id	sid	tid	token	lemma	pos
ejpam-4580	1	1	european	european	PROPN
ejpam-4580	1	2	journal	journal	PROPN
ejpam-4580	1	3	of	of	ADP
ejpam-4580	1	4	pure	pure	ADJ
ejpam-4580	1	5	and	and	CCONJ
ejpam-4580	1	6	applied	apply	VERB
ejpam-4580	1	7	mathematics	mathematic	NOUN
ejpam-4580	1	8	vol	vol	NOUN
ejpam-4580	1	9	.	.	PROPN
ejpam-4580	2	1	15	15	NUM
ejpam-4580	2	2	,	,	PUNCT
ejpam-4580	2	3	no	no	INTJ
ejpam-4580	2	4	.	.	NOUN
ejpam-4580	2	5	4	4	NUM
ejpam-4580	2	6	,	,	PUNCT
ejpam-4580	2	7	2022	2022	NUM
ejpam-4580	2	8	,	,	PUNCT
ejpam-4580	2	9	1836	1836	NUM
ejpam-4580	2	10	-	-	SYM
ejpam-4580	2	11	1853	1853	NUM
ejpam-4580	2	12	issn	issn	PROPN
ejpam-4580	2	13	1307	1307	NUM
ejpam-4580	2	14	-	-	SYM
ejpam-4580	2	15	5543	5543	NUM
ejpam-4580	2	16	–	–	PUNCT
ejpam-4580	2	17	ejpam.com	ejpam.com	X
ejpam-4580	2	18	published	publish	VERB
ejpam-4580	2	19	by	by	ADP
ejpam-4580	2	20	new	new	PROPN
ejpam-4580	2	21	york	york	PROPN
ejpam-4580	2	22	business	business	PROPN
ejpam-4580	2	23	global	global	ADJ
ejpam-4580	2	24	structural	structural	ADJ
ejpam-4580	2	25	and	and	CCONJ
ejpam-4580	2	26	spectral	spectral	ADJ
ejpam-4580	2	27	properties	property	NOUN
ejpam-4580	2	28	of	of	ADP
ejpam-4580	2	29	k−quasi	k−quasi	PROPN
ejpam-4580	2	30	class	class	NOUN
ejpam-4580	2	31	q(n	q(n	PROPN
ejpam-4580	2	32	)	)	PUNCT
ejpam-4580	2	33	and	and	CCONJ
ejpam-4580	2	34	k−quasi	k−quasi	PROPN
ejpam-4580	2	35	class	class	NOUN
ejpam-4580	2	36	q∗(n	q∗(n	PROPN
ejpam-4580	2	37	)	)	PUNCT
ejpam-4580	2	38	operators	operator	NOUN
ejpam-4580	2	39	shqipe	shqipe	VERB
ejpam-4580	2	40	lohaj	lohaj	PROPN
ejpam-4580	2	41	department	department	PROPN
ejpam-4580	2	42	of	of	ADP
ejpam-4580	2	43	mathematics	mathematic	NOUN
ejpam-4580	2	44	,	,	PUNCT
ejpam-4580	2	45	faculty	faculty	NOUN
ejpam-4580	2	46	of	of	ADP
ejpam-4580	2	47	electrical	electrical	ADJ
ejpam-4580	2	48	and	and	CCONJ
ejpam-4580	2	49	computer	computer	NOUN
ejpam-4580	2	50	engineering	engineering	NOUN
ejpam-4580	2	51	,	,	PUNCT
ejpam-4580	2	52	university	university	PROPN
ejpam-4580	2	53	of	of	ADP
ejpam-4580	2	54	prishtina	prishtina	PROPN
ejpam-4580	2	55	”	"	PUNCT
ejpam-4580	2	56	hasan	hasan	PROPN
ejpam-4580	2	57	prishtina	prishtina	PROPN
ejpam-4580	2	58	”	"	PUNCT
ejpam-4580	2	59	,	,	PUNCT
ejpam-4580	2	60	prishtinë	prishtinë	PROPN
ejpam-4580	2	61	,	,	PUNCT
ejpam-4580	2	62	10000	10000	NUM
ejpam-4580	2	63	,	,	PUNCT
ejpam-4580	2	64	kosovë	kosovë	NOUN
ejpam-4580	2	65	abstract	abstract	NOUN
ejpam-4580	2	66	.	.	PUNCT
ejpam-4580	3	1	let	let	VERB
ejpam-4580	3	2	t	t	NOUN
ejpam-4580	3	3	be	be	AUX
ejpam-4580	3	4	a	a	DET
ejpam-4580	3	5	bounded	bounded	ADJ
ejpam-4580	3	6	linear	linear	ADJ
ejpam-4580	3	7	operator	operator	NOUN
ejpam-4580	3	8	on	on	ADP
ejpam-4580	3	9	a	a	DET
ejpam-4580	3	10	complex	complex	ADJ
ejpam-4580	3	11	hilbert	hilbert	NOUN
ejpam-4580	3	12	space	space	NOUN
ejpam-4580	3	13	h.	h.	PROPN
ejpam-4580	3	14	in	in	ADP
ejpam-4580	3	15	this	this	DET
ejpam-4580	3	16	paper	paper	NOUN
ejpam-4580	3	17	we	we	PRON
ejpam-4580	3	18	introduce	introduce	VERB
ejpam-4580	3	19	two	two	NUM
ejpam-4580	3	20	new	new	ADJ
ejpam-4580	3	21	classes	class	NOUN
ejpam-4580	3	22	of	of	ADP
ejpam-4580	3	23	operators	operator	NOUN
ejpam-4580	3	24	:	:	PUNCT
ejpam-4580	3	25	k−quasi	k−quasi	PROPN
ejpam-4580	3	26	class	class	NOUN
ejpam-4580	3	27	q(n	q(n	PROPN
ejpam-4580	3	28	)	)	PUNCT
ejpam-4580	3	29	and	and	CCONJ
ejpam-4580	3	30	k−quasi	k−quasi	PROPN
ejpam-4580	3	31	class	class	NOUN
ejpam-4580	3	32	q∗(n	q∗(n	PROPN
ejpam-4580	3	33	)	)	PUNCT
ejpam-4580	3	34	.	.	PUNCT
ejpam-4580	4	1	an	an	DET
ejpam-4580	4	2	operator	operator	NOUN
ejpam-4580	4	3	t	t	PROPN
ejpam-4580	4	4	∈	∈	PROPN
ejpam-4580	4	5	l(h	l(h	PROPN
ejpam-4580	4	6	)	)	PUNCT
ejpam-4580	4	7	is	be	AUX
ejpam-4580	4	8	of	of	ADP
ejpam-4580	4	9	k−quasi	k−quasi	NOUN
ejpam-4580	4	10	class	class	NOUN
ejpam-4580	4	11	q(n	q(n	PROPN
ejpam-4580	4	12	)	)	PUNCT
ejpam-4580	4	13	for	for	ADP
ejpam-4580	4	14	a	a	DET
ejpam-4580	4	15	fixed	fix	VERB
ejpam-4580	4	16	real	real	ADJ
ejpam-4580	4	17	number	number	NOUN
ejpam-4580	4	18	n	n	CCONJ
ejpam-4580	4	19	≥	≥	NOUN
ejpam-4580	4	20	1	1	NUM
ejpam-4580	4	21	and	and	CCONJ
ejpam-4580	4	22	k	k	X
ejpam-4580	4	23	a	a	DET
ejpam-4580	4	24	natural	natural	ADJ
ejpam-4580	4	25	number	number	NOUN
ejpam-4580	4	26	,	,	PUNCT
ejpam-4580	4	27	if	if	SCONJ
ejpam-4580	4	28	t	t	PROPN
ejpam-4580	4	29	satisfies	satisfy	VERB
ejpam-4580	4	30	n∥t	n∥t	ADJ
ejpam-4580	4	31	k+1x∥2	k+1x∥2	NOUN
ejpam-4580	4	32	≤	≤	ADV
ejpam-4580	4	33	∥t	∥t	ADJ
ejpam-4580	4	34	k+2x∥2	k+2x∥2	NOUN
ejpam-4580	5	1	+	+	CCONJ
ejpam-4580	5	2	∥t	∥t	ADJ
ejpam-4580	5	3	kx∥2	kx∥2	NOUN
ejpam-4580	5	4	,	,	PUNCT
ejpam-4580	5	5	for	for	ADP
ejpam-4580	5	6	all	all	DET
ejpam-4580	5	7	x	x	SYM
ejpam-4580	5	8	∈	∈	PROPN
ejpam-4580	5	9	h.	h.	NOUN
ejpam-4580	5	10	an	an	DET
ejpam-4580	5	11	operator	operator	NOUN
ejpam-4580	5	12	t	t	PROPN
ejpam-4580	5	13	∈	∈	PROPN
ejpam-4580	5	14	l(h	l(h	PROPN
ejpam-4580	5	15	)	)	PUNCT
ejpam-4580	5	16	is	be	AUX
ejpam-4580	5	17	of	of	ADP
ejpam-4580	5	18	k−quasi	k−quasi	PROPN
ejpam-4580	5	19	class	class	NOUN
ejpam-4580	5	20	q∗(n	q∗(n	PROPN
ejpam-4580	5	21	)	)	PUNCT
ejpam-4580	5	22	for	for	ADP
ejpam-4580	5	23	a	a	DET
ejpam-4580	5	24	fixed	fix	VERB
ejpam-4580	5	25	real	real	ADJ
ejpam-4580	5	26	number	number	NOUN
ejpam-4580	5	27	n	n	CCONJ
ejpam-4580	5	28	≥	≥	NOUN
ejpam-4580	5	29	1	1	NUM
ejpam-4580	5	30	and	and	CCONJ
ejpam-4580	5	31	k	k	X
ejpam-4580	5	32	a	a	DET
ejpam-4580	5	33	natural	natural	ADJ
ejpam-4580	5	34	number	number	NOUN
ejpam-4580	5	35	,	,	PUNCT
ejpam-4580	5	36	if	if	SCONJ
ejpam-4580	5	37	t	t	PROPN
ejpam-4580	5	38	satisfies	satisfy	VERB
ejpam-4580	5	39	n∥t	n∥t	PROPN
ejpam-4580	5	40	∗t	∗t	PROPN
ejpam-4580	5	41	kx∥2	kx∥2	PROPN
ejpam-4580	5	42	≤	≤	NUM
ejpam-4580	5	43	∥t	∥t	ADJ
ejpam-4580	5	44	k+2x∥2	k+2x∥2	NOUN
ejpam-4580	6	1	+	+	CCONJ
ejpam-4580	6	2	∥t	∥t	ADJ
ejpam-4580	6	3	kx∥2	kx∥2	NOUN
ejpam-4580	6	4	,	,	PUNCT
ejpam-4580	6	5	for	for	ADP
ejpam-4580	6	6	all	all	DET
ejpam-4580	6	7	x	x	SYM
ejpam-4580	6	8	∈	∈	PROPN
ejpam-4580	6	9	h.	h.	NOUN
ejpam-4580	6	10	we	we	PRON
ejpam-4580	6	11	study	study	VERB
ejpam-4580	6	12	structural	structural	ADJ
ejpam-4580	6	13	and	and	CCONJ
ejpam-4580	6	14	spectral	spectral	ADJ
ejpam-4580	6	15	properties	property	NOUN
ejpam-4580	6	16	of	of	ADP
ejpam-4580	6	17	these	these	DET
ejpam-4580	6	18	classes	class	NOUN
ejpam-4580	6	19	of	of	ADP
ejpam-4580	6	20	operators	operator	NOUN
ejpam-4580	6	21	.	.	PUNCT
ejpam-4580	7	1	also	also	ADV
ejpam-4580	7	2	we	we	PRON
ejpam-4580	7	3	compare	compare	VERB
ejpam-4580	7	4	this	this	DET
ejpam-4580	7	5	new	new	ADJ
ejpam-4580	7	6	classes	class	NOUN
ejpam-4580	7	7	of	of	ADP
ejpam-4580	7	8	operators	operator	NOUN
ejpam-4580	7	9	with	with	ADP
ejpam-4580	7	10	other	other	ADJ
ejpam-4580	7	11	known	know	VERB
ejpam-4580	7	12	classes	class	NOUN
ejpam-4580	7	13	of	of	ADP
ejpam-4580	7	14	operators	operator	NOUN
ejpam-4580	7	15	.	.	PUNCT
ejpam-4580	8	1	2020	2020	NUM
ejpam-4580	8	2	mathematics	mathematic	NOUN
ejpam-4580	8	3	subject	subject	NOUN
ejpam-4580	8	4	classifications	classification	NOUN
ejpam-4580	8	5	:	:	PUNCT
ejpam-4580	8	6	47b47	47b47	NOUN
ejpam-4580	8	7	,	,	PUNCT
ejpam-4580	8	8	47b20	47b20	NUM
ejpam-4580	8	9	key	key	ADJ
ejpam-4580	8	10	words	word	NOUN
ejpam-4580	8	11	and	and	CCONJ
ejpam-4580	8	12	phrases	phrase	NOUN
ejpam-4580	8	13	:	:	PUNCT
ejpam-4580	8	14	k−quasi	k−quasi	PROPN
ejpam-4580	8	15	class	class	NOUN
ejpam-4580	8	16	q(n	q(n	PROPN
ejpam-4580	8	17	)	)	PUNCT
ejpam-4580	8	18	operator	operator	NOUN
ejpam-4580	8	19	,	,	PUNCT
ejpam-4580	8	20	k−quasi	k−quasi	PROPN
ejpam-4580	8	21	class	class	NOUN
ejpam-4580	8	22	q∗(n	q∗(n	PROPN
ejpam-4580	8	23	)	)	PUNCT
ejpam-4580	8	24	operator	operator	NOUN
ejpam-4580	8	25	,	,	PUNCT
ejpam-4580	8	26	unitary	unitary	ADJ
ejpam-4580	8	27	operator	operator	NOUN
ejpam-4580	8	28	,	,	PUNCT
ejpam-4580	8	29	approximate	approximate	ADJ
ejpam-4580	8	30	point	point	NOUN
ejpam-4580	8	31	spectrum	spectrum	NOUN
ejpam-4580	8	32	1	1	NUM
ejpam-4580	8	33	.	.	PUNCT
ejpam-4580	9	1	introduction	introduction	NOUN
ejpam-4580	9	2	in	in	ADP
ejpam-4580	9	3	this	this	DET
ejpam-4580	9	4	paper	paper	NOUN
ejpam-4580	9	5	let	let	AUX
ejpam-4580	9	6	l(h	l(h	PROPN
ejpam-4580	9	7	)	)	PUNCT
ejpam-4580	9	8	stand	stand	VERB
ejpam-4580	9	9	for	for	ADP
ejpam-4580	9	10	the	the	DET
ejpam-4580	9	11	c∗	c∗	PROPN
ejpam-4580	9	12	algebra	algebra	NOUN
ejpam-4580	9	13	of	of	ADP
ejpam-4580	9	14	all	all	DET
ejpam-4580	9	15	bounded	bound	VERB
ejpam-4580	9	16	linear	linear	PROPN
ejpam-4580	9	17	operators	operator	NOUN
ejpam-4580	9	18	on	on	ADP
ejpam-4580	9	19	an	an	DET
ejpam-4580	9	20	infinite	infinite	ADJ
ejpam-4580	9	21	dimensional	dimensional	ADJ
ejpam-4580	9	22	complex	complex	ADJ
ejpam-4580	9	23	hilbert	hilbert	NOUN
ejpam-4580	9	24	space	space	NOUN
ejpam-4580	9	25	h.	h.	PROPN
ejpam-4580	9	26	for	for	ADP
ejpam-4580	9	27	t	t	PROPN
ejpam-4580	9	28	∈	∈	PROPN
ejpam-4580	9	29	l(h	l(h	PROPN
ejpam-4580	9	30	)	)	PUNCT
ejpam-4580	9	31	,	,	PUNCT
ejpam-4580	9	32	we	we	PRON
ejpam-4580	9	33	denote	denote	VERB
ejpam-4580	9	34	by	by	ADP
ejpam-4580	9	35	kert	kert	PROPN
ejpam-4580	9	36	the	the	DET
ejpam-4580	9	37	null	null	ADJ
ejpam-4580	9	38	space	space	NOUN
ejpam-4580	9	39	,	,	PUNCT
ejpam-4580	9	40	by	by	ADP
ejpam-4580	9	41	t	t	PROPN
ejpam-4580	9	42	(	(	PUNCT
ejpam-4580	9	43	h	h	NOUN
ejpam-4580	9	44	)	)	PUNCT
ejpam-4580	9	45	the	the	DET
ejpam-4580	9	46	range	range	NOUN
ejpam-4580	9	47	of	of	ADP
ejpam-4580	9	48	t.	t.	PROPN
ejpam-4580	9	49	by	by	ADP
ejpam-4580	9	50	σ(t	σ(t	PROPN
ejpam-4580	9	51	)	)	PUNCT
ejpam-4580	10	1	we	we	PRON
ejpam-4580	10	2	write	write	VERB
ejpam-4580	10	3	the	the	DET
ejpam-4580	10	4	spectrum	spectrum	NOUN
ejpam-4580	10	5	of	of	ADP
ejpam-4580	10	6	t	t	PROPN
ejpam-4580	10	7	,	,	PUNCT
ejpam-4580	10	8	the	the	DET
ejpam-4580	10	9	r(t	r(t	NOUN
ejpam-4580	10	10	)	)	PUNCT
ejpam-4580	10	11	is	be	AUX
ejpam-4580	10	12	the	the	DET
ejpam-4580	10	13	spectral	spectral	ADJ
ejpam-4580	10	14	radius	radius	NOUN
ejpam-4580	10	15	of	of	ADP
ejpam-4580	10	16	operator	operator	NOUN
ejpam-4580	10	17	t	t	PROPN
ejpam-4580	10	18	which	which	PRON
ejpam-4580	10	19	is	be	AUX
ejpam-4580	10	20	defined	define	VERB
ejpam-4580	10	21	by	by	ADP
ejpam-4580	10	22	r(t	r(t	NOUN
ejpam-4580	10	23	)	)	PUNCT
ejpam-4580	11	1	=	=	NOUN
ejpam-4580	11	2	sup{|λ|	sup{|λ|	NOUN
ejpam-4580	11	3	:	:	PUNCT
ejpam-4580	11	4	λ	λ	X
ejpam-4580	11	5	∈	∈	PROPN
ejpam-4580	11	6	σ(t	σ(t	PROPN
ejpam-4580	11	7	)	)	PUNCT
ejpam-4580	11	8	}	}	PUNCT
ejpam-4580	11	9	.	.	PUNCT
ejpam-4580	12	1	the	the	PRON
ejpam-4580	12	2	σa(t	σa(t	NUM
ejpam-4580	12	3	)	)	PUNCT
ejpam-4580	12	4	is	be	AUX
ejpam-4580	12	5	the	the	DET
ejpam-4580	12	6	approximate	approximate	ADJ
ejpam-4580	12	7	point	point	NOUN
ejpam-4580	12	8	spectrum	spectrum	NOUN
ejpam-4580	12	9	of	of	ADP
ejpam-4580	12	10	operator	operator	NOUN
ejpam-4580	12	11	t	t	PROPN
ejpam-4580	12	12	and	and	CCONJ
ejpam-4580	12	13	it	it	PRON
ejpam-4580	12	14	is	be	AUX
ejpam-4580	12	15	proved	prove	VERB
ejpam-4580	12	16	that	that	SCONJ
ejpam-4580	12	17	if	if	SCONJ
ejpam-4580	12	18	λ	λ	PROPN
ejpam-4580	12	19	∈	∈	NOUN
ejpam-4580	12	20	σa(t	σa(t	PUNCT
ejpam-4580	12	21	)	)	PUNCT
ejpam-4580	12	22	,	,	PUNCT
ejpam-4580	12	23	then	then	ADV
ejpam-4580	12	24	there	there	PRON
ejpam-4580	12	25	exist	exist	VERB
ejpam-4580	12	26	the	the	DET
ejpam-4580	12	27	sequence	sequence	NOUN
ejpam-4580	12	28	(	(	PUNCT
ejpam-4580	12	29	xn	xn	PROPN
ejpam-4580	12	30	)	)	PUNCT
ejpam-4580	12	31	,	,	PUNCT
ejpam-4580	12	32	such	such	ADJ
ejpam-4580	12	33	as	as	ADP
ejpam-4580	12	34	∥xn∥	∥xn∥	PROPN
ejpam-4580	12	35	=	=	SYM
ejpam-4580	12	36	1	1	NUM
ejpam-4580	12	37	and	and	CCONJ
ejpam-4580	12	38	∥(t	∥(t	VERB
ejpam-4580	12	39	−	−	PUNCT
ejpam-4580	12	40	λi)xn∥	λi)xn∥	X
ejpam-4580	12	41	→	→	SYM
ejpam-4580	12	42	0	0	NUM
ejpam-4580	12	43	,	,	PUNCT
ejpam-4580	12	44	n	n	PRON
ejpam-4580	12	45	→	→	SYM
ejpam-4580	12	46	∞.	∞.	PROPN
ejpam-4580	12	47	the	the	DET
ejpam-4580	12	48	null	null	ADJ
ejpam-4580	12	49	operator	operator	NOUN
ejpam-4580	12	50	and	and	CCONJ
ejpam-4580	12	51	the	the	DET
ejpam-4580	12	52	identity	identity	NOUN
ejpam-4580	12	53	on	on	ADP
ejpam-4580	12	54	h	h	NOUN
ejpam-4580	12	55	will	will	AUX
ejpam-4580	12	56	be	be	AUX
ejpam-4580	12	57	denoted	denote	VERB
ejpam-4580	12	58	by	by	ADP
ejpam-4580	12	59	o	o	PROPN
ejpam-4580	12	60	and	and	CCONJ
ejpam-4580	12	61	i	i	PROPN
ejpam-4580	12	62	,	,	PUNCT
ejpam-4580	12	63	respectively	respectively	ADV
ejpam-4580	12	64	.	.	PUNCT
ejpam-4580	13	1	if	if	SCONJ
ejpam-4580	13	2	t	t	PROPN
ejpam-4580	13	3	is	be	AUX
ejpam-4580	13	4	an	an	DET
ejpam-4580	13	5	operator	operator	NOUN
ejpam-4580	13	6	,	,	PUNCT
ejpam-4580	13	7	then	then	ADV
ejpam-4580	13	8	t	t	PROPN
ejpam-4580	13	9	∗	∗	NOUN
ejpam-4580	13	10	is	be	AUX
ejpam-4580	13	11	its	its	PRON
ejpam-4580	13	12	adjoint	adjoint	NOUN
ejpam-4580	13	13	,	,	PUNCT
ejpam-4580	13	14	and	and	CCONJ
ejpam-4580	13	15	∥t∥	∥t∥	CCONJ
ejpam-4580	13	16	=	=	SYM
ejpam-4580	13	17	∥t	∥t	ADJ
ejpam-4580	13	18	∗∥.	∗∥.	NOUN
ejpam-4580	13	19	the	the	DET
ejpam-4580	13	20	operator	operator	NOUN
ejpam-4580	13	21	t	t	PROPN
ejpam-4580	13	22	is	be	AUX
ejpam-4580	13	23	an	an	DET
ejpam-4580	13	24	isometry	isometry	NOUN
ejpam-4580	13	25	if	if	SCONJ
ejpam-4580	13	26	∥tx∥	∥tx∥	ADP
ejpam-4580	13	27	=	=	SYM
ejpam-4580	13	28	∥x∥	∥x∥	PROPN
ejpam-4580	13	29	,	,	PUNCT
ejpam-4580	13	30	for	for	ADP
ejpam-4580	13	31	all	all	DET
ejpam-4580	13	32	x	x	SYM
ejpam-4580	13	33	∈	∈	PROPN
ejpam-4580	13	34	h.	h.	NOUN
ejpam-4580	13	35	the	the	DET
ejpam-4580	13	36	operator	operator	NOUN
ejpam-4580	13	37	t	t	PROPN
ejpam-4580	13	38	is	be	AUX
ejpam-4580	13	39	called	call	VERB
ejpam-4580	13	40	unitary	unitary	ADJ
ejpam-4580	13	41	operator	operator	NOUN
ejpam-4580	13	42	if	if	SCONJ
ejpam-4580	13	43	t	t	PROPN
ejpam-4580	13	44	∗t	∗t	PROPN
ejpam-4580	13	45	=	=	SYM
ejpam-4580	13	46	tt	tt	PROPN
ejpam-4580	13	47	∗	∗	NOUN
ejpam-4580	13	48	=	=	PUNCT
ejpam-4580	13	49	i.	i.	NOUN
ejpam-4580	13	50	the	the	DET
ejpam-4580	13	51	operator	operator	NOUN
ejpam-4580	13	52	t	t	NOUN
ejpam-4580	13	53	is	be	AUX
ejpam-4580	13	54	normaloid	normaloid	NOUN
ejpam-4580	13	55	if	if	SCONJ
ejpam-4580	13	56	r(t	r(t	NOUN
ejpam-4580	13	57	)	)	PUNCT
ejpam-4580	14	1	=	=	SYM
ejpam-4580	15	1	∥t∥	∥t∥	CCONJ
ejpam-4580	15	2	and	and	CCONJ
ejpam-4580	15	3	it	it	PRON
ejpam-4580	15	4	is	be	AUX
ejpam-4580	15	5	quasinilpotent	quasinilpotent	NOUN
ejpam-4580	15	6	if	if	SCONJ
ejpam-4580	15	7	r(t	r(t	NOUN
ejpam-4580	15	8	)	)	PUNCT
ejpam-4580	16	1	=	=	SYM
ejpam-4580	16	2	0	0	X
ejpam-4580	16	3	.	.	PUNCT
ejpam-4580	16	4	recall	recall	VERB
ejpam-4580	16	5	that	that	SCONJ
ejpam-4580	16	6	an	an	DET
ejpam-4580	16	7	operator	operator	NOUN
ejpam-4580	16	8	t	t	PROPN
ejpam-4580	16	9	∈	∈	PROPN
ejpam-4580	16	10	l(h	l(h	PROPN
ejpam-4580	16	11	)	)	PUNCT
ejpam-4580	16	12	is	be	AUX
ejpam-4580	16	13	said	say	VERB
ejpam-4580	16	14	to	to	PART
ejpam-4580	16	15	be	be	AUX
ejpam-4580	16	16	:	:	PUNCT
ejpam-4580	16	17	doi	doi	NOUN
ejpam-4580	16	18	:	:	PUNCT
ejpam-4580	16	19	https://doi.org/10.29020/nybg.ejpam.v15i4.4580	https://doi.org/10.29020/nybg.ejpam.v15i4.4580	ADJ
ejpam-4580	16	20	email	email	NOUN
ejpam-4580	16	21	address	address	NOUN
ejpam-4580	16	22	:	:	PUNCT
ejpam-4580	16	23	shqipe.lohaj@uni-pr.edu	shqipe.lohaj@uni-pr.edu	PROPN
ejpam-4580	16	24	(	(	PUNCT
ejpam-4580	16	25	sh	sh	PROPN
ejpam-4580	16	26	.	.	PROPN
ejpam-4580	16	27	lohaj	lohaj	PROPN
ejpam-4580	16	28	)	)	PUNCT
ejpam-4580	16	29	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4580	16	30	1836	1836	NUM
ejpam-4580	17	1	©	©	PROPN
ejpam-4580	17	2	2022	2022	NUM
ejpam-4580	17	3	ejpam	ejpam	VERB
ejpam-4580	17	4	all	all	DET
ejpam-4580	17	5	rights	right	NOUN
ejpam-4580	17	6	reserved	reserve	VERB
ejpam-4580	17	7	.	.	PUNCT
ejpam-4580	18	1	sh	sh	PROPN
ejpam-4580	18	2	.	.	PROPN
ejpam-4580	18	3	lohaj	lohaj	PROPN
ejpam-4580	18	4	/	/	SYM
ejpam-4580	18	5	eur	eur	PROPN
ejpam-4580	18	6	.	.	PUNCT
ejpam-4580	19	1	j.	j.	PROPN
ejpam-4580	19	2	pure	pure	PROPN
ejpam-4580	19	3	appl	appl	PROPN
ejpam-4580	19	4	.	.	PROPN
ejpam-4580	19	5	math	math	PROPN
ejpam-4580	19	6	,	,	PUNCT
ejpam-4580	19	7	15	15	NUM
ejpam-4580	19	8	(	(	PUNCT
ejpam-4580	19	9	4	4	NUM
ejpam-4580	19	10	)	)	PUNCT
ejpam-4580	19	11	(	(	PUNCT
ejpam-4580	19	12	2022	2022	NUM
ejpam-4580	19	13	)	)	PUNCT
ejpam-4580	19	14	,	,	PUNCT
ejpam-4580	19	15	1836	1836	NUM
ejpam-4580	19	16	-	-	SYM
ejpam-4580	19	17	1853	1853	NUM
ejpam-4580	19	18	1837	1837	NUM
ejpam-4580	19	19	•	•	ADP
ejpam-4580	19	20	k−quasi−paranormal	k−quasi−paranormal	PROPN
ejpam-4580	19	21	(	(	PUNCT
ejpam-4580	19	22	see	see	VERB
ejpam-4580	19	23	[	[	X
ejpam-4580	19	24	9	9	NUM
ejpam-4580	19	25	]	]	SYM
ejpam-4580	19	26	)	)	PUNCT
ejpam-4580	19	27	if	if	SCONJ
ejpam-4580	19	28	∥t	∥t	ADJ
ejpam-4580	19	29	k+1x∥2	k+1x∥2	NOUN
ejpam-4580	19	30	≤	≤	X
ejpam-4580	19	31	∥t	∥t	PROPN
ejpam-4580	19	32	k+2x∥∥t	k+2x∥∥t	NOUN
ejpam-4580	19	33	kx∥	kx∥	NOUN
ejpam-4580	19	34	,	,	PUNCT
ejpam-4580	19	35	for	for	ADP
ejpam-4580	19	36	all	all	DET
ejpam-4580	19	37	x	x	SYM
ejpam-4580	19	38	∈	∈	PROPN
ejpam-4580	19	39	h	h	NOUN
ejpam-4580	19	40	,	,	PUNCT
ejpam-4580	19	41	where	where	SCONJ
ejpam-4580	19	42	k	k	PROPN
ejpam-4580	19	43	is	be	AUX
ejpam-4580	19	44	a	a	DET
ejpam-4580	19	45	natural	natural	ADJ
ejpam-4580	19	46	number	number	NOUN
ejpam-4580	19	47	.	.	PUNCT
ejpam-4580	20	1	•	•	NUM
ejpam-4580	20	2	k−quasi−	k−quasi−	PROPN
ejpam-4580	20	3	∗	∗	NOUN
ejpam-4580	20	4	−paranormal	−paranormal	PROPN
ejpam-4580	20	5	(	(	PUNCT
ejpam-4580	20	6	see	see	VERB
ejpam-4580	20	7	[	[	X
ejpam-4580	20	8	5	5	NUM
ejpam-4580	20	9	]	]	PUNCT
ejpam-4580	20	10	)	)	PUNCT
ejpam-4580	20	11	if	if	SCONJ
ejpam-4580	20	12	∥t	∥t	PROPN
ejpam-4580	20	13	∗t	∗t	ADJ
ejpam-4580	20	14	kx∥2	kx∥2	NOUN
ejpam-4580	20	15	≤	≤	NUM
ejpam-4580	20	16	∥t	∥t	PROPN
ejpam-4580	20	17	k+2x∥∥t	k+2x∥∥t	NOUN
ejpam-4580	20	18	kx∥	kx∥	NOUN
ejpam-4580	20	19	,	,	PUNCT
ejpam-4580	20	20	for	for	ADP
ejpam-4580	20	21	all	all	DET
ejpam-4580	20	22	x	x	SYM
ejpam-4580	20	23	∈	∈	PROPN
ejpam-4580	20	24	h	h	NOUN
ejpam-4580	20	25	,	,	PUNCT
ejpam-4580	20	26	where	where	SCONJ
ejpam-4580	20	27	k	k	PROPN
ejpam-4580	20	28	is	be	AUX
ejpam-4580	20	29	a	a	DET
ejpam-4580	20	30	natural	natural	ADJ
ejpam-4580	20	31	number	number	NOUN
ejpam-4580	20	32	.	.	PUNCT
ejpam-4580	21	1	•	•	NUM
ejpam-4580	21	2	k−quasi−class	k−quasi−class	ADP
ejpam-4580	21	3	a	a	DET
ejpam-4580	21	4	operator	operator	NOUN
ejpam-4580	21	5	(	(	PUNCT
ejpam-4580	21	6	see	see	VERB
ejpam-4580	21	7	[	[	X
ejpam-4580	21	8	2	2	NUM
ejpam-4580	21	9	]	]	PUNCT
ejpam-4580	21	10	)	)	PUNCT
ejpam-4580	21	11	if	if	SCONJ
ejpam-4580	21	12	t	t	PROPN
ejpam-4580	21	13	∗k|t	∗k|t	PROPN
ejpam-4580	21	14	2|t	2|t	PROPN
ejpam-4580	21	15	k	k	PROPN
ejpam-4580	21	16	≥	≥	PROPN
ejpam-4580	21	17	t	t	PROPN
ejpam-4580	21	18	∗k|t	∗k|t	PROPN
ejpam-4580	21	19	|2	|2	NUM
ejpam-4580	21	20	t	t	PROPN
ejpam-4580	21	21	k.	k.	NOUN
ejpam-4580	21	22	•	•	PROPN
ejpam-4580	21	23	k−quasi−	k−quasi−	PROPN
ejpam-4580	21	24	∗	∗	NOUN
ejpam-4580	21	25	−class	−class	NOUN
ejpam-4580	21	26	a	a	DET
ejpam-4580	21	27	operator	operator	NOUN
ejpam-4580	21	28	(	(	PUNCT
ejpam-4580	21	29	see	see	VERB
ejpam-4580	21	30	[	[	X
ejpam-4580	21	31	10	10	NUM
ejpam-4580	21	32	]	]	NUM
ejpam-4580	21	33	)	)	PUNCT
ejpam-4580	21	34	,	,	PUNCT
ejpam-4580	21	35	if	if	SCONJ
ejpam-4580	21	36	t	t	PROPN
ejpam-4580	21	37	∗k|t	∗k|t	PROPN
ejpam-4580	21	38	2|t	2|t	PROPN
ejpam-4580	21	39	k	k	PROPN
ejpam-4580	21	40	≥	≥	PROPN
ejpam-4580	21	41	t	t	PROPN
ejpam-4580	21	42	∗k|t	∗k|t	PROPN
ejpam-4580	21	43	∗|2	∗|2	PROPN
ejpam-4580	21	44	t	t	PROPN
ejpam-4580	22	1	k.	k.	PROPN
ejpam-4580	22	2	•	•	NUM
ejpam-4580	22	3	k−quasi	k−quasi	PROPN
ejpam-4580	22	4	class	class	NOUN
ejpam-4580	22	5	q	q	PROPN
ejpam-4580	22	6	(	(	PUNCT
ejpam-4580	22	7	see	see	VERB
ejpam-4580	22	8	[	[	X
ejpam-4580	22	9	4	4	NUM
ejpam-4580	22	10	]	]	PUNCT
ejpam-4580	22	11	)	)	PUNCT
ejpam-4580	22	12	if	if	SCONJ
ejpam-4580	22	13	∥t	∥t	ADJ
ejpam-4580	22	14	k+1x∥2	k+1x∥2	NOUN
ejpam-4580	22	15	≤	≤	NOUN
ejpam-4580	22	16	1	1	NUM
ejpam-4580	22	17	2	2	NUM
ejpam-4580	22	18	(	(	PUNCT
ejpam-4580	22	19	∥t	∥t	ADJ
ejpam-4580	22	20	k+2x∥2	k+2x∥2	NOUN
ejpam-4580	22	21	+	+	CCONJ
ejpam-4580	22	22	∥t	∥t	ADJ
ejpam-4580	22	23	kx∥2	kx∥2	NOUN
ejpam-4580	22	24	)	)	PUNCT
ejpam-4580	22	25	,	,	PUNCT
ejpam-4580	22	26	for	for	ADP
ejpam-4580	22	27	all	all	DET
ejpam-4580	22	28	x	x	SYM
ejpam-4580	22	29	∈	∈	PROPN
ejpam-4580	22	30	h	h	NOUN
ejpam-4580	22	31	,	,	PUNCT
ejpam-4580	22	32	where	where	SCONJ
ejpam-4580	22	33	k	k	PROPN
ejpam-4580	22	34	is	be	AUX
ejpam-4580	22	35	a	a	DET
ejpam-4580	22	36	natural	natural	ADJ
ejpam-4580	22	37	number	number	NOUN
ejpam-4580	22	38	.	.	PUNCT
ejpam-4580	23	1	it	it	PRON
ejpam-4580	23	2	is	be	AUX
ejpam-4580	23	3	proved	prove	VERB
ejpam-4580	23	4	that	that	SCONJ
ejpam-4580	23	5	an	an	DET
ejpam-4580	23	6	operator	operator	NOUN
ejpam-4580	23	7	t	t	PROPN
ejpam-4580	23	8	∈	∈	PROPN
ejpam-4580	23	9	l(h	l(h	PROPN
ejpam-4580	23	10	)	)	PUNCT
ejpam-4580	23	11	is	be	AUX
ejpam-4580	23	12	of	of	ADP
ejpam-4580	23	13	the	the	DET
ejpam-4580	23	14	k−quasi	k−quasi	PROPN
ejpam-4580	23	15	class	class	NOUN
ejpam-4580	23	16	q	q	NOUN
ejpam-4580	23	17	if	if	SCONJ
ejpam-4580	23	18	t	t	PROPN
ejpam-4580	23	19	∗k(t	∗k(t	PROPN
ejpam-4580	23	20	∗2	∗2	PROPN
ejpam-4580	23	21	t	t	PROPN
ejpam-4580	23	22	2	2	NUM
ejpam-4580	23	23	−	−	PROPN
ejpam-4580	23	24	2	2	NUM
ejpam-4580	23	25	t	t	NOUN
ejpam-4580	23	26	∗t	∗t	NOUN
ejpam-4580	23	27	+	+	CCONJ
ejpam-4580	23	28	i)t	i)t	VERB
ejpam-4580	24	1	k	k	PRON
ejpam-4580	24	2	≥	≥	PROPN
ejpam-4580	24	3	o.	o.	NOUN
ejpam-4580	24	4	•	•	NUM
ejpam-4580	24	5	k−quasi	k−quasi	NOUN
ejpam-4580	24	6	class	class	NOUN
ejpam-4580	24	7	q∗	q∗	NOUN
ejpam-4580	24	8	(	(	PUNCT
ejpam-4580	24	9	see	see	VERB
ejpam-4580	24	10	[	[	X
ejpam-4580	24	11	6	6	NUM
ejpam-4580	24	12	]	]	SYM
ejpam-4580	24	13	)	)	PUNCT
ejpam-4580	24	14	if	if	SCONJ
ejpam-4580	24	15	∥t	∥t	PROPN
ejpam-4580	24	16	∗t	∗t	ADJ
ejpam-4580	24	17	kx∥2	kx∥2	NOUN
ejpam-4580	24	18	≤	≤	ADV
ejpam-4580	24	19	1	1	NUM
ejpam-4580	24	20	2	2	NUM
ejpam-4580	24	21	(	(	PUNCT
ejpam-4580	24	22	∥t	∥t	ADJ
ejpam-4580	24	23	k+2x∥2	k+2x∥2	NOUN
ejpam-4580	24	24	+	+	CCONJ
ejpam-4580	24	25	∥t	∥t	ADJ
ejpam-4580	24	26	kx∥2	kx∥2	NOUN
ejpam-4580	24	27	)	)	PUNCT
ejpam-4580	24	28	,	,	PUNCT
ejpam-4580	24	29	for	for	ADP
ejpam-4580	24	30	all	all	DET
ejpam-4580	24	31	x	x	SYM
ejpam-4580	24	32	∈	∈	PROPN
ejpam-4580	24	33	h	h	NOUN
ejpam-4580	24	34	,	,	PUNCT
ejpam-4580	24	35	where	where	SCONJ
ejpam-4580	24	36	k	k	PROPN
ejpam-4580	24	37	is	be	AUX
ejpam-4580	24	38	a	a	DET
ejpam-4580	24	39	natural	natural	ADJ
ejpam-4580	24	40	number	number	NOUN
ejpam-4580	24	41	.	.	PUNCT
ejpam-4580	25	1	it	it	PRON
ejpam-4580	25	2	is	be	AUX
ejpam-4580	25	3	proved	prove	VERB
ejpam-4580	25	4	that	that	SCONJ
ejpam-4580	25	5	an	an	DET
ejpam-4580	25	6	operator	operator	NOUN
ejpam-4580	25	7	t	t	PROPN
ejpam-4580	25	8	∈	∈	PROPN
ejpam-4580	25	9	l(h	l(h	PROPN
ejpam-4580	25	10	)	)	PUNCT
ejpam-4580	25	11	is	be	AUX
ejpam-4580	25	12	of	of	ADP
ejpam-4580	25	13	the	the	DET
ejpam-4580	25	14	k−quasi	k−quasi	PROPN
ejpam-4580	25	15	class	class	NOUN
ejpam-4580	25	16	q∗	q∗	NOUN
ejpam-4580	25	17	if	if	SCONJ
ejpam-4580	25	18	t	t	PROPN
ejpam-4580	25	19	∗k(t	∗k(t	PROPN
ejpam-4580	25	20	∗2	∗2	PROPN
ejpam-4580	25	21	t	t	PROPN
ejpam-4580	25	22	2	2	NUM
ejpam-4580	25	23	−	−	NOUN
ejpam-4580	25	24	2tt	2tt	ADJ
ejpam-4580	25	25	∗	∗	NOUN
ejpam-4580	25	26	+	+	CCONJ
ejpam-4580	25	27	i)t	i)t	NOUN
ejpam-4580	26	1	k	k	X
ejpam-4580	26	2	≥	≥	PROPN
ejpam-4580	26	3	o.	o.	NOUN
ejpam-4580	26	4	•	•	NUM
ejpam-4580	26	5	class	class	NOUN
ejpam-4580	26	6	q(n	q(n	PROPN
ejpam-4580	26	7	)	)	PUNCT
ejpam-4580	26	8	(	(	PUNCT
ejpam-4580	26	9	see	see	VERB
