id	sid	tid	token	lemma	pos
ejpam-6739	1	1	european	european	PROPN
ejpam-6739	1	2	journal	journal	PROPN
ejpam-6739	1	3	of	of	ADP
ejpam-6739	1	4	pure	pure	ADJ
ejpam-6739	1	5	and	and	CCONJ
ejpam-6739	1	6	applied	applied	ADJ
ejpam-6739	1	7	mathematics	mathematic	NOUN
ejpam-6739	1	8	2025	2025	NUM
ejpam-6739	1	9	,	,	PUNCT
ejpam-6739	1	10	vol	vol	NOUN
ejpam-6739	1	11	.	.	PROPN
ejpam-6739	1	12	18	18	NUM
ejpam-6739	1	13	,	,	PUNCT
ejpam-6739	1	14	issue	issue	NOUN
ejpam-6739	1	15	4	4	NUM
ejpam-6739	1	16	,	,	PUNCT
ejpam-6739	1	17	article	article	NOUN
ejpam-6739	1	18	number	number	NOUN
ejpam-6739	1	19	6739	6739	NUM
ejpam-6739	1	20	issn	issn	VERB
ejpam-6739	1	21	1307	1307	NUM
ejpam-6739	1	22	-	-	SYM
ejpam-6739	1	23	5543	5543	NUM
ejpam-6739	1	24	–	–	PUNCT
ejpam-6739	1	25	ejpam.com	ejpam.com	X
ejpam-6739	1	26	published	publish	VERB
ejpam-6739	1	27	by	by	ADP
ejpam-6739	1	28	new	new	PROPN
ejpam-6739	1	29	york	york	PROPN
ejpam-6739	1	30	business	business	PROPN
ejpam-6739	1	31	global	global	ADJ
ejpam-6739	1	32	invariant	invariant	PROPN
ejpam-6739	1	33	subspace	subspace	NOUN
ejpam-6739	1	34	problem	problem	NOUN
ejpam-6739	1	35	for	for	ADP
ejpam-6739	1	36	norm	norm	NOUN
ejpam-6739	1	37	attaining	attain	VERB
ejpam-6739	1	38	operators	operator	NOUN
ejpam-6739	2	1	aissa	aissa	ADJ
ejpam-6739	2	2	nasli	nasli	VERB
ejpam-6739	2	3	bakir1,2	bakir1,2	PROPN
ejpam-6739	2	4	,	,	PUNCT
ejpam-6739	2	5	ayyoub	ayyoub	PROPN
ejpam-6739	2	6	fellag	fellag	PROPN
ejpam-6739	2	7	ariouat1	ariouat1	PROPN
ejpam-6739	2	8	,	,	PUNCT
ejpam-6739	2	9	abdelkader	abdelkader	PROPN
ejpam-6739	2	10	benali1	benali1	PROPN
ejpam-6739	2	11	,	,	PUNCT
ejpam-6739	2	12	ibrahim	ibrahim	PROPN
ejpam-6739	2	13	alraddadi3,∗	alraddadi3,∗	PROPN
ejpam-6739	2	14	,	,	PUNCT
ejpam-6739	2	15	saad	saad	PROPN
ejpam-6739	2	16	m.	m.	PROPN
ejpam-6739	2	17	almuaddi4,5,∗	almuaddi4,5,∗	PROPN
ejpam-6739	2	18	1	1	NUM
ejpam-6739	2	19	department	department	NOUN
ejpam-6739	2	20	of	of	ADP
ejpam-6739	2	21	mathematics	mathematic	NOUN
ejpam-6739	2	22	,	,	PUNCT
ejpam-6739	2	23	faculty	faculty	NOUN
ejpam-6739	2	24	of	of	ADP
ejpam-6739	2	25	exact	exact	ADJ
ejpam-6739	2	26	sciences	science	NOUN
ejpam-6739	2	27	and	and	CCONJ
ejpam-6739	2	28	informatics	informatic	NOUN
ejpam-6739	2	29	,	,	PUNCT
ejpam-6739	2	30	laboratory	laboratory	NOUN
ejpam-6739	2	31	of	of	ADP
ejpam-6739	2	32	mathematics	mathematic	NOUN
ejpam-6739	2	33	and	and	CCONJ
ejpam-6739	2	34	application	application	NOUN
ejpam-6739	2	35	lma	lma	PROPN
ejpam-6739	2	36	,	,	PUNCT
ejpam-6739	2	37	hassiba	hassiba	PROPN
ejpam-6739	2	38	benbouali	benbouali	PROPN
ejpam-6739	2	39	university	university	PROPN
ejpam-6739	2	40	of	of	ADP
ejpam-6739	2	41	chlef	chlef	PROPN
ejpam-6739	2	42	,	,	PUNCT
ejpam-6739	2	43	algeria	algeria	PROPN
ejpam-6739	2	44	2	2	NUM
ejpam-6739	2	45	national	national	PROPN
ejpam-6739	2	46	higher	high	ADJ
ejpam-6739	2	47	school	school	NOUN
ejpam-6739	2	48	of	of	ADP
ejpam-6739	2	49	cybersecurity	cybersecurity	NOUN
ejpam-6739	2	50	,	,	PUNCT
ejpam-6739	2	51	sidi	sidi	NOUN
ejpam-6739	2	52	abdellah	abdellah	PROPN
ejpam-6739	2	53	,	,	PUNCT
ejpam-6739	2	54	algeria	algeria	PROPN
ejpam-6739	2	55	3	3	NUM
ejpam-6739	2	56	department	department	NOUN
ejpam-6739	2	57	of	of	ADP
ejpam-6739	2	58	mathematics	mathematic	NOUN
ejpam-6739	2	59	,	,	PUNCT
ejpam-6739	2	60	faculty	faculty	NOUN
ejpam-6739	2	61	of	of	ADP
ejpam-6739	2	62	science	science	NOUN
ejpam-6739	2	63	,	,	PUNCT
ejpam-6739	2	64	islamic	islamic	PROPN
ejpam-6739	2	65	university	university	PROPN
ejpam-6739	2	66	of	of	ADP
ejpam-6739	2	67	madinah	madinah	PROPN
ejpam-6739	2	68	,	,	PUNCT
ejpam-6739	2	69	madinah	madinah	PROPN
ejpam-6739	2	70	,	,	PUNCT
ejpam-6739	2	71	saudi	saudi	PROPN
ejpam-6739	2	72	arabia	arabia	PROPN
ejpam-6739	2	73	4	4	NUM
ejpam-6739	2	74	basic	basic	ADJ
ejpam-6739	2	75	&	&	CCONJ
ejpam-6739	2	76	applied	apply	VERB
ejpam-6739	2	77	scientific	scientific	ADJ
ejpam-6739	2	78	research	research	NOUN
ejpam-6739	2	79	center	center	NOUN
ejpam-6739	2	80	,	,	PUNCT
ejpam-6739	2	81	imam	imam	PROPN
ejpam-6739	2	82	abdulrahman	abdulrahman	PROPN
ejpam-6739	2	83	bin	bin	PROPN
ejpam-6739	2	84	faisal	faisal	PROPN
ejpam-6739	2	85	university	university	PROPN
ejpam-6739	2	86	,	,	PUNCT
ejpam-6739	2	87	p.o	p.o	PROPN
ejpam-6739	2	88	.	.	PROPN
ejpam-6739	2	89	box	box	PROPN
ejpam-6739	2	90	1982	1982	NUM
ejpam-6739	2	91	,	,	PUNCT
ejpam-6739	2	92	dammam	dammam	PROPN
ejpam-6739	2	93	31441	31441	NUM
ejpam-6739	2	94	,	,	PUNCT
ejpam-6739	2	95	saudi	saudi	PROPN
ejpam-6739	2	96	arabia	arabia	PROPN
ejpam-6739	2	97	5	5	NUM
ejpam-6739	2	98	mathematics	mathematics	PROPN
ejpam-6739	2	99	department	department	NOUN
ejpam-6739	2	100	,	,	PUNCT
ejpam-6739	2	101	college	college	NOUN
ejpam-6739	2	102	of	of	ADP
ejpam-6739	2	103	science	science	NOUN
ejpam-6739	2	104	,	,	PUNCT
ejpam-6739	2	105	imam	imam	PROPN
ejpam-6739	2	106	abdulrahman	abdulrahman	PROPN
ejpam-6739	2	107	bin	bin	PROPN
ejpam-6739	2	108	faisal	faisal	PROPN
ejpam-6739	2	109	university	university	PROPN
ejpam-6739	2	110	,	,	PUNCT
ejpam-6739	2	111	dammam	dammam	PROPN
ejpam-6739	2	112	31441	31441	NUM
ejpam-6739	2	113	,	,	PUNCT
ejpam-6739	2	114	saudi	saudi	PROPN
ejpam-6739	2	115	arabia	arabia	PROPN
ejpam-6739	2	116	abstract	abstract	NOUN
ejpam-6739	2	117	.	.	PUNCT
ejpam-6739	3	1	our	our	PRON
ejpam-6739	3	2	aim	aim	NOUN
ejpam-6739	3	3	is	be	AUX
ejpam-6739	3	4	to	to	PART
ejpam-6739	3	5	characterize	characterize	VERB
ejpam-6739	3	6	norm	norm	NOUN
ejpam-6739	3	7	attaining	attain	VERB
ejpam-6739	3	8	and	and	CCONJ
ejpam-6739	3	9	absolutely	absolutely	ADV
ejpam-6739	3	10	norm	norm	VERB
ejpam-6739	3	11	attaining	attain	VERB
ejpam-6739	3	12	quasi-∗paranormal	quasi-∗paranormal	ADJ
ejpam-6739	3	13	operators	operator	NOUN
ejpam-6739	3	14	and	and	CCONJ
ejpam-6739	3	15	class	class	NOUN
ejpam-6739	3	16	ωn	ωn	NOUN
ejpam-6739	3	17	operators	operator	NOUN
ejpam-6739	3	18	defined	define	VERB
ejpam-6739	3	19	on	on	ADP
ejpam-6739	3	20	a	a	DET
ejpam-6739	3	21	separable	separable	ADJ
ejpam-6739	3	22	hilbert	hilbert	NOUN
ejpam-6739	3	23	space	space	NOUN
ejpam-6739	3	24	.	.	PUNCT
ejpam-6739	4	1	we	we	PRON
ejpam-6739	4	2	define	define	VERB
ejpam-6739	4	3	invariant	invariant	ADJ
ejpam-6739	4	4	non	non	ADJ
ejpam-6739	4	5	trivial	trivial	ADJ
ejpam-6739	4	6	subspaces	subspace	NOUN
ejpam-6739	4	7	for	for	ADP
ejpam-6739	4	8	the	the	DET
ejpam-6739	4	9	considered	consider	VERB
ejpam-6739	4	10	operators	operator	NOUN
ejpam-6739	4	11	and	and	CCONJ
ejpam-6739	4	12	we	we	PRON
ejpam-6739	4	13	give	give	VERB
ejpam-6739	4	14	a	a	DET
ejpam-6739	4	15	matrix	matrix	NOUN
ejpam-6739	4	16	representation	representation	NOUN
ejpam-6739	4	17	under	under	ADP
ejpam-6739	4	18	certain	certain	ADJ
ejpam-6739	4	19	condition	condition	NOUN
ejpam-6739	4	20	.	.	PUNCT
ejpam-6739	5	1	compactness	compactness	NOUN
ejpam-6739	5	2	,	,	PUNCT
ejpam-6739	5	3	reducing	reduce	VERB
ejpam-6739	5	4	subspaces	subspace	NOUN
ejpam-6739	5	5	and	and	CCONJ
ejpam-6739	5	6	the	the	DET
ejpam-6739	5	7	normality	normality	NOUN
ejpam-6739	5	8	of	of	ADP
ejpam-6739	5	9	such	such	ADJ
ejpam-6739	5	10	operators	operator	NOUN
ejpam-6739	5	11	are	be	AUX
ejpam-6739	5	12	also	also	ADV
ejpam-6739	5	13	established	establish	VERB
ejpam-6739	5	14	.	.	PUNCT
ejpam-6739	6	1	2020	2020	NUM
ejpam-6739	6	2	mathematics	mathematics	PROPN
ejpam-6739	6	3	subject	subject	NOUN
ejpam-6739	6	4	classifications	classification	NOUN
ejpam-6739	6	5	:	:	PUNCT
ejpam-6739	6	6	47a30	47a30	NUM
ejpam-6739	6	7	,	,	PUNCT
ejpam-6739	6	8	47b47	47b47	NOUN
ejpam-6739	6	9	,	,	PUNCT
ejpam-6739	6	10	47b20	47b20	NUM
ejpam-6739	6	11	key	key	ADJ
ejpam-6739	6	12	words	word	NOUN
ejpam-6739	6	13	and	and	CCONJ
ejpam-6739	6	14	phrases	phrase	NOUN
ejpam-6739	6	15	:	:	PUNCT
ejpam-6739	6	16	quasi-∗-paranormal	quasi-∗-paranormal	NUM
ejpam-6739	6	17	operators	operator	NOUN
ejpam-6739	6	18	,	,	PUNCT
ejpam-6739	6	19	invariant	invariant	ADJ
ejpam-6739	6	20	subspaces	subspace	NOUN
ejpam-6739	6	21	,	,	PUNCT
ejpam-6739	6	22	norm	norm	NOUN
ejpam-6739	6	23	attaining	attain	VERB
ejpam-6739	6	24	operators	operator	NOUN
ejpam-6739	6	25	,	,	PUNCT
ejpam-6739	6	26	absolutely	absolutely	ADV
ejpam-6739	6	27	norm	norm	VERB
ejpam-6739	6	28	attaining	attain	VERB
ejpam-6739	6	29	operators	operator	NOUN
ejpam-6739	6	30	1	1	NUM
ejpam-6739	6	31	.	.	PUNCT
ejpam-6739	6	32	preliminaries	preliminary	NOUN
ejpam-6739	6	33	and	and	CCONJ
ejpam-6739	6	34	notations	notation	NOUN
ejpam-6739	6	35	let	let	VERB
ejpam-6739	6	36	h	h	NOUN
ejpam-6739	6	37	denote	denote	VERB
ejpam-6739	6	38	an	an	DET
ejpam-6739	6	39	infinite	infinite	ADJ
ejpam-6739	6	40	separable	separable	ADJ
ejpam-6739	6	41	complex	complex	ADJ
ejpam-6739	6	42	hilbert	hilbert	NOUN
ejpam-6739	6	43	space	space	NOUN
ejpam-6739	6	44	,	,	PUNCT
ejpam-6739	6	45	and	and	CCONJ
ejpam-6739	6	46	let	let	VERB
ejpam-6739	6	47	b(h	b(h	NOUN
ejpam-6739	6	48	)	)	PUNCT
ejpam-6739	6	49	be	be	VERB
ejpam-6739	6	50	the	the	DET
ejpam-6739	6	51	banach	banach	NOUN
ejpam-6739	6	52	algebra	algebra	NOUN
ejpam-6739	6	53	of	of	ADP
ejpam-6739	6	54	all	all	DET
ejpam-6739	6	55	bounded	bound	VERB
ejpam-6739	6	56	linear	linear	PROPN
ejpam-6739	6	57	operators	operator	NOUN
ejpam-6739	6	58	on	on	ADP
ejpam-6739	6	59	h.	h.	PROPN
ejpam-6739	6	60	an	an	DET
ejpam-6739	6	61	operator	operator	NOUN
ejpam-6739	6	62	t	t	PROPN
ejpam-6739	6	63	∈	∈	PROPN
ejpam-6739	6	64	b(h	b(h	PROPN
ejpam-6739	6	65	)	)	PUNCT
ejpam-6739	6	66	is	be	AUX
ejpam-6739	6	67	said	say	VERB
ejpam-6739	6	68	to	to	PART
ejpam-6739	6	69	be	be	AUX
ejpam-6739	6	70	norm	norm	NOUN
ejpam-6739	6	71	attaining	attain	VERB
ejpam-6739	6	72	,	,	PUNCT
ejpam-6739	6	73	if	if	SCONJ
ejpam-6739	6	74	there	there	PRON
ejpam-6739	6	75	exists	exist	VERB
ejpam-6739	6	76	a	a	DET
ejpam-6739	6	77	unit	unit	NOUN
ejpam-6739	6	78	vector	vector	NOUN
ejpam-6739	6	79	u	u	PROPN
ejpam-6739	6	80	∈	∈	NOUN
ejpam-6739	6	81	h	h	NOUN
ejpam-6739	6	82	satisfying	satisfy	VERB
ejpam-6739	6	83	∥tu∥	∥tu∥	NOUN
ejpam-6739	7	1	=	=	SYM
ejpam-6739	7	2	∥t∥	∥t∥	PROPN
ejpam-6739	7	3	,	,	PUNCT
ejpam-6739	7	4	[	[	X
ejpam-6739	7	5	1	1	NUM
ejpam-6739	7	6	]	]	PUNCT
ejpam-6739	7	7	,	,	PUNCT
ejpam-6739	7	8	and	and	CCONJ
ejpam-6739	7	9	t	t	PROPN
ejpam-6739	7	10	is	be	AUX
ejpam-6739	7	11	said	say	VERB
ejpam-6739	7	12	to	to	PART
ejpam-6739	7	13	be	be	AUX
ejpam-6739	7	14	absolutely	absolutely	ADV
ejpam-6739	7	15	norm	norm	ADJ
ejpam-6739	7	16	attaining	attain	VERB
ejpam-6739	7	17	,	,	PUNCT
ejpam-6739	7	18	briefly	briefly	ADV
ejpam-6739	7	19	,	,	PUNCT
ejpam-6739	7	20	an	an	DET
ejpam-6739	7	21	-operator	-operator	NOUN
ejpam-6739	7	22	,	,	PUNCT
ejpam-6739	7	23	if	if	SCONJ
ejpam-6739	7	24	its	its	PRON
ejpam-6739	7	25	restriction	restriction	NOUN
ejpam-6739	7	26	on	on	ADP
ejpam-6739	7	27	any	any	DET
ejpam-6739	7	28	closed	closed	ADJ
ejpam-6739	7	29	subspace	subspace	NOUN
ejpam-6739	7	30	of	of	ADP
ejpam-6739	7	31	h	h	NOUN
ejpam-6739	7	32	is	be	AUX
ejpam-6739	7	33	norm	norm	NOUN
ejpam-6739	7	34	attaining	attain	VERB
ejpam-6739	7	35	,	,	PUNCT
ejpam-6739	7	36	[	[	X
ejpam-6739	7	37	2	2	NUM
ejpam-6739	7	38	]	]	PUNCT
ejpam-6739	7	39	.	.	PUNCT
ejpam-6739	8	1	obviously	obviously	ADV
ejpam-6739	8	2	,	,	PUNCT
ejpam-6739	8	3	an	an	DET
ejpam-6739	8	4	-operators	-operator	NOUN
ejpam-6739	8	5	are	be	AUX
ejpam-6739	8	6	norm	norm	NOUN
ejpam-6739	8	7	attaining	attain	VERB
ejpam-6739	8	8	.	.	PUNCT
ejpam-6739	9	1	many	many	ADJ
ejpam-6739	9	2	authors	author	NOUN
ejpam-6739	9	3	∗corresponding	∗corresponde	VERB
ejpam-6739	9	4	author	author	NOUN
ejpam-6739	9	5	.	.	PUNCT
ejpam-6739	10	1	∗corresponding	∗corresponde	VERB
ejpam-6739	10	2	author	author	NOUN
ejpam-6739	10	3	.	.	PUNCT
ejpam-6739	11	1	doi	doi	NOUN
ejpam-6739	11	2	:	:	PUNCT
ejpam-6739	11	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6739	https://doi.org/10.29020/nybg.ejpam.v18i4.6739	PROPN
ejpam-6739	11	4	email	email	NOUN
ejpam-6739	11	5	addresses	address	NOUN
ejpam-6739	11	6	:	:	PUNCT
ejpam-6739	11	7	a.nasli@univ-chlef.dz	a.nasli@univ-chlef.dz	X
ejpam-6739	11	8	(	(	PUNCT
ejpam-6739	11	9	a.	a.	NOUN
ejpam-6739	11	10	nasli	nasli	PROPN
ejpam-6739	11	11	bakir	bakir	PROPN
ejpam-6739	11	12	)	)	PUNCT
ejpam-6739	11	13	,	,	PUNCT
ejpam-6739	11	14	a.fellagariouat@univ-chlef.dz	a.fellagariouat@univ-chlef.dz	PRON
ejpam-6739	11	15	(	(	PUNCT
ejpam-6739	11	16	a.	a.	NOUN
ejpam-6739	11	17	fellag	fellag	PROPN
ejpam-6739	11	18	ariouat	ariouat	NOUN
ejpam-6739	11	19	)	)	PUNCT
ejpam-6739	11	20	,	,	PUNCT
ejpam-6739	11	21	benali4848@gmail.com	benali4848@gmail.com	X
ejpam-6739	12	1	(	(	PUNCT
ejpam-6739	12	2	a.	a.	NOUN
ejpam-6739	12	3	benali	benali	PROPN
ejpam-6739	12	4	)	)	PUNCT
ejpam-6739	12	5	,	,	PUNCT
ejpam-6739	12	6	ialraddadi@iu.edu.sa	ialraddadi@iu.edu.sa	PROPN
ejpam-6739	12	7	(	(	PUNCT
ejpam-6739	12	8	i.	i.	NOUN
ejpam-6739	12	9	alraddadi	alraddadi	PROPN
ejpam-6739	12	10	)	)	PUNCT
ejpam-6739	12	11	,	,	PUNCT
ejpam-6739	12	12	smuaddi@iau.edu.sa	smuaddi@iau.edu.sa	PROPN
ejpam-6739	12	13	(	(	PUNCT
ejpam-6739	12	14	s.	s.	PROPN
ejpam-6739	12	15	m.	m.	PROPN
ejpam-6739	12	16	almuaddi	almuaddi	PROPN
ejpam-6739	12	17	)	)	PUNCT
ejpam-6739	12	18	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6739	13	1	1	1	NUM
ejpam-6739	13	2	copyright	copyright	NOUN
ejpam-6739	13	3	:	:	PUNCT
ejpam-6739	13	4	©	©	PROPN
ejpam-6739	13	5	2025	2025	NUM
ejpam-6739	13	6	the	the	DET
ejpam-6739	13	7	author(s	author(s	NOUN
ejpam-6739	13	8	)	)	PUNCT
ejpam-6739	13	9	.	.	PUNCT
ejpam-6739	14	1	(	(	PUNCT
ejpam-6739	14	2	cc	cc	NOUN
ejpam-6739	14	3	by	by	ADP
ejpam-6739	14	4	-	-	PUNCT
ejpam-6739	14	5	nc	nc	PROPN
ejpam-6739	14	6	4.0	4.0	NUM
ejpam-6739	14	7	)	)	PUNCT
ejpam-6739	14	8	a.	a.	NOUN
ejpam-6739	14	9	nasli	nasli	PROPN
ejpam-6739	14	10	bakir	bakir	VERB
ejpam-6739	14	11	et	et	PROPN
ejpam-6739	14	12	al	al	PROPN
ejpam-6739	14	13	.	.	PUNCT
ejpam-6739	14	14	/	/	SYM
ejpam-6739	14	15	eur	eur	PROPN
ejpam-6739	14	16	.	.	PUNCT
ejpam-6739	15	1	j.	j.	PROPN
ejpam-6739	15	2	pure	pure	PROPN
ejpam-6739	15	3	appl	appl	PROPN
ejpam-6739	15	4	.	.	PROPN
ejpam-6739	15	5	math	math	PROPN
ejpam-6739	15	6	,	,	PUNCT
ejpam-6739	15	7	18	18	NUM
ejpam-6739	15	8	(	(	PUNCT
ejpam-6739	15	9	4	4	NUM
ejpam-6739	15	10	)	)	PUNCT
ejpam-6739	15	11	(	(	PUNCT
ejpam-6739	15	12	2025	2025	NUM
ejpam-6739	15	13	)	)	PUNCT
ejpam-6739	15	14	,	,	PUNCT
ejpam-6739	15	15	6739	6739	NUM
ejpam-6739	15	16	2	2	NUM
ejpam-6739	15	17	of	of	ADP
ejpam-6739	15	18	10	10	NUM
ejpam-6739	15	19	studied	study	VERB
ejpam-6739	15	20	the	the	DET
ejpam-6739	15	21	structure	structure	NOUN
ejpam-6739	15	22	of	of	ADP
ejpam-6739	15	23	some	some	DET
ejpam-6739	15	24	classes	class	NOUN
ejpam-6739	15	25	of	of	ADP
ejpam-6739	15	26	norm	norm	NOUN
ejpam-6739	15	27	attaining	attain	VERB
ejpam-6739	15	28	non	non	PRON
ejpam-6739	15	29	normal	normal	ADJ
ejpam-6739	15	30	operators	operator	NOUN
ejpam-6739	15	31	,	,	PUNCT
ejpam-6739	15	32	see	see	VERB
ejpam-6739	15	33	[	[	X
ejpam-6739	15	34	3	3	NUM
ejpam-6739	15	35	,	,	PUNCT
ejpam-6739	15	36	4	4	NUM
ejpam-6739	15	37	]	]	PUNCT
ejpam-6739	15	38	and	and	CCONJ
ejpam-6739	15	39	[	[	X
ejpam-6739	15	40	5	5	NUM
ejpam-6739	15	41	]	]	PUNCT
ejpam-6739	15	42	.	.	PUNCT
ejpam-6739	16	1	authors	author	NOUN
ejpam-6739	16	2	in	in	ADP
ejpam-6739	16	3	[	[	X
ejpam-6739	16	4	5	5	NUM
ejpam-6739	16	5	,	,	PUNCT
ejpam-6739	16	6	6	6	NUM
ejpam-6739	16	7	]	]	PUNCT
ejpam-6739	16	8	analyzed	analyze	VERB
ejpam-6739	16	9	the	the	DET
ejpam-6739	16	10	properties	property	NOUN
ejpam-6739	16	11	of	of	ADP
ejpam-6739	16	12	norm	norm	NOUN
ejpam-6739	16	13	attaining	attain	VERB
ejpam-6739	16	14	and	and	CCONJ
ejpam-6739	16	15	absolutely	absolutely	ADV
ejpam-6739	16	16	norm	norm	VERB
ejpam-6739	16	17	attaining	attain	VERB
ejpam-6739	16	18	operators	operator	NOUN
ejpam-6739	16	19	,	,	PUNCT
ejpam-6739	16	20	and	and	CCONJ
ejpam-6739	16	21	provide	provide	VERB
ejpam-6739	16	22	a	a	DET
ejpam-6739	16	23	representation	representation	NOUN
ejpam-6739	16	24	for	for	ADP
ejpam-6739	16	25	the	the	DET
ejpam-6739	16	26	class	class	NOUN
ejpam-6739	16	27	of	of	ADP
ejpam-6739	16	28	∗-paranormal	∗-paranormal	ADJ
ejpam-6739	16	29	operators	operator	NOUN
ejpam-6739	16	30	under	under	ADP
ejpam-6739	16	31	an	an	DET
ejpam-6739	16	32	orthogonal	orthogonal	ADJ
ejpam-6739	16	33	decomposition	decomposition	NOUN
ejpam-6739	16	34	of	of	ADP
ejpam-6739	16	35	h.	h.	PROPN
ejpam-6739	16	36	authors	author	NOUN
ejpam-6739	16	37	in	in	ADP
ejpam-6739	16	38	[	[	X
ejpam-6739	16	39	4	4	NUM
ejpam-6739	16	40	]	]	PUNCT
ejpam-6739	16	41	showed	show	VERB
ejpam-6739	16	42	that	that	DET
ejpam-6739	16	43	compact	compact	ADJ
ejpam-6739	16	44	(	(	PUNCT
ejpam-6739	16	45	resp	resp	NOUN
ejpam-6739	16	46	.	.	PUNCT
ejpam-6739	16	47	isometric	isometric	ADJ
ejpam-6739	16	48	)	)	PUNCT
ejpam-6739	16	49	operators	operator	NOUN
ejpam-6739	16	50	are	be	AUX
ejpam-6739	16	51	an	an	DET
ejpam-6739	16	52	-operators	-operator	NOUN
ejpam-6739	16	53	since	since	SCONJ
ejpam-6739	16	54	their	their	PRON
ejpam-6739	16	55	restrictions	restriction	NOUN
ejpam-6739	16	56	on	on	ADP
ejpam-6739	16	57	closed	closed	ADJ
ejpam-6739	16	58	invariant	invariant	ADJ
ejpam-6739	16	59	subspaces	subspace	NOUN
ejpam-6739	16	60	remain	remain	VERB
ejpam-6739	16	61	compact	compact	ADJ
ejpam-6739	16	62	(	(	PUNCT
ejpam-6739	16	63	resp	resp	NOUN
ejpam-6739	16	64	.	.	PUNCT
ejpam-6739	16	65	isometric	isometric	ADJ
ejpam-6739	16	66	)	)	PUNCT
ejpam-6739	16	67	.	.	PUNCT
ejpam-6739	17	1	moreover	moreover	ADV
ejpam-6739	17	2	,	,	PUNCT
ejpam-6739	17	3	if	if	SCONJ
ejpam-6739	17	4	t	t	PROPN
ejpam-6739	17	5	is	be	AUX
ejpam-6739	17	6	an	an	DET
ejpam-6739	17	7	-operator	-operator	NOUN
ejpam-6739	17	8	,	,	PUNCT
ejpam-6739	17	9	then	then	ADV
