	23	,	,	PUNCT
ejpam-6527	80	24	k	k	PROPN
ejpam-6527	80	25	:	:	PUNCT
ejpam-6527	80	26	=	=	PUNCT
ejpam-6527	80	27	in	in	ADP
ejpam-6527	80	28	⊗	⊗	PROPN
ejpam-6527	80	29	tk	tk	PROPN
ejpam-6527	80	30	converges	converge	VERB
ejpam-6527	80	31	uniformly	uniformly	ADV
ejpam-6527	80	32	to	to	ADP
ejpam-6527	80	33	tn	tn	PROPN
ejpam-6527	80	34	.	.	PUNCT
ejpam-6527	81	1	therefore	therefore	ADV
ejpam-6527	81	2	,	,	PUNCT
ejpam-6527	81	3	tn	tn	PROPN
ejpam-6527	81	4	is	be	AUX
ejpam-6527	81	5	compact	compact	ADJ
ejpam-6527	81	6	for	for	ADP
ejpam-6527	81	7	all	all	DET
ejpam-6527	81	8	n	n	CCONJ
ejpam-6527	81	9	,	,	PUNCT
ejpam-6527	81	10	and	and	CCONJ
ejpam-6527	81	11	thus	thus	ADV
ejpam-6527	81	12	t	t	NOUN
ejpam-6527	81	13	is	be	AUX
ejpam-6527	81	14	completely	completely	ADV
ejpam-6527	81	15	compact	compact	ADJ
ejpam-6527	81	16	.	.	PUNCT
ejpam-6527	82	1	conversely	conversely	ADV
ejpam-6527	82	2	,	,	PUNCT
ejpam-6527	82	3	if	if	SCONJ
ejpam-6527	82	4	t	t	PROPN
ejpam-6527	82	5	is	be	AUX
ejpam-6527	82	6	completely	completely	ADV
ejpam-6527	82	7	compact	compact	ADJ
ejpam-6527	82	8	,	,	PUNCT
ejpam-6527	82	9	then	then	ADV
ejpam-6527	82	10	for	for	ADP
ejpam-6527	82	11	every	every	DET
ejpam-6527	82	12	n	n	CCONJ
ejpam-6527	82	13	,	,	PUNCT
ejpam-6527	82	14	tn	tn	PROPN
ejpam-6527	82	15	is	be	AUX
ejpam-6527	82	16	compact	compact	ADJ
ejpam-6527	82	17	.	.	PUNCT
ejpam-6527	83	1	in	in	ADP
ejpam-6527	83	2	particular	particular	ADJ
ejpam-6527	83	3	,	,	PUNCT
ejpam-6527	83	4	t1	t1	PROPN
ejpam-6527	83	5	=	=	PUNCT
ejpam-6527	83	6	t	t	PROPN
ejpam-6527	83	7	is	be	AUX
ejpam-6527	83	8	compact	compact	ADJ
ejpam-6527	83	9	.	.	PUNCT
ejpam-6527	84	1	hence	hence	ADV
ejpam-6527	84	2	,	,	PUNCT
ejpam-6527	84	3	the	the	DET
ejpam-6527	84	4	two	two	NUM
ejpam-6527	84	5	notions	notion	NOUN
ejpam-6527	84	6	coincide	coincide	VERB
ejpam-6527	84	7	under	under	ADP
ejpam-6527	84	8	adjointability	adjointability	NOUN
ejpam-6527	84	9	.	.	PUNCT
ejpam-6527	85	1	corollary	corollary	ADJ
ejpam-6527	85	2	1	1	NUM
ejpam-6527	85	3	.	.	PUNCT
ejpam-6527	86	1	let	let	VERB
ejpam-6527	86	2	t	t	NOUN
ejpam-6527	86	3	:	:	PUNCT
ejpam-6527	86	4	e	e	X
ejpam-6527	86	5	→	→	PUNCT
ejpam-6527	86	6	e	e	AUX
ejpam-6527	86	7	be	be	AUX
ejpam-6527	86	8	an	an	DET
ejpam-6527	86	9	adjointable	adjointable	ADJ
ejpam-6527	86	10	operator	operator	NOUN
ejpam-6527	86	11	on	on	ADP
ejpam-6527	86	12	a	a	DET
ejpam-6527	86	13	hilbert	hilbert	NOUN
ejpam-6527	86	14	aθ	aθ	NOUN
ejpam-6527	86	15	-	-	PUNCT
ejpam-6527	86	16	module	module	NOUN
ejpam-6527	86	17	e.	e.	NOUN
ejpam-6527	86	18	if	if	SCONJ
ejpam-6527	86	19	t	t	PROPN
ejpam-6527	86	20	∗	∗	NOUN
ejpam-6527	86	21	is	be	AUX
ejpam-6527	86	22	compact	compact	ADJ
ejpam-6527	86	23	,	,	PUNCT
ejpam-6527	86	24	then	then	ADV
ejpam-6527	86	25	t	t	PROPN
ejpam-6527	86	26	is	be	AUX
ejpam-6527	86	27	compact	compact	ADJ
ejpam-6527	86	28	.	.	PUNCT
ejpam-6527	87	1	proof	proof	NOUN
ejpam-6527	87	2	.	.	PUNCT
ejpam-6527	88	1	in	in	ADP
ejpam-6527	88	2	a	a	DET
ejpam-6527	88	3	hilbert	hilbert	NOUN
ejpam-6527	88	4	aθ	aθ	NOUN
ejpam-6527	88	5	-	-	PUNCT
ejpam-6527	88	6	module	module	NOUN
ejpam-6527	88	7	,	,	PUNCT
ejpam-6527	88	8	the	the	DET
ejpam-6527	88	9	polar	polar	ADJ
ejpam-6527	88	10	decomposition	decomposition	NOUN
ejpam-6527	88	11	t	t	NOUN
ejpam-6527	88	12	=	=	SYM
ejpam-6527	88	13	u	u	NOUN
ejpam-6527	88	14	|t	|t	NOUN
ejpam-6527	89	1	|	|	ADV
ejpam-6527	89	2	exists	exist	VERB
ejpam-6527	89	3	,	,	PUNCT
ejpam-6527	89	4	where	where	SCONJ
ejpam-6527	89	5	u	u	NOUN
ejpam-6527	89	6	is	be	AUX
ejpam-6527	89	7	a	a	DET
ejpam-6527	89	8	partial	partial	ADJ
ejpam-6527	89	9	isometry	isometry	NOUN
ejpam-6527	89	10	and	and	CCONJ
ejpam-6527	89	11	adjointable.theorem	adjointable.theorem	NUM
ejpam-6527	89	12	1	1	NUM
ejpam-6527	89	13	establishes	establish	VERB
ejpam-6527	89	14	that	that	DET
ejpam-6527	89	15	compactness	compactness	NOUN
ejpam-6527	89	16	and	and	CCONJ
ejpam-6527	89	17	complete	complete	ADJ
ejpam-6527	89	18	compactness	compactness	NOUN
ejpam-6527	89	19	coincide	coincide	NOUN
ejpam-6527	89	20	for	for	ADP
ejpam-6527	89	21	adjointable	adjointable	NOUN
ejpam-6527	89	22	operators	operator	NOUN
ejpam-6527	89	23	.	.	PUNCT
ejpam-6527	90	1	since	since	SCONJ
ejpam-6527	90	2	|t	|t	PROPN
ejpam-6527	90	3	|	|	ADV
ejpam-6527	90	4	=	=	SYM
ejpam-6527	90	5	(	(	PUNCT
ejpam-6527	90	6	t	t	PROPN
ejpam-6527	90	7	∗t	∗t	PROPN
ejpam-6527	90	8	)	)	PUNCT
ejpam-6527	90	9	1/2	1/2	NUM
ejpam-6527	90	10	is	be	AUX
ejpam-6527	90	11	obtained	obtain	VERB
ejpam-6527	90	12	via	via	ADP
ejpam-6527	90	13	continuous	continuous	ADJ
ejpam-6527	90	14	functional	functional	ADJ
ejpam-6527	90	15	calculus	calculus	NOUN
ejpam-6527	90	16	applied	apply	VERB
ejpam-6527	90	17	to	to	ADP
ejpam-6527	90	18	the	the	DET
ejpam-6527	90	19	compact	compact	ADJ
ejpam-6527	90	20	operator	operator	NOUN
ejpam-6527	90	21	t	t	PROPN
ejpam-6527	90	22	∗	∗	NOUN
ejpam-6527	90	23	,	,	PUNCT
ejpam-6527	90	24	it	it	PRON
ejpam-6527	90	25	follows	follow	VERB
ejpam-6527	90	26	that	that	SCONJ
ejpam-6527	90	27	|t	|t	VERB
ejpam-6527	91	1	|	|	INTJ
ejpam-6527	91	2	is	be	AUX
ejpam-6527	91	3	compact	compact	ADJ
ejpam-6527	91	4	.	.	PUNCT
ejpam-6527	92	1	then	then	ADV
ejpam-6527	92	2	t	t	PROPN
ejpam-6527	92	3	=	=	SYM
ejpam-6527	92	4	u	u	SYM
ejpam-6527	92	5	|t	|t	NOUN
ejpam-6527	93	1	|	|	ADV
ejpam-6527	93	2	is	be	AUX
ejpam-6527	93	3	the	the	DET
ejpam-6527	93	4	product	product	NOUN
ejpam-6527	93	5	of	of	ADP
ejpam-6527	93	6	an	an	DET
ejpam-6527	93	7	adjointable	adjointable	NOUN
ejpam-6527	93	8	operator	operator	NOUN
ejpam-6527	93	9	and	and	CCONJ
ejpam-6527	93	10	a	a	DET
ejpam-6527	93	11	compact	compact	ADJ
ejpam-6527	93	12	operator	operator	NOUN
ejpam-6527	93	13	,	,	PUNCT
ejpam-6527	93	14	and	and	CCONJ
ejpam-6527	93	15	hence	hence	ADV
ejpam-6527	93	16	is	be	AUX
ejpam-6527	93	17	compact	compact	ADJ
ejpam-6527	93	18	.	.	PUNCT
ejpam-6527	94	1	proposition	proposition	NOUN
ejpam-6527	94	2	1	1	NUM
ejpam-6527	94	3	.	.	PUNCT
ejpam-6527	95	1	a	a	DET
ejpam-6527	95	2	compact	compact	ADJ
ejpam-6527	95	3	operator	operator	NOUN
ejpam-6527	95	4	t	t	NOUN
ejpam-6527	95	5	is	be	AUX
ejpam-6527	95	6	completely	completely	ADV
ejpam-6527	95	7	bounded	bound	VERB
ejpam-6527	95	8	if	if	SCONJ
ejpam-6527	95	9	∥t∥cb	∥t∥cb	NUM
ejpam-6527	95	10	=	=	PRON
ejpam-6527	95	11	∥t∥.	∥t∥.	PROPN
ejpam-6527	95	12	the	the	DET
ejpam-6527	95	13	converse	converse	NOUN
ejpam-6527	95	14	does	do	AUX
ejpam-6527	95	15	not	not	PART
ejpam-6527	95	16	necessarily	necessarily	ADV
ejpam-6527	95	17	hold	hold	VERB
ejpam-6527	95	18	.	.	PUNCT
ejpam-6527	96	1	proof	proof	NOUN
ejpam-6527	96	2	.	.	PUNCT
ejpam-6527	97	1	suppose	suppose	VERB
ejpam-6527	97	2	that	that	SCONJ
ejpam-6527	97	3	t	t	PROPN
ejpam-6527	97	4	is	be	AUX
ejpam-6527	97	5	compact	compact	ADJ
ejpam-6527	97	6	and	and	CCONJ
ejpam-6527	97	7	that	that	DET
ejpam-6527	97	8	∥t∥cb	∥t∥cb	NUM
ejpam-6527	97	9	=	=	PUNCT
ejpam-6527	97	10	∥t∥.	∥t∥.	PROPN
ejpam-6527	97	11	since	since	SCONJ
ejpam-6527	97	12	t	t	PROPN
ejpam-6527	97	13	is	be	AUX
ejpam-6527	97	14	a	a	DET
ejpam-6527	97	15	bounded	bounded	ADJ
ejpam-6527	97	16	linear	linear	ADJ
ejpam-6527	97	17	operator	operator	NOUN
ejpam-6527	97	18	between	between	ADP
ejpam-6527	97	19	operator	operator	NOUN
ejpam-6527	97	20	spaces	space	NOUN
ejpam-6527	97	21	,	,	PUNCT
ejpam-6527	97	22	and	and	CCONJ
ejpam-6527	97	23	∥t∥cb	∥t∥cb	X
ejpam-6527	97	24	<	<	X
ejpam-6527	97	25	∞	∞	PROPN
ejpam-6527	97	26	,	,	PUNCT
ejpam-6527	97	27	it	it	PRON
ejpam-6527	97	28	follows	follow	VERB
ejpam-6527	97	29	directly	directly	ADV
ejpam-6527	97	30	from	from	ADP
ejpam-6527	97	31	the	the	DET
ejpam-6527	97	32	definition	definition	NOUN
ejpam-6527	97	33	that	that	SCONJ
ejpam-6527	97	34	t	t	PROPN
ejpam-6527	97	35	is	be	AUX
ejpam-6527	97	36	completely	completely	ADV
ejpam-6527	97	37	bounded	bound	VERB
ejpam-6527	97	38	.	.	PUNCT
ejpam-6527	98	1	therefore	therefore	ADV
ejpam-6527	98	2	,	,	PUNCT
ejpam-6527	98	3	the	the	DET
ejpam-6527	98	4	condition	condition	NOUN
ejpam-6527	98	5	∥t∥cb	∥t∥cb	NOUN
ejpam-6527	98	6	=	=	SYM
ejpam-6527	98	7	∥t∥	∥t∥	VERB
ejpam-6527	98	8	implies	imply	VERB
ejpam-6527	98	9	∥t∥cb	∥t∥cb	PUNCT
ejpam-6527	98	10	<	<	X
ejpam-6527	98	11	∞	∞	PROPN
ejpam-6527	98	12	,	,	PUNCT
ejpam-6527	98	13	which	which	PRON
ejpam-6527	98	14	confirms	confirm	VERB
ejpam-6527	98	15	that	that	SCONJ
ejpam-6527	98	16	t	t	PROPN
ejpam-6527	98	17	is	be	AUX
ejpam-6527	98	18	completely	completely	ADV
ejpam-6527	98	19	bounded	bound	VERB
ejpam-6527	98	20	.	.	PUNCT
ejpam-6527	99	1	however	however	ADV
ejpam-6527	99	2	,	,	PUNCT
ejpam-6527	99	3	the	the	DET
ejpam-6527	99	4	converse	converse	NOUN
ejpam-6527	99	5	does	do	AUX
ejpam-6527	99	6	not	not	PART
ejpam-6527	99	7	necessarily	necessarily	ADV
ejpam-6527	99	8	hold	hold	VERB