ejpam-4580	26	10	[	[	X
ejpam-4580	26	11	7	7	NUM
ejpam-4580	26	12	]	]	PUNCT
ejpam-4580	26	13	)	)	PUNCT
ejpam-4580	26	14	if	if	SCONJ
ejpam-4580	26	15	n∥tx∥2	n∥tx∥2	NOUN
ejpam-4580	26	16	≤	≤	X
ejpam-4580	26	17	∥t	∥t	ADJ
ejpam-4580	26	18	2x∥2	2x∥2	NOUN
ejpam-4580	26	19	+	+	CCONJ
ejpam-4580	26	20	∥x∥2	∥x∥2	NOUN
ejpam-4580	26	21	,	,	PUNCT
ejpam-4580	26	22	for	for	ADP
ejpam-4580	26	23	all	all	DET
ejpam-4580	26	24	x	x	SYM
ejpam-4580	26	25	∈	∈	PROPN
ejpam-4580	26	26	h.	h.	NOUN
ejpam-4580	26	27	it	it	PRON
ejpam-4580	26	28	is	be	AUX
ejpam-4580	26	29	proved	prove	VERB
ejpam-4580	26	30	that	that	SCONJ
ejpam-4580	26	31	an	an	DET
ejpam-4580	26	32	operator	operator	NOUN
ejpam-4580	26	33	t	t	PROPN
ejpam-4580	26	34	∈	∈	PROPN
ejpam-4580	26	35	l(h	l(h	PROPN
ejpam-4580	26	36	)	)	PUNCT
ejpam-4580	26	37	is	be	AUX
ejpam-4580	26	38	of	of	ADP
ejpam-4580	26	39	the	the	DET
ejpam-4580	26	40	class	class	NOUN
ejpam-4580	26	41	q(n	q(n	PROPN
ejpam-4580	26	42	)	)	PUNCT
ejpam-4580	26	43	if	if	SCONJ
ejpam-4580	26	44	t	t	PROPN
ejpam-4580	26	45	∗2	∗2	PROPN
ejpam-4580	26	46	t	t	PROPN
ejpam-4580	26	47	2	2	NUM
ejpam-4580	26	48	−nt	−nt	ADP
ejpam-4580	26	49	∗t	∗t	PROPN
ejpam-4580	27	1	+	+	CCONJ
ejpam-4580	27	2	i	i	PRON
ejpam-4580	27	3	≥	≥	VERB
ejpam-4580	27	4	o.	o.	PROPN
ejpam-4580	28	1	sh	sh	PROPN
ejpam-4580	28	2	.	.	PROPN
ejpam-4580	28	3	lohaj	lohaj	PROPN
ejpam-4580	28	4	/	/	SYM
ejpam-4580	28	5	eur	eur	PROPN
ejpam-4580	28	6	.	.	PUNCT
ejpam-4580	29	1	j.	j.	PROPN
ejpam-4580	29	2	pure	pure	PROPN
ejpam-4580	29	3	appl	appl	PROPN
ejpam-4580	29	4	.	.	PROPN
ejpam-4580	29	5	math	math	PROPN
ejpam-4580	29	6	,	,	PUNCT
ejpam-4580	29	7	15	15	NUM
ejpam-4580	29	8	(	(	PUNCT
ejpam-4580	29	9	4	4	NUM
ejpam-4580	29	10	)	)	PUNCT
ejpam-4580	29	11	(	(	PUNCT
ejpam-4580	29	12	2022	2022	NUM
ejpam-4580	29	13	)	)	PUNCT
ejpam-4580	29	14	,	,	PUNCT
ejpam-4580	29	15	1836	1836	NUM
ejpam-4580	29	16	-	-	SYM
ejpam-4580	29	17	1853	1853	NUM
ejpam-4580	29	18	1838	1838	NUM
ejpam-4580	29	19	•	•	NOUN
ejpam-4580	29	20	class	class	NOUN
ejpam-4580	29	21	q∗(n	q∗(n	PROPN
ejpam-4580	29	22	)	)	PUNCT
ejpam-4580	29	23	(	(	PUNCT
ejpam-4580	29	24	see	see	VERB
ejpam-4580	29	25	[	[	X
ejpam-4580	29	26	7	7	NUM
ejpam-4580	29	27	]	]	PUNCT
ejpam-4580	29	28	)	)	PUNCT
ejpam-4580	29	29	if	if	SCONJ
ejpam-4580	29	30	n∥t	n∥t	ADJ
ejpam-4580	29	31	∗x∥2	∗x∥2	NOUN
ejpam-4580	29	32	≤	≤	X
ejpam-4580	29	33	∥t	∥t	ADJ
ejpam-4580	29	34	2x∥2	2x∥2	NOUN
ejpam-4580	29	35	+	+	CCONJ
ejpam-4580	29	36	∥x∥2	∥x∥2	NOUN
ejpam-4580	29	37	,	,	PUNCT
ejpam-4580	29	38	for	for	ADP
ejpam-4580	29	39	all	all	DET
ejpam-4580	29	40	x	x	SYM
ejpam-4580	29	41	∈	∈	PROPN
ejpam-4580	29	42	h.	h.	NOUN
ejpam-4580	29	43	it	it	PRON
ejpam-4580	29	44	is	be	AUX
ejpam-4580	29	45	proved	prove	VERB
ejpam-4580	29	46	that	that	SCONJ
ejpam-4580	29	47	an	an	DET
ejpam-4580	29	48	operator	operator	NOUN
ejpam-4580	29	49	t	t	PROPN
ejpam-4580	29	50	∈	∈	PROPN
ejpam-4580	29	51	l(h	l(h	PROPN
ejpam-4580	29	52	)	)	PUNCT
ejpam-4580	29	53	is	be	AUX
ejpam-4580	29	54	of	of	ADP
ejpam-4580	29	55	the	the	DET
ejpam-4580	29	56	class	class	NOUN
ejpam-4580	29	57	q∗(n	q∗(n	PROPN
ejpam-4580	29	58	)	)	PUNCT
ejpam-4580	29	59	if	if	SCONJ
ejpam-4580	29	60	t	t	PROPN
ejpam-4580	29	61	∗2	∗2	PROPN
ejpam-4580	29	62	t	t	PROPN
ejpam-4580	29	63	2	2	NUM
ejpam-4580	29	64	−ntt	−ntt	NOUN
ejpam-4580	29	65	∗	∗	NOUN
ejpam-4580	30	1	+	+	X
ejpam-4580	31	1	i	i	PRON
ejpam-4580	31	2	≥	≥	VERB
ejpam-4580	31	3	o.	o.	INTJ
ejpam-4580	31	4	the	the	DET
ejpam-4580	31	5	following	follow	VERB
ejpam-4580	31	6	definitions	definition	NOUN
ejpam-4580	31	7	describes	describe	VERB
ejpam-4580	31	8	the	the	DET
ejpam-4580	31	9	classes	class	NOUN
ejpam-4580	31	10	of	of	ADP
ejpam-4580	31	11	operators	operator	NOUN
ejpam-4580	31	12	we	we	PRON
ejpam-4580	31	13	will	will	AUX
ejpam-4580	31	14	study	study	VERB
ejpam-4580	31	15	in	in	ADP
ejpam-4580	31	16	this	this	DET
ejpam-4580	31	17	paper	paper	NOUN
ejpam-4580	31	18	.	.	PUNCT
ejpam-4580	32	1	definition	definition	NOUN
ejpam-4580	32	2	1	1	NUM
ejpam-4580	32	3	.	.	PUNCT
ejpam-4580	33	1	an	an	DET
ejpam-4580	33	2	operator	operator	NOUN
ejpam-4580	33	3	t	t	PROPN
ejpam-4580	33	4	∈	∈	PROPN
ejpam-4580	33	5	l(h	l(h	PROPN
ejpam-4580	33	6	)	)	PUNCT
ejpam-4580	33	7	is	be	AUX
ejpam-4580	33	8	of	of	ADP
ejpam-4580	33	9	k−quasi	k−quasi	NOUN
ejpam-4580	33	10	class	class	NOUN
ejpam-4580	33	11	q(n	q(n	PROPN
ejpam-4580	33	12	)	)	PUNCT
ejpam-4580	33	13	,	,	PUNCT
ejpam-4580	33	14	for	for	ADP
ejpam-4580	33	15	a	a	DET
ejpam-4580	33	16	fixed	fix	VERB
ejpam-4580	33	17	real	real	ADJ
ejpam-4580	33	18	number	number	NOUN
ejpam-4580	33	19	n	n	CCONJ
ejpam-4580	33	20	≥	≥	NOUN
ejpam-4580	33	21	1	1	NUM
ejpam-4580	33	22	and	and	CCONJ
ejpam-4580	33	23	k	k	X
ejpam-4580	33	24	a	a	DET
ejpam-4580	33	25	natural	natural	ADJ
ejpam-4580	33	26	number	number	NOUN
ejpam-4580	33	27	,	,	PUNCT
ejpam-4580	33	28	if	if	SCONJ
ejpam-4580	33	29	t	t	PROPN
ejpam-4580	33	30	satisfies	satisfy	VERB
ejpam-4580	33	31	n∥t	n∥t	ADJ
ejpam-4580	33	32	k+1x∥2	k+1x∥2	NOUN
ejpam-4580	33	33	≤	≤	ADV
ejpam-4580	33	34	∥t	∥t	ADJ
ejpam-4580	33	35	k+2x∥2	k+2x∥2	NOUN
ejpam-4580	34	1	+	+	CCONJ
ejpam-4580	34	2	∥t	∥t	ADJ
ejpam-4580	34	3	kx∥2	kx∥2	NOUN
ejpam-4580	34	4	,	,	PUNCT
ejpam-4580	34	5	for	for	ADP
ejpam-4580	34	6	all	all	DET
ejpam-4580	34	7	x	x	SYM
ejpam-4580	34	8	∈	∈	PROPN
ejpam-4580	34	9	h.	h.	NOUN
ejpam-4580	34	10	definition	definition	NOUN
ejpam-4580	34	11	2	2	NUM
ejpam-4580	34	12	.	.	PUNCT
ejpam-4580	34	13	an	an	DET
ejpam-4580	34	14	operator	operator	NOUN
ejpam-4580	34	15	t	t	PROPN
ejpam-4580	34	16	∈	∈	PROPN
ejpam-4580	34	17	l(h	l(h	PROPN
ejpam-4580	34	18	)	)	PUNCT
ejpam-4580	34	19	is	be	AUX
ejpam-4580	34	20	of	of	ADP
ejpam-4580	34	21	quasi	quasi	ADJ
ejpam-4580	34	22	class	class	NOUN
ejpam-4580	34	23	q∗(n	q∗(n	PROPN
ejpam-4580	34	24	)	)	PUNCT
ejpam-4580	34	25	,	,	PUNCT
ejpam-4580	34	26	for	for	ADP
ejpam-4580	34	27	a	a	DET
ejpam-4580	34	28	fixed	fix	VERB
ejpam-4580	34	29	real	real	ADJ
ejpam-4580	34	30	number	number	NOUN
ejpam-4580	34	31	n	n	CCONJ
ejpam-4580	34	32	≥	≥	NOUN
ejpam-4580	34	33	1	1	NUM
ejpam-4580	34	34	and	and	CCONJ
ejpam-4580	34	35	k	k	X
ejpam-4580	34	36	a	a	DET
ejpam-4580	34	37	natural	natural	ADJ
ejpam-4580	34	38	number	number	NOUN
ejpam-4580	34	39	,	,	PUNCT
ejpam-4580	34	40	if	if	SCONJ
ejpam-4580	34	41	t	t	PROPN
ejpam-4580	34	42	satisfies	satisfy	VERB
ejpam-4580	34	43	n∥t	n∥t	PROPN
ejpam-4580	34	44	∗t	∗t	PROPN
ejpam-4580	34	45	kx∥2	kx∥2	PROPN
ejpam-4580	34	46	≤	≤	NUM
ejpam-4580	34	47	∥t	∥t	ADJ
ejpam-4580	34	48	k+2x∥2	k+2x∥2	NOUN
ejpam-4580	35	1	+	+	CCONJ
ejpam-4580	35	2	∥t	∥t	ADJ
ejpam-4580	35	3	kx∥2	kx∥2	NOUN
ejpam-4580	35	4	,	,	PUNCT
ejpam-4580	35	5	for	for	ADP
ejpam-4580	35	6	all	all	DET
ejpam-4580	35	7	x	x	SYM
ejpam-4580	35	8	∈	∈	PROPN
ejpam-4580	35	9	h.	h.	NOUN
ejpam-4580	35	10	in	in	ADP
ejpam-4580	35	11	this	this	DET
ejpam-4580	35	12	paper	paper	NOUN
ejpam-4580	35	13	we	we	PRON
ejpam-4580	35	14	give	give	VERB
ejpam-4580	35	15	basic	basic	ADJ
ejpam-4580	35	16	properties	property	NOUN
ejpam-4580	35	17	of	of	ADP
ejpam-4580	35	18	k−quasi	k−quasi	NOUN
ejpam-4580	35	19	class	class	NOUN
ejpam-4580	35	20	q(n	q(n	PROPN
ejpam-4580	35	21	)	)	PUNCT
ejpam-4580	35	22	and	and	CCONJ
ejpam-4580	35	23	k−quasi	k−quasi	PROPN
ejpam-4580	35	24	class	class	NOUN
ejpam-4580	35	25	q∗(n	q∗(n	PROPN
ejpam-4580	35	26	)	)	PUNCT
ejpam-4580	35	27	operators	operator	NOUN
ejpam-4580	35	28	.	.	PUNCT
ejpam-4580	36	1	we	we	PRON
ejpam-4580	36	2	discuss	discuss	VERB
ejpam-4580	36	3	some	some	DET
ejpam-4580	36	4	inclusion	inclusion	NOUN
ejpam-4580	36	5	relations	relation	NOUN
ejpam-4580	36	6	,	,	PUNCT
ejpam-4580	36	7	the	the	DET
ejpam-4580	36	8	structural	structural	ADJ
ejpam-4580	36	9	and	and	CCONJ
ejpam-4580	36	10	spectral	spectral	ADJ
ejpam-4580	36	11	properties	property	NOUN
ejpam-4580	36	12	and	and	CCONJ
ejpam-4580	36	13	also	also	ADV
ejpam-4580	36	14	we	we	PRON
ejpam-4580	36	15	obtained	obtain	VERB
ejpam-4580	36	16	a	a	DET
ejpam-4580	36	17	matrix	matrix	NOUN
ejpam-4580	36	18	representation	representation	NOUN
ejpam-4580	36	19	of	of	ADP
ejpam-4580	36	20	these	these	DET
ejpam-4580	36	21	new	new	ADJ
ejpam-4580	36	22	classes	class	NOUN
ejpam-4580	36	23	of	of	ADP
ejpam-4580	36	24	operators	operator	NOUN
ejpam-4580	36	25	.	.	PUNCT
ejpam-4580	37	1	2	2	X
ejpam-4580	37	2	.	.	X
ejpam-4580	37	3	inclusion	inclusion	NOUN
ejpam-4580	37	4	relations	relation	NOUN
ejpam-4580	37	5	and	and	CCONJ
ejpam-4580	37	6	basic	basic	ADJ
ejpam-4580	37	7	properties	property	NOUN
ejpam-4580	37	8	first	first	ADV
ejpam-4580	37	9	,	,	PUNCT
ejpam-4580	37	10	we	we	PRON
ejpam-4580	37	11	state	state	VERB
ejpam-4580	37	12	a	a	DET
ejpam-4580	37	13	proposition	proposition	NOUN
ejpam-4580	37	14	which	which	PRON
ejpam-4580	37	15	gives	give	VERB
ejpam-4580	37	16	necessary	necessary	ADJ
ejpam-4580	37	17	and	and	CCONJ
ejpam-4580	37	18	sufficient	sufficient	ADJ
ejpam-4580	37	19	conditions	condition	NOUN
ejpam-4580	37	20	for	for	SCONJ
ejpam-4580	37	21	an	an	DET
ejpam-4580	37	22	operator	operator	NOUN
ejpam-4580	37	23	t	t	NOUN
ejpam-4580	37	24	to	to	PART
ejpam-4580	37	25	be	be	AUX
ejpam-4580	37	26	of	of	ADP
ejpam-4580	37	27	k−quasi	k−quasi	NOUN
ejpam-4580	37	28	class	class	NOUN
ejpam-4580	37	29	q(n	q(n	PROPN
ejpam-4580	37	30	)	)	PUNCT
ejpam-4580	37	31	.	.	PUNCT
ejpam-4580	38	1	proposition	proposition	NOUN
ejpam-4580	38	2	1	1	NUM
ejpam-4580	38	3	.	.	PUNCT
ejpam-4580	39	1	an	an	DET
ejpam-4580	39	2	operator	operator	NOUN
ejpam-4580	39	3	t	t	PROPN
ejpam-4580	39	4	∈	∈	PROPN
ejpam-4580	39	5	l(h	l(h	PROPN
ejpam-4580	39	6	)	)	PUNCT
ejpam-4580	39	7	is	be	AUX
ejpam-4580	39	8	of	of	ADP
ejpam-4580	39	9	k−quasi	k−quasi	NOUN
ejpam-4580	39	10	class	class	NOUN
ejpam-4580	39	11	q(n	q(n	PROPN
ejpam-4580	39	12	)	)	PUNCT
ejpam-4580	40	1	if	if	SCONJ
ejpam-4580	40	2	and	and	CCONJ
ejpam-4580	40	3	only	only	ADV
ejpam-4580	40	4	if	if	SCONJ
ejpam-4580	40	5	t	t	PROPN
ejpam-4580	40	6	∗k(t	∗k(t	PROPN
ejpam-4580	40	7	∗2	∗2	PROPN
ejpam-4580	40	8	t	t	PROPN
ejpam-4580	40	9	2	2	NUM
ejpam-4580	40	10	−nt	−nt	ADP
ejpam-4580	40	11	∗t	∗t	PROPN
ejpam-4580	40	12	+	+	CCONJ
ejpam-4580	40	13	i)t	i)t	VERB
ejpam-4580	41	1	k	k	X
ejpam-4580	41	2	≥	≥	NUM
ejpam-4580	41	3	o	o	NOUN
ejpam-4580	41	4	,	,	PUNCT
ejpam-4580	41	5	for	for	ADP
ejpam-4580	41	6	a	a	DET
ejpam-4580	41	7	fixed	fix	VERB
ejpam-4580	41	8	real	real	ADJ
ejpam-4580	41	9	number	number	NOUN
ejpam-4580	41	10	n	n	CCONJ
ejpam-4580	41	11	≥	≥	NOUN
ejpam-4580	41	12	1	1	NUM
ejpam-4580	41	13	and	and	CCONJ
ejpam-4580	41	14	k	k	X
ejpam-4580	41	15	a	a	DET
ejpam-4580	41	16	natural	natural	ADJ
ejpam-4580	41	17	number	number	NOUN
ejpam-4580	41	18	.	.	PUNCT
ejpam-4580	42	1	proof	proof	NOUN
ejpam-4580	42	2	.	.	PUNCT
ejpam-4580	43	1	since	since	SCONJ
ejpam-4580	43	2	t	t	PROPN
ejpam-4580	43	3	is	be	AUX
ejpam-4580	43	4	of	of	ADP
ejpam-4580	43	5	k−quasi	k−quasi	NOUN
ejpam-4580	43	6	class	class	NOUN
ejpam-4580	43	7	q(n	q(n	PROPN
ejpam-4580	43	8	)	)	PUNCT
ejpam-4580	43	9	,	,	PUNCT
ejpam-4580	43	10	for	for	ADP
ejpam-4580	43	11	a	a	DET
ejpam-4580	43	12	fixed	fix	VERB
ejpam-4580	43	13	real	real	ADJ
ejpam-4580	43	14	number	number	NOUN
ejpam-4580	43	15	n	n	CCONJ
ejpam-4580	43	16	≥	≥	NOUN
ejpam-4580	43	17	1	1	NUM
ejpam-4580	43	18	and	and	CCONJ
ejpam-4580	43	19	k	k	PROPN
ejpam-4580	43	20	a	a	DET
ejpam-4580	43	21	natural	natural	ADJ
ejpam-4580	43	22	number	number	NOUN
ejpam-4580	43	23	then	then	ADV
ejpam-4580	43	24	n∥t	n∥t	ADJ
ejpam-4580	43	25	k+1x∥2	k+1x∥2	NOUN
ejpam-4580	43	26	≤	≤	X
ejpam-4580	43	27	∥t	∥t	ADJ
ejpam-4580	43	28	k+2x∥2	k+2x∥2	NOUN
ejpam-4580	43	29	+	+	CCONJ
ejpam-4580	43	30	∥t	∥t	ADJ
ejpam-4580	43	31	kx∥2	kx∥2	NOUN
ejpam-4580	43	32	,	,	PUNCT
ejpam-4580	43	33	for	for	ADP
ejpam-4580	43	34	all	all	DET
ejpam-4580	43	35	x	x	SYM
ejpam-4580	43	36	∈	∈	PROPN
ejpam-4580	43	37	h.	h.	NOUN
ejpam-4580	43	38	then	then	ADV
ejpam-4580	43	39	,	,	PUNCT
ejpam-4580	43	40	(	(	PUNCT
ejpam-4580	43	41	t	t	PROPN
ejpam-4580	43	42	k+2x|t	k+2x|t	PROPN
ejpam-4580	43	43	k+2x)−n(t	k+2x)−n(t	PRON
ejpam-4580	43	44	k+1x|t	k+1x|t	PROPN
ejpam-4580	43	45	k+1x	k+1x	PROPN
ejpam-4580	43	46	)	)	PUNCT
ejpam-4580	43	47	+	+	CCONJ
ejpam-4580	43	48	(	(	PUNCT
ejpam-4580	43	49	t	t	PROPN
ejpam-4580	43	50	kx|t	kx|t	PROPN
ejpam-4580	43	51	kx	kx	PROPN
ejpam-4580	43	52	)	)	PUNCT
ejpam-4580	43	53	≥	≥	PROPN
ejpam-4580	43	54	0	0	NUM
ejpam-4580	43	55	⇔	⇔	X
ejpam-4580	43	56	(	(	PUNCT
ejpam-4580	43	57	t	t	PROPN
ejpam-4580	43	58	∗(k+2)t	∗(k+2)t	PROPN
ejpam-4580	43	59	k+2x|x)−n(t	k+2x|x)−n(t	PROPN
ejpam-4580	43	60	∗(k+1)t	∗(k+1)t	PROPN
ejpam-4580	43	61	k+1x|x	k+1x|x	PROPN
ejpam-4580	43	62	)	)	PUNCT
ejpam-4580	44	1	+	+	CCONJ
ejpam-4580	44	2	(	(	PUNCT
ejpam-4580	44	3	t	t	PROPN
ejpam-4580	44	4	∗kt	∗kt	PUNCT
ejpam-4580	44	5	kx|x	kx|x	NOUN
ejpam-4580	44	6	)	)	PUNCT
ejpam-4580	44	7	≥	≥	NOUN
ejpam-4580	44	8	0	0	NUM
ejpam-4580	44	9	⇔	⇔	X
ejpam-4580	44	10	(	(	PUNCT
ejpam-4580	44	11	(	(	PUNCT
ejpam-4580	44	12	t	t	PROPN
ejpam-4580	44	13	∗(k+2)t	∗(k+2)t	NUM
ejpam-4580	44	14	k+2	k+2	PROPN
ejpam-4580	44	15	−nt	−nt	PROPN
ejpam-4580	44	16	∗(k+1)t	∗(k+1)t	NOUN
ejpam-4580	44	17	k+1	k+1	X
ejpam-4580	44	18	+	+	CCONJ
ejpam-4580	44	19	t	t	PROPN
ejpam-4580	44	20	∗kt	∗kt	SYM
ejpam-4580	44	21	k)x|x	k)x|x	NOUN
ejpam-4580	44	22	)	)	PUNCT
ejpam-4580	44	23	≥	≥	NOUN
ejpam-4580	44	24	0	0	NUM
ejpam-4580	44	25	⇔	⇔	PROPN
ejpam-4580	44	26	t	t	PROPN
ejpam-4580	44	27	∗k(t	∗k(t	PROPN
ejpam-4580	44	28	∗2	∗2	PROPN
ejpam-4580	44	29	t	t	PROPN
ejpam-4580	44	30	2	2	NUM
ejpam-4580	44	31	−nt	−nt	ADP
ejpam-4580	44	32	∗t	∗t	PROPN
ejpam-4580	44	33	+	+	CCONJ
ejpam-4580	44	34	i)t	i)t	VERB
ejpam-4580	45	1	k	k	X
ejpam-4580	45	2	≥	≥	NOUN
ejpam-4580	45	3	0	0	NUM
ejpam-4580	45	4	.	.	PUNCT
ejpam-4580	46	1	from	from	ADP
ejpam-4580	46	2	the	the	DET
ejpam-4580	46	3	definition	definition	NOUN
ejpam-4580	46	4	of	of	ADP
ejpam-4580	46	5	the	the	DET
ejpam-4580	46	6	k−quasi	k−quasi	PROPN
ejpam-4580	46	7	class	class	NOUN
ejpam-4580	46	8	q(n	q(n	PROPN
ejpam-4580	46	9	)	)	PUNCT
ejpam-4580	46	10	,	,	PUNCT
ejpam-4580	46	11	we	we	PRON
ejpam-4580	46	12	see	see	VERB
ejpam-4580	46	13	that	that	SCONJ
ejpam-4580	46	14	this	this	DET
ejpam-4580	46	15	new	new	ADJ
ejpam-4580	46	16	class	class	NOUN
ejpam-4580	46	17	of	of	ADP
ejpam-4580	46	18	operators	operator	NOUN
ejpam-4580	46	19	could	could	AUX
ejpam-4580	46	20	compare	compare	VERB
ejpam-4580	46	21	to	to	ADP
ejpam-4580	46	22	several	several	ADJ
ejpam-4580	46	23	classes	class	NOUN
ejpam-4580	46	24	of	of	ADP
ejpam-4580	46	25	operators	operator	NOUN
ejpam-4580	46	26	.	.	PUNCT
ejpam-4580	47	1	sh	sh	PROPN
ejpam-4580	47	2	.	.	PROPN
ejpam-4580	47	3	lohaj	lohaj	PROPN
ejpam-4580	47	4	/	/	SYM
ejpam-4580	47	5	eur	eur	PROPN
ejpam-4580	47	6	.	.	PUNCT
ejpam-4580	48	1	j.	j.	PROPN
ejpam-4580	48	2	pure	pure	PROPN
ejpam-4580	48	3	appl	appl	PROPN
ejpam-4580	48	4	.	.	PROPN
ejpam-4580	48	5	math	math	PROPN
ejpam-4580	48	6	,	,	PUNCT
ejpam-4580	48	7	15	15	NUM
ejpam-4580	48	8	(	(	PUNCT
ejpam-4580	48	9	4	4	NUM
ejpam-4580	48	10	)	)	PUNCT
ejpam-4580	48	11	(	(	PUNCT
ejpam-4580	48	12	2022	2022	NUM
ejpam-4580	48	13	)	)	PUNCT
ejpam-4580	48	14	,	,	PUNCT
ejpam-4580	48	15	1836	1836	NUM
ejpam-4580	48	16	-	-	SYM
ejpam-4580	48	17	1853	1853	NUM
ejpam-4580	48	18	1839	1839	NUM
ejpam-4580	48	19	proposition	proposition	NOUN
ejpam-4580	48	20	2	2	NUM
ejpam-4580	48	21	.	.	PUNCT
ejpam-4580	49	1	the	the	DET
ejpam-4580	49	2	following	follow	VERB
ejpam-4580	49	3	assertions	assertion	NOUN
ejpam-4580	49	4	hold	hold	VERB
ejpam-4580	49	5	.	.	PUNCT
ejpam-4580	50	1	(	(	PUNCT
ejpam-4580	50	2	i	i	NOUN
ejpam-4580	50	3	)	)	PUNCT
ejpam-4580	50	4	class	class	NOUN
ejpam-4580	50	5	q(n	q(n	PROPN
ejpam-4580	50	6	)	)	PUNCT
ejpam-4580	50	7	⊆	⊆	NUM
ejpam-4580	50	8	k−quasi	k−quasi	NOUN
ejpam-4580	50	9	class	class	NOUN
ejpam-4580	50	10	q(n	q(n	PROPN
ejpam-4580	50	11	)	)	PUNCT
ejpam-4580	50	12	.	.	PUNCT
ejpam-4580	51	1	(	(	PUNCT
ejpam-4580	51	2	ii	ii	NOUN
ejpam-4580	51	3	)	)	PUNCT
ejpam-4580	51	4	k−quasi	k−quasi	NOUN
ejpam-4580	51	5	class	class	NOUN
ejpam-4580	51	6	q	q	NOUN
ejpam-4580	51	7	=	=	PUNCT
ejpam-4580	51	8	k−quasi	k−quasi	NOUN
ejpam-4580	51	9	class	class	NOUN
ejpam-4580	51	10	q(2	q(2	PROPN
ejpam-4580	51	11	)	)	PUNCT
ejpam-4580	51	12	.	.	PUNCT
ejpam-4580	52	1	(	(	PUNCT
ejpam-4580	52	2	iii	iii	X
ejpam-4580	52	3	)	)	PUNCT
ejpam-4580	52	4	k−quasi−paranormal	k−quasi−paranormal	NUM
ejpam-4580	52	5	⊆	⊆	NUM
ejpam-4580	52	6	k−quasi	k−quasi	PROPN
ejpam-4580	52	7	class	class	NOUN
ejpam-4580	52	8	q(n	q(n	PROPN
ejpam-4580	52	9	)	)	PUNCT
ejpam-4580	52	10	for	for	ADP
ejpam-4580	52	11	n	n	DET
ejpam-4580	52	12	∈	∈	NOUN
ejpam-4580	53	1	[	[	X
ejpam-4580	53	2	1	1	NUM
ejpam-4580	53	3	,	,	PUNCT
ejpam-4580	53	4	2	2	NUM
ejpam-4580	53	5	]	]	PUNCT
ejpam-4580	53	6	.	.	PUNCT
ejpam-4580	54	1	(	(	PUNCT
ejpam-4580	54	2	iv	iv	X
ejpam-4580	54	3	)	)	PUNCT
ejpam-4580	54	4	k−quasi−class	k−quasi−class	ADP
ejpam-4580	54	5	a	a	DET
ejpam-4580	54	6	⊆	⊆	NUM
ejpam-4580	54	7	k−quasi	k−quasi	NOUN
ejpam-4580	54	8	class	class	NOUN
ejpam-4580	54	9	q(n	q(n	PROPN
ejpam-4580	54	10	)	)	PUNCT
ejpam-4580	54	11	for	for	ADP
ejpam-4580	54	12	n	n	DET
ejpam-4580	54	13	∈	∈	NOUN
ejpam-4580	55	1	[	[	X
ejpam-4580	55	2	1	1	NUM
ejpam-4580	55	3	,	,	PUNCT
ejpam-4580	55	4	2	2	NUM
ejpam-4580	55	5	]	]	PUNCT
ejpam-4580	55	6	.	.	PUNCT
ejpam-4580	56	1	(	(	PUNCT
ejpam-4580	56	2	v	v	NOUN
ejpam-4580	56	3	)	)	PUNCT
ejpam-4580	56	4	k−quasi	k−quasi	NOUN
ejpam-4580	56	5	class	class	NOUN
ejpam-4580	56	6	q(n	q(n	PROPN
ejpam-4580	56	7	)	)	PUNCT
ejpam-4580	56	8	⊆	⊆	NUM
ejpam-4580	56	9	k−quasi	k−quasi	NOUN
ejpam-4580	56	10	class	class	NOUN
ejpam-4580	56	11	q(n	q(n	PROPN
ejpam-4580	56	12	−	−	PROPN
ejpam-4580	56	13	1	1	NUM
ejpam-4580	56	14	)	)	PUNCT
ejpam-4580	56	15	for	for	ADP
ejpam-4580	56	16	n	n	X
ejpam-4580	56	17	≥	≥	NUM
ejpam-4580	56	18	2	2	NUM
ejpam-4580	56	19	.	.	PUNCT
ejpam-4580	56	20	proof	proof	NOUN
ejpam-4580	56	21	.	.	PUNCT
ejpam-4580	57	1	(	(	PUNCT
ejpam-4580	57	2	i	i	NOUN
ejpam-4580	57	3	)	)	PUNCT
ejpam-4580	57	4	from	from	ADP
ejpam-4580	57	5	the	the	DET
ejpam-4580	57	6	definition	definition	NOUN
ejpam-4580	57	7	of	of	ADP
ejpam-4580	57	8	the	the	DET
ejpam-4580	57	9	class	class	NOUN
ejpam-4580	57	10	q(n	q(n	NOUN
ejpam-4580	57	11	)	)	PUNCT
ejpam-4580	57	12	operator	operator	NOUN
ejpam-4580	57	13	t	t	PROPN
ejpam-4580	57	14	∗2	∗2	PROPN
ejpam-4580	57	15	t	t	PROPN
ejpam-4580	57	16	2	2	NUM
ejpam-4580	57	17	−nt	−nt	ADP
ejpam-4580	57	18	∗t	∗t	PROPN
ejpam-4580	58	1	+	+	CCONJ
ejpam-4580	58	2	i	i	PRON
ejpam-4580	58	3	≥	≥	VERB
ejpam-4580	58	4	o	o	NOUN
ejpam-4580	58	5	,	,	PUNCT
ejpam-4580	58	6	and	and	CCONJ
ejpam-4580	58	7	the	the	DET
ejpam-4580	58	8	proposition	proposition	NOUN
ejpam-4580	58	9	1	1	NUM
ejpam-4580	58	10	we	we	PRON
ejpam-4580	58	11	see	see	VERB
ejpam-4580	58	12	that	that	SCONJ
ejpam-4580	58	13	every	every	DET
ejpam-4580	58	14	operator	operator	NOUN
ejpam-4580	58	15	of	of	ADP
ejpam-4580	58	16	the	the	DET
ejpam-4580	58	17	class	class	NOUN
ejpam-4580	58	18	q(n	q(n	PROPN
ejpam-4580	58	19	)	)	PUNCT
ejpam-4580	58	20	is	be	AUX
ejpam-4580	58	21	also	also	ADV
ejpam-4580	58	22	an	an	DET
ejpam-4580	58	23	operator	operator	NOUN
ejpam-4580	58	24	of	of	ADP
ejpam-4580	58	25	the	the	DET
ejpam-4580	58	26	k−quasi	k−quasi	PROPN
ejpam-4580	58	27	class	class	NOUN
ejpam-4580	58	28	q(n	q(n	PROPN
ejpam-4580	58	29	)	)	PUNCT
ejpam-4580	58	30	.	.	PUNCT
ejpam-4580	59	1	thus	thus	ADV
ejpam-4580	59	2	,	,	PUNCT
ejpam-4580	59	3	we	we	PRON
ejpam-4580	59	4	have	have	VERB
ejpam-4580	59	5	the	the	DET
ejpam-4580	59	6	following	following	ADJ
ejpam-4580	59	7	implication	implication	NOUN
ejpam-4580	59	8	:	:	PUNCT
ejpam-4580	59	9	class	class	NOUN
ejpam-4580	59	10	q(n	q(n	PROPN
ejpam-4580	59	11	)	)	PUNCT
ejpam-4580	59	12	⊆	⊆	NUM
ejpam-4580	59	13	k−quasi	k−quasi	NOUN
ejpam-4580	59	14	class	class	NOUN
ejpam-4580	59	15	q(n	q(n	PROPN
ejpam-4580	59	16	)	)	PUNCT
ejpam-4580	59	17	.	.	PUNCT
ejpam-4580	60	1	(	(	PUNCT
ejpam-4580	60	2	ii	ii	X
ejpam-4580	60	3	)	)	PUNCT
ejpam-4580	60	4	it	it	PRON
ejpam-4580	60	5	is	be	AUX
ejpam-4580	60	6	clear	clear	ADJ
ejpam-4580	60	7	from	from	ADP
ejpam-4580	60	8	definitions	definition	NOUN
ejpam-4580	60	9	.	.	PUNCT
ejpam-4580	61	1	(	(	PUNCT
ejpam-4580	61	2	iii	iii	NOUN
ejpam-4580	61	3	)	)	PUNCT
ejpam-4580	61	4	from	from	ADP
ejpam-4580	61	5	the	the	DET
ejpam-4580	61	6	definition	definition	NOUN
ejpam-4580	61	7	of	of	ADP
ejpam-4580	61	8	k−quasi−paranormal	k−quasi−paranormal	PROPN
ejpam-4580	61	9	we	we	PRON
ejpam-4580	61	10	have	have	VERB
ejpam-4580	61	11	:	:	PUNCT
ejpam-4580	61	12	∥t	∥t	ADJ
ejpam-4580	61	13	k+1x∥2	k+1x∥2	NOUN
ejpam-4580	61	14	≤	≤	X
ejpam-4580	61	15	∥t	∥t	PROPN
ejpam-4580	61	16	k+2x∥∥t	k+2x∥∥t	NOUN
ejpam-4580	61	17	kx∥	kx∥	NOUN
ejpam-4580	61	18	≤	≤	NUM
ejpam-4580	61	19	1	1	NUM
ejpam-4580	61	20	2	2	NUM
ejpam-4580	61	21	(	(	PUNCT
ejpam-4580	61	22	∥t	∥t	ADJ
ejpam-4580	61	23	k+2x∥2	k+2x∥2	NOUN
ejpam-4580	61	24	+	+	CCONJ
ejpam-4580	61	25	∥t	∥t	ADJ
ejpam-4580	61	26	kx∥2	kx∥2	NOUN
ejpam-4580	61	27	)	)	PUNCT
ejpam-4580	61	28	≤	≤	NOUN
ejpam-4580	61	29	1	1	NUM
ejpam-4580	61	30	n	n	NOUN
ejpam-4580	61	31	(	(	PUNCT
ejpam-4580	61	32	∥t	∥t	ADJ
ejpam-4580	61	33	k+2x∥2	k+2x∥2	NOUN
ejpam-4580	61	34	+	+	CCONJ
ejpam-4580	61	35	∥t	∥t	ADJ
ejpam-4580	61	36	kx∥2	kx∥2	NOUN
ejpam-4580	61	37	)	)	PUNCT
ejpam-4580	61	38	,	,	PUNCT
ejpam-4580	61	39	for	for	ADP
ejpam-4580	61	40	a	a	DET
ejpam-4580	61	41	real	real	ADJ
ejpam-4580	61	42	number	number	NOUN
ejpam-4580	61	43	n	n	NOUN
ejpam-4580	61	44	∈	∈	NOUN
ejpam-4580	62	1	[	[	X
ejpam-4580	62	2	1	1	NUM
ejpam-4580	62	3	,	,	PUNCT
ejpam-4580	62	4	2	2	NUM
ejpam-4580	62	5	]	]	PUNCT
ejpam-4580	62	6	.	.	PUNCT
ejpam-4580	63	1	this	this	PRON
ejpam-4580	63	2	proves	prove	VERB
ejpam-4580	63	3	the	the	DET
ejpam-4580	63	4	result	result	NOUN
ejpam-4580	63	5	.	.	PUNCT
ejpam-4580	64	1	(	(	PUNCT
ejpam-4580	64	2	iv	iv	X
ejpam-4580	64	3	)	)	PUNCT
ejpam-4580	64	4	since	since	SCONJ
ejpam-4580	64	5	t	t	PROPN
ejpam-4580	64	6	belongs	belong	VERB
ejpam-4580	64	7	to	to	ADP
ejpam-4580	64	8	k−quasi−class	k−quasi−class	PROPN
ejpam-4580	64	9	a	a	X
ejpam-4580	64	10	,	,	PUNCT
ejpam-4580	64	11	we	we	PRON
ejpam-4580	64	12	have	have	AUX
ejpam-4580	64	13	t	t	NOUN
ejpam-4580	64	14	∗k|t	∗k|t	NUM
ejpam-4580	64	15	2|t	2|t	PROPN
ejpam-4580	64	16	k	k	PROPN
ejpam-4580	64	17	≥	≥	PROPN
ejpam-4580	64	18	t	t	PROPN
ejpam-4580	64	19	∗k|t	∗k|t	PROPN
ejpam-4580	64	20	|2	|2	NUM
ejpam-4580	64	21	t	t	NOUN
ejpam-4580	64	22	k.	k.	NOUN
ejpam-4580	64	23	let	let	VERB
ejpam-4580	64	24	x	x	X
ejpam-4580	64	25	∈	∈	PROPN
ejpam-4580	64	26	h.	h.	PROPN
ejpam-4580	64	27	then	then	ADV
ejpam-4580	64	28	2∥t	2∥t	NUM
ejpam-4580	64	29	k+1x∥2	k+1x∥2	NOUN
ejpam-4580	64	30	=	=	SYM
ejpam-4580	64	31	2⟨t	2⟨t	NUM
ejpam-4580	64	32	∗(k+1)t	∗(k+1)t	PROPN
ejpam-4580	64	33	k+1x	k+1x	PROPN
ejpam-4580	64	34	,	,	PUNCT
ejpam-4580	64	35	x⟩	x⟩	PUNCT
ejpam-4580	65	1	=	=	SYM
ejpam-4580	65	2	2⟨t	2⟨t	NUM
ejpam-4580	65	3	∗k|t	∗k|t	PROPN
ejpam-4580	65	4	|2	|2	NUM
ejpam-4580	65	5	t	t	X
ejpam-4580	65	6	kx	kx	PROPN
ejpam-4580	65	7	,	,	PUNCT
ejpam-4580	65	8	x⟩	x⟩	PUNCT
ejpam-4580	66	1	≤	≤	ADJ
ejpam-4580	66	2	2⟨t	2⟨t	NUM
ejpam-4580	66	3	∗k|t	∗k|t	PROPN
ejpam-4580	66	4	2|t	2|t	PROPN
ejpam-4580	66	5	kx	kx	PROPN
ejpam-4580	66	6	,	,	PUNCT
ejpam-4580	66	7	x⟩	x⟩	PUNCT
ejpam-4580	67	1	≤	≤	PROPN
ejpam-4580	67	2	sh	sh	PROPN
ejpam-4580	67	3	.	.	PROPN
ejpam-4580	67	4	lohaj	lohaj	PROPN
ejpam-4580	67	5	/	/	SYM
ejpam-4580	67	6	eur	eur	PROPN
ejpam-4580	67	7	.	.	PUNCT
ejpam-4580	68	1	j.	j.	PROPN
ejpam-4580	68	2	pure	pure	PROPN
ejpam-4580	68	3	appl	appl	PROPN
ejpam-4580	68	4	.	.	PROPN
ejpam-4580	68	5	math	math	PROPN
ejpam-4580	68	6	,	,	PUNCT
ejpam-4580	68	7	15	15	NUM
ejpam-4580	68	8	(	(	PUNCT
ejpam-4580	68	9	4	4	NUM
ejpam-4580	68	10	)	)	PUNCT
ejpam-4580	68	11	(	(	PUNCT