ejpam-6739	17	10	t	t	PROPN
ejpam-6739	17	11	∗	∗	NOUN
ejpam-6739	17	12	may	may	AUX
ejpam-6739	17	13	not	not	PART
ejpam-6739	17	14	be	be	AUX
ejpam-6739	17	15	one	one	NUM
ejpam-6739	17	16	,	,	PUNCT
ejpam-6739	17	17	see	see	VERB
ejpam-6739	17	18	[	[	X
ejpam-6739	17	19	4	4	NUM
ejpam-6739	17	20	,	,	PUNCT
ejpam-6739	17	21	7	7	NUM
ejpam-6739	17	22	]	]	PUNCT
ejpam-6739	17	23	where	where	SCONJ
ejpam-6739	17	24	it	it	PRON
ejpam-6739	17	25	’s	’s	AUX
ejpam-6739	17	26	shown	show	VERB
ejpam-6739	17	27	that	that	SCONJ
ejpam-6739	17	28	an	an	DET
ejpam-6739	17	29	isometry	isometry	ADJ
ejpam-6739	17	30	u	u	NOUN
ejpam-6739	17	31	:	:	PUNCT
ejpam-6739	17	32	ℓ2	ℓ2	PROPN
ejpam-6739	17	33	→	→	SYM
ejpam-6739	17	34	ℓ2	ℓ2	PROPN
ejpam-6739	17	35	onto	onto	ADP
ejpam-6739	17	36	a	a	DET
ejpam-6739	17	37	subspace	subspace	NOUN
ejpam-6739	17	38	with	with	ADP
ejpam-6739	17	39	infinite	infinite	ADJ
ejpam-6739	17	40	codimension	codimension	NOUN
ejpam-6739	17	41	is	be	AUX
ejpam-6739	17	42	an	an	DET
ejpam-6739	17	43	-operator	-operator	NOUN
ejpam-6739	17	44	,	,	PUNCT
ejpam-6739	17	45	whereas	whereas	SCONJ
ejpam-6739	17	46	its	its	PRON
ejpam-6739	17	47	adjoint	adjoint	NOUN
ejpam-6739	17	48	u∗	u∗	NOUN
ejpam-6739	17	49	is	be	AUX
ejpam-6739	17	50	not	not	PART
ejpam-6739	17	51	.	.	PUNCT
ejpam-6739	18	1	however	however	ADV
ejpam-6739	18	2	,	,	PUNCT
ejpam-6739	18	3	g.	g.	PROPN
ejpam-6739	18	4	ramesh	ramesh	PROPN
ejpam-6739	18	5	in	in	ADP
ejpam-6739	18	6	[	[	X
ejpam-6739	18	7	5	5	NUM
ejpam-6739	18	8	]	]	PUNCT
ejpam-6739	18	9	presented	present	VERB
ejpam-6739	18	10	an	an	DET
ejpam-6739	18	11	additional	additional	ADJ
ejpam-6739	18	12	condition	condition	NOUN
ejpam-6739	18	13	for	for	ADP
ejpam-6739	18	14	which	which	PRON
ejpam-6739	18	15	t	t	NOUN
ejpam-6739	18	16	∗	∗	NOUN
ejpam-6739	18	17	remains	remain	VERB
ejpam-6739	18	18	an	an	DET
ejpam-6739	18	19	an	an	DET
ejpam-6739	18	20	-operator	-operator	NOUN
ejpam-6739	18	21	.	.	PUNCT
ejpam-6739	19	1	an	an	DET
ejpam-6739	19	2	operator	operator	NOUN
ejpam-6739	19	3	t	t	PROPN
ejpam-6739	19	4	∈	∈	PROPN
ejpam-6739	19	5	b(h	b(h	PROPN
ejpam-6739	19	6	)	)	PUNCT
ejpam-6739	19	7	is	be	AUX
ejpam-6739	19	8	said	say	VERB
ejpam-6739	19	9	to	to	PART
ejpam-6739	19	10	be	be	AUX
ejpam-6739	19	11	non	non	ADJ
ejpam-6739	19	12	-	-	ADJ
ejpam-6739	19	13	negative	negative	ADJ
ejpam-6739	19	14	and	and	CCONJ
ejpam-6739	19	15	we	we	PRON
ejpam-6739	19	16	shall	shall	AUX
ejpam-6739	19	17	write	write	VERB
ejpam-6739	19	18	t	t	PROPN
ejpam-6739	19	19	≥	≥	NOUN
ejpam-6739	19	20	0	0	NUM
ejpam-6739	19	21	,	,	PUNCT
ejpam-6739	19	22	if	if	SCONJ
ejpam-6739	19	23	⟨tu	⟨tu	PROPN
ejpam-6739	19	24	,	,	PUNCT
ejpam-6739	19	25	u⟩	u⟩	PRON
ejpam-6739	19	26	≥	≥	NOUN
ejpam-6739	19	27	0	0	NUM
ejpam-6739	19	28	for	for	ADP
ejpam-6739	19	29	all	all	PRON
ejpam-6739	19	30	u	u	PROPN
ejpam-6739	19	31	∈	∈	PROPN
ejpam-6739	19	32	h	h	NOUN
ejpam-6739	19	33	and	and	CCONJ
ejpam-6739	19	34	a	a	PRON
ejpam-6739	19	35	is	be	AUX
ejpam-6739	19	36	said	say	VERB
ejpam-6739	19	37	to	to	PART
ejpam-6739	19	38	be	be	AUX
ejpam-6739	19	39	normal	normal	ADJ
ejpam-6739	19	40	if	if	SCONJ
ejpam-6739	19	41	t	t	PROPN
ejpam-6739	19	42	∗t	∗t	PROPN
ejpam-6739	19	43	=	=	SYM
ejpam-6739	19	44	tt	tt	PROPN
ejpam-6739	19	45	∗	∗	NOUN
ejpam-6739	19	46	,	,	PUNCT
ejpam-6739	19	47	isometric	isometric	ADJ
ejpam-6739	19	48	if	if	SCONJ
ejpam-6739	19	49	t	t	NOUN
ejpam-6739	20	1	∗t	∗t	PROPN
ejpam-6739	20	2	=	=	PUNCT
ejpam-6739	20	3	i	i	PROPN
ejpam-6739	20	4	,	,	PUNCT
ejpam-6739	20	5	where	where	SCONJ
ejpam-6739	20	6	i	i	PRON
ejpam-6739	20	7	is	be	AUX
ejpam-6739	20	8	the	the	DET
ejpam-6739	20	9	identity	identity	NOUN
ejpam-6739	20	10	operator	operator	NOUN
ejpam-6739	20	11	on	on	ADP
ejpam-6739	20	12	h.	h.	PROPN
ejpam-6739	20	13	if	if	SCONJ
ejpam-6739	20	14	t	t	PROPN
ejpam-6739	20	15	is	be	AUX
ejpam-6739	20	16	isometric	isometric	ADJ
ejpam-6739	20	17	and	and	CCONJ
ejpam-6739	20	18	onto	onto	ADP
ejpam-6739	20	19	,	,	PUNCT
ejpam-6739	20	20	then	then	ADV
ejpam-6739	20	21	t	t	PROPN
ejpam-6739	20	22	is	be	AUX
ejpam-6739	20	23	said	say	VERB
ejpam-6739	20	24	to	to	PART
ejpam-6739	20	25	be	be	AUX
ejpam-6739	20	26	unitary	unitary	ADJ
ejpam-6739	20	27	.	.	PUNCT
ejpam-6739	21	1	the	the	DET
ejpam-6739	21	2	operator	operator	NOUN
ejpam-6739	21	3	t	t	PROPN
ejpam-6739	21	4	∈	∈	PROPN
ejpam-6739	21	5	b(h	b(h	PROPN
ejpam-6739	21	6	)	)	PUNCT
ejpam-6739	21	7	is	be	AUX
ejpam-6739	21	8	said	say	VERB
ejpam-6739	21	9	to	to	PART
ejpam-6739	21	10	be	be	AUX
ejpam-6739	21	11	∗-paranormal	∗-paranormal	ADJ
ejpam-6739	21	12	if	if	SCONJ
ejpam-6739	21	13	t	t	PROPN
ejpam-6739	21	14	∗2	∗2	PROPN
ejpam-6739	21	15	t	t	PROPN
ejpam-6739	21	16	2	2	NUM
ejpam-6739	21	17	−	−	PROPN
ejpam-6739	21	18	2λtt	2λtt	NUM
ejpam-6739	21	19	∗	∗	NOUN
ejpam-6739	22	1	+	+	X
ejpam-6739	22	2	λ2	λ2	NOUN
ejpam-6739	22	3	≥	≥	NOUN
ejpam-6739	22	4	0	0	NUM
ejpam-6739	22	5	for	for	ADP
ejpam-6739	22	6	each	each	DET
ejpam-6739	22	7	λ	λ	PROPN
ejpam-6739	22	8	>	>	X
ejpam-6739	22	9	0	0	PROPN
ejpam-6739	22	10	,	,	PUNCT
ejpam-6739	22	11	that	that	ADV
ejpam-6739	22	12	is	is	ADV
ejpam-6739	22	13	,	,	PUNCT
ejpam-6739	22	14	∥t	∥t	ADJ
ejpam-6739	22	15	∗u∥2	∗u∥2	NOUN
ejpam-6739	22	16	≤	≤	NUM
ejpam-6739	22	17	∥t	∥t	PROPN
ejpam-6739	22	18	2u∥∥u∥	2u∥∥u∥	PROPN
ejpam-6739	22	19	for	for	ADP
ejpam-6739	22	20	all	all	DET
ejpam-6739	22	21	u	u	NOUN
ejpam-6739	22	22	∈	∈	ADJ
ejpam-6739	22	23	h	h	NOUN
ejpam-6739	23	1	[	[	X
ejpam-6739	23	2	8	8	NUM
ejpam-6739	23	3	]	]	PUNCT
ejpam-6739	23	4	.	.	PUNCT
ejpam-6739	24	1	also	also	ADV
ejpam-6739	24	2	,	,	PUNCT
ejpam-6739	24	3	t	t	PROPN
ejpam-6739	24	4	is	be	AUX
ejpam-6739	24	5	said	say	VERB
ejpam-6739	24	6	to	to	PART
ejpam-6739	24	7	be	be	AUX
ejpam-6739	24	8	quasi-∗-paranormal	quasi-∗-paranormal	ADJ
ejpam-6739	24	9	if	if	SCONJ
ejpam-6739	24	10	t	t	PROPN
ejpam-6739	24	11	∗(t	∗(t	PROPN
ejpam-6739	24	12	∗2	∗2	PROPN
ejpam-6739	24	13	t	t	NOUN
ejpam-6739	24	14	2	2	NUM
ejpam-6739	24	15	−	−	PROPN
ejpam-6739	24	16	2λtt	2λtt	NUM
ejpam-6739	24	17	∗	∗	NOUN
ejpam-6739	24	18	+	+	CCONJ
ejpam-6739	24	19	λ2)t	λ2)t	PROPN
ejpam-6739	24	20	≥	≥	NOUN
ejpam-6739	24	21	0	0	NUM
ejpam-6739	24	22	for	for	ADP
ejpam-6739	24	23	all	all	DET
ejpam-6739	24	24	λ	λ	PROPN
ejpam-6739	24	25	>	>	X
ejpam-6739	24	26	0	0	NUM
ejpam-6739	24	27	,	,	PUNCT
ejpam-6739	24	28	[	[	X
ejpam-6739	24	29	9	9	NUM
ejpam-6739	24	30	]	]	PUNCT
ejpam-6739	24	31	.	.	PUNCT
ejpam-6739	25	1	clearly	clearly	ADV
ejpam-6739	25	2	,	,	PUNCT
ejpam-6739	25	3	a	a	DET
ejpam-6739	25	4	∗-paranormal	∗-paranormal	ADJ
ejpam-6739	25	5	operator	operator	NOUN
ejpam-6739	25	6	is	be	AUX
ejpam-6739	25	7	quasi-∗-paranormal	quasi-∗-paranormal	ADJ
ejpam-6739	25	8	while	while	SCONJ
ejpam-6739	25	9	the	the	DET
ejpam-6739	25	10	converse	converse	NOUN
ejpam-6739	25	11	is	be	AUX
ejpam-6739	25	12	in	in	ADP
ejpam-6739	25	13	general	general	ADJ
ejpam-6739	25	14	false	false	ADJ
ejpam-6739	25	15	,	,	PUNCT
ejpam-6739	25	16	see	see	VERB
ejpam-6739	25	17	[	[	X
ejpam-6739	25	18	10	10	NUM
ejpam-6739	25	19	]	]	PUNCT
ejpam-6739	25	20	.	.	PUNCT
ejpam-6739	26	1	it	it	PRON
ejpam-6739	26	2	is	be	AUX
ejpam-6739	26	3	known	know	VERB
ejpam-6739	26	4	that	that	SCONJ
ejpam-6739	26	5	quasi-∗-paranormal	quasi-∗-paranormal	PROPN
ejpam-6739	26	6	operators	operator	NOUN
ejpam-6739	26	7	are	be	AUX
ejpam-6739	26	8	normaloid	normaloid	NOUN
ejpam-6739	26	9	,	,	PUNCT
ejpam-6739	26	10	that	that	ADV
ejpam-6739	26	11	is	is	ADV
ejpam-6739	26	12	,	,	PUNCT
ejpam-6739	26	13	r(t	r(t	NOUN
ejpam-6739	26	14	)	)	PUNCT
ejpam-6739	27	1	=	=	SYM
ejpam-6739	27	2	∥t∥	∥t∥	PROPN
ejpam-6739	27	3	,	,	PUNCT
ejpam-6739	27	4	where	where	SCONJ
ejpam-6739	27	5	r(t	r(t	NOUN
ejpam-6739	27	6	)	)	PUNCT
ejpam-6739	28	1	=	=	NOUN
ejpam-6739	28	2	sup{|λ|	sup{|λ|	NOUN
ejpam-6739	28	3	:	:	PUNCT
ejpam-6739	28	4	λ	λ	X
ejpam-6739	28	5	∈	∈	PROPN
ejpam-6739	28	6	σ(t	σ(t	PROPN
ejpam-6739	28	7	)	)	PUNCT
ejpam-6739	28	8	}	}	PUNCT
ejpam-6739	28	9	is	be	AUX
ejpam-6739	28	10	the	the	DET
ejpam-6739	28	11	spectral	spectral	ADJ
ejpam-6739	28	12	radius	radius	NOUN
ejpam-6739	28	13	of	of	ADP
ejpam-6739	28	14	t.	t.	ADJ
ejpam-6739	28	15	ample	ample	ADJ
ejpam-6739	28	16	properties	property	NOUN
ejpam-6739	28	17	of	of	ADP
ejpam-6739	28	18	these	these	DET
ejpam-6739	28	19	classes	class	NOUN
ejpam-6739	28	20	can	can	AUX
ejpam-6739	28	21	be	be	AUX
ejpam-6739	28	22	found	find	VERB
ejpam-6739	28	23	in	in	ADP
ejpam-6739	28	24	[	[	X
ejpam-6739	28	25	11	11	NUM
ejpam-6739	28	26	]	]	PUNCT
ejpam-6739	28	27	and	and	CCONJ
ejpam-6739	28	28	[	[	X
ejpam-6739	28	29	12	12	NUM
ejpam-6739	28	30	]	]	PUNCT
ejpam-6739	28	31	.	.	PUNCT
ejpam-6739	29	1	the	the	DET
ejpam-6739	29	2	operator	operator	NOUN
ejpam-6739	29	3	t	t	PROPN
ejpam-6739	29	4	in	in	ADP
ejpam-6739	29	5	b(h	b(h	PROPN
ejpam-6739	29	6	)	)	PUNCT
ejpam-6739	29	7	is	be	AUX
ejpam-6739	29	8	said	say	VERB
ejpam-6739	29	9	to	to	PART
ejpam-6739	29	10	be	be	AUX
ejpam-6739	29	11	quasi	quasi	ADJ
ejpam-6739	29	12	-	-	ADJ
ejpam-6739	29	13	normal	normal	ADJ
ejpam-6739	29	14	of	of	ADP
ejpam-6739	29	15	order	order	NOUN
ejpam-6739	29	16	n	n	PRON
ejpam-6739	29	17	for	for	ADP
ejpam-6739	29	18	certain	certain	ADJ
ejpam-6739	29	19	integer	integer	NOUN
ejpam-6739	29	20	n	n	CCONJ
ejpam-6739	29	21	,	,	PUNCT
ejpam-6739	29	22	and	and	CCONJ
ejpam-6739	29	23	we	we	PRON
ejpam-6739	29	24	shall	shall	AUX
ejpam-6739	29	25	write	write	VERB
ejpam-6739	29	26	t	t	PROPN
ejpam-6739	29	27	∈	∈	PROPN
ejpam-6739	29	28	ωn	ωn	ADP
ejpam-6739	29	29	,	,	PUNCT
ejpam-6739	29	30	if	if	SCONJ
ejpam-6739	29	31	tt	tt	PROPN
ejpam-6739	29	32	⋆ntn	⋆ntn	NOUN
ejpam-6739	29	33	=	=	PROPN
ejpam-6739	29	34	t	t	PROPN
ejpam-6739	29	35	⋆ntn+1	⋆ntn+1	NOUN
ejpam-6739	29	36	.	.	PUNCT
ejpam-6739	30	1	for	for	ADP
ejpam-6739	30	2	more	more	ADJ
ejpam-6739	30	3	information	information	NOUN
ejpam-6739	30	4	on	on	ADP
ejpam-6739	30	5	the	the	DET
ejpam-6739	30	6	class	class	NOUN
ejpam-6739	30	7	ωn	ωn	NUM
ejpam-6739	30	8	,	,	PUNCT
ejpam-6739	30	9	we	we	PRON
ejpam-6739	30	10	refer	refer	VERB
ejpam-6739	30	11	the	the	DET
ejpam-6739	30	12	reader	reader	NOUN
ejpam-6739	30	13	to	to	ADP
ejpam-6739	30	14	[	[	X
ejpam-6739	30	15	13	13	NUM
ejpam-6739	30	16	,	,	PUNCT
ejpam-6739	30	17	14	14	NUM
ejpam-6739	30	18	]	]	PUNCT
ejpam-6739	30	19	.	.	PUNCT
ejpam-6739	31	1	for	for	ADP
ejpam-6739	31	2	an	an	DET
ejpam-6739	31	3	operator	operator	NOUN
ejpam-6739	31	4	t	t	PROPN
ejpam-6739	31	5	∈	∈	PROPN
ejpam-6739	31	6	b(h	b(h	PROPN
ejpam-6739	31	7	)	)	PUNCT
ejpam-6739	31	8	,	,	PUNCT
ejpam-6739	31	9	the	the	DET
ejpam-6739	31	10	range	range	NOUN
ejpam-6739	31	11	of	of	ADP
ejpam-6739	31	12	t	t	PROPN
ejpam-6739	31	13	,	,	PUNCT
ejpam-6739	31	14	the	the	DET
ejpam-6739	31	15	null	null	ADJ
ejpam-6739	31	16	space	space	NOUN
ejpam-6739	31	17	and	and	CCONJ
ejpam-6739	31	18	the	the	DET
ejpam-6739	31	19	modulus	modulus	NOUN
ejpam-6739	31	20	of	of	ADP
ejpam-6739	31	21	t	t	PROPN
ejpam-6739	31	22	will	will	AUX
ejpam-6739	31	23	be	be	AUX
ejpam-6739	31	24	denoted	denote	VERB
ejpam-6739	31	25	by	by	ADP
ejpam-6739	31	26	r(t	r(t	NOUN
ejpam-6739	31	27	)	)	PUNCT
ejpam-6739	31	28	,	,	PUNCT
ejpam-6739	31	29	n(t	n(t	PROPN
ejpam-6739	31	30	)	)	PUNCT
ejpam-6739	31	31	and	and	CCONJ
ejpam-6739	31	32	|t	|t	VERB
ejpam-6739	32	1	|	|	ADV
ejpam-6739	32	2	=	=	SYM
ejpam-6739	32	3	√	√	PROPN
ejpam-6739	32	4	t	t	NOUN
ejpam-6739	32	5	∗t	∗t	PROPN
ejpam-6739	32	6	respectively	respectively	ADV
ejpam-6739	32	7	.	.	PUNCT
ejpam-6739	33	1	if	if	SCONJ
ejpam-6739	33	2	t	t	PROPN
ejpam-6739	33	3	∈	∈	PROPN
ejpam-6739	33	4	b(h	b(h	PROPN
ejpam-6739	33	5	)	)	PUNCT
ejpam-6739	33	6	,	,	PUNCT
ejpam-6739	33	7	then	then	ADV
ejpam-6739	33	8	t	t	PROPN
ejpam-6739	33	9	=	=	SYM
ejpam-6739	33	10	u	u	SYM
ejpam-6739	33	11	|t	|t	NOUN
ejpam-6739	34	1	|	|	ADV
ejpam-6739	34	2	is	be	AUX
ejpam-6739	34	3	the	the	DET
ejpam-6739	34	4	polar	polar	ADJ
ejpam-6739	34	5	decomposition	decomposition	NOUN
ejpam-6739	34	6	of	of	ADP
ejpam-6739	34	7	t	t	PROPN
ejpam-6739	34	8	,	,	PUNCT
ejpam-6739	34	9	where	where	SCONJ
ejpam-6739	34	10	u	u	NOUN
ejpam-6739	34	11	is	be	AUX
ejpam-6739	34	12	a	a	DET
ejpam-6739	34	13	partial	partial	ADJ
ejpam-6739	34	14	isometry	isometry	NOUN
ejpam-6739	34	15	,	,	PUNCT
ejpam-6739	34	16	that	that	ADV
ejpam-6739	34	17	is	is	ADV
ejpam-6739	34	18	,	,	PUNCT
ejpam-6739	34	19	u	u	NOUN
ejpam-6739	34	20	∣∣	∣∣	PROPN
ejpam-6739	34	21	n(a)⊥	n(a)⊥	PROPN
ejpam-6739	34	22	is	be	AUX
ejpam-6739	34	23	an	an	DET
ejpam-6739	34	24	isometry	isometry	NOUN
ejpam-6739	34	25	,	,	PUNCT
ejpam-6739	34	26	r(u	r(u	PROPN
ejpam-6739	34	27	)	)	PUNCT
ejpam-6739	34	28	=	=	PUNCT
ejpam-6739	34	29	r(|t	r(|t	VERB
ejpam-6739	34	30	|).according	|).accorde	VERB
ejpam-6739	34	31	to	to	ADP
ejpam-6739	34	32	[	[	X
ejpam-6739	34	33	15	15	NUM
ejpam-6739	34	34	]	]	PUNCT
ejpam-6739	34	35	,	,	PUNCT
ejpam-6739	34	36	u	u	NOUN
ejpam-6739	34	37	is	be	AUX
ejpam-6739	34	38	a	a	DET
ejpam-6739	34	39	partial	partial	ADJ
ejpam-6739	34	40	isometry	isometry	NOUN
ejpam-6739	34	41	if	if	SCONJ
ejpam-6739	34	42	and	and	CCONJ
ejpam-6739	34	43	only	only	ADV
ejpam-6739	34	44	if	if	SCONJ
ejpam-6739	34	45	uu∗u	uu∗u	PROPN
ejpam-6739	34	46	=	=	PUNCT
ejpam-6739	34	47	u.	u.	VERB
ejpam-6739	34	48	the	the	DET
ejpam-6739	34	49	sets	set	NOUN
ejpam-6739	34	50	σ(t	σ(t	PROPN
ejpam-6739	34	51	)	)	PUNCT
ejpam-6739	34	52	,	,	PUNCT
ejpam-6739	34	53	σp(t	σp(t	PUNCT
ejpam-6739	34	54	)	)	PUNCT
ejpam-6739	34	55	denote	denote	VERB
ejpam-6739	34	56	respectively	respectively	ADV
ejpam-6739	34	57	,	,	PUNCT
ejpam-6739	34	58	the	the	DET
ejpam-6739	34	59	spectrum	spectrum	NOUN
ejpam-6739	34	60	and	and	CCONJ
ejpam-6739	34	61	the	the	DET
ejpam-6739	34	62	set	set	NOUN
ejpam-6739	34	63	of	of	ADP
ejpam-6739	34	64	eigenvalues	eigenvalue	NOUN
ejpam-6739	34	65	of	of	ADP
ejpam-6739	34	66	t.	t.	PROPN
ejpam-6739	34	67	for	for	ADP
ejpam-6739	34	68	a	a	DET
ejpam-6739	34	69	selfadjoint	selfadjoint	NOUN
ejpam-6739	34	70	operator	operator	NOUN
ejpam-6739	34	71	t	t	PROPN
ejpam-6739	34	72	∈	∈	PROPN
ejpam-6739	34	73	b(h	b(h	PROPN
ejpam-6739	34	74	)	)	PUNCT
ejpam-6739	34	75	,	,	PUNCT
ejpam-6739	34	76	that	that	ADV
ejpam-6739	34	77	is	is	ADV
ejpam-6739	34	78	,	,	PUNCT
ejpam-6739	34	79	t	t	PROPN
ejpam-6739	34	80	∗	∗	NOUN
ejpam-6739	34	81	=	=	SYM
ejpam-6739	34	82	t	t	PROPN
ejpam-6739	34	83	,	,	PUNCT
ejpam-6739	34	84	the	the	DET
ejpam-6739	34	85	discrete	discrete	ADJ
ejpam-6739	34	86	spectrum	spectrum	NOUN
ejpam-6739	34	87	of	of	ADP
ejpam-6739	34	88	t	t	PROPN
ejpam-6739	34	89	is	be	AUX
ejpam-6739	34	90	the	the	DET
ejpam-6739	34	91	set	set	NOUN
ejpam-6739	34	92	σd(t	σd(t	X
ejpam-6739	34	93	)	)	PUNCT
ejpam-6739	34	94	=	=	SYM
ejpam-6739	34	95	{	{	PUNCT
ejpam-6739	34	96	λ	λ	X
ejpam-6739	34	97	∈	∈	PROPN
ejpam-6739	34	98	σp(t	σp(t	PUNCT
ejpam-6739	34	99	)	)	PUNCT
ejpam-6739	34	100	:	:	PUNCT
ejpam-6739	35	1	λ	λ	NOUN
ejpam-6739	35	2	is	be	AUX
ejpam-6739	35	3	isolated	isolate	VERB
ejpam-6739	35	4	and	and	CCONJ
ejpam-6739	35	5	has	have	VERB
ejpam-6739	35	6	a	a	DET
ejpam-6739	35	7	finite	finite	ADJ
ejpam-6739	35	8	multiplicity	multiplicity	NOUN
ejpam-6739	35	9	}	}	PUNCT
ejpam-6739	35	10	.	.	PUNCT
ejpam-6739	36	1	the	the	DET
ejpam-6739	36	2	set	set	VERB
ejpam-6739	36	3	σess(t	σess(t	PROPN
ejpam-6739	36	4	)	)	PUNCT
ejpam-6739	36	5	=	=	SYM
ejpam-6739	36	6	σ(t	σ(t	PROPN
ejpam-6739	36	7	)	)	PUNCT
ejpam-6739	36	8	\	\	NOUN
ejpam-6739	36	9	σd(t	σd(t	PUNCT
ejpam-6739	36	10	)	)	PUNCT
ejpam-6739	36	11	is	be	AUX
ejpam-6739	36	12	said	say	VERB
ejpam-6739	36	13	to	to	PART
ejpam-6739	36	14	be	be	AUX
ejpam-6739	36	15	the	the	DET
ejpam-6739	36	16	essential	essential	ADJ
ejpam-6739	36	17	spectrum	spectrum	NOUN
ejpam-6739	36	18	of	of	ADP
ejpam-6739	36	19	t	t	PROPN
ejpam-6739	36	20	,	,	PUNCT
ejpam-6739	36	21	[	[	X
ejpam-6739	36	22	16	16	NUM
ejpam-6739	36	23	]	]	PUNCT
ejpam-6739	36	24	.	.	PUNCT
ejpam-6739	37	1	if	if	SCONJ
ejpam-6739	37	2	dimh	dimh	VERB
ejpam-6739	37	3	<	<	X
ejpam-6739	37	4	+	+	NOUN
ejpam-6739	37	5	∞	∞	PROPN
ejpam-6739	37	6	,	,	PUNCT
ejpam-6739	37	7	then	then	ADV
ejpam-6739	37	8	σess(t	σess(t	NOUN
ejpam-6739	37	9	)	)	PUNCT
ejpam-6739	38	1	=	=	PUNCT
ejpam-6739	38	2	∅.	∅.	VERB
ejpam-6739	38	3	the	the	DET
ejpam-6739	38	4	positive	positive	ADJ
ejpam-6739	38	5	real	real	ADJ
ejpam-6739	38	6	number	number	NOUN
ejpam-6739	38	7	m(t	m(t	NOUN
ejpam-6739	38	8	)	)	PUNCT
ejpam-6739	39	1	=	=	PUNCT
ejpam-6739	39	2	inf{∥tu∥	inf{∥tu∥	ADV
ejpam-6739	39	3	:	:	PUNCT
ejpam-6739	39	4	u	u	NOUN
ejpam-6739	39	5	∈	∈	PROPN
ejpam-6739	39	6	h	h	NOUN
ejpam-6739	39	7	and	and	CCONJ
ejpam-6739	39	8	∥u∥	∥u∥	NOUN
ejpam-6739	39	9	=	=	SYM
ejpam-6739	39	10	1	1	X
ejpam-6739	39	11	}	}	PUNCT
ejpam-6739	39	12	is	be	AUX
ejpam-6739	39	13	said	say	VERB
ejpam-6739	39	14	to	to	PART
ejpam-6739	39	15	be	be	AUX
ejpam-6739	39	16	the	the	DET
ejpam-6739	39	17	minimum	minimum	ADJ
ejpam-6739	39	18	modulus	modulus	NOUN
ejpam-6739	39	19	of	of	ADP
ejpam-6739	39	20	t	t	PROPN
ejpam-6739	39	21	∈	∈	PROPN
ejpam-6739	39	22	b(h	b(h	PROPN
ejpam-6739	39	23	)	)	PUNCT
ejpam-6739	39	24	,	,	PUNCT
ejpam-6739	39	25	and	and	CCONJ
ejpam-6739	39	26	the	the	DET
ejpam-6739	39	27	quantity	quantity	NOUN
ejpam-6739	39	28	me(t	me(t	PUNCT
ejpam-6739	39	29	)	)	PUNCT
ejpam-6739	40	1	=	=	SYM
ejpam-6739	40	2	inf{λ	inf{λ	NOUN
ejpam-6739	40	3	:	:	PUNCT
ejpam-6739	40	4	λ	λ	X
ejpam-6739	40	5	∈	∈	PROPN
ejpam-6739	40	6	σ(|t	σ(|t	NOUN
ejpam-6739	40	7	|	|	ADV
ejpam-6739	40	8	)	)	PUNCT
ejpam-6739	40	9	}	}	PUNCT
ejpam-6739	40	10	is	be	AUX
ejpam-6739	40	11	said	say	VERB
ejpam-6739	40	12	to	to	PART
ejpam-6739	40	13	be	be	AUX
ejpam-6739	40	14	the	the	DET
ejpam-6739	40	15	essential	essential	ADJ
ejpam-6739	40	16	minimum	minimum	ADJ
ejpam-6739	40	17	modulus	modulus	NOUN