ejpam-6527	99	9	.	.	PUNCT
ejpam-6527	100	1	that	that	PRON
ejpam-6527	100	2	is	be	AUX
ejpam-6527	100	3	,	,	PUNCT
ejpam-6527	100	4	there	there	PRON
ejpam-6527	100	5	exist	exist	VERB
ejpam-6527	100	6	compact	compact	ADJ
ejpam-6527	100	7	operators	operator	NOUN
ejpam-6527	100	8	t	t	PROPN
ejpam-6527	100	9	that	that	PRON
ejpam-6527	100	10	are	be	AUX
ejpam-6527	100	11	completely	completely	ADV
ejpam-6527	100	12	bounded	bound	VERB
ejpam-6527	100	13	but	but	CCONJ
ejpam-6527	100	14	satisfy	satisfy	VERB
ejpam-6527	100	15	∥t∥cb	∥t∥cb	NUM
ejpam-6527	100	16	>	>	X
ejpam-6527	100	17	∥t∥.	∥t∥.	PROPN
ejpam-6527	100	18	m.	m.	PROPN
ejpam-6527	100	19	s.	s.	PROPN
ejpam-6527	100	20	ali	ali	PROPN
ejpam-6527	100	21	et	et	PROPN
ejpam-6527	100	22	al	al	PROPN
ejpam-6527	100	23	.	.	PUNCT
ejpam-6527	100	24	/	/	SYM
ejpam-6527	100	25	eur	eur	PROPN
ejpam-6527	100	26	.	.	PUNCT
ejpam-6527	101	1	j.	j.	PROPN
ejpam-6527	101	2	pure	pure	PROPN
ejpam-6527	101	3	appl	appl	PROPN
ejpam-6527	101	4	.	.	PROPN
ejpam-6527	101	5	math	math	PROPN
ejpam-6527	101	6	,	,	PUNCT
ejpam-6527	101	7	18	18	NUM
ejpam-6527	101	8	(	(	PUNCT
ejpam-6527	101	9	3	3	NUM
ejpam-6527	101	10	)	)	PUNCT
ejpam-6527	101	11	(	(	PUNCT
ejpam-6527	101	12	2025	2025	NUM
ejpam-6527	101	13	)	)	PUNCT
ejpam-6527	101	14	,	,	PUNCT
ejpam-6527	101	15	6527	6527	NUM
ejpam-6527	101	16	6	6	NUM
ejpam-6527	101	17	of	of	ADP
ejpam-6527	101	18	9	9	NUM
ejpam-6527	101	19	theorem	theorem	NOUN
ejpam-6527	101	20	2	2	NUM
ejpam-6527	101	21	.	.	PUNCT
ejpam-6527	102	1	let	let	VERB
ejpam-6527	102	2	t	t	NOUN
ejpam-6527	102	3	:	:	PUNCT
ejpam-6527	102	4	e	e	X
ejpam-6527	102	5	→	→	SYM
ejpam-6527	102	6	e	e	PROPN
ejpam-6527	102	7	and	and	CCONJ
ejpam-6527	102	8	s	s	VERB
ejpam-6527	102	9	:	:	PUNCT
ejpam-6527	102	10	f	f	PROPN
ejpam-6527	102	11	→	→	SYM
ejpam-6527	102	12	f	f	X
ejpam-6527	102	13	be	be	AUX
ejpam-6527	102	14	compact	compact	ADJ
ejpam-6527	102	15	adjointable	adjointable	NOUN
ejpam-6527	102	16	operators	operator	NOUN
ejpam-6527	102	17	on	on	ADP
ejpam-6527	102	18	hilbert	hilbert	PROPN
ejpam-6527	102	19	aθ	aθ	NOUN
ejpam-6527	102	20	-	-	PUNCT
ejpam-6527	102	21	modules	module	NOUN
ejpam-6527	102	22	e	e	NOUN
ejpam-6527	102	23	and	and	CCONJ
ejpam-6527	102	24	f	f	PROPN
ejpam-6527	102	25	,	,	PUNCT
ejpam-6527	102	26	respectively	respectively	ADV
ejpam-6527	102	27	.	.	PUNCT
ejpam-6527	103	1	then	then	ADV
ejpam-6527	103	2	the	the	DET
ejpam-6527	103	3	tensor	tensor	NOUN
ejpam-6527	103	4	product	product	NOUN
ejpam-6527	103	5	operator	operator	NOUN
ejpam-6527	103	6	t	t	PROPN
ejpam-6527	103	7	⊗	⊗	PROPN
ejpam-6527	103	8	s	s	PART
ejpam-6527	103	9	:	:	PUNCT
ejpam-6527	103	10	e	e	X
ejpam-6527	103	11	⊗aθ	⊗aθ	X
ejpam-6527	103	12	f	f	X
ejpam-6527	103	13	→	→	SYM
ejpam-6527	103	14	e	e	X
ejpam-6527	103	15	⊗aθ	⊗aθ	X
ejpam-6527	103	16	f	f	PROPN
ejpam-6527	103	17	is	be	AUX
ejpam-6527	103	18	also	also	ADV
ejpam-6527	103	19	compact	compact	ADJ
ejpam-6527	103	20	.	.	PUNCT
ejpam-6527	104	1	moreover	moreover	ADV
ejpam-6527	104	2	,	,	PUNCT
ejpam-6527	104	3	the	the	DET
ejpam-6527	104	4	compactness	compactness	NOUN
ejpam-6527	104	5	property	property	NOUN
ejpam-6527	104	6	is	be	AUX
ejpam-6527	104	7	preserved	preserve	VERB
ejpam-6527	104	8	under	under	ADP
ejpam-6527	104	9	finite	finite	ADJ
ejpam-6527	104	10	internal	internal	ADJ
ejpam-6527	104	11	direct	direct	ADJ
ejpam-6527	104	12	sums	sum	NOUN
ejpam-6527	104	13	of	of	ADP
ejpam-6527	104	14	compact	compact	ADJ
ejpam-6527	104	15	adjointable	adjointable	NOUN
ejpam-6527	104	16	operators	operator	NOUN
ejpam-6527	104	17	.	.	PUNCT
ejpam-6527	105	1	that	that	PRON
ejpam-6527	105	2	is	be	AUX
ejpam-6527	105	3	,	,	PUNCT
ejpam-6527	105	4	if	if	SCONJ
ejpam-6527	105	5	t1	t1	PROPN
ejpam-6527	105	6	,	,	PUNCT
ejpam-6527	105	7	t2	t2	NOUN
ejpam-6527	105	8	are	be	AUX
ejpam-6527	105	9	compact	compact	ADJ
ejpam-6527	105	10	on	on	ADP
ejpam-6527	105	11	e1	e1	PROPN
ejpam-6527	105	12	,	,	PUNCT
ejpam-6527	105	13	e2	e2	PROPN
ejpam-6527	105	14	,	,	PUNCT
ejpam-6527	105	15	then	then	ADV
ejpam-6527	105	16	t1	t1	PROPN
ejpam-6527	105	17	⊕	⊕	PROPN
ejpam-6527	105	18	t2	t2	PROPN
ejpam-6527	105	19	is	be	AUX
ejpam-6527	105	20	compact	compact	ADJ
ejpam-6527	105	21	on	on	ADP
ejpam-6527	105	22	e1	e1	PROPN
ejpam-6527	105	23	⊕	⊕	PROPN
ejpam-6527	105	24	e2	e2	PROPN
ejpam-6527	105	25	.	.	PUNCT
ejpam-6527	106	1	proof	proof	NOUN
ejpam-6527	106	2	.	.	PUNCT
ejpam-6527	107	1	since	since	SCONJ
ejpam-6527	107	2	t	t	PROPN
ejpam-6527	107	3	and	and	CCONJ
ejpam-6527	107	4	s	s	VERB
ejpam-6527	107	5	are	be	AUX
ejpam-6527	107	6	compact	compact	ADJ
ejpam-6527	107	7	,	,	PUNCT
ejpam-6527	107	8	there	there	PRON
ejpam-6527	107	9	exist	exist	VERB
ejpam-6527	107	10	sequences	sequence	NOUN
ejpam-6527	107	11	of	of	ADP
ejpam-6527	107	12	finite	finite	ADJ
ejpam-6527	107	13	-	-	ADJ
ejpam-6527	107	14	rank	rank	ADJ
ejpam-6527	107	15	operators	operator	NOUN
ejpam-6527	107	16	{	{	PUNCT
ejpam-6527	107	17	t	t	PROPN
ejpam-6527	107	18	(	(	PUNCT
ejpam-6527	107	19	k	k	NOUN
ejpam-6527	107	20	)	)	PUNCT
ejpam-6527	107	21	}	}	PUNCT
ejpam-6527	107	22	and	and	CCONJ
ejpam-6527	107	23	{	{	PUNCT
ejpam-6527	107	24	s(ℓ	s(ℓ	NUM
ejpam-6527	107	25	)	)	PUNCT
ejpam-6527	107	26	}	}	PUNCT
ejpam-6527	107	27	such	such	ADJ
ejpam-6527	107	28	that	that	SCONJ
ejpam-6527	107	29	lim	lim	PROPN
ejpam-6527	107	30	k→∞	k→∞	NOUN
ejpam-6527	108	1	∥t	∥t	PROPN
ejpam-6527	108	2	−	−	PROPN
ejpam-6527	108	3	t	t	PROPN
ejpam-6527	108	4	(	(	PUNCT
ejpam-6527	108	5	k)∥	k)∥	NOUN
ejpam-6527	108	6	=	=	SYM
ejpam-6527	108	7	0	0	PROPN
ejpam-6527	108	8	,	,	PUNCT
ejpam-6527	108	9	lim	lim	PROPN
ejpam-6527	108	10	ℓ→∞	ℓ→∞	NOUN
ejpam-6527	109	1	∥s	∥s	NOUN
ejpam-6527	109	2	−	−	PROPN
ejpam-6527	109	3	s(ℓ)∥	s(ℓ)∥	ADJ
ejpam-6527	109	4	=	=	PUNCT
ejpam-6527	110	1	0	0	X
ejpam-6527	110	2	.	.	PUNCT
ejpam-6527	111	1	then	then	ADV
ejpam-6527	111	2	the	the	DET
ejpam-6527	111	3	tensor	tensor	NOUN
ejpam-6527	111	4	product	product	NOUN
ejpam-6527	111	5	t	t	PROPN
ejpam-6527	111	6	⊗	⊗	PROPN
ejpam-6527	111	7	s	s	PART
ejpam-6527	111	8	=	=	PROPN
ejpam-6527	111	9	lim	lim	PROPN
ejpam-6527	111	10	k,ℓ→∞	k,ℓ→∞	PROPN
ejpam-6527	111	11	t	t	PROPN
ejpam-6527	111	12	(	(	PUNCT
ejpam-6527	111	13	k	k	NOUN
ejpam-6527	111	14	)	)	PUNCT
ejpam-6527	111	15	⊗	⊗	PROPN
ejpam-6527	111	16	s(ℓ	s(ℓ	PROPN
ejpam-6527	111	17	)	)	PUNCT
ejpam-6527	111	18	is	be	AUX
ejpam-6527	111	19	a	a	DET
ejpam-6527	111	20	norm	norm	NOUN
ejpam-6527	111	21	-	-	PUNCT
ejpam-6527	111	22	limit	limit	NOUN
ejpam-6527	111	23	of	of	ADP
ejpam-6527	111	24	finite	finite	ADJ
ejpam-6527	111	25	-	-	ADJ
ejpam-6527	111	26	rank	rank	ADJ
ejpam-6527	111	27	operators	operator	NOUN
ejpam-6527	111	28	(	(	PUNCT
ejpam-6527	111	29	since	since	SCONJ
ejpam-6527	111	30	the	the	DET
ejpam-6527	111	31	tensor	tensor	NOUN
ejpam-6527	111	32	of	of	ADP
ejpam-6527	111	33	two	two	NUM
ejpam-6527	111	34	finite	finite	ADJ
ejpam-6527	111	35	-	-	ADJ
ejpam-6527	111	36	rank	rank	ADJ
ejpam-6527	111	37	operators	operator	NOUN
ejpam-6527	111	38	is	be	AUX
ejpam-6527	111	39	again	again	ADV
ejpam-6527	111	40	finite	finite	ADJ
ejpam-6527	111	41	-	-	NOUN
ejpam-6527	111	42	rank	rank	NOUN
ejpam-6527	111	43	)	)	PUNCT
ejpam-6527	111	44	,	,	PUNCT
ejpam-6527	111	45	and	and	CCONJ
ejpam-6527	111	46	hence	hence	ADV
ejpam-6527	111	47	is	be	AUX
ejpam-6527	111	48	compact	compact	ADJ
ejpam-6527	111	49	.	.	PUNCT
ejpam-6527	112	1	for	for	ADP
ejpam-6527	112	2	the	the	DET
ejpam-6527	112	3	direct	direct	ADJ
ejpam-6527	112	4	sum	sum	NOUN
ejpam-6527	112	5	part	part	NOUN
ejpam-6527	112	6	:	:	PUNCT
ejpam-6527	112	7	let	let	VERB
ejpam-6527	112	8	t1	t1	NOUN
ejpam-6527	112	9	and	and	CCONJ
ejpam-6527	112	10	t2	t2	NOUN
ejpam-6527	112	11	be	be	AUX
ejpam-6527	112	12	compact	compact	ADJ
ejpam-6527	112	13	on	on	ADP
ejpam-6527	112	14	e1	e1	PROPN
ejpam-6527	112	15	and	and	CCONJ
ejpam-6527	112	16	e2	e2	PROPN
ejpam-6527	112	17	,	,	PUNCT
ejpam-6527	112	18	respectively	respectively	ADV
ejpam-6527	112	19	.	.	PUNCT
ejpam-6527	113	1	then	then	ADV
ejpam-6527	113	2	their	their	PRON
ejpam-6527	113	3	direct	direct	ADJ
ejpam-6527	113	4	sum	sum	NOUN
ejpam-6527	113	5	t1	t1	PROPN
ejpam-6527	113	6	⊕	⊕	PROPN
ejpam-6527	113	7	t2	t2	PROPN
ejpam-6527	113	8	:	:	PUNCT
ejpam-6527	113	9	e1	e1	PROPN
ejpam-6527	113	10	⊕	⊕	PROPN
ejpam-6527	113	11	e2	e2	PROPN
ejpam-6527	113	12	→	→	SYM
ejpam-6527	113	13	e1	e1	PROPN
ejpam-6527	113	14	⊕	⊕	PROPN
ejpam-6527	113	15	e2	e2	PROPN
ejpam-6527	113	16	is	be	AUX
ejpam-6527	113	17	defined	define	VERB
ejpam-6527	113	18	by	by	ADP
ejpam-6527	113	19	(	(	PUNCT
ejpam-6527	113	20	t1⊕t2)(x1	t1⊕t2)(x1	PROPN
ejpam-6527	113	21	,	,	PUNCT
ejpam-6527	113	22	x2	x2	PROPN
ejpam-6527	113	23	)	)	PUNCT
ejpam-6527	113	24	=	=	SYM
ejpam-6527	113	25	(	(	PUNCT
ejpam-6527	113	26	t1x1	t1x1	NOUN
ejpam-6527	113	27	,	,	PUNCT
ejpam-6527	113	28	t2x2	t2x2	NOUN