ejpam-4580	68	12	2022	2022	NUM
ejpam-4580	68	13	)	)	PUNCT
ejpam-4580	68	14	,	,	PUNCT
ejpam-4580	68	15	1836	1836	NUM
ejpam-4580	68	16	-	-	SYM
ejpam-4580	68	17	1853	1853	NUM
ejpam-4580	68	18	1840	1840	NUM
ejpam-4580	68	19	2∥|t	2∥|t	NUM
ejpam-4580	68	20	2|t	2|t	NUM
ejpam-4580	68	21	kx∥	kx∥	PROPN
ejpam-4580	68	22	·	·	PUNCT
ejpam-4580	68	23	∥t	∥t	ADJ
ejpam-4580	68	24	kx∥	kx∥	NOUN
ejpam-4580	68	25	=	=	SYM
ejpam-4580	68	26	2∥t	2∥t	NUM
ejpam-4580	68	27	k+2x∥	k+2x∥	X
ejpam-4580	68	28	·	·	PUNCT
ejpam-4580	68	29	∥t	∥t	PROPN
ejpam-4580	68	30	k∥	k∥	NOUN
ejpam-4580	68	31	≤	≤	ADV
ejpam-4580	68	32	∥t	∥t	ADJ
ejpam-4580	68	33	k+2x∥2	k+2x∥2	NOUN
ejpam-4580	69	1	+	+	CCONJ
ejpam-4580	69	2	∥t	∥t	ADJ
ejpam-4580	69	3	kx∥2	kx∥2	NOUN
ejpam-4580	69	4	therefore	therefore	ADV
ejpam-4580	69	5	∥t	∥t	ADJ
ejpam-4580	69	6	k+1x∥2	k+1x∥2	NOUN
ejpam-4580	69	7	≤	≤	NOUN
ejpam-4580	69	8	1	1	NUM
ejpam-4580	69	9	2	2	NUM
ejpam-4580	69	10	(	(	PUNCT
ejpam-4580	69	11	∥t	∥t	ADJ
ejpam-4580	69	12	k+2x∥2	k+2x∥2	NOUN
ejpam-4580	69	13	+	+	CCONJ
ejpam-4580	69	14	∥t	∥t	ADJ
ejpam-4580	69	15	kx∥2	kx∥2	NOUN
ejpam-4580	69	16	)	)	PUNCT
ejpam-4580	69	17	≤	≤	NOUN
ejpam-4580	69	18	1	1	NUM
ejpam-4580	69	19	n	n	NOUN
ejpam-4580	69	20	(	(	PUNCT
ejpam-4580	69	21	∥t	∥t	ADJ
ejpam-4580	69	22	k+2x∥2	k+2x∥2	NOUN
ejpam-4580	69	23	+	+	CCONJ
ejpam-4580	69	24	∥t	∥t	ADJ
ejpam-4580	69	25	kx∥2	kx∥2	NOUN
ejpam-4580	69	26	)	)	PUNCT
ejpam-4580	69	27	,	,	PUNCT
ejpam-4580	69	28	for	for	ADP
ejpam-4580	69	29	a	a	DET
ejpam-4580	69	30	real	real	ADJ
ejpam-4580	69	31	number	number	NOUN
ejpam-4580	69	32	n	n	NOUN
ejpam-4580	69	33	∈	∈	NOUN
ejpam-4580	70	1	[	[	X
ejpam-4580	70	2	1	1	NUM
ejpam-4580	70	3	,	,	PUNCT
ejpam-4580	70	4	2	2	NUM
ejpam-4580	70	5	]	]	PUNCT
ejpam-4580	70	6	.	.	PUNCT
ejpam-4580	71	1	this	this	PRON
ejpam-4580	71	2	proves	prove	VERB
ejpam-4580	71	3	the	the	DET
ejpam-4580	71	4	result	result	NOUN
ejpam-4580	71	5	.	.	PUNCT
ejpam-4580	72	1	(	(	PUNCT
ejpam-4580	72	2	v	v	NOUN
ejpam-4580	72	3	)	)	PUNCT
ejpam-4580	72	4	since	since	SCONJ
ejpam-4580	72	5	t	t	PROPN
ejpam-4580	72	6	is	be	AUX
ejpam-4580	72	7	of	of	ADP
ejpam-4580	72	8	k−quasi	k−quasi	NOUN
ejpam-4580	72	9	class	class	NOUN
ejpam-4580	72	10	q(n	q(n	PROPN
ejpam-4580	72	11	)	)	PUNCT
ejpam-4580	72	12	,	,	PUNCT
ejpam-4580	72	13	for	for	ADP
ejpam-4580	72	14	a	a	DET
ejpam-4580	72	15	fixed	fix	VERB
ejpam-4580	72	16	real	real	ADJ
ejpam-4580	72	17	number	number	NOUN
ejpam-4580	72	18	n	n	CCONJ
ejpam-4580	72	19	≥	≥	NOUN
ejpam-4580	72	20	2	2	NUM
ejpam-4580	72	21	and	and	CCONJ
ejpam-4580	72	22	k	k	X
ejpam-4580	72	23	a	a	DET
ejpam-4580	72	24	natural	natural	ADJ
ejpam-4580	72	25	number	number	NOUN
ejpam-4580	72	26	then	then	ADV
ejpam-4580	72	27	n∥t	n∥t	ADJ
ejpam-4580	72	28	k+1x∥2	k+1x∥2	NOUN
ejpam-4580	72	29	≤	≤	X
ejpam-4580	72	30	∥t	∥t	ADJ
ejpam-4580	72	31	k+2x∥2	k+2x∥2	NOUN
ejpam-4580	73	1	+	+	CCONJ
ejpam-4580	73	2	∥t	∥t	ADJ
ejpam-4580	73	3	kx∥2	kx∥2	NOUN
ejpam-4580	73	4	,	,	PUNCT
ejpam-4580	73	5	for	for	ADP
ejpam-4580	73	6	all	all	DET
ejpam-4580	73	7	x	x	SYM
ejpam-4580	73	8	∈	∈	PROPN
ejpam-4580	73	9	h.	h.	NOUN
ejpam-4580	73	10	then	then	ADV
ejpam-4580	73	11	,	,	PUNCT
ejpam-4580	73	12	(	(	PUNCT
ejpam-4580	73	13	n	n	CCONJ
ejpam-4580	73	14	−	−	PROPN
ejpam-4580	73	15	1)∥t	1)∥t	NUM
ejpam-4580	73	16	k+1x∥2	k+1x∥2	NOUN
ejpam-4580	73	17	≤	≤	X
ejpam-4580	73	18	n∥t	n∥t	ADJ
ejpam-4580	73	19	k+1x∥2	k+1x∥2	NOUN
ejpam-4580	73	20	≤	≤	ADV
ejpam-4580	73	21	∥t	∥t	ADJ
ejpam-4580	73	22	k+2x∥2	k+2x∥2	NOUN
ejpam-4580	73	23	+	+	CCONJ
ejpam-4580	73	24	∥t	∥t	ADJ
ejpam-4580	73	25	kx∥2	kx∥2	NOUN
ejpam-4580	73	26	.	.	PUNCT
ejpam-4580	74	1	hence	hence	ADV
ejpam-4580	74	2	,	,	PUNCT
ejpam-4580	74	3	t	t	PROPN
ejpam-4580	74	4	is	be	AUX
ejpam-4580	74	5	an	an	DET
ejpam-4580	74	6	operator	operator	NOUN
ejpam-4580	74	7	of	of	ADP
ejpam-4580	74	8	k−quasi	k−quasi	PROPN
ejpam-4580	74	9	class	class	NOUN
ejpam-4580	74	10	q(n	q(n	PROPN
ejpam-4580	74	11	−	−	PROPN
ejpam-4580	74	12	1	1	NUM
ejpam-4580	74	13	)	)	PUNCT
ejpam-4580	74	14	.	.	PUNCT
ejpam-4580	75	1	it	it	PRON
ejpam-4580	75	2	follows	follow	VERB
ejpam-4580	75	3	that	that	SCONJ
ejpam-4580	75	4	,	,	PUNCT
ejpam-4580	75	5	k−quasi	k−quasi	PROPN
ejpam-4580	75	6	class	class	NOUN
ejpam-4580	75	7	q(n	q(n	PROPN
ejpam-4580	75	8	)	)	PUNCT
ejpam-4580	75	9	⊆	⊆	NUM
ejpam-4580	75	10	k−quasi	k−quasi	NOUN
ejpam-4580	75	11	class	class	NOUN
ejpam-4580	75	12	q(n	q(n	PROPN
ejpam-4580	75	13	−	−	PROPN
ejpam-4580	75	14	1	1	NUM
ejpam-4580	75	15	)	)	PUNCT
ejpam-4580	75	16	⊆	⊆	NUM
ejpam-4580	75	17	.	.	PUNCT
ejpam-4580	75	18	.	.	PUNCT
ejpam-4580	75	19	.	.	PUNCT
ejpam-4580	76	1	⊆	⊆	NUM
ejpam-4580	76	2	k−quasi	k−quasi	PROPN
ejpam-4580	76	3	class	class	NOUN
ejpam-4580	76	4	q(3	q(3	PROPN
ejpam-4580	76	5	)	)	PUNCT
ejpam-4580	76	6	⊆	⊆	NUM
ejpam-4580	76	7	k−quasi	k−quasi	PROPN
ejpam-4580	76	8	class	class	NOUN
ejpam-4580	76	9	q(2	q(2	PROPN
ejpam-4580	76	10	)	)	PUNCT
ejpam-4580	76	11	.	.	PUNCT
ejpam-4580	77	1	similarly	similarly	ADV
ejpam-4580	77	2	,	,	PUNCT
ejpam-4580	77	3	we	we	PRON
ejpam-4580	77	4	state	state	VERB
ejpam-4580	77	5	a	a	DET
ejpam-4580	77	6	proposition	proposition	NOUN
ejpam-4580	77	7	giving	give	VERB
ejpam-4580	77	8	necessary	necessary	ADJ
ejpam-4580	77	9	and	and	CCONJ
ejpam-4580	77	10	sufficient	sufficient	ADJ
ejpam-4580	77	11	conditions	condition	NOUN
ejpam-4580	77	12	for	for	SCONJ
ejpam-4580	77	13	an	an	DET
ejpam-4580	77	14	operator	operator	NOUN
ejpam-4580	77	15	t	t	NOUN
ejpam-4580	77	16	to	to	PART
ejpam-4580	77	17	be	be	AUX
ejpam-4580	77	18	of	of	ADP
ejpam-4580	77	19	k−quasi	k−quasi	PROPN
ejpam-4580	77	20	class	class	NOUN
ejpam-4580	77	21	q∗(n	q∗(n	PROPN
ejpam-4580	77	22	)	)	PUNCT
ejpam-4580	77	23	and	and	CCONJ
ejpam-4580	77	24	also	also	ADV
ejpam-4580	77	25	the	the	DET
ejpam-4580	77	26	proposition	proposition	NOUN
ejpam-4580	77	27	where	where	SCONJ
ejpam-4580	77	28	we	we	PRON
ejpam-4580	77	29	compare	compare	VERB
ejpam-4580	77	30	this	this	DET
ejpam-4580	77	31	class	class	NOUN
ejpam-4580	77	32	of	of	ADP
ejpam-4580	77	33	operator	operator	NOUN
ejpam-4580	77	34	with	with	ADP
ejpam-4580	77	35	other	other	ADJ
ejpam-4580	77	36	existing	exist	VERB
ejpam-4580	77	37	classes	class	NOUN
ejpam-4580	77	38	of	of	ADP
ejpam-4580	77	39	operators	operator	NOUN
ejpam-4580	77	40	.	.	PUNCT
ejpam-4580	78	1	since	since	SCONJ
ejpam-4580	78	2	the	the	DET
ejpam-4580	78	3	techniqes	techniqes	NOUN
ejpam-4580	78	4	of	of	ADP
ejpam-4580	78	5	the	the	DET
ejpam-4580	78	6	proofs	proof	NOUN
ejpam-4580	78	7	of	of	ADP
ejpam-4580	78	8	the	the	DET
ejpam-4580	78	9	resultes	resulte	NOUN
ejpam-4580	78	10	for	for	ADP
ejpam-4580	78	11	both	both	DET
ejpam-4580	78	12	classes	class	NOUN
ejpam-4580	78	13	are	be	AUX
ejpam-4580	78	14	almost	almost	ADV
ejpam-4580	78	15	the	the	DET
ejpam-4580	78	16	same	same	ADJ
ejpam-4580	78	17	we	we	PRON
ejpam-4580	78	18	omit	omit	VERB
ejpam-4580	78	19	the	the	DET
ejpam-4580	78	20	proofs	proof	NOUN
ejpam-4580	78	21	of	of	ADP
ejpam-4580	78	22	the	the	DET
ejpam-4580	78	23	results	result	NOUN
ejpam-4580	78	24	of	of	ADP
ejpam-4580	78	25	k−quasi	k−quasi	PROPN
ejpam-4580	78	26	class	class	NOUN
ejpam-4580	78	27	q∗(n	q∗(n	PROPN
ejpam-4580	78	28	)	)	PUNCT
ejpam-4580	78	29	.	.	PUNCT
ejpam-4580	79	1	proposition	proposition	NOUN
ejpam-4580	79	2	3	3	NUM
ejpam-4580	79	3	.	.	PUNCT
ejpam-4580	80	1	an	an	DET
ejpam-4580	80	2	operator	operator	NOUN
ejpam-4580	80	3	t	t	PROPN
ejpam-4580	80	4	∈	∈	PROPN
ejpam-4580	80	5	l(h	l(h	PROPN
ejpam-4580	80	6	)	)	PUNCT
ejpam-4580	80	7	is	be	AUX
ejpam-4580	80	8	of	of	ADP
ejpam-4580	80	9	k−quasi	k−quasi	PROPN
ejpam-4580	80	10	class	class	NOUN
ejpam-4580	80	11	q∗(n	q∗(n	PROPN
ejpam-4580	80	12	)	)	PUNCT
ejpam-4580	80	13	,	,	PUNCT
ejpam-4580	80	14	if	if	SCONJ
ejpam-4580	80	15	and	and	CCONJ
ejpam-4580	80	16	only	only	ADV
ejpam-4580	80	17	if	if	SCONJ
ejpam-4580	80	18	t	t	PROPN
ejpam-4580	80	19	∗k(t	∗k(t	PROPN
ejpam-4580	80	20	∗2	∗2	PROPN
ejpam-4580	80	21	t	t	PROPN
ejpam-4580	80	22	2	2	NUM
ejpam-4580	80	23	−ntt	−ntt	NOUN
ejpam-4580	80	24	∗	∗	NOUN
ejpam-4580	80	25	+	+	CCONJ
ejpam-4580	80	26	i)t	i)t	NOUN
ejpam-4580	81	1	k	k	X
ejpam-4580	81	2	≥	≥	NUM
ejpam-4580	81	3	o	o	NOUN
ejpam-4580	81	4	,	,	PUNCT
ejpam-4580	81	5	for	for	ADP
ejpam-4580	81	6	a	a	DET
ejpam-4580	81	7	fixed	fix	VERB
ejpam-4580	81	8	real	real	ADJ
ejpam-4580	81	9	number	number	NOUN
ejpam-4580	81	10	n	n	CCONJ
ejpam-4580	81	11	≥	≥	NOUN
ejpam-4580	81	12	1	1	NUM
ejpam-4580	81	13	and	and	CCONJ
ejpam-4580	81	14	k	k	X
ejpam-4580	81	15	a	a	DET
ejpam-4580	81	16	natural	natural	ADJ
ejpam-4580	81	17	number	number	NOUN
ejpam-4580	81	18	.	.	PUNCT
ejpam-4580	82	1	proposition	proposition	NOUN
ejpam-4580	82	2	4	4	NUM
ejpam-4580	82	3	.	.	PUNCT
ejpam-4580	83	1	the	the	DET
ejpam-4580	83	2	following	follow	VERB
ejpam-4580	83	3	assertions	assertion	NOUN
ejpam-4580	83	4	hold	hold	VERB
ejpam-4580	83	5	.	.	PUNCT
ejpam-4580	84	1	(	(	PUNCT
ejpam-4580	84	2	i	i	NOUN
ejpam-4580	84	3	)	)	PUNCT
ejpam-4580	84	4	class	class	NOUN
ejpam-4580	84	5	q∗(n	q∗(n	PROPN
ejpam-4580	84	6	)	)	PUNCT
ejpam-4580	84	7	⊆	⊆	NUM
ejpam-4580	84	8	k−quasi	k−quasi	PROPN
ejpam-4580	84	9	class	class	NOUN
ejpam-4580	84	10	q∗(n	q∗(n	PROPN
ejpam-4580	84	11	)	)	PUNCT
ejpam-4580	84	12	.	.	PUNCT
ejpam-4580	85	1	(	(	PUNCT
ejpam-4580	85	2	ii	ii	NOUN
ejpam-4580	85	3	)	)	PUNCT
ejpam-4580	85	4	k−quasi	k−quasi	NOUN
ejpam-4580	85	5	class	class	NOUN
ejpam-4580	85	6	q∗	q∗	NOUN
ejpam-4580	85	7	=	=	SYM
ejpam-4580	85	8	k−quasi	k−quasi	NOUN
ejpam-4580	85	9	class	class	NOUN
ejpam-4580	85	10	q∗(2	q∗(2	NOUN
ejpam-4580	85	11	)	)	PUNCT
ejpam-4580	85	12	.	.	PUNCT
ejpam-4580	86	1	(	(	PUNCT
ejpam-4580	86	2	iii	iii	X
ejpam-4580	86	3	)	)	PUNCT
ejpam-4580	86	4	k−quasi−	k−quasi−	PROPN
ejpam-4580	86	5	∗	∗	NOUN
ejpam-4580	86	6	−paranormal	−paranormal	NOUN
ejpam-4580	86	7	⊆	⊆	NUM
ejpam-4580	86	8	k−quasi	k−quasi	NOUN
ejpam-4580	86	9	class	class	NOUN
ejpam-4580	86	10	q∗(n)for	q∗(n)for	NOUN
ejpam-4580	86	11	n	n	PRON
ejpam-4580	86	12	∈	∈	PROPN
ejpam-4580	87	1	[	[	X
ejpam-4580	87	2	1	1	NUM
ejpam-4580	87	3	,	,	PUNCT
ejpam-4580	87	4	2	2	NUM
ejpam-4580	87	5	]	]	PUNCT
ejpam-4580	87	6	.	.	PUNCT
ejpam-4580	88	1	(	(	PUNCT
ejpam-4580	88	2	iv	iv	X
ejpam-4580	88	3	)	)	PUNCT
ejpam-4580	88	4	k−quasi−	k−quasi−	PROPN
ejpam-4580	88	5	∗	∗	VERB
ejpam-4580	88	6	−class	−class	NOUN
ejpam-4580	88	7	a	a	DET
ejpam-4580	88	8	⊆	⊆	NUM
ejpam-4580	88	9	k−quasi	k−quasi	NOUN
ejpam-4580	88	10	class	class	NOUN
ejpam-4580	88	11	q∗(n	q∗(n	PROPN
ejpam-4580	88	12	)	)	PUNCT
ejpam-4580	88	13	for	for	ADP
ejpam-4580	88	14	n	n	DET
ejpam-4580	88	15	∈	∈	NOUN
ejpam-4580	89	1	[	[	X
ejpam-4580	89	2	1	1	NUM
ejpam-4580	89	3	,	,	PUNCT
ejpam-4580	89	4	2	2	NUM
ejpam-4580	89	5	]	]	PUNCT
ejpam-4580	89	6	.	.	PUNCT
ejpam-4580	90	1	(	(	PUNCT
ejpam-4580	90	2	v	v	NOUN
ejpam-4580	90	3	)	)	PUNCT
ejpam-4580	90	4	k−quasi	k−quasi	NOUN
ejpam-4580	90	5	class	class	NOUN
ejpam-4580	90	6	q∗(n	q∗(n	PROPN
ejpam-4580	90	7	)	)	PUNCT
ejpam-4580	90	8	⊆	⊆	NUM
ejpam-4580	90	9	k−quasi	k−quasi	NOUN
ejpam-4580	90	10	class	class	NOUN
ejpam-4580	90	11	q∗(n	q∗(n	NOUN
ejpam-4580	91	1	−	−	PROPN
ejpam-4580	91	2	1	1	NUM
ejpam-4580	91	3	)	)	PUNCT
ejpam-4580	91	4	for	for	ADP
ejpam-4580	91	5	n	n	X
ejpam-4580	91	6	≥	≥	NUM
ejpam-4580	91	7	2	2	NUM
ejpam-4580	91	8	.	.	PUNCT
ejpam-4580	91	9	sh	sh	PROPN
ejpam-4580	91	10	.	.	PROPN
ejpam-4580	91	11	lohaj	lohaj	PROPN
ejpam-4580	91	12	/	/	SYM
ejpam-4580	91	13	eur	eur	PROPN
ejpam-4580	91	14	.	.	PUNCT
ejpam-4580	92	1	j.	j.	PROPN
ejpam-4580	92	2	pure	pure	PROPN
ejpam-4580	92	3	appl	appl	PROPN
ejpam-4580	92	4	.	.	PROPN
ejpam-4580	92	5	math	math	PROPN
ejpam-4580	92	6	,	,	PUNCT
ejpam-4580	92	7	15	15	NUM
ejpam-4580	92	8	(	(	PUNCT
ejpam-4580	92	9	4	4	NUM
ejpam-4580	92	10	)	)	PUNCT
ejpam-4580	92	11	(	(	PUNCT
ejpam-4580	92	12	2022	2022	NUM
ejpam-4580	92	13	)	)	PUNCT
ejpam-4580	92	14	,	,	PUNCT
ejpam-4580	92	15	1836	1836	NUM
ejpam-4580	92	16	-	-	SYM
ejpam-4580	92	17	1853	1853	NUM
ejpam-4580	92	18	1841	1841	NUM
ejpam-4580	92	19	in	in	ADP
ejpam-4580	92	20	the	the	DET
ejpam-4580	92	21	following	following	NOUN
ejpam-4580	92	22	we	we	PRON
ejpam-4580	92	23	state	state	VERB
ejpam-4580	92	24	a	a	DET
ejpam-4580	92	25	proposition	proposition	NOUN
ejpam-4580	92	26	which	which	PRON
ejpam-4580	92	27	gives	give	VERB
ejpam-4580	92	28	conditions	condition	NOUN
ejpam-4580	92	29	for	for	ADP
ejpam-4580	92	30	an	an	DET
ejpam-4580	92	31	operator	operator	NOUN
ejpam-4580	92	32	t	t	NOUN
ejpam-4580	92	33	of	of	ADP
ejpam-4580	92	34	the	the	DET
ejpam-4580	92	35	k−quasi	k−quasi	PROPN
ejpam-4580	92	36	class	class	NOUN
ejpam-4580	92	37	q(n	q(n	PROPN
ejpam-4580	92	38	)	)	PUNCT
ejpam-4580	92	39	to	to	PART
ejpam-4580	92	40	be	be	AUX
ejpam-4580	92	41	an	an	DET
ejpam-4580	92	42	operator	operator	NOUN
ejpam-4580	92	43	of	of	ADP
ejpam-4580	92	44	the	the	DET
ejpam-4580	92	45	class	class	NOUN
ejpam-4580	92	46	q(n	q(n	PROPN
ejpam-4580	92	47	)	)	PUNCT
ejpam-4580	92	48	.	.	PUNCT
ejpam-4580	93	1	proposition	proposition	NOUN
ejpam-4580	93	2	5	5	NUM
ejpam-4580	93	3	.	.	PUNCT
ejpam-4580	94	1	let	let	VERB
ejpam-4580	94	2	t	t	PROPN
ejpam-4580	94	3	∈	∈	PROPN
ejpam-4580	94	4	l(h	l(h	PROPN
ejpam-4580	94	5	)	)	PUNCT
ejpam-4580	94	6	be	be	AUX
ejpam-4580	94	7	an	an	DET
ejpam-4580	94	8	operator	operator	NOUN
ejpam-4580	94	9	of	of	ADP
ejpam-4580	94	10	the	the	DET
ejpam-4580	94	11	k−quasi	k−quasi	PROPN
ejpam-4580	94	12	class	class	NOUN
ejpam-4580	94	13	q(n	q(n	PROPN
ejpam-4580	94	14	)	)	PUNCT
ejpam-4580	94	15	.	.	PUNCT
ejpam-4580	95	1	if	if	SCONJ
ejpam-4580	95	2	t	t	PROPN
ejpam-4580	95	3	has	have	VERB
ejpam-4580	95	4	dense	dense	ADJ
ejpam-4580	95	5	range	range	NOUN
ejpam-4580	95	6	,	,	PUNCT
ejpam-4580	95	7	then	then	ADV
ejpam-4580	95	8	t	t	PROPN
ejpam-4580	95	9	is	be	AUX
ejpam-4580	95	10	an	an	DET
ejpam-4580	95	11	operator	operator	NOUN
ejpam-4580	95	12	of	of	ADP
ejpam-4580	95	13	the	the	DET
ejpam-4580	95	14	class	class	NOUN
ejpam-4580	95	15	q(n	q(n	PROPN
ejpam-4580	95	16	)	)	PUNCT
ejpam-4580	95	17	.	.	PUNCT
ejpam-4580	96	1	proof	proof	NOUN
ejpam-4580	96	2	.	.	PUNCT
ejpam-4580	97	1	since	since	SCONJ
ejpam-4580	97	2	t	t	PROPN
ejpam-4580	97	3	k	k	PROPN
ejpam-4580	97	4	has	have	VERB
ejpam-4580	97	5	dense	dense	ADJ
ejpam-4580	97	6	range	range	NOUN
ejpam-4580	97	7	then	then	ADV
ejpam-4580	97	8	,	,	PUNCT
ejpam-4580	97	9	t	t	PROPN
ejpam-4580	97	10	k(h	k(h	PROPN
ejpam-4580	97	11	)	)	PUNCT
ejpam-4580	98	1	=	=	SYM
ejpam-4580	98	2	h.	h.	PROPN
ejpam-4580	98	3	let	let	VERB
ejpam-4580	98	4	y	y	PROPN
ejpam-4580	98	5	∈	∈	PROPN
ejpam-4580	98	6	h.	h.	PROPN
ejpam-4580	99	1	then	then	ADV
ejpam-4580	99	2	,	,	PUNCT
ejpam-4580	99	3	there	there	PRON
ejpam-4580	99	4	exists	exist	VERB
ejpam-4580	99	5	a	a	DET
ejpam-4580	99	6	sequence	sequence	NOUN
ejpam-4580	99	7	{	{	PUNCT
ejpam-4580	99	8	xn}∞n=1	xn}∞n=1	PROPN
ejpam-4580	99	9	in	in	ADP
ejpam-4580	99	10	h	h	PRON
ejpam-4580	99	11	such	such	ADJ
ejpam-4580	99	12	that	that	SCONJ
ejpam-4580	99	13	t	t	PROPN
ejpam-4580	99	14	k(xn	k(xn	PROPN
ejpam-4580	99	15	)	)	PUNCT
ejpam-4580	99	16	→	→	SYM
ejpam-4580	99	17	y	y	PROPN
ejpam-4580	99	18	,	,	PUNCT
ejpam-4580	99	19	n	n	PROPN
ejpam-4580	99	20	→	→	SYM
ejpam-4580	99	21	∞.	∞.	PROPN
ejpam-4580	99	22	since	since	SCONJ
ejpam-4580	99	23	t	t	PROPN
ejpam-4580	99	24	is	be	AUX
ejpam-4580	99	25	an	an	DET
ejpam-4580	99	26	operator	operator	NOUN
ejpam-4580	99	27	of	of	ADP
ejpam-4580	99	28	the	the	DET
ejpam-4580	99	29	k−quasi	k−quasi	PROPN
ejpam-4580	99	30	class	class	NOUN
ejpam-4580	99	31	q(n	q(n	PROPN
ejpam-4580	99	32	)	)	PUNCT
ejpam-4580	99	33	,	,	PUNCT
ejpam-4580	99	34	then	then	ADV
ejpam-4580	99	35	〈	〈	PROPN
ejpam-4580	99	36	(	(	PUNCT
ejpam-4580	99	37	t	t	PROPN
ejpam-4580	99	38	∗k(t	∗k(t	PROPN
ejpam-4580	99	39	∗2	∗2	PROPN
ejpam-4580	99	40	t	t	PROPN
ejpam-4580	99	41	2	2	NUM
ejpam-4580	99	42	−nt	−nt	ADP
ejpam-4580	99	43	∗t	∗t	PROPN
ejpam-4580	99	44	+	+	CCONJ
ejpam-4580	99	45	i)t	i)t	VERB
ejpam-4580	100	1	k)xn	k)xn	PROPN
ejpam-4580	100	2	,	,	PUNCT
ejpam-4580	100	3	xn	xn	PROPN
ejpam-4580	100	4	〉	〉	NOUN
ejpam-4580	100	5	≥	≥	NUM
ejpam-4580	100	6	0	0	NUM
ejpam-4580	100	7	,	,	PUNCT
ejpam-4580	100	8	⟨(t	⟨(t	PROPN
ejpam-4580	100	9	∗2	∗2	PROPN
ejpam-4580	100	10	t	t	PROPN
ejpam-4580	100	11	2	2	NUM
ejpam-4580	100	12	−nt	−nt	ADP
ejpam-4580	100	13	∗t	∗t	PROPN
ejpam-4580	100	14	+	+	CCONJ
ejpam-4580	100	15	i)t	i)t	VERB
ejpam-4580	100	16	kxn	kxn	PROPN
ejpam-4580	100	17	,	,	PUNCT
ejpam-4580	100	18	t	t	PROPN
ejpam-4580	100	19	kxn⟩	kxn⟩	NOUN
ejpam-4580	100	20	≥	≥	PROPN
ejpam-4580	100	21	0	0	NUM
ejpam-4580	100	22	,	,	PUNCT
ejpam-4580	100	23	for	for	ADP
ejpam-4580	100	24	all	all	DET
ejpam-4580	100	25	n	n	PRON
ejpam-4580	100	26	∈	∈	NOUN
ejpam-4580	100	27	n.	n.	NOUN
ejpam-4580	100	28	by	by	ADP
ejpam-4580	100	29	the	the	DET
ejpam-4580	100	30	continuity	continuity	NOUN
ejpam-4580	100	31	of	of	ADP
ejpam-4580	100	32	the	the	DET
ejpam-4580	100	33	inner	inner	ADJ
ejpam-4580	100	34	product	product	NOUN
ejpam-4580	100	35	,	,	PUNCT
ejpam-4580	100	36	we	we	PRON
ejpam-4580	100	37	have	have	VERB
ejpam-4580	100	38	⟨(t	⟨(t	PRON
ejpam-4580	100	39	∗2	∗2	PROPN
ejpam-4580	100	40	t	t	PROPN
ejpam-4580	100	41	2	2	NUM
ejpam-4580	100	42	−nt	−nt	ADP
ejpam-4580	100	43	∗t	∗t	PROPN
ejpam-4580	100	44	+	+	CCONJ
ejpam-4580	100	45	i)y	i)y	ADJ
ejpam-4580	100	46	,	,	PUNCT
ejpam-4580	100	47	y⟩	y⟩	NOUN
ejpam-4580	100	48	≥	≥	NOUN
ejpam-4580	100	49	0	0	PUNCT
ejpam-4580	100	50	therefore	therefore	ADV
ejpam-4580	100	51	t	t	PROPN
ejpam-4580	100	52	is	be	AUX
ejpam-4580	100	53	an	an	DET
ejpam-4580	100	54	operator	operator	NOUN
ejpam-4580	100	55	of	of	ADP
ejpam-4580	100	56	the	the	DET
ejpam-4580	100	57	class	class	NOUN
ejpam-4580	100	58	q(n	q(n	PROPN
ejpam-4580	100	59	)	)	PUNCT
ejpam-4580	100	60	.	.	PUNCT
ejpam-4580	101	1	similarly	similarly	ADV
ejpam-4580	101	2	,	,	PUNCT
ejpam-4580	101	3	we	we	PRON
ejpam-4580	101	4	state	state	VERB
ejpam-4580	101	5	a	a	DET
ejpam-4580	101	6	proposition	proposition	NOUN
ejpam-4580	101	7	which	which	PRON
ejpam-4580	101	8	gives	give	VERB
ejpam-4580	101	9	conditions	condition	NOUN
ejpam-4580	101	10	for	for	ADP
ejpam-4580	101	11	an	an	DET
ejpam-4580	101	12	operator	operator	NOUN
ejpam-4580	101	13	t	t	NOUN
ejpam-4580	101	14	of	of	ADP
ejpam-4580	101	15	the	the	DET
ejpam-4580	101	16	k−quasi	k−quasi	PROPN
ejpam-4580	101	17	class	class	NOUN
ejpam-4580	101	18	q∗(n	q∗(n	PROPN
ejpam-4580	101	19	)	)	PUNCT
ejpam-4580	101	20	to	to	PART
ejpam-4580	101	21	be	be	AUX
ejpam-4580	101	22	an	an	DET
ejpam-4580	101	23	operator	operator	NOUN
ejpam-4580	101	24	of	of	ADP
ejpam-4580	101	25	the	the	DET
ejpam-4580	101	26	class	class	NOUN
ejpam-4580	101	27	q∗(n	q∗(n	PROPN
ejpam-4580	101	28	)	)	PUNCT
ejpam-4580	101	29	.	.	PUNCT
ejpam-4580	102	1	proposition	proposition	NOUN
ejpam-4580	102	2	6	6	NUM
ejpam-4580	102	3	.	.	PUNCT
ejpam-4580	103	1	let	let	VERB
ejpam-4580	103	2	t	t	PROPN
ejpam-4580	103	3	∈	∈	PROPN
ejpam-4580	103	4	l(h	l(h	PROPN
ejpam-4580	103	5	)	)	PUNCT
ejpam-4580	103	6	be	be	AUX
ejpam-4580	103	7	an	an	DET
ejpam-4580	103	8	operator	operator	NOUN
ejpam-4580	103	9	of	of	ADP
ejpam-4580	103	10	the	the	DET
ejpam-4580	103	11	k−quasi	k−quasi	PROPN
ejpam-4580	103	12	class	class	NOUN
ejpam-4580	103	13	q∗(n	q∗(n	PROPN
ejpam-4580	103	14	)	)	PUNCT
ejpam-4580	103	15	.	.	PUNCT
ejpam-4580	104	1	if	if	SCONJ
ejpam-4580	104	2	t	t	PROPN
ejpam-4580	104	3	k	k	PROPN
ejpam-4580	104	4	has	have	VERB
ejpam-4580	104	5	dense	dense	ADJ
ejpam-4580	104	6	range	range	NOUN
ejpam-4580	104	7	,	,	PUNCT
ejpam-4580	104	8	then	then	ADV
ejpam-4580	104	9	t	t	PROPN
ejpam-4580	104	10	is	be	AUX
ejpam-4580	104	11	an	an	DET
ejpam-4580	104	12	operator	operator	NOUN
ejpam-4580	104	13	of	of	ADP
ejpam-4580	104	14	the	the	DET
ejpam-4580	104	15	class	class	NOUN
ejpam-4580	104	16	q∗(n	q∗(n	PROPN
ejpam-4580	104	17	)	)	PUNCT
ejpam-4580	104	18	.	.	PUNCT
ejpam-4580	105	1	in	in	ADP
ejpam-4580	105	2	the	the	DET
ejpam-4580	105	3	following	following	NOUN
ejpam-4580	105	4	we	we	PRON
ejpam-4580	105	5	give	give	VERB
ejpam-4580	105	6	a	a	DET
ejpam-4580	105	7	proposition	proposition	NOUN
ejpam-4580	105	8	which	which	PRON
ejpam-4580	105	9	gives	give	VERB
ejpam-4580	105	10	conditions	condition	NOUN
ejpam-4580	105	11	for	for	ADP
ejpam-4580	105	12	an	an	DET
ejpam-4580	105	13	operator	operator	NOUN
ejpam-4580	105	14	t	t	NOUN
ejpam-4580	105	15	of	of	ADP
ejpam-4580	105	16	the	the	DET
ejpam-4580	105	17	k−quasi	k−quasi	PROPN
ejpam-4580	105	18	class	class	NOUN
ejpam-4580	105	19	q(n	q(n	PROPN
ejpam-4580	105	20	)	)	PUNCT
ejpam-4580	105	21	to	to	PART
ejpam-4580	105	22	be	be	AUX
ejpam-4580	105	23	an	an	DET
ejpam-4580	105	24	k−quasi−paranormal	k−quasi−paranormal	NOUN
ejpam-4580	105	25	operator	operator	NOUN
ejpam-4580	105	26	.	.	PUNCT
ejpam-4580	106	1	proposition	proposition	NOUN
ejpam-4580	106	2	7	7	NUM
ejpam-4580	106	3	.	.	PUNCT
ejpam-4580	107	1	if	if	SCONJ
ejpam-4580	107	2	t	t	PROPN
ejpam-4580	107	3	is	be	AUX
ejpam-4580	107	4	a	a	DET
ejpam-4580	107	5	k−quasi	k−quasi	PROPN
ejpam-4580	107	6	class	class	NOUN
ejpam-4580	107	7	q(n	q(n	PROPN
ejpam-4580	107	8	)	)	PUNCT
ejpam-4580	107	9	operator	operator	NOUN
ejpam-4580	107	10	and	and	CCONJ
ejpam-4580	107	11	t	t	PROPN
ejpam-4580	107	12	2	2	NUM
ejpam-4580	107	13	is	be	AUX
ejpam-4580	107	14	an	an	DET
ejpam-4580	107	15	isometry	isometry	NOUN
ejpam-4580	107	16	,	,	PUNCT
ejpam-4580	107	17	then	then	ADV
ejpam-4580	107	18	t	t	PROPN
ejpam-4580	107	19	is	be	AUX
ejpam-4580	107	20	k−quasi−paranormal	k−quasi−paranormal	PROPN
ejpam-4580	107	21	operator	operator	NOUN
ejpam-4580	107	22	for	for	ADP
ejpam-4580	107	23	n	n	PRON
ejpam-4580	107	24	≥	≥	NUM
ejpam-4580	107	25	2	2	NUM
ejpam-4580	107	26	.	.	PUNCT
ejpam-4580	107	27	proof	proof	NOUN
ejpam-4580	107	28	.	.	PUNCT
ejpam-4580	108	1	let	let	VERB
ejpam-4580	108	2	t	t	NOUN
ejpam-4580	108	3	be	be	AUX
ejpam-4580	108	4	a	a	DET
ejpam-4580	108	5	k−quasi	k−quasi	NOUN
ejpam-4580	108	6	class	class	NOUN
ejpam-4580	108	7	q(n	q(n	PROPN
ejpam-4580	108	8	)	)	PUNCT
ejpam-4580	108	9	operator	operator	NOUN
ejpam-4580	108	10	.	.	PUNCT
ejpam-4580	109	1	then	then	ADV
ejpam-4580	109	2	n∥t	n∥t	ADJ
ejpam-4580	109	3	k+1x∥2	k+1x∥2	NOUN
ejpam-4580	109	4	≤	≤	X
ejpam-4580	109	5	∥t	∥t	ADJ
ejpam-4580	109	6	k+2x∥2	k+2x∥2	NOUN
ejpam-4580	110	1	+	+	CCONJ
ejpam-4580	110	2	∥t	∥t	ADJ
ejpam-4580	110	3	kx∥2	kx∥2	NOUN
ejpam-4580	110	4	=	=	SYM
ejpam-4580	110	5	(	(	PUNCT
ejpam-4580	110	6	∥t	∥t	PROPN
ejpam-4580	110	7	k+2x∥	k+2x∥	PROPN
ejpam-4580	110	8	−	−	PROPN
ejpam-4580	110	9	∥t	∥t	PROPN
ejpam-4580	110	10	kx∥)2	kx∥)2	PROPN
ejpam-4580	110	11	+	+	CCONJ
ejpam-4580	110	12	2∥t	2∥t	NUM
ejpam-4580	110	13	k+2x∥∥t	k+2x∥∥t	VERB
ejpam-4580	110	14	kx∥.	kx∥.	NOUN
ejpam-4580	110	15	suppose	suppose	VERB
ejpam-4580	110	16	that	that	SCONJ
ejpam-4580	110	17	t	t	PROPN
ejpam-4580	110	18	2	2	NUM
ejpam-4580	110	19	is	be	AUX
ejpam-4580	110	20	isometry	isometry	NOUN
ejpam-4580	110	21	,	,	PUNCT
ejpam-4580	110	22	then	then	ADV
ejpam-4580	110	23	∥t	∥t	ADJ
ejpam-4580	110	24	2x∥	2x∥	NOUN
ejpam-4580	110	25	=	=	SYM
ejpam-4580	110	26	∥x∥	∥x∥	NOUN
ejpam-4580	110	27	⇒	⇒	VERB
ejpam-4580	110	28	∥t	∥t	ADJ
ejpam-4580	110	29	4x∥	4x∥	NOUN
ejpam-4580	111	1	=	=	SYM
ejpam-4580	111	2	∥t	∥t	ADJ
ejpam-4580	111	3	2x∥	2x∥	NOUN
ejpam-4580	111	4	⇒	⇒	NOUN
ejpam-4580	111	5	·	·	PUNCT
ejpam-4580	111	6	·	·	PUNCT
ejpam-4580	111	7	·	·	PUNCT
ejpam-4580	111	8	⇒	⇒	VERB
ejpam-4580	111	9	∥t	∥t	PRON
ejpam-4580	111	10	k+2x∥	k+2x∥	NOUN
ejpam-4580	111	11	=	=	SYM
ejpam-4580	111	12	∥t	∥t	ADJ
ejpam-4580	111	13	kx∥	kx∥	NOUN
ejpam-4580	111	14	for	for	ADP
ejpam-4580	111	15	all	all	DET
ejpam-4580	111	16	x	x	SYM
ejpam-4580	111	17	∈	∈	PROPN
ejpam-4580	111	18	h.	h.	NOUN
ejpam-4580	111	19	from	from	ADP
ejpam-4580	111	20	this	this	PRON
ejpam-4580	111	21	we	we	PRON
ejpam-4580	111	22	have	have	VERB
ejpam-4580	111	23	∥t	∥t	ADJ
ejpam-4580	111	24	k+1x∥2	k+1x∥2	NOUN