ejpam-6739	40	18	of	of	ADP
ejpam-6739	40	19	t.	t.	NOUN
ejpam-6739	40	20	for	for	ADP
ejpam-6739	40	21	more	more	ADJ
ejpam-6739	40	22	details	detail	NOUN
ejpam-6739	40	23	,	,	PUNCT
ejpam-6739	40	24	reader	reader	NOUN
ejpam-6739	40	25	is	be	AUX
ejpam-6739	40	26	referred	refer	VERB
ejpam-6739	40	27	to	to	ADP
ejpam-6739	40	28	[	[	X
ejpam-6739	40	29	4	4	NUM
ejpam-6739	40	30	,	,	PUNCT
ejpam-6739	40	31	17	17	NUM
ejpam-6739	40	32	]	]	PUNCT
ejpam-6739	40	33	and	and	CCONJ
ejpam-6739	41	1	[	[	X
ejpam-6739	41	2	16	16	NUM
ejpam-6739	41	3	]	]	PUNCT
ejpam-6739	41	4	.	.	PUNCT
ejpam-6739	42	1	in	in	ADP
ejpam-6739	42	2	[	[	X
ejpam-6739	42	3	18	18	NUM
ejpam-6739	42	4	]	]	PUNCT
ejpam-6739	42	5	,	,	PUNCT
ejpam-6739	42	6	authors	author	NOUN
ejpam-6739	42	7	gave	give	VERB
ejpam-6739	42	8	a	a	DET
ejpam-6739	42	9	characterization	characterization	NOUN
ejpam-6739	42	10	of	of	ADP
ejpam-6739	42	11	norm	norm	NOUN
ejpam-6739	42	12	attaining	attain	VERB
ejpam-6739	42	13	and	and	CCONJ
ejpam-6739	42	14	absolutely	absolutely	ADV
ejpam-6739	42	15	norm	norm	VERB
ejpam-6739	42	16	attaining	attain	VERB
ejpam-6739	42	17	∗-paranormal	∗-paranormal	ADJ
ejpam-6739	42	18	operators	operator	NOUN
ejpam-6739	42	19	and	and	CCONJ
ejpam-6739	42	20	defined	define	VERB
ejpam-6739	42	21	a	a	DET
ejpam-6739	42	22	closed	closed	ADJ
ejpam-6739	42	23	non	non	PRON
ejpam-6739	42	24	trivial	trivial	ADJ
ejpam-6739	42	25	invariant	invariant	ADJ
ejpam-6739	42	26	subspace	subspace	NOUN
ejpam-6739	42	27	for	for	ADP
ejpam-6739	42	28	this	this	DET
ejpam-6739	42	29	class	class	NOUN
ejpam-6739	42	30	of	of	ADP
ejpam-6739	42	31	operators	operator	NOUN
ejpam-6739	42	32	.	.	PUNCT
ejpam-6739	43	1	in	in	ADP
ejpam-6739	43	2	this	this	DET
ejpam-6739	43	3	article	article	NOUN
ejpam-6739	43	4	,	,	PUNCT
ejpam-6739	43	5	we	we	PRON
ejpam-6739	43	6	generalize	generalize	VERB
ejpam-6739	43	7	these	these	DET
ejpam-6739	43	8	results	result	NOUN
ejpam-6739	43	9	for	for	ADP
ejpam-6739	43	10	a	a	DET
ejpam-6739	43	11	large	large	ADJ
ejpam-6739	43	12	class	class	NOUN
ejpam-6739	43	13	of	of	ADP
ejpam-6739	43	14	quasi-∗-paranormal	quasi-∗-paranormal	ADJ
ejpam-6739	43	15	operators	operator	NOUN
ejpam-6739	43	16	.	.	PUNCT
ejpam-6739	44	1	we	we	PRON
ejpam-6739	44	2	show	show	VERB
ejpam-6739	44	3	several	several	ADJ
ejpam-6739	44	4	spectral	spectral	ADJ
ejpam-6739	44	5	properties	property	NOUN
ejpam-6739	44	6	.	.	PUNCT
ejpam-6739	45	1	we	we	PRON
ejpam-6739	45	2	also	also	ADV
ejpam-6739	45	3	provide	provide	VERB
ejpam-6739	45	4	invariant	invariant	ADJ
ejpam-6739	45	5	subspaces	subspace	NOUN
ejpam-6739	45	6	for	for	ADP
ejpam-6739	45	7	both	both	PRON
ejpam-6739	45	8	of	of	ADP
ejpam-6739	45	9	classes	class	NOUN
ejpam-6739	45	10	of	of	ADP
ejpam-6739	45	11	quasi-∗-paranormal	quasi-∗-paranormal	PROPN
ejpam-6739	45	12	operators	operator	NOUN
ejpam-6739	45	13	and	and	CCONJ
ejpam-6739	45	14	class	class	NOUN
ejpam-6739	45	15	ωn	ωn	PROPN
ejpam-6739	45	16	operators	operator	NOUN
ejpam-6739	45	17	,	,	PUNCT
ejpam-6739	45	18	and	and	CCONJ
ejpam-6739	45	19	we	we	PRON
ejpam-6739	45	20	show	show	VERB
ejpam-6739	45	21	that	that	SCONJ
ejpam-6739	45	22	the	the	DET
ejpam-6739	45	23	given	give	VERB
ejpam-6739	45	24	subspaces	subspace	NOUN
ejpam-6739	45	25	become	become	AUX
ejpam-6739	45	26	reducing	reduce	VERB
ejpam-6739	45	27	under	under	ADP
ejpam-6739	45	28	certain	certain	ADJ
ejpam-6739	45	29	conditions	condition	NOUN
ejpam-6739	45	30	.	.	PUNCT
ejpam-6739	46	1	other	other	ADJ
ejpam-6739	46	2	properties	property	NOUN
ejpam-6739	46	3	related	relate	VERB
ejpam-6739	46	4	to	to	ADP
ejpam-6739	46	5	the	the	DET
ejpam-6739	46	6	compactness	compactness	NOUN
ejpam-6739	46	7	,	,	PUNCT
ejpam-6739	46	8	the	the	DET
ejpam-6739	46	9	normality	normality	NOUN
ejpam-6739	46	10	and	and	CCONJ
ejpam-6739	46	11	the	the	DET
ejpam-6739	46	12	matrix	matrix	NOUN
ejpam-6739	46	13	representation	representation	NOUN
ejpam-6739	46	14	are	be	AUX
ejpam-6739	46	15	also	also	ADV
ejpam-6739	46	16	established	establish	VERB
ejpam-6739	46	17	.	.	PUNCT
ejpam-6739	47	1	a.	a.	NOUN
ejpam-6739	47	2	nasli	nasli	PROPN
ejpam-6739	47	3	bakir	bakir	VERB
ejpam-6739	47	4	et	et	PROPN
ejpam-6739	47	5	al	al	PROPN
ejpam-6739	47	6	.	.	PUNCT
ejpam-6739	47	7	/	/	SYM
ejpam-6739	47	8	eur	eur	PROPN
ejpam-6739	47	9	.	.	PUNCT
ejpam-6739	48	1	j.	j.	PROPN
ejpam-6739	48	2	pure	pure	PROPN
ejpam-6739	48	3	appl	appl	PROPN
ejpam-6739	48	4	.	.	PROPN
ejpam-6739	48	5	math	math	PROPN
ejpam-6739	48	6	,	,	PUNCT
ejpam-6739	48	7	18	18	NUM
ejpam-6739	48	8	(	(	PUNCT
ejpam-6739	48	9	4	4	NUM
ejpam-6739	48	10	)	)	PUNCT
ejpam-6739	48	11	(	(	PUNCT
ejpam-6739	48	12	2025	2025	NUM
ejpam-6739	48	13	)	)	PUNCT
ejpam-6739	48	14	,	,	PUNCT
ejpam-6739	48	15	6739	6739	NUM
ejpam-6739	48	16	3	3	NUM
ejpam-6739	48	17	of	of	ADP
ejpam-6739	48	18	10	10	NUM
ejpam-6739	48	19	2	2	NUM
ejpam-6739	48	20	.	.	PUNCT
ejpam-6739	48	21	norm	norm	NOUN
ejpam-6739	48	22	attaining	attain	VERB
ejpam-6739	48	23	quasi-∗-paranormal	quasi-∗-paranormal	ADJ
ejpam-6739	48	24	operators	operator	NOUN
ejpam-6739	48	25	definition	definition	NOUN
ejpam-6739	48	26	1	1	NUM
ejpam-6739	48	27	.	.	PUNCT
ejpam-6739	49	1	[	[	X
ejpam-6739	49	2	19	19	NUM
ejpam-6739	49	3	,	,	PUNCT
ejpam-6739	49	4	20	20	NUM
ejpam-6739	49	5	]	]	PUNCT
ejpam-6739	49	6	an	an	DET
ejpam-6739	49	7	operator	operator	NOUN
ejpam-6739	49	8	t	t	PROPN
ejpam-6739	49	9	∈	∈	PROPN
ejpam-6739	49	10	b(h	b(h	PROPN
ejpam-6739	49	11	)	)	PUNCT
ejpam-6739	49	12	is	be	AUX
ejpam-6739	49	13	said	say	VERB
ejpam-6739	49	14	to	to	PART
ejpam-6739	49	15	be	be	AUX
ejpam-6739	49	16	quasi-∗-paranormal	quasi-∗-paranormal	ADJ
ejpam-6739	49	17	if	if	SCONJ
ejpam-6739	49	18	t	t	PROPN
ejpam-6739	49	19	∗(t	∗(t	PROPN
ejpam-6739	49	20	∗2	∗2	PROPN
ejpam-6739	49	21	t	t	NOUN
ejpam-6739	49	22	2	2	NUM
ejpam-6739	49	23	−	−	PROPN
ejpam-6739	49	24	2λtt	2λtt	NUM
ejpam-6739	49	25	∗	∗	NOUN
ejpam-6739	49	26	+	+	CCONJ
ejpam-6739	49	27	λ2)t	λ2)t	PROPN
ejpam-6739	49	28	≥	≥	NOUN
ejpam-6739	49	29	0	0	NUM
ejpam-6739	49	30	for	for	ADP
ejpam-6739	49	31	all	all	DET
ejpam-6739	49	32	λ	λ	PROPN
ejpam-6739	49	33	>	>	X
ejpam-6739	49	34	0	0	NUM
ejpam-6739	49	35	.	.	PUNCT
ejpam-6739	50	1	the	the	DET
ejpam-6739	50	2	given	give	VERB
ejpam-6739	50	3	definition	definition	NOUN
ejpam-6739	50	4	implies	imply	VERB
ejpam-6739	50	5	that	that	SCONJ
ejpam-6739	50	6	∥t	∥t	PROPN
ejpam-6739	50	7	∗tu∥2	∗tu∥2	NOUN
ejpam-6739	50	8	≤	≤	NOUN
ejpam-6739	50	9	∥t	∥t	ADJ
ejpam-6739	50	10	3u∥∥tu∥	3u∥∥tu∥	NOUN
ejpam-6739	50	11	for	for	ADP
ejpam-6739	50	12	all	all	DET
ejpam-6739	50	13	u	u	PROPN
ejpam-6739	50	14	∈	∈	PROPN
ejpam-6739	50	15	h.	h.	NOUN
ejpam-6739	50	16	example	example	NOUN
ejpam-6739	51	1	1	1	X
ejpam-6739	51	2	.	.	PUNCT
ejpam-6739	52	1	[	[	X
ejpam-6739	52	2	11	11	NUM
ejpam-6739	52	3	]	]	PUNCT
ejpam-6739	52	4	let	let	VERB
ejpam-6739	52	5	µ	µ	X
ejpam-6739	52	6	=	=	PUNCT
ejpam-6739	52	7	(	(	PUNCT
ejpam-6739	52	8	µn)n≥1	µn)n≥1	NOUN
ejpam-6739	52	9	be	be	AUX
ejpam-6739	52	10	a	a	DET
ejpam-6739	52	11	positive	positive	ADJ
ejpam-6739	52	12	real	real	ADJ
ejpam-6739	52	13	sequence	sequence	NOUN
ejpam-6739	52	14	.	.	PUNCT
ejpam-6739	53	1	define	define	VERB
ejpam-6739	53	2	the	the	DET
ejpam-6739	53	3	weighted	weight	VERB
ejpam-6739	53	4	shift	shift	NOUN
ejpam-6739	53	5	sµ	sµ	NOUN
ejpam-6739	53	6	on	on	ADP
ejpam-6739	53	7	the	the	DET
ejpam-6739	53	8	hilbert	hilbert	NOUN
ejpam-6739	53	9	space	space	NOUN
ejpam-6739	53	10	ℓ2	ℓ2	PROPN
ejpam-6739	53	11	by	by	ADP
ejpam-6739	53	12	sµen	sµen	ADJ
ejpam-6739	53	13	=	=	SYM
ejpam-6739	53	14	µnen+1	µnen+1	PROPN
ejpam-6739	53	15	,	,	PUNCT
ejpam-6739	53	16	n	n	PRON
ejpam-6739	53	17	≥	≥	NOUN
ejpam-6739	53	18	1	1	NUM
ejpam-6739	53	19	where	where	SCONJ
ejpam-6739	53	20	(	(	PUNCT
ejpam-6739	53	21	en)n≥1	en)n≥1	VERB
ejpam-6739	53	22	is	be	AUX
ejpam-6739	53	23	the	the	DET
ejpam-6739	53	24	standard	standard	ADJ
ejpam-6739	53	25	basis	basis	NOUN
ejpam-6739	53	26	of	of	ADP
ejpam-6739	53	27	ℓ2	ℓ2	PROPN
ejpam-6739	53	28	.	.	PUNCT
ejpam-6739	54	1	then	then	ADV
ejpam-6739	54	2	,	,	PUNCT
ejpam-6739	54	3	sµ	sµ	PROPN
ejpam-6739	54	4	is	be	AUX
ejpam-6739	54	5	quasi-∗-paranormal	quasi-∗-paranormal	ADJ
ejpam-6739	54	6	if	if	SCONJ
ejpam-6739	54	7	and	and	CCONJ
ejpam-6739	54	8	only	only	ADV
ejpam-6739	54	9	if	if	SCONJ
ejpam-6739	54	10	the	the	DET
ejpam-6739	54	11	inequality	inequality	NOUN
ejpam-6739	54	12	µ2	µ2	PROPN
ejpam-6739	54	13	n	n	CCONJ
ejpam-6739	54	14	≤	≤	NUM
ejpam-6739	54	15	µn+1µn+2	µn+1µn+2	NOUN
ejpam-6739	54	16	holds	hold	VERB
ejpam-6739	54	17	for	for	ADP
ejpam-6739	54	18	any	any	DET
ejpam-6739	54	19	n	n	CCONJ
ejpam-6739	54	20	,	,	PUNCT
ejpam-6739	54	21	n	n	PRON
ejpam-6739	54	22	≥	≥	NOUN
ejpam-6739	54	23	1	1	NUM
ejpam-6739	54	24	.	.	PUNCT
ejpam-6739	55	1	[	[	X
ejpam-6739	55	2	20	20	NUM
ejpam-6739	55	3	]	]	PUNCT
ejpam-6739	55	4	the	the	DET
ejpam-6739	55	5	restriction	restriction	NOUN
ejpam-6739	55	6	of	of	ADP
ejpam-6739	55	7	a	a	DET
ejpam-6739	55	8	quasi-∗-paranormal	quasi-∗-paranormal	ADJ
ejpam-6739	55	9	operator	operator	NOUN
ejpam-6739	55	10	on	on	ADP
ejpam-6739	55	11	a	a	DET
ejpam-6739	55	12	closed	close	VERB
ejpam-6739	55	13	invariant	invariant	ADJ
ejpam-6739	55	14	subspace	subspace	NOUN
ejpam-6739	55	15	is	be	AUX
ejpam-6739	55	16	also	also	ADV
ejpam-6739	55	17	quasi-∗-paranormal	quasi-∗-paranormal	ADJ
ejpam-6739	55	18	.	.	PUNCT
ejpam-6739	56	1	[	[	X
ejpam-6739	56	2	10	10	NUM
ejpam-6739	56	3	,	,	PUNCT
ejpam-6739	56	4	lemma	lemma	PROPN
ejpam-6739	56	5	3.4	3.4	NUM
ejpam-6739	56	6	]	]	PUNCT
ejpam-6739	56	7	for	for	ADP
ejpam-6739	56	8	any	any	DET
ejpam-6739	56	9	quasi-∗-paranormal	quasi-∗-paranormal	ADJ
ejpam-6739	56	10	operator	operator	NOUN
ejpam-6739	56	11	t	t	PROPN
ejpam-6739	56	12	∈	∈	PROPN
ejpam-6739	56	13	b(h	b(h	PROPN
ejpam-6739	56	14	)	)	PUNCT
ejpam-6739	56	15	,	,	PUNCT
ejpam-6739	56	16	and	and	CCONJ
ejpam-6739	56	17	each	each	DET
ejpam-6739	56	18	non	non	ADJ
ejpam-6739	56	19	-	-	ADJ
ejpam-6739	56	20	zero	zero	ADJ
ejpam-6739	56	21	complex	complex	ADJ
ejpam-6739	56	22	scalar	scalar	ADJ
ejpam-6739	56	23	λ	λ	NOUN
ejpam-6739	56	24	,	,	PUNCT
ejpam-6739	56	25	we	we	PRON
ejpam-6739	56	26	’ve	’ve	VERB
ejpam-6739	56	27	n(t	n(t	PROPN
ejpam-6739	56	28	−	−	PROPN
ejpam-6739	56	29	λi	λi	NOUN
ejpam-6739	56	30	)	)	PUNCT
ejpam-6739	56	31	⊂	⊂	PROPN
ejpam-6739	56	32	n(t	n(t	PROPN
ejpam-6739	56	33	−	−	PRON
ejpam-6739	56	34	λi)∗.	λi)∗.	ADV
ejpam-6739	56	35	remark	remark	NOUN
ejpam-6739	56	36	1	1	NUM
ejpam-6739	56	37	.	.	PUNCT
ejpam-6739	57	1	lemma	lemma	PROPN
ejpam-6739	57	2	2	2	PROPN
ejpam-6739	57	3	is	be	AUX
ejpam-6739	57	4	in	in	ADP
ejpam-6739	57	5	general	general	ADJ
ejpam-6739	57	6	not	not	PART
ejpam-6739	57	7	true	true	ADJ
ejpam-6739	57	8	for	for	ADP
ejpam-6739	57	9	λ	λ	X
ejpam-6739	57	10	=	=	SYM
ejpam-6739	57	11	0	0	PROPN
ejpam-6739	57	12	.	.	PUNCT
ejpam-6739	58	1	a	a	DET
ejpam-6739	58	2	counter	counter	NOUN
ejpam-6739	58	3	-	-	NOUN
ejpam-6739	58	4	example	example	NOUN
ejpam-6739	58	5	can	can	AUX
ejpam-6739	58	6	be	be	AUX
ejpam-6739	58	7	found	find	VERB
ejpam-6739	58	8	in	in	ADP
ejpam-6739	58	9	[	[	X
ejpam-6739	58	10	9	9	NUM
ejpam-6739	58	11	]	]	PUNCT
ejpam-6739	58	12	.	.	PUNCT
ejpam-6739	59	1	definition	definition	NOUN
ejpam-6739	59	2	2	2	NUM
ejpam-6739	59	3	.	.	PUNCT
ejpam-6739	60	1	[	[	X
ejpam-6739	60	2	4	4	X
ejpam-6739	60	3	]	]	X
ejpam-6739	60	4	an	an	DET
ejpam-6739	60	5	operator	operator	NOUN
ejpam-6739	60	6	t	t	PROPN
ejpam-6739	60	7	∈	∈	PROPN
ejpam-6739	60	8	b(h	b(h	PROPN
ejpam-6739	60	9	)	)	PUNCT
ejpam-6739	60	10	is	be	AUX
ejpam-6739	60	11	said	say	VERB
ejpam-6739	60	12	to	to	PART
ejpam-6739	60	13	be	be	AUX
ejpam-6739	60	14	norm	norm	NOUN
ejpam-6739	60	15	attaining	attain	VERB
ejpam-6739	60	16	(	(	PUNCT
ejpam-6739	60	17	or	or	CCONJ
ejpam-6739	60	18	achieving	achieve	VERB
ejpam-6739	60	19	the	the	DET
ejpam-6739	60	20	norm	norm	NOUN
ejpam-6739	60	21	)	)	PUNCT
ejpam-6739	60	22	if	if	SCONJ
ejpam-6739	60	23	there	there	PRON
ejpam-6739	60	24	exists	exist	VERB
ejpam-6739	60	25	a	a	DET
ejpam-6739	60	26	unit	unit	NOUN
ejpam-6739	60	27	vector	vector	NOUN
ejpam-6739	60	28	u	u	PROPN
ejpam-6739	60	29	∈	∈	PROPN
ejpam-6739	60	30	h	h	NOUN
ejpam-6739	60	31	for	for	ADP
ejpam-6739	60	32	which	which	PRON
ejpam-6739	60	33	∥tu∥	∥tu∥	NOUN
ejpam-6739	60	34	=	=	PUNCT
ejpam-6739	60	35	∥t∥.	∥t∥.	PROPN
ejpam-6739	60	36	example	example	NOUN
ejpam-6739	61	1	2	2	NUM
ejpam-6739	61	2	.	.	PUNCT
ejpam-6739	62	1	[	[	X
ejpam-6739	62	2	21	21	NUM
ejpam-6739	62	3	]	]	X
ejpam-6739	62	4	let	let	VERB
ejpam-6739	62	5	θ	θ	PROPN
ejpam-6739	62	6	=	=	PUNCT
ejpam-6739	62	7	(	(	PUNCT
ejpam-6739	62	8	θn)n≥1	θn)n≥1	ADJ
ejpam-6739	62	9	be	be	VERB
ejpam-6739	62	10	a	a	DET
ejpam-6739	62	11	real	real	ADV
ejpam-6739	62	12	strictly	strictly	ADV
ejpam-6739	62	13	increasing	increase	VERB
ejpam-6739	62	14	sequence	sequence	NOUN
ejpam-6739	62	15	.	.	PUNCT
ejpam-6739	63	1	the	the	DET
ejpam-6739	63	2	operator	operator	NOUN
ejpam-6739	63	3	tθ	tθ	PART
ejpam-6739	63	4	defined	define	VERB
ejpam-6739	63	5	on	on	ADP
ejpam-6739	63	6	the	the	DET
ejpam-6739	63	7	usual	usual	ADJ
ejpam-6739	63	8	hilbert	hilbert	NOUN
ejpam-6739	63	9	space	space	NOUN
ejpam-6739	63	10	ℓ2	ℓ2	NOUN
ejpam-6739	63	11	by	by	ADP
ejpam-6739	63	12	tθx	tθx	NOUN
ejpam-6739	63	13	=	=	PUNCT
ejpam-6739	63	14	(	(	PUNCT
ejpam-6739	63	15	θnxn)n≥1	θnxn)n≥1	PROPN
ejpam-6739	63	16	,	,	PUNCT
ejpam-6739	63	17	x	x	SYM
ejpam-6739	63	18	=	=	SYM
ejpam-6739	63	19	(	(	PUNCT
ejpam-6739	63	20	xn)n≥1	xn)n≥1	NOUN
ejpam-6739	63	21	∈	∈	PROPN
ejpam-6739	63	22	ℓ2	ℓ2	NOUN
ejpam-6739	63	23	is	be	AUX
ejpam-6739	63	24	not	not	PART
ejpam-6739	63	25	norm	norm	NOUN
ejpam-6739	63	26	attaining	attain	VERB
ejpam-6739	63	27	.	.	PUNCT
ejpam-6739	64	1	example	example	NOUN
ejpam-6739	65	1	3	3	NUM
ejpam-6739	65	2	.	.	PUNCT
ejpam-6739	66	1	[	[	X
ejpam-6739	66	2	18	18	NUM
ejpam-6739	66	3	]	]	PUNCT
ejpam-6739	66	4	the	the	DET
ejpam-6739	66	5	usual	usual	ADJ
ejpam-6739	66	6	hilbert	hilbert	NOUN
ejpam-6739	66	7	space	space	NOUN
ejpam-6739	66	8	ℓ2	ℓ2	NOUN
ejpam-6739	66	9	is	be	AUX
ejpam-6739	66	10	equipped	equip	VERB
ejpam-6739	66	11	with	with	ADP
ejpam-6739	66	12	its	its	PRON
ejpam-6739	66	13	standard	standard	ADJ
ejpam-6739	66	14	orthonormal	orthonormal	ADJ
ejpam-6739	66	15	basis	basis	NOUN
ejpam-6739	66	16	(	(	PUNCT
ejpam-6739	66	17	en)n≥1	en)n≥1	VERB
ejpam-6739	66	18	,	,	PUNCT
ejpam-6739	66	19	and	and	CCONJ
ejpam-6739	66	20	s	s	VERB
ejpam-6739	66	21	is	be	AUX
ejpam-6739	66	22	the	the	DET
ejpam-6739	66	23	unilateral	unilateral	ADJ
ejpam-6739	66	24	left	left	ADJ
ejpam-6739	66	25	shift	shift	NOUN
ejpam-6739	66	26	on	on	ADP
ejpam-6739	66	27	ℓ2	ℓ2	NOUN
ejpam-6739	66	28	defined	define	VERB
ejpam-6739	66	29	by	by	ADP
ejpam-6739	66	30	sen	sen	PROPN
ejpam-6739	66	31	=	=	PROPN
ejpam-6739	66	32	en−1	en−1	PROPN
ejpam-6739	66	33	,	,	PUNCT
ejpam-6739	66	34	n	n	PRON
ejpam-6739	66	35	≥	≥	NOUN
ejpam-6739	66	36	2	2	NUM
ejpam-6739	66	37	and	and	CCONJ
ejpam-6739	66	38	se1	se1	PROPN
ejpam-6739	66	39	=	=	NOUN
ejpam-6739	66	40	0	0	PUNCT
ejpam-6739	66	41	then	then	ADV
ejpam-6739	66	42	,	,	PUNCT
ejpam-6739	66	43	s	s	NOUN
ejpam-6739	66	44	is	be	AUX
ejpam-6739	66	45	norm	norm	NOUN
ejpam-6739	66	46	attaining	attain	VERB
ejpam-6739	66	47	since	since	SCONJ
ejpam-6739	66	48	∥se2∥	∥se2∥	ADJ
ejpam-6739	66	49	=	=	NOUN
ejpam-6739	66	50	∥s∥	∥s∥	NOUN
ejpam-6739	66	51	=	=	SYM
ejpam-6739	66	52	1	1	X
ejpam-6739	66	53	.	.	PUNCT
ejpam-6739	66	54	a.	a.	NOUN
ejpam-6739	66	55	nasli	nasli	PROPN
ejpam-6739	66	56	bakir	bakir	VERB
ejpam-6739	66	57	et	et	PROPN
ejpam-6739	66	58	al	al	PROPN
ejpam-6739	66	59	.	.	PUNCT
ejpam-6739	66	60	/	/	SYM
ejpam-6739	66	61	eur	eur	PROPN
ejpam-6739	66	62	.	.	PUNCT
ejpam-6739	67	1	j.	j.	PROPN
ejpam-6739	67	2	pure	pure	PROPN
ejpam-6739	67	3	appl	appl	PROPN
ejpam-6739	67	4	.	.	PROPN
ejpam-6739	67	5	math	math	PROPN
ejpam-6739	67	6	,	,	PUNCT
ejpam-6739	67	7	18	18	NUM
ejpam-6739	67	8	(	(	PUNCT
ejpam-6739	67	9	4	4	NUM
ejpam-6739	67	10	)	)	PUNCT
ejpam-6739	67	11	(	(	PUNCT
ejpam-6739	67	12	2025	2025	NUM
ejpam-6739	67	13	)	)	PUNCT
ejpam-6739	67	14	,	,	PUNCT
ejpam-6739	67	15	6739	6739	NUM
ejpam-6739	67	16	4	4	NUM
ejpam-6739	67	17	of	of	ADP
ejpam-6739	67	18	10	10	NUM
ejpam-6739	67	19	recall	recall	NOUN
ejpam-6739	67	20	that	that	SCONJ
ejpam-6739	67	21	a	a	DET
ejpam-6739	67	22	closed	closed	ADJ
ejpam-6739	67	23	subspace	subspace	NOUN
ejpam-6739	67	24	m	m	PROPN
ejpam-6739	67	25	⊂	⊂	PROPN
ejpam-6739	67	26	h	h	PROPN
ejpam-6739	67	27	is	be	AUX
ejpam-6739	67	28	said	say	VERB
ejpam-6739	67	29	to	to	PART
ejpam-6739	67	30	be	be	AUX
ejpam-6739	67	31	invariant	invariant	ADJ
ejpam-6739	67	32	for	for	ADP
ejpam-6739	67	33	an	an	DET
ejpam-6739	67	34	operator	operator	NOUN
ejpam-6739	67	35	t	t	PROPN
ejpam-6739	67	36	∈	∈	PROPN
ejpam-6739	67	37	b(h	b(h	PROPN
ejpam-6739	67	38	)	)	PUNCT
ejpam-6739	67	39	,	,	PUNCT
ejpam-6739	67	40	if	if	SCONJ
ejpam-6739	67	41	tu	tu	PROPN
ejpam-6739	67	42	∈	∈	PROPN
ejpam-6739	67	43	m	m	VERB
ejpam-6739	67	44	for	for	ADP
ejpam-6739	67	45	each	each	DET
ejpam-6739	67	46	u	u	PROPN
ejpam-6739	67	47	∈	∈	PROPN
ejpam-6739	67	48	m	m	PROPN
ejpam-6739	67	49	,	,	PUNCT
ejpam-6739	67	50	and	and	CCONJ
ejpam-6739	67	51	m	m	PROPN
ejpam-6739	67	52	is	be	AUX
ejpam-6739	67	53	said	say	VERB
ejpam-6739	67	54	to	to	PART
ejpam-6739	67	55	be	be	AUX
ejpam-6739	67	56	reducing	reduce	VERB
ejpam-6739	67	57	for	for	ADP
ejpam-6739	67	58	t	t	PROPN
ejpam-6739	67	59	if	if	SCONJ
ejpam-6739	67	60	m	m	NOUN
ejpam-6739	67	61	is	be	AUX
ejpam-6739	67	62	invariant	invariant	ADJ
ejpam-6739	67	63	for	for	ADP
ejpam-6739	67	64	both	both	DET
ejpam-6739	67	65	t	t	PROPN
ejpam-6739	67	66	and	and	CCONJ
ejpam-6739	67	67	t	t	PROPN