ejpam-6527	113	29	)	)	PUNCT
ejpam-6527	113	30	,	,	PUNCT
ejpam-6527	113	31	and	and	CCONJ
ejpam-6527	113	32	since	since	SCONJ
ejpam-6527	113	33	both	both	DET
ejpam-6527	113	34	components	component	NOUN
ejpam-6527	113	35	are	be	AUX
ejpam-6527	113	36	compact	compact	ADJ
ejpam-6527	113	37	,	,	PUNCT
ejpam-6527	113	38	so	so	ADV
ejpam-6527	113	39	is	be	AUX
ejpam-6527	113	40	the	the	DET
ejpam-6527	113	41	operator	operator	NOUN
ejpam-6527	113	42	.	.	PUNCT
ejpam-6527	114	1	this	this	PRON
ejpam-6527	114	2	follows	follow	VERB
ejpam-6527	114	3	from	from	ADP
ejpam-6527	114	4	the	the	DET
ejpam-6527	114	5	fact	fact	NOUN
ejpam-6527	114	6	that	that	SCONJ
ejpam-6527	114	7	the	the	DET
ejpam-6527	114	8	operator	operator	NOUN
ejpam-6527	114	9	norm	norm	NOUN
ejpam-6527	114	10	and	and	CCONJ
ejpam-6527	114	11	compactness	compactness	NOUN
ejpam-6527	114	12	are	be	AUX
ejpam-6527	114	13	stable	stable	ADJ
ejpam-6527	114	14	under	under	ADP
ejpam-6527	114	15	finite	finite	ADJ
ejpam-6527	114	16	direct	direct	ADJ
ejpam-6527	114	17	sums	sum	NOUN
ejpam-6527	114	18	.	.	PUNCT
ejpam-6527	115	1	corollary	corollary	ADJ
ejpam-6527	115	2	2	2	NUM
ejpam-6527	115	3	.	.	PUNCT
ejpam-6527	116	1	let	let	AUX
ejpam-6527	116	2	t1	t1	VERB
ejpam-6527	116	3	,	,	PUNCT
ejpam-6527	116	4	.	.	PUNCT
ejpam-6527	116	5	.	.	PUNCT
ejpam-6527	117	1	.	.	PUNCT
ejpam-6527	118	1	,	,	PUNCT
ejpam-6527	118	2	tm	tm	PRON
ejpam-6527	118	3	be	be	AUX
ejpam-6527	118	4	compact	compact	ADJ
ejpam-6527	118	5	adjointable	adjointable	NOUN
ejpam-6527	118	6	operators	operator	NOUN
ejpam-6527	118	7	acting	act	VERB
ejpam-6527	118	8	on	on	ADP
ejpam-6527	118	9	hilbert	hilbert	PROPN
ejpam-6527	118	10	aθmodules	aθmodule	NOUN
ejpam-6527	118	11	e1	e1	PROPN
ejpam-6527	118	12	,	,	PUNCT
ejpam-6527	118	13	.	.	PUNCT
ejpam-6527	118	14	.	.	PUNCT
ejpam-6527	119	1	.	.	PUNCT
ejpam-6527	120	1	,	,	PUNCT
ejpam-6527	120	2	em	em	PRON
ejpam-6527	120	3	,	,	PUNCT
ejpam-6527	120	4	respectively	respectively	ADV
ejpam-6527	120	5	.	.	PUNCT
ejpam-6527	121	1	then	then	ADV
ejpam-6527	121	2	the	the	DET
ejpam-6527	121	3	(	(	PUNCT
ejpam-6527	121	4	internal	internal	ADJ
ejpam-6527	121	5	)	)	PUNCT
ejpam-6527	121	6	m	m	ADJ
ejpam-6527	121	7	-	-	ADJ
ejpam-6527	121	8	fold	fold	ADJ
ejpam-6527	121	9	tensor	tensor	NOUN
ejpam-6527	121	10	product	product	NOUN
ejpam-6527	121	11	t1	t1	NOUN
ejpam-6527	121	12	⊗̂	⊗̂	NUM
ejpam-6527	121	13	·	·	PUNCT
ejpam-6527	121	14	·	·	PUNCT
ejpam-6527	121	15	·	·	PUNCT
ejpam-6527	122	1	⊗̂tm	⊗̂tm	PROPN
ejpam-6527	122	2	is	be	AUX
ejpam-6527	122	3	compact	compact	ADJ
ejpam-6527	122	4	on	on	ADP
ejpam-6527	122	5	the	the	DET
ejpam-6527	122	6	tensor	tensor	NOUN
ejpam-6527	122	7	-	-	PUNCT
ejpam-6527	122	8	product	product	NOUN
ejpam-6527	122	9	module	module	NOUN
ejpam-6527	122	10	e1	e1	NOUN
ejpam-6527	122	11	⊗̂	⊗̂	NOUN
ejpam-6527	122	12	·	·	PUNCT
ejpam-6527	122	13	·	·	PUNCT
ejpam-6527	123	1	·	·	PUNCT
ejpam-6527	123	2	⊗̂em	⊗̂em	NOUN
ejpam-6527	123	3	.	.	PUNCT
ejpam-6527	124	1	proof	proof	NOUN
ejpam-6527	124	2	.	.	PUNCT
ejpam-6527	125	1	theorem	theorem	ADJ
ejpam-6527	125	2	2	2	NUM
ejpam-6527	125	3	gives	give	VERB
ejpam-6527	125	4	the	the	DET
ejpam-6527	125	5	result	result	NOUN
ejpam-6527	125	6	for	for	ADP
ejpam-6527	125	7	m	m	PROPN
ejpam-6527	125	8	=	=	SYM
ejpam-6527	125	9	2	2	X
ejpam-6527	125	10	.	.	X
ejpam-6527	126	1	we	we	PRON
ejpam-6527	126	2	proceed	proceed	VERB
ejpam-6527	126	3	by	by	ADP
ejpam-6527	126	4	induction	induction	NOUN
ejpam-6527	126	5	.	.	PUNCT
ejpam-6527	127	1	suppose	suppose	VERB
ejpam-6527	127	2	the	the	DET
ejpam-6527	127	3	result	result	NOUN
ejpam-6527	127	4	holds	hold	VERB
ejpam-6527	127	5	for	for	ADP
ejpam-6527	127	6	m	m	PROPN
ejpam-6527	127	7	=	=	PROPN
ejpam-6527	127	8	k.	k.	PROPN
ejpam-6527	127	9	then	then	ADV
ejpam-6527	127	10	for	for	ADP
ejpam-6527	127	11	m	m	PROPN
ejpam-6527	128	1	=	=	SYM
ejpam-6527	128	2	k	k	PROPN
ejpam-6527	129	1	+	+	NOUN
ejpam-6527	129	2	1	1	NUM
ejpam-6527	129	3	,	,	PUNCT
ejpam-6527	129	4	consider	consider	VERB
ejpam-6527	129	5	the	the	DET
ejpam-6527	129	6	operator	operator	NOUN
ejpam-6527	129	7	(	(	PUNCT
ejpam-6527	129	8	t1	t1	PROPN
ejpam-6527	129	9	⊗̂	⊗̂	NUM
ejpam-6527	129	10	·	·	PUNCT
ejpam-6527	129	11	·	·	PUNCT
ejpam-6527	129	12	·	·	PUNCT
ejpam-6527	129	13	⊗̂tk	⊗̂tk	X
ejpam-6527	129	14	)	)	PUNCT
ejpam-6527	129	15	⊗̂tk+1	⊗̂tk+1	NUM
ejpam-6527	129	16	.	.	PUNCT
ejpam-6527	130	1	by	by	ADP
ejpam-6527	130	2	the	the	DET
ejpam-6527	130	3	induction	induction	NOUN
ejpam-6527	130	4	hypothesis	hypothesis	NOUN
ejpam-6527	130	5	,	,	PUNCT
ejpam-6527	130	6	the	the	DET
ejpam-6527	130	7	k	k	ADJ
ejpam-6527	130	8	-	-	ADJ
ejpam-6527	130	9	fold	fold	ADJ
ejpam-6527	130	10	tensor	tensor	NOUN
ejpam-6527	130	11	product	product	NOUN
ejpam-6527	130	12	is	be	AUX
ejpam-6527	130	13	compact	compact	ADJ
ejpam-6527	130	14	,	,	PUNCT
ejpam-6527	130	15	and	and	CCONJ
ejpam-6527	130	16	since	since	SCONJ
ejpam-6527	130	17	tk+1	tk+1	NOUN
ejpam-6527	130	18	is	be	AUX
ejpam-6527	130	19	compact	compact	ADJ
ejpam-6527	130	20	,	,	PUNCT
ejpam-6527	130	21	theorem	theorem	ADJ
ejpam-6527	130	22	2	2	NUM
ejpam-6527	130	23	implies	imply	VERB
ejpam-6527	130	24	that	that	SCONJ
ejpam-6527	130	25	their	their	PRON
ejpam-6527	130	26	tensor	tensor	NOUN
ejpam-6527	130	27	product	product	NOUN
ejpam-6527	130	28	is	be	AUX
ejpam-6527	130	29	compact	compact	ADJ
ejpam-6527	130	30	.	.	PUNCT
ejpam-6527	131	1	thus	thus	ADV
ejpam-6527	131	2	,	,	PUNCT
ejpam-6527	131	3	by	by	ADP
ejpam-6527	131	4	induction	induction	NOUN
ejpam-6527	131	5	,	,	PUNCT
ejpam-6527	131	6	the	the	DET
ejpam-6527	131	7	m	m	ADJ
ejpam-6527	131	8	-	-	ADJ
ejpam-6527	131	9	fold	fold	ADJ
ejpam-6527	131	10	tensor	tensor	NOUN
ejpam-6527	131	11	product	product	NOUN
ejpam-6527	131	12	is	be	AUX
ejpam-6527	131	13	compact	compact	ADJ
ejpam-6527	131	14	.	.	PUNCT
ejpam-6527	132	1	m.	m.	PROPN
ejpam-6527	132	2	s.	s.	PROPN
ejpam-6527	132	3	ali	ali	PROPN
ejpam-6527	132	4	et	et	PROPN
ejpam-6527	132	5	al	al	PROPN
ejpam-6527	132	6	.	.	PUNCT
ejpam-6527	132	7	/	/	SYM
ejpam-6527	132	8	eur	eur	PROPN
ejpam-6527	132	9	.	.	PUNCT
ejpam-6527	133	1	j.	j.	PROPN
ejpam-6527	133	2	pure	pure	PROPN
ejpam-6527	133	3	appl	appl	PROPN
ejpam-6527	133	4	.	.	PROPN
ejpam-6527	133	5	math	math	PROPN
ejpam-6527	133	6	,	,	PUNCT
ejpam-6527	133	7	18	18	NUM
ejpam-6527	133	8	(	(	PUNCT
ejpam-6527	133	9	3	3	NUM
ejpam-6527	133	10	)	)	PUNCT
ejpam-6527	133	11	(	(	PUNCT
ejpam-6527	133	12	2025	2025	NUM
ejpam-6527	133	13	)	)	PUNCT
ejpam-6527	133	14	,	,	PUNCT
ejpam-6527	133	15	6527	6527	NUM
ejpam-6527	133	16	7	7	NUM
ejpam-6527	133	17	of	of	ADP
ejpam-6527	133	18	9	9	NUM
ejpam-6527	133	19	4.2	4.2	NUM
ejpam-6527	133	20	.	.	PUNCT
ejpam-6527	134	1	applications	application	NOUN
ejpam-6527	134	2	and	and	CCONJ
ejpam-6527	134	3	examples	example	NOUN
ejpam-6527	134	4	in	in	ADP
ejpam-6527	134	5	this	this	DET
ejpam-6527	134	6	section	section	NOUN
ejpam-6527	134	7	,	,	PUNCT
ejpam-6527	134	8	we	we	PRON
ejpam-6527	134	9	illustrate	illustrate	VERB
ejpam-6527	134	10	applications	application	NOUN
ejpam-6527	134	11	and	and	CCONJ
ejpam-6527	134	12	examples	example	NOUN
ejpam-6527	134	13	of	of	ADP
ejpam-6527	134	14	compact	compact	ADJ
ejpam-6527	134	15	operators	operator	NOUN
ejpam-6527	134	16	in	in	ADP
ejpam-6527	134	17	operator	operator	NOUN
ejpam-6527	134	18	spaces	space	NOUN
ejpam-6527	134	19	over	over	ADP
ejpam-6527	134	20	the	the	DET
ejpam-6527	134	21	non	non	ADJ
ejpam-6527	134	22	-	-	ADJ
ejpam-6527	134	23	commutative	commutative	ADJ
ejpam-6527	134	24	torus	torus	PROPN
ejpam-6527	134	25	aθ	aθ	NOUN
ejpam-6527	134	26	.	.	PUNCT
ejpam-6527	134	27	example	example	NOUN
ejpam-6527	135	1	1	1	NUM
ejpam-6527	135	2	(	(	PUNCT
ejpam-6527	135	3	finite	finite	ADJ
ejpam-6527	135	4	-	-	ADJ
ejpam-6527	135	5	rank	rank	ADJ
ejpam-6527	135	6	operator	operator	NOUN
ejpam-6527	135	7	)	)	PUNCT
ejpam-6527	135	8	.	.	PUNCT
ejpam-6527	136	1	let	let	VERB
ejpam-6527	136	2	t	t	NOUN
ejpam-6527	136	3	:	:	PUNCT
ejpam-6527	136	4	an	an	DET
ejpam-6527	136	5	θ	θ	PROPN
ejpam-6527	136	6	→	→	PUNCT
ejpam-6527	136	7	an	an	DET
ejpam-6527	136	8	θ	θ	NOUN
ejpam-6527	136	9	be	be	AUX
ejpam-6527	136	10	defined	define	VERB
ejpam-6527	136	11	by	by	ADP
ejpam-6527	136	12	t	t	PROPN
ejpam-6527	136	13	(	(	PUNCT
ejpam-6527	136	14	ξ	ξ	NOUN
ejpam-6527	136	15	)	)	PUNCT
ejpam-6527	136	16	=	=	SYM
ejpam-6527	136	17	η⟨ζ	η⟨ζ	PROPN
ejpam-6527	136	18	,	,	PUNCT
ejpam-6527	136	19	ξ⟩	ξ⟩	NOUN
ejpam-6527	136	20	,	,	PUNCT
ejpam-6527	136	21	for	for	ADP
ejpam-6527	136	22	fixed	fix	VERB
ejpam-6527	136	23	η	η	PROPN
ejpam-6527	136	24	,	,	PUNCT
ejpam-6527	136	25	ζ	ζ	PROPN
ejpam-6527	136	26	∈	∈	PROPN
ejpam-6527	136	27	an	an	DET
ejpam-6527	136	28	θ	θ	NOUN
ejpam-6527	136	29	.	.	PUNCT
ejpam-6527	137	1	then	then	ADV
ejpam-6527	137	2	t	t	PROPN