ejpam-4580	111	25	≤	≤	ADV
ejpam-4580	111	26	2	2	NUM
ejpam-4580	111	27	n	n	NUM
ejpam-4580	111	28	∥t	∥t	ADJ
ejpam-4580	111	29	k+2x∥∥t	k+2x∥∥t	NOUN
ejpam-4580	111	30	kx∥	kx∥	NOUN
ejpam-4580	111	31	≤	≤	NUM
ejpam-4580	111	32	∥t	∥t	PROPN
ejpam-4580	111	33	k+2x∥∥t	k+2x∥∥t	NOUN
ejpam-4580	111	34	kx∥	kx∥	NOUN
ejpam-4580	111	35	,	,	PUNCT
ejpam-4580	111	36	for	for	ADP
ejpam-4580	111	37	n	n	X
ejpam-4580	111	38	≥	≥	NUM
ejpam-4580	111	39	2	2	NUM
ejpam-4580	111	40	.	.	PUNCT
ejpam-4580	112	1	this	this	PRON
ejpam-4580	112	2	proves	prove	VERB
ejpam-4580	112	3	the	the	DET
ejpam-4580	112	4	result	result	NOUN
ejpam-4580	112	5	.	.	PUNCT
ejpam-4580	113	1	similarly	similarly	ADV
ejpam-4580	113	2	,	,	PUNCT
ejpam-4580	113	3	we	we	PRON
ejpam-4580	113	4	give	give	VERB
ejpam-4580	113	5	a	a	DET
ejpam-4580	113	6	proposition	proposition	NOUN
ejpam-4580	113	7	which	which	PRON
ejpam-4580	113	8	gives	give	VERB
ejpam-4580	113	9	conditions	condition	NOUN
ejpam-4580	113	10	for	for	ADP
ejpam-4580	113	11	an	an	DET
ejpam-4580	113	12	operator	operator	NOUN
ejpam-4580	113	13	t	t	NOUN
ejpam-4580	113	14	of	of	ADP
ejpam-4580	113	15	the	the	DET
ejpam-4580	113	16	k−quasi	k−quasi	PROPN
ejpam-4580	113	17	class	class	NOUN
ejpam-4580	113	18	q∗(n	q∗(n	PROPN
ejpam-4580	113	19	)	)	PUNCT
ejpam-4580	113	20	to	to	PART
ejpam-4580	113	21	be	be	AUX
ejpam-4580	113	22	an	an	DET
ejpam-4580	113	23	k−quasi−	k−quasi−	PROPN
ejpam-4580	113	24	∗	∗	NOUN
ejpam-4580	113	25	−paranormal	−paranormal	NOUN
ejpam-4580	113	26	operator	operator	NOUN
ejpam-4580	113	27	.	.	PUNCT
ejpam-4580	114	1	sh	sh	PROPN
ejpam-4580	114	2	.	.	PROPN
ejpam-4580	114	3	lohaj	lohaj	PROPN
ejpam-4580	114	4	/	/	SYM
ejpam-4580	114	5	eur	eur	PROPN
ejpam-4580	114	6	.	.	PUNCT
ejpam-4580	115	1	j.	j.	PROPN
ejpam-4580	115	2	pure	pure	PROPN
ejpam-4580	115	3	appl	appl	PROPN
ejpam-4580	115	4	.	.	PROPN
ejpam-4580	115	5	math	math	PROPN
ejpam-4580	115	6	,	,	PUNCT
ejpam-4580	115	7	15	15	NUM
ejpam-4580	115	8	(	(	PUNCT
ejpam-4580	115	9	4	4	NUM
ejpam-4580	115	10	)	)	PUNCT
ejpam-4580	115	11	(	(	PUNCT
ejpam-4580	115	12	2022	2022	NUM
ejpam-4580	115	13	)	)	PUNCT
ejpam-4580	115	14	,	,	PUNCT
ejpam-4580	115	15	1836	1836	NUM
ejpam-4580	115	16	-	-	SYM
ejpam-4580	115	17	1853	1853	NUM
ejpam-4580	115	18	1842	1842	NUM
ejpam-4580	115	19	proposition	proposition	NOUN
ejpam-4580	115	20	8	8	NUM
ejpam-4580	115	21	.	.	PUNCT
ejpam-4580	116	1	if	if	SCONJ
ejpam-4580	116	2	t	t	PROPN
ejpam-4580	116	3	is	be	AUX
ejpam-4580	116	4	a	a	DET
ejpam-4580	116	5	k−quasi	k−quasi	PROPN
ejpam-4580	116	6	class	class	NOUN
ejpam-4580	116	7	q∗(n	q∗(n	NOUN
ejpam-4580	116	8	)	)	PUNCT
ejpam-4580	116	9	operator	operator	NOUN
ejpam-4580	116	10	and	and	CCONJ
ejpam-4580	116	11	t	t	PROPN
ejpam-4580	116	12	2	2	NUM
ejpam-4580	116	13	is	be	AUX
ejpam-4580	116	14	an	an	DET
ejpam-4580	116	15	isometry	isometry	NOUN
ejpam-4580	116	16	,	,	PUNCT
ejpam-4580	116	17	then	then	ADV
ejpam-4580	116	18	t	t	PROPN
ejpam-4580	116	19	is	be	AUX
ejpam-4580	116	20	k−quasi−	k−quasi−	PROPN
ejpam-4580	116	21	∗	∗	NOUN
ejpam-4580	116	22	−paranormal	−paranormal	ADJ
ejpam-4580	116	23	operator	operator	NOUN
ejpam-4580	116	24	for	for	ADP
ejpam-4580	116	25	n	n	PRON
ejpam-4580	116	26	≥	≥	NUM
ejpam-4580	116	27	2	2	NUM
ejpam-4580	116	28	.	.	PUNCT
ejpam-4580	117	1	now	now	ADV
ejpam-4580	117	2	we	we	PRON
ejpam-4580	117	3	will	will	AUX
ejpam-4580	117	4	prove	prove	VERB
ejpam-4580	117	5	some	some	DET
ejpam-4580	117	6	properties	property	NOUN
ejpam-4580	117	7	of	of	ADP
ejpam-4580	117	8	these	these	DET
ejpam-4580	117	9	new	new	ADJ
ejpam-4580	117	10	classes	class	NOUN
ejpam-4580	117	11	of	of	ADP
ejpam-4580	117	12	operators	operator	NOUN
ejpam-4580	117	13	.	.	PUNCT
ejpam-4580	118	1	proposition	proposition	NOUN
ejpam-4580	118	2	9	9	NUM
ejpam-4580	118	3	.	.	PUNCT
ejpam-4580	119	1	let	let	VERB
ejpam-4580	119	2	t	t	NOUN
ejpam-4580	119	3	be	be	AUX
ejpam-4580	119	4	an	an	DET
ejpam-4580	119	5	operator	operator	NOUN
ejpam-4580	119	6	of	of	ADP
ejpam-4580	119	7	k−quasi	k−quasi	PROPN
ejpam-4580	119	8	class	class	NOUN
ejpam-4580	119	9	q(n	q(n	PROPN
ejpam-4580	119	10	)	)	PUNCT
ejpam-4580	119	11	.	.	PUNCT
ejpam-4580	120	1	(	(	PUNCT
ejpam-4580	120	2	i	i	NOUN
ejpam-4580	120	3	)	)	PUNCT
ejpam-4580	120	4	if	if	SCONJ
ejpam-4580	120	5	t	t	PROPN
ejpam-4580	120	6	commutes	commute	VERB
ejpam-4580	120	7	with	with	ADP
ejpam-4580	120	8	an	an	DET
ejpam-4580	120	9	isometric	isometric	ADJ
ejpam-4580	120	10	operator	operator	NOUN
ejpam-4580	120	11	s	s	PART
ejpam-4580	120	12	,	,	PUNCT
ejpam-4580	120	13	then	then	ADV
ejpam-4580	120	14	ts	ts	PROPN
ejpam-4580	120	15	is	be	AUX
ejpam-4580	120	16	an	an	DET
ejpam-4580	120	17	operator	operator	NOUN
ejpam-4580	120	18	of	of	ADP
ejpam-4580	120	19	the	the	DET
ejpam-4580	120	20	k−quasi	k−quasi	PROPN
ejpam-4580	120	21	class	class	NOUN
ejpam-4580	120	22	q(n	q(n	PROPN
ejpam-4580	120	23	)	)	PUNCT
ejpam-4580	120	24	.	.	PUNCT
ejpam-4580	121	1	(	(	PUNCT
ejpam-4580	121	2	ii	ii	X
ejpam-4580	121	3	)	)	PUNCT
ejpam-4580	121	4	if	if	SCONJ
ejpam-4580	121	5	s	s	NOUN
ejpam-4580	121	6	is	be	AUX
ejpam-4580	121	7	unitarily	unitarily	ADV
ejpam-4580	121	8	equivalent	equivalent	ADJ
ejpam-4580	121	9	to	to	PART
ejpam-4580	121	10	operator	operator	VERB
ejpam-4580	121	11	t	t	PROPN
ejpam-4580	121	12	,	,	PUNCT
ejpam-4580	121	13	then	then	ADV
ejpam-4580	121	14	s	s	VERB
ejpam-4580	121	15	is	be	AUX
ejpam-4580	121	16	an	an	DET
ejpam-4580	121	17	operator	operator	NOUN
ejpam-4580	121	18	of	of	ADP
ejpam-4580	121	19	the	the	DET
ejpam-4580	121	20	k−quasi	k−quasi	PROPN
ejpam-4580	121	21	class	class	NOUN
ejpam-4580	121	22	q(n	q(n	PROPN
ejpam-4580	121	23	)	)	PUNCT
ejpam-4580	121	24	.	.	PUNCT
ejpam-4580	122	1	proof	proof	NOUN
ejpam-4580	122	2	.	.	PUNCT
ejpam-4580	123	1	similarly	similarly	ADV
ejpam-4580	123	2	as	as	ADP
ejpam-4580	123	3	proposition	proposition	NOUN
ejpam-4580	123	4	2.4	2.4	NUM
ejpam-4580	123	5	.	.	PUNCT
ejpam-4580	124	1	in	in	ADP
ejpam-4580	124	2	[	[	X
ejpam-4580	124	3	7	7	NUM
ejpam-4580	124	4	]	]	PUNCT
ejpam-4580	124	5	.	.	PUNCT
ejpam-4580	125	1	proposition	proposition	NOUN
ejpam-4580	125	2	10	10	NUM
ejpam-4580	125	3	.	.	PUNCT
ejpam-4580	126	1	let	let	VERB
ejpam-4580	126	2	t	t	NOUN
ejpam-4580	126	3	be	be	AUX
ejpam-4580	126	4	an	an	DET
ejpam-4580	126	5	operator	operator	NOUN
ejpam-4580	126	6	of	of	ADP
ejpam-4580	126	7	k−quasi	k−quasi	PROPN
ejpam-4580	126	8	class	class	NOUN
ejpam-4580	126	9	q∗(n	q∗(n	PROPN
ejpam-4580	126	10	)	)	PUNCT
ejpam-4580	126	11	.	.	PUNCT
ejpam-4580	127	1	(	(	PUNCT
ejpam-4580	127	2	i	i	NOUN
ejpam-4580	127	3	)	)	PUNCT
ejpam-4580	127	4	if	if	SCONJ
ejpam-4580	127	5	t	t	PROPN
ejpam-4580	127	6	commutes	commute	VERB
ejpam-4580	127	7	with	with	ADP
ejpam-4580	127	8	an	an	DET
ejpam-4580	127	9	unitary	unitary	ADJ
ejpam-4580	127	10	operator	operator	NOUN
ejpam-4580	127	11	s	s	NOUN
ejpam-4580	127	12	,	,	PUNCT
ejpam-4580	127	13	then	then	ADV
ejpam-4580	127	14	ts	ts	PROPN
ejpam-4580	127	15	is	be	AUX
ejpam-4580	127	16	an	an	DET
ejpam-4580	127	17	operator	operator	NOUN
ejpam-4580	127	18	of	of	ADP
ejpam-4580	127	19	the	the	DET
ejpam-4580	127	20	k−quasi	k−quasi	PROPN
ejpam-4580	127	21	class	class	NOUN
ejpam-4580	127	22	q∗(n	q∗(n	PROPN
ejpam-4580	127	23	)	)	PUNCT
ejpam-4580	127	24	.	.	PUNCT
ejpam-4580	128	1	(	(	PUNCT
ejpam-4580	128	2	ii	ii	X
ejpam-4580	128	3	)	)	PUNCT
ejpam-4580	128	4	if	if	SCONJ
ejpam-4580	128	5	s	s	NOUN
ejpam-4580	128	6	is	be	AUX
ejpam-4580	128	7	unitarily	unitarily	ADV
ejpam-4580	128	8	equivalent	equivalent	ADJ
ejpam-4580	128	9	to	to	PART
ejpam-4580	128	10	operator	operator	VERB
ejpam-4580	128	11	t	t	PROPN
ejpam-4580	128	12	,	,	PUNCT
ejpam-4580	128	13	then	then	ADV
ejpam-4580	128	14	s	s	VERB
ejpam-4580	128	15	is	be	AUX
ejpam-4580	128	16	an	an	DET
ejpam-4580	128	17	operator	operator	NOUN
ejpam-4580	128	18	of	of	ADP
ejpam-4580	128	19	the	the	DET
ejpam-4580	128	20	k−quasi	k−quasi	PROPN
ejpam-4580	128	21	class	class	NOUN
ejpam-4580	128	22	q∗(n	q∗(n	PROPN
ejpam-4580	128	23	)	)	PUNCT
ejpam-4580	128	24	.	.	PUNCT
ejpam-4580	129	1	proposition	proposition	NOUN
ejpam-4580	129	2	11	11	NUM
ejpam-4580	129	3	.	.	PUNCT
ejpam-4580	130	1	let	let	VERB
ejpam-4580	130	2	t	t	PROPN
ejpam-4580	130	3	∈	∈	PROPN
ejpam-4580	130	4	l(h	l(h	PROPN
ejpam-4580	130	5	)	)	PUNCT
ejpam-4580	130	6	.	.	PUNCT
ejpam-4580	131	1	if	if	SCONJ
ejpam-4580	131	2	∥t∥	∥t∥	VERB
ejpam-4580	131	3	≤	≤	ADJ
ejpam-4580	131	4	1√	1√	PROPN
ejpam-4580	131	5	n	n	NOUN
ejpam-4580	131	6	,	,	PUNCT
ejpam-4580	131	7	then	then	ADV
ejpam-4580	131	8	t	t	PROPN
ejpam-4580	131	9	is	be	AUX
ejpam-4580	131	10	an	an	DET
ejpam-4580	131	11	operator	operator	NOUN
ejpam-4580	131	12	of	of	ADP
ejpam-4580	131	13	k−quasi	k−quasi	PROPN
ejpam-4580	131	14	class	class	NOUN
ejpam-4580	131	15	q(n	q(n	PROPN
ejpam-4580	131	16	)	)	PUNCT
ejpam-4580	131	17	.	.	PUNCT
ejpam-4580	132	1	proof	proof	NOUN
ejpam-4580	132	2	.	.	PUNCT
ejpam-4580	133	1	from	from	ADP
ejpam-4580	133	2	∥t∥	∥t∥	ADV
ejpam-4580	133	3	≤	≤	NUM
ejpam-4580	133	4	1√	1√	PROPN
ejpam-4580	133	5	n	n	NOUN
ejpam-4580	133	6	,	,	PUNCT
ejpam-4580	133	7	we	we	PRON
ejpam-4580	133	8	have	have	VERB
ejpam-4580	133	9	∥t∥2	∥t∥2	NOUN
ejpam-4580	133	10	≤	≤	ADV
ejpam-4580	133	11	1	1	NUM
ejpam-4580	133	12	n	n	NOUN
ejpam-4580	133	13	.	.	PUNCT
ejpam-4580	134	1	then	then	ADV
ejpam-4580	134	2	,	,	PUNCT
ejpam-4580	134	3	∥tx∥2	∥tx∥2	PROPN
ejpam-4580	134	4	≤	≤	NUM
ejpam-4580	134	5	1	1	NUM
ejpam-4580	134	6	n	n	PRON
ejpam-4580	134	7	∥x∥	∥x∥	NOUN
ejpam-4580	134	8	,	,	PUNCT
ejpam-4580	134	9	for	for	ADP
ejpam-4580	134	10	allx	allx	PROPN
ejpam-4580	134	11	∈	∈	PROPN
ejpam-4580	134	12	h	h	NOUN
ejpam-4580	134	13	(	(	PUNCT
ejpam-4580	134	14	tx	tx	PROPN
ejpam-4580	134	15	,	,	PUNCT
ejpam-4580	134	16	tx)−	tx)−	PROPN
ejpam-4580	134	17	1	1	NUM
ejpam-4580	134	18	n	n	PROPN
ejpam-4580	134	19	(	(	PUNCT
ejpam-4580	134	20	x	x	NOUN
ejpam-4580	134	21	,	,	PUNCT
ejpam-4580	134	22	x	x	NOUN
ejpam-4580	134	23	)	)	PUNCT
ejpam-4580	134	24	≤	≤	NUM
ejpam-4580	134	25	0	0	NUM
ejpam-4580	134	26	,	,	PUNCT
ejpam-4580	134	27	for	for	ADP
ejpam-4580	134	28	allx	allx	PROPN
ejpam-4580	134	29	∈	∈	PROPN
ejpam-4580	134	30	h	h	NOUN
ejpam-4580	134	31	(	(	PUNCT
ejpam-4580	134	32	(	(	PUNCT
ejpam-4580	134	33	i	i	PRON
ejpam-4580	134	34	−nt	−nt	VERB
ejpam-4580	134	35	∗t	∗t	PROPN
ejpam-4580	134	36	)	)	PUNCT
ejpam-4580	134	37	x	x	SYM
ejpam-4580	134	38	,	,	PUNCT
ejpam-4580	134	39	x	x	X
ejpam-4580	134	40	)	)	PUNCT
ejpam-4580	134	41	≥	≥	NOUN
ejpam-4580	134	42	0	0	NUM
ejpam-4580	134	43	,	,	PUNCT
ejpam-4580	134	44	for	for	ADP
ejpam-4580	134	45	allx	allx	PROPN
ejpam-4580	134	46	∈	∈	PROPN
ejpam-4580	134	47	h	h	NOUN
ejpam-4580	134	48	i	i	PRON
ejpam-4580	134	49	−nt	−nt	VERB
ejpam-4580	134	50	∗t	∗t	PROPN
ejpam-4580	134	51	≥	≥	NUM
ejpam-4580	134	52	0	0	NUM
ejpam-4580	134	53	t	t	PROPN
ejpam-4580	134	54	∗2	∗2	PROPN
ejpam-4580	134	55	t	t	PROPN
ejpam-4580	134	56	2	2	NUM
ejpam-4580	134	57	−nt	−nt	ADP
ejpam-4580	134	58	∗t	∗t	PROPN
ejpam-4580	134	59	+	+	CCONJ
ejpam-4580	134	60	i	i	PRON
ejpam-4580	134	61	≥	≥	VERB
ejpam-4580	134	62	0	0	NUM
ejpam-4580	134	63	t	t	PROPN
ejpam-4580	134	64	∗k(t	∗k(t	PROPN
ejpam-4580	134	65	∗2	∗2	PROPN
ejpam-4580	134	66	t	t	PROPN
ejpam-4580	134	67	2	2	NUM
ejpam-4580	134	68	−nt	−nt	ADP
ejpam-4580	134	69	∗t	∗t	PROPN
ejpam-4580	134	70	+	+	CCONJ
ejpam-4580	134	71	i)t	i)t	VERB
ejpam-4580	135	1	k	k	X
ejpam-4580	135	2	≥	≥	NOUN
ejpam-4580	135	3	0	0	NUM
ejpam-4580	136	1	so	so	ADV
ejpam-4580	136	2	t	t	PROPN
ejpam-4580	136	3	is	be	AUX
ejpam-4580	136	4	an	an	DET
ejpam-4580	136	5	operator	operator	NOUN
ejpam-4580	136	6	of	of	ADP
ejpam-4580	136	7	k−quasi	k−quasi	PROPN
ejpam-4580	136	8	class	class	NOUN
ejpam-4580	136	9	q(n	q(n	PROPN
ejpam-4580	136	10	)	)	PUNCT
ejpam-4580	136	11	.	.	PUNCT
ejpam-4580	137	1	sh	sh	PROPN
ejpam-4580	137	2	.	.	PROPN
ejpam-4580	137	3	lohaj	lohaj	PROPN
ejpam-4580	137	4	/	/	SYM
ejpam-4580	137	5	eur	eur	PROPN
ejpam-4580	137	6	.	.	PUNCT
ejpam-4580	138	1	j.	j.	PROPN
ejpam-4580	138	2	pure	pure	PROPN
ejpam-4580	138	3	appl	appl	PROPN
ejpam-4580	138	4	.	.	PROPN
ejpam-4580	138	5	math	math	PROPN
ejpam-4580	138	6	,	,	PUNCT
ejpam-4580	138	7	15	15	NUM
ejpam-4580	138	8	(	(	PUNCT
ejpam-4580	138	9	4	4	NUM
ejpam-4580	138	10	)	)	PUNCT
ejpam-4580	138	11	(	(	PUNCT
ejpam-4580	138	12	2022	2022	NUM
ejpam-4580	138	13	)	)	PUNCT
ejpam-4580	138	14	,	,	PUNCT
ejpam-4580	138	15	1836	1836	NUM
ejpam-4580	138	16	-	-	SYM
ejpam-4580	138	17	1853	1853	NUM
ejpam-4580	138	18	1843	1843	NUM
ejpam-4580	138	19	proposition	proposition	NOUN
ejpam-4580	138	20	12	12	NUM
ejpam-4580	138	21	.	.	PUNCT
ejpam-4580	139	1	let	let	VERB
ejpam-4580	139	2	t	t	PROPN
ejpam-4580	139	3	∈	∈	PROPN
ejpam-4580	139	4	l(h	l(h	PROPN
ejpam-4580	139	5	)	)	PUNCT
ejpam-4580	139	6	.	.	PUNCT
ejpam-4580	140	1	if	if	SCONJ
ejpam-4580	140	2	∥t	∥t	PROPN
ejpam-4580	140	3	∗∥	∗∥	PUNCT
ejpam-4580	140	4	≤	≤	NUM
ejpam-4580	140	5	1√	1√	PROPN
ejpam-4580	140	6	n	n	NOUN
ejpam-4580	140	7	,	,	PUNCT
ejpam-4580	140	8	then	then	ADV
ejpam-4580	140	9	t	t	PROPN
ejpam-4580	140	10	is	be	AUX
ejpam-4580	140	11	an	an	DET
ejpam-4580	140	12	operator	operator	NOUN
ejpam-4580	140	13	of	of	ADP
ejpam-4580	140	14	k−quasi	k−quasi	PROPN
ejpam-4580	140	15	class	class	NOUN
ejpam-4580	140	16	q∗(n	q∗(n	PROPN
ejpam-4580	140	17	)	)	PUNCT
ejpam-4580	140	18	.	.	PUNCT
ejpam-4580	141	1	proposition	proposition	NOUN
ejpam-4580	141	2	13	13	NUM
ejpam-4580	141	3	.	.	PUNCT
ejpam-4580	142	1	let	let	VERB
ejpam-4580	142	2	m	m	PRON
ejpam-4580	142	3	be	be	AUX
ejpam-4580	142	4	a	a	DET
ejpam-4580	142	5	closed	close	VERB
ejpam-4580	142	6	invariant	invariant	ADJ
ejpam-4580	142	7	subspace	subspace	NOUN
ejpam-4580	142	8	of	of	ADP
ejpam-4580	142	9	h	h	NOUN
ejpam-4580	142	10	for	for	ADP
ejpam-4580	142	11	the	the	DET
ejpam-4580	142	12	operator	operator	NOUN
ejpam-4580	142	13	t	t	PROPN
ejpam-4580	142	14	of	of	ADP
ejpam-4580	142	15	k−quasi	k−quasi	PROPN
ejpam-4580	142	16	class	class	NOUN
ejpam-4580	142	17	q(n	q(n	PROPN
ejpam-4580	142	18	)	)	PUNCT
ejpam-4580	142	19	.	.	PUNCT
ejpam-4580	143	1	then	then	ADV
ejpam-4580	143	2	,	,	PUNCT
ejpam-4580	143	3	the	the	DET
ejpam-4580	143	4	restriction	restriction	NOUN
ejpam-4580	143	5	t|tk(m	t|tk(m	PROPN
ejpam-4580	143	6	)	)	PUNCT
ejpam-4580	143	7	is	be	AUX
ejpam-4580	143	8	of	of	ADP
ejpam-4580	143	9	class	class	NOUN
ejpam-4580	143	10	q(n	q(n	PROPN
ejpam-4580	143	11	)	)	PUNCT
ejpam-4580	143	12	.	.	PUNCT
ejpam-4580	144	1	proof	proof	NOUN
ejpam-4580	144	2	.	.	PUNCT
ejpam-4580	145	1	let	let	VERB
ejpam-4580	145	2	u	u	PRON
ejpam-4580	145	3	∈	∈	PROPN
ejpam-4580	145	4	m.	m.	NOUN
ejpam-4580	145	5	then	then	ADV
ejpam-4580	145	6	t	t	PROPN
ejpam-4580	145	7	∗k(t	∗k(t	PROPN
ejpam-4580	145	8	∗2	∗2	PROPN
ejpam-4580	145	9	t	t	PROPN
ejpam-4580	145	10	2	2	NUM
ejpam-4580	145	11	−nt	−nt	ADP
ejpam-4580	145	12	∗t	∗t	PROPN
ejpam-4580	145	13	+	+	CCONJ
ejpam-4580	145	14	i)t	i)t	VERB
ejpam-4580	146	1	k	k	X
ejpam-4580	146	2	≥	≥	X
ejpam-4580	146	3	0	0	NUM
ejpam-4580	147	1	(	(	PUNCT
ejpam-4580	147	2	t	t	PROPN
ejpam-4580	147	3	∗k(t	∗k(t	PROPN
ejpam-4580	147	4	∗2	∗2	PROPN
ejpam-4580	147	5	t	t	PROPN
ejpam-4580	147	6	2	2	NUM
ejpam-4580	147	7	−nt	−nt	ADP
ejpam-4580	147	8	∗t	∗t	PROPN
ejpam-4580	147	9	+	+	CCONJ
ejpam-4580	147	10	i)t	i)t	VERB
ejpam-4580	147	11	ku	ku	PROPN
ejpam-4580	147	12	,	,	PUNCT
ejpam-4580	147	13	u	u	PROPN
ejpam-4580	147	14	)	)	PUNCT
ejpam-4580	147	15	≥	≥	X
ejpam-4580	147	16	0	0	NUM
ejpam-4580	147	17	(	(	PUNCT
ejpam-4580	147	18	(	(	PUNCT
ejpam-4580	147	19	t	t	PROPN
ejpam-4580	147	20	∗2	∗2	PROPN
ejpam-4580	147	21	t	t	PROPN
ejpam-4580	147	22	2	2	NUM
ejpam-4580	147	23	−nt	−nt	ADP
ejpam-4580	147	24	∗t	∗t	PROPN
ejpam-4580	147	25	+	+	CCONJ
ejpam-4580	147	26	i)t	i)t	VERB
ejpam-4580	147	27	ku	ku	PROPN
ejpam-4580	147	28	,	,	PUNCT
ejpam-4580	147	29	t	t	PROPN
ejpam-4580	147	30	ku	ku	PROPN
ejpam-4580	147	31	)	)	PUNCT
ejpam-4580	147	32	≥	≥	PROPN
ejpam-4580	147	33	0	0	NUM
ejpam-4580	147	34	(	(	PUNCT
ejpam-4580	147	35	(	(	PUNCT
ejpam-4580	147	36	t	t	PROPN
ejpam-4580	147	37	∗2	∗2	PROPN
ejpam-4580	147	38	t	t	PROPN
ejpam-4580	147	39	2	2	NUM
ejpam-4580	147	40	−nt	−nt	ADP
ejpam-4580	147	41	∗t	∗t	PROPN
ejpam-4580	147	42	+	+	CCONJ
ejpam-4580	147	43	i)y	i)y	ADJ
ejpam-4580	147	44	,	,	PUNCT
ejpam-4580	147	45	y	y	NOUN
ejpam-4580	147	46	)	)	PUNCT
ejpam-4580	147	47	≥	≥	NOUN
ejpam-4580	147	48	0	0	NUM
ejpam-4580	147	49	,	,	PUNCT
ejpam-4580	147	50	y	y	PROPN
ejpam-4580	147	51	=	=	SYM
ejpam-4580	147	52	t	t	PROPN
ejpam-4580	147	53	ku	ku	PROPN
ejpam-4580	147	54	∈	∈	PROPN
ejpam-4580	147	55	m.	m.	NOUN
ejpam-4580	147	56	it	it	PRON
ejpam-4580	147	57	follows	follow	VERB
ejpam-4580	147	58	that	that	SCONJ
ejpam-4580	147	59	the	the	DET
ejpam-4580	147	60	restriction	restriction	NOUN
ejpam-4580	147	61	t|tk(m	t|tk(m	PROPN
ejpam-4580	147	62	)	)	PUNCT
ejpam-4580	147	63	is	be	AUX
ejpam-4580	147	64	of	of	ADP
ejpam-4580	147	65	class	class	NOUN
ejpam-4580	147	66	q(n	q(n	PROPN
ejpam-4580	147	67	)	)	PUNCT
ejpam-4580	147	68	.	.	PUNCT
ejpam-4580	148	1	proposition	proposition	NOUN
ejpam-4580	148	2	14	14	NUM
ejpam-4580	148	3	.	.	PUNCT
ejpam-4580	149	1	let	let	VERB
ejpam-4580	149	2	m	m	PRON
ejpam-4580	149	3	be	be	AUX
ejpam-4580	149	4	a	a	DET
ejpam-4580	149	5	closed	close	VERB
ejpam-4580	149	6	invariant	invariant	ADJ
ejpam-4580	149	7	subspace	subspace	NOUN
ejpam-4580	149	8	of	of	ADP
ejpam-4580	149	9	h	h	NOUN
ejpam-4580	149	10	for	for	ADP
ejpam-4580	149	11	the	the	DET
ejpam-4580	149	12	operator	operator	NOUN
ejpam-4580	149	13	t	t	PROPN
ejpam-4580	149	14	of	of	ADP
ejpam-4580	149	15	k−quasi	k−quasi	PROPN
ejpam-4580	149	16	class	class	NOUN
ejpam-4580	149	17	q∗(n	q∗(n	PROPN
ejpam-4580	149	18	)	)	PUNCT
ejpam-4580	149	19	.	.	PUNCT
ejpam-4580	150	1	then	then	ADV
ejpam-4580	150	2	,	,	PUNCT
ejpam-4580	150	3	the	the	DET
ejpam-4580	150	4	restriction	restriction	NOUN
ejpam-4580	150	5	t|tk(m	t|tk(m	PROPN
ejpam-4580	150	6	)	)	PUNCT
ejpam-4580	150	7	is	be	AUX
ejpam-4580	150	8	of	of	ADP
ejpam-4580	150	9	class	class	NOUN
ejpam-4580	150	10	q∗(n	q∗(n	PROPN
ejpam-4580	150	11	)	)	PUNCT
ejpam-4580	150	12	.	.	PUNCT
ejpam-4580	151	1	proposition	proposition	NOUN
ejpam-4580	151	2	15	15	NUM
ejpam-4580	151	3	.	.	PUNCT
ejpam-4580	152	1	let	let	VERB
ejpam-4580	152	2	t	t	PROPN
ejpam-4580	152	3	∈	∈	PROPN
ejpam-4580	152	4	l(h	l(h	PROPN
ejpam-4580	152	5	)	)	PUNCT
ejpam-4580	152	6	be	be	AUX
ejpam-4580	152	7	an	an	DET
ejpam-4580	152	8	invertible	invertible	ADJ
ejpam-4580	152	9	operator	operator	NOUN
ejpam-4580	152	10	and	and	CCONJ
ejpam-4580	152	11	s	s	AUX
ejpam-4580	152	12	be	be	AUX
ejpam-4580	152	13	an	an	DET
ejpam-4580	152	14	operator	operator	NOUN
ejpam-4580	152	15	such	such	ADJ
ejpam-4580	152	16	that	that	PRON
ejpam-4580	152	17	s	s	VERB
ejpam-4580	152	18	commutes	commute	NOUN
ejpam-4580	152	19	with	with	ADP
ejpam-4580	152	20	operator	operator	NOUN
ejpam-4580	152	21	t	t	PROPN
ejpam-4580	152	22	∗t	∗t	PROPN
ejpam-4580	152	23	.	.	PUNCT
ejpam-4580	153	1	then	then	ADV
ejpam-4580	153	2	,	,	PUNCT
ejpam-4580	153	3	s	s	X
ejpam-4580	153	4	is	be	AUX
ejpam-4580	153	5	of	of	ADP
ejpam-4580	153	6	k−quasi	k−quasi	NOUN
ejpam-4580	153	7	class	class	NOUN
ejpam-4580	153	8	q(n	q(n	PROPN
ejpam-4580	153	9	)	)	PUNCT
ejpam-4580	154	1	if	if	SCONJ
ejpam-4580	154	2	and	and	CCONJ
ejpam-4580	154	3	only	only	ADV
ejpam-4580	154	4	if	if	SCONJ
ejpam-4580	154	5	tst−1	tst−1	PROPN
ejpam-4580	154	6	is	be	AUX
ejpam-4580	154	7	of	of	ADP
ejpam-4580	154	8	k−quasi	k−quasi	NOUN
ejpam-4580	154	9	class	class	NOUN
ejpam-4580	154	10	q(n	q(n	PROPN
ejpam-4580	154	11	)	)	PUNCT
ejpam-4580	154	12	.	.	PUNCT
ejpam-4580	155	1	proof	proof	NOUN
ejpam-4580	155	2	.	.	PUNCT
ejpam-4580	156	1	let	let	VERB
ejpam-4580	156	2	s	s	PRON
ejpam-4580	156	3	be	be	AUX
ejpam-4580	156	4	an	an	DET
ejpam-4580	156	5	operator	operator	NOUN
ejpam-4580	156	6	of	of	ADP
ejpam-4580	156	7	k−quasi	k−quasi	PROPN
ejpam-4580	156	8	class	class	NOUN
ejpam-4580	156	9	q(n	q(n	PROPN
ejpam-4580	156	10	)	)	PUNCT
ejpam-4580	156	11	.	.	PUNCT
ejpam-4580	157	1	then	then	ADV
ejpam-4580	157	2	s∗k(s∗2s2	s∗k(s∗2s2	NOUN
ejpam-4580	157	3	−ns∗s	−ns∗s	X
ejpam-4580	157	4	+	+	X
ejpam-4580	157	5	i)sk	i)sk	PROPN
ejpam-4580	157	6	≥	≥	NOUN
ejpam-4580	157	7	0	0	NUM
ejpam-4580	157	8	.	.	PUNCT
ejpam-4580	158	1	from	from	ADP
ejpam-4580	158	2	this	this	PRON
ejpam-4580	158	3	we	we	PRON
ejpam-4580	158	4	have	have	VERB
ejpam-4580	158	5	ts∗k(s∗2s2	ts∗k(s∗2s2	NUM
ejpam-4580	158	6	−ns∗s	−ns∗s	NOUN
ejpam-4580	158	7	+	+	CCONJ
ejpam-4580	158	8	i)skt	i)skt	PROPN
ejpam-4580	158	9	∗	∗	PROPN
ejpam-4580	158	10	≥	≥	NOUN
ejpam-4580	158	11	0	0	NUM
ejpam-4580	158	12	.	.	PUNCT
ejpam-4580	159	1	now	now	ADV
ejpam-4580	159	2	,	,	PUNCT
ejpam-4580	159	3	we	we	PRON
ejpam-4580	159	4	prove	prove	VERB
ejpam-4580	159	5	that	that	DET
ejpam-4580	159	6	operator	operator	NOUN
ejpam-4580	159	7	tt	tt	PROPN
ejpam-4580	159	8	∗	∗	NOUN
ejpam-4580	159	9	commutes	commute	NOUN
ejpam-4580	159	10	with	with	ADP
ejpam-4580	159	11	operator	operator	NOUN
ejpam-4580	159	12	ts∗k(s∗2s2−ns∗s+i)skt	ts∗k(s∗2s2−ns∗s+i)skt	PROPN
ejpam-4580	159	13	∗.	∗.	PUNCT
ejpam-4580	159	14	since	since	SCONJ
ejpam-4580	159	15	operator	operator	NOUN
ejpam-4580	159	16	s	s	PART
ejpam-4580	159	17	commutes	commute	NOUN
ejpam-4580	159	18	with	with	ADP
ejpam-4580	159	19	operator	operator	NOUN
ejpam-4580	159	20	t	t	PROPN
ejpam-4580	159	21	∗t	∗t	PROPN
ejpam-4580	159	22	,	,	PUNCT
ejpam-4580	159	23	operator	operator	NOUN
ejpam-4580	159	24	s∗	s∗	PROPN
ejpam-4580	159	25	also	also	ADV
ejpam-4580	159	26	commutes	commute	VERB
ejpam-4580	159	27	with	with	ADP
ejpam-4580	159	28	operator	operator	NOUN
ejpam-4580	159	29	t	t	PROPN
ejpam-4580	159	30	∗t	∗t	PROPN
ejpam-4580	159	31	.	.	PUNCT
ejpam-4580	160	1	from	from	ADP
ejpam-4580	160	2	this	this	PRON
ejpam-4580	160	3	we	we	PRON
ejpam-4580	160	4	have	have	VERB
ejpam-4580	160	5	ts∗k(s∗2s2	ts∗k(s∗2s2	NUM
ejpam-4580	160	6	−ns∗s	−ns∗s	NOUN
ejpam-4580	160	7	+	+	CCONJ
ejpam-4580	160	8	i)skt	i)skt	PROPN
ejpam-4580	160	9	∗[tt	∗[tt	ADP
ejpam-4580	160	10	∗	∗	NOUN
ejpam-4580	160	11	]	]	PUNCT
ejpam-4580	160	12	=	=	SYM
ejpam-4580	160	13	ts∗k(s∗2s2	ts∗k(s∗2s2	NUM
ejpam-4580	160	14	−ns∗s	−ns∗s	X
ejpam-4580	160	15	+	+	SYM
ejpam-4580	160	16	i)sk[t	i)sk[t	PROPN
ejpam-4580	160	17	∗t	∗t	PROPN
ejpam-4580	160	18	]	]	PUNCT
ejpam-4580	160	19	t	t	NOUN
ejpam-4580	160	20	∗	∗	NOUN
ejpam-4580	161	1	=	=	SYM
ejpam-4580	161	2	t	t	PROPN
ejpam-4580	162	1	[	[	X
ejpam-4580	162	2	t	t	X
ejpam-4580	162	3	∗t	∗t	PROPN
ejpam-4580	162	4	]	]	PUNCT
ejpam-4580	162	5	s∗k(s∗2s2	s∗k(s∗2s2	NOUN
ejpam-4580	162	6	−ns∗s	−ns∗s	NOUN
ejpam-4580	162	7	+	+	NUM
ejpam-4580	162	8	i)skt	i)skt	PROPN
ejpam-4580	162	9	∗	∗	NOUN
ejpam-4580	162	10	=	=	PUNCT
ejpam-4580	163	1	[	[	X
ejpam-4580	163	2	tt	tt	X
ejpam-4580	163	3	∗]ts∗k(s∗2s2	∗]ts∗k(s∗2s2	PROPN
ejpam-4580	163	4	−ns∗s	−ns∗s	NOUN
ejpam-4580	163	5	+	+	CCONJ
ejpam-4580	163	6	i)skt	i)skt	PROPN
ejpam-4580	163	7	∗	∗	NOUN
ejpam-4580	163	8	thus	thus	ADV
ejpam-4580	163	9	operator	operator	NOUN
ejpam-4580	163	10	tt	tt	PROPN
ejpam-4580	163	11	∗	∗	NOUN
ejpam-4580	163	12	commutes	commute	NOUN
ejpam-4580	163	13	with	with	ADP
ejpam-4580	163	14	operator	operator	NOUN
ejpam-4580	163	15	ts∗k(s∗2s2−ns∗s+i)skt	ts∗k(s∗2s2−ns∗s+i)skt	PROPN
ejpam-4580	163	16	∗.	∗.	PUNCT
ejpam-4580	163	17	then	then	ADV
ejpam-4580	163	18	,	,	PUNCT
ejpam-4580	163	19	operator	operator	NOUN
ejpam-4580	164	1	[	[	X
ejpam-4580	164	2	tt	tt	X
ejpam-4580	164	3	∗]−1	∗]−1	PRON
ejpam-4580	164	4	also	also	ADV
ejpam-4580	164	5	commutes	commute	VERB
ejpam-4580	164	6	with	with	ADP
ejpam-4580	164	7	operator	operator	NOUN
ejpam-4580	164	8	ts∗k(s∗2s2	ts∗k(s∗2s2	NUM
ejpam-4580	164	9	−ns∗s	−ns∗s	NOUN
ejpam-4580	164	10	+	+	CCONJ
ejpam-4580	164	11	i)skt	i)skt	PROPN
ejpam-4580	164	12	∗.	∗.	PROPN
ejpam-4580	164	13	since	since	SCONJ
ejpam-4580	164	14	the	the	DET
ejpam-4580	164	15	operator	operator	NOUN