ejpam-6739	67	68	∗.	∗.	PROPN
ejpam-6739	67	69	as	as	ADP
ejpam-6739	67	70	an	an	DET
ejpam-6739	67	71	extension	extension	NOUN
ejpam-6739	67	72	of	of	ADP
ejpam-6739	67	73	results	result	NOUN
ejpam-6739	67	74	given	give	VERB
ejpam-6739	67	75	in	in	ADP
ejpam-6739	67	76	[	[	X
ejpam-6739	67	77	18	18	NUM
ejpam-6739	67	78	]	]	PUNCT
ejpam-6739	67	79	and	and	CCONJ
ejpam-6739	67	80	[	[	X
ejpam-6739	67	81	5	5	NUM
ejpam-6739	67	82	]	]	PUNCT
ejpam-6739	67	83	,	,	PUNCT
ejpam-6739	67	84	where	where	SCONJ
ejpam-6739	67	85	are	be	AUX
ejpam-6739	67	86	provided	provide	VERB
ejpam-6739	67	87	invariant	invariant	ADJ
ejpam-6739	67	88	non	non	ADJ
ejpam-6739	67	89	trivial	trivial	ADJ
ejpam-6739	67	90	subspaces	subspace	NOUN
ejpam-6739	67	91	for	for	ADP
ejpam-6739	67	92	both	both	PRON
ejpam-6739	67	93	of	of	ADP
ejpam-6739	67	94	norm	norm	NOUN
ejpam-6739	67	95	achieving	achieve	VERB
ejpam-6739	67	96	∗-paranormal	∗-paranormal	ADJ
ejpam-6739	67	97	and	and	CCONJ
ejpam-6739	67	98	norm	norm	NOUN
ejpam-6739	67	99	achieving	achieve	VERB
ejpam-6739	67	100	paranormal	paranormal	ADJ
ejpam-6739	67	101	operators	operator	NOUN
ejpam-6739	67	102	respectively	respectively	ADV
ejpam-6739	67	103	,	,	PUNCT
ejpam-6739	67	104	we	we	PRON
ejpam-6739	67	105	shall	shall	AUX
ejpam-6739	67	106	define	define	VERB
ejpam-6739	67	107	in	in	ADP
ejpam-6739	67	108	the	the	DET
ejpam-6739	67	109	following	following	NOUN
ejpam-6739	67	110	,	,	PUNCT
ejpam-6739	67	111	a	a	DET
ejpam-6739	67	112	non	non	ADJ
ejpam-6739	67	113	trivial	trivial	ADJ
ejpam-6739	67	114	subspace	subspace	NOUN
ejpam-6739	67	115	for	for	ADP
ejpam-6739	67	116	norm	norm	NOUN
ejpam-6739	67	117	attaining	attain	VERB
ejpam-6739	67	118	quasi-∗-paranormal	quasi-∗-paranormal	PROPN
ejpam-6739	67	119	operators	operator	NOUN
ejpam-6739	67	120	as	as	ADP
ejpam-6739	67	121	a	a	DET
ejpam-6739	67	122	positive	positive	ADJ
ejpam-6739	67	123	answer	answer	NOUN
ejpam-6739	67	124	to	to	ADP
ejpam-6739	67	125	the	the	DET
ejpam-6739	67	126	problem	problem	NOUN
ejpam-6739	67	127	of	of	ADP
ejpam-6739	67	128	invariant	invariant	ADJ
ejpam-6739	67	129	subspaces	subspace	NOUN
ejpam-6739	67	130	for	for	ADP
ejpam-6739	67	131	operators	operator	NOUN
ejpam-6739	67	132	on	on	ADP
ejpam-6739	67	133	hilbert	hilbert	PROPN
ejpam-6739	67	134	spaces	space	NOUN
ejpam-6739	67	135	that	that	PRON
ejpam-6739	67	136	asks	ask	VERB
ejpam-6739	67	137	if	if	SCONJ
ejpam-6739	67	138	any	any	DET
ejpam-6739	67	139	bounded	bounded	ADJ
ejpam-6739	67	140	linear	linear	ADJ
ejpam-6739	67	141	operator	operator	NOUN
ejpam-6739	67	142	acting	act	VERB
ejpam-6739	67	143	on	on	ADP
ejpam-6739	67	144	a	a	DET
ejpam-6739	67	145	hilbert	hilbert	NOUN
ejpam-6739	67	146	space	space	NOUN
ejpam-6739	67	147	admits	admit	VERB
ejpam-6739	67	148	at	at	ADP
ejpam-6739	67	149	least	least	ADJ
ejpam-6739	67	150	,	,	PUNCT
ejpam-6739	67	151	a	a	DET
ejpam-6739	67	152	non	non	ADJ
ejpam-6739	67	153	trivial	trivial	ADJ
ejpam-6739	67	154	invariant	invariant	ADJ
ejpam-6739	67	155	subspace	subspace	NOUN
ejpam-6739	67	156	.	.	PUNCT
ejpam-6739	68	1	theorem	theorem	NOUN
ejpam-6739	68	2	1	1	NUM
ejpam-6739	68	3	.	.	PUNCT
ejpam-6739	69	1	let	let	AUX
ejpam-6739	69	2	t	t	PROPN
ejpam-6739	69	3	∈	∈	PROPN
ejpam-6739	69	4	b(h	b(h	PROPN
ejpam-6739	69	5	)	)	PUNCT
ejpam-6739	69	6	be	be	VERB
ejpam-6739	69	7	a	a	DET
ejpam-6739	69	8	quasi-∗-paranormal	quasi-∗-paranormal	ADJ
ejpam-6739	69	9	operator	operator	NOUN
ejpam-6739	69	10	that	that	PRON
ejpam-6739	69	11	achieves	achieve	VERB
ejpam-6739	69	12	the	the	DET
ejpam-6739	69	13	norm	norm	NOUN
ejpam-6739	69	14	.	.	PUNCT
ejpam-6739	70	1	then	then	ADV
ejpam-6739	70	2	,	,	PUNCT
ejpam-6739	70	3	the	the	DET
ejpam-6739	70	4	subspace	subspace	NOUN
ejpam-6739	70	5	m	m	VERB
ejpam-6739	70	6	=	=	PUNCT
ejpam-6739	70	7	{	{	PUNCT
ejpam-6739	70	8	u	u	NOUN
ejpam-6739	70	9	∈	∈	PROPN
ejpam-6739	70	10	h	h	NOUN
ejpam-6739	70	11	:	:	PUNCT
ejpam-6739	70	12	∥tu∥	∥tu∥	X
ejpam-6739	70	13	=	=	SYM
ejpam-6739	70	14	∥t∥∥u∥	∥t∥∥u∥	PROPN
ejpam-6739	70	15	}	}	PUNCT
ejpam-6739	70	16	is	be	AUX
ejpam-6739	70	17	invariant	invariant	ADJ
ejpam-6739	70	18	for	for	ADP
ejpam-6739	70	19	t.	t.	NOUN
ejpam-6739	70	20	proof	proof	NOUN
ejpam-6739	70	21	.	.	PUNCT
ejpam-6739	71	1	since	since	SCONJ
ejpam-6739	71	2	t	t	PROPN
ejpam-6739	71	3	is	be	AUX
ejpam-6739	71	4	norm	norm	NOUN
ejpam-6739	71	5	attaining	attain	VERB
ejpam-6739	71	6	,	,	PUNCT
ejpam-6739	71	7	m	m	VERB
ejpam-6739	71	8	=	=	ADJ
ejpam-6739	71	9	n(t	n(t	PROPN
ejpam-6739	71	10	∗t	∗t	PROPN
ejpam-6739	71	11	−∥t∥2i	−∥t∥2i	NOUN
ejpam-6739	71	12	)	)	PUNCT
ejpam-6739	71	13	is	be	AUX
ejpam-6739	71	14	a	a	DET
ejpam-6739	71	15	non	non	ADJ
ejpam-6739	71	16	-	-	ADJ
ejpam-6739	71	17	zero	zero	NUM
ejpam-6739	71	18	closed	closed	ADJ
ejpam-6739	71	19	subspace	subspace	NOUN
ejpam-6739	71	20	of	of	ADP
ejpam-6739	71	21	h.	h.	PROPN
ejpam-6739	71	22	next	next	ADV
ejpam-6739	71	23	,	,	PUNCT
ejpam-6739	71	24	as	as	SCONJ
ejpam-6739	71	25	t	t	PROPN
ejpam-6739	71	26	is	be	AUX
ejpam-6739	71	27	quasi-∗-paranormal	quasi-∗-paranormal	ADJ
ejpam-6739	71	28	,	,	PUNCT
ejpam-6739	71	29	∥t∥2∥u∥2	∥t∥2∥u∥2	NOUN
ejpam-6739	71	30	=	=	SYM
ejpam-6739	71	31	∥tu∥2	∥tu∥2	AUX
ejpam-6739	71	32	=	=	SYM
ejpam-6739	71	33	⟨t	⟨t	VERB
ejpam-6739	71	34	∗tu	∗tu	NOUN
ejpam-6739	71	35	,	,	PUNCT
ejpam-6739	71	36	u⟩	u⟩	VERB
ejpam-6739	71	37	≤	≤	X
ejpam-6739	71	38	∥t	∥t	PROPN
ejpam-6739	71	39	∗tu∥∥u∥	∗tu∥∥u∥	PUNCT
ejpam-6739	71	40	≤	≤	NOUN
ejpam-6739	71	41	√	√	VERB
ejpam-6739	71	42	∥t	∥t	PROPN
ejpam-6739	71	43	3u∥∥tu∥∥u∥	3u∥∥tu∥∥u∥	NUM
ejpam-6739	71	44	≤	≤	NOUN
ejpam-6739	71	45	√	√	PUNCT
ejpam-6739	71	46	∥t	∥t	VERB
ejpam-6739	71	47	2∥∥tu∥2∥u∥	2∥∥tu∥2∥u∥	NUM
ejpam-6739	71	48	≤	≤	NUM
ejpam-6739	71	49	√	√	DET
ejpam-6739	71	50	∥t∥2∥tu∥2∥u∥	∥t∥2∥tu∥2∥u∥	NUM
ejpam-6739	71	51	≤	≤	NUM
ejpam-6739	71	52	∥t∥∥tu∥∥u∥	∥t∥∥tu∥∥u∥	NOUN
ejpam-6739	71	53	≤	≤	NOUN
ejpam-6739	71	54	∥t∥2∥u∥2	∥t∥2∥u∥2	NOUN
ejpam-6739	71	55	for	for	ADP
ejpam-6739	71	56	each	each	DET
ejpam-6739	71	57	u	u	PROPN
ejpam-6739	71	58	∈	∈	PROPN
ejpam-6739	71	59	m.	m.	NOUN
ejpam-6739	71	60	hence	hence	ADV
ejpam-6739	71	61	,	,	PUNCT
ejpam-6739	71	62	∥t∥2∥u∥2	∥t∥2∥u∥2	PROPN
ejpam-6739	72	1	=	=	SYM
ejpam-6739	72	2	∥t	∥t	PROPN
ejpam-6739	72	3	∗tu∥∥u∥	∗tu∥∥u∥	PUNCT
ejpam-6739	72	4	=	=	PRON
ejpam-6739	72	5	∥tu∥2	∥tu∥2	X
ejpam-6739	72	6	i.e.	i.e.	X
ejpam-6739	72	7	,	,	PUNCT
ejpam-6739	72	8	∥t∥∥tu∥	∥t∥∥tu∥	NOUN
ejpam-6739	72	9	=	=	PUNCT
ejpam-6739	72	10	∥t∥2∥u∥	∥t∥2∥u∥	NOUN
ejpam-6739	72	11	=	=	SYM
ejpam-6739	72	12	∥t	∥t	ADJ
ejpam-6739	72	13	∗tu∥	∗tu∥	NOUN
ejpam-6739	72	14	,	,	PUNCT
ejpam-6739	72	15	u	u	PROPN
ejpam-6739	72	16	∈	∈	PROPN
ejpam-6739	72	17	m	m	VERB
ejpam-6739	72	18	(	(	PUNCT
ejpam-6739	72	19	1	1	X
ejpam-6739	72	20	)	)	PUNCT
ejpam-6739	72	21	using	use	VERB
ejpam-6739	72	22	equality	equality	NOUN
ejpam-6739	72	23	(	(	PUNCT
ejpam-6739	72	24	1	1	NUM
ejpam-6739	72	25	)	)	PUNCT
ejpam-6739	72	26	,	,	PUNCT
ejpam-6739	72	27	the	the	DET
ejpam-6739	72	28	fact	fact	NOUN
ejpam-6739	72	29	that	that	SCONJ
ejpam-6739	72	30	∥t	∥t	ADJ
ejpam-6739	72	31	∗t∥	∗t∥	X
ejpam-6739	72	32	=	=	SYM
ejpam-6739	72	33	∥t∥2	∥t∥2	NOUN
ejpam-6739	72	34	and	and	CCONJ
ejpam-6739	72	35	by	by	ADP
ejpam-6739	72	36	cauchy	cauchy	PROPN
ejpam-6739	72	37	-	-	PUNCT
ejpam-6739	72	38	schwarz	schwarz	PROPN
ejpam-6739	72	39	’s	’s	PART
ejpam-6739	72	40	inequality	inequality	NOUN
ejpam-6739	72	41	,	,	PUNCT
ejpam-6739	72	42	we	we	PRON
ejpam-6739	72	43	get	get	VERB
ejpam-6739	72	44	for	for	ADP
ejpam-6739	72	45	each	each	DET
ejpam-6739	72	46	vector	vector	NOUN
ejpam-6739	72	47	u	u	NOUN
ejpam-6739	72	48	in	in	ADP
ejpam-6739	72	49	m	m	PROPN
ejpam-6739	72	50	,	,	PUNCT
ejpam-6739	72	51	∥t	∥t	ADJ
ejpam-6739	72	52	2u∥2	2u∥2	NOUN
ejpam-6739	72	53	=	=	SYM
ejpam-6739	72	54	⟨t	⟨t	VERB
ejpam-6739	72	55	∗t	∗t	PROPN
ejpam-6739	72	56	2u	2u	NOUN
ejpam-6739	72	57	,	,	PUNCT
ejpam-6739	72	58	tu⟩	tu⟩	NOUN
ejpam-6739	72	59	≤	≤	NUM
ejpam-6739	73	1	∥t	∥t	PROPN
ejpam-6739	73	2	∗t∥∥tu∥2	∗t∥∥tu∥2	NOUN
ejpam-6739	73	3	=	=	SYM
ejpam-6739	73	4	∥t∥2∥tu∥2	∥t∥2∥tu∥2	PROPN
ejpam-6739	73	5	=	=	SYM
ejpam-6739	73	6	∥t	∥t	PROPN
ejpam-6739	73	7	∗tu∥2	∗tu∥2	NOUN
ejpam-6739	73	8	that	that	PRON
ejpam-6739	73	9	is	be	AUX
ejpam-6739	73	10	,	,	PUNCT
ejpam-6739	73	11	∥t	∥t	ADJ
ejpam-6739	73	12	2u∥	2u∥	NOUN
ejpam-6739	73	13	≤	≤	ADV
ejpam-6739	73	14	∥t	∥t	ADJ
ejpam-6739	73	15	∗tu∥	∗tu∥	NOUN
ejpam-6739	73	16	(	(	PUNCT
ejpam-6739	73	17	2	2	NUM
ejpam-6739	73	18	)	)	PUNCT
ejpam-6739	73	19	for	for	ADP
ejpam-6739	73	20	all	all	DET
ejpam-6739	73	21	u	u	PROPN
ejpam-6739	73	22	∈	∈	PROPN
ejpam-6739	73	23	m.	m.	NOUN
ejpam-6739	73	24	on	on	ADP
ejpam-6739	73	25	another	another	DET
ejpam-6739	73	26	hand	hand	NOUN
ejpam-6739	73	27	,	,	PUNCT
ejpam-6739	73	28	∥t	∥t	PROPN
ejpam-6739	73	29	∗tu∥2	∗tu∥2	NOUN
ejpam-6739	73	30	≤	≤	NOUN
ejpam-6739	73	31	∥t	∥t	ADJ
ejpam-6739	73	32	3u∥∥tu∥	3u∥∥tu∥	NOUN
ejpam-6739	73	33	≤	≤	NOUN
ejpam-6739	74	1	∥t	∥t	ADJ
ejpam-6739	74	2	2u∥∥t∥∥tu∥	2u∥∥t∥∥tu∥	NUM
ejpam-6739	74	3	=	=	SYM
ejpam-6739	74	4	∥t	∥t	ADJ
ejpam-6739	74	5	2u∥∥t	2u∥∥t	NUM
ejpam-6739	74	6	∗tu∥	∗tu∥	NOUN
ejpam-6739	74	7	hence	hence	ADV
ejpam-6739	74	8	,	,	PUNCT
ejpam-6739	74	9	for	for	ADP
ejpam-6739	74	10	all	all	PRON
ejpam-6739	74	11	u	u	PROPN
ejpam-6739	74	12	∈	∈	PROPN
ejpam-6739	74	13	m	m	PROPN
ejpam-6739	74	14	,	,	PUNCT
ejpam-6739	74	15	∥t	∥t	ADJ
ejpam-6739	74	16	∗tu∥	∗tu∥	NOUN
ejpam-6739	74	17	≤	≤	NOUN
ejpam-6739	74	18	∥t	∥t	ADJ
ejpam-6739	74	19	2u∥	2u∥	NOUN
ejpam-6739	74	20	(	(	PUNCT
ejpam-6739	74	21	3	3	X
ejpam-6739	74	22	)	)	PUNCT
ejpam-6739	74	23	a.	a.	NOUN
ejpam-6739	74	24	nasli	nasli	PROPN
ejpam-6739	74	25	bakir	bakir	VERB
ejpam-6739	74	26	et	et	PROPN
ejpam-6739	74	27	al	al	PROPN
ejpam-6739	74	28	.	.	PUNCT
ejpam-6739	74	29	/	/	SYM
ejpam-6739	74	30	eur	eur	PROPN
ejpam-6739	74	31	.	.	PUNCT
ejpam-6739	75	1	j.	j.	PROPN
ejpam-6739	75	2	pure	pure	PROPN
ejpam-6739	75	3	appl	appl	PROPN
ejpam-6739	75	4	.	.	PROPN
ejpam-6739	75	5	math	math	PROPN
ejpam-6739	75	6	,	,	PUNCT
ejpam-6739	75	7	18	18	NUM
ejpam-6739	75	8	(	(	PUNCT
ejpam-6739	75	9	4	4	NUM
ejpam-6739	75	10	)	)	PUNCT
ejpam-6739	75	11	(	(	PUNCT
ejpam-6739	75	12	2025	2025	NUM
ejpam-6739	75	13	)	)	PUNCT
ejpam-6739	75	14	,	,	PUNCT
ejpam-6739	75	15	6739	6739	NUM
ejpam-6739	75	16	5	5	NUM
ejpam-6739	75	17	of	of	ADP
ejpam-6739	75	18	10	10	NUM
ejpam-6739	75	19	by	by	ADP
ejpam-6739	75	20	(	(	PUNCT
ejpam-6739	75	21	2	2	NUM
ejpam-6739	75	22	)	)	PUNCT
ejpam-6739	75	23	and	and	CCONJ
ejpam-6739	75	24	(	(	PUNCT
ejpam-6739	75	25	3	3	NUM
ejpam-6739	75	26	)	)	PUNCT
ejpam-6739	75	27	,	,	PUNCT
ejpam-6739	75	28	∥t	∥t	PROPN
ejpam-6739	75	29	∗tu∥	∗tu∥	NOUN
ejpam-6739	75	30	=	=	NOUN
ejpam-6739	75	31	∥t∥∥tu∥	∥t∥∥tu∥	NOUN
ejpam-6739	75	32	=	=	PUNCT
ejpam-6739	75	33	∥t	∥t	ADJ
ejpam-6739	75	34	2u∥	2u∥	NOUN
ejpam-6739	75	35	for	for	ADP
ejpam-6739	75	36	each	each	DET
ejpam-6739	75	37	u	u	PROPN
ejpam-6739	75	38	∈	∈	PROPN
ejpam-6739	75	39	m.	m.	NOUN
ejpam-6739	75	40	this	this	PRON
ejpam-6739	75	41	shows	show	VERB
ejpam-6739	75	42	that	that	SCONJ
ejpam-6739	75	43	m	m	NOUN
ejpam-6739	75	44	is	be	AUX
ejpam-6739	75	45	invariant	invariant	ADJ
ejpam-6739	75	46	for	for	ADP
ejpam-6739	75	47	t.	t.	NOUN
ejpam-6739	75	48	by	by	ADP
ejpam-6739	75	49	a	a	DET
ejpam-6739	75	50	similar	similar	ADJ
ejpam-6739	75	51	way	way	NOUN
ejpam-6739	75	52	as	as	ADP
ejpam-6739	75	53	in	in	ADP
ejpam-6739	75	54	[	[	X
ejpam-6739	75	55	5	5	NUM
ejpam-6739	75	56	,	,	PUNCT
ejpam-6739	75	57	lemma	lemma	PROPN
ejpam-6739	75	58	3.1	3.1	NUM
ejpam-6739	75	59	]	]	PUNCT
ejpam-6739	75	60	,	,	PUNCT
ejpam-6739	75	61	we	we	PRON
ejpam-6739	75	62	can	can	AUX
ejpam-6739	75	63	easily	easily	ADV
ejpam-6739	75	64	prove	prove	VERB
ejpam-6739	75	65	the	the	DET
ejpam-6739	75	66	following	follow	VERB
ejpam-6739	75	67	result	result	NOUN
ejpam-6739	75	68	for	for	ADP
ejpam-6739	75	69	an	an	DET
ejpam-6739	75	70	operator	operator	NOUN
ejpam-6739	75	71	t	t	PROPN
ejpam-6739	75	72	∈	∈	PROPN
ejpam-6739	75	73	b(h	b(h	PROPN
ejpam-6739	75	74	)	)	PUNCT
ejpam-6739	75	75	,	,	PUNCT
ejpam-6739	75	76	m	m	VERB
ejpam-6739	75	77	=	=	SYM
ejpam-6739	75	78	n(∥t∥2i−tt	n(∥t∥2i−tt	NOUN
ejpam-6739	75	79	∗	∗	NOUN
ejpam-6739	75	80	)	)	PUNCT
ejpam-6739	75	81	=	=	SYM
ejpam-6739	75	82	n(|t	n(|t	NOUN
ejpam-6739	75	83	∗|−∥t∥i	∗|−∥t∥i	NUM
ejpam-6739	75	84	)	)	PUNCT
ejpam-6739	75	85	.	.	PUNCT
ejpam-6739	76	1	furthermore	furthermore	ADV
ejpam-6739	76	2	,	,	PUNCT
ejpam-6739	76	3	if	if	SCONJ
ejpam-6739	76	4	t	t	PROPN
ejpam-6739	76	5	∗	∗	NOUN
ejpam-6739	76	6	is	be	AUX
ejpam-6739	76	7	norm	norm	NOUN
ejpam-6739	76	8	attaining	attain	VERB
ejpam-6739	76	9	,	,	PUNCT
ejpam-6739	76	10	then	then	ADV
ejpam-6739	76	11	m	m	VERB
ejpam-6739	76	12	̸=	̸=	PROPN
ejpam-6739	76	13	{	{	PUNCT
ejpam-6739	76	14	0	0	NUM
ejpam-6739	76	15	}	}	PUNCT
ejpam-6739	76	16	.	.	PUNCT
ejpam-6739	77	1	[	[	X
ejpam-6739	77	2	7	7	X
ejpam-6739	77	3	]	]	X
ejpam-6739	77	4	let	let	VERB
ejpam-6739	77	5	t	t	PROPN
ejpam-6739	77	6	∈	∈	PROPN
ejpam-6739	77	7	b(h	b(h	PROPN
ejpam-6739	77	8	)	)	PUNCT
ejpam-6739	77	9	.	.	PUNCT
ejpam-6739	78	1	the	the	DET
ejpam-6739	78	2	following	follow	VERB
ejpam-6739	78	3	statements	statement	NOUN
ejpam-6739	78	4	are	be	AUX
ejpam-6739	78	5	equivalent	equivalent	ADJ
ejpam-6739	78	6	a.	a.	NOUN
ejpam-6739	78	7	t	t	PROPN
ejpam-6739	78	8	achieves	achieve	VERB
ejpam-6739	78	9	the	the	DET
ejpam-6739	78	10	norm	norm	NOUN
ejpam-6739	78	11	.	.	PUNCT
ejpam-6739	79	1	b.	b.	PROPN
ejpam-6739	79	2	t	t	PROPN
ejpam-6739	79	3	∗	∗	NOUN
ejpam-6739	79	4	achieves	achieve	VERB
ejpam-6739	79	5	the	the	DET
ejpam-6739	79	6	norm	norm	NOUN
ejpam-6739	79	7	.	.	PUNCT
ejpam-6739	80	1	c.	c.	PROPN
ejpam-6739	80	2	|t	|t	PROPN
ejpam-6739	81	1	|	|	ADV
ejpam-6739	81	2	achieves	achieve	VERB
ejpam-6739	81	3	the	the	DET
ejpam-6739	81	4	norm	norm	NOUN
ejpam-6739	81	5	.	.	PUNCT
ejpam-6739	82	1	d.	d.	PROPN
ejpam-6739	82	2	|t	|t	PROPN
ejpam-6739	82	3	∗|	∗|	PROPN
ejpam-6739	82	4	achieves	achieve	VERB
ejpam-6739	82	5	the	the	DET
ejpam-6739	82	6	norm	norm	NOUN
ejpam-6739	82	7	.	.	PUNCT
ejpam-6739	83	1	e.	e.	PROPN
ejpam-6739	83	2	∥t∥	∥t∥	PROPN
ejpam-6739	83	3	is	be	AUX
ejpam-6739	83	4	an	an	DET
ejpam-6739	83	5	eigenvalue	eigenvalue	NOUN
ejpam-6739	83	6	of	of	ADP
ejpam-6739	83	7	t.	t.	PROPN
ejpam-6739	83	8	f.	f.	PROPN
ejpam-6739	83	9	∥t∥	∥t∥	PROPN
ejpam-6739	83	10	is	be	AUX
ejpam-6739	83	11	an	an	DET
ejpam-6739	83	12	eigenvalue	eigenvalue	NOUN
ejpam-6739	83	13	of	of	ADP
ejpam-6739	83	14	t	t	PROPN
ejpam-6739	83	15	∗.	∗.	PROPN
ejpam-6739	83	16	corollary	corollary	ADJ
ejpam-6739	83	17	1	1	NUM
ejpam-6739	83	18	.	.	PUNCT
ejpam-6739	84	1	let	let	AUX
ejpam-6739	84	2	t	t	PROPN
ejpam-6739	84	3	∈	∈	PROPN
ejpam-6739	84	4	b(h	b(h	PROPN
ejpam-6739	84	5	)	)	PUNCT
ejpam-6739	84	6	be	be	VERB
ejpam-6739	84	7	a	a	DET
ejpam-6739	84	8	quasi-∗-paranormal	quasi-∗-paranormal	ADJ
ejpam-6739	84	9	operator	operator	NOUN
ejpam-6739	84	10	achieving	achieve	VERB
ejpam-6739	84	11	the	the	DET
ejpam-6739	84	12	norm	norm	NOUN
ejpam-6739	84	13	.	.	PUNCT
ejpam-6739	85	1	then	then	ADV
ejpam-6739	85	2	∥t∥	∥t∥	CCONJ
ejpam-6739	85	3	is	be	VERB
ejpam-6739	85	4	an	an	DET
ejpam-6739	85	5	eigenvalue	eigenvalue	NOUN
ejpam-6739	85	6	of	of	ADP
ejpam-6739	85	7	|t	|t	PROPN
ejpam-6739	85	8	|	|	NOUN
ejpam-6739	85	9	.	.	PUNCT
ejpam-6739	86	1	proof	proof	NOUN
ejpam-6739	86	2	.	.	PUNCT
ejpam-6739	87	1	the	the	DET
ejpam-6739	87	2	operator	operator	NOUN
ejpam-6739	87	3	|t	|t	VERB
ejpam-6739	87	4	∗|−∥t∥i	∗|−∥t∥i	PUNCT
ejpam-6739	87	5	is	be	AUX
ejpam-6739	87	6	not	not	PART
ejpam-6739	87	7	one	one	NUM
ejpam-6739	87	8	-	-	PUNCT
ejpam-6739	87	9	to	to	ADP
ejpam-6739	87	10	-	-	PUNCT
ejpam-6739	87	11	one	one	NOUN
ejpam-6739	87	12	acoording	acoorde	VERB
ejpam-6739	87	13	to	to	PART
ejpam-6739	87	14	corollary	corollary	VERB
ejpam-6739	87	15	1	1	NUM
ejpam-6739	87	16	and	and	CCONJ
ejpam-6739	87	17	lemma	lemma	PROPN
ejpam-6739	87	18	2	2	NUM
ejpam-6739	87	19	.	.	PUNCT
ejpam-6739	88	1	then	then	ADV
ejpam-6739	88	2	,	,	PUNCT
ejpam-6739	88	3	the	the	DET
ejpam-6739	88	4	result	result	NOUN
ejpam-6739	88	5	holds	hold	VERB
ejpam-6739	88	6	by	by	ADP
ejpam-6739	88	7	lemma	lemma	PROPN
ejpam-6739	88	8	2	2	NUM
ejpam-6739	88	9	.	.	PUNCT
ejpam-6739	88	10	corollary	corollary	ADJ
ejpam-6739	88	11	2	2	NUM
ejpam-6739	88	12	.	.	PUNCT
ejpam-6739	89	1	if	if	SCONJ
ejpam-6739	89	2	both	both	PRON
ejpam-6739	89	3	of	of	ADP
ejpam-6739	89	4	t	t	PROPN
ejpam-6739	89	5	and	and	CCONJ
ejpam-6739	89	6	t	t	PROPN
ejpam-6739	89	7	∗	∗	NOUN
ejpam-6739	89	8	are	be	AUX
ejpam-6739	89	9	quasi-∗-paranormal	quasi-∗-paranormal	ADJ
ejpam-6739	89	10	in	in	ADP
ejpam-6739	89	11	b(h	b(h	PROPN
ejpam-6739	89	12	)	)	PUNCT
ejpam-6739	89	13	,	,	PUNCT
ejpam-6739	89	14	then	then	ADV
ejpam-6739	89	15	the	the	DET
ejpam-6739	89	16	subspace	subspace	NOUN
ejpam-6739	89	17	m	m	NOUN
ejpam-6739	89	18	=	=	NOUN
ejpam-6739	89	19	n(∥t∥2i	n(∥t∥2i	PROPN
ejpam-6739	89	20	−	−	PROPN
ejpam-6739	89	21	tt	tt	PROPN
ejpam-6739	89	22	∗	∗	NOUN
ejpam-6739	89	23	)	)	PUNCT
ejpam-6739	89	24	reduces	reduce	VERB
ejpam-6739	89	25	t.	t.	NOUN
ejpam-6739	89	26	proof	proof	NOUN
ejpam-6739	89	27	.	.	PUNCT
ejpam-6739	90	1	by	by	ADP
ejpam-6739	90	2	corollary	corollary	ADJ
ejpam-6739	90	3	1	1	NUM
ejpam-6739	90	4	,	,	PUNCT
ejpam-6739	90	5	m	m	VERB
ejpam-6739	90	6	is	be	AUX
ejpam-6739	90	7	invariant	invariant	ADJ
ejpam-6739	90	8	for	for	ADP
ejpam-6739	90	9	t	t	PROPN
ejpam-6739	90	10	,	,	PUNCT
ejpam-6739	90	11	and	and	CCONJ
ejpam-6739	90	12	m	m	PROPN
ejpam-6739	90	13	⊂	⊂	NOUN
ejpam-6739	90	14	n(∥t∥2i	n(∥t∥2i	X
ejpam-6739	90	15	−	−	PROPN
ejpam-6739	90	16	t	t	PROPN
ejpam-6739	90	17	∗t	∗t	PROPN
ejpam-6739	90	18	)	)	PUNCT
ejpam-6739	90	19	according	accord	VERB
ejpam-6739	90	20	to	to	ADP