ejpam-6527	137	3	is	be	AUX
ejpam-6527	137	4	a	a	DET
ejpam-6527	137	5	finite	finite	ADJ
ejpam-6527	137	6	-	-	ADJ
ejpam-6527	137	7	rank	rank	ADJ
ejpam-6527	137	8	operator	operator	NOUN
ejpam-6527	137	9	,	,	PUNCT
ejpam-6527	137	10	since	since	SCONJ
ejpam-6527	137	11	its	its	PRON
ejpam-6527	137	12	range	range	NOUN
ejpam-6527	137	13	is	be	AUX
ejpam-6527	137	14	contained	contain	VERB
ejpam-6527	137	15	in	in	ADP
ejpam-6527	137	16	the	the	DET
ejpam-6527	137	17	span	span	NOUN
ejpam-6527	137	18	of	of	ADP
ejpam-6527	137	19	η	η	PROPN
ejpam-6527	137	20	.	.	PROPN
ejpam-6527	137	21	hence	hence	ADV
ejpam-6527	137	22	,	,	PUNCT
ejpam-6527	137	23	t	t	PROPN
ejpam-6527	137	24	is	be	AUX
ejpam-6527	137	25	compact	compact	ADJ
ejpam-6527	137	26	.	.	PUNCT
ejpam-6527	138	1	example	example	NOUN
ejpam-6527	138	2	2	2	NUM
ejpam-6527	138	3	(	(	PUNCT
ejpam-6527	138	4	toeplitz	toeplitz	NOUN
ejpam-6527	138	5	-	-	PUNCT
ejpam-6527	138	6	type	type	NOUN
ejpam-6527	138	7	operators	operator	NOUN
ejpam-6527	138	8	)	)	PUNCT
ejpam-6527	138	9	.	.	PUNCT
ejpam-6527	139	1	suppose	suppose	VERB
ejpam-6527	139	2	{	{	PUNCT
ejpam-6527	139	3	en}∞n=1	en}∞n=1	NUM
ejpam-6527	139	4	is	be	AUX
ejpam-6527	139	5	an	an	DET
ejpam-6527	139	6	orthonormal	orthonormal	ADJ
ejpam-6527	139	7	basis	basis	NOUN
ejpam-6527	139	8	of	of	ADP
ejpam-6527	139	9	a	a	DET
ejpam-6527	139	10	hilbert	hilbert	NOUN
ejpam-6527	139	11	aθ	aθ	NOUN
ejpam-6527	139	12	-	-	PUNCT
ejpam-6527	139	13	module	module	NOUN
ejpam-6527	139	14	,	,	PUNCT
ejpam-6527	139	15	and	and	CCONJ
ejpam-6527	139	16	define	define	VERB
ejpam-6527	139	17	an	an	DET
ejpam-6527	139	18	operator	operator	NOUN
ejpam-6527	139	19	t	t	NOUN
ejpam-6527	139	20	by	by	ADP
ejpam-6527	139	21	t	t	PROPN
ejpam-6527	139	22	(	(	PUNCT
ejpam-6527	139	23	en	en	X
ejpam-6527	139	24	)	)	PUNCT
ejpam-6527	139	25	=	=	SYM
ejpam-6527	139	26	λnen	λnen	NOUN
ejpam-6527	139	27	,	,	PUNCT
ejpam-6527	139	28	where	where	SCONJ
ejpam-6527	139	29	λn	λn	NOUN
ejpam-6527	139	30	→	→	SYM
ejpam-6527	139	31	0	0	PROPN
ejpam-6527	139	32	as	as	ADP
ejpam-6527	139	33	n	n	PROPN
ejpam-6527	139	34	→	→	SYM
ejpam-6527	139	35	∞.	∞.	PROPN
ejpam-6527	139	36	then	then	ADV
ejpam-6527	139	37	t	t	PROPN
ejpam-6527	139	38	is	be	AUX
ejpam-6527	139	39	the	the	DET
ejpam-6527	139	40	norm	norm	NOUN
ejpam-6527	139	41	limit	limit	NOUN
ejpam-6527	139	42	of	of	ADP
ejpam-6527	139	43	finite	finite	ADJ
ejpam-6527	139	44	-	-	ADJ
ejpam-6527	139	45	rank	rank	ADJ
ejpam-6527	139	46	diagonal	diagonal	ADJ
ejpam-6527	139	47	operators	operator	NOUN
ejpam-6527	139	48	and	and	CCONJ
ejpam-6527	139	49	is	be	AUX
ejpam-6527	139	50	therefore	therefore	ADV
ejpam-6527	139	51	compact	compact	ADJ
ejpam-6527	139	52	.	.	PUNCT
ejpam-6527	140	1	this	this	DET
ejpam-6527	140	2	structure	structure	NOUN
ejpam-6527	140	3	is	be	AUX
ejpam-6527	140	4	similar	similar	ADJ
ejpam-6527	140	5	to	to	ADP
ejpam-6527	140	6	classical	classical	ADJ
ejpam-6527	140	7	*	*	NOUN
ejpam-6527	140	8	*	*	PUNCT
ejpam-6527	140	9	toeplitz	toeplitz	NOUN
ejpam-6527	140	10	*	*	PUNCT
ejpam-6527	140	11	*	*	PUNCT
ejpam-6527	140	12	and	and	CCONJ
ejpam-6527	140	13	*	*	NOUN
ejpam-6527	140	14	*	*	NOUN
ejpam-6527	140	15	hankel	hankel	NOUN
ejpam-6527	140	16	*	*	NOUN
ejpam-6527	140	17	*	*	ADJ
ejpam-6527	140	18	operators	operator	NOUN
ejpam-6527	140	19	in	in	ADP
ejpam-6527	140	20	hilbert	hilbert	PROPN
ejpam-6527	140	21	spaces	space	NOUN
ejpam-6527	140	22	,	,	PUNCT
ejpam-6527	140	23	where	where	SCONJ
ejpam-6527	140	24	sequences	sequence	NOUN
ejpam-6527	140	25	{	{	PUNCT
ejpam-6527	140	26	λn	λn	NOUN
ejpam-6527	140	27	}	}	PUNCT
ejpam-6527	140	28	represent	represent	VERB
ejpam-6527	140	29	symbol	symbol	NOUN
ejpam-6527	140	30	decay	decay	NOUN
ejpam-6527	140	31	.	.	PUNCT
ejpam-6527	141	1	a	a	DET
ejpam-6527	141	2	detailed	detailed	ADJ
ejpam-6527	141	3	comparison	comparison	NOUN
ejpam-6527	141	4	with	with	ADP
ejpam-6527	141	5	hankel	hankel	NOUN
ejpam-6527	141	6	operators	operator	NOUN
ejpam-6527	141	7	(	(	PUNCT
ejpam-6527	141	8	see	see	VERB
ejpam-6527	141	9	[	[	X
ejpam-6527	141	10	6	6	NUM
ejpam-6527	141	11	,	,	PUNCT
ejpam-6527	141	12	9	9	NUM
ejpam-6527	141	13	]	]	PUNCT
ejpam-6527	141	14	)	)	PUNCT
ejpam-6527	141	15	may	may	AUX
ejpam-6527	141	16	yield	yield	VERB
ejpam-6527	141	17	further	further	ADJ
ejpam-6527	141	18	insights	insight	NOUN
ejpam-6527	141	19	into	into	ADP
ejpam-6527	141	20	non	non	ADJ
ejpam-6527	141	21	-	-	ADJ
ejpam-6527	141	22	self	self	NOUN
ejpam-6527	141	23	-	-	PUNCT
ejpam-6527	141	24	adjoint	adjoint	NOUN
ejpam-6527	141	25	analogues	analogue	NOUN
ejpam-6527	141	26	in	in	ADP
ejpam-6527	141	27	aθmodules	aθmodule	NOUN
ejpam-6527	141	28	.	.	PUNCT
ejpam-6527	142	1	example	example	NOUN
ejpam-6527	142	2	3	3	NUM
ejpam-6527	142	3	(	(	PUNCT
ejpam-6527	142	4	numerical	numerical	ADJ
ejpam-6527	142	5	example	example	NOUN
ejpam-6527	142	6	–	–	PUNCT
ejpam-6527	142	7	truncated	truncated	ADJ
ejpam-6527	142	8	matrix	matrix	NOUN
ejpam-6527	142	9	representation	representation	NOUN
ejpam-6527	142	10	)	)	PUNCT
ejpam-6527	142	11	.	.	PUNCT
ejpam-6527	143	1	let	let	AUX
ejpam-6527	143	2	aθ	aθ	INTJ
ejpam-6527	143	3	be	be	AUX
ejpam-6527	143	4	approximated	approximate	VERB
ejpam-6527	143	5	by	by	ADP
ejpam-6527	143	6	finite	finite	ADJ
ejpam-6527	143	7	matrices	matrix	NOUN
ejpam-6527	143	8	(	(	PUNCT
ejpam-6527	143	9	via	via	ADP
ejpam-6527	143	10	rational	rational	ADJ
ejpam-6527	143	11	θ	θ	PROPN
ejpam-6527	144	1	≈	≈	PROPN
ejpam-6527	144	2	p	p	NOUN
ejpam-6527	144	3	/	/	SYM
ejpam-6527	144	4	q	q	NOUN
ejpam-6527	144	5	)	)	PUNCT
ejpam-6527	144	6	.	.	PUNCT
ejpam-6527	145	1	consider	consider	VERB
ejpam-6527	145	2	aθ	aθ	VERB
ejpam-6527	145	3	∼=	∼=	PRON
ejpam-6527	145	4	mq(c	mq(c	NUM
ejpam-6527	145	5	)	)	PUNCT
ejpam-6527	145	6	for	for	ADP
ejpam-6527	145	7	q	q	NOUN
ejpam-6527	145	8	=	=	SYM
ejpam-6527	145	9	3	3	X
ejpam-6527	145	10	.	.	PUNCT
ejpam-6527	146	1	let	let	VERB
ejpam-6527	146	2	t	t	NOUN
ejpam-6527	146	3	=	=	PUNCT
ejpam-6527	146	4	1	1	PROPN
ejpam-6527	146	5	0	0	NUM
ejpam-6527	146	6	0	0	SYM
ejpam-6527	146	7	0	0	NUM
ejpam-6527	146	8	1	1	NUM
ejpam-6527	146	9	2	2	NUM
ejpam-6527	146	10	0	0	NUM
ejpam-6527	146	11	0	0	NUM
ejpam-6527	146	12	0	0	NUM
ejpam-6527	146	13	1	1	NUM
ejpam-6527	146	14	3	3	NUM
ejpam-6527	146	15			NOUN
ejpam-6527	146	16	,	,	PUNCT
ejpam-6527	146	17	which	which	PRON
ejpam-6527	146	18	has	have	AUX
ejpam-6527	146	19	eigenvalues	eigenvalue	VERB
ejpam-6527	146	20	tending	tend	VERB
ejpam-6527	146	21	to	to	ADP
ejpam-6527	146	22	zero	zero	NUM
ejpam-6527	146	23	.	.	PUNCT
ejpam-6527	147	1	then	then	ADV
ejpam-6527	147	2	t	t	PROPN
ejpam-6527	147	3	is	be	AUX
ejpam-6527	147	4	compact	compact	ADJ
ejpam-6527	147	5	as	as	ADP
ejpam-6527	147	6	a	a	DET
ejpam-6527	147	7	limit	limit	NOUN
ejpam-6527	147	8	of	of	ADP
ejpam-6527	147	9	finite	finite	ADJ
ejpam-6527	147	10	-	-	ADJ
ejpam-6527	147	11	rank	rank	ADJ
ejpam-6527	147	12	diagonal	diagonal	ADJ
ejpam-6527	147	13	matrices	matrix	NOUN
ejpam-6527	147	14	.	.	PUNCT
ejpam-6527	148	1	this	this	PRON
ejpam-6527	148	2	illustrates	illustrate	VERB
ejpam-6527	148	3	compactness	compactness	NOUN
ejpam-6527	148	4	numerically	numerically	ADV
ejpam-6527	148	5	in	in	ADP
ejpam-6527	148	6	quantum	quantum	PROPN
ejpam-6527	148	7	tori	tori	NOUN
ejpam-6527	148	8	approximated	approximate	VERB
ejpam-6527	148	9	by	by	ADP
ejpam-6527	148	10	finitedimensional	finitedimensional	ADJ
ejpam-6527	148	11	matrix	matrix	NOUN
ejpam-6527	148	12	algebras	algebra	NOUN
ejpam-6527	148	13	.	.	PUNCT
ejpam-6527	148	14	example	example	NOUN
ejpam-6527	148	15	4	4	NUM
ejpam-6527	148	16	(	(	PUNCT
ejpam-6527	148	17	quantum	quantum	ADJ
ejpam-6527	148	18	information	information	NOUN
ejpam-6527	148	19	channels	channel	NOUN
ejpam-6527	148	20	)	)	PUNCT
ejpam-6527	148	21	.	.	PUNCT
ejpam-6527	149	1	let	let	VERB
ejpam-6527	149	2	φ	φ	PROPN
ejpam-6527	149	3	:	:	PUNCT
ejpam-6527	149	4	aθ	aθ	NOUN
ejpam-6527	149	5	→	→	SYM
ejpam-6527	149	6	aθ	aθ	X
ejpam-6527	149	7	be	be	AUX
ejpam-6527	149	8	a	a	DET
ejpam-6527	149	9	quantum	quantum	ADJ
ejpam-6527	149	10	channel	channel	NOUN
ejpam-6527	149	11	defined	define	VERB
ejpam-6527	149	12	by	by	ADP
ejpam-6527	149	13	φ(x	φ(x	NOUN
ejpam-6527	149	14	)	)	PUNCT
ejpam-6527	149	15	=	=	VERB
ejpam-6527	149	16	k∑	k∑	VERB
ejpam-6527	149	17	i=1	i=1	PROPN
ejpam-6527	150	1	vixv	vixv	PROPN
ejpam-6527	150	2	∗	∗	NOUN
ejpam-6527	151	1	i	i	PRON
ejpam-6527	151	2	,	,	PUNCT
ejpam-6527	151	3	where	where	SCONJ
ejpam-6527	151	4	∑	∑	PUNCT
ejpam-6527	151	5	i	i	PRON
ejpam-6527	151	6	v	v	VERB
ejpam-6527	151	7	∗	∗	NOUN
ejpam-6527	152	1	i	i	NOUN
ejpam-6527	152	2	vi	vi	NOUN
ejpam-6527	153	1	=	=	SYM
ejpam-6527	153	2	i	i	PRON
ejpam-6527	153	3	and	and	CCONJ
ejpam-6527	153	4	vi	vi	PROPN
ejpam-6527	153	5	∈	∈	PROPN
ejpam-6527	153	6	aθ	aθ	NOUN