ejpam-4580	164	16	[	[	X
ejpam-4580	164	17	tt	tt	X
ejpam-4580	164	18	∗]−1	∗]−1	INTJ
ejpam-4580	164	19	and	and	CCONJ
ejpam-4580	164	20	ts∗k(s∗2s2	ts∗k(s∗2s2	NUM
ejpam-4580	164	21	−ns∗s	−ns∗s	X
ejpam-4580	164	22	+	+	CCONJ
ejpam-4580	164	23	i)skt	i)skt	PROPN
ejpam-4580	164	24	∗	∗	NOUN
ejpam-4580	164	25	are	be	AUX
ejpam-4580	164	26	positive	positive	ADJ
ejpam-4580	164	27	,	,	PUNCT
ejpam-4580	164	28	then	then	ADV
ejpam-4580	164	29	ts∗k(s∗2s2	ts∗k(s∗2s2	NUM
ejpam-4580	164	30	−ns∗s	−ns∗s	X
ejpam-4580	164	31	+	+	CCONJ
ejpam-4580	164	32	i)skt	i)skt	PROPN
ejpam-4580	165	1	∗[tt	∗[tt	PROPN
ejpam-4580	165	2	∗]−1	∗]−1	PROPN
ejpam-4580	165	3	≥	≥	NOUN
ejpam-4580	165	4	0	0	NUM
ejpam-4580	165	5	.	.	PUNCT
ejpam-4580	166	1	sh	sh	PROPN
ejpam-4580	166	2	.	.	PROPN
ejpam-4580	166	3	lohaj	lohaj	PROPN
ejpam-4580	166	4	/	/	SYM
ejpam-4580	166	5	eur	eur	PROPN
ejpam-4580	166	6	.	.	PUNCT
ejpam-4580	167	1	j.	j.	PROPN
ejpam-4580	167	2	pure	pure	PROPN
ejpam-4580	167	3	appl	appl	PROPN
ejpam-4580	167	4	.	.	PROPN
ejpam-4580	167	5	math	math	PROPN
ejpam-4580	167	6	,	,	PUNCT
ejpam-4580	167	7	15	15	NUM
ejpam-4580	167	8	(	(	PUNCT
ejpam-4580	167	9	4	4	NUM
ejpam-4580	167	10	)	)	PUNCT
ejpam-4580	167	11	(	(	PUNCT
ejpam-4580	167	12	2022	2022	NUM
ejpam-4580	167	13	)	)	PUNCT
ejpam-4580	167	14	,	,	PUNCT
ejpam-4580	167	15	1836	1836	NUM
ejpam-4580	167	16	-	-	SYM
ejpam-4580	167	17	1853	1853	NUM
ejpam-4580	167	18	1844	1844	NUM
ejpam-4580	167	19	since	since	SCONJ
ejpam-4580	167	20	operator	operator	NOUN
ejpam-4580	167	21	s	s	PART
ejpam-4580	167	22	commutes	commute	NOUN
ejpam-4580	167	23	with	with	ADP
ejpam-4580	167	24	operator	operator	NOUN
ejpam-4580	167	25	t	t	PROPN
ejpam-4580	167	26	∗t	∗t	PROPN
ejpam-4580	167	27	,	,	PUNCT
ejpam-4580	167	28	we	we	PRON
ejpam-4580	167	29	get	get	VERB
ejpam-4580	167	30	(	(	PUNCT
ejpam-4580	167	31	tst−1)∗k	tst−1)∗k	PROPN
ejpam-4580	167	32	=	=	PUNCT
ejpam-4580	167	33	(	(	PUNCT
ejpam-4580	167	34	tst−1)∗(tst−1)∗	tst−1)∗(tst−1)∗	ADJ
ejpam-4580	167	35	.	.	PUNCT
ejpam-4580	167	36	.	.	PUNCT
ejpam-4580	167	37	.	.	PUNCT
ejpam-4580	168	1	(	(	PUNCT
ejpam-4580	168	2	tst−1)∗	tst−1)∗	PROPN
ejpam-4580	168	3	=	=	SYM
ejpam-4580	168	4	t	t	PROPN
ejpam-4580	168	5	∗−1s∗t	∗−1s∗t	PROPN
ejpam-4580	168	6	∗	∗	NOUN
ejpam-4580	168	7	t	t	PROPN
ejpam-4580	168	8	∗−1s∗t	∗−1s∗t	PROPN
ejpam-4580	168	9	∗	∗	NOUN
ejpam-4580	168	10	.	.	PUNCT
ejpam-4580	168	11	.	.	PUNCT
ejpam-4580	168	12	.	.	PUNCT
ejpam-4580	169	1	t	t	PROPN
ejpam-4580	169	2	∗−1s∗t	∗−1s∗t	PROPN
ejpam-4580	169	3	∗	∗	NOUN
ejpam-4580	169	4	=	=	SYM
ejpam-4580	169	5	t	t	PROPN
ejpam-4580	169	6	∗−1s∗kt	∗−1s∗kt	NOUN
ejpam-4580	169	7	∗	∗	NOUN
ejpam-4580	169	8	(	(	PUNCT
ejpam-4580	169	9	tst−1)k	tst−1)k	NUM
ejpam-4580	169	10	=	=	SYM
ejpam-4580	169	11	tskt−1	tskt−1	X
ejpam-4580	169	12	(	(	PUNCT
ejpam-4580	169	13	tst−1)∗(tst−1	tst−1)∗(tst−1	X
ejpam-4580	169	14	)	)	PUNCT
ejpam-4580	169	15	=	=	SYM
ejpam-4580	170	1	t	t	PROPN
ejpam-4580	170	2	∗−1s∗t	∗−1s∗t	X
ejpam-4580	170	3	∗tst−1	∗tst−1	PROPN
ejpam-4580	170	4	=	=	NOUN
ejpam-4580	170	5	ts∗st−1	ts∗st−1	NOUN
ejpam-4580	170	6	(	(	PUNCT
ejpam-4580	170	7	tst−1)∗2(tst−1)2	tst−1)∗2(tst−1)2	PROPN
ejpam-4580	170	8	=	=	SYM
ejpam-4580	170	9	t	t	PROPN
ejpam-4580	170	10	∗−1s∗2	∗−1s∗2	PROPN
ejpam-4580	170	11	t	t	PROPN
ejpam-4580	170	12	∗ts2t−1	∗ts2t−1	NOUN
ejpam-4580	170	13	=	=	PROPN
ejpam-4580	170	14	ts∗2s2t−1	ts∗2s2t−1	PROPN
ejpam-4580	170	15	to	to	PART
ejpam-4580	170	16	prove	prove	VERB
ejpam-4580	170	17	that	that	DET
ejpam-4580	170	18	operator	operator	NOUN
ejpam-4580	170	19	tst−1	tst−1	PROPN
ejpam-4580	171	1	=	=	PUNCT
ejpam-4580	171	2	m	m	VERB
ejpam-4580	171	3	is	be	AUX
ejpam-4580	171	4	an	an	DET
ejpam-4580	171	5	operator	operator	NOUN
ejpam-4580	171	6	of	of	ADP
ejpam-4580	171	7	k−quasi	k−quasi	PROPN
ejpam-4580	171	8	class	class	NOUN
ejpam-4580	171	9	q(n	q(n	PROPN
ejpam-4580	171	10	)	)	PUNCT
ejpam-4580	171	11	,	,	PUNCT
ejpam-4580	171	12	we	we	PRON
ejpam-4580	171	13	substitute	substitute	VERB
ejpam-4580	171	14	last	last	ADJ
ejpam-4580	171	15	equations	equation	NOUN
ejpam-4580	171	16	in	in	ADP
ejpam-4580	171	17	the	the	DET
ejpam-4580	171	18	above	above	ADJ
ejpam-4580	171	19	expression	expression	NOUN
ejpam-4580	171	20	and	and	CCONJ
ejpam-4580	171	21	obtain	obtain	AUX
ejpam-4580	171	22	m∗k(m∗2m2	m∗k(m∗2m2	NOUN
ejpam-4580	171	23	−nm∗m	−nm∗m	PROPN
ejpam-4580	171	24	+	+	PUNCT
ejpam-4580	172	1	i)mk	i)mk	PROPN
ejpam-4580	172	2	t	t	PROPN
ejpam-4580	172	3	∗−1s∗kt	∗−1s∗kt	NOUN
ejpam-4580	172	4	∗[ts∗2s2t−1	∗[ts∗2s2t−1	PROPN
ejpam-4580	172	5	−nts∗st−1	−nts∗st−1	NOUN
ejpam-4580	173	1	+	+	CCONJ
ejpam-4580	173	2	i]tskt−1	i]tskt−1	PROPN
ejpam-4580	173	3	=	=	NOUN
ejpam-4580	173	4	ts∗k(s∗2s2	ts∗k(s∗2s2	NUM
ejpam-4580	173	5	−ns∗s	−ns∗s	NOUN
ejpam-4580	173	6	+	+	X
ejpam-4580	173	7	i)skt−1	i)skt−1	PROPN
ejpam-4580	173	8	now	now	ADV
ejpam-4580	173	9	we	we	PRON
ejpam-4580	173	10	prove	prove	VERB
ejpam-4580	173	11	that	that	SCONJ
ejpam-4580	173	12	the	the	DET
ejpam-4580	173	13	last	last	ADJ
ejpam-4580	173	14	expression	expression	NOUN
ejpam-4580	173	15	is	be	AUX
ejpam-4580	173	16	positive	positive	ADJ
ejpam-4580	173	17	.	.	PUNCT
ejpam-4580	174	1	since	since	SCONJ
ejpam-4580	174	2	ts∗k(s∗2s2	ts∗k(s∗2s2	NUM
ejpam-4580	174	3	−ns∗s	−ns∗s	X
ejpam-4580	174	4	+	+	CCONJ
ejpam-4580	174	5	i)skt	i)skt	PROPN
ejpam-4580	175	1	∗[tt	∗[tt	PROPN
ejpam-4580	175	2	∗]−1	∗]−1	PROPN
ejpam-4580	175	3	≥	≥	NOUN
ejpam-4580	175	4	0	0	NUM
ejpam-4580	175	5	ts∗k(s∗2s2	ts∗k(s∗2s2	NUM
ejpam-4580	175	6	−ns∗s	−ns∗s	NOUN
ejpam-4580	175	7	+	+	CCONJ
ejpam-4580	175	8	i)skt	i)skt	PROPN
ejpam-4580	175	9	∗t	∗t	PROPN
ejpam-4580	175	10	∗−1t−1	∗−1t−1	PUNCT
ejpam-4580	175	11	≥	≥	X
ejpam-4580	175	12	0	0	NUM
ejpam-4580	175	13	ts∗k(s∗2s2	ts∗k(s∗2s2	NUM
ejpam-4580	175	14	−ns∗s	−ns∗s	X
ejpam-4580	175	15	+	+	CCONJ
ejpam-4580	175	16	i)skt−1	i)skt−1	PROPN
ejpam-4580	175	17	≥	≥	NOUN
ejpam-4580	175	18	0	0	NUM
ejpam-4580	175	19	hence	hence	ADV
ejpam-4580	175	20	,	,	PUNCT
ejpam-4580	175	21	operator	operator	NOUN
ejpam-4580	175	22	tst−1	tst−1	PROPN
ejpam-4580	175	23	is	be	AUX
ejpam-4580	175	24	an	an	DET
ejpam-4580	175	25	operator	operator	NOUN
ejpam-4580	175	26	of	of	ADP
ejpam-4580	175	27	k−quasi	k−quasi	PROPN
ejpam-4580	175	28	class	class	NOUN
ejpam-4580	175	29	q(n	q(n	PROPN
ejpam-4580	175	30	)	)	PUNCT
ejpam-4580	175	31	.	.	PUNCT
ejpam-4580	176	1	conversely	conversely	ADV
ejpam-4580	176	2	,	,	PUNCT
ejpam-4580	176	3	let	let	VERB
ejpam-4580	176	4	tst−1	tst−1	PROPN
ejpam-4580	176	5	=	=	VERB
ejpam-4580	176	6	m	m	AUX
ejpam-4580	176	7	be	be	VERB
ejpam-4580	176	8	an	an	DET
ejpam-4580	176	9	operator	operator	NOUN
ejpam-4580	176	10	of	of	ADP
ejpam-4580	176	11	k−quasi	k−quasi	PROPN
ejpam-4580	176	12	class	class	NOUN
ejpam-4580	176	13	q(n	q(n	PROPN
ejpam-4580	176	14	)	)	PUNCT
ejpam-4580	176	15	.	.	PUNCT
ejpam-4580	177	1	then	then	ADV
ejpam-4580	177	2	m∗k(m∗2m2	m∗k(m∗2m2	VERB
ejpam-4580	177	3	−nm∗m	−nm∗m	PROPN
ejpam-4580	177	4	+	+	PUNCT
ejpam-4580	178	1	i)mk	i)mk	PROPN
ejpam-4580	178	2	≥	≥	NOUN
ejpam-4580	178	3	0	0	NUM
ejpam-4580	178	4	.	.	PUNCT
ejpam-4580	179	1	similarly	similarly	ADV
ejpam-4580	179	2	,	,	PUNCT
ejpam-4580	179	3	we	we	PRON
ejpam-4580	179	4	have	have	VERB
ejpam-4580	179	5	that	that	PRON
ejpam-4580	179	6	ts∗k(s∗2s2	ts∗k(s∗2s2	NUM
ejpam-4580	179	7	−ns∗s	−ns∗s	X
ejpam-4580	179	8	+	+	CCONJ
ejpam-4580	179	9	i)skt−1	i)skt−1	PROPN
ejpam-4580	180	1	≥	≥	NOUN
ejpam-4580	180	2	0	0	NUM
ejpam-4580	180	3	t	t	PROPN
ejpam-4580	180	4	∗ts∗k(s∗2s2	∗ts∗k(s∗2s2	NOUN
ejpam-4580	180	5	−ns∗s	−ns∗s	X
ejpam-4580	180	6	+	+	CCONJ
ejpam-4580	180	7	i)skt−1	i)skt−1	PROPN
ejpam-4580	180	8	t	t	NOUN
ejpam-4580	180	9	≥	≥	NOUN
ejpam-4580	180	10	0	0	NUM
ejpam-4580	181	1	[	[	X
ejpam-4580	181	2	t	t	X
ejpam-4580	181	3	∗t	∗t	PROPN
ejpam-4580	181	4	]	]	PUNCT
ejpam-4580	181	5	s∗k(s∗2s2	s∗k(s∗2s2	NOUN
ejpam-4580	181	6	−ns∗s	−ns∗s	NOUN
ejpam-4580	181	7	+	+	X
ejpam-4580	181	8	i)sk	i)sk	PROPN
ejpam-4580	181	9	≥	≥	NUM
ejpam-4580	181	10	0	0	NUM
ejpam-4580	181	11	.	.	PUNCT
ejpam-4580	181	12	operator	operator	NOUN
ejpam-4580	181	13	t	t	PROPN
ejpam-4580	181	14	∗t	∗t	PROPN
ejpam-4580	181	15	commutes	commute	NOUN
ejpam-4580	181	16	with	with	ADP
ejpam-4580	181	17	operator	operator	NOUN
ejpam-4580	181	18	s	s	NOUN
ejpam-4580	181	19	and	and	CCONJ
ejpam-4580	181	20	hence	hence	ADV
ejpam-4580	181	21	with	with	ADP
ejpam-4580	181	22	operator	operator	NOUN
ejpam-4580	181	23	[	[	X
ejpam-4580	181	24	t	t	X
ejpam-4580	181	25	∗t	∗t	PROPN
ejpam-4580	181	26	]	]	PUNCT
ejpam-4580	181	27	s∗k(s∗2s2	s∗k(s∗2s2	NOUN
ejpam-4580	181	28	−	−	PROPN
ejpam-4580	181	29	ns∗s+i)sk	ns∗s+i)sk	NOUN
ejpam-4580	181	30	.	.	PUNCT
ejpam-4580	182	1	therefore	therefore	ADV
ejpam-4580	182	2	,	,	PUNCT
ejpam-4580	182	3	operator	operator	NOUN
ejpam-4580	182	4	[	[	X
ejpam-4580	182	5	t	t	X
ejpam-4580	182	6	∗t	∗t	PROPN
ejpam-4580	182	7	]	]	PUNCT
ejpam-4580	182	8	−1	−1	NOUN
ejpam-4580	182	9	also	also	ADV
ejpam-4580	182	10	commutes	commute	VERB
ejpam-4580	182	11	with	with	ADP
ejpam-4580	182	12	operator	operator	NOUN
ejpam-4580	182	13	[	[	X
ejpam-4580	182	14	t	t	X
ejpam-4580	182	15	∗t	∗t	PROPN
ejpam-4580	182	16	]	]	PUNCT
ejpam-4580	182	17	s∗k(s∗2s2−	s∗k(s∗2s2−	PROPN
ejpam-4580	182	18	ns∗s	ns∗s	PROPN
ejpam-4580	182	19	+	+	PROPN
ejpam-4580	182	20	i)sk	i)sk	NOUN
ejpam-4580	182	21	.	.	PUNCT
ejpam-4580	183	1	since	since	SCONJ
ejpam-4580	183	2	these	these	DET
ejpam-4580	183	3	operators	operator	NOUN
ejpam-4580	183	4	are	be	AUX
ejpam-4580	183	5	positive	positive	ADJ
ejpam-4580	183	6	,	,	PUNCT
ejpam-4580	183	7	we	we	PRON
ejpam-4580	183	8	have	have	VERB
ejpam-4580	183	9	[	[	X
ejpam-4580	183	10	t	t	X
ejpam-4580	183	11	∗t	∗t	PROPN
ejpam-4580	183	12	]	]	PUNCT
ejpam-4580	183	13	−1[t	−1[t	NOUN
ejpam-4580	183	14	∗t	∗t	PROPN
ejpam-4580	183	15	]	]	SYM
ejpam-4580	183	16	s∗k(s∗2s2	s∗k(s∗2s2	NOUN
ejpam-4580	183	17	−ns∗s	−ns∗s	NOUN
ejpam-4580	183	18	+	+	X
ejpam-4580	183	19	i)sk	i)sk	PROPN
ejpam-4580	183	20	≥	≥	NUM
ejpam-4580	183	21	0	0	NUM
ejpam-4580	183	22	.	.	PUNCT
ejpam-4580	184	1	therefore	therefore	ADV
ejpam-4580	184	2	,	,	PUNCT
ejpam-4580	184	3	s∗k(s∗2s2	s∗k(s∗2s2	NOUN
ejpam-4580	184	4	−ns∗s	−ns∗s	NOUN
ejpam-4580	184	5	+	+	X
ejpam-4580	184	6	i)sk	i)sk	PROPN
ejpam-4580	184	7	≥	≥	NOUN
ejpam-4580	184	8	0	0	NUM
ejpam-4580	184	9	.	.	PUNCT
ejpam-4580	185	1	what	what	PRON
ejpam-4580	185	2	does	do	AUX
ejpam-4580	185	3	it	it	PRON
ejpam-4580	185	4	mean	mean	VERB
ejpam-4580	185	5	that	that	DET
ejpam-4580	185	6	operator	operator	NOUN
ejpam-4580	185	7	s	s	VERB
ejpam-4580	185	8	is	be	AUX
ejpam-4580	185	9	of	of	ADP
ejpam-4580	185	10	k−quasi	k−quasi	NOUN
ejpam-4580	185	11	class	class	NOUN
ejpam-4580	185	12	q(n	q(n	PROPN
ejpam-4580	185	13	)	)	PUNCT
ejpam-4580	185	14	.	.	PUNCT
ejpam-4580	186	1	sh	sh	PROPN
ejpam-4580	186	2	.	.	PROPN
ejpam-4580	186	3	lohaj	lohaj	PROPN
ejpam-4580	186	4	/	/	SYM
ejpam-4580	186	5	eur	eur	PROPN
ejpam-4580	186	6	.	.	PUNCT
ejpam-4580	187	1	j.	j.	PROPN
ejpam-4580	187	2	pure	pure	PROPN
ejpam-4580	187	3	appl	appl	PROPN
ejpam-4580	187	4	.	.	PROPN
ejpam-4580	187	5	math	math	PROPN
ejpam-4580	187	6	,	,	PUNCT
ejpam-4580	187	7	15	15	NUM
ejpam-4580	187	8	(	(	PUNCT
ejpam-4580	187	9	4	4	NUM
ejpam-4580	187	10	)	)	PUNCT
ejpam-4580	187	11	(	(	PUNCT
ejpam-4580	187	12	2022	2022	NUM
ejpam-4580	187	13	)	)	PUNCT
ejpam-4580	187	14	,	,	PUNCT
ejpam-4580	187	15	1836	1836	NUM
ejpam-4580	187	16	-	-	SYM
ejpam-4580	187	17	1853	1853	NUM
ejpam-4580	187	18	1845	1845	NUM
ejpam-4580	187	19	proposition	proposition	NOUN
ejpam-4580	187	20	16	16	NUM
ejpam-4580	187	21	.	.	PUNCT
ejpam-4580	188	1	let	let	VERB
ejpam-4580	188	2	t	t	PROPN
ejpam-4580	188	3	∈	∈	PROPN
ejpam-4580	188	4	l(h	l(h	PROPN
ejpam-4580	188	5	)	)	PUNCT
ejpam-4580	188	6	be	be	AUX
ejpam-4580	188	7	an	an	DET
ejpam-4580	188	8	invertible	invertible	ADJ
ejpam-4580	188	9	operator	operator	NOUN
ejpam-4580	188	10	and	and	CCONJ
ejpam-4580	188	11	s	s	AUX
ejpam-4580	188	12	be	be	AUX
ejpam-4580	188	13	an	an	DET
ejpam-4580	188	14	operator	operator	NOUN
ejpam-4580	188	15	such	such	ADJ
ejpam-4580	188	16	that	that	PRON
ejpam-4580	188	17	s	s	VERB
ejpam-4580	188	18	commutes	commute	NOUN
ejpam-4580	188	19	with	with	ADP
ejpam-4580	188	20	operator	operator	NOUN
ejpam-4580	188	21	t	t	PROPN
ejpam-4580	188	22	∗t	∗t	PROPN
ejpam-4580	188	23	.	.	PUNCT
ejpam-4580	189	1	then	then	ADV
ejpam-4580	189	2	,	,	PUNCT
ejpam-4580	189	3	s	s	X
ejpam-4580	189	4	is	be	AUX
ejpam-4580	189	5	of	of	ADP
ejpam-4580	189	6	k−quasi	k−quasi	PROPN
ejpam-4580	189	7	class	class	NOUN
ejpam-4580	189	8	q∗(n	q∗(n	PROPN
ejpam-4580	189	9	)	)	PUNCT
ejpam-4580	189	10	if	if	SCONJ
ejpam-4580	189	11	and	and	CCONJ
ejpam-4580	189	12	only	only	ADV
ejpam-4580	189	13	if	if	SCONJ
ejpam-4580	189	14	tst−1	tst−1	PROPN
ejpam-4580	189	15	is	be	AUX
ejpam-4580	189	16	of	of	ADP
ejpam-4580	189	17	k−quasi	k−quasi	PROPN
ejpam-4580	189	18	class	class	NOUN
ejpam-4580	189	19	q∗(n	q∗(n	PROPN
ejpam-4580	189	20	)	)	PUNCT
ejpam-4580	189	21	.	.	PUNCT
ejpam-4580	190	1	the	the	DET
ejpam-4580	190	2	next	next	ADJ
ejpam-4580	190	3	proposition	proposition	NOUN
ejpam-4580	190	4	give	give	VERB
ejpam-4580	190	5	necessary	necessary	ADJ
ejpam-4580	190	6	and	and	CCONJ
ejpam-4580	190	7	sufficient	sufficient	ADJ
ejpam-4580	190	8	conditions	condition	NOUN
ejpam-4580	190	9	for	for	ADP
ejpam-4580	190	10	a	a	DET
ejpam-4580	190	11	weighted	weight	VERB
ejpam-4580	190	12	shift	shift	NOUN
ejpam-4580	190	13	operator	operator	NOUN
ejpam-4580	190	14	t	t	PROPN
ejpam-4580	190	15	with	with	ADP
ejpam-4580	190	16	decreasing	decrease	VERB
ejpam-4580	190	17	weighted	weight	VERB
ejpam-4580	190	18	sequence	sequence	NOUN
ejpam-4580	190	19	(	(	PUNCT
ejpam-4580	190	20	αn	αn	NOUN
ejpam-4580	190	21	)	)	PUNCT
ejpam-4580	190	22	to	to	PART
ejpam-4580	190	23	be	be	AUX
ejpam-4580	190	24	an	an	DET
ejpam-4580	190	25	operator	operator	NOUN
ejpam-4580	190	26	of	of	ADP
ejpam-4580	190	27	this	this	DET
ejpam-4580	190	28	class	class	NOUN
ejpam-4580	190	29	of	of	ADP
ejpam-4580	190	30	operators	operator	NOUN
ejpam-4580	190	31	.	.	PUNCT
ejpam-4580	191	1	proposition	proposition	NOUN
ejpam-4580	191	2	17	17	NUM
ejpam-4580	191	3	.	.	PUNCT
ejpam-4580	192	1	a	a	DET
ejpam-4580	192	2	weighted	weight	VERB
ejpam-4580	192	3	shift	shift	NOUN
ejpam-4580	192	4	operator	operator	NOUN
ejpam-4580	192	5	t	t	PROPN
ejpam-4580	192	6	with	with	ADP
ejpam-4580	192	7	decreasing	decrease	VERB
ejpam-4580	192	8	weighted	weight	VERB
ejpam-4580	192	9	sequence	sequence	NOUN
ejpam-4580	192	10	(	(	PUNCT
ejpam-4580	192	11	αn	αn	NOUN
ejpam-4580	192	12	)	)	PUNCT
ejpam-4580	192	13	is	be	AUX
ejpam-4580	192	14	an	an	DET
ejpam-4580	192	15	operator	operator	NOUN
ejpam-4580	192	16	of	of	ADP
ejpam-4580	192	17	k−	k−	PROPN
ejpam-4580	192	18	quasi	quasi	PROPN
ejpam-4580	192	19	class	class	PROPN
ejpam-4580	192	20	q(n	q(n	PROPN
ejpam-4580	192	21	)	)	PUNCT
ejpam-4580	193	1	if	if	SCONJ
ejpam-4580	193	2	and	and	CCONJ
ejpam-4580	193	3	only	only	ADV
ejpam-4580	194	1	if	if	SCONJ
ejpam-4580	194	2	|αn+k|2|αn+k+1|2	|αn+k|2|αn+k+1|2	PROPN
ejpam-4580	194	3	−n	−n	ADJ
ejpam-4580	194	4	|αn+k|2	|αn+k|2	NOUN
ejpam-4580	194	5	+	+	NUM
ejpam-4580	194	6	1	1	NUM
ejpam-4580	194	7	≥	≥	NOUN
ejpam-4580	194	8	0	0	NUM
ejpam-4580	194	9	.	.	PUNCT
ejpam-4580	195	1	for	for	ADP
ejpam-4580	195	2	every	every	DET
ejpam-4580	195	3	n	n	NOUN
ejpam-4580	195	4	and	and	CCONJ
ejpam-4580	195	5	k	k	ADJ
ejpam-4580	195	6	natural	natural	ADJ
ejpam-4580	195	7	numbers	number	NOUN
ejpam-4580	195	8	.	.	PUNCT
ejpam-4580	196	1	proof	proof	NOUN
ejpam-4580	196	2	.	.	PUNCT
ejpam-4580	197	1	since	since	SCONJ
ejpam-4580	197	2	t	t	PROPN
ejpam-4580	197	3	is	be	AUX
ejpam-4580	197	4	a	a	DET
ejpam-4580	197	5	weighted	weighted	ADJ
ejpam-4580	197	6	shift	shift	NOUN
ejpam-4580	197	7	,	,	PUNCT
ejpam-4580	197	8	its	its	PRON
ejpam-4580	197	9	adjoint	adjoint	NOUN
ejpam-4580	197	10	t	t	PROPN
ejpam-4580	197	11	∗	∗	NOUN
ejpam-4580	197	12	is	be	AUX
ejpam-4580	197	13	also	also	ADV
ejpam-4580	197	14	a	a	DET
ejpam-4580	197	15	weighted	weighted	ADJ
ejpam-4580	197	16	shift	shift	NOUN
ejpam-4580	197	17	and	and	CCONJ
ejpam-4580	197	18	defined	define	VERB
ejpam-4580	197	19	by	by	ADP
ejpam-4580	197	20	t	t	PROPN
ejpam-4580	197	21	(	(	PUNCT
ejpam-4580	197	22	en	en	X
ejpam-4580	197	23	)	)	PUNCT
ejpam-4580	197	24	=	=	SYM
ejpam-4580	197	25	|an|en+1	|an|en+1	NOUN
ejpam-4580	197	26	,	,	PUNCT
ejpam-4580	197	27	t	t	PROPN
ejpam-4580	197	28	∗(en	∗(en	NOUN
ejpam-4580	197	29	)	)	PUNCT
ejpam-4580	197	30	=	=	SYM
ejpam-4580	198	1	|an−1|en−1	|an−1|en−1	PROPN
ejpam-4580	198	2	.	.	PUNCT
ejpam-4580	198	3	thus	thus	ADV
ejpam-4580	198	4	,	,	PUNCT
ejpam-4580	198	5	we	we	PRON
ejpam-4580	198	6	have	have	VERB
ejpam-4580	198	7	(	(	PUNCT
ejpam-4580	198	8	t	t	NOUN
ejpam-4580	198	9	∗t	∗t	PROPN
ejpam-4580	198	10	)	)	PUNCT
ejpam-4580	198	11	(	(	PUNCT
ejpam-4580	198	12	en	en	X
ejpam-4580	198	13	)	)	PUNCT
ejpam-4580	198	14	=	=	SYM
ejpam-4580	199	1	|an|2en	|an|2en	PROPN
ejpam-4580	199	2	(	(	PUNCT
ejpam-4580	199	3	t	t	NOUN
ejpam-4580	199	4	∗2	∗2	PROPN
ejpam-4580	199	5	t	t	PROPN
ejpam-4580	199	6	2)(en	2)(en	NUM
ejpam-4580	199	7	)	)	PUNCT
ejpam-4580	199	8	=	=	PUNCT
ejpam-4580	199	9	|an|2|an+1|2en	|an|2|an+1|2en	NUM
ejpam-4580	199	10	t	t	NOUN
ejpam-4580	199	11	k(en	k(en	PROPN
ejpam-4580	199	12	)	)	PUNCT
ejpam-4580	199	13	=	=	SYM
ejpam-4580	200	1	|an||an+1|	|an||an+1|	PROPN
ejpam-4580	200	2	.	.	PUNCT
ejpam-4580	200	3	.	.	PUNCT
ejpam-4580	200	4	.	.	PUNCT
ejpam-4580	201	1	|an+k−1en+k	|an+k−1en+k	PROPN
ejpam-4580	201	2	(	(	PUNCT
ejpam-4580	201	3	t	t	X
ejpam-4580	201	4	∗t	∗t	PROPN
ejpam-4580	201	5	)	)	PUNCT
ejpam-4580	201	6	(	(	PUNCT
ejpam-4580	201	7	en+k	en+k	NOUN
ejpam-4580	201	8	)	)	PUNCT
ejpam-4580	201	9	=	=	SYM
ejpam-4580	201	10	|an+k|2en+k	|an+k|2en+k	PROPN
ejpam-4580	201	11	(	(	PUNCT
ejpam-4580	201	12	t	t	PROPN
ejpam-4580	201	13	∗2	∗2	PROPN
ejpam-4580	201	14	t	t	NOUN
ejpam-4580	201	15	2)(en+k	2)(en+k	NUM
ejpam-4580	201	16	)	)	PUNCT
ejpam-4580	201	17	=	=	PRON
ejpam-4580	201	18	|an+k|2|an+k+1|2en+k	|an+k|2|an+k+1|2en+k	PROPN
ejpam-4580	201	19	t	t	NOUN
ejpam-4580	201	20	∗k(en+k	∗k(en+k	PROPN
ejpam-4580	201	21	)	)	PUNCT
ejpam-4580	201	22	=	=	SYM
ejpam-4580	201	23	|an+k−1||an+k−2|	|an+k−1||an+k−2|	PROPN
ejpam-4580	201	24	.	.	PUNCT
ejpam-4580	201	25	.	.	PUNCT
ejpam-4580	202	1	.	.	PUNCT
ejpam-4580	203	1	|an|en	|an|en	PUNCT
ejpam-4580	203	2	now	now	ADV
ejpam-4580	203	3	,	,	PUNCT
ejpam-4580	203	4	since	since	SCONJ
ejpam-4580	203	5	t	t	PROPN
ejpam-4580	203	6	is	be	AUX
ejpam-4580	203	7	an	an	DET
ejpam-4580	203	8	operator	operator	NOUN
ejpam-4580	203	9	of	of	ADP
ejpam-4580	203	10	k−	k−	PROPN
ejpam-4580	203	11	quasi	quasi	PROPN
ejpam-4580	203	12	class	class	PROPN
ejpam-4580	203	13	q(n	q(n	PROPN
ejpam-4580	203	14	)	)	PUNCT
ejpam-4580	203	15	,	,	PUNCT
ejpam-4580	203	16	we	we	PRON
ejpam-4580	203	17	have	have	VERB
ejpam-4580	203	18	t	t	PROPN
ejpam-4580	203	19	∗k(t	∗k(t	PROPN
ejpam-4580	203	20	∗2	∗2	PROPN
ejpam-4580	203	21	t	t	PROPN
ejpam-4580	203	22	2	2	NUM
ejpam-4580	203	23	−nt	−nt	ADP
ejpam-4580	203	24	∗t	∗t	PROPN
ejpam-4580	203	25	+	+	CCONJ
ejpam-4580	203	26	i)t	i)t	VERB
ejpam-4580	204	1	k	k	X
ejpam-4580	204	2	≥	≥	NOUN
ejpam-4580	204	3	0	0	NUM
ejpam-4580	204	4	.	.	PUNCT
ejpam-4580	205	1	from	from	ADP
ejpam-4580	205	2	t	t	PROPN
ejpam-4580	205	3	∗k(t	∗k(t	PROPN
ejpam-4580	205	4	∗2	∗2	PROPN
ejpam-4580	205	5	t	t	PROPN
ejpam-4580	205	6	2	2	NUM
ejpam-4580	205	7	−nt	−nt	ADP
ejpam-4580	205	8	∗t	∗t	PROPN
ejpam-4580	205	9	+	+	CCONJ
ejpam-4580	205	10	i)t	i)t	NOUN
ejpam-4580	205	11	k(en	k(en	NOUN
ejpam-4580	205	12	)	)	PUNCT
ejpam-4580	205	13	=	=	SYM
ejpam-4580	205	14	|an||an+1|	|an||an+1|	PROPN
ejpam-4580	205	15	.	.	PUNCT
ejpam-4580	205	16	.	.	PUNCT
ejpam-4580	205	17	.	.	PUNCT
ejpam-4580	206	1	|an+k−1|t	|an+k−1|t	PROPN
ejpam-4580	206	2	∗k(t	∗k(t	PROPN
ejpam-4580	206	3	∗2	∗2	PROPN
ejpam-4580	206	4	t	t	PROPN
ejpam-4580	206	5	2	2	NUM
ejpam-4580	206	6	−nt	−nt	ADP
ejpam-4580	206	7	∗t	∗t	PROPN
ejpam-4580	206	8	+	+	CCONJ
ejpam-4580	206	9	i)(en+k	i)(en+k	NOUN
ejpam-4580	206	10	)	)	PUNCT
ejpam-4580	207	1	=	=	SYM
ejpam-4580	207	2	|an||an+1|	|an||an+1|	PROPN
ejpam-4580	207	3	.	.	PUNCT
ejpam-4580	207	4	.	.	PUNCT
ejpam-4580	207	5	.	.	PUNCT
ejpam-4580	208	1	|an+k−1|(|an+k|2|an+k+1|2	|an+k−1|(|an+k|2|an+k+1|2	PROPN
ejpam-4580	209	1	−n	−n	PROPN
ejpam-4580	209	2	|an+k|2	|an+k|2	ADJ
ejpam-4580	209	3	+	+	CCONJ
ejpam-4580	209	4	1)t	1)t	PROPN
ejpam-4580	209	5	∗k(en+k	∗k(en+k	NUM
ejpam-4580	209	6	)	)	PUNCT
ejpam-4580	209	7	=	=	PROPN
ejpam-4580	209	8	|an|2|an+1|2	|an|2|an+1|2	PROPN
ejpam-4580	209	9	.	.	PUNCT
ejpam-4580	209	10	.	.	PUNCT
ejpam-4580	209	11	.	.	PUNCT
ejpam-4580	210	1	|an+k−1|2(|an+k|2|an+k+1|2	|an+k−1|2(|an+k|2|an+k+1|2	PROPN
ejpam-4580	210	2	−n	−n	ADV
ejpam-4580	210	3	|an+k|2	|an+k|2	ADJ
ejpam-4580	210	4	+	+	NUM
ejpam-4580	210	5	1)(en	1)(en	NUM
ejpam-4580	210	6	)	)	PUNCT
ejpam-4580	210	7	≥	≥	NOUN
ejpam-4580	211	1	o.	o.	INTJ
ejpam-4580	211	2	we	we	PRON
ejpam-4580	211	3	have	have	VERB
ejpam-4580	211	4	inequality	inequality	NOUN
ejpam-4580	212	1	|an+k|2|an+k+1|2	|an+k|2|an+k+1|2	PROPN
ejpam-4580	212	2	−n	−n	NOUN
ejpam-4580	212	3	|an+k|2	|an+k|2	PART
ejpam-4580	212	4	+	+	NUM
ejpam-4580	212	5	1	1	NUM
ejpam-4580	212	6	≥	≥	NOUN
ejpam-4580	212	7	0	0	NUM
ejpam-4580	212	8	.	.	PUNCT
ejpam-4580	212	9	example	example	NOUN
ejpam-4580	212	10	1	1	X
ejpam-4580	212	11	.	.	X
ejpam-4580	213	1	consider	consider	VERB
ejpam-4580	213	2	the	the	DET
ejpam-4580	213	3	operator	operator	NOUN
ejpam-4580	213	4	t	t	NOUN
ejpam-4580	213	5	:	:	PUNCT
ejpam-4580	213	6	l2	l2	NOUN
ejpam-4580	213	7	→	→	SYM
ejpam-4580	213	8	l2	l2	NOUN
ejpam-4580	213	9	defined	define	VERB
ejpam-4580	213	10	by	by	ADP
ejpam-4580	213	11	t	t	PROPN
ejpam-4580	213	12	(	(	PUNCT
ejpam-4580	213	13	x	x	NOUN
ejpam-4580	213	14	)	)	PUNCT
ejpam-4580	213	15	=	=	SYM
ejpam-4580	213	16	(	(	PUNCT
ejpam-4580	213	17	0	0	NUM
ejpam-4580	213	18	,	,	PUNCT
ejpam-4580	213	19	α1x1	α1x1	NOUN
ejpam-4580	213	20	,	,	PUNCT
ejpam-4580	213	21	α2x2	α2x2	PROPN
ejpam-4580	213	22	,	,	PUNCT
ejpam-4580	213	23	.	.	PUNCT
ejpam-4580	213	24	.	.	PUNCT
ejpam-4580	214	1	.	.	PUNCT
ejpam-4580	214	2	)	)	PUNCT
ejpam-4580	215	1	where	where	SCONJ
ejpam-4580	215	2	αn	αn	NOUN
ejpam-4580	215	3	=	=	SYM
ejpam-4580	215	4	n	n	PRON
ejpam-4580	215	5	2n	2n	NUM
ejpam-4580	215	6	for	for	ADP
ejpam-4580	215	7	a	a	DET
ejpam-4580	215	8	natural	natural	ADJ
ejpam-4580	215	9	number	number	NOUN
ejpam-4580	215	10	n	n	PART
ejpam-4580	215	11	≥	≥	NOUN
ejpam-4580	215	12	1	1	NUM
ejpam-4580	215	13	.	.	PUNCT
ejpam-4580	216	1	sh	sh	PROPN
ejpam-4580	216	2	.	.	PROPN
ejpam-4580	216	3	lohaj	lohaj	PROPN
ejpam-4580	216	4	/	/	SYM
ejpam-4580	216	5	eur	eur	PROPN
ejpam-4580	216	6	.	.	PUNCT
ejpam-4580	217	1	j.	j.	PROPN
ejpam-4580	217	2	pure	pure	PROPN
ejpam-4580	217	3	appl	appl	PROPN
ejpam-4580	217	4	.	.	PROPN
ejpam-4580	217	5	math	math	PROPN
ejpam-4580	217	6	,	,	PUNCT
ejpam-4580	217	7	15	15	NUM
ejpam-4580	217	8	(	(	PUNCT
ejpam-4580	217	9	4	4	NUM
ejpam-4580	217	10	)	)	PUNCT
ejpam-4580	217	11	(	(	PUNCT
ejpam-4580	217	12	2022	2022	NUM
ejpam-4580	217	13	)	)	PUNCT
ejpam-4580	217	14	,	,	PUNCT
ejpam-4580	217	15	1836	1836	NUM
ejpam-4580	217	16	-	-	SYM
ejpam-4580	217	17	1853	1853	NUM
ejpam-4580	217	18	1846	1846	NUM
ejpam-4580	217	19	this	this	DET
ejpam-4580	217	20	operator	operator	NOUN
ejpam-4580	217	21	t	t	NOUN
ejpam-4580	217	22	is	be	AUX
ejpam-4580	217	23	of	of	ADP
ejpam-4580	217	24	k−quasi	k−quasi	NOUN
ejpam-4580	217	25	class	class	NOUN
ejpam-4580	217	26	q(n	q(n	PROPN
ejpam-4580	217	27	)	)	PUNCT
ejpam-4580	217	28	and	and	CCONJ
ejpam-4580	217	29	quasi	quasi	ADJ
ejpam-4580	217	30	nilpotent	nilpotent	NOUN
ejpam-4580	217	31	but	but	CCONJ
ejpam-4580	217	32	it	it	PRON
ejpam-4580	217	33	is	be	AUX
ejpam-4580	217	34	not	not	PART
ejpam-4580	217	35	quasihyponormal	quasihyponormal	ADJ