ejpam-6739	90	21	the	the	DET
ejpam-6739	90	22	proof	proof	NOUN
ejpam-6739	90	23	of	of	ADP
ejpam-6739	90	24	theorem	theorem	NOUN
ejpam-6739	90	25	1	1	NUM
ejpam-6739	90	26	.	.	PUNCT
ejpam-6739	91	1	since	since	SCONJ
ejpam-6739	91	2	t	t	PROPN
ejpam-6739	91	3	∗	∗	NOUN
ejpam-6739	91	4	is	be	AUX
ejpam-6739	91	5	also	also	ADV
ejpam-6739	91	6	quasi-∗-paranormal	quasi-∗-paranormal	ADJ
ejpam-6739	91	7	,	,	PUNCT
ejpam-6739	91	8	n(∥t∥2i	n(∥t∥2i	PROPN
ejpam-6739	91	9	−t	−t	PROPN
ejpam-6739	91	10	∗t	∗t	PROPN
ejpam-6739	91	11	)	)	PUNCT
ejpam-6739	92	1	⊂	⊂	PROPN
ejpam-6739	92	2	m	m	VERB
ejpam-6739	92	3	is	be	AUX
ejpam-6739	92	4	an	an	DET
ejpam-6739	92	5	invariant	invariant	ADJ
ejpam-6739	92	6	subspace	subspace	NOUN
ejpam-6739	92	7	for	for	ADP
ejpam-6739	92	8	t	t	PROPN
ejpam-6739	92	9	∗.	∗.	PUNCT
ejpam-6739	92	10	thus	thus	ADV
ejpam-6739	92	11	,	,	PUNCT
ejpam-6739	92	12	m	m	VERB
ejpam-6739	92	13	=	=	ADJ
ejpam-6739	92	14	n(∥t∥2i	n(∥t∥2i	NOUN
ejpam-6739	92	15	−	−	PROPN
ejpam-6739	92	16	t	t	PROPN
ejpam-6739	92	17	∗t	∗t	PROPN
ejpam-6739	92	18	)	)	PUNCT
ejpam-6739	92	19	is	be	AUX
ejpam-6739	92	20	a	a	DET
ejpam-6739	92	21	reducing	reduce	VERB
ejpam-6739	92	22	subspace	subspace	NOUN
ejpam-6739	92	23	for	for	ADP
ejpam-6739	92	24	t.	t.	NOUN
ejpam-6739	92	25	theorem	theorem	PROPN
ejpam-6739	92	26	2	2	X
ejpam-6739	92	27	.	.	PUNCT
ejpam-6739	93	1	let	let	AUX
ejpam-6739	93	2	t	t	PROPN
ejpam-6739	93	3	∈	∈	PROPN
ejpam-6739	93	4	b(h	b(h	PROPN
ejpam-6739	93	5	)	)	PUNCT
ejpam-6739	93	6	be	be	VERB
ejpam-6739	93	7	a	a	DET
ejpam-6739	93	8	norm	norm	NOUN
ejpam-6739	93	9	attaining	attain	VERB
ejpam-6739	93	10	quasi-∗-paranormal	quasi-∗-paranormal	ADJ
ejpam-6739	93	11	operator	operator	NOUN
ejpam-6739	93	12	.	.	PUNCT
ejpam-6739	94	1	if	if	SCONJ
ejpam-6739	94	2	m	m	PROPN
ejpam-6739	94	3	=	=	SYM
ejpam-6739	94	4	n(t	n(t	PROPN
ejpam-6739	94	5	∗t	∗t	PROPN
ejpam-6739	94	6	−	−	PROPN
ejpam-6739	94	7	∥t∥2i	∥t∥2i	PROPN
ejpam-6739	94	8	)	)	PUNCT
ejpam-6739	94	9	is	be	AUX
ejpam-6739	94	10	finite	finite	ADJ
ejpam-6739	94	11	dimensional	dimensional	ADJ
ejpam-6739	94	12	,	,	PUNCT
ejpam-6739	94	13	then	then	ADV
ejpam-6739	94	14	a.	a.	PROPN
ejpam-6739	94	15	m	m	PROPN
ejpam-6739	94	16	is	be	AUX
ejpam-6739	94	17	a	a	DET
ejpam-6739	94	18	reducing	reduce	VERB
ejpam-6739	94	19	subspace	subspace	NOUN
ejpam-6739	94	20	for	for	ADP
ejpam-6739	94	21	t.	t.	PROPN
ejpam-6739	94	22	b.	b.	PROPN
ejpam-6739	95	1	the	the	DET
ejpam-6739	95	2	restriction	restriction	NOUN
ejpam-6739	95	3	t	t	X
ejpam-6739	95	4	∣∣	∣∣	NUM
ejpam-6739	95	5	m⊥	m⊥	NOUN
ejpam-6739	95	6	of	of	ADP
ejpam-6739	95	7	t	t	PROPN
ejpam-6739	95	8	on	on	ADP
ejpam-6739	95	9	m	m	PROPN
ejpam-6739	95	10	is	be	AUX
ejpam-6739	95	11	also	also	ADV
ejpam-6739	95	12	quasi-∗-paranormal	quasi-∗-paranormal	ADJ
ejpam-6739	95	13	.	.	PUNCT
ejpam-6739	96	1	proof	proof	NOUN
ejpam-6739	96	2	.	.	PUNCT
ejpam-6739	97	1	a.	a.	NOUN
ejpam-6739	97	2	by	by	ADP
ejpam-6739	97	3	theorem	theorem	NOUN
ejpam-6739	97	4	1	1	NUM
ejpam-6739	97	5	,	,	PUNCT
ejpam-6739	97	6	m	m	VERB
ejpam-6739	97	7	is	be	AUX
ejpam-6739	97	8	an	an	DET
ejpam-6739	97	9	invariant	invariant	ADJ
ejpam-6739	97	10	subspace	subspace	NOUN
ejpam-6739	97	11	for	for	ADP
ejpam-6739	97	12	t.	t.	PROPN
ejpam-6739	97	13	since	since	SCONJ
ejpam-6739	97	14	m	m	PROPN
ejpam-6739	97	15	is	be	AUX
ejpam-6739	97	16	of	of	ADP
ejpam-6739	97	17	finite	finite	ADJ
ejpam-6739	97	18	dimension	dimension	NOUN
ejpam-6739	97	19	,	,	PUNCT
ejpam-6739	97	20	the	the	DET
ejpam-6739	97	21	isometry	isometry	PROPN
ejpam-6739	97	22	t	t	PROPN
ejpam-6739	97	23	∗	∗	NOUN
ejpam-6739	97	24	∥t∥	∥t∥	VERB
ejpam-6739	97	25	is	be	AUX
ejpam-6739	97	26	unitary	unitary	ADJ
ejpam-6739	97	27	on	on	ADP
ejpam-6739	97	28	m.	m.	NOUN
ejpam-6739	97	29	we	we	PRON
ejpam-6739	97	30	can	can	AUX
ejpam-6739	97	31	then	then	ADV
ejpam-6739	97	32	write	write	VERB
ejpam-6739	97	33	t	t	PROPN
ejpam-6739	97	34	=	=	PUNCT
ejpam-6739	97	35	(	(	PUNCT
ejpam-6739	97	36	t	t	X
ejpam-6739	97	37	∣∣	∣∣	NUM
ejpam-6739	97	38	m	m	PROPN
ejpam-6739	97	39	s	s	NOUN
ejpam-6739	97	40	0	0	NUM
ejpam-6739	97	41	r	r	NOUN
ejpam-6739	97	42	)	)	PUNCT
ejpam-6739	97	43	a.	a.	NOUN
ejpam-6739	97	44	nasli	nasli	PROPN
ejpam-6739	97	45	bakir	bakir	VERB
ejpam-6739	97	46	et	et	PROPN
ejpam-6739	97	47	al	al	PROPN
ejpam-6739	97	48	.	.	PUNCT
ejpam-6739	97	49	/	/	SYM
ejpam-6739	97	50	eur	eur	PROPN
ejpam-6739	97	51	.	.	PUNCT
ejpam-6739	98	1	j.	j.	PROPN
ejpam-6739	98	2	pure	pure	PROPN
ejpam-6739	98	3	appl	appl	PROPN
ejpam-6739	98	4	.	.	PROPN
ejpam-6739	98	5	math	math	PROPN
ejpam-6739	98	6	,	,	PUNCT
ejpam-6739	98	7	18	18	NUM
ejpam-6739	98	8	(	(	PUNCT
ejpam-6739	98	9	4	4	NUM
ejpam-6739	98	10	)	)	PUNCT
ejpam-6739	98	11	(	(	PUNCT
ejpam-6739	98	12	2025	2025	NUM
ejpam-6739	98	13	)	)	PUNCT
ejpam-6739	98	14	,	,	PUNCT
ejpam-6739	98	15	6739	6739	NUM
ejpam-6739	98	16	6	6	NUM
ejpam-6739	98	17	of	of	ADP
ejpam-6739	98	18	10	10	NUM
ejpam-6739	98	19	under	under	ADP
ejpam-6739	98	20	the	the	DET
ejpam-6739	98	21	decomposition	decomposition	NOUN
ejpam-6739	98	22	h	h	NOUN
ejpam-6739	98	23	=	=	NOUN
ejpam-6739	98	24	m	m	PROPN
ejpam-6739	98	25	⊕	⊕	PROPN
ejpam-6739	98	26	m⊥	m⊥	NOUN
ejpam-6739	98	27	,	,	PUNCT
ejpam-6739	98	28	where	where	SCONJ
ejpam-6739	98	29	s	s	VERB
ejpam-6739	98	30	∈	∈	PROPN
ejpam-6739	98	31	b(m⊥,m	b(m⊥,m	NUM
ejpam-6739	98	32	)	)	PUNCT
ejpam-6739	98	33	and	and	CCONJ
ejpam-6739	98	34	r	r	NOUN
ejpam-6739	98	35	∈	∈	PROPN
ejpam-6739	98	36	b(m⊥,m⊥	b(m⊥,m⊥	NOUN
ejpam-6739	98	37	)	)	PUNCT
ejpam-6739	98	38	.	.	PUNCT
ejpam-6739	99	1	since	since	SCONJ
ejpam-6739	99	2	t	t	PROPN
ejpam-6739	99	3	is	be	AUX
ejpam-6739	99	4	quasi-∗-paranormal	quasi-∗-paranormal	ADJ
ejpam-6739	99	5	,	,	PUNCT
ejpam-6739	99	6	0	0	NUM
ejpam-6739	99	7	≤	≤	NUM
ejpam-6739	99	8	t	t	PROPN
ejpam-6739	99	9	∗(t	∗(t	PROPN
ejpam-6739	99	10	∗2	∗2	PROPN
ejpam-6739	99	11	t	t	NOUN
ejpam-6739	99	12	2	2	NUM
ejpam-6739	99	13	−	−	PROPN
ejpam-6739	99	14	2λtt	2λtt	NUM
ejpam-6739	99	15	∗	∗	NOUN
ejpam-6739	99	16	+	+	CCONJ
ejpam-6739	99	17	λ2)t	λ2)t	NOUN
ejpam-6739	99	18	=	=	SYM
ejpam-6739	99	19	(	(	PUNCT
ejpam-6739	99	20	(	(	PUNCT
ejpam-6739	99	21	t	t	X
ejpam-6739	99	22	∣∣	∣∣	X
ejpam-6739	99	23	m	m	NOUN
ejpam-6739	99	24	)	)	PUNCT
ejpam-6739	99	25	∗xt	∗xt	PUNCT
ejpam-6739	100	1	∣∣	∣∣	NUM
ejpam-6739	100	2	m	m	PROPN
ejpam-6739	100	3	(	(	PUNCT
ejpam-6739	100	4	t	t	PROPN
ejpam-6739	100	5	∣∣	∣∣	NUM
ejpam-6739	100	6	m	m	NOUN
ejpam-6739	100	7	)	)	PUNCT
ejpam-6739	100	8	∗(xs	∗(xs	PUNCT
ejpam-6739	101	1	+	+	CCONJ
ejpam-6739	101	2	y	y	PROPN
ejpam-6739	101	3	r	r	NOUN
ejpam-6739	101	4	)	)	PUNCT
ejpam-6739	101	5	(	(	PUNCT
ejpam-6739	101	6	s∗x	s∗x	PUNCT
ejpam-6739	101	7	+	+	ADJ
ejpam-6739	101	8	r∗y	r∗y	X
ejpam-6739	101	9	∗)t	∗)t	PROPN
ejpam-6739	101	10	∣∣	∣∣	NUM
ejpam-6739	101	11	m	m	VERB
ejpam-6739	101	12	(	(	PUNCT
ejpam-6739	101	13	s∗x	s∗x	PUNCT
ejpam-6739	101	14	+	+	ADJ
ejpam-6739	101	15	r∗y	r∗y	PRON
ejpam-6739	101	16	∗)s	∗)s	X
ejpam-6739	101	17	+	+	CCONJ
ejpam-6739	101	18	(	(	PUNCT
ejpam-6739	101	19	s∗y	s∗y	ADV
ejpam-6739	101	20	+	+	ADV
ejpam-6739	101	21	r∗z)r	r∗z)r	NUM
ejpam-6739	101	22	)	)	PUNCT
ejpam-6739	101	23	for	for	ADP
ejpam-6739	101	24	all	all	DET
ejpam-6739	101	25	λ	λ	PROPN
ejpam-6739	101	26	>	>	X
ejpam-6739	101	27	0	0	PROPN
ejpam-6739	101	28	,	,	PUNCT
ejpam-6739	101	29	where	where	SCONJ
ejpam-6739	101	30	x	x	X
ejpam-6739	101	31	=	=	PRON
ejpam-6739	101	32	(	(	PUNCT
ejpam-6739	101	33	t	t	X
ejpam-6739	101	34	∣∣	∣∣	NUM
ejpam-6739	101	35	m	m	NOUN
ejpam-6739	101	36	)	)	PUNCT
ejpam-6739	101	37	∗2(t	∗2(t	PROPN
ejpam-6739	102	1	∣∣	∣∣	NUM
ejpam-6739	102	2	m	m	NOUN
ejpam-6739	102	3	)	)	PUNCT
ejpam-6739	102	4	2	2	NUM
ejpam-6739	102	5	−	−	PROPN
ejpam-6739	102	6	2λ(t	2λ(t	NUM
ejpam-6739	102	7	∣∣	∣∣	NUM
ejpam-6739	102	8	m	m	PROPN
ejpam-6739	102	9	(	(	PUNCT
ejpam-6739	102	10	t	t	PROPN
ejpam-6739	102	11	∣∣	∣∣	NUM
ejpam-6739	102	12	m	m	NOUN
ejpam-6739	102	13	)	)	PUNCT
ejpam-6739	102	14	∗	∗	NOUN
ejpam-6739	102	15	+	+	CCONJ
ejpam-6739	102	16	ss∗	ss∗	NOUN
ejpam-6739	103	1	+	+	X
ejpam-6739	103	2	λ2i	λ2i	X
ejpam-6739	103	3	y	y	SYM
ejpam-6739	103	4	=	=	SYM
ejpam-6739	103	5	(	(	PUNCT
ejpam-6739	103	6	t	t	X
ejpam-6739	103	7	∣∣	∣∣	NUM
ejpam-6739	103	8	m	m	NOUN
ejpam-6739	103	9	)	)	PUNCT
ejpam-6739	103	10	∗2(t	∗2(t	PROPN
ejpam-6739	104	1	∣∣	∣∣	NUM
ejpam-6739	104	2	m	m	PROPN
ejpam-6739	104	3	s	s	PART
ejpam-6739	104	4	+	+	NUM
ejpam-6739	104	5	sr)−	sr)−	NOUN
ejpam-6739	104	6	2λsr∗	2λsr∗	NUM
ejpam-6739	104	7	z	z	X
ejpam-6739	104	8	=	=	SYM
ejpam-6739	104	9	(	(	PUNCT
ejpam-6739	104	10	t	t	X
ejpam-6739	104	11	∣∣	∣∣	NUM
ejpam-6739	104	12	m	m	PROPN
ejpam-6739	104	13	s	s	PART
ejpam-6739	104	14	+	+	NUM
ejpam-6739	104	15	sr)∗(t	sr)∗(t	NOUN
ejpam-6739	104	16	∣∣	∣∣	VERB
ejpam-6739	104	17	m	m	PROPN
ejpam-6739	104	18	s	s	PART
ejpam-6739	104	19	+	+	NUM
ejpam-6739	104	20	sr	sr	X
ejpam-6739	104	21	)	)	PUNCT
ejpam-6739	105	1	+	+	ADP
ejpam-6739	105	2	r∗2r2	r∗2r2	NOUN
ejpam-6739	105	3	−	−	X
ejpam-6739	105	4	2λrr∗	2λrr∗	NOUN
ejpam-6739	105	5	+	+	CCONJ
ejpam-6739	105	6	λ2i	λ2i	X
ejpam-6739	105	7	by	by	ADP
ejpam-6739	105	8	[	[	PUNCT
ejpam-6739	105	9	22	22	NUM
ejpam-6739	105	10	,	,	PUNCT
ejpam-6739	105	11	theorem	theorem	VERB
ejpam-6739	105	12	6	6	NUM
ejpam-6739	105	13	]	]	PUNCT
ejpam-6739	105	14	,	,	PUNCT
ejpam-6739	105	15	we	we	PRON
ejpam-6739	105	16	get	get	VERB
ejpam-6739	105	17	(	(	PUNCT
ejpam-6739	105	18	t	t	X
ejpam-6739	105	19	∣∣	∣∣	NUM
ejpam-6739	105	20	m	m	NOUN
ejpam-6739	105	21	)	)	PUNCT
ejpam-6739	105	22	∗xt	∗xt	PUNCT
ejpam-6739	106	1	∣∣	∣∣	NUM
ejpam-6739	106	2	m	m	VERB
ejpam-6739	106	3	≥	≥	NOUN
ejpam-6739	106	4	0	0	NUM
ejpam-6739	106	5	and	and	CCONJ
ejpam-6739	106	6	(	(	PUNCT
ejpam-6739	106	7	s∗x	s∗x	PUNCT
ejpam-6739	106	8	+	+	ADJ
ejpam-6739	106	9	r∗y	r∗y	PRON
ejpam-6739	106	10	∗)s	∗)s	X
ejpam-6739	106	11	+	+	CCONJ
ejpam-6739	106	12	(	(	PUNCT
ejpam-6739	106	13	s∗y	s∗y	NUM
ejpam-6739	106	14	+	+	ADV
ejpam-6739	106	15	r∗z)r	r∗z)r	NOUN
ejpam-6739	106	16	≥	≥	NOUN
ejpam-6739	106	17	0	0	NUM
ejpam-6739	106	18	hence	hence	ADV
ejpam-6739	106	19	,	,	PUNCT
ejpam-6739	106	20	(	(	PUNCT
ejpam-6739	106	21	t	t	X
ejpam-6739	106	22	∣∣	∣∣	NUM
ejpam-6739	106	23	m	m	NOUN
ejpam-6739	106	24	)	)	PUNCT
ejpam-6739	106	25	∗2	∗2	PROPN
ejpam-6739	106	26	(	(	PUNCT
ejpam-6739	106	27	t	t	X
ejpam-6739	106	28	∣∣	∣∣	NUM
ejpam-6739	106	29	m	m	NOUN
ejpam-6739	106	30	)	)	PUNCT
ejpam-6739	106	31	2	2	NUM
ejpam-6739	106	32	−	−	PROPN
ejpam-6739	106	33	2λ(t	2λ(t	NUM
ejpam-6739	106	34	∣∣	∣∣	NUM
ejpam-6739	106	35	m	m	PROPN
ejpam-6739	106	36	(	(	PUNCT
ejpam-6739	106	37	t	t	PROPN
ejpam-6739	106	38	∣∣	∣∣	NUM
ejpam-6739	106	39	m	m	NOUN
ejpam-6739	106	40	)	)	PUNCT
ejpam-6739	106	41	∗	∗	NOUN
ejpam-6739	106	42	+	+	NUM
ejpam-6739	106	43	ss∗)+	ss∗)+	NOUN
ejpam-6739	106	44	λ2i	λ2i	X
ejpam-6739	106	45	≥	≥	X
ejpam-6739	106	46	0	0	NUM
ejpam-6739	106	47	for	for	ADP
ejpam-6739	106	48	all	all	DET
ejpam-6739	106	49	λ	λ	PROPN
ejpam-6739	106	50	>	>	X
ejpam-6739	106	51	0	0	NUM
ejpam-6739	106	52	.	.	PUNCT
ejpam-6739	107	1	as	as	ADP
ejpam-6739	107	2	the	the	DET
ejpam-6739	107	3	operator	operator	NOUN
ejpam-6739	107	4	1	1	NUM
ejpam-6739	107	5	∥t∥(t	∥t∥(t	ADJ
ejpam-6739	107	6	∣∣	∣∣	NUM
ejpam-6739	107	7	m	m	NOUN
ejpam-6739	107	8	)	)	PUNCT
ejpam-6739	107	9	∗	∗	NOUN
ejpam-6739	107	10	is	be	AUX
ejpam-6739	107	11	unitary	unitary	ADJ
ejpam-6739	107	12	,	,	PUNCT
ejpam-6739	107	13	we	we	PRON
ejpam-6739	107	14	get	get	VERB
ejpam-6739	107	15	for	for	ADP
ejpam-6739	107	16	λ	λ	NOUN
ejpam-6739	107	17	=	=	NOUN
ejpam-6739	107	18	1	1	NUM
ejpam-6739	107	19	that	that	PRON
ejpam-6739	107	20	ss∗	ss∗	VERB
ejpam-6739	107	21	≤	≤	NOUN
ejpam-6739	107	22	0	0	NUM
ejpam-6739	107	23	.	.	PUNCT
ejpam-6739	108	1	hence	hence	ADV
ejpam-6739	108	2	,	,	PUNCT
ejpam-6739	108	3	s	s	PART
ejpam-6739	108	4	=	=	NOUN
ejpam-6739	108	5	0	0	PROPN
ejpam-6739	108	6	.	.	PUNCT
ejpam-6739	109	1	this	this	PRON
ejpam-6739	109	2	shows	show	VERB
ejpam-6739	109	3	that	that	SCONJ
ejpam-6739	109	4	t	t	NOUN
ejpam-6739	109	5	=	=	PUNCT
ejpam-6739	109	6	(	(	PUNCT
ejpam-6739	109	7	t	t	X
ejpam-6739	109	8	∣∣	∣∣	NUM
ejpam-6739	109	9	m	m	VERB
ejpam-6739	109	10	0	0	NUM
ejpam-6739	109	11	0	0	NUM
ejpam-6739	109	12	r	r	NOUN
ejpam-6739	109	13	)	)	PUNCT
ejpam-6739	109	14	thus	thus	ADV
ejpam-6739	109	15	,	,	PUNCT
ejpam-6739	109	16	the	the	DET
ejpam-6739	109	17	subspace	subspace	NOUN
ejpam-6739	109	18	m	m	VERB
ejpam-6739	109	19	reduces	reduce	VERB
ejpam-6739	109	20	t.	t.	PROPN
ejpam-6739	109	21	b.	b.	PROPN
ejpam-6739	110	1	the	the	DET
ejpam-6739	110	2	operator	operator	NOUN
ejpam-6739	110	3	r∗zr	r∗zr	ADV
ejpam-6739	110	4	=	=	SYM
ejpam-6739	110	5	r∗(r∗2r2	r∗(r∗2r2	NOUN
ejpam-6739	110	6	−	−	PROPN
ejpam-6739	110	7	2λrr∗	2λrr∗	NUM
ejpam-6739	111	1	+	+	CCONJ
ejpam-6739	111	2	λ2i)r	λ2i)r	PRON
ejpam-6739	111	3	is	be	AUX
ejpam-6739	111	4	non	non	ADJ
ejpam-6739	111	5	-	-	ADJ
ejpam-6739	111	6	negative	negative	ADJ
ejpam-6739	111	7	for	for	ADP
ejpam-6739	111	8	all	all	DET
ejpam-6739	111	9	λ	λ	PROPN
ejpam-6739	111	10	>	>	X
ejpam-6739	111	11	0	0	NUM
ejpam-6739	111	12	.	.	PUNCT
ejpam-6739	112	1	thus	thus	ADV
ejpam-6739	112	2	,	,	PUNCT
ejpam-6739	112	3	the	the	DET
ejpam-6739	112	4	restriction	restriction	NOUN
ejpam-6739	112	5	r	r	NOUN
ejpam-6739	112	6	=	=	SYM
ejpam-6739	112	7	t	t	X
ejpam-6739	112	8	∣∣	∣∣	NUM
ejpam-6739	112	9	m⊥	m⊥	NOUN
ejpam-6739	112	10	is	be	AUX
ejpam-6739	112	11	also	also	ADV
ejpam-6739	112	12	quasi-∗-paranormal	quasi-∗-paranormal	PROPN
ejpam-6739	112	13	.	.	PUNCT
ejpam-6739	113	1	corollary	corollary	ADJ
ejpam-6739	113	2	3	3	X
ejpam-6739	113	3	.	.	PUNCT
ejpam-6739	114	1	let	let	AUX
ejpam-6739	114	2	t	t	PROPN
ejpam-6739	114	3	∈	∈	PROPN
ejpam-6739	114	4	b(h	b(h	PROPN
ejpam-6739	114	5	)	)	PUNCT
ejpam-6739	114	6	be	be	VERB
ejpam-6739	114	7	a	a	DET
ejpam-6739	114	8	compact	compact	ADJ
ejpam-6739	114	9	quasi-∗-paranormal	quasi-∗-paranormal	ADJ
ejpam-6739	114	10	operator	operator	NOUN
ejpam-6739	114	11	.	.	PUNCT
ejpam-6739	115	1	then	then	ADV
ejpam-6739	115	2	,	,	PUNCT
ejpam-6739	115	3	the	the	DET
ejpam-6739	115	4	subspace	subspace	NOUN
ejpam-6739	115	5	m	m	NOUN
ejpam-6739	115	6	=	=	NOUN
ejpam-6739	115	7	n(∥t∥2i	n(∥t∥2i	PROPN
ejpam-6739	115	8	−	−	PROPN
ejpam-6739	115	9	tt	tt	PROPN
ejpam-6739	115	10	∗	∗	NOUN
ejpam-6739	115	11	)	)	PUNCT
ejpam-6739	115	12	is	be	AUX
ejpam-6739	115	13	reducing	reduce	VERB
ejpam-6739	115	14	for	for	ADP
ejpam-6739	115	15	t.	t.	NOUN
ejpam-6739	115	16	proof	proof	NOUN
ejpam-6739	115	17	.	.	PUNCT
ejpam-6739	116	1	by	by	ADP
ejpam-6739	116	2	the	the	DET
ejpam-6739	116	3	hypothesis	hypothesis	NOUN
ejpam-6739	116	4	,	,	PUNCT
ejpam-6739	116	5	the	the	DET
ejpam-6739	116	6	operator	operator	NOUN
ejpam-6739	116	7	tt	tt	PROPN
ejpam-6739	116	8	∗	∗	NOUN
ejpam-6739	116	9	is	be	AUX
ejpam-6739	116	10	also	also	ADV
ejpam-6739	116	11	compact	compact	ADJ
ejpam-6739	116	12	.	.	PUNCT
ejpam-6739	117	1	then	then	ADV
ejpam-6739	117	2	,	,	PUNCT
ejpam-6739	117	3	m	m	PROPN
ejpam-6739	117	4	is	be	AUX
ejpam-6739	117	5	a	a	DET
ejpam-6739	117	6	nonzero	nonzero	ADJ
ejpam-6739	117	7	finite	finite	ADJ
ejpam-6739	117	8	dimensional	dimensional	ADJ
ejpam-6739	117	9	subspace	subspace	NOUN
ejpam-6739	117	10	by	by	ADP
ejpam-6739	117	11	fredholm	fredholm	NOUN
ejpam-6739	117	12	alternative	alternative	NOUN
ejpam-6739	117	13	.	.	PUNCT
ejpam-6739	118	1	the	the	DET
ejpam-6739	118	2	desired	desire	VERB
ejpam-6739	118	3	result	result	NOUN
ejpam-6739	118	4	follows	follow	VERB
ejpam-6739	118	5	then	then	ADV
ejpam-6739	118	6	by	by	ADP
ejpam-6739	118	7	theorem	theorem	NOUN
ejpam-6739	118	8	2	2	NUM
ejpam-6739	118	9	.	.	NOUN
ejpam-6739	118	10	3	3	NUM
ejpam-6739	118	11	.	.	X
ejpam-6739	119	1	absolutely	absolutely	ADV
ejpam-6739	119	2	norm	norm	VERB
ejpam-6739	119	3	attaining	attain	VERB
ejpam-6739	119	4	quasi-*-paranormal	quasi-*-paranormal	ADJ
ejpam-6739	119	5	operators	operator	NOUN
ejpam-6739	119	6	in	in	ADP
ejpam-6739	119	7	the	the	DET
ejpam-6739	119	8	sequel	sequel	NOUN
ejpam-6739	119	9	,	,	PUNCT
ejpam-6739	119	10	we	we	PRON
ejpam-6739	119	11	present	present	VERB
ejpam-6739	119	12	certain	certain	ADJ
ejpam-6739	119	13	structure	structure	NOUN
ejpam-6739	119	14	results	result	NOUN
ejpam-6739	119	15	on	on	ADP
ejpam-6739	119	16	the	the	DET
ejpam-6739	119	17	absolutely	absolutely	ADV
ejpam-6739	119	18	norm	norm	NOUN
ejpam-6739	119	19	attaining	attain	VERB
ejpam-6739	119	20	quasi-∗-paranormal	quasi-∗-paranormal	ADJ
ejpam-6739	119	21	operators	operator	NOUN
ejpam-6739	119	22	as	as	ADP
ejpam-6739	119	23	an	an	DET
ejpam-6739	119	24	extension	extension	NOUN
ejpam-6739	119	25	of	of	ADP
ejpam-6739	119	26	certain	certain	ADJ
ejpam-6739	119	27	results	result	NOUN
ejpam-6739	119	28	given	give	VERB
ejpam-6739	119	29	in	in	ADP
ejpam-6739	119	30	[	[	X
ejpam-6739	119	31	3	3	NUM
ejpam-6739	119	32	]	]	PUNCT
ejpam-6739	119	33	and	and	CCONJ
ejpam-6739	119	34	[	[	X
ejpam-6739	119	35	18	18	NUM
ejpam-6739	119	36	]	]	PUNCT
ejpam-6739	119	37	.	.	PUNCT
ejpam-6739	120	1	a.	a.	PROPN
ejpam-6739	120	2	nasli	nasli	PROPN
ejpam-6739	120	3	bakir	bakir	VERB
ejpam-6739	120	4	et	et	PROPN
ejpam-6739	120	5	al	al	PROPN
ejpam-6739	120	6	.	.	PUNCT
ejpam-6739	120	7	/	/	SYM
ejpam-6739	120	8	eur	eur	PROPN
ejpam-6739	120	9	.	.	PUNCT
ejpam-6739	121	1	j.	j.	PROPN
ejpam-6739	121	2	pure	pure	PROPN
ejpam-6739	121	3	appl	appl	PROPN
ejpam-6739	121	4	.	.	PROPN
ejpam-6739	121	5	math	math	PROPN
ejpam-6739	121	6	,	,	PUNCT
ejpam-6739	121	7	18	18	NUM
ejpam-6739	121	8	(	(	PUNCT
ejpam-6739	121	9	4	4	NUM
ejpam-6739	121	10	)	)	PUNCT
ejpam-6739	121	11	(	(	PUNCT
ejpam-6739	121	12	2025	2025	NUM
ejpam-6739	121	13	)	)	PUNCT
ejpam-6739	121	14	,	,	PUNCT
ejpam-6739	121	15	6739	6739	NUM
ejpam-6739	121	16	7	7	NUM