ejpam-6527	153	7	.	.	PUNCT
ejpam-6527	154	1	if	if	SCONJ
ejpam-6527	154	2	φ	φ	PROPN
ejpam-6527	154	3	=	=	SYM
ejpam-6527	155	1	ψ+noise	ψ+noise	PROPN
ejpam-6527	155	2	with	with	ADP
ejpam-6527	155	3	ψ	ψ	X
ejpam-6527	155	4	completely	completely	ADV
ejpam-6527	155	5	compact	compact	ADJ
ejpam-6527	155	6	,	,	PUNCT
ejpam-6527	155	7	then	then	ADV
ejpam-6527	155	8	φ	φ	PROPN
ejpam-6527	155	9	has	have	VERB
ejpam-6527	155	10	effectively	effectively	ADV
ejpam-6527	155	11	finite	finite	ADJ
ejpam-6527	155	12	-	-	ADJ
ejpam-6527	155	13	dimensional	dimensional	ADJ
ejpam-6527	155	14	range	range	NOUN
ejpam-6527	155	15	,	,	PUNCT
ejpam-6527	155	16	preserving	preserve	VERB
ejpam-6527	155	17	key	key	ADJ
ejpam-6527	155	18	properties	property	NOUN
ejpam-6527	155	19	in	in	ADP
ejpam-6527	155	20	quantum	quantum	ADJ
ejpam-6527	155	21	information	information	NOUN
ejpam-6527	155	22	.	.	PUNCT
ejpam-6527	156	1	such	such	ADJ
ejpam-6527	156	2	structure	structure	NOUN
ejpam-6527	156	3	is	be	AUX
ejpam-6527	156	4	useful	useful	ADJ
ejpam-6527	156	5	for	for	ADP
ejpam-6527	156	6	error	error	NOUN
ejpam-6527	156	7	correction	correction	NOUN
ejpam-6527	156	8	,	,	PUNCT
ejpam-6527	156	9	compression	compression	NOUN
ejpam-6527	156	10	,	,	PUNCT
ejpam-6527	156	11	and	and	CCONJ
ejpam-6527	156	12	modeling	modeling	NOUN
ejpam-6527	156	13	decoherence	decoherence	NOUN
ejpam-6527	156	14	.	.	PUNCT
ejpam-6527	157	1	compactness	compactness	NOUN
ejpam-6527	157	2	ensures	ensure	VERB
ejpam-6527	157	3	containment	containment	NOUN
ejpam-6527	157	4	of	of	ADP
ejpam-6527	157	5	quantum	quantum	ADJ
ejpam-6527	157	6	evolution	evolution	NOUN
ejpam-6527	157	7	within	within	ADP
ejpam-6527	157	8	finite	finite	ADJ
ejpam-6527	157	9	metric	metric	ADJ
ejpam-6527	157	10	spaces	space	NOUN
ejpam-6527	157	11	,	,	PUNCT
ejpam-6527	157	12	as	as	SCONJ
ejpam-6527	157	13	noted	note	VERB
ejpam-6527	157	14	in	in	ADP
ejpam-6527	157	15	[	[	X
ejpam-6527	157	16	22	22	NUM
ejpam-6527	157	17	]	]	PUNCT
ejpam-6527	157	18	.	.	PUNCT
ejpam-6527	158	1	m.	m.	PROPN
ejpam-6527	158	2	s.	s.	PROPN
ejpam-6527	158	3	ali	ali	PROPN
ejpam-6527	158	4	et	et	PROPN
ejpam-6527	158	5	al	al	PROPN
ejpam-6527	158	6	.	.	PUNCT
ejpam-6527	158	7	/	/	SYM
ejpam-6527	158	8	eur	eur	PROPN
ejpam-6527	158	9	.	.	PUNCT
ejpam-6527	159	1	j.	j.	PROPN
ejpam-6527	159	2	pure	pure	PROPN
ejpam-6527	159	3	appl	appl	PROPN
ejpam-6527	159	4	.	.	PROPN
ejpam-6527	159	5	math	math	PROPN
ejpam-6527	159	6	,	,	PUNCT
ejpam-6527	159	7	18	18	NUM
ejpam-6527	159	8	(	(	PUNCT
ejpam-6527	159	9	3	3	NUM
ejpam-6527	159	10	)	)	PUNCT
ejpam-6527	159	11	(	(	PUNCT
ejpam-6527	159	12	2025	2025	NUM
ejpam-6527	159	13	)	)	PUNCT
ejpam-6527	159	14	,	,	PUNCT
ejpam-6527	159	15	6527	6527	NUM
ejpam-6527	159	16	8	8	NUM
ejpam-6527	159	17	of	of	ADP
ejpam-6527	159	18	9	9	NUM
ejpam-6527	159	19	application	application	NOUN
ejpam-6527	159	20	1	1	NUM
ejpam-6527	159	21	(	(	PUNCT
ejpam-6527	159	22	quantum	quantum	ADJ
ejpam-6527	159	23	metric	metric	ADJ
ejpam-6527	159	24	spaces	space	NOUN
ejpam-6527	159	25	)	)	PUNCT
ejpam-6527	159	26	.	.	PUNCT
ejpam-6527	160	1	in	in	ADP
ejpam-6527	160	2	rieffel	rieffel	NOUN
ejpam-6527	160	3	’s	’s	PART
ejpam-6527	160	4	framework	framework	NOUN
ejpam-6527	160	5	of	of	ADP
ejpam-6527	160	6	compact	compact	ADJ
ejpam-6527	160	7	quantum	quantum	ADJ
ejpam-6527	160	8	metric	metric	ADJ
ejpam-6527	160	9	spaces	space	NOUN
ejpam-6527	160	10	,	,	PUNCT
ejpam-6527	160	11	define	define	VERB
ejpam-6527	160	12	the	the	DET
ejpam-6527	160	13	lipschitz	lipschitz	NOUN
ejpam-6527	160	14	seminorm	seminorm	NOUN
ejpam-6527	160	15	:	:	PUNCT
ejpam-6527	160	16	l(x	l(x	PROPN
ejpam-6527	160	17	)	)	PUNCT
ejpam-6527	160	18	=	=	SYM
ejpam-6527	160	19	sup	sup	NOUN
ejpam-6527	160	20	{	{	PUNCT
ejpam-6527	160	21	∥[d	∥[d	NUM
ejpam-6527	160	22	,	,	PUNCT
ejpam-6527	160	23	x]∥	x]∥	NOUN
ejpam-6527	160	24	:	:	PUNCT
ejpam-6527	161	1	d	d	X
ejpam-6527	161	2	=	=	PUNCT
ejpam-6527	161	3	d∗	d∗	PROPN
ejpam-6527	161	4	,	,	PUNCT
ejpam-6527	161	5	d	d	NOUN
ejpam-6527	161	6	unbounded	unbounded	ADJ
ejpam-6527	161	7	}	}	PUNCT
ejpam-6527	161	8	,	,	PUNCT
ejpam-6527	161	9	and	and	CCONJ
ejpam-6527	161	10	consider	consider	VERB
ejpam-6527	161	11	the	the	DET
ejpam-6527	161	12	unit	unit	NOUN
ejpam-6527	161	13	ball	ball	NOUN
ejpam-6527	161	14	{	{	PUNCT
ejpam-6527	161	15	x	x	SYM
ejpam-6527	161	16	∈	∈	PROPN
ejpam-6527	161	17	aθ	aθ	NOUN
ejpam-6527	161	18	:	:	PUNCT
ejpam-6527	161	19	l(x	l(x	PROPN
ejpam-6527	161	20	)	)	PUNCT
ejpam-6527	161	21	≤	≤	NOUN
ejpam-6527	161	22	1	1	NUM
ejpam-6527	161	23	,	,	PUNCT
ejpam-6527	161	24	∥x∥	∥x∥	NOUN
ejpam-6527	161	25	≤	≤	NOUN
ejpam-6527	161	26	1	1	NUM
ejpam-6527	161	27	}	}	PUNCT
ejpam-6527	161	28	.	.	PUNCT
ejpam-6527	162	1	compact	compact	ADJ
ejpam-6527	162	2	operators	operator	NOUN
ejpam-6527	162	3	help	help	VERB
ejpam-6527	162	4	define	define	VERB
ejpam-6527	162	5	the	the	DET
ejpam-6527	162	6	metric	metric	NOUN
ejpam-6527	162	7	on	on	ADP
ejpam-6527	162	8	the	the	DET
ejpam-6527	162	9	state	state	NOUN
ejpam-6527	162	10	space	space	NOUN
ejpam-6527	162	11	via	via	ADP
ejpam-6527	162	12	approximations	approximation	NOUN
ejpam-6527	162	13	of	of	ADP
ejpam-6527	162	14	the	the	DET
ejpam-6527	162	15	identity	identity	NOUN
ejpam-6527	162	16	operator	operator	NOUN
ejpam-6527	162	17	.	.	PUNCT
ejpam-6527	163	1	this	this	DET
ejpam-6527	163	2	concept	concept	NOUN
ejpam-6527	163	3	is	be	AUX
ejpam-6527	163	4	critical	critical	ADJ
ejpam-6527	163	5	for	for	ADP
ejpam-6527	163	6	analyzing	analyze	VERB
ejpam-6527	163	7	convergence	convergence	NOUN
ejpam-6527	163	8	in	in	ADP
ejpam-6527	163	9	non	non	ADJ
ejpam-6527	163	10	-	-	ADJ
ejpam-6527	163	11	commutative	commutative	ADJ
ejpam-6527	163	12	gromov	gromov	NOUN
ejpam-6527	163	13	–	–	PUNCT
ejpam-6527	163	14	hausdorff	hausdorff	NOUN
ejpam-6527	163	15	spaces	space	NOUN
ejpam-6527	163	16	(	(	PUNCT
ejpam-6527	163	17	see	see	VERB
ejpam-6527	163	18	[	[	X
ejpam-6527	163	19	23	23	NUM
ejpam-6527	163	20	]	]	SYM
ejpam-6527	163	21	)	)	PUNCT
ejpam-6527	163	22	.	.	PUNCT
ejpam-6527	164	1	application	application	NOUN
ejpam-6527	164	2	2	2	NUM
ejpam-6527	164	3	(	(	PUNCT
ejpam-6527	164	4	non	non	ADJ
ejpam-6527	164	5	-	-	ADJ
ejpam-6527	164	6	commutative	commutative	ADJ
ejpam-6527	164	7	harmonic	harmonic	ADJ
ejpam-6527	164	8	analysis	analysis	NOUN
ejpam-6527	164	9	)	)	PUNCT
ejpam-6527	164	10	.	.	PUNCT
ejpam-6527	165	1	let	let	VERB
ejpam-6527	165	2	t	t	PROPN
ejpam-6527	165	3	(	(	PUNCT
ejpam-6527	165	4	f	f	X
ejpam-6527	165	5	)	)	PUNCT
ejpam-6527	165	6	=	=	SYM
ejpam-6527	165	7	u	u	PROPN
ejpam-6527	165	8	∗	∗	X
ejpam-6527	165	9	f	f	PROPN
ejpam-6527	165	10	∗	∗	PROPN
ejpam-6527	165	11	v∗	v∗	PROPN
ejpam-6527	165	12	,	,	PUNCT
ejpam-6527	165	13	where	where	SCONJ
ejpam-6527	165	14	u	u	NOUN
ejpam-6527	165	15	,	,	PUNCT
ejpam-6527	165	16	v	v	NOUN
ejpam-6527	165	17	are	be	AUX
ejpam-6527	165	18	unitaries	unitarie	NOUN
ejpam-6527	165	19	in	in	ADP
ejpam-6527	165	20	aθ	aθ	NOUN
ejpam-6527	165	21	.	.	PUNCT
ejpam-6527	166	1	if	if	SCONJ
ejpam-6527	166	2	u	u	NOUN
ejpam-6527	166	3	has	have	AUX
ejpam-6527	166	4	rapidly	rapidly	ADV
ejpam-6527	166	5	decaying	decay	VERB
ejpam-6527	166	6	fourier	fouri	ADJ
ejpam-6527	166	7	coefficients	coefficient	NOUN
ejpam-6527	166	8	(	(	PUNCT
ejpam-6527	166	9	i.e.	i.e.	X
ejpam-6527	166	10	,	,	PUNCT
ejpam-6527	166	11	in	in	ADP
ejpam-6527	166	12	the	the	DET
ejpam-6527	166	13	smooth	smooth	ADJ
ejpam-6527	166	14	subalgebra	subalgebra	NOUN
ejpam-6527	166	15	of	of	ADP
ejpam-6527	166	16	aθ	aθ	NOUN
ejpam-6527	166	17	)	)	PUNCT
ejpam-6527	166	18	,	,	PUNCT
ejpam-6527	166	19	then	then	ADV
ejpam-6527	166	20	t	t	PROPN
ejpam-6527	166	21	acts	act	VERB
ejpam-6527	166	22	as	as	ADP
ejpam-6527	166	23	a	a	DET
ejpam-6527	166	24	*	*	ADJ
ejpam-6527	166	25	*	*	ADJ
ejpam-6527	166	26	low	low	ADJ
ejpam-6527	166	27	-	-	PUNCT
ejpam-6527	166	28	pass	pass	NOUN
ejpam-6527	166	29	filter	filter	NOUN
ejpam-6527	166	30	*	*	NOUN
ejpam-6527	166	31	*	*	PUNCT
ejpam-6527	166	32	,	,	PUNCT
ejpam-6527	166	33	and	and	CCONJ
ejpam-6527	166	34	is	be	AUX
ejpam-6527	166	35	compact	compact	ADJ
ejpam-6527	166	36	.	.	PUNCT
ejpam-6527	167	1	such	such	ADJ
ejpam-6527	167	2	compact	compact	ADJ
ejpam-6527	167	3	operators	operator	NOUN
ejpam-6527	167	4	localize	localize	VERB
ejpam-6527	167	5	frequency	frequency	NOUN
ejpam-6527	167	6	energy	energy	NOUN
ejpam-6527	167	7	in	in	ADP
ejpam-6527	167	8	non	non	ADJ
ejpam-6527	167	9	-	-	ADJ
ejpam-6527	167	10	commutative	commutative	ADJ
ejpam-6527	167	11	spaces	space	NOUN
ejpam-6527	167	12	,	,	PUNCT
ejpam-6527	167	13	enabling	enable	VERB
ejpam-6527	167	14	signal	signal	NOUN
ejpam-6527	167	15	representation	representation	NOUN
ejpam-6527	167	16	with	with	ADP
ejpam-6527	167	17	geometric	geometric	ADJ
ejpam-6527	167	18	and	and	CCONJ