ejpam-4580	217	36	.	.	PUNCT
ejpam-4580	218	1	to	to	PART
ejpam-4580	218	2	prove	prove	VERB
ejpam-4580	218	3	that	that	PRON
ejpam-4580	218	4	operator	operator	NOUN
ejpam-4580	218	5	t	t	NOUN
ejpam-4580	218	6	is	be	AUX
ejpam-4580	218	7	of	of	ADP
ejpam-4580	218	8	k−quasi	k−quasi	NOUN
ejpam-4580	218	9	class	class	NOUN
ejpam-4580	218	10	q(n	q(n	PROPN
ejpam-4580	218	11	)	)	PUNCT
ejpam-4580	218	12	and	and	CCONJ
ejpam-4580	218	13	quasi	quasi	ADJ
ejpam-4580	218	14	nilpotent	nilpotent	NOUN
ejpam-4580	218	15	it	it	PRON
ejpam-4580	218	16	is	be	AUX
ejpam-4580	218	17	similarly	similarly	ADV
ejpam-4580	218	18	as	as	ADP
ejpam-4580	218	19	example	example	NOUN
ejpam-4580	218	20	2.5	2.5	NUM
ejpam-4580	218	21	in	in	ADP
ejpam-4580	218	22	[	[	X
ejpam-4580	218	23	6	6	NUM
ejpam-4580	218	24	]	]	PUNCT
ejpam-4580	218	25	.	.	PUNCT
ejpam-4580	219	1	this	this	DET
ejpam-4580	219	2	operator	operator	NOUN
ejpam-4580	219	3	is	be	AUX
ejpam-4580	219	4	not	not	PART
ejpam-4580	219	5	quasi	quasi	ADJ
ejpam-4580	219	6	-	-	ADJ
ejpam-4580	219	7	hyponormal	hyponormal	ADJ
ejpam-4580	219	8	from	from	ADP
ejpam-4580	219	9	the	the	DET
ejpam-4580	219	10	fact	fact	NOUN
ejpam-4580	219	11	that	that	SCONJ
ejpam-4580	219	12	:	:	PUNCT
ejpam-4580	219	13	αn	αn	NOUN
ejpam-4580	219	14	̸≤	̸≤	X
ejpam-4580	219	15	αn+1	αn+1	NUM
ejpam-4580	219	16	(	(	PUNCT
ejpam-4580	219	17	see	see	VERB
ejpam-4580	219	18	proposition	proposition	NOUN
ejpam-4580	219	19	3.4	3.4	NUM
ejpam-4580	219	20	in	in	ADP
ejpam-4580	219	21	[	[	X
ejpam-4580	219	22	8	8	NUM
ejpam-4580	219	23	]	]	NUM
ejpam-4580	219	24	)	)	PUNCT
ejpam-4580	219	25	.	.	PUNCT
ejpam-4580	220	1	similarly	similarly	ADV
ejpam-4580	220	2	,	,	PUNCT
ejpam-4580	220	3	the	the	DET
ejpam-4580	220	4	next	next	ADJ
ejpam-4580	220	5	proposition	proposition	NOUN
ejpam-4580	220	6	give	give	VERB
ejpam-4580	220	7	necessary	necessary	ADJ
ejpam-4580	220	8	and	and	CCONJ
ejpam-4580	220	9	sufficient	sufficient	ADJ
ejpam-4580	220	10	conditions	condition	NOUN
ejpam-4580	220	11	for	for	ADP
ejpam-4580	220	12	a	a	DET
ejpam-4580	220	13	weighted	weight	VERB
ejpam-4580	220	14	shift	shift	NOUN
ejpam-4580	220	15	operator	operator	NOUN
ejpam-4580	220	16	t	t	PROPN
ejpam-4580	220	17	with	with	ADP
ejpam-4580	220	18	decreasing	decrease	VERB
ejpam-4580	220	19	weighted	weight	VERB
ejpam-4580	220	20	sequence	sequence	NOUN
ejpam-4580	220	21	(	(	PUNCT
ejpam-4580	220	22	αn	αn	NOUN
ejpam-4580	220	23	)	)	PUNCT
ejpam-4580	220	24	to	to	PART
ejpam-4580	220	25	be	be	AUX
ejpam-4580	220	26	an	an	DET
ejpam-4580	220	27	operator	operator	NOUN
ejpam-4580	220	28	of	of	ADP
ejpam-4580	220	29	this	this	DET
ejpam-4580	220	30	class	class	NOUN
ejpam-4580	220	31	of	of	ADP
ejpam-4580	220	32	operators	operator	NOUN
ejpam-4580	220	33	.	.	PUNCT
ejpam-4580	221	1	proposition	proposition	NOUN
ejpam-4580	221	2	18	18	NUM
ejpam-4580	221	3	.	.	PUNCT
ejpam-4580	222	1	a	a	DET
ejpam-4580	222	2	weighted	weight	VERB
ejpam-4580	222	3	shift	shift	NOUN
ejpam-4580	222	4	operator	operator	NOUN
ejpam-4580	222	5	t	t	PROPN
ejpam-4580	222	6	with	with	ADP
ejpam-4580	222	7	decreasing	decrease	VERB
ejpam-4580	222	8	weighted	weight	VERB
ejpam-4580	222	9	sequence	sequence	NOUN
ejpam-4580	222	10	(	(	PUNCT
ejpam-4580	222	11	αn	αn	NOUN
ejpam-4580	222	12	)	)	PUNCT
ejpam-4580	222	13	is	be	AUX
ejpam-4580	222	14	an	an	DET
ejpam-4580	222	15	operator	operator	NOUN
ejpam-4580	222	16	of	of	ADP
ejpam-4580	222	17	k−	k−	PROPN
ejpam-4580	222	18	quasi	quasi	PROPN
ejpam-4580	222	19	class	class	PROPN
ejpam-4580	222	20	q∗(n	q∗(n	PROPN
ejpam-4580	222	21	)	)	PUNCT
ejpam-4580	223	1	if	if	SCONJ
ejpam-4580	224	1	and	and	CCONJ
ejpam-4580	224	2	only	only	ADV
ejpam-4580	224	3	if	if	SCONJ
ejpam-4580	224	4	|αn+k|2|αn+k+1|2	|αn+k|2|αn+k+1|2	PROPN
ejpam-4580	224	5	−n	−n	ADV
ejpam-4580	224	6	|αn+k−1|2	|αn+k−1|2	VERB
ejpam-4580	224	7	+	+	CCONJ
ejpam-4580	224	8	1	1	NUM
ejpam-4580	224	9	≥	≥	NOUN
ejpam-4580	224	10	0	0	NUM
ejpam-4580	224	11	for	for	ADP
ejpam-4580	224	12	every	every	DET
ejpam-4580	224	13	n.	n.	NOUN
ejpam-4580	224	14	in	in	ADP
ejpam-4580	224	15	following	follow	VERB
ejpam-4580	224	16	propositions	proposition	NOUN
ejpam-4580	224	17	we	we	PRON
ejpam-4580	224	18	give	give	VERB
ejpam-4580	224	19	the	the	DET
ejpam-4580	224	20	inclusion	inclusion	NOUN
ejpam-4580	224	21	of	of	ADP
ejpam-4580	224	22	approximate	approximate	ADJ
ejpam-4580	224	23	point	point	NOUN
ejpam-4580	224	24	spectrum	spectrum	NOUN
ejpam-4580	224	25	of	of	ADP
ejpam-4580	224	26	these	these	DET
ejpam-4580	224	27	classes	class	NOUN
ejpam-4580	224	28	of	of	ADP
ejpam-4580	224	29	operators	operator	NOUN
ejpam-4580	224	30	.	.	PUNCT
ejpam-4580	225	1	proposition	proposition	NOUN
ejpam-4580	225	2	19	19	NUM
ejpam-4580	225	3	.	.	PUNCT
ejpam-4580	226	1	let	let	VERB
ejpam-4580	226	2	t	t	PROPN
ejpam-4580	226	3	∈	∈	PROPN
ejpam-4580	226	4	l(h	l(h	PROPN
ejpam-4580	226	5	)	)	PUNCT
ejpam-4580	226	6	be	be	AUX
ejpam-4580	226	7	a	a	DET
ejpam-4580	226	8	regular	regular	ADJ
ejpam-4580	226	9	k−quasi	k−quasi	NOUN
ejpam-4580	226	10	class	class	NOUN
ejpam-4580	226	11	q(n	q(n	PROPN
ejpam-4580	226	12	)	)	PUNCT
ejpam-4580	226	13	operator	operator	NOUN
ejpam-4580	226	14	.	.	PUNCT
ejpam-4580	227	1	then	then	ADV
ejpam-4580	227	2	the	the	DET
ejpam-4580	227	3	approximate	approximate	ADJ
ejpam-4580	227	4	point	point	NOUN
ejpam-4580	227	5	spectrum	spectrum	NOUN
ejpam-4580	227	6	of	of	ADP
ejpam-4580	227	7	operator	operator	NOUN
ejpam-4580	227	8	t	t	PROPN
ejpam-4580	227	9	lies	lie	VERB
ejpam-4580	227	10	in	in	ADP
ejpam-4580	227	11	the	the	DET
ejpam-4580	227	12	disc	disc	NOUN
ejpam-4580	227	13	σa(t	σa(t	PUNCT
ejpam-4580	227	14	)	)	PUNCT
ejpam-4580	227	15	⊆	⊆	NUM
ejpam-4580	227	16	{	{	PUNCT
ejpam-4580	227	17	λ	λ	X
ejpam-4580	227	18	∈	∈	NOUN
ejpam-4580	227	19	c	c	NOUN
ejpam-4580	227	20	:	:	PUNCT
ejpam-4580	228	1	√	√	PROPN
ejpam-4580	228	2	n	n	CCONJ
ejpam-4580	228	3	∥t−k−1∥	∥t−k−1∥	AUX
ejpam-4580	228	4	·	·	PUNCT
ejpam-4580	228	5	√	√	NUM
ejpam-4580	229	1	∥t	∥t	INTJ
ejpam-4580	229	2	k+1∥2	k+1∥2	PROPN
ejpam-4580	230	1	+	+	CCONJ
ejpam-4580	230	2	∥t	∥t	ADJ
ejpam-4580	230	3	k−1∥2	k−1∥2	ADJ
ejpam-4580	230	4	≤	≤	PUNCT
ejpam-4580	230	5	|λ|	|λ|	NOUN
ejpam-4580	230	6	≤	≤	NOUN
ejpam-4580	230	7	∥t∥	∥t∥	ADV
ejpam-4580	230	8	}	}	PUNCT
ejpam-4580	230	9	.	.	PUNCT
ejpam-4580	231	1	proof	proof	NOUN
ejpam-4580	231	2	.	.	PUNCT
ejpam-4580	232	1	let	let	VERB
ejpam-4580	232	2	t	t	NOUN
ejpam-4580	232	3	be	be	AUX
ejpam-4580	232	4	a	a	DET
ejpam-4580	232	5	regular	regular	ADJ
ejpam-4580	232	6	k−quasi	k−quasi	NOUN
ejpam-4580	232	7	class	class	NOUN
ejpam-4580	232	8	q(n	q(n	PROPN
ejpam-4580	232	9	)	)	PUNCT
ejpam-4580	232	10	operator	operator	NOUN
ejpam-4580	232	11	.	.	PUNCT
ejpam-4580	233	1	for	for	ADP
ejpam-4580	233	2	every	every	DET
ejpam-4580	233	3	unit	unit	NOUN
ejpam-4580	233	4	vector	vector	NOUN
ejpam-4580	233	5	x	x	PUNCT
ejpam-4580	233	6	in	in	ADP
ejpam-4580	233	7	hilbert	hilbert	NOUN
ejpam-4580	233	8	space	space	NOUN
ejpam-4580	233	9	h	h	NOUN
ejpam-4580	233	10	,	,	PUNCT
ejpam-4580	233	11	we	we	PRON
ejpam-4580	233	12	have	have	VERB
ejpam-4580	233	13	:	:	PUNCT
ejpam-4580	233	14	∥x∥2	∥x∥2	NOUN
ejpam-4580	233	15	=	=	SYM
ejpam-4580	233	16	∥(t	∥(t	X
ejpam-4580	234	1	k+1)−1	k+1)−1	X
ejpam-4580	234	2	·	·	PUNCT
ejpam-4580	234	3	(	(	PUNCT
ejpam-4580	234	4	t	t	NOUN
ejpam-4580	234	5	k+1)x∥2	k+1)x∥2	PROPN
ejpam-4580	234	6	≤∥(t	≤∥(t	PROPN
ejpam-4580	234	7	k+1)−1∥2	k+1)−1∥2	NOUN
ejpam-4580	234	8	·	·	PUNCT
ejpam-4580	234	9	∥t	∥t	ADJ
ejpam-4580	234	10	k+1x∥2	k+1x∥2	NOUN
ejpam-4580	234	11	≤∥(t	≤∥(t	PROPN
ejpam-4580	234	12	k+1)−1∥2	k+1)−1∥2	X
ejpam-4580	234	13	·	·	SYM
ejpam-4580	234	14	1	1	NUM
ejpam-4580	234	15	n	n	NOUN
ejpam-4580	234	16	·	·	PUNCT
ejpam-4580	234	17	(	(	PUNCT
ejpam-4580	234	18	∥t	∥t	ADJ
ejpam-4580	234	19	k+2x∥2	k+2x∥2	NOUN
ejpam-4580	234	20	+	+	CCONJ
ejpam-4580	234	21	∥t	∥t	ADJ
ejpam-4580	234	22	kx∥2	kx∥2	NOUN
ejpam-4580	234	23	)	)	PUNCT
ejpam-4580	234	24	≤	≤	NOUN
ejpam-4580	234	25	1	1	NUM
ejpam-4580	234	26	n	n	PRON
ejpam-4580	234	27	·	·	PUNCT
ejpam-4580	234	28	∥(t	∥(t	X
ejpam-4580	234	29	k+1)−1∥2	k+1)−1∥2	X
ejpam-4580	234	30	·	·	PUNCT
ejpam-4580	234	31	(	(	PUNCT
ejpam-4580	234	32	∥t	∥t	INTJ
ejpam-4580	234	33	k+1∥2	k+1∥2	PROPN
ejpam-4580	234	34	·	·	PUNCT
ejpam-4580	234	35	∥tx∥2	∥tx∥2	PUNCT
ejpam-4580	235	1	+	+	CCONJ
ejpam-4580	235	2	∥t	∥t	ADJ
ejpam-4580	235	3	k−1∥2	k−1∥2	ADJ
ejpam-4580	235	4	·	·	PUNCT
ejpam-4580	235	5	∥tx∥2	∥tx∥2	NUM
ejpam-4580	235	6	)	)	PUNCT
ejpam-4580	235	7	.	.	PUNCT
ejpam-4580	236	1	so	so	ADV
ejpam-4580	236	2	,	,	PUNCT
ejpam-4580	236	3	n	n	CCONJ
ejpam-4580	236	4	≤	≤	NOUN
ejpam-4580	236	5	∥tx∥2	∥tx∥2	PUNCT
ejpam-4580	236	6	·	·	PUNCT
ejpam-4580	236	7	∥(t	∥(t	X
ejpam-4580	236	8	k+1)−1∥2	k+1)−1∥2	X
ejpam-4580	236	9	·	·	PUNCT
ejpam-4580	236	10	(	(	PUNCT
ejpam-4580	236	11	∥t	∥t	INTJ
ejpam-4580	236	12	k+1∥2	k+1∥2	PROPN
ejpam-4580	237	1	+	+	CCONJ
ejpam-4580	237	2	∥t	∥t	ADJ
ejpam-4580	237	3	k−1∥2	k−1∥2	NOUN
ejpam-4580	237	4	)	)	PUNCT
ejpam-4580	237	5	,	,	PUNCT
ejpam-4580	237	6	sh	sh	PROPN
ejpam-4580	237	7	.	.	PROPN
ejpam-4580	237	8	lohaj	lohaj	PROPN
ejpam-4580	237	9	/	/	SYM
ejpam-4580	237	10	eur	eur	PROPN
ejpam-4580	237	11	.	.	PUNCT
ejpam-4580	238	1	j.	j.	PROPN
ejpam-4580	238	2	pure	pure	PROPN
ejpam-4580	238	3	appl	appl	PROPN
ejpam-4580	238	4	.	.	PROPN
ejpam-4580	238	5	math	math	PROPN
ejpam-4580	238	6	,	,	PUNCT
ejpam-4580	238	7	15	15	NUM
ejpam-4580	238	8	(	(	PUNCT
ejpam-4580	238	9	4	4	NUM
ejpam-4580	238	10	)	)	PUNCT
ejpam-4580	238	11	(	(	PUNCT
ejpam-4580	238	12	2022	2022	NUM
ejpam-4580	238	13	)	)	PUNCT
ejpam-4580	238	14	,	,	PUNCT
ejpam-4580	238	15	1836	1836	NUM
ejpam-4580	238	16	-	-	SYM
ejpam-4580	238	17	1853	1853	NUM
ejpam-4580	238	18	1847	1847	NUM
ejpam-4580	238	19	where	where	SCONJ
ejpam-4580	238	20	we	we	PRON
ejpam-4580	238	21	have	have	VERB
ejpam-4580	238	22	∥tx∥	∥tx∥	ADJ
ejpam-4580	238	23	≥	≥	NOUN
ejpam-4580	238	24	√	√	PROPN
ejpam-4580	238	25	n	n	CCONJ
ejpam-4580	238	26	∥t−k−1∥	∥t−k−1∥	PROPN
ejpam-4580	238	27	·	·	PUNCT
ejpam-4580	238	28	√	√	NUM
ejpam-4580	239	1	∥t	∥t	INTJ
ejpam-4580	239	2	k+1∥2	k+1∥2	PROPN
ejpam-4580	240	1	+	+	CCONJ
ejpam-4580	240	2	∥t	∥t	ADJ
ejpam-4580	240	3	k−1∥2	k−1∥2	ADJ
ejpam-4580	240	4	.	.	PUNCT
ejpam-4580	241	1	now	now	ADV
ejpam-4580	241	2	,	,	PUNCT
ejpam-4580	241	3	assume	assume	VERB
ejpam-4580	241	4	that	that	SCONJ
ejpam-4580	241	5	λ	λ	PROPN
ejpam-4580	241	6	∈	∈	PROPN
ejpam-4580	241	7	σa(t	σa(t	PUNCT
ejpam-4580	241	8	)	)	PUNCT
ejpam-4580	241	9	,	,	PUNCT
ejpam-4580	241	10	then	then	ADV
ejpam-4580	241	11	there	there	PRON
ejpam-4580	241	12	exists	exist	VERB
ejpam-4580	241	13	a	a	DET
ejpam-4580	241	14	sequence	sequence	NOUN
ejpam-4580	241	15	(	(	PUNCT
ejpam-4580	241	16	xn	xn	PROPN
ejpam-4580	241	17	)	)	PUNCT
ejpam-4580	241	18	,	,	PUNCT
ejpam-4580	241	19	such	such	ADJ
ejpam-4580	241	20	as	as	ADP
ejpam-4580	241	21	∥xn∥	∥xn∥	PROPN
ejpam-4580	241	22	=	=	SYM
ejpam-4580	241	23	1	1	NUM
ejpam-4580	241	24	and	and	CCONJ
ejpam-4580	241	25	∥(t	∥(t	VERB
ejpam-4580	241	26	−	−	PUNCT
ejpam-4580	241	27	λi)xn∥	λi)xn∥	X
ejpam-4580	241	28	→	→	SYM
ejpam-4580	241	29	0	0	NUM
ejpam-4580	241	30	,	,	PUNCT
ejpam-4580	241	31	n	n	PROPN
ejpam-4580	241	32	→	→	SYM
ejpam-4580	241	33	∞.	∞.	PROPN
ejpam-4580	241	34	from	from	ADP
ejpam-4580	241	35	the	the	DET
ejpam-4580	241	36	last	last	ADJ
ejpam-4580	241	37	inequation	inequation	NOUN
ejpam-4580	241	38	we	we	PRON
ejpam-4580	241	39	have	have	AUX
ejpam-4580	241	40	:	:	PUNCT
ejpam-4580	241	41	∥txn	∥txn	VERB
ejpam-4580	241	42	−	−	PROPN
ejpam-4580	241	43	λxn∥	λxn∥	SYM
ejpam-4580	241	44	≥	≥	PROPN
ejpam-4580	241	45	∥txn∥	∥txn∥	PUNCT
ejpam-4580	242	1	−	−	PROPN
ejpam-4580	242	2	|λ|	|λ|	PROPN
ejpam-4580	242	3	·	·	PUNCT
ejpam-4580	242	4	∥xn∥	∥xn∥	PROPN
ejpam-4580	242	5	≥	≥	NOUN
ejpam-4580	242	6	√	√	NUM
ejpam-4580	242	7	n	n	CCONJ
ejpam-4580	242	8	∥t−k−1∥	∥t−k−1∥	PROPN
ejpam-4580	242	9	·	·	PUNCT
ejpam-4580	242	10	√	√	NUM
ejpam-4580	243	1	∥t	∥t	INTJ
ejpam-4580	243	2	k+1∥2	k+1∥2	PROPN
ejpam-4580	244	1	+	+	CCONJ
ejpam-4580	244	2	∥t	∥t	ADJ
ejpam-4580	244	3	k−1∥2	k−1∥2	ADJ
ejpam-4580	244	4	−	−	NOUN
ejpam-4580	244	5	|λ|	|λ|	NOUN
ejpam-4580	244	6	.	.	PUNCT
ejpam-4580	245	1	now	now	ADV
ejpam-4580	245	2	,	,	PUNCT
ejpam-4580	245	3	when	when	SCONJ
ejpam-4580	245	4	n	n	X
ejpam-4580	245	5	→	→	SYM
ejpam-4580	245	6	∞	∞	PROPN
ejpam-4580	245	7	we	we	PRON
ejpam-4580	245	8	have	have	VERB
ejpam-4580	245	9	|λ|	|λ|	ADP
ejpam-4580	245	10	≥	≥	NOUN
ejpam-4580	245	11	√	√	PROPN
ejpam-4580	245	12	n	n	CCONJ
ejpam-4580	245	13	∥t−k−1∥	∥t−k−1∥	PROPN
ejpam-4580	245	14	·	·	PUNCT
ejpam-4580	245	15	√	√	NUM
ejpam-4580	246	1	∥t	∥t	INTJ
ejpam-4580	246	2	k+1∥2	k+1∥2	PROPN
ejpam-4580	247	1	+	+	CCONJ
ejpam-4580	247	2	∥t	∥t	ADJ
ejpam-4580	247	3	k−1∥2	k−1∥2	ADJ
ejpam-4580	247	4	.	.	PUNCT
ejpam-4580	248	1	so	so	ADV
ejpam-4580	248	2	,	,	PUNCT
ejpam-4580	248	3	we	we	PRON
ejpam-4580	248	4	have	have	VERB
ejpam-4580	248	5	σa(t	σa(t	PUNCT
ejpam-4580	248	6	)	)	PUNCT
ejpam-4580	249	1	⊆	⊆	X
ejpam-4580	249	2	{	{	PUNCT
ejpam-4580	249	3	λ	λ	X
ejpam-4580	249	4	∈	∈	NOUN
ejpam-4580	249	5	c	c	NOUN
ejpam-4580	249	6	:	:	PUNCT
ejpam-4580	249	7	√	√	PROPN
ejpam-4580	249	8	n	n	CCONJ
ejpam-4580	249	9	∥t−k−1∥	∥t−k−1∥	AUX
ejpam-4580	249	10	·	·	PUNCT
ejpam-4580	249	11	√	√	NUM
ejpam-4580	250	1	∥t	∥t	INTJ
ejpam-4580	250	2	k+1∥2	k+1∥2	PROPN
ejpam-4580	251	1	+	+	CCONJ
ejpam-4580	251	2	∥t	∥t	ADJ
ejpam-4580	251	3	k−1∥2	k−1∥2	ADJ
ejpam-4580	251	4	≤	≤	PUNCT
ejpam-4580	251	5	|λ|	|λ|	NOUN
ejpam-4580	251	6	≤	≤	NOUN
ejpam-4580	251	7	∥t∥	∥t∥	ADV
ejpam-4580	251	8	}	}	PUNCT
ejpam-4580	251	9	.	.	PUNCT
ejpam-4580	252	1	therefore	therefore	ADV
ejpam-4580	252	2	the	the	DET
ejpam-4580	252	3	proof	proof	NOUN
ejpam-4580	252	4	is	be	AUX
ejpam-4580	252	5	completed	complete	VERB
ejpam-4580	252	6	.	.	PUNCT
ejpam-4580	253	1	proposition	proposition	NOUN
ejpam-4580	253	2	20	20	NUM
ejpam-4580	253	3	.	.	PUNCT
ejpam-4580	254	1	let	let	VERB
ejpam-4580	254	2	t	t	PROPN
ejpam-4580	254	3	∈	∈	PROPN
ejpam-4580	254	4	l(h	l(h	PROPN
ejpam-4580	254	5	)	)	PUNCT
ejpam-4580	254	6	be	be	AUX
ejpam-4580	254	7	a	a	DET
ejpam-4580	254	8	regular	regular	ADJ
ejpam-4580	254	9	k−quasi	k−quasi	NOUN
ejpam-4580	254	10	class	class	NOUN
ejpam-4580	254	11	q∗(n	q∗(n	NOUN
ejpam-4580	254	12	)	)	PUNCT
ejpam-4580	254	13	operator	operator	NOUN
ejpam-4580	254	14	.	.	PUNCT
ejpam-4580	255	1	then	then	ADV
ejpam-4580	255	2	the	the	DET
ejpam-4580	255	3	approximate	approximate	ADJ
ejpam-4580	255	4	point	point	NOUN
ejpam-4580	255	5	spectrum	spectrum	NOUN
ejpam-4580	255	6	of	of	ADP
ejpam-4580	255	7	operator	operator	NOUN
ejpam-4580	255	8	t	t	PROPN
ejpam-4580	255	9	lies	lie	VERB
ejpam-4580	255	10	in	in	ADP
ejpam-4580	255	11	the	the	DET
ejpam-4580	255	12	disc	disc	NOUN
ejpam-4580	255	13	σa(t	σa(t	PUNCT
ejpam-4580	255	14	)	)	PUNCT
ejpam-4580	255	15	⊆	⊆	NUM
ejpam-4580	255	16	{	{	PUNCT
ejpam-4580	255	17	λ	λ	X
ejpam-4580	255	18	∈	∈	NOUN
ejpam-4580	255	19	c	c	NOUN
ejpam-4580	255	20	:	:	PUNCT
ejpam-4580	255	21	√	√	NOUN
ejpam-4580	255	22	n	n	PRON
ejpam-4580	255	23	∥(t	∥(t	VERB
ejpam-4580	255	24	∗t	∗t	ADJ
ejpam-4580	255	25	k)−1∥	k)−1∥	NOUN
ejpam-4580	255	26	·	·	PUNCT
ejpam-4580	255	27	√	√	PUNCT
ejpam-4580	256	1	∥t	∥t	INTJ
ejpam-4580	256	2	k+1∥2	k+1∥2	PROPN
ejpam-4580	257	1	+	+	CCONJ
ejpam-4580	257	2	∥t	∥t	ADJ
ejpam-4580	257	3	k−1∥2	k−1∥2	ADJ
ejpam-4580	257	4	≤	≤	NUM
ejpam-4580	257	5	λ	λ	NOUN
ejpam-4580	257	6	≤	≤	NOUN
ejpam-4580	257	7	∥t∥	∥t∥	ADV
ejpam-4580	257	8	}	}	PUNCT
ejpam-4580	257	9	.	.	PUNCT
ejpam-4580	258	1	let	let	AUX
ejpam-4580	258	2	t	t	NOUN
ejpam-4580	258	3	=	=	SYM
ejpam-4580	258	4	u	u	NOUN
ejpam-4580	258	5	|t	|t	VERB
ejpam-4580	258	6	|	|	ADV
ejpam-4580	258	7	be	be	AUX
ejpam-4580	258	8	the	the	DET
ejpam-4580	258	9	polar	polar	ADJ
ejpam-4580	258	10	decomposition	decomposition	NOUN
ejpam-4580	258	11	of	of	ADP
ejpam-4580	258	12	operator	operator	NOUN
ejpam-4580	258	13	t.	t.	PROPN
ejpam-4580	258	14	the	the	DET
ejpam-4580	258	15	aluthge	aluthge	ADJ
ejpam-4580	258	16	transformation	transformation	NOUN
ejpam-4580	258	17	of	of	ADP
ejpam-4580	258	18	operator	operator	NOUN
ejpam-4580	258	19	t	t	NOUN
ejpam-4580	258	20	given	give	VERB
ejpam-4580	258	21	by	by	ADP
ejpam-4580	258	22	t̃	t̃	PROPN
ejpam-4580	258	23	=	=	PUNCT
ejpam-4580	258	24	|t	|t	NOUN
ejpam-4580	259	1	|	|	ADV
ejpam-4580	259	2	1	1	NUM
ejpam-4580	259	3	2u	2u	NOUN
ejpam-4580	259	4	|t	|t	VERB
ejpam-4580	259	5	|	|	ADV
ejpam-4580	259	6	1	1	NUM
ejpam-4580	259	7	2	2	NUM
ejpam-4580	259	8	was	be	AUX
ejpam-4580	259	9	introduced	introduce	VERB
ejpam-4580	259	10	by	by	ADP
ejpam-4580	259	11	aluthge	aluthge	PROPN
ejpam-4580	259	12	(	(	PUNCT
ejpam-4580	259	13	see	see	VERB
ejpam-4580	259	14	[	[	X
ejpam-4580	259	15	1	1	NUM
ejpam-4580	259	16	]	]	NUM
ejpam-4580	259	17	)	)	PUNCT
ejpam-4580	259	18	.	.	PUNCT
ejpam-4580	260	1	the	the	DET
ejpam-4580	260	2	adjoint	adjoint	PROPN
ejpam-4580	260	3	of	of	ADP
ejpam-4580	260	4	aluthge	aluthge	ADJ
ejpam-4580	260	5	transformation	transformation	NOUN
ejpam-4580	260	6	,	,	PUNCT
ejpam-4580	260	7	the	the	DET
ejpam-4580	260	8	∗−aluthge	∗−aluthge	PROPN
ejpam-4580	260	9	transformation	transformation	NOUN
ejpam-4580	260	10	is	be	AUX
ejpam-4580	260	11	defined	define	VERB
ejpam-4580	260	12	by	by	ADP
ejpam-4580	260	13	yamazaki	yamazaki	PROPN
ejpam-4580	260	14	(	(	PUNCT
ejpam-4580	260	15	see	see	VERB
ejpam-4580	260	16	[	[	X
ejpam-4580	260	17	11	11	NUM
ejpam-4580	260	18	]	]	PUNCT
ejpam-4580	260	19	)	)	PUNCT
ejpam-4580	260	20	as	as	ADP
ejpam-4580	260	21	t̃	t̃	PROPN
ejpam-4580	260	22	(	(	PUNCT
ejpam-4580	260	23	∗	∗	NOUN
ejpam-4580	260	24	)	)	PUNCT
ejpam-4580	260	25	def	def	NOUN
ejpam-4580	260	26	=	=	SYM
ejpam-4580	260	27	(	(	PUNCT
ejpam-4580	260	28	t̃	t̃	PROPN
ejpam-4580	260	29	∗)∗	∗)∗	NOUN
ejpam-4580	260	30	=	=	PUNCT
ejpam-4580	260	31	|t	|t	NOUN
ejpam-4580	261	1	∗|	∗|	NOUN
ejpam-4580	261	2	1	1	NUM
ejpam-4580	261	3	2u	2u	NOUN
ejpam-4580	261	4	|t	|t	VERB
ejpam-4580	262	1	∗|	∗|	NOUN
ejpam-4580	262	2	1	1	NUM
ejpam-4580	262	3	2	2	NUM
ejpam-4580	262	4	.	.	PUNCT
ejpam-4580	263	1	the	the	DET
ejpam-4580	263	2	following	follow	VERB
ejpam-4580	263	3	propositions	proposition	NOUN
ejpam-4580	263	4	give	give	VERB
ejpam-4580	263	5	the	the	DET
ejpam-4580	263	6	equivalence	equivalence	NOUN
ejpam-4580	263	7	between	between	ADP
ejpam-4580	263	8	aluthge	aluthge	ADJ
ejpam-4580	263	9	transformation	transformation	NOUN
ejpam-4580	263	10	and	and	CCONJ
ejpam-4580	263	11	∗−aluthge	∗−aluthge	DET
ejpam-4580	263	12	transformation	transformation	NOUN
ejpam-4580	263	13	of	of	ADP
ejpam-4580	263	14	these	these	DET
ejpam-4580	263	15	new	new	ADJ
ejpam-4580	263	16	classes	class	NOUN
ejpam-4580	263	17	of	of	ADP
ejpam-4580	263	18	operators	operator	NOUN
ejpam-4580	263	19	.	.	PUNCT
ejpam-4580	264	1	proposition	proposition	NOUN
ejpam-4580	264	2	21	21	NUM
ejpam-4580	264	3	.	.	PUNCT
ejpam-4580	265	1	let	let	VERB
ejpam-4580	265	2	t	t	PROPN
ejpam-4580	265	3	∈	∈	PROPN
ejpam-4580	265	4	l(h	l(h	PROPN
ejpam-4580	265	5	)	)	PUNCT
ejpam-4580	265	6	.	.	PUNCT
ejpam-4580	266	1	then	then	ADV
ejpam-4580	266	2	,	,	PUNCT
ejpam-4580	266	3	t̃	t̃	PROPN
ejpam-4580	266	4	is	be	AUX
ejpam-4580	266	5	an	an	DET
ejpam-4580	266	6	operator	operator	NOUN
ejpam-4580	266	7	of	of	ADP
ejpam-4580	266	8	quasi	quasi	ADJ
ejpam-4580	266	9	class	class	PROPN
ejpam-4580	266	10	q(n	q(n	PROPN
ejpam-4580	266	11	)	)	PUNCT
ejpam-4580	267	1	if	if	SCONJ
ejpam-4580	267	2	and	and	CCONJ
ejpam-4580	267	3	only	only	ADV
ejpam-4580	267	4	if	if	SCONJ
ejpam-4580	267	5	t̃	t̃	PROPN
ejpam-4580	267	6	(	(	PUNCT
ejpam-4580	267	7	∗	∗	NOUN
ejpam-4580	267	8	)	)	PUNCT
ejpam-4580	267	9	is	be	AUX
ejpam-4580	267	10	an	an	DET
ejpam-4580	267	11	operator	operator	NOUN
ejpam-4580	267	12	of	of	ADP
ejpam-4580	267	13	quasi	quasi	ADJ
ejpam-4580	267	14	class	class	PROPN
ejpam-4580	267	15	q(n	q(n	PROPN
ejpam-4580	267	16	)	)	PUNCT
ejpam-4580	267	17	.	.	PUNCT
ejpam-4580	268	1	proof	proof	NOUN
ejpam-4580	268	2	.	.	PUNCT
ejpam-4580	269	1	similarly	similarly	ADV
ejpam-4580	269	2	as	as	SCONJ
ejpam-4580	269	3	theorem	theorem	VERB
ejpam-4580	269	4	2.14	2.14	NUM
ejpam-4580	269	5	in	in	ADP
ejpam-4580	269	6	[	[	X
ejpam-4580	269	7	7	7	NUM
ejpam-4580	269	8	]	]	PUNCT
ejpam-4580	269	9	.	.	PUNCT
ejpam-4580	270	1	proposition	proposition	NOUN
ejpam-4580	270	2	22	22	NUM
ejpam-4580	270	3	.	.	PUNCT
ejpam-4580	271	1	let	let	VERB
ejpam-4580	271	2	t	t	PROPN
ejpam-4580	271	3	∈	∈	PROPN
ejpam-4580	271	4	l(h	l(h	PROPN
ejpam-4580	271	5	)	)	PUNCT
ejpam-4580	271	6	.	.	PUNCT
ejpam-4580	272	1	then	then	ADV
ejpam-4580	272	2	,	,	PUNCT
ejpam-4580	272	3	t̃	t̃	PROPN
ejpam-4580	272	4	is	be	AUX
ejpam-4580	272	5	an	an	DET
ejpam-4580	272	6	operator	operator	NOUN
ejpam-4580	272	7	of	of	ADP
ejpam-4580	272	8	quasi	quasi	ADJ
ejpam-4580	272	9	class	class	NOUN
ejpam-4580	272	10	q∗(n	q∗(n	PROPN
ejpam-4580	272	11	)	)	PUNCT
ejpam-4580	272	12	if	if	SCONJ
ejpam-4580	272	13	and	and	CCONJ
ejpam-4580	272	14	only	only	ADV
ejpam-4580	272	15	if	if	SCONJ
ejpam-4580	272	16	t̃	t̃	PROPN
ejpam-4580	272	17	(	(	PUNCT
ejpam-4580	272	18	∗	∗	NOUN
ejpam-4580	272	19	)	)	PUNCT
ejpam-4580	272	20	is	be	AUX
ejpam-4580	272	21	an	an	DET
ejpam-4580	272	22	operator	operator	NOUN
ejpam-4580	272	23	of	of	ADP
ejpam-4580	272	24	quasi	quasi	ADJ
ejpam-4580	272	25	class	class	NOUN
ejpam-4580	272	26	q∗(n	q∗(n	PROPN
ejpam-4580	272	27	)	)	PUNCT
ejpam-4580	272	28	.	.	PUNCT
ejpam-4580	273	1	sh	sh	PROPN
ejpam-4580	273	2	.	.	PROPN
ejpam-4580	273	3	lohaj	lohaj	PROPN
ejpam-4580	273	4	/	/	SYM
ejpam-4580	273	5	eur	eur	PROPN
ejpam-4580	273	6	.	.	PUNCT
ejpam-4580	274	1	j.	j.	PROPN
ejpam-4580	274	2	pure	pure	PROPN
ejpam-4580	274	3	appl	appl	PROPN
ejpam-4580	274	4	.	.	PROPN
ejpam-4580	274	5	math	math	PROPN
ejpam-4580	274	6	,	,	PUNCT
ejpam-4580	274	7	15	15	NUM
ejpam-4580	274	8	(	(	PUNCT
ejpam-4580	274	9	4	4	NUM
ejpam-4580	274	10	)	)	PUNCT
ejpam-4580	274	11	(	(	PUNCT
ejpam-4580	274	12	2022	2022	NUM
ejpam-4580	274	13	)	)	PUNCT
ejpam-4580	274	14	,	,	PUNCT
ejpam-4580	274	15	1836	1836	NUM
ejpam-4580	274	16	-	-	SYM
ejpam-4580	274	17	1853	1853	NUM
ejpam-4580	274	18	1848	1848	NUM
ejpam-4580	274	19	3	3	NUM
ejpam-4580	274	20	.	.	PUNCT
ejpam-4580	275	1	a	a	DET
ejpam-4580	275	2	matrix	matrix	NOUN
ejpam-4580	275	3	representation	representation	NOUN
ejpam-4580	275	4	in	in	ADP
ejpam-4580	275	5	this	this	DET
ejpam-4580	275	6	section	section	NOUN
ejpam-4580	275	7	we	we	PRON
ejpam-4580	275	8	give	give	VERB
ejpam-4580	275	9	some	some	DET
ejpam-4580	275	10	results	result	NOUN
ejpam-4580	275	11	for	for	ADP
ejpam-4580	275	12	the	the	DET
ejpam-4580	275	13	matrix	matrix	NOUN
ejpam-4580	275	14	representation	representation	NOUN
ejpam-4580	275	15	of	of	ADP
ejpam-4580	275	16	these	these	DET
ejpam-4580	275	17	classes	class	NOUN
ejpam-4580	275	18	of	of	ADP
ejpam-4580	275	19	operators	operator	NOUN
ejpam-4580	275	20	.	.	PUNCT
ejpam-4580	276	1	proposition	proposition	NOUN
ejpam-4580	276	2	23	23	NUM
ejpam-4580	276	3	.	.	PUNCT
ejpam-4580	277	1	let	let	VERB
ejpam-4580	277	2	t	t	PROPN
ejpam-4580	277	3	∈	∈	PROPN
ejpam-4580	277	4	l(h	l(h	PROPN
ejpam-4580	277	5	)	)	PUNCT
ejpam-4580	277	6	be	be	VERB
ejpam-4580	277	7	the	the	DET
ejpam-4580	277	8	operator	operator	NOUN
ejpam-4580	277	9	defined	define	VERB
ejpam-4580	277	10	as	as	ADP
ejpam-4580	277	11	t	t	PROPN
ejpam-4580	277	12	=	=	PUNCT
ejpam-4580	277	13	(	(	PUNCT
ejpam-4580	277	14	a	a	DET
ejpam-4580	277	15	b	b	NOUN
ejpam-4580	277	16	0	0	NUM
ejpam-4580	277	17	0	0	NUM
ejpam-4580	277	18	)	)	PUNCT
ejpam-4580	277	19	,	,	PUNCT
ejpam-4580	277	20	b	b	X
ejpam-4580	277	21	is	be	AUX
ejpam-4580	277	22	any	any	DET
ejpam-4580	277	23	operator	operator	NOUN
ejpam-4580	277	24	.	.	PUNCT
ejpam-4580	278	1	if	if	SCONJ
ejpam-4580	278	2	a	a	PRON
ejpam-4580	278	3	is	be	AUX
ejpam-4580	278	4	operator	operator	NOUN
ejpam-4580	278	5	of	of	ADP