ejpam-6739	121	17	of	of	ADP
ejpam-6739	121	18	10	10	NUM
ejpam-6739	121	19	definition	definition	NOUN
ejpam-6739	121	20	3	3	NUM
ejpam-6739	121	21	.	.	PUNCT
ejpam-6739	122	1	[	[	X
ejpam-6739	122	2	4	4	X
ejpam-6739	122	3	]	]	X
ejpam-6739	122	4	an	an	DET
ejpam-6739	122	5	operator	operator	NOUN
ejpam-6739	122	6	t	t	PROPN
ejpam-6739	122	7	∈	∈	PROPN
ejpam-6739	122	8	b(h	b(h	PROPN
ejpam-6739	122	9	)	)	PUNCT
ejpam-6739	122	10	is	be	AUX
ejpam-6739	122	11	said	say	VERB
ejpam-6739	122	12	to	to	PART
ejpam-6739	122	13	be	be	AUX
ejpam-6739	122	14	absolutely	absolutely	ADV
ejpam-6739	122	15	norm	norm	ADJ
ejpam-6739	122	16	attaining	attain	VERB
ejpam-6739	122	17	,	,	PUNCT
ejpam-6739	122	18	briefly	briefly	ADV
ejpam-6739	122	19	an	an	DET
ejpam-6739	122	20	-operator	-operator	NOUN
ejpam-6739	122	21	,	,	PUNCT
ejpam-6739	122	22	if	if	SCONJ
ejpam-6739	122	23	the	the	DET
ejpam-6739	122	24	restriction	restriction	NOUN
ejpam-6739	122	25	t	t	X
ejpam-6739	122	26	∣∣	∣∣	NUM
ejpam-6739	122	27	v	v	NOUN
ejpam-6739	122	28	is	be	AUX
ejpam-6739	122	29	norm	norm	NOUN
ejpam-6739	122	30	attaining	attain	VERB
ejpam-6739	122	31	for	for	ADP
ejpam-6739	122	32	any	any	DET
ejpam-6739	122	33	closed	closed	ADJ
ejpam-6739	122	34	subspace	subspace	NOUN
ejpam-6739	122	35	v	v	ADP
ejpam-6739	122	36	⊂	⊂	PROPN
ejpam-6739	122	37	h	h	NOUN
ejpam-6739	122	38	,	,	PUNCT
ejpam-6739	122	39	that	that	ADV
ejpam-6739	122	40	is	is	ADV
ejpam-6739	122	41	,	,	PUNCT
ejpam-6739	122	42	there	there	PRON
ejpam-6739	122	43	exists	exist	VERB
ejpam-6739	122	44	a	a	DET
ejpam-6739	122	45	unit	unit	NOUN
ejpam-6739	122	46	vector	vector	NOUN
ejpam-6739	122	47	u	u	PROPN
ejpam-6739	122	48	∈	∈	PROPN
ejpam-6739	122	49	v	v	NOUN
ejpam-6739	122	50	for	for	ADP
ejpam-6739	122	51	which	which	PRON
ejpam-6739	122	52	∥t	∥t	PROPN
ejpam-6739	122	53	∣∣	∣∣	NUM
ejpam-6739	122	54	v	v	ADP
ejpam-6739	122	55	u∥	u∥	NOUN
ejpam-6739	123	1	=	=	PUNCT
ejpam-6739	123	2	∥tu∥	∥tu∥	NOUN
ejpam-6739	123	3	=	=	PUNCT
ejpam-6739	123	4	∥t	∥t	PROPN
ejpam-6739	123	5	∣∣	∣∣	NUM
ejpam-6739	123	6	v	v	PART
ejpam-6739	123	7	∥	∥	PRON
ejpam-6739	123	8	example	example	NOUN
ejpam-6739	123	9	4	4	NUM
ejpam-6739	123	10	.	.	PUNCT
ejpam-6739	124	1	[	[	X
ejpam-6739	124	2	7	7	X
ejpam-6739	124	3	]	]	X
ejpam-6739	124	4	the	the	DET
ejpam-6739	124	5	operator	operator	NOUN
ejpam-6739	124	6	s	s	AUX
ejpam-6739	124	7	defined	define	VERB
ejpam-6739	124	8	on	on	ADP
ejpam-6739	124	9	the	the	DET
ejpam-6739	124	10	hilbert	hilbert	NOUN
ejpam-6739	124	11	space	space	NOUN
ejpam-6739	124	12	ℓ2	ℓ2	PROPN
ejpam-6739	124	13	by	by	ADP
ejpam-6739	124	14	se1	se1	PROPN
ejpam-6739	124	15	=	=	SYM
ejpam-6739	124	16	1	1	NUM
ejpam-6739	124	17	2e1	2e1	NUM
ejpam-6739	124	18	and	and	CCONJ
ejpam-6739	124	19	sen	sen	PROPN
ejpam-6739	124	20	=	=	PROPN
ejpam-6739	124	21	en	en	X
ejpam-6739	124	22	,	,	PUNCT
ejpam-6739	124	23	(	(	PUNCT
ejpam-6739	124	24	n	n	CCONJ
ejpam-6739	124	25	≥	≥	NOUN
ejpam-6739	124	26	2	2	NUM
ejpam-6739	124	27	)	)	PUNCT
ejpam-6739	124	28	is	be	AUX
ejpam-6739	124	29	absolutely	absolutely	ADV
ejpam-6739	124	30	norm	norm	ADJ
ejpam-6739	124	31	attaining	attain	VERB
ejpam-6739	124	32	.	.	PUNCT
ejpam-6739	125	1	example	example	NOUN
ejpam-6739	125	2	5	5	NUM
ejpam-6739	125	3	.	.	PUNCT
ejpam-6739	126	1	in	in	ADP
ejpam-6739	126	2	[	[	X
ejpam-6739	126	3	3	3	NUM
ejpam-6739	126	4	]	]	PUNCT
ejpam-6739	126	5	,	,	PUNCT
ejpam-6739	126	6	author	author	NOUN
ejpam-6739	126	7	showed	show	VERB
ejpam-6739	126	8	that	that	SCONJ
ejpam-6739	126	9	the	the	DET
ejpam-6739	126	10	operator	operator	NOUN
ejpam-6739	126	11	a	a	DET
ejpam-6739	126	12	∈	∈	NOUN
ejpam-6739	126	13	l	l	NOUN
ejpam-6739	126	14	(	(	PUNCT
ejpam-6739	126	15	ℓ2	ℓ2	PROPN
ejpam-6739	126	16	⊕	⊕	PROPN
ejpam-6739	126	17	ℓ2	ℓ2	PROPN
ejpam-6739	126	18	)	)	PUNCT
ejpam-6739	126	19	defined	define	VERB
ejpam-6739	126	20	by	by	ADP
ejpam-6739	126	21	a(x	a(x	NOUN
ejpam-6739	126	22	,	,	PUNCT
ejpam-6739	126	23	y	y	NOUN
ejpam-6739	126	24	)	)	PUNCT
ejpam-6739	126	25	=	=	SYM
ejpam-6739	126	26	(	(	PUNCT
ejpam-6739	126	27	(	(	PUNCT
ejpam-6739	126	28	y1	y1	INTJ
ejpam-6739	126	29	,	,	PUNCT
ejpam-6739	126	30	x1	x1	PROPN
ejpam-6739	126	31	,	,	PUNCT
ejpam-6739	126	32	x2	x2	PROPN
ejpam-6739	126	33	2	2	NUM
ejpam-6739	126	34	,	,	PUNCT
ejpam-6739	126	35	x3	x3	NOUN
ejpam-6739	126	36	3	3	NUM
ejpam-6739	126	37	,	,	PUNCT
ejpam-6739	126	38	...	...	PUNCT
ejpam-6739	126	39	,	,	PUNCT
ejpam-6739	126	40	xn	xn	PROPN
ejpam-6739	126	41	n	n	PROPN
ejpam-6739	126	42	,	,	PUNCT
ejpam-6739	126	43	....	....	PUNCT
ejpam-6739	126	44	)	)	PUNCT
ejpam-6739	126	45	,	,	PUNCT
ejpam-6739	126	46	(	(	PUNCT
ejpam-6739	126	47	y2	y2	PROPN
ejpam-6739	126	48	,	,	PUNCT
ejpam-6739	126	49	y3	y3	PROPN
ejpam-6739	126	50	,	,	PUNCT
ejpam-6739	126	51	....	....	PUNCT
ejpam-6739	126	52	,	,	PUNCT
ejpam-6739	126	53	yn	yn	PROPN
ejpam-6739	126	54	,	,	PUNCT
ejpam-6739	126	55	yn+1	yn+1	PROPN
ejpam-6739	126	56	,	,	PUNCT
ejpam-6739	126	57	....	....	PUNCT
ejpam-6739	126	58	)	)	PUNCT
ejpam-6739	126	59	)	)	PUNCT
ejpam-6739	126	60	for	for	ADP
ejpam-6739	126	61	all	all	PRON
ejpam-6739	126	62	x	x	X
ejpam-6739	126	63	=	=	SYM
ejpam-6739	126	64	(	(	PUNCT
ejpam-6739	126	65	xk)k≥1	xk)k≥1	NOUN
ejpam-6739	126	66	,	,	PUNCT
ejpam-6739	126	67	y	y	PROPN
ejpam-6739	126	68	=	=	SYM
ejpam-6739	126	69	(	(	PUNCT
ejpam-6739	126	70	yk)k≥1	yk)k≥1	NOUN
ejpam-6739	126	71	∈	∈	PROPN
ejpam-6739	126	72	ℓ2	ℓ2	NOUN
ejpam-6739	126	73	,	,	PUNCT
ejpam-6739	126	74	is	be	AUX
ejpam-6739	126	75	not	not	PART
ejpam-6739	126	76	absolutely	absolutely	ADV
ejpam-6739	126	77	norm	norm	VERB
ejpam-6739	126	78	attaining	attain	VERB
ejpam-6739	126	79	on	on	ADP
ejpam-6739	126	80	ℓ2	ℓ2	PROPN
ejpam-6739	126	81	⊕	⊕	PROPN
ejpam-6739	126	82	ℓ2	ℓ2	PROPN
ejpam-6739	126	83	.	.	PUNCT
ejpam-6739	127	1	theorem	theorem	NOUN
ejpam-6739	127	2	3	3	X
ejpam-6739	127	3	.	.	PUNCT
ejpam-6739	128	1	let	let	AUX
ejpam-6739	128	2	t	t	PROPN
ejpam-6739	128	3	∈	∈	PROPN
ejpam-6739	128	4	b(h	b(h	PROPN
ejpam-6739	128	5	)	)	PUNCT
ejpam-6739	128	6	be	be	VERB
ejpam-6739	128	7	an	an	DET
ejpam-6739	128	8	absolutely	absolutely	ADV
ejpam-6739	128	9	norm	norm	NOUN
ejpam-6739	128	10	attaining	attain	VERB
ejpam-6739	128	11	quasi-∗-paranormal	quasi-∗-paranormal	ADJ
ejpam-6739	128	12	operator	operator	NOUN
ejpam-6739	128	13	.	.	PUNCT
ejpam-6739	129	1	if	if	SCONJ
ejpam-6739	129	2	σess(|t	σess(|t	PRON
ejpam-6739	129	3	|	|	ADV
ejpam-6739	129	4	)	)	PUNCT
ejpam-6739	129	5	=	=	PUNCT
ejpam-6739	129	6	{	{	PUNCT
ejpam-6739	129	7	∥t∥	∥t∥	ADV
ejpam-6739	129	8	}	}	PUNCT
ejpam-6739	129	9	,	,	PUNCT
ejpam-6739	129	10	then	then	ADV
ejpam-6739	129	11	t	t	PROPN
ejpam-6739	129	12	=	=	SYM
ejpam-6739	129	13	(	(	PUNCT
ejpam-6739	129	14	∥t∥s	∥t∥s	NOUN
ejpam-6739	129	15	b	b	X
ejpam-6739	129	16	0	0	NUM
ejpam-6739	129	17	c	c	NOUN
ejpam-6739	129	18	)	)	PUNCT
ejpam-6739	129	19	under	under	ADP
ejpam-6739	129	20	the	the	DET
ejpam-6739	129	21	orthogonal	orthogonal	ADJ
ejpam-6739	129	22	decomposition	decomposition	NOUN
ejpam-6739	129	23	h	h	NOUN
ejpam-6739	130	1	=	=	NOUN
ejpam-6739	130	2	m	m	VERB
ejpam-6739	130	3	⊕m⊥	⊕m⊥	NOUN
ejpam-6739	130	4	,	,	PUNCT
ejpam-6739	130	5	where	where	SCONJ
ejpam-6739	130	6	1	1	X
ejpam-6739	130	7	.	.	PUNCT
ejpam-6739	130	8	s	s	PART
ejpam-6739	130	9	∈	∈	PROPN
ejpam-6739	130	10	b(m	b(m	PROPN
ejpam-6739	130	11	)	)	PUNCT
ejpam-6739	130	12	is	be	AUX
ejpam-6739	130	13	an	an	DET
ejpam-6739	130	14	isometry	isometry	NOUN
ejpam-6739	130	15	.	.	PUNCT
ejpam-6739	131	1	2	2	NUM
ejpam-6739	131	2	.	.	X
ejpam-6739	131	3	b∗s	b∗s	NUM
ejpam-6739	131	4	=	=	SYM
ejpam-6739	131	5	0	0	X
ejpam-6739	131	6	.	.	PUNCT
ejpam-6739	132	1	proof	proof	NOUN
ejpam-6739	132	2	.	.	PUNCT
ejpam-6739	133	1	1	1	X
ejpam-6739	133	2	.	.	X
ejpam-6739	133	3	let	let	AUX
ejpam-6739	133	4	t	t	NOUN
ejpam-6739	133	5	=	=	SYM
ejpam-6739	133	6	u	u	NOUN
ejpam-6739	133	7	|t	|t	VERB
ejpam-6739	133	8	|	|	ADV
ejpam-6739	133	9	be	be	AUX
ejpam-6739	133	10	the	the	DET
ejpam-6739	133	11	polar	polar	ADJ
ejpam-6739	133	12	decomposition	decomposition	NOUN
ejpam-6739	133	13	of	of	ADP
ejpam-6739	133	14	t.	t.	PROPN
ejpam-6739	133	15	then	then	ADV
ejpam-6739	133	16	,	,	PUNCT
ejpam-6739	133	17	for	for	ADP
ejpam-6739	133	18	all	all	PRON
ejpam-6739	133	19	u	u	PROPN
ejpam-6739	133	20	∈	∈	PROPN
ejpam-6739	133	21	m	m	PRON
ejpam-6739	133	22	,	,	PUNCT
ejpam-6739	133	23	we	we	PRON
ejpam-6739	133	24	get	get	VERB
ejpam-6739	133	25	tu	tu	PROPN
ejpam-6739	133	26	=	=	SYM
ejpam-6739	133	27	u	u	PROPN
ejpam-6739	133	28	|t	|t	VERB
ejpam-6739	133	29	|u	|u	ADJ
ejpam-6739	133	30	=	=	PUNCT
ejpam-6739	133	31	∥t∥uu	∥t∥uu	CCONJ
ejpam-6739	133	32	that	that	PRON
ejpam-6739	133	33	is	be	AUX
ejpam-6739	133	34	,	,	PUNCT
ejpam-6739	133	35	t	t	PROPN
ejpam-6739	133	36	∣∣	∣∣	NUM
ejpam-6739	134	1	m	m	NOUN
ejpam-6739	134	2	=	=	PUNCT
ejpam-6739	134	3	∥t∥u	∥t∥u	NOUN
ejpam-6739	134	4	∣∣	∣∣	NUM
ejpam-6739	134	5	m	m	NOUN
ejpam-6739	134	6	=	=	PUNCT
ejpam-6739	134	7	∥t∥s	∥t∥s	NOUN
ejpam-6739	134	8	since	since	SCONJ
ejpam-6739	134	9	u	u	PRON
ejpam-6739	134	10	∣∣	∣∣	NUM
ejpam-6739	134	11	m	m	VERB
ejpam-6739	134	12	is	be	AUX
ejpam-6739	134	13	an	an	DET
ejpam-6739	134	14	isometry	isometry	NOUN
ejpam-6739	134	15	,	,	PUNCT
ejpam-6739	134	16	the	the	DET
ejpam-6739	134	17	operator	operator	NOUN
ejpam-6739	134	18	s	s	VERB
ejpam-6739	134	19	so	so	ADV
ejpam-6739	134	20	is	be	AUX
ejpam-6739	134	21	.	.	PUNCT
ejpam-6739	135	1	2	2	X
ejpam-6739	135	2	.	.	X
ejpam-6739	135	3	the	the	DET
ejpam-6739	135	4	subspace	subspace	NOUN
ejpam-6739	135	5	m	m	VERB
ejpam-6739	135	6	is	be	AUX
ejpam-6739	135	7	invariant	invariant	ADJ
ejpam-6739	135	8	for	for	ADP
ejpam-6739	135	9	t.	t.	NOUN
ejpam-6739	135	10	hence	hence	ADV
ejpam-6739	135	11	,	,	PUNCT
ejpam-6739	135	12	on	on	ADP
ejpam-6739	135	13	h	h	NOUN
ejpam-6739	136	1	=	=	NOUN
ejpam-6739	136	2	m	m	VERB
ejpam-6739	136	3	⊕m⊥	⊕m⊥	NOUN
ejpam-6739	136	4	,	,	PUNCT
ejpam-6739	136	5	t	t	PROPN
ejpam-6739	136	6	=	=	PUNCT
ejpam-6739	136	7	(	(	PUNCT
ejpam-6739	136	8	∥t∥s	∥t∥s	NOUN
ejpam-6739	136	9	b	b	X
ejpam-6739	136	10	0	0	NUM
ejpam-6739	136	11	c	c	NOUN
ejpam-6739	136	12	)	)	PUNCT
ejpam-6739	136	13	since	since	SCONJ
ejpam-6739	136	14	t	t	PROPN
ejpam-6739	136	15	is	be	AUX
ejpam-6739	136	16	quasi-∗-paranormal	quasi-∗-paranormal	PROPN
ejpam-6739	136	17	,	,	PUNCT
ejpam-6739	136	18	we	we	PRON
ejpam-6739	136	19	get	get	VERB
ejpam-6739	136	20	for	for	ADP
ejpam-6739	136	21	all	all	DET
ejpam-6739	136	22	λ	λ	PROPN
ejpam-6739	136	23	>	>	X
ejpam-6739	136	24	0	0	PROPN
ejpam-6739	136	25	,	,	PUNCT
ejpam-6739	136	26	t	t	PROPN
ejpam-6739	136	27	∗(t	∗(t	PROPN
ejpam-6739	136	28	∗2	∗2	PROPN
ejpam-6739	136	29	t	t	NOUN
ejpam-6739	136	30	2	2	NUM
ejpam-6739	136	31	−	−	PROPN
ejpam-6739	136	32	2λtt	2λtt	NUM
ejpam-6739	136	33	∗	∗	NOUN
ejpam-6739	136	34	+	+	CCONJ
ejpam-6739	136	35	λ2)t	λ2)t	NOUN
ejpam-6739	136	36	=	=	SYM
ejpam-6739	136	37	(	(	PUNCT
ejpam-6739	136	38	x	x	X
ejpam-6739	136	39	y	y	PROPN
ejpam-6739	136	40	z	z	PROPN
ejpam-6739	136	41	w	w	PROPN
ejpam-6739	136	42	)	)	PUNCT
ejpam-6739	136	43	≥	≥	NOUN
ejpam-6739	136	44	0	0	NUM
ejpam-6739	137	1	where	where	SCONJ
ejpam-6739	137	2	x	x	ADP
ejpam-6739	137	3	=	=	SYM
ejpam-6739	137	4	∥t∥2s∗(∥t∥4	∥t∥2s∗(∥t∥4	PROPN
ejpam-6739	137	5	+	+	CCONJ
ejpam-6739	137	6	λ2	λ2	PROPN
ejpam-6739	137	7	−	−	PROPN
ejpam-6739	137	8	2λ∥t∥2ss∗	2λ∥t∥2ss∗	NUM
ejpam-6739	137	9	−	−	PROPN
ejpam-6739	137	10	2λbb∗)s	2λbb∗)s	NUM
ejpam-6739	137	11	≥	≥	NOUN
ejpam-6739	137	12	0	0	NUM
ejpam-6739	137	13	and	and	CCONJ
ejpam-6739	137	14	for	for	ADP
ejpam-6739	137	15	some	some	DET
ejpam-6739	137	16	bounded	bound	VERB
ejpam-6739	137	17	linear	linear	PROPN
ejpam-6739	137	18	operators	operators	PROPN
ejpam-6739	137	19	y	y	PROPN
ejpam-6739	137	20	,	,	PUNCT
ejpam-6739	137	21	z	z	PROPN
ejpam-6739	137	22	,	,	PUNCT
ejpam-6739	137	23	w.	w.	PROPN
ejpam-6739	137	24	then	then	ADV
ejpam-6739	137	25	,	,	PUNCT
ejpam-6739	137	26	for	for	ADP
ejpam-6739	137	27	λ	λ	PROPN
ejpam-6739	137	28	=	=	SYM
ejpam-6739	137	29	∥t∥2	∥t∥2	PROPN
ejpam-6739	137	30	,	,	PUNCT
ejpam-6739	137	31	and	and	CCONJ
ejpam-6739	137	32	since	since	SCONJ
ejpam-6739	137	33	s	s	NOUN
ejpam-6739	137	34	is	be	AUX
ejpam-6739	137	35	an	an	DET
ejpam-6739	137	36	isometry	isometry	NOUN
ejpam-6739	137	37	,	,	PUNCT
ejpam-6739	137	38	s∗bb∗s	s∗bb∗s	CCONJ
ejpam-6739	137	39	=	=	SYM
ejpam-6739	137	40	(	(	PUNCT
ejpam-6739	137	41	b∗s)∗(b∗s	b∗s)∗(b∗s	PROPN
ejpam-6739	137	42	)	)	PUNCT
ejpam-6739	137	43	≤	≤	NUM
ejpam-6739	137	44	0	0	NUM
ejpam-6739	137	45	.	.	PUNCT
ejpam-6739	138	1	thus	thus	ADV
ejpam-6739	138	2	,	,	PUNCT
ejpam-6739	138	3	b∗s	b∗s	X
ejpam-6739	138	4	=	=	SYM
ejpam-6739	138	5	0	0	PROPN
ejpam-6739	138	6	since	since	SCONJ
ejpam-6739	138	7	b∗s	b∗s	NUM
ejpam-6739	138	8	is	be	AUX
ejpam-6739	138	9	a	a	DET
ejpam-6739	138	10	positive	positive	ADJ
ejpam-6739	138	11	operator	operator	NOUN
ejpam-6739	138	12	.	.	PUNCT
ejpam-6739	139	1	a.	a.	NOUN
ejpam-6739	139	2	nasli	nasli	PROPN
ejpam-6739	139	3	bakir	bakir	VERB
ejpam-6739	139	4	et	et	PROPN
ejpam-6739	139	5	al	al	PROPN
ejpam-6739	139	6	.	.	PUNCT
ejpam-6739	139	7	/	/	SYM
ejpam-6739	139	8	eur	eur	PROPN
ejpam-6739	139	9	.	.	PUNCT
ejpam-6739	140	1	j.	j.	PROPN
ejpam-6739	140	2	pure	pure	PROPN
ejpam-6739	140	3	appl	appl	PROPN
ejpam-6739	140	4	.	.	PROPN
ejpam-6739	140	5	math	math	PROPN
ejpam-6739	140	6	,	,	PUNCT
ejpam-6739	140	7	18	18	NUM
ejpam-6739	140	8	(	(	PUNCT
ejpam-6739	140	9	4	4	NUM
ejpam-6739	140	10	)	)	PUNCT
ejpam-6739	140	11	(	(	PUNCT
ejpam-6739	140	12	2025	2025	NUM
ejpam-6739	140	13	)	)	PUNCT
ejpam-6739	140	14	,	,	PUNCT
ejpam-6739	140	15	6739	6739	NUM
ejpam-6739	140	16	8	8	NUM
ejpam-6739	140	17	of	of	ADP
ejpam-6739	140	18	10	10	NUM
ejpam-6739	140	19	4	4	NUM
ejpam-6739	140	20	.	.	PUNCT
ejpam-6739	141	1	norm	norm	NOUN
ejpam-6739	141	2	attaining	attain	VERB
ejpam-6739	141	3	class	class	NOUN
ejpam-6739	141	4	ωn	ωn	NOUN
ejpam-6739	141	5	operators	operator	NOUN
ejpam-6739	141	6	definition	definition	NOUN
ejpam-6739	141	7	4	4	NUM
ejpam-6739	141	8	.	.	PUNCT
ejpam-6739	142	1	[	[	X
ejpam-6739	142	2	13	13	NUM
ejpam-6739	142	3	]	]	X
ejpam-6739	142	4	an	an	DET
ejpam-6739	142	5	operator	operator	NOUN
ejpam-6739	142	6	t	t	PROPN
ejpam-6739	142	7	∈	∈	PROPN
ejpam-6739	142	8	b(h	b(h	PROPN
ejpam-6739	142	9	)	)	PUNCT
ejpam-6739	142	10	is	be	AUX
ejpam-6739	142	11	said	say	VERB
ejpam-6739	142	12	to	to	PART
ejpam-6739	142	13	be	be	AUX
ejpam-6739	142	14	quasi	quasi	ADJ
ejpam-6739	142	15	-	-	ADJ
ejpam-6739	142	16	normal	normal	ADJ
ejpam-6739	142	17	of	of	ADP
ejpam-6739	142	18	order	order	NOUN
ejpam-6739	142	19	n	n	NOUN
ejpam-6739	142	20	for	for	ADP
ejpam-6739	142	21	some	some	DET
ejpam-6739	142	22	integer	integer	NOUN
ejpam-6739	142	23	n	n	CCONJ
ejpam-6739	142	24	,	,	PUNCT
ejpam-6739	142	25	or	or	CCONJ
ejpam-6739	142	26	a	a	DET
ejpam-6739	142	27	class	class	NOUN
ejpam-6739	142	28	ωn	ωn	NOUN
ejpam-6739	142	29	operator	operator	NOUN
ejpam-6739	142	30	if	if	SCONJ
ejpam-6739	142	31	tt	tt	PROPN
ejpam-6739	142	32	⋆ntn	⋆ntn	NOUN
ejpam-6739	142	33	=	=	PROPN
ejpam-6739	142	34	t	t	PROPN
ejpam-6739	142	35	⋆ntn+1	⋆ntn+1	NOUN
ejpam-6739	142	36	.	.	PUNCT
ejpam-6739	143	1	example	example	NOUN
ejpam-6739	143	2	6	6	NUM
ejpam-6739	143	3	.	.	PUNCT
ejpam-6739	144	1	[	[	X
ejpam-6739	144	2	13	13	NUM
ejpam-6739	144	3	]	]	PUNCT
ejpam-6739	144	4	matrices	matrix	NOUN
ejpam-6739	144	5	s	s	PART
ejpam-6739	144	6	=	=	PUNCT
ejpam-6739	144	7	(	(	PUNCT
ejpam-6739	144	8	1	1	NUM
ejpam-6739	144	9	0	0	NUM
ejpam-6739	144	10	0	0	NUM
ejpam-6739	144	11	0	0	NUM
ejpam-6739	144	12	)	)	PUNCT
ejpam-6739	144	13	and	and	CCONJ
ejpam-6739	144	14	b	b	X
ejpam-6739	144	15	=	=	SYM
ejpam-6739	144	16	(	(	PUNCT
ejpam-6739	144	17	0	0	NUM
ejpam-6739	144	18	0	0	NUM
ejpam-6739	144	19	1	1	NUM
ejpam-6739	144	20	0	0	NUM
ejpam-6739	144	21	)	)	PUNCT
ejpam-6739	144	22	are	be	AUX
ejpam-6739	144	23	quasi	quasi	ADJ
ejpam-6739	144	24	-	-	ADJ
ejpam-6739	144	25	normal	normal	ADJ
ejpam-6739	144	26	operators	operator	NOUN
ejpam-6739	144	27	of	of	ADP
ejpam-6739	144	28	order	order	NOUN
ejpam-6739	144	29	2	2	NUM
ejpam-6739	144	30	,	,	PUNCT
ejpam-6739	144	31	i.e.	i.e.	X
ejpam-6739	144	32	,	,	PUNCT
ejpam-6739	144	33	b	b	NOUN
ejpam-6739	144	34	,	,	PUNCT
ejpam-6739	144	35	s	s	NOUN
ejpam-6739	144	36	∈	∈	PROPN
ejpam-6739	144	37	ω2	ω2	NOUN
ejpam-6739	144	38	.	.	PUNCT
ejpam-6739	145	1	in	in	ADP
ejpam-6739	145	2	the	the	DET
ejpam-6739	145	3	following	following	NOUN
ejpam-6739	145	4	,	,	PUNCT
ejpam-6739	145	5	we	we	PRON
ejpam-6739	145	6	provide	provide	VERB
ejpam-6739	145	7	invaraiant	invaraiant	NOUN
ejpam-6739	145	8	subspaces	subspace	NOUN
ejpam-6739	145	9	for	for	ADP
ejpam-6739	145	10	operators	operator	NOUN
ejpam-6739	145	11	belonging	belong	VERB
ejpam-6739	145	12	to	to	ADP
ejpam-6739	145	13	class	class	NOUN
ejpam-6739	145	14	ωn	ωn	NOUN
ejpam-6739	145	15	.	.	PUNCT
ejpam-6739	145	16	theorem	theorem	NOUN
ejpam-6739	145	17	4	4	NUM
ejpam-6739	145	18	.	.	PUNCT
ejpam-6739	146	1	let	let	AUX
ejpam-6739	146	2	t	t	PROPN
ejpam-6739	146	3	∈	∈	PROPN
ejpam-6739	146	4	b(h	b(h	PROPN
ejpam-6739	146	5	)	)	PUNCT
ejpam-6739	146	6	be	be	VERB
ejpam-6739	146	7	quasi	quasi	ADJ
ejpam-6739	146	8	-	-	ADJ
ejpam-6739	146	9	normal	normal	ADJ
ejpam-6739	146	10	operator	operator	NOUN
ejpam-6739	146	11	of	of	ADP
ejpam-6739	146	12	order	order	NOUN
ejpam-6739	146	13	2	2	NUM
ejpam-6739	146	14	such	such	ADJ
ejpam-6739	146	15	that	that	SCONJ
ejpam-6739	146	16	t	t	PROPN
ejpam-6739	146	17	2	2	NUM
ejpam-6739	146	18	achieves	achieve	VERB
ejpam-6739	146	19	the	the	DET
ejpam-6739	146	20	norm	norm	NOUN
ejpam-6739	146	21	.	.	PUNCT
ejpam-6739	147	1	then	then	ADV
ejpam-6739	147	2	,	,	PUNCT
ejpam-6739	147	3	the	the	DET
ejpam-6739	147	4	subspace	subspace	NOUN