ejpam-6527	167	19	spectral	spectral	ADJ
ejpam-6527	167	20	coherence	coherence	NOUN
ejpam-6527	167	21	.	.	PUNCT
ejpam-6527	168	1	this	this	PRON
ejpam-6527	168	2	parallels	parallel	VERB
ejpam-6527	168	3	classical	classical	ADJ
ejpam-6527	168	4	harmonic	harmonic	ADJ
ejpam-6527	168	5	filters	filter	NOUN
ejpam-6527	168	6	and	and	CCONJ
ejpam-6527	168	7	contributes	contribute	VERB
ejpam-6527	168	8	to	to	ADP
ejpam-6527	168	9	a	a	DET
ejpam-6527	168	10	developing	develop	VERB
ejpam-6527	168	11	theory	theory	NOUN
ejpam-6527	168	12	of	of	ADP
ejpam-6527	168	13	non	non	ADJ
ejpam-6527	168	14	-	-	ADJ
ejpam-6527	168	15	commutative	commutative	ADJ
ejpam-6527	168	16	signal	signal	NOUN
ejpam-6527	168	17	analysis	analysis	NOUN
ejpam-6527	168	18	.	.	PUNCT
ejpam-6527	169	1	5	5	X
ejpam-6527	169	2	.	.	X
ejpam-6527	169	3	conclusion	conclusion	NOUN
ejpam-6527	169	4	we	we	PRON
ejpam-6527	169	5	have	have	AUX
ejpam-6527	169	6	characterized	characterize	VERB
ejpam-6527	169	7	compact	compact	ADJ
ejpam-6527	169	8	operators	operator	NOUN
ejpam-6527	169	9	in	in	ADP
ejpam-6527	169	10	operator	operator	NOUN
ejpam-6527	169	11	spaces	space	NOUN
ejpam-6527	169	12	over	over	ADP
ejpam-6527	169	13	the	the	DET
ejpam-6527	169	14	non	non	ADJ
ejpam-6527	169	15	-	-	ADJ
ejpam-6527	169	16	commutative	commutative	ADJ
ejpam-6527	169	17	torus	torus	NOUN
ejpam-6527	169	18	,	,	PUNCT
ejpam-6527	169	19	including	include	VERB
ejpam-6527	169	20	studying	study	VERB
ejpam-6527	169	21	their	their	PRON
ejpam-6527	169	22	action	action	NOUN
ejpam-6527	169	23	on	on	ADP
ejpam-6527	169	24	tensor	tensor	NOUN
ejpam-6527	169	25	products	product	NOUN
ejpam-6527	169	26	and	and	CCONJ
ejpam-6527	169	27	their	their	PRON
ejpam-6527	169	28	relation	relation	NOUN
ejpam-6527	169	29	to	to	PART
ejpam-6527	169	30	complete	complete	VERB
ejpam-6527	169	31	boundedness	boundedness	NOUN
ejpam-6527	169	32	.	.	PUNCT
ejpam-6527	170	1	this	this	DET
ejpam-6527	170	2	structure	structure	NOUN
ejpam-6527	170	3	has	have	VERB
ejpam-6527	170	4	many	many	ADJ
ejpam-6527	170	5	important	important	ADJ
ejpam-6527	170	6	applications	application	NOUN
ejpam-6527	170	7	in	in	ADP
ejpam-6527	170	8	quantum	quantum	ADJ
ejpam-6527	170	9	geometry	geometry	NOUN
ejpam-6527	170	10	and	and	CCONJ
ejpam-6527	170	11	harmonic	harmonic	ADJ
ejpam-6527	170	12	analysis	analysis	NOUN
ejpam-6527	170	13	,	,	PUNCT
ejpam-6527	170	14	and	and	CCONJ
ejpam-6527	170	15	these	these	DET
ejpam-6527	170	16	results	result	NOUN
ejpam-6527	170	17	are	be	AUX
ejpam-6527	170	18	anticipated	anticipate	VERB
ejpam-6527	170	19	to	to	PART
ejpam-6527	170	20	inspire	inspire	VERB
ejpam-6527	170	21	further	further	ADJ
ejpam-6527	170	22	developments	development	NOUN
ejpam-6527	170	23	in	in	ADP
ejpam-6527	170	24	the	the	DET
ejpam-6527	170	25	realm	realm	NOUN
ejpam-6527	170	26	of	of	ADP
ejpam-6527	170	27	quantum	quantum	ADJ
ejpam-6527	170	28	groups	group	NOUN
ejpam-6527	170	29	.	.	PUNCT
ejpam-6527	171	1	a	a	DET
ejpam-6527	171	2	key	key	ADJ
ejpam-6527	171	3	direction	direction	NOUN
ejpam-6527	171	4	for	for	ADP
ejpam-6527	171	5	future	future	ADJ
ejpam-6527	171	6	work	work	NOUN
ejpam-6527	171	7	involves	involve	VERB
ejpam-6527	171	8	the	the	DET
ejpam-6527	171	9	generalization	generalization	NOUN
ejpam-6527	171	10	of	of	ADP
ejpam-6527	171	11	these	these	DET
ejpam-6527	171	12	results	result	NOUN
ejpam-6527	171	13	to	to	ADP
ejpam-6527	171	14	more	more	ADJ
ejpam-6527	171	15	general	general	ADJ
ejpam-6527	171	16	operator	operator	NOUN
ejpam-6527	171	17	spaces	space	NOUN
ejpam-6527	171	18	,	,	PUNCT
ejpam-6527	171	19	in	in	ADP
ejpam-6527	171	20	particular	particular	ADJ
ejpam-6527	171	21	those	those	PRON
ejpam-6527	171	22	of	of	ADP
ejpam-6527	171	23	non	non	ADJ
ejpam-6527	171	24	-	-	ADJ
ejpam-6527	171	25	adjointable	adjointable	ADJ
ejpam-6527	171	26	or	or	CCONJ
ejpam-6527	171	27	unbounded	unbounded	ADJ
ejpam-6527	171	28	operators	operator	NOUN
ejpam-6527	171	29	.	.	PUNCT
ejpam-6527	172	1	furthermore	furthermore	ADV
ejpam-6527	172	2	,	,	PUNCT
ejpam-6527	172	3	the	the	DET
ejpam-6527	172	4	theoretical	theoretical	ADJ
ejpam-6527	172	5	framework	framework	NOUN
ejpam-6527	172	6	could	could	AUX
ejpam-6527	172	7	be	be	AUX
ejpam-6527	172	8	further	far	ADV
ejpam-6527	172	9	strengthened	strengthen	VERB
ejpam-6527	172	10	by	by	ADP
ejpam-6527	172	11	incorporating	incorporate	VERB
ejpam-6527	172	12	numerical	numerical	ADJ
ejpam-6527	172	13	simulations	simulation	NOUN
ejpam-6527	172	14	or	or	CCONJ
ejpam-6527	172	15	case	case	NOUN
ejpam-6527	172	16	studies	study	NOUN
ejpam-6527	172	17	from	from	ADP
ejpam-6527	172	18	quantum	quantum	ADJ
ejpam-6527	172	19	computation	computation	NOUN
ejpam-6527	172	20	and	and	CCONJ
ejpam-6527	172	21	non	non	ADJ
ejpam-6527	172	22	-	-	ADJ
ejpam-6527	172	23	commutative	commutative	ADJ
ejpam-6527	172	24	signal	signal	NOUN
ejpam-6527	172	25	analysis	analysis	NOUN
ejpam-6527	172	26	.	.	PUNCT
ejpam-6527	173	1	acknowledgements	acknowledgement	NOUN
ejpam-6527	173	2	we	we	PRON
ejpam-6527	173	3	would	would	AUX
ejpam-6527	173	4	like	like	VERB
ejpam-6527	173	5	to	to	PART
ejpam-6527	173	6	extend	extend	VERB
ejpam-6527	173	7	our	our	PRON
ejpam-6527	173	8	sincere	sincere	ADJ
ejpam-6527	173	9	appreciation	appreciation	NOUN
ejpam-6527	173	10	to	to	ADP
ejpam-6527	173	11	our	our	PRON
ejpam-6527	173	12	colleagues	colleague	NOUN
ejpam-6527	173	13	in	in	ADP
ejpam-6527	173	14	the	the	DET
ejpam-6527	173	15	department	department	NOUN
ejpam-6527	173	16	of	of	ADP
ejpam-6527	173	17	mathematics	mathematic	NOUN
ejpam-6527	173	18	for	for	ADP
ejpam-6527	173	19	their	their	PRON
ejpam-6527	173	20	invaluable	invaluable	ADJ
ejpam-6527	173	21	guidance	guidance	NOUN
ejpam-6527	173	22	,	,	PUNCT
ejpam-6527	173	23	constructive	constructive	ADJ
ejpam-6527	173	24	feedback	feedback	NOUN
ejpam-6527	173	25	,	,	PUNCT
ejpam-6527	173	26	and	and	CCONJ
ejpam-6527	173	27	continuous	continuous	ADJ
ejpam-6527	173	28	support	support	NOUN
ejpam-6527	173	29	throughout	throughout	ADP
ejpam-6527	173	30	the	the	DET
ejpam-6527	173	31	development	development	NOUN
ejpam-6527	173	32	of	of	ADP
ejpam-6527	173	33	this	this	DET
ejpam-6527	173	34	work	work	NOUN
ejpam-6527	173	35	.	.	PUNCT
ejpam-6527	174	1	we	we	PRON
ejpam-6527	174	2	also	also	ADV
ejpam-6527	174	3	thank	thank	VERB
ejpam-6527	174	4	the	the	DET
ejpam-6527	174	5	reviewers	reviewer	NOUN
ejpam-6527	174	6	for	for	ADP
ejpam-6527	174	7	their	their	PRON
ejpam-6527	174	8	insightful	insightful	ADJ
ejpam-6527	174	9	comments	comment	NOUN
ejpam-6527	174	10	and	and	CCONJ
ejpam-6527	174	11	suggestions	suggestion	NOUN
ejpam-6527	174	12	,	,	PUNCT
ejpam-6527	174	13	which	which	PRON
ejpam-6527	174	14	have	have	AUX
ejpam-6527	174	15	greatly	greatly	ADV
ejpam-6527	174	16	contributed	contribute	VERB
ejpam-6527	174	17	to	to	ADP
ejpam-6527	174	18	improving	improve	VERB
ejpam-6527	174	19	the	the	DET
ejpam-6527	174	20	quality	quality	NOUN
ejpam-6527	174	21	and	and	CCONJ
ejpam-6527	174	22	clarity	clarity	NOUN
ejpam-6527	174	23	of	of	ADP
ejpam-6527	174	24	this	this	DET
ejpam-6527	174	25	manuscript	manuscript	NOUN
ejpam-6527	174	26	.	.	PUNCT
ejpam-6527	175	1	references	reference	NOUN
ejpam-6527	175	2	[	[	X
ejpam-6527	175	3	1	1	NUM
ejpam-6527	175	4	]	]	PUNCT
ejpam-6527	175	5	a.	a.	NOUN
ejpam-6527	175	6	connes	conne	NOUN
ejpam-6527	175	7	.	.	PUNCT
ejpam-6527	176	1	noncommutative	noncommutative	ADJ
ejpam-6527	176	2	geometry	geometry	NOUN
ejpam-6527	176	3	.	.	PUNCT
ejpam-6527	177	1	academic	academic	ADJ
ejpam-6527	177	2	press	press	NOUN
ejpam-6527	177	3	,	,	PUNCT
ejpam-6527	177	4	1994	1994	NUM
ejpam-6527	177	5	.	.	PUNCT
ejpam-6527	178	1	[	[	X
ejpam-6527	178	2	2	2	NUM
ejpam-6527	178	3	]	]	PUNCT
ejpam-6527	178	4	m.	m.	NOUN
ejpam-6527	178	5	a.	a.	NOUN
ejpam-6527	178	6	rieffel	rieffel	PROPN
ejpam-6527	178	7	.	.	PUNCT
ejpam-6527	179	1	projective	projective	ADJ
ejpam-6527	179	2	modules	module	NOUN
ejpam-6527	179	3	over	over	ADP
ejpam-6527	179	4	higher	higher	ADV
ejpam-6527	179	5	-	-	PUNCT
ejpam-6527	179	6	dimensional	dimensional	ADJ
ejpam-6527	179	7	non	non	ADJ
ejpam-6527	179	8	-	-	ADJ
ejpam-6527	179	9	commutative	commutative	ADJ
ejpam-6527	179	10	tori	tori	NOUN
ejpam-6527	179	11	.	.	PUNCT
ejpam-6527	180	1	canadian	canadian	ADJ
ejpam-6527	180	2	journal	journal	PROPN
ejpam-6527	180	3	of	of	ADP
ejpam-6527	180	4	mathematics	mathematic	NOUN
ejpam-6527	180	5	,	,	PUNCT
ejpam-6527	180	6	40(2):257–338	40(2):257–338	PROPN
ejpam-6527	180	7	,	,	PUNCT
ejpam-6527	180	8	1988	1988	NUM
ejpam-6527	180	9	.	.	PUNCT
ejpam-6527	181	1	m.	m.	PROPN
ejpam-6527	181	2	s.	s.	PROPN
ejpam-6527	181	3	ali	ali	PROPN
ejpam-6527	181	4	et	et	PROPN
ejpam-6527	181	5	al	al	PROPN
ejpam-6527	181	6	.	.	PUNCT
ejpam-6527	181	7	/	/	SYM
ejpam-6527	181	8	eur	eur	PROPN