ejpam-4580	278	6	class	class	NOUN
ejpam-4580	278	7	q(n	q(n	PROPN
ejpam-4580	278	8	)	)	PUNCT
ejpam-4580	278	9	then	then	ADV
ejpam-4580	278	10	t	t	PROPN
ejpam-4580	278	11	is	be	AUX
ejpam-4580	278	12	an	an	DET
ejpam-4580	278	13	operator	operator	NOUN
ejpam-4580	278	14	of	of	ADP
ejpam-4580	278	15	k−quasi	k−quasi	PROPN
ejpam-4580	278	16	class	class	NOUN
ejpam-4580	278	17	q(n	q(n	PROPN
ejpam-4580	278	18	)	)	PUNCT
ejpam-4580	278	19	.	.	PUNCT
ejpam-4580	279	1	proof	proof	NOUN
ejpam-4580	279	2	.	.	PUNCT
ejpam-4580	280	1	let	let	AUX
ejpam-4580	280	2	be	be	AUX
ejpam-4580	280	3	d	d	NOUN
ejpam-4580	280	4	=	=	SYM
ejpam-4580	280	5	a∗2a2	a∗2a2	PROPN
ejpam-4580	280	6	−na∗a+	−na∗a+	NUM
ejpam-4580	280	7	i.	i.	NOUN
ejpam-4580	280	8	a	a	DET
ejpam-4580	280	9	simple	simple	ADJ
ejpam-4580	280	10	calculation	calculation	NOUN
ejpam-4580	280	11	shows	show	VERB
ejpam-4580	280	12	that	that	SCONJ
ejpam-4580	280	13	:	:	PUNCT
ejpam-4580	280	14	t	t	NOUN
ejpam-4580	280	15	∗	∗	NOUN
ejpam-4580	280	16	=	=	SYM
ejpam-4580	280	17	(	(	PUNCT
ejpam-4580	280	18	a∗	a∗	NOUN
ejpam-4580	280	19	0	0	SYM
ejpam-4580	280	20	b∗	b∗	ADJ
ejpam-4580	280	21	0	0	NUM
ejpam-4580	280	22	)	)	PUNCT
ejpam-4580	280	23	,	,	PUNCT
ejpam-4580	280	24	t	t	PROPN
ejpam-4580	280	25	∗(k+2	∗(k+2	PUNCT
ejpam-4580	280	26	)	)	PUNCT
ejpam-4580	280	27	=	=	PRON
ejpam-4580	280	28	(	(	PUNCT
ejpam-4580	280	29	a∗(k+2	a∗(k+2	NUM
ejpam-4580	280	30	)	)	PUNCT
ejpam-4580	280	31	0	0	NUM
ejpam-4580	281	1	b∗a∗(k+1	b∗a∗(k+1	NOUN
ejpam-4580	281	2	)	)	PUNCT
ejpam-4580	281	3	0	0	NUM
ejpam-4580	281	4	)	)	PUNCT
ejpam-4580	281	5	,	,	PUNCT
ejpam-4580	281	6	t	t	PROPN
ejpam-4580	281	7	(	(	PUNCT
ejpam-4580	281	8	k+2	k+2	NUM
ejpam-4580	281	9	)	)	PUNCT
ejpam-4580	281	10	=	=	SYM
ejpam-4580	281	11	(	(	PUNCT
ejpam-4580	281	12	a(k+2	a(k+2	NUM
ejpam-4580	281	13	)	)	PUNCT
ejpam-4580	281	14	a(k+1)b	a(k+1)b	NOUN
ejpam-4580	281	15	0	0	NUM
ejpam-4580	281	16	0	0	NUM
ejpam-4580	281	17	)	)	PUNCT
ejpam-4580	281	18	,	,	PUNCT
ejpam-4580	281	19	t	t	PROPN
ejpam-4580	281	20	∗(k+2)t	∗(k+2)t	PROPN
ejpam-4580	281	21	(	(	PUNCT
ejpam-4580	281	22	k+2	k+2	NUM
ejpam-4580	281	23	)	)	PUNCT
ejpam-4580	281	24	=	=	SYM
ejpam-4580	281	25	(	(	PUNCT
ejpam-4580	281	26	a∗(k+2)a(k+2	a∗(k+2)a(k+2	NUM
ejpam-4580	281	27	)	)	PUNCT
ejpam-4580	281	28	a∗(k+2)a(k+1)b	a∗(k+2)a(k+1)b	PROPN
ejpam-4580	282	1	b∗a∗(k+1)a(k+2	b∗a∗(k+1)a(k+2	NOUN
ejpam-4580	282	2	)	)	PUNCT
ejpam-4580	282	3	b∗a∗(k+1)a(k+1)b	b∗a∗(k+1)a(k+1)b	PROPN
ejpam-4580	282	4	)	)	PUNCT
ejpam-4580	282	5	.	.	PUNCT
ejpam-4580	283	1	t	t	PROPN
ejpam-4580	283	2	∗k(t	∗k(t	PROPN
ejpam-4580	283	3	∗2	∗2	PROPN
ejpam-4580	283	4	t	t	PROPN
ejpam-4580	283	5	2	2	NUM
ejpam-4580	283	6	−nt	−nt	ADP
ejpam-4580	283	7	∗t	∗t	PROPN
ejpam-4580	283	8	+	+	CCONJ
ejpam-4580	283	9	i)t	i)t	NOUN
ejpam-4580	283	10	k	k	X
ejpam-4580	283	11	=	=	X
ejpam-4580	283	12	t	t	X
ejpam-4580	283	13	∗(k+2)t	∗(k+2)t	PROPN
ejpam-4580	283	14	(	(	PUNCT
ejpam-4580	283	15	k+2	k+2	NUM
ejpam-4580	283	16	)	)	PUNCT
ejpam-4580	283	17	−nt	−nt	NOUN
ejpam-4580	283	18	∗(k+1)t	∗(k+1)t	PROPN
ejpam-4580	283	19	(	(	PUNCT
ejpam-4580	283	20	k+1	k+1	NOUN
ejpam-4580	283	21	)	)	PUNCT
ejpam-4580	283	22	+	+	NUM
ejpam-4580	283	23	t	t	NOUN
ejpam-4580	283	24	∗kt	∗kt	PUNCT
ejpam-4580	283	25	k	k	X
ejpam-4580	283	26	=	=	PUNCT
ejpam-4580	283	27	(	(	PUNCT
ejpam-4580	283	28	a∗kdak	a∗kdak	ADV
ejpam-4580	283	29	a∗kda(k−1)b	a∗kda(k−1)b	PROPN
ejpam-4580	283	30	b∗a∗(k−1)dak	b∗a∗(k−1)dak	PROPN
ejpam-4580	283	31	b∗a∗(k−1)da(k−1)b	b∗a∗(k−1)da(k−1)b	PROPN
ejpam-4580	283	32	)	)	PUNCT
ejpam-4580	283	33	let	let	VERB
ejpam-4580	283	34	u	u	PRON
ejpam-4580	283	35	=	=	PROPN
ejpam-4580	283	36	x⊕	x⊕	PROPN
ejpam-4580	283	37	y	y	PROPN
ejpam-4580	283	38	∈	∈	PROPN
ejpam-4580	283	39	h	h	NOUN
ejpam-4580	283	40	⊕h	⊕h	NOUN
ejpam-4580	283	41	.	.	PUNCT
ejpam-4580	284	1	then	then	ADV
ejpam-4580	284	2	,	,	PUNCT
ejpam-4580	284	3	⟨(t	⟨(t	PROPN
ejpam-4580	284	4	∗(k+2)t	∗(k+2)t	PROPN
ejpam-4580	284	5	(	(	PUNCT
ejpam-4580	284	6	k+2	k+2	NUM
ejpam-4580	284	7	)	)	PUNCT
ejpam-4580	284	8	−nt	−nt	NOUN
ejpam-4580	284	9	∗(k+1)t	∗(k+1)t	PROPN
ejpam-4580	284	10	(	(	PUNCT
ejpam-4580	284	11	k+1	k+1	NOUN
ejpam-4580	284	12	)	)	PUNCT
ejpam-4580	284	13	+	+	NUM
ejpam-4580	284	14	t	t	NOUN
ejpam-4580	284	15	∗kt	∗kt	NUM
ejpam-4580	284	16	k)u	k)u	NOUN
ejpam-4580	284	17	,	,	PUNCT
ejpam-4580	284	18	u⟩	u⟩	NOUN
ejpam-4580	284	19	=	=	PUNCT
ejpam-4580	284	20	⟨a∗kdakx	⟨a∗kdakx	NOUN
ejpam-4580	284	21	,	,	PUNCT
ejpam-4580	284	22	x⟩+	x⟩+	PROPN
ejpam-4580	284	23	⟨a∗kda(k−1)by	⟨a∗kda(k−1)by	PROPN
ejpam-4580	284	24	,	,	PUNCT
ejpam-4580	284	25	x⟩	x⟩	PUNCT
ejpam-4580	285	1	+	+	CCONJ
ejpam-4580	285	2	⟨b∗a∗(k−1)dakx	⟨b∗a∗(k−1)dakx	NUM
ejpam-4580	285	3	,	,	PUNCT
ejpam-4580	285	4	y⟩+	y⟩+	ADJ
ejpam-4580	285	5	⟨b∗a∗(k−1)da(k−1)by	⟨b∗a∗(k−1)da(k−1)by	NOUN
ejpam-4580	285	6	,	,	PUNCT
ejpam-4580	285	7	y⟩	y⟩	NOUN
ejpam-4580	285	8	=	=	PUNCT
ejpam-4580	286	1	⟨dakx	⟨dakx	X
ejpam-4580	286	2	,	,	PUNCT
ejpam-4580	286	3	akx⟩+	akx⟩+	NOUN
ejpam-4580	286	4	⟨da(k−1)by	⟨da(k−1)by	NOUN
ejpam-4580	286	5	,	,	PUNCT
ejpam-4580	286	6	akx⟩	akx⟩	NOUN
ejpam-4580	287	1	+	+	CCONJ
ejpam-4580	288	1	⟨dakx	⟨dakx	ADP
ejpam-4580	288	2	,	,	PUNCT
ejpam-4580	288	3	a(k−1)by⟩+	a(k−1)by⟩+	ADJ
ejpam-4580	288	4	⟨da(k−1)by	⟨da(k−1)by	NOUN
ejpam-4580	288	5	,	,	PUNCT
ejpam-4580	288	6	a(k−1)by⟩	a(k−1)by⟩	NOUN
ejpam-4580	288	7	=	=	SYM
ejpam-4580	288	8	⟨d(akx+a(k−1)by	⟨d(akx+a(k−1)by	PROPN
ejpam-4580	288	9	)	)	PUNCT
ejpam-4580	288	10	,	,	PUNCT
ejpam-4580	288	11	(	(	PUNCT
ejpam-4580	288	12	akx+a(k−1)by)⟩	akx+a(k−1)by)⟩	X
ejpam-4580	288	13	≥	≥	NOUN
ejpam-4580	288	14	0	0	NUM
ejpam-4580	288	15	because	because	SCONJ
ejpam-4580	288	16	a	a	PRON
ejpam-4580	288	17	is	be	AUX
ejpam-4580	288	18	operator	operator	NOUN
ejpam-4580	288	19	of	of	ADP
ejpam-4580	288	20	class	class	NOUN
ejpam-4580	288	21	q(n	q(n	PROPN
ejpam-4580	288	22	)	)	PUNCT
ejpam-4580	288	23	then	then	ADV
ejpam-4580	288	24	,	,	PUNCT
ejpam-4580	288	25	d	d	PROPN
ejpam-4580	288	26	=	=	SYM
ejpam-4580	288	27	a∗2a2	a∗2a2	PROPN
ejpam-4580	288	28	−na∗a+	−na∗a+	PRON
ejpam-4580	289	1	i	i	PRON
ejpam-4580	289	2	≥	≥	VERB
ejpam-4580	289	3	o	o	NOUN
ejpam-4580	289	4	,	,	PUNCT
ejpam-4580	289	5	so	so	SCONJ
ejpam-4580	289	6	t	t	PROPN
ejpam-4580	289	7	is	be	AUX
ejpam-4580	289	8	operator	operator	NOUN
ejpam-4580	289	9	of	of	ADP
ejpam-4580	289	10	k−quasi	k−quasi	PROPN
ejpam-4580	289	11	class	class	NOUN
ejpam-4580	289	12	q(n	q(n	PROPN
ejpam-4580	289	13	)	)	PUNCT
ejpam-4580	289	14	.	.	PUNCT
ejpam-4580	290	1	proposition	proposition	NOUN
ejpam-4580	290	2	24	24	NUM
ejpam-4580	290	3	.	.	PUNCT
ejpam-4580	290	4	suppose	suppose	VERB
ejpam-4580	290	5	that	that	SCONJ
ejpam-4580	290	6	t	t	PROPN
ejpam-4580	290	7	k	k	PROPN
ejpam-4580	290	8	does	do	AUX
ejpam-4580	290	9	not	not	PART
ejpam-4580	290	10	have	have	VERB
ejpam-4580	290	11	a	a	DET
ejpam-4580	290	12	dense	dense	ADJ
ejpam-4580	290	13	range	range	NOUN
ejpam-4580	290	14	,	,	PUNCT
ejpam-4580	290	15	then	then	ADV
ejpam-4580	290	16	the	the	DET
ejpam-4580	290	17	following	following	ADJ
ejpam-4580	290	18	statements	statement	NOUN
ejpam-4580	290	19	are	be	AUX
ejpam-4580	290	20	equivalent	equivalent	ADJ
ejpam-4580	290	21	:	:	PUNCT
ejpam-4580	290	22	sh	sh	PROPN
ejpam-4580	290	23	.	.	PROPN
ejpam-4580	290	24	lohaj	lohaj	PROPN
ejpam-4580	290	25	/	/	SYM
ejpam-4580	290	26	eur	eur	PROPN
ejpam-4580	290	27	.	.	PUNCT
ejpam-4580	291	1	j.	j.	PROPN
ejpam-4580	291	2	pure	pure	PROPN
ejpam-4580	291	3	appl	appl	PROPN
ejpam-4580	291	4	.	.	PROPN
ejpam-4580	291	5	math	math	PROPN
ejpam-4580	291	6	,	,	PUNCT
ejpam-4580	291	7	15	15	NUM
ejpam-4580	291	8	(	(	PUNCT
ejpam-4580	291	9	4	4	NUM
ejpam-4580	291	10	)	)	PUNCT
ejpam-4580	291	11	(	(	PUNCT
ejpam-4580	291	12	2022	2022	NUM
ejpam-4580	291	13	)	)	PUNCT
ejpam-4580	291	14	,	,	PUNCT
ejpam-4580	291	15	1836	1836	NUM
ejpam-4580	291	16	-	-	SYM
ejpam-4580	291	17	1853	1853	NUM
ejpam-4580	291	18	1849	1849	NUM
ejpam-4580	291	19	(	(	PUNCT
ejpam-4580	291	20	i	i	NOUN
ejpam-4580	291	21	)	)	PUNCT
ejpam-4580	291	22	operator	operator	NOUN
ejpam-4580	291	23	t	t	PROPN
ejpam-4580	291	24	is	be	AUX
ejpam-4580	291	25	a	a	DET
ejpam-4580	291	26	k−quasi	k−quasi	PROPN
ejpam-4580	291	27	class	class	NOUN
ejpam-4580	291	28	q(n	q(n	PROPN
ejpam-4580	291	29	)	)	PUNCT
ejpam-4580	291	30	operator	operator	NOUN
ejpam-4580	291	31	;	;	PUNCT
ejpam-4580	291	32	(	(	PUNCT
ejpam-4580	291	33	ii	ii	NOUN
ejpam-4580	291	34	)	)	PUNCT
ejpam-4580	291	35	t	t	NOUN
ejpam-4580	291	36	=	=	SYM
ejpam-4580	291	37	(	(	PUNCT
ejpam-4580	291	38	a	a	DET
ejpam-4580	291	39	b	b	NOUN
ejpam-4580	291	40	0	0	NUM
ejpam-4580	291	41	c	c	NOUN
ejpam-4580	291	42	)	)	PUNCT
ejpam-4580	291	43	on	on	ADP
ejpam-4580	291	44	h	h	NOUN
ejpam-4580	291	45	=	=	SYM
ejpam-4580	291	46	t	t	PROPN
ejpam-4580	291	47	k(h)⊕kert	k(h)⊕kert	NOUN
ejpam-4580	291	48	∗k	∗k	NOUN
ejpam-4580	291	49	,	,	PUNCT
ejpam-4580	291	50	where	where	SCONJ
ejpam-4580	291	51	a	a	PRON
ejpam-4580	291	52	is	be	AUX
ejpam-4580	291	53	an	an	DET
ejpam-4580	291	54	operator	operator	NOUN
ejpam-4580	291	55	of	of	ADP
ejpam-4580	291	56	the	the	DET
ejpam-4580	291	57	class	class	NOUN
ejpam-4580	291	58	q(n	q(n	PROPN
ejpam-4580	291	59	)	)	PUNCT
ejpam-4580	291	60	on	on	ADP
ejpam-4580	291	61	t	t	PROPN
ejpam-4580	291	62	k(h	k(h	PROPN
ejpam-4580	291	63	)	)	PUNCT
ejpam-4580	291	64	,	,	PUNCT
ejpam-4580	291	65	ck	ck	NOUN
ejpam-4580	291	66	=	=	SYM
ejpam-4580	291	67	0	0	NUM
ejpam-4580	291	68	and	and	CCONJ
ejpam-4580	291	69	σ(t	σ(t	PROPN
ejpam-4580	291	70	)	)	PUNCT
ejpam-4580	292	1	=	=	SYM
ejpam-4580	292	2	σ(a	σ(a	PROPN
ejpam-4580	292	3	)	)	PUNCT
ejpam-4580	292	4	∪	∪	X
ejpam-4580	292	5	{	{	PUNCT
ejpam-4580	292	6	0	0	NUM
ejpam-4580	292	7	}	}	PUNCT
ejpam-4580	292	8	,	,	PUNCT
ejpam-4580	292	9	b	b	X
ejpam-4580	292	10	is	be	AUX
ejpam-4580	292	11	any	any	DET
ejpam-4580	292	12	operator	operator	NOUN
ejpam-4580	292	13	.	.	PUNCT
ejpam-4580	293	1	proof	proof	NOUN
ejpam-4580	293	2	.	.	PUNCT
ejpam-4580	294	1	(	(	PUNCT
ejpam-4580	294	2	1	1	X
ejpam-4580	294	3	)	)	PUNCT
ejpam-4580	294	4	⇒	⇒	NOUN
ejpam-4580	294	5	(	(	PUNCT
ejpam-4580	294	6	2	2	X
ejpam-4580	294	7	)	)	PUNCT
ejpam-4580	294	8	suppose	suppose	VERB
ejpam-4580	294	9	that	that	SCONJ
ejpam-4580	294	10	t	t	PROPN
ejpam-4580	294	11	∈	∈	PROPN
ejpam-4580	294	12	l(h	l(h	PROPN
ejpam-4580	294	13	)	)	PUNCT
ejpam-4580	294	14	is	be	AUX
ejpam-4580	294	15	an	an	DET
ejpam-4580	294	16	operator	operator	NOUN
ejpam-4580	294	17	of	of	ADP
ejpam-4580	294	18	k−quasi	k−quasi	PROPN
ejpam-4580	294	19	class	class	NOUN
ejpam-4580	294	20	q(n	q(n	PROPN
ejpam-4580	294	21	)	)	PUNCT
ejpam-4580	294	22	.	.	PUNCT
ejpam-4580	295	1	since	since	SCONJ
ejpam-4580	295	2	that	that	PRON
ejpam-4580	295	3	t	t	PROPN
ejpam-4580	295	4	k	k	PROPN
ejpam-4580	295	5	does	do	AUX
ejpam-4580	295	6	not	not	PART
ejpam-4580	295	7	have	have	VERB
ejpam-4580	295	8	dense	dense	ADJ
ejpam-4580	295	9	range	range	NOUN
ejpam-4580	295	10	,	,	PUNCT
ejpam-4580	295	11	we	we	PRON
ejpam-4580	295	12	can	can	AUX
ejpam-4580	295	13	represent	represent	VERB
ejpam-4580	295	14	t	t	PROPN
ejpam-4580	295	15	as	as	ADP
ejpam-4580	295	16	the	the	DET
ejpam-4580	295	17	upper	upper	ADJ
ejpam-4580	295	18	triangular	triangular	NOUN
ejpam-4580	295	19	matrix	matrix	NOUN
ejpam-4580	295	20	:	:	PUNCT
ejpam-4580	295	21	t	t	NOUN
ejpam-4580	295	22	=	=	SYM
ejpam-4580	295	23	(	(	PUNCT
ejpam-4580	295	24	a	a	DET
ejpam-4580	295	25	b	b	NOUN
ejpam-4580	295	26	0	0	NUM
ejpam-4580	295	27	c	c	NOUN
ejpam-4580	295	28	)	)	PUNCT
ejpam-4580	295	29	on	on	ADP
ejpam-4580	295	30	h	h	NOUN
ejpam-4580	295	31	=	=	PROPN
ejpam-4580	295	32	t	t	PROPN
ejpam-4580	295	33	k(h)⊕	k(h)⊕	PROPN
ejpam-4580	295	34	kert	kert	PROPN
ejpam-4580	295	35	∗k	∗k	PROPN
ejpam-4580	295	36	.	.	PUNCT
ejpam-4580	296	1	since	since	SCONJ
ejpam-4580	296	2	t	t	PROPN
ejpam-4580	296	3	is	be	AUX
ejpam-4580	296	4	an	an	DET
ejpam-4580	296	5	operator	operator	NOUN
ejpam-4580	296	6	of	of	ADP
ejpam-4580	296	7	k−quasi	k−quasi	PROPN
ejpam-4580	296	8	class	class	NOUN
ejpam-4580	296	9	q(n	q(n	PROPN
ejpam-4580	296	10	)	)	PUNCT
ejpam-4580	296	11	,	,	PUNCT
ejpam-4580	296	12	we	we	PRON
ejpam-4580	296	13	have	have	VERB
ejpam-4580	296	14	t	t	PROPN
ejpam-4580	296	15	∗k(t	∗k(t	PROPN
ejpam-4580	296	16	∗2	∗2	PROPN
ejpam-4580	296	17	t	t	PROPN
ejpam-4580	296	18	2	2	NUM
ejpam-4580	296	19	−nt	−nt	ADP
ejpam-4580	296	20	∗t	∗t	PROPN
ejpam-4580	296	21	+	+	CCONJ
ejpam-4580	296	22	i)t	i)t	VERB
ejpam-4580	297	1	k	k	X
ejpam-4580	297	2	≥	≥	NUM
ejpam-4580	297	3	0	0	NUM
ejpam-4580	297	4	.	.	PUNCT
ejpam-4580	298	1	therefore	therefore	ADV
ejpam-4580	298	2	,	,	PUNCT
ejpam-4580	298	3	after	after	ADP
ejpam-4580	298	4	some	some	DET
ejpam-4580	298	5	calculation	calculation	NOUN
ejpam-4580	298	6	similar	similar	ADJ
ejpam-4580	298	7	as	as	ADP
ejpam-4580	298	8	in	in	ADP
ejpam-4580	298	9	proposition	proposition	NOUN
ejpam-4580	298	10	9	9	NUM
ejpam-4580	298	11	we	we	PRON
ejpam-4580	298	12	get	get	VERB
ejpam-4580	298	13	:	:	PUNCT
ejpam-4580	298	14	⟨(t	⟨(t	PROPN
ejpam-4580	298	15	∗2	∗2	PROPN
ejpam-4580	298	16	t	t	PROPN
ejpam-4580	298	17	2	2	NUM
ejpam-4580	298	18	−nt	−nt	ADP
ejpam-4580	298	19	∗t	∗t	PROPN
ejpam-4580	298	20	+	+	CCONJ
ejpam-4580	298	21	i)x	i)x	ADV
ejpam-4580	298	22	,	,	PUNCT
ejpam-4580	298	23	x⟩	x⟩	PUNCT
ejpam-4580	299	1	=	=	SYM
ejpam-4580	299	2	⟨(a∗2a2	⟨(a∗2a2	PROPN
ejpam-4580	299	3	−na∗a+	−na∗a+	NOUN
ejpam-4580	299	4	i)x	i)x	NOUN
ejpam-4580	299	5	,	,	PUNCT
ejpam-4580	299	6	x⟩	x⟩	PUNCT
ejpam-4580	299	7	≥	≥	NOUN
ejpam-4580	299	8	0	0	NUM
ejpam-4580	299	9	,	,	PUNCT
ejpam-4580	299	10	for	for	ADP
ejpam-4580	299	11	all	all	DET
ejpam-4580	299	12	x	x	SYM
ejpam-4580	299	13	∈	∈	PROPN
ejpam-4580	299	14	t	t	PROPN
ejpam-4580	299	15	k(h	k(h	PROPN
ejpam-4580	299	16	)	)	PUNCT
ejpam-4580	299	17	.	.	PUNCT
ejpam-4580	300	1	hence	hence	ADV
ejpam-4580	300	2	a∗2a2	a∗2a2	PROPN
ejpam-4580	300	3	−na∗a+	−na∗a+	PRON
ejpam-4580	301	1	i	i	PRON
ejpam-4580	301	2	≥	≥	VERB
ejpam-4580	301	3	0	0	NUM
ejpam-4580	301	4	.	.	PUNCT
ejpam-4580	302	1	this	this	PRON
ejpam-4580	302	2	shows	show	VERB
ejpam-4580	302	3	that	that	SCONJ
ejpam-4580	302	4	a	a	PRON
ejpam-4580	302	5	is	be	AUX
ejpam-4580	302	6	an	an	DET
ejpam-4580	302	7	operator	operator	NOUN
ejpam-4580	302	8	of	of	ADP
ejpam-4580	302	9	the	the	DET
ejpam-4580	302	10	class	class	NOUN
ejpam-4580	302	11	q(n	q(n	PROPN
ejpam-4580	302	12	)	)	PUNCT
ejpam-4580	302	13	on	on	ADP
ejpam-4580	302	14	t	t	PROPN
ejpam-4580	302	15	k(h	k(h	PROPN
ejpam-4580	302	16	)	)	PUNCT
ejpam-4580	302	17	.	.	PUNCT
ejpam-4580	303	1	let	let	VERB
ejpam-4580	303	2	p	p	PRON
ejpam-4580	303	3	be	be	AUX
ejpam-4580	303	4	the	the	DET
ejpam-4580	303	5	orthogonal	orthogonal	ADJ
ejpam-4580	303	6	projection	projection	NOUN
ejpam-4580	303	7	of	of	ADP
ejpam-4580	303	8	h	h	NOUN
ejpam-4580	303	9	onto	onto	ADP
ejpam-4580	303	10	t	t	PROPN
ejpam-4580	303	11	k(h	k(h	PROPN
ejpam-4580	303	12	)	)	PUNCT
ejpam-4580	303	13	.	.	PUNCT
ejpam-4580	304	1	for	for	ADP
ejpam-4580	304	2	any	any	PRON
ejpam-4580	304	3	x	x	SYM
ejpam-4580	304	4	=	=	SYM
ejpam-4580	304	5	(	(	PUNCT
ejpam-4580	304	6	x1	x1	PROPN
ejpam-4580	304	7	x2	x2	PROPN
ejpam-4580	304	8	)	)	PUNCT
ejpam-4580	304	9	∈	∈	PROPN
ejpam-4580	304	10	h	h	NOUN
ejpam-4580	304	11	=	=	PROPN
ejpam-4580	304	12	t	t	PROPN
ejpam-4580	304	13	k(h)⊕	k(h)⊕	PROPN
ejpam-4580	304	14	kert	kert	PROPN
ejpam-4580	304	15	∗k	∗k	PROPN
ejpam-4580	304	16	.	.	PUNCT
ejpam-4580	305	1	then	then	ADV
ejpam-4580	305	2	⟨ckx2	⟨ckx2	PROPN
ejpam-4580	305	3	,	,	PUNCT
ejpam-4580	305	4	x2⟩	x2⟩	PUNCT
ejpam-4580	306	1	=	=	SYM
ejpam-4580	306	2	⟨t	⟨t	X
ejpam-4580	306	3	k(i	k(i	PROPN
ejpam-4580	306	4	−	−	PROPN
ejpam-4580	306	5	p	p	NOUN
ejpam-4580	306	6	)	)	PUNCT
ejpam-4580	306	7	x	x	NOUN
ejpam-4580	306	8	,	,	PUNCT
ejpam-4580	306	9	(	(	PUNCT
ejpam-4580	306	10	i	i	PRON
ejpam-4580	306	11	−	−	PROPN
ejpam-4580	306	12	p	p	NOUN
ejpam-4580	306	13	)	)	PUNCT
ejpam-4580	306	14	x⟩	x⟩	PUNCT
ejpam-4580	307	1	=	=	SYM
ejpam-4580	307	2	⟨(i	⟨(i	PROPN
ejpam-4580	308	1	−	−	PROPN
ejpam-4580	308	2	p	p	PROPN
ejpam-4580	308	3	)	)	PUNCT
ejpam-4580	308	4	x	x	PROPN
ejpam-4580	308	5	,	,	PUNCT
ejpam-4580	308	6	t	t	PROPN
ejpam-4580	308	7	∗k(i	∗k(i	PROPN
ejpam-4580	308	8	−	−	PROPN
ejpam-4580	308	9	p	p	NOUN
ejpam-4580	308	10	)	)	PUNCT
ejpam-4580	308	11	x⟩	x⟩	PUNCT
ejpam-4580	309	1	=	=	PUNCT
ejpam-4580	309	2	0	0	X
ejpam-4580	309	3	.	.	PUNCT
ejpam-4580	310	1	thus	thus	ADV
ejpam-4580	310	2	t	t	X
ejpam-4580	310	3	∗k	∗k	NOUN
ejpam-4580	310	4	=	=	SYM
ejpam-4580	310	5	0	0	X
ejpam-4580	310	6	.	.	PUNCT
ejpam-4580	311	1	since	since	SCONJ
ejpam-4580	311	2	σ(a)∪σ(c	σ(a)∪σ(c	NUM
ejpam-4580	311	3	)	)	PUNCT
ejpam-4580	311	4	=	=	SYM
ejpam-4580	311	5	σ(t	σ(t	PROPN
ejpam-4580	311	6	)	)	PUNCT
ejpam-4580	311	7	∪ϑ	∪ϑ	PROPN
ejpam-4580	311	8	,	,	PUNCT
ejpam-4580	311	9	where	where	SCONJ
ejpam-4580	311	10	ϑ	ϑ	PROPN
ejpam-4580	311	11	is	be	AUX
ejpam-4580	311	12	the	the	DET
ejpam-4580	311	13	union	union	NOUN
ejpam-4580	311	14	of	of	ADP
ejpam-4580	311	15	the	the	DET
ejpam-4580	311	16	holes	hole	NOUN
ejpam-4580	311	17	in	in	ADP
ejpam-4580	311	18	σ(t	σ(t	PROPN
ejpam-4580	311	19	)	)	PUNCT
ejpam-4580	311	20	,	,	PUNCT
ejpam-4580	311	21	which	which	PRON
ejpam-4580	311	22	happen	happen	VERB
ejpam-4580	311	23	to	to	PART
ejpam-4580	311	24	be	be	AUX
ejpam-4580	311	25	a	a	DET
ejpam-4580	311	26	subset	subset	NOUN
ejpam-4580	311	27	of	of	ADP
ejpam-4580	311	28	σ(a)∩σ(c	σ(a)∩σ(c	PROPN
ejpam-4580	311	29	)	)	PUNCT
ejpam-4580	311	30	by	by	ADP
ejpam-4580	311	31	[	[	X
ejpam-4580	311	32	3	3	NUM
ejpam-4580	311	33	,	,	PUNCT
ejpam-4580	311	34	corollary	corollary	ADJ
ejpam-4580	311	35	7	7	NUM
ejpam-4580	311	36	]	]	PUNCT
ejpam-4580	311	37	.	.	PUNCT
ejpam-4580	312	1	since	since	SCONJ
ejpam-4580	312	2	σ(a)∩σ(c	σ(a)∩σ(c	PROPN
ejpam-4580	312	3	)	)	PUNCT
ejpam-4580	312	4	has	have	VERB
ejpam-4580	312	5	no	no	DET
ejpam-4580	312	6	interior	interior	ADJ
ejpam-4580	312	7	points	point	NOUN
ejpam-4580	312	8	,	,	PUNCT
ejpam-4580	312	9	then	then	ADV
ejpam-4580	312	10	σ(t	σ(t	X
ejpam-4580	312	11	)	)	PUNCT
ejpam-4580	313	1	=	=	SYM
ejpam-4580	313	2	σ(a	σ(a	PROPN
ejpam-4580	313	3	)	)	PUNCT
ejpam-4580	313	4	∪	∪	ADP
ejpam-4580	313	5	σ(c	σ(c	PROPN
ejpam-4580	313	6	)	)	PUNCT
ejpam-4580	313	7	=	=	SYM
ejpam-4580	314	1	σ(a	σ(a	PROPN
ejpam-4580	314	2	)	)	PUNCT
ejpam-4580	314	3	∪	∪	ADP
ejpam-4580	314	4	{	{	PUNCT
ejpam-4580	314	5	0	0	NUM
ejpam-4580	314	6	}	}	PUNCT
ejpam-4580	314	7	and	and	CCONJ
ejpam-4580	314	8	ck	ck	NOUN
ejpam-4580	314	9	=	=	NOUN
ejpam-4580	314	10	0	0	PROPN
ejpam-4580	314	11	.	.	PUNCT
ejpam-4580	315	1	(	(	PUNCT
ejpam-4580	315	2	2	2	X
ejpam-4580	315	3	)	)	PUNCT
ejpam-4580	315	4	⇒	⇒	NOUN
ejpam-4580	315	5	(	(	PUNCT
ejpam-4580	315	6	1	1	X
ejpam-4580	315	7	)	)	PUNCT
ejpam-4580	315	8	suppose	suppose	VERB
ejpam-4580	315	9	that	that	SCONJ
ejpam-4580	315	10	t	t	NOUN
ejpam-4580	315	11	=	=	PUNCT
ejpam-4580	315	12	(	(	PUNCT
ejpam-4580	315	13	a	a	DET
ejpam-4580	315	14	b	b	NOUN
ejpam-4580	315	15	0	0	NUM
ejpam-4580	315	16	c	c	NOUN
ejpam-4580	315	17	)	)	PUNCT
ejpam-4580	315	18	on	on	ADP
ejpam-4580	315	19	h	h	PROPN
ejpam-4580	315	20	=	=	PROPN
ejpam-4580	315	21	t	t	PROPN
ejpam-4580	315	22	k(h	k(h	PROPN
ejpam-4580	315	23	)	)	PUNCT
ejpam-4580	315	24	⊕	⊕	PROPN
ejpam-4580	315	25	kert	kert	PROPN
ejpam-4580	315	26	∗k	∗k	PROPN
ejpam-4580	315	27	,	,	PUNCT
ejpam-4580	315	28	where	where	SCONJ
ejpam-4580	315	29	a	a	PRON
ejpam-4580	315	30	is	be	AUX
ejpam-4580	315	31	an	an	DET
ejpam-4580	315	32	operator	operator	NOUN
ejpam-4580	315	33	of	of	ADP
ejpam-4580	315	34	the	the	DET
ejpam-4580	315	35	class	class	NOUN
ejpam-4580	315	36	q(n	q(n	PROPN
ejpam-4580	315	37	)	)	PUNCT
ejpam-4580	315	38	on	on	ADP
ejpam-4580	315	39	t	t	PROPN
ejpam-4580	315	40	k(h	k(h	PROPN
ejpam-4580	315	41	)	)	PUNCT
ejpam-4580	315	42	,	,	PUNCT
ejpam-4580	315	43	and	and	CCONJ
ejpam-4580	315	44	ck	ck	NOUN
ejpam-4580	315	45	=	=	NOUN
ejpam-4580	316	1	o.	o.	PROPN
ejpam-4580	316	2	a	a	DET
ejpam-4580	316	3	simple	simple	ADJ
ejpam-4580	316	4	calculation	calculation	NOUN
ejpam-4580	316	5	shows	show	VERB
ejpam-4580	316	6	that	that	SCONJ
ejpam-4580	316	7	:	:	PUNCT
ejpam-4580	316	8	t	t	NOUN
ejpam-4580	316	9	∗	∗	NOUN
ejpam-4580	316	10	=	=	SYM
ejpam-4580	316	11	(	(	PUNCT
ejpam-4580	316	12	a∗	a∗	ADJ
ejpam-4580	316	13	0	0	NUM
ejpam-4580	316	14	b∗	b∗	ADJ
ejpam-4580	316	15	c∗	c∗	PROPN
ejpam-4580	316	16	)	)	PUNCT
ejpam-4580	316	17	,	,	PUNCT
ejpam-4580	316	18	t	t	X
ejpam-4580	316	19	∗t	∗t	PROPN
ejpam-4580	316	20	=	=	SYM
ejpam-4580	316	21	(	(	PUNCT
ejpam-4580	316	22	a∗a	a∗a	NUM
ejpam-4580	316	23	a∗b	a∗b	NUM
ejpam-4580	316	24	b∗a	b∗a	PROPN
ejpam-4580	316	25	b∗b	b∗b	NOUN
ejpam-4580	316	26	+	+	CCONJ
ejpam-4580	316	27	c∗c	c∗c	NUM
ejpam-4580	316	28	)	)	PUNCT
ejpam-4580	316	29	,	,	PUNCT
ejpam-4580	316	30	sh	sh	PROPN
ejpam-4580	316	31	.	.	PROPN
ejpam-4580	316	32	lohaj	lohaj	PROPN
ejpam-4580	316	33	/	/	SYM
ejpam-4580	316	34	eur	eur	PROPN
ejpam-4580	316	35	.	.	PUNCT
ejpam-4580	317	1	j.	j.	PROPN
ejpam-4580	317	2	pure	pure	PROPN
ejpam-4580	317	3	appl	appl	PROPN
ejpam-4580	317	4	.	.	PROPN
ejpam-4580	317	5	math	math	PROPN
ejpam-4580	317	6	,	,	PUNCT
ejpam-4580	317	7	15	15	NUM
ejpam-4580	317	8	(	(	PUNCT
ejpam-4580	317	9	4	4	NUM
ejpam-4580	317	10	)	)	PUNCT
ejpam-4580	317	11	(	(	PUNCT
ejpam-4580	317	12	2022	2022	NUM
ejpam-4580	317	13	)	)	PUNCT
ejpam-4580	317	14	,	,	PUNCT
ejpam-4580	317	15	1836	1836	NUM
ejpam-4580	317	16	-	-	SYM
ejpam-4580	317	17	1853	1853	NUM
ejpam-4580	317	18	1850	1850	NUM
ejpam-4580	317	19	t	t	NOUN
ejpam-4580	317	20	∗k	∗k	NOUN
ejpam-4580	317	21	=	=	SYM
ejpam-4580	317	22	(	(	PUNCT
ejpam-4580	317	23	a∗k	a∗k	PROPN
ejpam-4580	317	24	0	0	NUM
ejpam-4580	317	25	(	(	PUNCT
ejpam-4580	317	26	∑k−1	∑k−1	X
ejpam-4580	317	27	j=0	j=0	PROPN
ejpam-4580	317	28	a	a	DET
ejpam-4580	317	29	jbck−1−j)∗	jbck−1−j)∗	PROPN
ejpam-4580	317	30	0	0	NUM
ejpam-4580	317	31	)	)	PUNCT
ejpam-4580	317	32	,	,	PUNCT
ejpam-4580	317	33	t	t	PROPN
ejpam-4580	317	34	k	k	PROPN
ejpam-4580	318	1	=	=	PRON
ejpam-4580	318	2	(	(	PUNCT
ejpam-4580	318	3	ak	ak	PROPN
ejpam-4580	318	4	(	(	PUNCT
ejpam-4580	318	5	∑k−1	∑k−1	PROPN
ejpam-4580	318	6	j=0	j=0	PROPN
ejpam-4580	318	7	a	a	DET
ejpam-4580	318	8	jbck−1−j	jbck−1−j	PROPN
ejpam-4580	318	9	)	)	PUNCT
ejpam-4580	318	10	0	0	NUM
ejpam-4580	318	11	0	0	NUM
ejpam-4580	318	12	)	)	PUNCT
ejpam-4580	318	13	,	,	PUNCT
ejpam-4580	318	14	then	then	ADV
ejpam-4580	318	15	,	,	PUNCT
ejpam-4580	318	16	we	we	PRON
ejpam-4580	318	17	have	have	VERB
ejpam-4580	318	18	t	t	PROPN
ejpam-4580	318	19	∗k(t	∗k(t	PROPN
ejpam-4580	318	20	∗2	∗2	PROPN
ejpam-4580	318	21	t	t	PROPN
ejpam-4580	318	22	2	2	NUM
ejpam-4580	318	23	−nt	−nt	ADP
ejpam-4580	318	24	∗t	∗t	PROPN
ejpam-4580	318	25	+	+	CCONJ
ejpam-4580	318	26	i)t	i)t	NOUN
ejpam-4580	319	1	k	k	X
ejpam-4580	319	2	=	=	PUNCT
ejpam-4580	319	3	(	(	PUNCT
ejpam-4580	319	4	a∗k	a∗k	PROPN
ejpam-4580	319	5	0	0	NUM
ejpam-4580	319	6	(	(	PUNCT
ejpam-4580	319	7	∑k−1	∑k−1	X
ejpam-4580	319	8	j=0	j=0	PROPN
ejpam-4580	319	9	a	a	DET
ejpam-4580	319	10	jbck−1−j)∗	jbck−1−j)∗	PROPN
ejpam-4580	319	11	0	0	NUM
ejpam-4580	319	12	)	)	PUNCT
ejpam-4580	319	13	×	×	NOUN
ejpam-4580	319	14	(	(	PUNCT
ejpam-4580	319	15	d	d	X
ejpam-4580	319	16	a∗2ab	a∗2ab	X
ejpam-4580	319	17	+	+	ADJ
ejpam-4580	319	18	a∗2bc	a∗2bc	X
ejpam-4580	319	19	b∗a∗a2	b∗a∗a2	NOUN
ejpam-4580	319	20	+	+	CCONJ
ejpam-4580	319	21	c∗b∗a2	c∗b∗a2	VERB
ejpam-4580	319	22	−	−	PROPN
ejpam-4580	319	23	2b∗a	2b∗a	NOUN
ejpam-4580	319	24	|ab	|ab	X
ejpam-4580	319	25	+	+	ADP
ejpam-4580	319	26	bc|2	bc|2	ADV
ejpam-4580	319	27	+	+	CCONJ
ejpam-4580	319	28	|c2|2	|c2|2	PUNCT
ejpam-4580	319	29	−n(b∗b	−n(b∗b	NOUN
ejpam-4580	319	30	+	+	CCONJ
ejpam-4580	319	31	c∗c	c∗c	NUM
ejpam-4580	319	32	)	)	PUNCT
ejpam-4580	319	33	+	+	CCONJ
ejpam-4580	319	34	i	i	PRON
ejpam-4580	319	35	)	)	PUNCT
ejpam-4580	319	36	×	×	PROPN
ejpam-4580	319	37	(	(	PUNCT
ejpam-4580	319	38	ak	ak	PROPN