ejpam-6739	147	5	v	v	X
ejpam-6739	147	6	=	=	PUNCT
ejpam-6739	147	7	{	{	PUNCT
ejpam-6739	147	8	u	u	NOUN
ejpam-6739	147	9	∈	∈	PROPN
ejpam-6739	147	10	h	h	NOUN
ejpam-6739	147	11	:	:	PUNCT
ejpam-6739	147	12	∥t	∥t	ADJ
ejpam-6739	147	13	2u∥	2u∥	NOUN
ejpam-6739	147	14	=	=	SYM
ejpam-6739	147	15	∥t	∥t	ADJ
ejpam-6739	147	16	2∥∥u∥	2∥∥u∥	NOUN
ejpam-6739	147	17	}	}	PUNCT
ejpam-6739	147	18	is	be	AUX
ejpam-6739	147	19	invariant	invariant	ADJ
ejpam-6739	147	20	for	for	ADP
ejpam-6739	147	21	t	t	PROPN
ejpam-6739	147	22	2	2	NUM
ejpam-6739	147	23	.	.	PUNCT
ejpam-6739	148	1	proof	proof	NOUN
ejpam-6739	148	2	.	.	PUNCT
ejpam-6739	149	1	since	since	SCONJ
ejpam-6739	149	2	t	t	PROPN
ejpam-6739	149	3	∈	∈	PROPN
ejpam-6739	149	4	ω2	ω2	PROPN
ejpam-6739	149	5	,	,	PUNCT
ejpam-6739	149	6	tt	tt	PROPN
ejpam-6739	149	7	⋆2	⋆2	X
ejpam-6739	149	8	t	t	PROPN
ejpam-6739	149	9	2	2	NUM
ejpam-6739	149	10	=	=	SYM
ejpam-6739	149	11	t	t	PROPN
ejpam-6739	149	12	⋆2	⋆2	PROPN
ejpam-6739	149	13	t	t	PROPN
ejpam-6739	149	14	3	3	NUM
ejpam-6739	149	15	.	.	PUNCT
ejpam-6739	149	16	then	then	ADV
ejpam-6739	149	17	,	,	PUNCT
ejpam-6739	149	18	(	(	PUNCT
ejpam-6739	149	19	t	t	PROPN
ejpam-6739	149	20	∗2	∗2	AUX
ejpam-6739	149	21	t	t	PROPN
ejpam-6739	149	22	2)2	2)2	NUM
ejpam-6739	149	23	=	=	SYM
ejpam-6739	149	24	t	t	NOUN
ejpam-6739	149	25	∗4	∗4	PROPN
ejpam-6739	149	26	t	t	PROPN
ejpam-6739	149	27	4	4	NUM
ejpam-6739	149	28	.	.	PUNCT
ejpam-6739	150	1	hence	hence	ADV
ejpam-6739	150	2	,	,	PUNCT
ejpam-6739	150	3	for	for	ADP
ejpam-6739	150	4	all	all	DET
ejpam-6739	150	5	u	u	PROPN
ejpam-6739	150	6	∈	∈	PROPN
ejpam-6739	150	7	h	h	NOUN
ejpam-6739	150	8	,	,	PUNCT
ejpam-6739	150	9	∥t	∥t	PROPN
ejpam-6739	150	10	∗2	∗2	PROPN
ejpam-6739	150	11	t	t	NOUN
ejpam-6739	150	12	2u∥	2u∥	NOUN
ejpam-6739	150	13	=	=	SYM
ejpam-6739	150	14	∥t	∥t	PROPN
ejpam-6739	150	15	4u∥.	4u∥.	PROPN
ejpam-6739	150	16	by	by	ADP
ejpam-6739	150	17	cauchy	cauchy	PROPN
ejpam-6739	150	18	-	-	PUNCT
ejpam-6739	150	19	schwarz	schwarz	PROPN
ejpam-6739	150	20	’s	’s	PART
ejpam-6739	150	21	inequality	inequality	NOUN
ejpam-6739	150	22	,	,	PUNCT
ejpam-6739	150	23	∥t	∥t	PROPN
ejpam-6739	150	24	2u∥2	2u∥2	NOUN
ejpam-6739	150	25	=	=	SYM
ejpam-6739	150	26	⟨t	⟨t	X
ejpam-6739	150	27	2u	2u	NOUN
ejpam-6739	150	28	,	,	PUNCT
ejpam-6739	150	29	t	t	PROPN
ejpam-6739	150	30	2u⟩	2u⟩	NUM
ejpam-6739	150	31	=	=	SYM
ejpam-6739	150	32	⟨t	⟨t	X
ejpam-6739	150	33	∗2	∗2	PROPN
ejpam-6739	150	34	t	t	NOUN
ejpam-6739	150	35	2u	2u	NOUN
ejpam-6739	150	36	,	,	PUNCT
ejpam-6739	150	37	u⟩	u⟩	VERB
ejpam-6739	150	38	≤	≤	NUM
ejpam-6739	151	1	∥t	∥t	PROPN
ejpam-6739	151	2	∗2	∗2	PROPN
ejpam-6739	151	3	t	t	NOUN
ejpam-6739	151	4	2u∥∥u∥	2u∥∥u∥	NUM
ejpam-6739	151	5	≤	≤	NOUN
ejpam-6739	152	1	∥t	∥t	ADJ
ejpam-6739	152	2	4u∥∥u∥	4u∥∥u∥	NUM
ejpam-6739	152	3	≤	≤	NOUN
ejpam-6739	152	4	∥t	∥t	ADJ
ejpam-6739	152	5	2(t	2(t	NUM
ejpam-6739	152	6	2u)∥∥u∥	2u)∥∥u∥	NUM
ejpam-6739	152	7	≤	≤	NUM
ejpam-6739	152	8	∥t	∥t	PROPN
ejpam-6739	152	9	2∥∥t	2∥∥t	PROPN
ejpam-6739	152	10	2u∥∥u∥	2u∥∥u∥	NUM
ejpam-6739	152	11	that	that	PRON
ejpam-6739	152	12	is	be	AUX
ejpam-6739	152	13	for	for	ADP
ejpam-6739	152	14	all	all	PRON
ejpam-6739	152	15	u	u	NOUN
ejpam-6739	152	16	∈	∈	PROPN
ejpam-6739	152	17	v	v	NOUN
ejpam-6739	152	18	,	,	PUNCT
ejpam-6739	152	19	∥t	∥t	ADJ
ejpam-6739	152	20	2∥2∥u∥	2∥2∥u∥	NOUN
ejpam-6739	152	21	≤	≤	X
ejpam-6739	152	22	∥t	∥t	ADJ
ejpam-6739	152	23	4u∥	4u∥	NOUN
ejpam-6739	152	24	≤	≤	PUNCT
ejpam-6739	153	1	∥t	∥t	ADJ
ejpam-6739	153	2	2∥2∥u∥	2∥2∥u∥	NOUN
ejpam-6739	153	3	since	since	SCONJ
ejpam-6739	153	4	∥t	∥t	ADJ
ejpam-6739	153	5	2u∥	2u∥	NOUN
ejpam-6739	153	6	=	=	SYM
ejpam-6739	153	7	∥t	∥t	NUM
ejpam-6739	153	8	2∥∥u∥	2∥∥u∥	NOUN
ejpam-6739	153	9	,	,	PUNCT
ejpam-6739	153	10	u	u	PROPN
ejpam-6739	153	11	∈	∈	PROPN
ejpam-6739	153	12	v.	v.	CCONJ
ejpam-6739	153	13	thus	thus	ADV
ejpam-6739	153	14	,	,	PUNCT
ejpam-6739	153	15	∥t	∥t	ADJ
ejpam-6739	153	16	4u∥	4u∥	NOUN
ejpam-6739	153	17	=	=	SYM
ejpam-6739	154	1	∥t	∥t	PROPN
ejpam-6739	154	2	2(t	2(t	NUM
ejpam-6739	154	3	2u)∥	2u)∥	NUM
ejpam-6739	154	4	=	=	SYM
ejpam-6739	154	5	∥t	∥t	ADJ
ejpam-6739	154	6	2∥2∥u∥	2∥2∥u∥	NOUN
ejpam-6739	154	7	=	=	SYM
ejpam-6739	154	8	∥t	∥t	PROPN
ejpam-6739	154	9	2∥∥t	2∥∥t	NUM
ejpam-6739	154	10	2u∥	2u∥	NOUN
ejpam-6739	154	11	for	for	ADP
ejpam-6739	154	12	each	each	DET
ejpam-6739	154	13	u	u	NOUN
ejpam-6739	154	14	∈	∈	PROPN
ejpam-6739	154	15	v.	v.	ADP
ejpam-6739	154	16	this	this	PRON
ejpam-6739	154	17	achieves	achieve	VERB
ejpam-6739	154	18	the	the	DET
ejpam-6739	154	19	proof	proof	NOUN
ejpam-6739	154	20	.	.	PUNCT
ejpam-6739	155	1	corollary	corollary	ADJ
ejpam-6739	155	2	4	4	NUM
ejpam-6739	155	3	.	.	PUNCT
ejpam-6739	156	1	let	let	VERB
ejpam-6739	156	2	t	t	PROPN
ejpam-6739	156	3	∈	∈	PROPN
ejpam-6739	156	4	b(h	b(h	PROPN
ejpam-6739	156	5	)	)	PUNCT
ejpam-6739	156	6	a	a	DET
ejpam-6739	156	7	class	class	NOUN
ejpam-6739	156	8	ω2	ω2	NOUN
ejpam-6739	156	9	operator	operator	NOUN
ejpam-6739	156	10	.	.	PUNCT
ejpam-6739	157	1	if	if	SCONJ
ejpam-6739	157	2	t	t	PROPN
ejpam-6739	157	3	∗2	∗2	PROPN
ejpam-6739	157	4	achieves	achieve	VERB
ejpam-6739	157	5	the	the	DET
ejpam-6739	157	6	norm	norm	NOUN
ejpam-6739	157	7	,	,	PUNCT
ejpam-6739	157	8	then	then	ADV
ejpam-6739	157	9	the	the	DET
ejpam-6739	157	10	subspace	subspace	NOUN
ejpam-6739	157	11	v∗	v∗	PROPN
ejpam-6739	157	12	=	=	SYM
ejpam-6739	157	13	{	{	PUNCT
ejpam-6739	157	14	u	u	NOUN
ejpam-6739	157	15	∈	∈	PROPN
ejpam-6739	157	16	h	h	NOUN
ejpam-6739	157	17	:	:	PUNCT
ejpam-6739	158	1	∥t	∥t	ADJ
ejpam-6739	158	2	∗2u∥	∗2u∥	PUNCT
ejpam-6739	158	3	=	=	SYM
ejpam-6739	158	4	∥t	∥t	ADJ
ejpam-6739	158	5	2∥∥u∥	2∥∥u∥	NOUN
ejpam-6739	158	6	}	}	PUNCT
ejpam-6739	158	7	is	be	AUX
ejpam-6739	158	8	invariant	invariant	ADJ
ejpam-6739	158	9	under	under	ADP
ejpam-6739	158	10	t	t	PROPN
ejpam-6739	158	11	∗2	∗2	PROPN
ejpam-6739	158	12	.	.	PROPN
ejpam-6739	159	1	5	5	NUM
ejpam-6739	159	2	.	.	X
ejpam-6739	159	3	conclusion	conclusion	NOUN
ejpam-6739	159	4	structures	structure	NOUN
ejpam-6739	159	5	of	of	ADP
ejpam-6739	159	6	norm	norm	NOUN
ejpam-6739	159	7	attaining	attain	VERB
ejpam-6739	159	8	quasi-∗-paranormal	quasi-∗-paranormal	PROPN
ejpam-6739	159	9	operators	operator	NOUN
ejpam-6739	159	10	and	and	CCONJ
ejpam-6739	159	11	class	class	NOUN
ejpam-6739	159	12	ωn	ωn	VERB
ejpam-6739	159	13	are	be	AUX
ejpam-6739	159	14	established	establish	VERB
ejpam-6739	159	15	in	in	ADP
ejpam-6739	159	16	the	the	DET
ejpam-6739	159	17	present	present	ADJ
ejpam-6739	159	18	manuscript	manuscript	NOUN
ejpam-6739	159	19	.	.	PUNCT
ejpam-6739	160	1	it	it	PRON
ejpam-6739	160	2	’s	’s	AUX
ejpam-6739	160	3	shown	show	VERB
ejpam-6739	160	4	that	that	SCONJ
ejpam-6739	160	5	elements	element	NOUN
ejpam-6739	160	6	of	of	ADP
ejpam-6739	160	7	these	these	DET
ejpam-6739	160	8	classes	class	NOUN
ejpam-6739	160	9	of	of	ADP
ejpam-6739	160	10	operators	operator	NOUN
ejpam-6739	160	11	admit	admit	VERB
ejpam-6739	160	12	at	at	ADP
ejpam-6739	160	13	least	least	ADJ
ejpam-6739	160	14	an	an	DET
ejpam-6739	160	15	invariant	invariant	ADJ
ejpam-6739	160	16	non	non	ADJ
ejpam-6739	160	17	trivial	trivial	ADJ
ejpam-6739	160	18	subspace	subspace	NOUN
ejpam-6739	160	19	.	.	PUNCT
ejpam-6739	161	1	some	some	DET
ejpam-6739	161	2	results	result	NOUN
ejpam-6739	161	3	depending	depend	VERB
ejpam-6739	161	4	on	on	ADP
ejpam-6739	161	5	compactness	compactness	NOUN
ejpam-6739	161	6	,	,	PUNCT
ejpam-6739	161	7	and	and	CCONJ
ejpam-6739	161	8	finite	finite	ADJ
ejpam-6739	161	9	dimension	dimension	NOUN
ejpam-6739	161	10	are	be	AUX
ejpam-6739	161	11	given	give	VERB
ejpam-6739	161	12	too	too	ADV
ejpam-6739	161	13	.	.	PUNCT
ejpam-6739	162	1	as	as	ADP
ejpam-6739	162	2	perspective	perspective	NOUN
ejpam-6739	162	3	works	work	NOUN
ejpam-6739	162	4	,	,	PUNCT
ejpam-6739	162	5	we	we	PRON
ejpam-6739	162	6	ask	ask	VERB
ejpam-6739	162	7	if	if	SCONJ
ejpam-6739	162	8	a	a	DET
ejpam-6739	162	9	such	such	ADJ
ejpam-6739	162	10	structure	structure	NOUN
ejpam-6739	162	11	can	can	AUX
ejpam-6739	162	12	be	be	AUX
ejpam-6739	162	13	provided	provide	VERB
ejpam-6739	162	14	for	for	ADP
ejpam-6739	162	15	large	large	ADJ
ejpam-6739	162	16	classes	class	NOUN
ejpam-6739	162	17	of	of	ADP
ejpam-6739	162	18	norm	norm	NOUN
ejpam-6739	162	19	achieving	achieve	VERB
ejpam-6739	162	20	k	k	PROPN
ejpam-6739	162	21	-	-	ADJ
ejpam-6739	162	22	quasi-∗-paranormal	quasi-∗-paranormal	ADJ
ejpam-6739	162	23	operators	operator	NOUN
ejpam-6739	162	24	,	,	PUNCT
ejpam-6739	162	25	and	and	CCONJ
ejpam-6739	162	26	class	class	NOUN
ejpam-6739	162	27	ωn	ωn	PROPN
ejpam-6739	162	28	,	,	PUNCT
ejpam-6739	162	29	k	k	PROPN
ejpam-6739	162	30	operators	operator	NOUN
ejpam-6739	162	31	defined	define	VERB
ejpam-6739	162	32	for	for	ADP
ejpam-6739	162	33	certain	certain	ADJ
ejpam-6739	162	34	integer	integer	NOUN
ejpam-6739	162	35	k	k	PROPN
ejpam-6739	162	36	as	as	ADP
ejpam-6739	162	37	t	t	PROPN
ejpam-6739	162	38	∗k(tt	∗k(tt	PROPN
ejpam-6739	163	1	⋆ntn	⋆ntn	VERB
ejpam-6739	163	2	−	−	PROPN
ejpam-6739	163	3	t	t	PROPN
ejpam-6739	164	1	⋆ntn+1)t	⋆ntn+1)t	NOUN
ejpam-6739	164	2	k	k	PROPN
ejpam-6739	164	3	=	=	PUNCT
ejpam-6739	164	4	0	0	PROPN
ejpam-6739	164	5	.	.	PUNCT
ejpam-6739	164	6	a.	a.	NOUN
ejpam-6739	164	7	nasli	nasli	PROPN
ejpam-6739	164	8	bakir	bakir	VERB
ejpam-6739	164	9	et	et	PROPN
ejpam-6739	164	10	al	al	PROPN
ejpam-6739	164	11	.	.	PUNCT
ejpam-6739	164	12	/	/	SYM
ejpam-6739	164	13	eur	eur	PROPN
ejpam-6739	164	14	.	.	PUNCT
ejpam-6739	165	1	j.	j.	PROPN
ejpam-6739	165	2	pure	pure	PROPN
ejpam-6739	165	3	appl	appl	PROPN
ejpam-6739	165	4	.	.	PROPN
ejpam-6739	165	5	math	math	PROPN
ejpam-6739	165	6	,	,	PUNCT
ejpam-6739	165	7	18	18	NUM
ejpam-6739	165	8	(	(	PUNCT
ejpam-6739	165	9	4	4	NUM
ejpam-6739	165	10	)	)	PUNCT
ejpam-6739	165	11	(	(	PUNCT
ejpam-6739	165	12	2025	2025	NUM
ejpam-6739	165	13	)	)	PUNCT
ejpam-6739	165	14	,	,	PUNCT
ejpam-6739	165	15	6739	6739	NUM
ejpam-6739	165	16	9	9	NUM
ejpam-6739	165	17	of	of	ADP
ejpam-6739	165	18	10	10	NUM
ejpam-6739	165	19	author	author	NOUN
ejpam-6739	165	20	contributions	contribution	NOUN
ejpam-6739	165	21	a.	a.	NOUN
ejpam-6739	165	22	nasli	nasli	PROPN
ejpam-6739	165	23	bakir	bakir	VERB
ejpam-6739	165	24	:	:	PUNCT
ejpam-6739	165	25	conceptualization	conceptualization	NOUN
ejpam-6739	165	26	,	,	PUNCT
ejpam-6739	165	27	methodology	methodology	NOUN
ejpam-6739	165	28	,	,	PUNCT
ejpam-6739	165	29	writing	writing	NOUN
ejpam-6739	165	30	—	—	PUNCT
ejpam-6739	165	31	original	original	ADJ
ejpam-6739	165	32	draft	draft	NOUN
ejpam-6739	165	33	,	,	PUNCT
ejpam-6739	165	34	supervision	supervision	NOUN
ejpam-6739	165	35	.	.	PUNCT
ejpam-6739	166	1	a.	a.	PROPN
ejpam-6739	166	2	fellag	fellag	PROPN
ejpam-6739	166	3	ariouat	ariouat	NOUN
ejpam-6739	166	4	:	:	PUNCT
ejpam-6739	167	1	investigation	investigation	NOUN
ejpam-6739	167	2	,	,	PUNCT
ejpam-6739	167	3	data	datum	NOUN
ejpam-6739	167	4	analysis	analysis	NOUN
ejpam-6739	167	5	,	,	PUNCT
ejpam-6739	167	6	writing	writing	NOUN
ejpam-6739	167	7	—	—	PUNCT
ejpam-6739	167	8	original	original	ADJ
ejpam-6739	167	9	draft	draft	NOUN
ejpam-6739	167	10	.	.	PUNCT
ejpam-6739	168	1	a.	a.	PROPN
ejpam-6739	168	2	benali	benali	PROPN
ejpam-6739	168	3	:	:	PUNCT
ejpam-6739	168	4	formal	formal	ADJ
ejpam-6739	168	5	analysis	analysis	NOUN
ejpam-6739	168	6	,	,	PUNCT
ejpam-6739	168	7	validation	validation	NOUN
ejpam-6739	168	8	,	,	PUNCT
ejpam-6739	168	9	writing	writing	NOUN
ejpam-6739	168	10	—	—	PUNCT
ejpam-6739	168	11	review	review	NOUN
ejpam-6739	168	12	and	and	CCONJ
ejpam-6739	168	13	editing	editing	NOUN
ejpam-6739	168	14	.	.	PUNCT
ejpam-6739	169	1	i.	i.	PROPN
ejpam-6739	169	2	alraddadi	alraddadi	PROPN
ejpam-6739	169	3	:	:	PUNCT
ejpam-6739	169	4	software	software	NOUN
ejpam-6739	169	5	,	,	PUNCT
ejpam-6739	169	6	visualization	visualization	NOUN
ejpam-6739	169	7	,	,	PUNCT
ejpam-6739	169	8	project	project	NOUN
ejpam-6739	169	9	administration	administration	NOUN
ejpam-6739	169	10	,	,	PUNCT
ejpam-6739	169	11	funding	funding	NOUN
ejpam-6739	169	12	acquisition	acquisition	NOUN
ejpam-6739	169	13	.	.	PUNCT
ejpam-6739	170	1	s.m	s.m	PROPN
ejpam-6739	170	2	.	.	PROPN
ejpam-6739	170	3	almuaddi	almuaddi	NOUN
ejpam-6739	170	4	:	:	PUNCT
ejpam-6739	171	1	resources	resource	NOUN
ejpam-6739	171	2	,	,	PUNCT
ejpam-6739	171	3	formal	formal	ADJ
ejpam-6739	171	4	analysis	analysis	NOUN
ejpam-6739	171	5	,	,	PUNCT
ejpam-6739	171	6	data	data	NOUN
ejpam-6739	171	7	curation	curation	NOUN
ejpam-6739	171	8	,	,	PUNCT
ejpam-6739	171	9	writing	writing	NOUN
ejpam-6739	171	10	—	—	PUNCT
ejpam-6739	171	11	review	review	NOUN
ejpam-6739	171	12	and	and	CCONJ
ejpam-6739	171	13	editing	editing	NOUN
ejpam-6739	171	14	.	.	PUNCT
ejpam-6739	172	1	all	all	DET
ejpam-6739	172	2	authors	author	NOUN
ejpam-6739	172	3	have	have	AUX
ejpam-6739	172	4	read	read	VERB
ejpam-6739	172	5	and	and	CCONJ
ejpam-6739	172	6	agreed	agree	VERB
ejpam-6739	172	7	to	to	ADP
ejpam-6739	172	8	the	the	DET
ejpam-6739	172	9	published	publish	VERB
ejpam-6739	172	10	version	version	NOUN
ejpam-6739	172	11	of	of	ADP
ejpam-6739	172	12	the	the	DET
ejpam-6739	172	13	manuscript	manuscript	NOUN
ejpam-6739	172	14	references	reference	NOUN
ejpam-6739	172	15	[	[	X
ejpam-6739	172	16	1	1	NUM
ejpam-6739	172	17	]	]	PUNCT
ejpam-6739	172	18	w.	w.	NOUN
ejpam-6739	172	19	schachermayer	schachermayer	PROPN
ejpam-6739	172	20	.	.	PUNCT
ejpam-6739	173	1	norm	norm	NOUN
ejpam-6739	173	2	attaining	attain	VERB
ejpam-6739	173	3	operators	operator	NOUN
ejpam-6739	173	4	on	on	ADP
ejpam-6739	173	5	some	some	DET
ejpam-6739	173	6	classical	classical	ADJ
ejpam-6739	173	7	banach	banach	NOUN
ejpam-6739	173	8	spaces	space	NOUN
ejpam-6739	173	9	.	.	PUNCT
ejpam-6739	174	1	pac	pac	PROPN
ejpam-6739	174	2	.	.	PUNCT
ejpam-6739	175	1	j.	j.	PROPN
ejpam-6739	175	2	math	math	PROPN
ejpam-6739	175	3	.	.	PROPN
ejpam-6739	175	4	,	,	PUNCT
ejpam-6739	175	5	105:427–438	105:427–438	NUM
ejpam-6739	175	6	,	,	PUNCT
ejpam-6739	175	7	1983	1983	NUM
ejpam-6739	175	8	.	.	PUNCT
ejpam-6739	176	1	[	[	X
ejpam-6739	176	2	2	2	X
ejpam-6739	176	3	]	]	X
ejpam-6739	176	4	g.	g.	PROPN
ejpam-6739	176	5	ramesh	ramesh	PROPN
ejpam-6739	176	6	and	and	CCONJ
ejpam-6739	176	7	d.	d.	PROPN
ejpam-6739	176	8	v.	v.	CCONJ
ejpam-6739	176	9	naido	naido	NOUN
ejpam-6739	176	10	.	.	PUNCT
ejpam-6739	177	1	on	on	ADP
ejpam-6739	177	2	absolutely	absolutely	ADV
ejpam-6739	177	3	norm	norm	VERB
ejpam-6739	177	4	attaining	attain	VERB
ejpam-6739	177	5	operators	operator	NOUN
ejpam-6739	177	6	.	.	PUNCT
ejpam-6739	178	1	math	math	NOUN
ejpam-6739	178	2	.	.	PUNCT
ejpam-6739	179	1	anal	anal	PROPN
ejpam-6739	179	2	.	.	PUNCT
ejpam-6739	179	3	appl	appl	PROPN
ejpam-6739	179	4	.	.	PROPN
ejpam-6739	179	5	,	,	PUNCT
ejpam-6739	179	6	465:547–556	465:547–556	NUM
ejpam-6739	179	7	,	,	PUNCT
ejpam-6739	179	8	2018	2018	NUM
ejpam-6739	179	9	.	.	PUNCT
ejpam-6739	180	1	preprint	preprint	NOUN
ejpam-6739	180	2	,	,	PUNCT
ejpam-6739	180	3	https://arxiv.org/abs/1801.02432.2016	https://arxiv.org/abs/1801.02432.2016	PROPN
ejpam-6739	180	4	.	.	PUNCT
ejpam-6739	181	1	[	[	X
ejpam-6739	181	2	3	3	NUM
ejpam-6739	181	3	]	]	X
ejpam-6739	181	4	n.	n.	PROPN
ejpam-6739	181	5	bala	bala	PROPN
ejpam-6739	181	6	.	.	PUNCT
ejpam-6739	181	7	representation	representation	NOUN
ejpam-6739	181	8	and	and	CCONJ
ejpam-6739	181	9	normality	normality	NOUN
ejpam-6739	181	10	of	of	ADP
ejpam-6739	181	11	∗-paranormal	∗-paranormal	ADJ
ejpam-6739	181	12	absolutely	absolutely	ADV
ejpam-6739	181	13	norm	norm	NOUN
ejpam-6739	181	14	attaining	attain	VERB
ejpam-6739	181	15	operators	operator	NOUN
ejpam-6739	181	16	.	.	PUNCT
ejpam-6739	182	1	acta	acta	PROPN
ejpam-6739	182	2	scient	scient	PROPN
ejpam-6739	182	3	.	.	PUNCT
ejpam-6739	183	1	math	math	NOUN
ejpam-6739	183	2	.	.	PUNCT
ejpam-6739	183	3	,	,	PUNCT
ejpam-6739	184	1	89:167–181	89:167–181	PROPN
ejpam-6739	184	2	,	,	PUNCT
ejpam-6739	184	3	2023	2023	NUM
ejpam-6739	184	4	.	.	PUNCT
ejpam-6739	185	1	[	[	X
ejpam-6739	185	2	4	4	X
ejpam-6739	185	3	]	]	PUNCT
ejpam-6739	185	4	x.	x.	NOUN
ejpam-6739	185	5	carvajal	carvajal	PROPN
ejpam-6739	185	6	and	and	CCONJ
ejpam-6739	185	7	w.	w.	PROPN
ejpam-6739	185	8	neves	neve	NOUN
ejpam-6739	185	9	.	.	PUNCT
ejpam-6739	186	1	operators	operator	NOUN
ejpam-6739	186	2	that	that	PRON
ejpam-6739	186	3	achieve	achieve	VERB
ejpam-6739	186	4	the	the	DET
ejpam-6739	186	5	norm	norm	NOUN
ejpam-6739	186	6	.	.	PUNCT
ejpam-6739	187	1	int	int	NOUN
ejpam-6739	187	2	.	.	PUNCT
ejpam-6739	188	1	equa	equa	NOUN
ejpam-6739	188	2	.	.	PUNCT
ejpam-6739	189	1	oper	oper	PROPN
ejpam-6739	189	2	.	.	PROPN
ejpam-6739	189	3	theory	theory	NOUN
ejpam-6739	189	4	,	,	PUNCT
ejpam-6739	189	5	72:179–195	72:179–195	NUM
ejpam-6739	189	6	,	,	PUNCT
ejpam-6739	189	7	2012	2012	NUM
ejpam-6739	189	8	.	.	PUNCT
ejpam-6739	190	1	[	[	X
ejpam-6739	190	2	5	5	NUM
ejpam-6739	190	3	]	]	X
ejpam-6739	190	4	g.	g.	PROPN
ejpam-6739	190	5	ramesh	ramesh	PROPN
ejpam-6739	190	6	.	.	PUNCT
ejpam-6739	191	1	absolutely	absolutely	ADV
ejpam-6739	191	2	norm	norm	VERB
ejpam-6739	191	3	attaining	attain	VERB
ejpam-6739	191	4	paranormal	paranormal	ADJ
ejpam-6739	191	5	operators	operator	NOUN
ejpam-6739	191	6	.	.	PUNCT
ejpam-6739	192	1	j.	j.	PROPN
ejpam-6739	192	2	math	math	PROPN
ejpam-6739	192	3	.	.	PUNCT
ejpam-6739	193	1	anal	anal	PROPN
ejpam-6739	193	2	.	.	PUNCT
ejpam-6739	194	1	appl	appl	PROPN
ejpam-6739	194	2	.	.	PROPN
ejpam-6739	194	3	,	,	PUNCT
ejpam-6739	194	4	465:547–556	465:547–556	NUM
ejpam-6739	194	5	,	,	PUNCT
ejpam-6739	194	6	2018	2018	NUM
ejpam-6739	194	7	.	.	PUNCT
ejpam-6739	195	1	[	[	X
ejpam-6739	195	2	6	6	NUM
ejpam-6739	195	3	]	]	X
ejpam-6739	195	4	n.	n.	NOUN
ejpam-6739	195	5	bala	bala	PROPN
ejpam-6739	195	6	and	and	CCONJ
ejpam-6739	195	7	g.	g.	PROPN