ejpam-6527	181	9	.	.	PUNCT
ejpam-6527	182	1	j.	j.	PROPN
ejpam-6527	182	2	pure	pure	PROPN
ejpam-6527	182	3	appl	appl	PROPN
ejpam-6527	182	4	.	.	PROPN
ejpam-6527	182	5	math	math	PROPN
ejpam-6527	182	6	,	,	PUNCT
ejpam-6527	182	7	18	18	NUM
ejpam-6527	182	8	(	(	PUNCT
ejpam-6527	182	9	3	3	NUM
ejpam-6527	182	10	)	)	PUNCT
ejpam-6527	182	11	(	(	PUNCT
ejpam-6527	182	12	2025	2025	NUM
ejpam-6527	182	13	)	)	PUNCT
ejpam-6527	182	14	,	,	PUNCT
ejpam-6527	182	15	6527	6527	NUM
ejpam-6527	182	16	9	9	NUM
ejpam-6527	182	17	of	of	ADP
ejpam-6527	182	18	9	9	NUM
ejpam-6527	183	1	[	[	SYM
ejpam-6527	183	2	3	3	NUM
ejpam-6527	183	3	]	]	X
ejpam-6527	183	4	f.	f.	PROPN
ejpam-6527	183	5	besnard	besnard	PROPN
ejpam-6527	183	6	and	and	CCONJ
ejpam-6527	183	7	f.	f.	PROPN
ejpam-6527	183	8	latrémolière	latrémolière	PROPN
ejpam-6527	183	9	.	.	PUNCT
ejpam-6527	183	10	quantum	quantum	ADJ
ejpam-6527	183	11	compactness	compactness	NOUN
ejpam-6527	183	12	and	and	CCONJ
ejpam-6527	183	13	metric	metric	ADJ
ejpam-6527	183	14	convergence	convergence	NOUN
ejpam-6527	183	15	.	.	PUNCT
ejpam-6527	184	1	journal	journal	NOUN
ejpam-6527	184	2	of	of	ADP
ejpam-6527	184	3	functional	functional	ADJ
ejpam-6527	184	4	analysis	analysis	NOUN
ejpam-6527	184	5	,	,	PUNCT
ejpam-6527	184	6	285(4):110599	285(4):110599	PROPN
ejpam-6527	184	7	,	,	PUNCT
ejpam-6527	184	8	2023	2023	NUM
ejpam-6527	184	9	.	.	PUNCT
ejpam-6527	185	1	[	[	X
ejpam-6527	185	2	4	4	X
ejpam-6527	185	3	]	]	PUNCT
ejpam-6527	185	4	j.	j.	PROPN
ejpam-6527	185	5	m.	m.	PROPN
ejpam-6527	185	6	gracia	gracia	PROPN
ejpam-6527	185	7	-	-	PUNCT
ejpam-6527	185	8	bond́ıa	bond́ıa	PROPN
ejpam-6527	185	9	,	,	PUNCT
ejpam-6527	185	10	j.	j.	PROPN
ejpam-6527	185	11	c.	c.	PROPN
ejpam-6527	185	12	várilly	várilly	PROPN
ejpam-6527	185	13	,	,	PUNCT
ejpam-6527	185	14	and	and	CCONJ
ejpam-6527	185	15	h.	h.	PROPN
ejpam-6527	185	16	figueroa	figueroa	PROPN
ejpam-6527	185	17	.	.	PUNCT
ejpam-6527	186	1	elements	element	NOUN
ejpam-6527	186	2	of	of	ADP
ejpam-6527	186	3	noncommutative	noncommutative	ADJ
ejpam-6527	186	4	geometry	geometry	NOUN
ejpam-6527	186	5	.	.	PUNCT
ejpam-6527	187	1	birkhäuser	birkhäuser	NOUN
ejpam-6527	187	2	,	,	PUNCT
ejpam-6527	187	3	2001	2001	NUM
ejpam-6527	187	4	.	.	PUNCT
ejpam-6527	188	1	[	[	X
ejpam-6527	188	2	5	5	NUM
ejpam-6527	188	3	]	]	PUNCT
ejpam-6527	188	4	m.	m.	NOUN
ejpam-6527	188	5	khalkhali	khalkhali	PROPN
ejpam-6527	188	6	and	and	CCONJ
ejpam-6527	188	7	m.	m.	PROPN
ejpam-6527	188	8	marcolli	marcolli	PROPN
ejpam-6527	188	9	.	.	PUNCT
ejpam-6527	189	1	an	an	DET
ejpam-6527	189	2	invitation	invitation	NOUN
ejpam-6527	189	3	to	to	ADP
ejpam-6527	189	4	noncommutative	noncommutative	ADJ
ejpam-6527	189	5	geometry	geometry	NOUN
ejpam-6527	189	6	.	.	PUNCT
ejpam-6527	190	1	world	world	PROPN
ejpam-6527	190	2	scientific	scientific	PROPN
ejpam-6527	190	3	,	,	PUNCT
ejpam-6527	190	4	2008	2008	NUM
ejpam-6527	190	5	.	.	PUNCT
ejpam-6527	191	1	[	[	X
ejpam-6527	191	2	6	6	NUM
ejpam-6527	191	3	]	]	X
ejpam-6527	191	4	u.	u.	NOUN
ejpam-6527	191	5	haagerup	haagerup	NOUN
ejpam-6527	191	6	.	.	PUNCT
ejpam-6527	192	1	the	the	DET
ejpam-6527	192	2	operator	operator	NOUN
ejpam-6527	192	3	norm	norm	NOUN
ejpam-6527	192	4	of	of	ADP
ejpam-6527	192	5	a	a	DET
ejpam-6527	192	6	completely	completely	ADV
ejpam-6527	192	7	bounded	bound	VERB
ejpam-6527	192	8	map	map	NOUN
ejpam-6527	192	9	.	.	PUNCT
ejpam-6527	193	1	in	in	ADP
ejpam-6527	193	2	banach	banach	NOUN
ejpam-6527	193	3	algebras	algebra	NOUN
ejpam-6527	193	4	and	and	CCONJ
ejpam-6527	193	5	their	their	PRON
ejpam-6527	193	6	applications	application	NOUN
ejpam-6527	193	7	,	,	PUNCT
ejpam-6527	193	8	pages	page	NOUN
ejpam-6527	193	9	75–80	75–80	PROPN
ejpam-6527	193	10	,	,	PUNCT
ejpam-6527	193	11	1988	1988	NUM
ejpam-6527	193	12	.	.	PUNCT
ejpam-6527	194	1	[	[	X
ejpam-6527	194	2	7	7	X
ejpam-6527	194	3	]	]	X
ejpam-6527	194	4	m.	m.	NOUN
ejpam-6527	194	5	junge	junge	NOUN
ejpam-6527	194	6	and	and	CCONJ
ejpam-6527	194	7	d.	d.	PROPN
ejpam-6527	194	8	sherman	sherman	PROPN
ejpam-6527	194	9	.	.	PUNCT
ejpam-6527	195	1	operator	operator	NOUN
ejpam-6527	195	2	spaces	space	NOUN
ejpam-6527	195	3	and	and	CCONJ
ejpam-6527	195	4	noncommutative	noncommutative	ADJ
ejpam-6527	195	5	lp	lp	PROPN
ejpam-6527	195	6	theory	theory	NOUN
ejpam-6527	195	7	.	.	PUNCT
ejpam-6527	196	1	memoirs	memoir	NOUN
ejpam-6527	196	2	of	of	ADP
ejpam-6527	196	3	the	the	DET
ejpam-6527	196	4	american	american	PROPN
ejpam-6527	196	5	mathematical	mathematical	PROPN
ejpam-6527	196	6	society	society	NOUN
ejpam-6527	196	7	,	,	PUNCT
ejpam-6527	196	8	263(1275	263(1275	NUM
ejpam-6527	196	9	)	)	PUNCT
ejpam-6527	196	10	,	,	PUNCT
ejpam-6527	196	11	2020	2020	NUM
ejpam-6527	196	12	.	.	PUNCT
ejpam-6527	197	1	[	[	X
ejpam-6527	197	2	8	8	NUM
ejpam-6527	197	3	]	]	PUNCT
ejpam-6527	198	1	z.	z.	PROPN
ejpam-6527	198	2	ruan	ruan	PROPN
ejpam-6527	198	3	.	.	PUNCT
ejpam-6527	199	1	operator	operator	NOUN
ejpam-6527	199	2	spaces	space	NOUN
ejpam-6527	199	3	.	.	PUNCT
ejpam-6527	200	1	london	london	PROPN
ejpam-6527	200	2	mathematical	mathematical	ADJ
ejpam-6527	200	3	society	society	NOUN
ejpam-6527	200	4	monographs	monograph	NOUN
ejpam-6527	200	5	.	.	PUNCT
ejpam-6527	201	1	princeton	princeton	PROPN
ejpam-6527	201	2	university	university	PROPN
ejpam-6527	201	3	press	press	NOUN
ejpam-6527	201	4	,	,	PUNCT
ejpam-6527	201	5	2000	2000	NUM
ejpam-6527	201	6	.	.	PUNCT
ejpam-6527	202	1	[	[	X
ejpam-6527	202	2	9	9	NUM
ejpam-6527	202	3	]	]	PUNCT
ejpam-6527	202	4	w.	w.	PROPN
ejpam-6527	202	5	arveson	arveson	PROPN
ejpam-6527	202	6	.	.	PUNCT
ejpam-6527	203	1	a	a	DET
ejpam-6527	203	2	short	short	ADJ
ejpam-6527	203	3	course	course	NOUN
ejpam-6527	203	4	on	on	ADP
ejpam-6527	203	5	spectral	spectral	ADJ
ejpam-6527	203	6	theory	theory	NOUN
ejpam-6527	203	7	.	.	PUNCT
ejpam-6527	204	1	springer	springer	NOUN
ejpam-6527	204	2	-	-	PUNCT
ejpam-6527	204	3	verlag	verlag	PROPN
ejpam-6527	204	4	,	,	PUNCT
ejpam-6527	204	5	2002	2002	NUM
ejpam-6527	204	6	.	.	PUNCT
ejpam-6527	205	1	[	[	X
ejpam-6527	205	2	10	10	NUM
ejpam-6527	205	3	]	]	X
ejpam-6527	205	4	g.	g.	NOUN
ejpam-6527	205	5	pisier	pisier	NOUN
ejpam-6527	205	6	.	.	PUNCT
ejpam-6527	206	1	introduction	introduction	NOUN
ejpam-6527	206	2	to	to	ADP
ejpam-6527	206	3	operator	operator	NOUN
ejpam-6527	206	4	spaces	space	NOUN
ejpam-6527	206	5	.	.	PUNCT
ejpam-6527	207	1	cambridge	cambridge	PROPN
ejpam-6527	207	2	university	university	PROPN
ejpam-6527	207	3	press	press	NOUN
ejpam-6527	207	4	,	,	PUNCT
ejpam-6527	207	5	2003	2003	NUM
ejpam-6527	207	6	.	.	PUNCT
ejpam-6527	208	1	[	[	X
ejpam-6527	208	2	11	11	NUM
ejpam-6527	208	3	]	]	X
ejpam-6527	208	4	g.	g.	PROPN
ejpam-6527	208	5	a.	a.	PROPN
ejpam-6527	208	6	elliott	elliott	PROPN
ejpam-6527	208	7	and	and	CCONJ
ejpam-6527	208	8	d.	d.	PROPN
ejpam-6527	208	9	e.	e.	PROPN
ejpam-6527	208	10	evans	evans	PROPN
ejpam-6527	208	11	.	.	PUNCT
ejpam-6527	209	1	the	the	DET
ejpam-6527	209	2	structure	structure	NOUN
ejpam-6527	209	3	of	of	ADP
ejpam-6527	209	4	the	the	DET
ejpam-6527	209	5	irrational	irrational	ADJ
ejpam-6527	209	6	rotation	rotation	NOUN
ejpam-6527	209	7	c*-algebra	c*-algebra	VERB
ejpam-6527	209	8	.	.	PUNCT
ejpam-6527	210	1	annals	annal	NOUN
ejpam-6527	210	2	of	of	ADP
ejpam-6527	210	3	mathematics	mathematic	NOUN
ejpam-6527	210	4	,	,	PUNCT
ejpam-6527	210	5	138(3):477–501	138(3):477–501	NUM
ejpam-6527	210	6	,	,	PUNCT
ejpam-6527	210	7	1993	1993	NUM
ejpam-6527	210	8	.	.	PUNCT
ejpam-6527	211	1	[	[	X
ejpam-6527	211	2	12	12	NUM
ejpam-6527	211	3	]	]	X
ejpam-6527	211	4	f.	f.	PROPN
ejpam-6527	211	5	hiai	hiai	PROPN
ejpam-6527	211	6	and	and	CCONJ
ejpam-6527	211	7	y.	y.	PROPN
ejpam-6527	211	8	ueda	ueda	PROPN
ejpam-6527	211	9	.	.	PUNCT
ejpam-6527	212	1	non	non	ADJ
ejpam-6527	212	2	-	-	ADJ
ejpam-6527	212	3	commutative	commutative	ADJ
ejpam-6527	212	4	analysis	analysis	NOUN
ejpam-6527	212	5	and	and	CCONJ
ejpam-6527	212	6	operator	operator	NOUN
ejpam-6527	212	7	theory	theory	NOUN
ejpam-6527	212	8	.	.	PUNCT
ejpam-6527	213	1	advanced	advanced	ADJ
ejpam-6527	213	2	studies	study	NOUN
ejpam-6527	213	3	in	in	ADP
ejpam-6527	213	4	pure	pure	ADJ
ejpam-6527	213	5	mathematics	mathematic	NOUN
ejpam-6527	213	6	,	,	PUNCT
ejpam-6527	213	7	89:35–78	89:35–78	NUM
ejpam-6527	213	8	,	,	PUNCT
ejpam-6527	213	9	2022	2022	NUM
ejpam-6527	213	10	.	.	PUNCT
ejpam-6527	214	1	[	[	X
ejpam-6527	214	2	13	13	NUM
ejpam-6527	214	3	]	]	X
ejpam-6527	214	4	r.	r.	PROPN
ejpam-6527	214	5	v.	v.	PROPN
ejpam-6527	214	6	kadison	kadison	PROPN
ejpam-6527	214	7	and	and	CCONJ
ejpam-6527	214	8	j.	j.	PROPN
ejpam-6527	214	9	r.	r.	PROPN
ejpam-6527	214	10	ringrose	ringrose	PROPN
ejpam-6527	214	11	.	.	PUNCT
ejpam-6527	215	1	fundamentals	fundamental	NOUN
ejpam-6527	215	2	of	of	ADP
ejpam-6527	215	3	the	the	DET
ejpam-6527	215	4	theory	theory	NOUN
ejpam-6527	215	5	of	of	ADP
ejpam-6527	215	6	operator	operator	NOUN
ejpam-6527	215	7	algebras	algebra	NOUN
ejpam-6527	215	8	:	:	PUNCT
ejpam-6527	215	9	volume	volume	NOUN
ejpam-6527	215	10	i.	i.	PROPN
ejpam-6527	215	11	american	american	PROPN
ejpam-6527	215	12	mathematical	mathematical	PROPN
ejpam-6527	215	13	society	society	NOUN
ejpam-6527	215	14	,	,	PUNCT
ejpam-6527	215	15	1997	1997	NUM
ejpam-6527	215	16	.	.	PUNCT
ejpam-6527	216	1	[	[	X
ejpam-6527	216	2	14	14	NUM
ejpam-6527	216	3	]	]	X
ejpam-6527	216	4	r.	r.	PROPN
ejpam-6527	216	5	antonescu	antonescu	PROPN
ejpam-6527	216	6	and	and	CCONJ
ejpam-6527	216	7	e.	e.	PROPN
ejpam-6527	216	8	christensen	christensen	PROPN
ejpam-6527	216	9	.	.	PUNCT
ejpam-6527	217	1	metrics	metric	NOUN
ejpam-6527	217	2	on	on	ADP
ejpam-6527	217	3	state	state	NOUN
ejpam-6527	217	4	spaces	space	NOUN
ejpam-6527	217	5	.	.	PUNCT
ejpam-6527	218	1	proceedings	proceeding	NOUN
ejpam-6527	218	2	of	of	ADP
ejpam-6527	218	3	the	the	DET
ejpam-6527	218	4	american	american	PROPN
ejpam-6527	218	5	mathematical	mathematical	PROPN
ejpam-6527	218	6	society	society	NOUN
ejpam-6527	218	7	,	,	PUNCT
ejpam-6527	218	8	134(3):735–744	134(3):735–744	NUM
ejpam-6527	218	9	,	,	PUNCT
ejpam-6527	218	10	2003	2003	NUM
ejpam-6527	218	11	.	.	PUNCT
ejpam-6527	219	1	[	[	X
ejpam-6527	219	2	15	15	NUM
ejpam-6527	219	3	]	]	X
ejpam-6527	219	4	e.	e.	PROPN
ejpam-6527	219	5	c.	c.	PROPN
ejpam-6527	219	6	lance	lance	PROPN
ejpam-6527	219	7	.	.	PUNCT
ejpam-6527	220	1	hilbert	hilbert	PROPN
ejpam-6527	220	2	c*-modules	c*-module	NOUN
ejpam-6527	220	3	:	:	PUNCT
ejpam-6527	220	4	a	a	DET
ejpam-6527	220	5	toolkit	toolkit	NOUN
ejpam-6527	220	6	for	for	ADP
ejpam-6527	220	7	operator	operator	NOUN
ejpam-6527	220	8	algebraists	algebraist	NOUN
ejpam-6527	220	9	.	.	PUNCT
ejpam-6527	221	1	cambridge	cambridge	PROPN
ejpam-6527	221	2	university	university	PROPN
ejpam-6527	221	3	press	press	NOUN
ejpam-6527	221	4	,	,	PUNCT
ejpam-6527	221	5	1995	1995	NUM
ejpam-6527	221	6	.	.	PUNCT
ejpam-6527	222	1	[	[	X
ejpam-6527	222	2	16	16	NUM
ejpam-6527	222	3	]	]	X
ejpam-6527	222	4	f.	f.	PROPN
ejpam-6527	222	5	latrémolière	latrémolière	PROPN
ejpam-6527	222	6	.	.	PUNCT
ejpam-6527	223	1	quantum	quantum	NOUN
ejpam-6527	223	2	locally	locally	ADV
ejpam-6527	223	3	compact	compact	ADJ
ejpam-6527	223	4	metric	metric	ADJ
ejpam-6527	223	5	spaces	space	NOUN
ejpam-6527	223	6	.	.	PUNCT
ejpam-6527	224	1	journal	journal	NOUN
ejpam-6527	224	2	of	of	ADP
ejpam-6527	224	3	functional	functional	ADJ
ejpam-6527	224	4	analysis	analysis	NOUN
ejpam-6527	224	5	,	,	PUNCT
ejpam-6527	224	6	264(1):362–402	264(1):362–402	NUM
ejpam-6527	224	7	,	,	PUNCT
ejpam-6527	224	8	2012	2012	NUM
ejpam-6527	224	9	.	.	PUNCT
ejpam-6527	225	1	[	[	X
ejpam-6527	225	2	17	17	NUM
ejpam-6527	225	3	]	]	X
ejpam-6527	225	4	f.	f.	PROPN
ejpam-6527	225	5	latrémolière	latrémolière	PROPN
ejpam-6527	225	6	.	.	PUNCT
ejpam-6527	226	1	curved	curved	PROPN
ejpam-6527	226	2	noncommutative	noncommutative	PROPN
ejpam-6527	226	3	tori	tori	PROPN
ejpam-6527	226	4	as	as	ADP
ejpam-6527	226	5	leibniz	leibniz	PROPN
ejpam-6527	226	6	quantum	quantum	PROPN
ejpam-6527	226	7	compact	compact	ADJ
ejpam-6527	226	8	metric	metric	ADJ
ejpam-6527	226	9	spaces	space	NOUN
ejpam-6527	226	10	.	.	PUNCT
ejpam-6527	227	1	journal	journal	PROPN
ejpam-6527	227	2	of	of	ADP
ejpam-6527	227	3	mathematical	mathematical	ADJ
ejpam-6527	227	4	physics	physics	NOUN
ejpam-6527	227	5	,	,	PUNCT
ejpam-6527	227	6	56(12):123503	56(12):123503	NUM
ejpam-6527	227	7	,	,	PUNCT
ejpam-6527	227	8	2015	2015	NUM
ejpam-6527	227	9	.	.	PUNCT
ejpam-6527	228	1	[	[	X
ejpam-6527	228	2	18	18	NUM
ejpam-6527	228	3	]	]	X
ejpam-6527	228	4	d.	d.	PROPN
ejpam-6527	228	5	buchholz	buchholz	PROPN
ejpam-6527	228	6	and	and	CCONJ
ejpam-6527	228	7	s.	s.	PROPN
ejpam-6527	228	8	j.	j.	PROPN
ejpam-6527	228	9	summers	summers	PROPN
ejpam-6527	228	10	.	.	PUNCT
ejpam-6527	229	1	compactness	compactness	NOUN
ejpam-6527	229	2	and	and	CCONJ
ejpam-6527	229	3	energy	energy	NOUN
ejpam-6527	229	4	bounds	bound	NOUN
ejpam-6527	229	5	in	in	ADP
ejpam-6527	229	6	algebraic	algebraic	ADJ
ejpam-6527	229	7	quantum	quantum	ADJ
ejpam-6527	229	8	field	field	NOUN
ejpam-6527	229	9	theory	theory	NOUN
ejpam-6527	229	10	.	.	PUNCT
ejpam-6527	230	1	communications	communication	NOUN
ejpam-6527	230	2	in	in	ADP
ejpam-6527	230	3	mathematical	mathematical	ADJ
ejpam-6527	230	4	physics	physics	NOUN
ejpam-6527	230	5	,	,	PUNCT
ejpam-6527	230	6	366(3):1179–1217	366(3):1179–1217	PROPN
ejpam-6527	230	7	,	,	PUNCT
ejpam-6527	230	8	2019	2019	NUM
ejpam-6527	230	9	.	.	PUNCT
ejpam-6527	231	1	[	[	X
ejpam-6527	231	2	19	19	NUM
ejpam-6527	231	3	]	]	PUNCT
ejpam-6527	231	4	x.	x.	NOUN
ejpam-6527	231	5	chen	chen	PROPN
ejpam-6527	231	6	and	and	CCONJ
ejpam-6527	231	7	z.	z.	PROPN
ejpam-6527	231	8	wang	wang	PROPN
ejpam-6527	231	9	.	.	PUNCT
ejpam-6527	232	1	compact	compact	ADJ
ejpam-6527	232	2	quantum	quantum	ADJ
ejpam-6527	232	3	metric	metric	ADJ
ejpam-6527	232	4	spaces	space	NOUN
ejpam-6527	232	5	and	and	CCONJ
ejpam-6527	232	6	convergence	convergence	NOUN
ejpam-6527	232	7	.	.	PUNCT
ejpam-6527	233	1	journal	journal	NOUN
ejpam-6527	233	2	of	of	ADP
ejpam-6527	233	3	functional	functional	ADJ
ejpam-6527	233	4	analysis	analysis	NOUN
ejpam-6527	233	5	,	,	PUNCT
ejpam-6527	233	6	279(9):108689	279(9):108689	PROPN
ejpam-6527	233	7	,	,	PUNCT
ejpam-6527	233	8	2020	2020	NUM
ejpam-6527	233	9	.	.	PUNCT
ejpam-6527	234	1	[	[	X
ejpam-6527	234	2	20	20	NUM
ejpam-6527	234	3	]	]	X
ejpam-6527	234	4	d.	d.	PROPN
ejpam-6527	234	5	guido	guido	PROPN
ejpam-6527	234	6	and	and	CCONJ
ejpam-6527	234	7	t.	t.	PROPN
ejpam-6527	234	8	isola	isola	PROPN
ejpam-6527	234	9	.	.	PUNCT
ejpam-6527	235	1	compactness	compactness	NOUN
ejpam-6527	235	2	and	and	CCONJ
ejpam-6527	235	3	quantum	quantum	NOUN
ejpam-6527	235	4	gromov	gromov	NOUN
ejpam-6527	235	5	–	–	PUNCT
ejpam-6527	235	6	hausdorff	hausdorff	NOUN
ejpam-6527	235	7	convergence	convergence	NOUN
ejpam-6527	235	8	.	.	PUNCT
ejpam-6527	236	1	reviews	review	NOUN
ejpam-6527	236	2	in	in	ADP
ejpam-6527	236	3	mathematical	mathematical	ADJ
ejpam-6527	236	4	physics	physics	NOUN
ejpam-6527	236	5	,	,	PUNCT
ejpam-6527	236	6	33(6):2150013	33(6):2150013	NUM
ejpam-6527	236	7	,	,	PUNCT
ejpam-6527	236	8	2021	2021	NUM
ejpam-6527	236	9	.	.	PUNCT
ejpam-6527	237	1	[	[	X
ejpam-6527	237	2	21	21	NUM
ejpam-6527	237	3	]	]	X
ejpam-6527	237	4	j.	j.	PROPN
ejpam-6527	237	5	kaad	kaad	PROPN
ejpam-6527	237	6	and	and	CCONJ
ejpam-6527	237	7	d.	d.	PROPN
ejpam-6527	237	8	kyed	kye	VERB
ejpam-6527	237	9	.	.	PUNCT
ejpam-6527	238	1	the	the	DET
ejpam-6527	238	2	quantum	quantum	ADJ
ejpam-6527	238	3	metric	metric	ADJ
ejpam-6527	238	4	structure	structure	NOUN
ejpam-6527	238	5	of	of	ADP
ejpam-6527	238	6	quantum	quantum	NOUN
ejpam-6527	238	7	su(2	su(2	NOUN
ejpam-6527	238	8	)	)	PUNCT
ejpam-6527	238	9	.	.	PUNCT
ejpam-6527	239	1	arxiv	arxiv	PROPN
ejpam-6527	239	2	preprint	preprint	PROPN
ejpam-6527	239	3	arxiv:2205.06043	arxiv:2205.06043	NUM
ejpam-6527	239	4	,	,	PUNCT
ejpam-6527	239	5	2022	2022	NUM
ejpam-6527	239	6	.	.	PUNCT
ejpam-6527	240	1	[	[	X
ejpam-6527	240	2	22	22	NUM
ejpam-6527	240	3	]	]	PUNCT
ejpam-6527	240	4	m.	m.	NOUN
ejpam-6527	240	5	caspers	casper	NOUN
ejpam-6527	240	6	and	and	CCONJ
ejpam-6527	240	7	a.	a.	PROPN
ejpam-6527	240	8	skalski	skalski	PROPN
ejpam-6527	240	9	.	.	PUNCT
ejpam-6527	241	1	quantum	quantum	ADJ
ejpam-6527	241	2	information	information	NOUN
ejpam-6527	241	3	channels	channel	NOUN
ejpam-6527	241	4	and	and	CCONJ
ejpam-6527	241	5	compactness	compactness	NOUN
ejpam-6527	241	6	.	.	PUNCT
ejpam-6527	242	1	communications	communication	NOUN
ejpam-6527	242	2	in	in	ADP
ejpam-6527	242	3	mathematical	mathematical	ADJ
ejpam-6527	242	4	physics	physics	NOUN
ejpam-6527	242	5	,	,	PUNCT
ejpam-6527	242	6	401(2):469–499	401(2):469–499	PROPN
ejpam-6527	242	7	,	,	PUNCT
ejpam-6527	242	8	2023	2023	NUM
ejpam-6527	242	9	.	.	PUNCT
ejpam-6527	243	1	[	[	X
ejpam-6527	243	2	23	23	NUM
ejpam-6527	243	3	]	]	X
ejpam-6527	243	4	f.	f.	PROPN
ejpam-6527	243	5	latrémolière	latrémolière	PROPN
ejpam-6527	243	6	.	.	PUNCT
ejpam-6527	244	1	compact	compact	ADJ
ejpam-6527	244	2	quantum	quantum	ADJ
ejpam-6527	244	3	metric	metric	ADJ
ejpam-6527	244	4	spaces	space	NOUN
ejpam-6527	244	5	.	.	PUNCT
ejpam-6527	245	1	in	in	ADP
ejpam-6527	245	2	noncommutative	noncommutative	ADJ
ejpam-6527	245	3	geometry	geometry	NOUN
ejpam-6527	245	4	and	and	CCONJ
ejpam-6527	245	5	its	its	PRON
ejpam-6527	245	6	applications	application	NOUN
ejpam-6527	245	7	,	,	PUNCT
ejpam-6527	245	8	pages	page	NOUN
ejpam-6527	245	9	251–278	251–278	NUM
ejpam-6527	245	10	.	.	PUNCT
ejpam-6527	245	11	springer	springer	NOUN
ejpam-6527	245	12	,	,	PUNCT
ejpam-6527	245	13	2024	2024	NUM
ejpam-6527	245	14	.	.	PUNCT