ejpam-6739	195	8	ramesh	ramesh	PROPN
ejpam-6739	195	9	.	.	PUNCT
ejpam-6739	196	1	a	a	DET
ejpam-6739	196	2	representation	representation	NOUN
ejpam-6739	196	3	of	of	ADP
ejpam-6739	196	4	hyponormal	hyponormal	ADJ
ejpam-6739	196	5	absolutely	absolutely	ADV
ejpam-6739	196	6	norm	norm	VERB
ejpam-6739	196	7	attaining	attain	VERB
ejpam-6739	196	8	operators	operator	NOUN
ejpam-6739	196	9	.	.	PUNCT
ejpam-6739	197	1	bull	bull	NOUN
ejpam-6739	197	2	.	.	PUNCT
ejpam-6739	198	1	sci	sci	PROPN
ejpam-6739	198	2	.	.	PUNCT
ejpam-6739	198	3	math	math	PROPN
ejpam-6739	198	4	.	.	PUNCT
ejpam-6739	198	5	,	,	PUNCT
ejpam-6739	198	6	171:1–15	171:1–15	NUM
ejpam-6739	198	7	,	,	PUNCT
ejpam-6739	198	8	2021	2021	NUM
ejpam-6739	198	9	.	.	PUNCT
ejpam-6739	199	1	[	[	X
ejpam-6739	199	2	7	7	X
ejpam-6739	199	3	]	]	PUNCT
ejpam-6739	199	4	s.	s.	PROPN
ejpam-6739	199	5	k.	k.	PROPN
ejpam-6739	199	6	pandey	pandey	PROPN
ejpam-6739	199	7	and	and	CCONJ
ejpam-6739	199	8	v.	v.	PROPN
ejpam-6739	199	9	i.	i.	PROPN
ejpam-6739	199	10	paulsen	paulsen	PROPN
ejpam-6739	199	11	.	.	PUNCT
ejpam-6739	200	1	a	a	DET
ejpam-6739	200	2	spectral	spectral	ADJ
ejpam-6739	200	3	characterization	characterization	NOUN
ejpam-6739	200	4	of	of	ADP
ejpam-6739	200	5	an	an	DET
ejpam-6739	200	6	operators	operator	NOUN
ejpam-6739	200	7	.	.	PUNCT
ejpam-6739	201	1	j.	j.	PROPN
ejpam-6739	201	2	aust	aust	PROPN
ejpam-6739	201	3	.	.	PUNCT
ejpam-6739	202	1	math	math	PROPN
ejpam-6739	202	2	.	.	PUNCT
ejpam-6739	203	1	soc	soc	PROPN
ejpam-6739	203	2	.	.	PUNCT
ejpam-6739	203	3	,	,	PUNCT
ejpam-6739	203	4	102:369–391	102:369–391	NUM
ejpam-6739	203	5	,	,	PUNCT
ejpam-6739	203	6	2017	2017	NUM
ejpam-6739	203	7	.	.	PUNCT
ejpam-6739	204	1	mr3650963	mr3650963	PROPN
ejpam-6739	204	2	.	.	PUNCT
ejpam-6739	205	1	[	[	X
ejpam-6739	205	2	8	8	X
ejpam-6739	205	3	]	]	PUNCT
ejpam-6739	205	4	k.	k.	NOUN
ejpam-6739	205	5	tanahashi	tanahashi	PROPN
ejpam-6739	205	6	and	and	CCONJ
ejpam-6739	205	7	a.	a.	NOUN
ejpam-6739	205	8	uchiyama	uchiyama	NOUN
ejpam-6739	205	9	.	.	PUNCT
ejpam-6739	206	1	a	a	DET
ejpam-6739	206	2	note	note	NOUN
ejpam-6739	206	3	on	on	ADP
ejpam-6739	206	4	∗-paranormal	∗-paranormal	ADJ
ejpam-6739	206	5	operators	operator	NOUN
ejpam-6739	206	6	and	and	CCONJ
ejpam-6739	206	7	related	related	ADJ
ejpam-6739	206	8	classes	class	NOUN
ejpam-6739	206	9	of	of	ADP
ejpam-6739	206	10	operators	operator	NOUN
ejpam-6739	206	11	.	.	PUNCT
ejpam-6739	207	1	bull	bull	NOUN
ejpam-6739	207	2	.	.	PUNCT
ejpam-6739	208	1	korean	korean	ADJ
ejpam-6739	208	2	math	math	PROPN
ejpam-6739	208	3	.	.	PUNCT
ejpam-6739	209	1	soc	soc	PROPN
ejpam-6739	209	2	.	.	PUNCT
ejpam-6739	209	3	,	,	PUNCT
ejpam-6739	209	4	51:357–371	51:357–371	NUM
ejpam-6739	209	5	,	,	PUNCT
ejpam-6739	209	6	2014	2014	NUM
ejpam-6739	209	7	.	.	PUNCT
ejpam-6739	210	1	[	[	X
ejpam-6739	210	2	9	9	X
ejpam-6739	210	3	]	]	PUNCT
ejpam-6739	210	4	j.	j.	PROPN
ejpam-6739	210	5	l.	l.	PROPN
ejpam-6739	210	6	shen	shen	PROPN
ejpam-6739	210	7	and	and	CCONJ
ejpam-6739	210	8	c.	c.	PROPN
ejpam-6739	210	9	alatancang	alatancang	PROPN
ejpam-6739	210	10	.	.	PUNCT
ejpam-6739	211	1	the	the	DET
ejpam-6739	211	2	spectrum	spectrum	NOUN
ejpam-6739	211	3	properties	property	NOUN
ejpam-6739	211	4	of	of	ADP
ejpam-6739	211	5	quasi-∗-paranaormal	quasi-∗-paranaormal	ADJ
ejpam-6739	211	6	operators	operator	NOUN
ejpam-6739	211	7	.	.	PUNCT
ejpam-6739	212	1	chinese	chinese	PROPN
ejpam-6739	212	2	ann	ann	PROPN
ejpam-6739	212	3	.	.	PUNCT
ejpam-6739	212	4	math	math	PROPN
ejpam-6739	212	5	.	.	PUNCT
ejpam-6739	212	6	,	,	PUNCT
ejpam-6739	213	1	34:663–670	34:663–670	PROPN
ejpam-6739	213	2	,	,	PUNCT
ejpam-6739	213	3	2013	2013	NUM
ejpam-6739	213	4	.	.	PUNCT
ejpam-6739	214	1	in	in	ADP
ejpam-6739	214	2	chinese	chinese	PROPN
ejpam-6739	214	3	.	.	PUNCT
ejpam-6739	215	1	[	[	X
ejpam-6739	215	2	10	10	NUM
ejpam-6739	215	3	]	]	X
ejpam-6739	215	4	f.	f.	PROPN
ejpam-6739	215	5	zuo	zuo	PROPN
ejpam-6739	215	6	and	and	CCONJ
ejpam-6739	215	7	h.	h.	PROPN
ejpam-6739	215	8	zuo	zuo	PROPN
ejpam-6739	215	9	.	.	PROPN
ejpam-6739	215	10	structural	structural	ADJ
ejpam-6739	215	11	and	and	CCONJ
ejpam-6739	215	12	spectral	spectral	ADJ
ejpam-6739	215	13	properties	property	NOUN
ejpam-6739	215	14	of	of	ADP
ejpam-6739	215	15	k	k	ADJ
ejpam-6739	215	16	-	-	ADJ
ejpam-6739	215	17	quasi-∗-paranormal	quasi-∗-paranormal	ADJ
ejpam-6739	215	18	operators	operator	NOUN
ejpam-6739	215	19	.	.	PUNCT
ejpam-6739	216	1	kor	kor	PROPN
ejpam-6739	216	2	.	.	PUNCT
ejpam-6739	217	1	j.	j.	PROPN
ejpam-6739	217	2	math	math	PROPN
ejpam-6739	217	3	.	.	PUNCT
ejpam-6739	217	4	,	,	PUNCT
ejpam-6739	217	5	23:249–257	23:249–257	PROPN
ejpam-6739	217	6	,	,	PUNCT
ejpam-6739	217	7	2015	2015	NUM
ejpam-6739	217	8	.	.	PUNCT
ejpam-6739	218	1	[	[	X
ejpam-6739	218	2	11	11	NUM
ejpam-6739	218	3	]	]	PUNCT
ejpam-6739	218	4	i.	i.	PROPN
ejpam-6739	218	5	hoxha	hoxha	PROPN
ejpam-6739	218	6	,	,	PUNCT
ejpam-6739	218	7	n.	n.	PROPN
ejpam-6739	218	8	l.	l.	PROPN
ejpam-6739	218	9	braha	braha	PROPN
ejpam-6739	218	10	,	,	PUNCT
ejpam-6739	218	11	and	and	CCONJ
ejpam-6739	218	12	a.	a.	NOUN
ejpam-6739	218	13	tato	tato	PROPN
ejpam-6739	218	14	.	.	PUNCT
ejpam-6739	219	1	riesz	riesz	VERB
ejpam-6739	219	2	idempotent	idempotent	NOUN
ejpam-6739	219	3	and	and	CCONJ
ejpam-6739	219	4	weyl	weyl	PROPN
ejpam-6739	219	5	’s	’s	PART
ejpam-6739	219	6	theorem	theorem	NOUN
ejpam-6739	219	7	for	for	ADP
ejpam-6739	219	8	kquasi-∗-paranormal	kquasi-∗-paranormal	PROPN
ejpam-6739	219	9	operators	operator	NOUN
ejpam-6739	219	10	.	.	PUNCT
ejpam-6739	220	1	appl	appl	PROPN
ejpam-6739	220	2	.	.	PROPN
ejpam-6739	220	3	math	math	NOUN
ejpam-6739	220	4	.	.	PUNCT
ejpam-6739	221	1	e	e	X
ejpam-6739	221	2	-	-	NOUN
ejpam-6739	221	3	notes	note	NOUN
ejpam-6739	221	4	,	,	PUNCT
ejpam-6739	221	5	19:80–100	19:80–100	NUM
ejpam-6739	221	6	,	,	PUNCT
ejpam-6739	221	7	2019	2019	NUM
ejpam-6739	221	8	.	.	PUNCT
ejpam-6739	222	1	[	[	X
ejpam-6739	222	2	12	12	NUM
ejpam-6739	222	3	]	]	X
ejpam-6739	222	4	f.	f.	PROPN
ejpam-6739	222	5	zuo	zuo	PROPN
ejpam-6739	222	6	and	and	CCONJ
ejpam-6739	222	7	j.	j.	PROPN
ejpam-6739	222	8	shen	shen	PROPN
ejpam-6739	222	9	.	.	PUNCT
ejpam-6739	223	1	polaroid	polaroid	PROPN
ejpam-6739	223	2	and	and	CCONJ
ejpam-6739	223	3	k	k	ADJ
ejpam-6739	223	4	-	-	ADJ
ejpam-6739	223	5	quasi-∗-paranormal	quasi-∗-paranormal	ADJ
ejpam-6739	223	6	operators	operator	NOUN
ejpam-6739	223	7	.	.	PUNCT
ejpam-6739	224	1	filomat	filomat	PROPN
ejpam-6739	224	2	,	,	PUNCT
ejpam-6739	224	3	30:313	30:313	NUM
ejpam-6739	224	4	–	–	PUNCT
ejpam-6739	224	5	319	319	NUM
ejpam-6739	224	6	,	,	PUNCT
ejpam-6739	224	7	2016	2016	NUM
ejpam-6739	224	8	.	.	PUNCT
ejpam-6739	225	1	[	[	X
ejpam-6739	225	2	13	13	NUM
ejpam-6739	225	3	]	]	PUNCT
ejpam-6739	225	4	a.	a.	NOUN
ejpam-6739	225	5	fellag	fellag	PROPN
ejpam-6739	225	6	ariouat	ariouat	NOUN
ejpam-6739	225	7	,	,	PUNCT
ejpam-6739	225	8	a.	a.	NOUN
ejpam-6739	225	9	nasli	nasli	PROPN
ejpam-6739	225	10	bakir	bakir	PROPN
ejpam-6739	225	11	,	,	PUNCT
ejpam-6739	225	12	and	and	CCONJ
ejpam-6739	225	13	a.	a.	PROPN
ejpam-6739	225	14	benali	benali	PROPN
ejpam-6739	225	15	.	.	PUNCT
ejpam-6739	226	1	bishop	bishop	PROPN
ejpam-6739	226	2	’s	’s	PART
ejpam-6739	226	3	property	property	NOUN
ejpam-6739	226	4	,	,	PUNCT
ejpam-6739	226	5	weyl	weyl	PROPN
ejpam-6739	226	6	’s	’s	PART
ejpam-6739	226	7	theorem	theorem	NOUN
ejpam-6739	226	8	and	and	CCONJ
ejpam-6739	226	9	riesz	riesz	VERB
ejpam-6739	226	10	idempotent	idempotent	NOUN
ejpam-6739	226	11	.	.	PUNCT
ejpam-6739	227	1	j.	j.	PROPN
ejpam-6739	227	2	comp	comp	PROPN
ejpam-6739	227	3	.	.	PUNCT
ejpam-6739	228	1	anal	anal	PROPN
ejpam-6739	228	2	.	.	PUNCT
ejpam-6739	229	1	appl	appl	PROPN
ejpam-6739	229	2	.	.	PROPN
ejpam-6739	229	3	,	,	PUNCT
ejpam-6739	230	1	34:323–340	34:323–340	NUM
ejpam-6739	230	2	,	,	PUNCT
ejpam-6739	230	3	2025	2025	NUM
ejpam-6739	230	4	.	.	PUNCT
ejpam-6739	231	1	[	[	X
ejpam-6739	231	2	14	14	NUM
ejpam-6739	231	3	]	]	X
ejpam-6739	231	4	m.	m.	NOUN
ejpam-6739	231	5	maadani	maadani	PROPN
ejpam-6739	231	6	,	,	PUNCT
ejpam-6739	231	7	a.	a.	PROPN
ejpam-6739	231	8	benali	benali	PROPN
ejpam-6739	231	9	,	,	PUNCT
ejpam-6739	231	10	and	and	CCONJ
ejpam-6739	231	11	a.	a.	NOUN
ejpam-6739	231	12	nasli	nasli	PROPN
ejpam-6739	231	13	bakir	bakir	VERB
ejpam-6739	231	14	.	.	PUNCT
ejpam-6739	232	1	on	on	ADP
ejpam-6739	232	2	quasi	quasi	PROPN
ejpam-6739	232	3	totally	totally	ADV
ejpam-6739	232	4	m	m	NOUN
ejpam-6739	232	5	-	-	PUNCT
ejpam-6739	232	6	class	class	NOUN
ejpam-6739	232	7	a∗	a∗	PROPN
ejpam-6739	232	8	k	k	PROPN
ejpam-6739	232	9	operators	operators	PROPN
ejpam-6739	232	10	.	.	PUNCT
ejpam-6739	233	1	j.	j.	PROPN
ejpam-6739	233	2	comp	comp	PROPN
ejpam-6739	233	3	.	.	PUNCT
ejpam-6739	234	1	anal	anal	PROPN
ejpam-6739	234	2	.	.	PUNCT
ejpam-6739	235	1	appl	appl	PROPN
ejpam-6739	235	2	.	.	PROPN
ejpam-6739	235	3	,	,	PUNCT
ejpam-6739	236	1	35:104–119	35:104–119	NUM
ejpam-6739	236	2	,	,	PUNCT
ejpam-6739	236	3	2025	2025	NUM
ejpam-6739	236	4	.	.	PUNCT
ejpam-6739	237	1	[	[	X
ejpam-6739	237	2	15	15	NUM
ejpam-6739	237	3	]	]	X
ejpam-6739	237	4	j.	j.	PROPN
ejpam-6739	237	5	b.	b.	PROPN
ejpam-6739	237	6	conway	conway	PROPN
ejpam-6739	237	7	.	.	PUNCT
ejpam-6739	238	1	a	a	DET
ejpam-6739	238	2	course	course	NOUN
ejpam-6739	238	3	in	in	ADP
ejpam-6739	238	4	functional	functional	ADJ
ejpam-6739	238	5	analysis	analysis	NOUN
ejpam-6739	238	6	.	.	PUNCT
ejpam-6739	239	1	springer	springer	NOUN
ejpam-6739	239	2	verlag	verlag	PROPN
ejpam-6739	239	3	,	,	PUNCT
ejpam-6739	239	4	second	second	ADJ
ejpam-6739	239	5	edition	edition	NOUN
ejpam-6739	239	6	,	,	PUNCT
ejpam-6739	239	7	1990	1990	NUM
ejpam-6739	239	8	.	.	PUNCT
ejpam-6739	240	1	[	[	X
ejpam-6739	240	2	16	16	NUM
ejpam-6739	240	3	]	]	X
ejpam-6739	240	4	v.	v.	ADP
ejpam-6739	240	5	müller	müller	NOUN
ejpam-6739	240	6	.	.	PUNCT
ejpam-6739	241	1	spectral	spectral	ADJ
ejpam-6739	241	2	theory	theory	NOUN
ejpam-6739	241	3	of	of	ADP
ejpam-6739	241	4	linear	linear	PROPN
ejpam-6739	241	5	operators	operator	NOUN
ejpam-6739	241	6	and	and	CCONJ
ejpam-6739	241	7	spectral	spectral	ADJ
ejpam-6739	241	8	systems	system	NOUN
ejpam-6739	241	9	in	in	ADP
ejpam-6739	241	10	banach	banach	NOUN
ejpam-6739	241	11	algebras	algebra	NOUN
ejpam-6739	241	12	.	.	PUNCT
ejpam-6739	242	1	operator	operator	NOUN
ejpam-6739	242	2	theory	theory	NOUN
ejpam-6739	242	3	:	:	PUNCT
ejpam-6739	242	4	advances	advance	NOUN
ejpam-6739	242	5	and	and	CCONJ
ejpam-6739	242	6	applications	application	NOUN
ejpam-6739	242	7	.	.	PUNCT
ejpam-6739	243	1	birkhäuser	birkhäuser	X
ejpam-6739	243	2	verlag	verlag	PROPN
ejpam-6739	243	3	,	,	PUNCT
ejpam-6739	243	4	basel	basel	PROPN
ejpam-6739	243	5	,	,	PUNCT
ejpam-6739	243	6	second	second	ADJ
ejpam-6739	243	7	edition	edition	NOUN
ejpam-6739	243	8	,	,	PUNCT
ejpam-6739	243	9	2007	2007	NUM
ejpam-6739	243	10	.	.	PUNCT
ejpam-6739	244	1	a.	a.	NOUN
ejpam-6739	244	2	nasli	nasli	PROPN
ejpam-6739	244	3	bakir	bakir	VERB
ejpam-6739	244	4	et	et	PROPN
ejpam-6739	244	5	al	al	PROPN
ejpam-6739	244	6	.	.	PUNCT
ejpam-6739	244	7	/	/	SYM
ejpam-6739	244	8	eur	eur	PROPN
ejpam-6739	244	9	.	.	PUNCT
ejpam-6739	245	1	j.	j.	PROPN
ejpam-6739	245	2	pure	pure	PROPN
ejpam-6739	245	3	appl	appl	PROPN
ejpam-6739	245	4	.	.	PROPN
ejpam-6739	245	5	math	math	PROPN
ejpam-6739	245	6	,	,	PUNCT
ejpam-6739	245	7	18	18	NUM
ejpam-6739	245	8	(	(	PUNCT
ejpam-6739	245	9	4	4	NUM
ejpam-6739	245	10	)	)	PUNCT
ejpam-6739	245	11	(	(	PUNCT
ejpam-6739	245	12	2025	2025	NUM
ejpam-6739	245	13	)	)	PUNCT
ejpam-6739	245	14	,	,	PUNCT
ejpam-6739	245	15	6739	6739	NUM
ejpam-6739	245	16	10	10	NUM
ejpam-6739	245	17	of	of	ADP
ejpam-6739	245	18	10	10	NUM
ejpam-6739	245	19	[	[	SYM
ejpam-6739	245	20	17	17	NUM
ejpam-6739	245	21	]	]	PUNCT
ejpam-6739	245	22	j.	j.	PROPN
ejpam-6739	245	23	ganesh	ganesh	PROPN
ejpam-6739	245	24	,	,	PUNCT
ejpam-6739	245	25	g.	g.	PROPN
ejpam-6739	245	26	ramesh	ramesh	PROPN
ejpam-6739	245	27	,	,	PUNCT
ejpam-6739	245	28	and	and	CCONJ
ejpam-6739	245	29	d.	d.	PROPN
ejpam-6739	245	30	sukumar	sukumar	PROPN
ejpam-6739	245	31	.	.	PUNCT
ejpam-6739	246	1	on	on	ADP
ejpam-6739	246	2	the	the	DET
ejpam-6739	246	3	structure	structure	NOUN
ejpam-6739	246	4	of	of	ADP
ejpam-6739	246	5	absolutely	absolutely	ADV
ejpam-6739	246	6	minimum	minimum	ADJ
ejpam-6739	246	7	attaining	attain	VERB
ejpam-6739	246	8	operators	operator	NOUN
ejpam-6739	246	9	.	.	PUNCT
ejpam-6739	247	1	j.	j.	PROPN
ejpam-6739	247	2	math	math	PROPN
ejpam-6739	247	3	.	.	PUNCT
ejpam-6739	248	1	anal	anal	PROPN
ejpam-6739	248	2	.	.	PUNCT
ejpam-6739	249	1	appl	appl	PROPN
ejpam-6739	249	2	.	.	PROPN
ejpam-6739	249	3	,	,	PUNCT
ejpam-6739	249	4	428:457–470	428:457–470	NUM
ejpam-6739	249	5	,	,	PUNCT
ejpam-6739	249	6	2015	2015	NUM
ejpam-6739	249	7	.	.	PUNCT
ejpam-6739	250	1	[	[	X
ejpam-6739	250	2	18	18	NUM
ejpam-6739	250	3	]	]	X
ejpam-6739	250	4	s.	s.	PROPN
ejpam-6739	250	5	mecheri	mecheri	PROPN
ejpam-6739	250	6	and	and	CCONJ
ejpam-6739	250	7	a.	a.	NOUN
ejpam-6739	250	8	nasli	nasli	PROPN
ejpam-6739	250	9	bakir	bakir	PROPN
ejpam-6739	250	10	.	.	PUNCT
ejpam-6739	251	1	norm	norm	NOUN
ejpam-6739	251	2	attaining	attain	VERB
ejpam-6739	251	3	and	and	CCONJ
ejpam-6739	251	4	absolutely	absolutely	ADV
ejpam-6739	251	5	norm	norm	VERB
ejpam-6739	251	6	attaining	attain	VERB
ejpam-6739	251	7	of	of	ADP
ejpam-6739	251	8	∗-paranormal	∗-paranormal	ADJ
ejpam-6739	251	9	operators	operator	NOUN
ejpam-6739	251	10	.	.	PUNCT
ejpam-6739	252	1	filomat	filomat	PROPN
ejpam-6739	252	2	,	,	PUNCT
ejpam-6739	252	3	38:2381–2386	38:2381–2386	NUM
ejpam-6739	252	4	,	,	PUNCT
ejpam-6739	252	5	2024	2024	NUM
ejpam-6739	252	6	.	.	PUNCT
ejpam-6739	253	1	[	[	X
ejpam-6739	253	2	19	19	NUM
ejpam-6739	253	3	]	]	X
ejpam-6739	253	4	y.	y.	PROPN
ejpam-6739	253	5	m.	m.	PROPN
ejpam-6739	253	6	han	han	PROPN
ejpam-6739	253	7	and	and	CCONJ
ejpam-6739	253	8	a.	a.	PROPN
ejpam-6739	253	9	h.	h.	PROPN
ejpam-6739	253	10	kim	kim	PROPN
ejpam-6739	253	11	.	.	PUNCT
ejpam-6739	254	1	a	a	DET
ejpam-6739	254	2	note	note	NOUN
ejpam-6739	254	3	on	on	ADP
ejpam-6739	254	4	∗-paranormal	∗-paranormal	ADJ
ejpam-6739	254	5	operators	operator	NOUN
ejpam-6739	254	6	.	.	PUNCT
ejpam-6739	255	1	int	int	NOUN
ejpam-6739	255	2	.	.	PUNCT
ejpam-6739	256	1	equa	equa	NOUN
ejpam-6739	256	2	.	.	PUNCT
ejpam-6739	257	1	oper	oper	PROPN
ejpam-6739	257	2	.	.	PUNCT
ejpam-6739	258	1	theo	theo	PROPN
ejpam-6739	258	2	.	.	PROPN
ejpam-6739	258	3	,	,	PUNCT
ejpam-6739	258	4	49:435–444	49:435–444	PROPN
ejpam-6739	258	5	,	,	PUNCT
ejpam-6739	258	6	2004	2004	NUM
ejpam-6739	258	7	.	.	PUNCT
ejpam-6739	259	1	[	[	X
ejpam-6739	259	2	20	20	NUM
ejpam-6739	259	3	]	]	PUNCT
ejpam-6739	259	4	i.	i.	PROPN
ejpam-6739	259	5	hoxha	hoxha	PROPN
ejpam-6739	259	6	and	and	CCONJ
ejpam-6739	259	7	n.	n.	PROPN
ejpam-6739	259	8	l.	l.	PROPN
ejpam-6739	259	9	braha	braha	PROPN
ejpam-6739	259	10	.	.	PUNCT
ejpam-6739	260	1	a	a	DET
ejpam-6739	260	2	note	note	NOUN
ejpam-6739	260	3	on	on	ADP
ejpam-6739	260	4	k	k	ADJ
ejpam-6739	260	5	-	-	ADJ
ejpam-6739	260	6	quasi-∗-paranormal	quasi-∗-paranormal	ADJ
ejpam-6739	260	7	operators	operator	NOUN
ejpam-6739	260	8	.	.	PUNCT
ejpam-6739	261	1	j.	j.	PROPN
ejpam-6739	261	2	ineq	ineq	PROPN
ejpam-6739	261	3	.	.	PUNCT
ejpam-6739	262	1	appl	appl	PROPN
ejpam-6739	262	2	.	.	PROPN
ejpam-6739	262	3	,	,	PUNCT
ejpam-6739	262	4	2013(350):1–7	2013(350):1–7	NUM
ejpam-6739	262	5	,	,	PUNCT
ejpam-6739	262	6	2013	2013	NUM
ejpam-6739	262	7	.	.	PUNCT
ejpam-6739	263	1	[	[	X
ejpam-6739	263	2	21	21	NUM
ejpam-6739	263	3	]	]	X
ejpam-6739	263	4	j.	j.	PROPN
ejpam-6739	263	5	i.	i.	PROPN
ejpam-6739	263	6	lee	lee	PROPN
ejpam-6739	263	7	.	.	PROPN
ejpam-6739	264	1	on	on	ADP
ejpam-6739	264	2	the	the	DET
ejpam-6739	264	3	norm	norm	NOUN
ejpam-6739	264	4	attaining	attain	VERB
ejpam-6739	264	5	operators	operator	NOUN
ejpam-6739	264	6	.	.	PUNCT
ejpam-6739	265	1	kor	kor	PROPN
ejpam-6739	265	2	.	.	PUNCT
ejpam-6739	266	1	j.	j.	PROPN
ejpam-6739	266	2	math	math	PROPN
ejpam-6739	266	3	.	.	PUNCT
ejpam-6739	266	4	,	,	PUNCT
ejpam-6739	266	5	20:485–491	20:485–491	PROPN
ejpam-6739	266	6	,	,	PUNCT
ejpam-6739	266	7	2012	2012	NUM
ejpam-6739	266	8	.	.	PUNCT
ejpam-6739	267	1	[	[	X
ejpam-6739	267	2	22	22	NUM
ejpam-6739	267	3	]	]	PUNCT
ejpam-6739	267	4	m.	m.	NOUN
ejpam-6739	267	5	dehghani	dehghani	PROPN
ejpam-6739	267	6	,	,	PUNCT
ejpam-6739	267	7	s.	s.	PROPN
ejpam-6739	267	8	m.	m.	PROPN
ejpam-6739	267	9	s.	s.	PROPN
ejpam-6739	267	10	modarres	modarres	PROPN
ejpam-6739	267	11	,	,	PUNCT
ejpam-6739	267	12	and	and	CCONJ
ejpam-6739	267	13	m.	m.	PROPN
ejpam-6739	267	14	s.	s.	PROPN
ejpam-6739	267	15	moslehian	moslehian	PROPN
ejpam-6739	267	16	.	.	PUNCT
ejpam-6739	268	1	positive	positive	ADJ
ejpam-6739	268	2	block	block	NOUN
ejpam-6739	268	3	matrices	matrix	NOUN
ejpam-6739	268	4	on	on	ADP
ejpam-6739	268	5	hilbert	hilbert	NOUN
ejpam-6739	268	6	and	and	CCONJ
ejpam-6739	268	7	krein	krein	PROPN
ejpam-6739	268	8	c∗-modules	c∗-modules	PROPN
ejpam-6739	268	9	.	.	PUNCT
ejpam-6739	269	1	surveys	survey	NOUN
ejpam-6739	269	2	in	in	ADP
ejpam-6739	269	3	math	math	NOUN
ejpam-6739	269	4	.	.	PUNCT
ejpam-6739	270	1	appl	appl	PROPN
ejpam-6739	270	2	.	.	PROPN
ejpam-6739	270	3	,	,	PUNCT
ejpam-6739	270	4	8:23–34	8:23–34	NUM
ejpam-6739	270	5	,	,	PUNCT
ejpam-6739	270	6	2013	2013	NUM
ejpam-6739	270	7	.	.	PUNCT
ejpam-6739	271	1	issn	issn	PROPN
ejpam-6739	271	2	18426298	18426298	NUM
ejpam-6739	271	3	(	(	PUNCT
ejpam-6739	271	4	electronic	electronic	ADJ
ejpam-6739	271	5	)	)	PUNCT
ejpam-6739	271	6	,	,	PUNCT
ejpam-6739	271	7	1843	1843	NUM
ejpam-6739	271	8	-	-	SYM
ejpam-6739	271	9	7265	7265	NUM
ejpam-6739	271	10	(	(	PUNCT
ejpam-6739	271	11	print	print	NOUN
ejpam-6739	271	12	)	)	PUNCT
ejpam-6739	271	13	.	.	PUNCT