ejpam-4580	319	39	∑k−1	∑k−1	PROPN
ejpam-4580	319	40	j=0	j=0	PROPN
ejpam-4580	319	41	a	a	DET
ejpam-4580	319	42	jbck−1−j	jbck−1−j	PROPN
ejpam-4580	319	43	0	0	NUM
ejpam-4580	319	44	0	0	NUM
ejpam-4580	319	45	)	)	PUNCT
ejpam-4580	320	1	=	=	PRON
ejpam-4580	320	2	(	(	PUNCT
ejpam-4580	320	3	a∗kdak	a∗kdak	ADV
ejpam-4580	320	4	a∗kd	a∗kd	PROPN
ejpam-4580	320	5	∑k−1	∑k−1	PROPN
ejpam-4580	320	6	j=0	j=0	PROPN
ejpam-4580	320	7	a	a	DET
ejpam-4580	320	8	jbck−1−j	jbck−1−j	PROPN
ejpam-4580	320	9	(	(	PUNCT
ejpam-4580	320	10	∑k−1	∑k−1	X
ejpam-4580	320	11	j=0	j=0	PROPN
ejpam-4580	320	12	a	a	DET
ejpam-4580	320	13	jbck−1−j)∗dak	jbck−1−j)∗dak	NOUN
ejpam-4580	320	14	m	m	NOUN
ejpam-4580	320	15	)	)	PUNCT
ejpam-4580	320	16	,	,	PUNCT
ejpam-4580	321	1	where	where	SCONJ
ejpam-4580	321	2	d	d	NOUN
ejpam-4580	321	3	=	=	SYM
ejpam-4580	321	4	a∗2a2	a∗2a2	PROPN
ejpam-4580	321	5	−	−	NOUN
ejpam-4580	322	1	na∗a	na∗a	PROPN
ejpam-4580	323	1	+	+	CCONJ
ejpam-4580	323	2	i	i	PRON
ejpam-4580	323	3	,	,	PUNCT
ejpam-4580	323	4	m	m	VERB
ejpam-4580	323	5	=	=	PUNCT
ejpam-4580	323	6	(	(	PUNCT
ejpam-4580	323	7	∑k−1	∑k−1	ADP
ejpam-4580	323	8	j=0	j=0	PROPN
ejpam-4580	323	9	a	a	DET
ejpam-4580	323	10	jbck−1−j)∗d	jbck−1−j)∗d	PROPN
ejpam-4580	323	11	∑k−1	∑k−1	X
ejpam-4580	323	12	j=0	j=0	PROPN
ejpam-4580	323	13	a	a	DET
ejpam-4580	323	14	jbck−1−j	jbck−1−j	PROPN
ejpam-4580	323	15	.	.	PUNCT
ejpam-4580	324	1	let	let	VERB
ejpam-4580	324	2	v	v	VERB
ejpam-4580	324	3	=	=	SYM
ejpam-4580	324	4	x⊕	x⊕	PROPN
ejpam-4580	324	5	y	y	PROPN
ejpam-4580	324	6	be	be	AUX
ejpam-4580	324	7	a	a	DET
ejpam-4580	324	8	vector	vector	NOUN
ejpam-4580	324	9	in	in	ADP
ejpam-4580	324	10	h	h	NOUN
ejpam-4580	324	11	=	=	PROPN
ejpam-4580	324	12	t	t	PROPN
ejpam-4580	324	13	k(h)⊕	k(h)⊕	PROPN
ejpam-4580	324	14	kert	kert	PROPN
ejpam-4580	324	15	∗k	∗k	PROPN
ejpam-4580	324	16	,	,	PUNCT
ejpam-4580	324	17	where	where	SCONJ
ejpam-4580	324	18	x	x	PUNCT
ejpam-4580	324	19	∈	∈	PROPN
ejpam-4580	324	20	t	t	PROPN
ejpam-4580	324	21	k(h	k(h	PROPN
ejpam-4580	324	22	)	)	PUNCT
ejpam-4580	324	23	and	and	CCONJ
ejpam-4580	324	24	y	y	PROPN
ejpam-4580	324	25	∈	∈	PROPN
ejpam-4580	324	26	kert	kert	PROPN
ejpam-4580	324	27	∗k	∗k	PROPN
ejpam-4580	324	28	.	.	PUNCT
ejpam-4580	325	1	then	then	ADV
ejpam-4580	325	2	,	,	PUNCT
ejpam-4580	325	3	〈	〈	PROPN
ejpam-4580	325	4	t	t	PROPN
ejpam-4580	325	5	∗k(t	∗k(t	PROPN
ejpam-4580	325	6	∗2	∗2	PROPN
ejpam-4580	325	7	t	t	PROPN
ejpam-4580	325	8	2	2	NUM
ejpam-4580	325	9	−nt	−nt	ADP
ejpam-4580	325	10	∗t	∗t	PROPN
ejpam-4580	325	11	+	+	CCONJ
ejpam-4580	325	12	i)t	i)t	VERB
ejpam-4580	325	13	kv	kv	PROPN
ejpam-4580	325	14	,	,	PUNCT
ejpam-4580	325	15	v	v	ADP
ejpam-4580	325	16	〉	〉	NOUN
ejpam-4580	325	17	=	=	SYM
ejpam-4580	325	18	〈	〈	NOUN
ejpam-4580	325	19	a∗kdakx	a∗kdakx	NOUN
ejpam-4580	325	20	,	,	PUNCT
ejpam-4580	325	21	x	x	SYM
ejpam-4580	325	22	〉	〉	NOUN
ejpam-4580	325	23	+	+	NUM
ejpam-4580	325	24	〈	〈	PROPN
ejpam-4580	325	25	a∗kd	a∗kd	PROPN
ejpam-4580	325	26	k−1∑	k−1∑	PROPN
ejpam-4580	325	27	j=0	j=0	PROPN
ejpam-4580	325	28	ajbck−1−jy	ajbck−1−jy	PROPN
ejpam-4580	325	29	,	,	PUNCT
ejpam-4580	325	30	x	x	SYM
ejpam-4580	325	31	〉	〉	NOUN
ejpam-4580	325	32	+	+	CCONJ
ejpam-4580	325	33	〈	〈	PROPN
ejpam-4580	325	34	(	(	PUNCT
ejpam-4580	325	35	k−1∑	k−1∑	PROPN
ejpam-4580	325	36	j=0	j=0	PROPN
ejpam-4580	325	37	ajbck−1−j)∗dakx	ajbck−1−j)∗dakx	PROPN
ejpam-4580	325	38	,	,	PUNCT
ejpam-4580	325	39	y	y	PROPN
ejpam-4580	325	40	〉	〉	NOUN
ejpam-4580	325	41	+	+	CCONJ
ejpam-4580	325	42	〈	〈	PROPN
ejpam-4580	325	43	(	(	PUNCT
ejpam-4580	325	44	k−1∑	k−1∑	PROPN
ejpam-4580	325	45	j=0	j=0	PROPN
ejpam-4580	325	46	ajbck−1−j)∗d	ajbck−1−j)∗d	PROPN
ejpam-4580	325	47	k−1∑	k−1∑	PROPN
ejpam-4580	325	48	j=0	j=0	PROPN
ejpam-4580	325	49	ajbck−1−jy	ajbck−1−jy	PROPN
ejpam-4580	325	50	,	,	PUNCT
ejpam-4580	325	51	y	y	PROPN
ejpam-4580	325	52	〉	〉	NOUN
ejpam-4580	325	53	=	=	SYM
ejpam-4580	325	54	〈	〈	NOUN
ejpam-4580	325	55	d(akx+	d(akx+	NOUN
ejpam-4580	325	56	k−1∑	k−1∑	PROPN
ejpam-4580	325	57	j=0	j=0	X
ejpam-4580	325	58	ajbck−1−jy	ajbck−1−jy	PROPN
ejpam-4580	325	59	)	)	PUNCT
ejpam-4580	325	60	,	,	PUNCT
ejpam-4580	325	61	akx+	akx+	NOUN
ejpam-4580	325	62	k−1∑	k−1∑	PROPN
ejpam-4580	325	63	j=0	j=0	PROPN
ejpam-4580	325	64	ajbck−1−jy	ajbck−1−jy	PROPN
ejpam-4580	325	65	〉	〉	NOUN
ejpam-4580	325	66	.	.	PUNCT
ejpam-4580	326	1	since	since	SCONJ
ejpam-4580	326	2	a	a	PRON
ejpam-4580	326	3	is	be	AUX
ejpam-4580	326	4	an	an	DET
ejpam-4580	326	5	operator	operator	NOUN
ejpam-4580	326	6	of	of	ADP
ejpam-4580	326	7	the	the	DET
ejpam-4580	326	8	class	class	NOUN
ejpam-4580	326	9	q(n	q(n	PROPN
ejpam-4580	326	10	)	)	PUNCT
ejpam-4580	326	11	,	,	PUNCT
ejpam-4580	326	12	we	we	PRON
ejpam-4580	326	13	have	have	VERB
ejpam-4580	326	14	that	that	DET
ejpam-4580	326	15	d	d	NOUN
ejpam-4580	326	16	=	=	SYM
ejpam-4580	326	17	a∗2a2	a∗2a2	PROPN
ejpam-4580	327	1	−na∗a+	−na∗a+	PRON
ejpam-4580	328	1	i	i	PRON
ejpam-4580	328	2	≥	≥	VERB
ejpam-4580	328	3	0	0	NUM
ejpam-4580	328	4	.	.	PUNCT
ejpam-4580	329	1	therefore	therefore	ADV
ejpam-4580	329	2	,	,	PUNCT
ejpam-4580	329	3	〈	〈	PROPN
ejpam-4580	329	4	t	t	PROPN
ejpam-4580	329	5	∗k(t	∗k(t	PROPN
ejpam-4580	329	6	∗2	∗2	PROPN
ejpam-4580	329	7	t	t	PROPN
ejpam-4580	329	8	2	2	NUM
ejpam-4580	329	9	−nt	−nt	ADP
ejpam-4580	329	10	∗t	∗t	PROPN
ejpam-4580	329	11	+	+	CCONJ
ejpam-4580	329	12	i)t	i)t	VERB
ejpam-4580	329	13	kv	kv	PROPN
ejpam-4580	329	14	,	,	PUNCT
ejpam-4580	329	15	v	v	ADP
ejpam-4580	329	16	〉	〉	NUM
ejpam-4580	329	17	≥	≥	NOUN
ejpam-4580	329	18	0	0	NUM
ejpam-4580	329	19	sh	sh	PROPN
ejpam-4580	329	20	.	.	PROPN
ejpam-4580	329	21	lohaj	lohaj	PROPN
ejpam-4580	329	22	/	/	SYM
ejpam-4580	329	23	eur	eur	PROPN
ejpam-4580	329	24	.	.	PUNCT
ejpam-4580	330	1	j.	j.	PROPN
ejpam-4580	330	2	pure	pure	PROPN
ejpam-4580	330	3	appl	appl	PROPN
ejpam-4580	330	4	.	.	PROPN
ejpam-4580	330	5	math	math	PROPN
ejpam-4580	330	6	,	,	PUNCT
ejpam-4580	330	7	15	15	NUM
ejpam-4580	330	8	(	(	PUNCT
ejpam-4580	330	9	4	4	NUM
ejpam-4580	330	10	)	)	PUNCT
ejpam-4580	330	11	(	(	PUNCT
ejpam-4580	330	12	2022	2022	NUM
ejpam-4580	330	13	)	)	PUNCT
ejpam-4580	330	14	,	,	PUNCT
ejpam-4580	330	15	1836	1836	NUM
ejpam-4580	330	16	-	-	SYM
ejpam-4580	330	17	1853	1853	NUM
ejpam-4580	330	18	1851	1851	NUM
ejpam-4580	330	19	for	for	ADP
ejpam-4580	330	20	all	all	DET
ejpam-4580	330	21	v	v	PROPN
ejpam-4580	330	22	∈	∈	PROPN
ejpam-4580	330	23	h.	h.	NOUN
ejpam-4580	330	24	hence	hence	ADV
ejpam-4580	330	25	,	,	PUNCT
ejpam-4580	330	26	t	t	PROPN
ejpam-4580	330	27	∗k(t	∗k(t	PROPN
ejpam-4580	330	28	∗2	∗2	PROPN
ejpam-4580	330	29	t	t	PROPN
ejpam-4580	330	30	2	2	NUM
ejpam-4580	330	31	−nt	−nt	ADP
ejpam-4580	330	32	∗t	∗t	PROPN
ejpam-4580	330	33	+	+	CCONJ
ejpam-4580	330	34	i)t	i)t	VERB
ejpam-4580	331	1	k	k	X
ejpam-4580	331	2	≥	≥	NOUN
ejpam-4580	331	3	0	0	NUM
ejpam-4580	332	1	so	so	CCONJ
ejpam-4580	332	2	we	we	PRON
ejpam-4580	332	3	have	have	VERB
ejpam-4580	332	4	that	that	DET
ejpam-4580	332	5	t	t	PROPN
ejpam-4580	332	6	is	be	AUX
ejpam-4580	332	7	a	a	DET
ejpam-4580	332	8	k−quasi	k−quasi	PROPN
ejpam-4580	332	9	class	class	NOUN
ejpam-4580	332	10	q(n	q(n	PROPN
ejpam-4580	332	11	)	)	PUNCT
ejpam-4580	332	12	operator	operator	NOUN
ejpam-4580	332	13	.	.	PUNCT
ejpam-4580	333	1	proposition	proposition	NOUN
ejpam-4580	333	2	25	25	NUM
ejpam-4580	333	3	.	.	PUNCT
ejpam-4580	334	1	if	if	SCONJ
ejpam-4580	334	2	t	t	PROPN
ejpam-4580	334	3	k	k	PROPN
ejpam-4580	334	4	does	do	AUX
ejpam-4580	334	5	not	not	PART
ejpam-4580	334	6	have	have	VERB
ejpam-4580	334	7	a	a	DET
ejpam-4580	334	8	dense	dense	ADJ
ejpam-4580	334	9	range	range	NOUN
ejpam-4580	334	10	,	,	PUNCT
ejpam-4580	334	11	then	then	ADV
ejpam-4580	334	12	the	the	DET
ejpam-4580	334	13	following	following	ADJ
ejpam-4580	334	14	statements	statement	NOUN
ejpam-4580	334	15	are	be	AUX
ejpam-4580	334	16	equivalent	equivalent	ADJ
ejpam-4580	334	17	:	:	PUNCT
ejpam-4580	334	18	(	(	PUNCT
ejpam-4580	334	19	i	i	NOUN
ejpam-4580	334	20	)	)	PUNCT
ejpam-4580	334	21	t	t	PROPN
ejpam-4580	335	1	=	=	SYM
ejpam-4580	335	2	(	(	PUNCT
ejpam-4580	335	3	a	a	DET
ejpam-4580	335	4	b	b	NOUN
ejpam-4580	335	5	0	0	NUM
ejpam-4580	335	6	c	c	NOUN
ejpam-4580	335	7	)	)	PUNCT
ejpam-4580	335	8	on	on	ADP
ejpam-4580	335	9	h	h	PROPN
ejpam-4580	335	10	=	=	PROPN
ejpam-4580	335	11	t	t	PROPN
ejpam-4580	335	12	k(h	k(h	PROPN
ejpam-4580	335	13	)	)	PUNCT
ejpam-4580	335	14	⊕	⊕	PROPN
ejpam-4580	335	15	kert	kert	PROPN
ejpam-4580	335	16	∗k	∗k	PROPN
ejpam-4580	335	17	,	,	PUNCT
ejpam-4580	335	18	where	where	SCONJ
ejpam-4580	335	19	a∗2a2	a∗2a2	PROPN
ejpam-4580	335	20	−	−	PROPN
ejpam-4580	335	21	n(aa∗	n(aa∗	NOUN
ejpam-4580	335	22	+	+	CCONJ
ejpam-4580	335	23	bb∗	bb∗	NOUN
ejpam-4580	335	24	)	)	PUNCT
ejpam-4580	336	1	+	+	CCONJ
ejpam-4580	336	2	i	i	PRON
ejpam-4580	336	3	≥	≥	VERB
ejpam-4580	336	4	0	0	NUM
ejpam-4580	336	5	,	,	PUNCT
ejpam-4580	336	6	ck	ck	NOUN
ejpam-4580	336	7	=	=	SYM
ejpam-4580	336	8	o	o	PROPN
ejpam-4580	336	9	and	and	CCONJ
ejpam-4580	336	10	σ(t	σ(t	PROPN
ejpam-4580	336	11	)	)	PUNCT
ejpam-4580	337	1	=	=	SYM
ejpam-4580	337	2	σ(a	σ(a	PROPN
ejpam-4580	337	3	)	)	PUNCT
ejpam-4580	337	4	∪	∪	X
ejpam-4580	337	5	{	{	PUNCT
ejpam-4580	337	6	0	0	NUM
ejpam-4580	337	7	}	}	PUNCT
ejpam-4580	337	8	,	,	PUNCT
ejpam-4580	337	9	b	b	X
ejpam-4580	337	10	is	be	AUX
ejpam-4580	337	11	any	any	DET
ejpam-4580	337	12	operator	operator	NOUN
ejpam-4580	337	13	;	;	PUNCT
ejpam-4580	337	14	(	(	PUNCT
ejpam-4580	337	15	ii	ii	NOUN
ejpam-4580	337	16	)	)	PUNCT
ejpam-4580	337	17	operator	operator	NOUN
ejpam-4580	337	18	t	t	PROPN
ejpam-4580	337	19	is	be	AUX
ejpam-4580	337	20	a	a	DET
ejpam-4580	337	21	k−quasi	k−quasi	PROPN
ejpam-4580	337	22	class	class	NOUN
ejpam-4580	337	23	q∗(n	q∗(n	NOUN
ejpam-4580	337	24	)	)	PUNCT
ejpam-4580	337	25	operator	operator	NOUN
ejpam-4580	337	26	.	.	PUNCT
ejpam-4580	338	1	proof	proof	NOUN
ejpam-4580	338	2	.	.	PUNCT
ejpam-4580	339	1	(	(	PUNCT
ejpam-4580	339	2	1	1	X
ejpam-4580	339	3	)	)	PUNCT
ejpam-4580	339	4	⇒	⇒	NOUN
ejpam-4580	339	5	(	(	PUNCT
ejpam-4580	339	6	2	2	X
ejpam-4580	339	7	)	)	PUNCT
ejpam-4580	339	8	suppose	suppose	VERB
ejpam-4580	339	9	that	that	SCONJ
ejpam-4580	339	10	t	t	NOUN
ejpam-4580	339	11	=	=	PUNCT
ejpam-4580	339	12	(	(	PUNCT
ejpam-4580	339	13	a	a	DET
ejpam-4580	339	14	b	b	NOUN
ejpam-4580	339	15	0	0	NUM
ejpam-4580	339	16	c	c	NOUN
ejpam-4580	339	17	)	)	PUNCT
ejpam-4580	339	18	on	on	ADP
ejpam-4580	339	19	h	h	PROPN
ejpam-4580	339	20	=	=	PROPN
ejpam-4580	339	21	t	t	PROPN
ejpam-4580	339	22	k(h	k(h	PROPN
ejpam-4580	339	23	)	)	PUNCT
ejpam-4580	339	24	⊕	⊕	PROPN
ejpam-4580	339	25	kert	kert	PROPN
ejpam-4580	339	26	∗k	∗k	PROPN
ejpam-4580	339	27	,	,	PUNCT
ejpam-4580	339	28	where	where	SCONJ
ejpam-4580	339	29	a∗2a2	a∗2a2	PROPN
ejpam-4580	339	30	−	−	PROPN
ejpam-4580	339	31	n(aa∗	n(aa∗	NOUN
ejpam-4580	340	1	+	+	NOUN
ejpam-4580	340	2	bb∗	bb∗	NOUN
ejpam-4580	340	3	)	)	PUNCT
ejpam-4580	341	1	+	+	CCONJ
ejpam-4580	341	2	i	i	PRON
ejpam-4580	341	3	≥	≥	VERB
ejpam-4580	341	4	0	0	NUM
ejpam-4580	341	5	and	and	CCONJ
ejpam-4580	341	6	ck	ck	NOUN
ejpam-4580	342	1	=	=	NOUN
ejpam-4580	342	2	o.	o.	PROPN
ejpam-4580	342	3	a	a	DET
ejpam-4580	342	4	simple	simple	ADJ
ejpam-4580	342	5	calculation	calculation	NOUN
ejpam-4580	342	6	shows	show	VERB
ejpam-4580	342	7	that	that	SCONJ
ejpam-4580	342	8	:	:	PUNCT
ejpam-4580	342	9	t	t	NOUN
ejpam-4580	342	10	∗	∗	NOUN
ejpam-4580	342	11	=	=	SYM
ejpam-4580	342	12	(	(	PUNCT
ejpam-4580	342	13	a∗	a∗	ADJ
ejpam-4580	342	14	0	0	NUM
ejpam-4580	342	15	b∗	b∗	ADJ
ejpam-4580	342	16	c∗	c∗	PROPN
ejpam-4580	342	17	)	)	PUNCT
ejpam-4580	342	18	,	,	PUNCT
ejpam-4580	342	19	tt	tt	PROPN
ejpam-4580	342	20	∗	∗	NOUN
ejpam-4580	342	21	=	=	PUNCT
ejpam-4580	342	22	(	(	PUNCT
ejpam-4580	342	23	aa∗	aa∗	X
ejpam-4580	343	1	+	+	ADP
ejpam-4580	343	2	bb∗	bb∗	NOUN
ejpam-4580	343	3	bc∗	bc∗	ADJ
ejpam-4580	343	4	cb∗	cb∗	ADJ
ejpam-4580	343	5	cc∗	cc∗	NOUN
ejpam-4580	343	6	)	)	PUNCT
ejpam-4580	343	7	,	,	PUNCT
ejpam-4580	343	8	t	t	PROPN
ejpam-4580	343	9	∗k	∗k	NOUN
ejpam-4580	343	10	=	=	SYM
ejpam-4580	343	11	(	(	PUNCT
ejpam-4580	343	12	a∗k	a∗k	PROPN
ejpam-4580	343	13	0	0	NUM
ejpam-4580	343	14	(	(	PUNCT
ejpam-4580	343	15	∑k−1	∑k−1	X
ejpam-4580	343	16	j=0	j=0	PROPN
ejpam-4580	343	17	a	a	DET
ejpam-4580	343	18	jbck−1−j)∗	jbck−1−j)∗	PROPN
ejpam-4580	343	19	0	0	NUM
ejpam-4580	343	20	)	)	PUNCT
ejpam-4580	343	21	,	,	PUNCT
ejpam-4580	343	22	t	t	PROPN
ejpam-4580	343	23	k	k	PROPN
ejpam-4580	343	24	=	=	PRON
ejpam-4580	343	25	(	(	PUNCT
ejpam-4580	343	26	ak	ak	PROPN
ejpam-4580	343	27	(	(	PUNCT
ejpam-4580	343	28	∑k−1	∑k−1	PROPN
ejpam-4580	343	29	j=0	j=0	PROPN
ejpam-4580	343	30	a	a	DET
ejpam-4580	343	31	jbck−1−j	jbck−1−j	PROPN
ejpam-4580	343	32	)	)	PUNCT
ejpam-4580	343	33	0	0	NUM
ejpam-4580	343	34	0	0	NUM
ejpam-4580	343	35	)	)	PUNCT
ejpam-4580	343	36	,	,	PUNCT
ejpam-4580	343	37	then	then	ADV
ejpam-4580	343	38	,	,	PUNCT
ejpam-4580	343	39	we	we	PRON
ejpam-4580	343	40	have	have	VERB
ejpam-4580	343	41	t	t	PROPN
ejpam-4580	343	42	∗k(t	∗k(t	PROPN
ejpam-4580	343	43	∗2	∗2	PROPN
ejpam-4580	343	44	t	t	PROPN
ejpam-4580	343	45	2	2	NUM
ejpam-4580	343	46	−ntt	−ntt	NOUN
ejpam-4580	343	47	∗	∗	NOUN
ejpam-4580	343	48	+	+	CCONJ
ejpam-4580	343	49	i)t	i)t	NOUN
ejpam-4580	343	50	k	k	X
ejpam-4580	344	1	=	=	PUNCT
ejpam-4580	344	2	(	(	PUNCT
ejpam-4580	344	3	a∗kdak	a∗kdak	ADV
ejpam-4580	344	4	a∗kd	a∗kd	PROPN
ejpam-4580	344	5	∑k−1	∑k−1	PROPN
ejpam-4580	344	6	j=0	j=0	PROPN
ejpam-4580	344	7	a	a	DET
ejpam-4580	344	8	jbck−1−j	jbck−1−j	PROPN
ejpam-4580	344	9	(	(	PUNCT
ejpam-4580	344	10	∑k−1	∑k−1	X
ejpam-4580	344	11	j=0	j=0	PROPN
ejpam-4580	344	12	a	a	DET
ejpam-4580	344	13	jbck−1−j)∗dak	jbck−1−j)∗dak	NOUN
ejpam-4580	344	14	m	m	NOUN
ejpam-4580	344	15	)	)	PUNCT
ejpam-4580	344	16	,	,	PUNCT
ejpam-4580	344	17	where	where	SCONJ
ejpam-4580	344	18	d	d	NOUN
ejpam-4580	344	19	=	=	SYM
ejpam-4580	344	20	a∗2a2	a∗2a2	PROPN
ejpam-4580	344	21	−n(aa∗	−n(aa∗	X
ejpam-4580	344	22	+	+	CCONJ
ejpam-4580	344	23	bb∗	bb∗	NOUN
ejpam-4580	344	24	)	)	PUNCT
ejpam-4580	344	25	+	+	CCONJ
ejpam-4580	344	26	i	i	PRON
ejpam-4580	344	27	,	,	PUNCT
ejpam-4580	344	28	m	m	VERB
ejpam-4580	344	29	=	=	PUNCT
ejpam-4580	344	30	(	(	PUNCT
ejpam-4580	344	31	∑k−1	∑k−1	ADP
ejpam-4580	344	32	j=0	j=0	PROPN
ejpam-4580	344	33	a	a	DET
ejpam-4580	344	34	jbck−1−j)∗d	jbck−1−j)∗d	PROPN
ejpam-4580	344	35	∑k−1	∑k−1	X
ejpam-4580	344	36	j=0	j=0	PROPN
ejpam-4580	344	37	a	a	DET
ejpam-4580	344	38	jbck−1−j	jbck−1−j	PROPN
ejpam-4580	344	39	.	.	PUNCT
ejpam-4580	345	1	let	let	VERB
ejpam-4580	345	2	v	v	VERB
ejpam-4580	345	3	=	=	SYM
ejpam-4580	345	4	x	x	SYM
ejpam-4580	345	5	⊕	⊕	NOUN
ejpam-4580	345	6	y	y	PROPN
ejpam-4580	345	7	be	be	AUX
ejpam-4580	345	8	a	a	DET
ejpam-4580	345	9	vector	vector	NOUN
ejpam-4580	345	10	in	in	ADP
ejpam-4580	345	11	h	h	NOUN
ejpam-4580	345	12	=	=	PROPN
ejpam-4580	345	13	t	t	PROPN
ejpam-4580	345	14	k(h	k(h	PROPN
ejpam-4580	345	15	)	)	PUNCT
ejpam-4580	345	16	⊕	⊕	PROPN
ejpam-4580	345	17	kert	kert	PROPN
ejpam-4580	345	18	∗k	∗k	NOUN
ejpam-4580	345	19	,	,	PUNCT
ejpam-4580	345	20	where	where	SCONJ
ejpam-4580	345	21	x	x	PUNCT
ejpam-4580	345	22	∈	∈	PROPN
ejpam-4580	345	23	t	t	PROPN
ejpam-4580	345	24	k(h	k(h	PROPN
ejpam-4580	345	25	)	)	PUNCT
ejpam-4580	345	26	and	and	CCONJ
ejpam-4580	345	27	y	y	PROPN
ejpam-4580	345	28	∈	∈	PROPN
ejpam-4580	345	29	kert	kert	PROPN
ejpam-4580	345	30	∗k	∗k	PROPN
ejpam-4580	345	31	.	.	PUNCT
ejpam-4580	346	1	then	then	ADV
ejpam-4580	346	2	,	,	PUNCT
ejpam-4580	346	3	〈	〈	PROPN
ejpam-4580	346	4	t	t	PROPN
ejpam-4580	346	5	∗k(t	∗k(t	PROPN
ejpam-4580	346	6	∗2	∗2	PROPN
ejpam-4580	346	7	t	t	PROPN
ejpam-4580	346	8	2	2	NUM
ejpam-4580	346	9	−ntt	−ntt	NOUN
ejpam-4580	346	10	∗	∗	NOUN
ejpam-4580	346	11	+	+	CCONJ
ejpam-4580	346	12	i)t	i)t	X
ejpam-4580	346	13	kv	kv	PROPN
ejpam-4580	346	14	,	,	PUNCT
ejpam-4580	346	15	v	v	ADP
ejpam-4580	346	16	〉	〉	NOUN
ejpam-4580	346	17	=	=	SYM
ejpam-4580	346	18	〈	〈	NOUN
ejpam-4580	346	19	a∗kdakx	a∗kdakx	NOUN
ejpam-4580	346	20	,	,	PUNCT
ejpam-4580	346	21	x	x	SYM
ejpam-4580	346	22	〉	〉	NOUN
ejpam-4580	346	23	sh	sh	PROPN
ejpam-4580	346	24	.	.	PROPN
ejpam-4580	346	25	lohaj	lohaj	PROPN
ejpam-4580	346	26	/	/	SYM
ejpam-4580	346	27	eur	eur	PROPN
ejpam-4580	346	28	.	.	PUNCT
ejpam-4580	347	1	j.	j.	PROPN
ejpam-4580	347	2	pure	pure	PROPN
ejpam-4580	347	3	appl	appl	PROPN
ejpam-4580	347	4	.	.	PROPN
ejpam-4580	347	5	math	math	PROPN
ejpam-4580	347	6	,	,	PUNCT
ejpam-4580	347	7	15	15	NUM
ejpam-4580	347	8	(	(	PUNCT
ejpam-4580	347	9	4	4	NUM
ejpam-4580	347	10	)	)	PUNCT
ejpam-4580	347	11	(	(	PUNCT
ejpam-4580	347	12	2022	2022	NUM
ejpam-4580	347	13	)	)	PUNCT
ejpam-4580	347	14	,	,	PUNCT
ejpam-4580	347	15	1836	1836	NUM
ejpam-4580	347	16	-	-	SYM
ejpam-4580	347	17	1853	1853	NUM
ejpam-4580	347	18	1852	1852	NUM
ejpam-4580	348	1	+	+	CCONJ
ejpam-4580	348	2	〈	〈	PROPN
ejpam-4580	348	3	a∗kd	a∗kd	PROPN
ejpam-4580	348	4	k−1∑	k−1∑	PROPN
ejpam-4580	348	5	j=0	j=0	PROPN
ejpam-4580	348	6	ajbck−1−jy	ajbck−1−jy	PROPN
ejpam-4580	348	7	,	,	PUNCT
ejpam-4580	348	8	x	x	SYM
ejpam-4580	348	9	〉	〉	NOUN
ejpam-4580	348	10	+	+	CCONJ
ejpam-4580	348	11	〈	〈	PROPN
ejpam-4580	348	12	(	(	PUNCT
ejpam-4580	348	13	k−1∑	k−1∑	PROPN
ejpam-4580	348	14	j=0	j=0	PROPN
ejpam-4580	348	15	ajbck−1−j)∗dakx	ajbck−1−j)∗dakx	PROPN
ejpam-4580	348	16	,	,	PUNCT
ejpam-4580	348	17	y	y	PROPN
ejpam-4580	348	18	〉	〉	NOUN
ejpam-4580	348	19	+	+	CCONJ
ejpam-4580	348	20	〈	〈	PROPN
ejpam-4580	348	21	(	(	PUNCT
ejpam-4580	348	22	k−1∑	k−1∑	PROPN
ejpam-4580	348	23	j=0	j=0	PROPN
ejpam-4580	348	24	ajbck−1−j)∗d	ajbck−1−j)∗d	PROPN
ejpam-4580	348	25	k−1∑	k−1∑	PROPN
ejpam-4580	348	26	j=0	j=0	PROPN
ejpam-4580	348	27	ajbck−1−jy	ajbck−1−jy	PROPN
ejpam-4580	348	28	,	,	PUNCT
ejpam-4580	348	29	y	y	PROPN
ejpam-4580	348	30	〉	〉	NOUN
ejpam-4580	348	31	=	=	SYM
ejpam-4580	348	32	〈	〈	NOUN
ejpam-4580	348	33	d(akx+	d(akx+	NOUN
ejpam-4580	348	34	k−1∑	k−1∑	PROPN
ejpam-4580	348	35	j=0	j=0	X
ejpam-4580	348	36	ajbck−1−jy	ajbck−1−jy	PROPN
ejpam-4580	348	37	)	)	PUNCT
ejpam-4580	348	38	,	,	PUNCT
ejpam-4580	348	39	akx+	akx+	NOUN
ejpam-4580	348	40	k−1∑	k−1∑	PROPN
ejpam-4580	348	41	j=0	j=0	PROPN
ejpam-4580	348	42	ajbck−1−jy	ajbck−1−jy	PROPN
ejpam-4580	348	43	〉	〉	NOUN
ejpam-4580	348	44	.	.	PUNCT
ejpam-4580	349	1	since	since	SCONJ
ejpam-4580	349	2	d	d	PROPN
ejpam-4580	349	3	=	=	SYM
ejpam-4580	349	4	a∗2a2	a∗2a2	PROPN
ejpam-4580	349	5	−n(aa∗	−n(aa∗	X
ejpam-4580	350	1	+	+	NOUN
ejpam-4580	350	2	bb∗	bb∗	NOUN
ejpam-4580	350	3	)	)	PUNCT
ejpam-4580	351	1	+	+	CCONJ
ejpam-4580	351	2	i	i	PRON
ejpam-4580	351	3	≥	≥	VERB
ejpam-4580	351	4	0	0	NUM
ejpam-4580	351	5	,	,	PUNCT
ejpam-4580	351	6	we	we	PRON
ejpam-4580	351	7	have	have	VERB
ejpam-4580	351	8	〈	〈	PROPN
ejpam-4580	351	9	t	t	PROPN
ejpam-4580	351	10	∗k(t	∗k(t	PROPN
ejpam-4580	351	11	∗2	∗2	PROPN
ejpam-4580	351	12	t	t	PROPN
ejpam-4580	351	13	2	2	NUM
ejpam-4580	351	14	−ntt	−ntt	NOUN
ejpam-4580	351	15	∗	∗	NOUN
ejpam-4580	351	16	+	+	CCONJ
ejpam-4580	351	17	i)t	i)t	X
ejpam-4580	351	18	kv	kv	PROPN
ejpam-4580	351	19	,	,	PUNCT
ejpam-4580	351	20	v	v	ADP
ejpam-4580	351	21	〉	〉	NOUN
ejpam-4580	351	22	≥	≥	NOUN
ejpam-4580	351	23	0	0	NUM
ejpam-4580	351	24	for	for	ADP
ejpam-4580	351	25	all	all	DET
ejpam-4580	351	26	v	v	NOUN
ejpam-4580	351	27	∈	∈	PROPN
ejpam-4580	351	28	h.	h.	NOUN
ejpam-4580	351	29	hence	hence	ADV
ejpam-4580	351	30	,	,	PUNCT
ejpam-4580	351	31	t	t	PROPN
ejpam-4580	351	32	∗k(t	∗k(t	PROPN
ejpam-4580	351	33	∗2	∗2	PROPN
ejpam-4580	351	34	t	t	PROPN
ejpam-4580	351	35	2	2	NUM
ejpam-4580	351	36	−ntt	−ntt	NOUN
ejpam-4580	351	37	∗	∗	NOUN
ejpam-4580	351	38	+	+	CCONJ
ejpam-4580	351	39	i)t	i)t	NOUN
ejpam-4580	352	1	k	k	X
ejpam-4580	352	2	≥	≥	NOUN
ejpam-4580	352	3	0	0	NUM
ejpam-4580	353	1	so	so	CCONJ
ejpam-4580	353	2	we	we	PRON
ejpam-4580	353	3	have	have	VERB
ejpam-4580	353	4	that	that	DET
ejpam-4580	353	5	t	t	PROPN
ejpam-4580	353	6	is	be	AUX
ejpam-4580	353	7	a	a	DET
ejpam-4580	353	8	k−quasi	k−quasi	PROPN
ejpam-4580	353	9	class	class	NOUN
ejpam-4580	353	10	q∗(n	q∗(n	NOUN
ejpam-4580	353	11	)	)	PUNCT
ejpam-4580	353	12	operator	operator	NOUN
ejpam-4580	353	13	.	.	PUNCT
ejpam-4580	354	1	(	(	PUNCT
ejpam-4580	354	2	2	2	X
ejpam-4580	354	3	)	)	PUNCT
ejpam-4580	354	4	⇒	⇒	NOUN
ejpam-4580	354	5	(	(	PUNCT
ejpam-4580	354	6	1	1	X
ejpam-4580	354	7	)	)	PUNCT
ejpam-4580	354	8	suppose	suppose	VERB
ejpam-4580	354	9	that	that	SCONJ
ejpam-4580	354	10	t	t	PROPN
ejpam-4580	354	11	∈	∈	PROPN
ejpam-4580	354	12	l(h	l(h	PROPN
ejpam-4580	354	13	)	)	PUNCT
ejpam-4580	354	14	is	be	AUX
ejpam-4580	354	15	an	an	DET
ejpam-4580	354	16	operator	operator	NOUN
ejpam-4580	354	17	of	of	ADP
ejpam-4580	354	18	k−quasi	k−quasi	PROPN
ejpam-4580	354	19	class	class	NOUN
ejpam-4580	354	20	q∗(n	q∗(n	PROPN
ejpam-4580	354	21	)	)	PUNCT
ejpam-4580	354	22	.	.	PUNCT
ejpam-4580	355	1	since	since	SCONJ
ejpam-4580	355	2	that	that	PRON
ejpam-4580	355	3	t	t	PROPN
ejpam-4580	355	4	k	k	PROPN
ejpam-4580	355	5	does	do	AUX
ejpam-4580	355	6	not	not	PART
ejpam-4580	355	7	have	have	VERB
ejpam-4580	355	8	dense	dense	ADJ
ejpam-4580	355	9	range	range	NOUN
ejpam-4580	355	10	,	,	PUNCT
ejpam-4580	355	11	we	we	PRON
ejpam-4580	355	12	can	can	AUX
ejpam-4580	355	13	represent	represent	VERB
ejpam-4580	355	14	t	t	PROPN
ejpam-4580	355	15	as	as	ADP
ejpam-4580	355	16	the	the	DET
ejpam-4580	355	17	upper	upper	ADJ
ejpam-4580	355	18	triangular	triangular	NOUN
ejpam-4580	355	19	matrix	matrix	NOUN
ejpam-4580	355	20	:	:	PUNCT
ejpam-4580	355	21	t	t	NOUN
ejpam-4580	355	22	=	=	SYM
ejpam-4580	355	23	(	(	PUNCT
ejpam-4580	355	24	a	a	DET
ejpam-4580	355	25	b	b	NOUN
ejpam-4580	355	26	0	0	NUM
ejpam-4580	355	27	c	c	NOUN
ejpam-4580	355	28	)	)	PUNCT
ejpam-4580	355	29	on	on	ADP
ejpam-4580	355	30	h	h	NOUN
ejpam-4580	355	31	=	=	PROPN
ejpam-4580	355	32	t	t	PROPN
ejpam-4580	355	33	k(h)⊕	k(h)⊕	PROPN
ejpam-4580	355	34	kert	kert	PROPN
ejpam-4580	355	35	∗k	∗k	PROPN
ejpam-4580	355	36	.	.	PUNCT
ejpam-4580	356	1	since	since	SCONJ
ejpam-4580	356	2	t	t	PROPN
ejpam-4580	356	3	is	be	AUX
ejpam-4580	356	4	an	an	DET
ejpam-4580	356	5	operator	operator	NOUN
ejpam-4580	356	6	of	of	ADP
ejpam-4580	356	7	k−quasi	k−quasi	PROPN
ejpam-4580	356	8	class	class	NOUN
ejpam-4580	356	9	q∗(n	q∗(n	PROPN
ejpam-4580	356	10	)	)	PUNCT
ejpam-4580	356	11	,	,	PUNCT
ejpam-4580	356	12	we	we	PRON
ejpam-4580	356	13	have	have	VERB
ejpam-4580	356	14	t	t	PROPN
ejpam-4580	356	15	∗k(t	∗k(t	PROPN
ejpam-4580	356	16	∗2	∗2	PROPN
ejpam-4580	356	17	t	t	PROPN
ejpam-4580	356	18	2	2	NUM
ejpam-4580	356	19	−ntt	−ntt	NOUN
ejpam-4580	356	20	∗	∗	NOUN
ejpam-4580	356	21	+	+	CCONJ
ejpam-4580	356	22	i)t	i)t	NOUN
ejpam-4580	357	1	k	k	X
ejpam-4580	357	2	≥	≥	NOUN
ejpam-4580	357	3	0	0	NUM
ejpam-4580	357	4	.	.	PUNCT
ejpam-4580	358	1	let	let	VERB
ejpam-4580	358	2	p	p	PRON
ejpam-4580	358	3	be	be	AUX
ejpam-4580	358	4	the	the	DET
ejpam-4580	358	5	projection	projection	NOUN
ejpam-4580	358	6	onto	onto	ADP
ejpam-4580	358	7	t	t	PROPN
ejpam-4580	358	8	k(h	k(h	PROPN
ejpam-4580	358	9	)	)	PUNCT
ejpam-4580	358	10	.	.	PUNCT
ejpam-4580	359	1	than	than	SCONJ
ejpam-4580	359	2	we	we	PRON
ejpam-4580	359	3	have	have	VERB
ejpam-4580	359	4	p	p	PROPN
ejpam-4580	359	5	(	(	PUNCT
ejpam-4580	359	6	t	t	PROPN
ejpam-4580	359	7	∗2	∗2	PROPN
ejpam-4580	359	8	t	t	PROPN
ejpam-4580	359	9	2	2	NUM
ejpam-4580	359	10	−ntt	−ntt	NOUN
ejpam-4580	359	11	∗	∗	NOUN
ejpam-4580	359	12	+	+	CCONJ
ejpam-4580	359	13	i)p	i)p	ADJ
ejpam-4580	359	14	≥	≥	NOUN
ejpam-4580	359	15	0	0	NUM
ejpam-4580	359	16	.	.	PUNCT
ejpam-4580	360	1	therefore	therefore	ADV
ejpam-4580	360	2	,	,	PUNCT
ejpam-4580	360	3	a∗2a2	a∗2a2	PROPN
ejpam-4580	360	4	−n(aa∗	−n(aa∗	X
ejpam-4580	361	1	+	+	ADJ
ejpam-4580	361	2	bb∗	bb∗	NOUN
ejpam-4580	361	3	)	)	PUNCT
ejpam-4580	362	1	+	+	CCONJ
ejpam-4580	362	2	i	i	PRON
ejpam-4580	362	3	≥	≥	VERB
ejpam-4580	362	4	0	0	NUM
ejpam-4580	362	5	.	.	PUNCT
ejpam-4580	363	1	on	on	ADP
ejpam-4580	363	2	the	the	DET
ejpam-4580	363	3	other	other	ADJ
ejpam-4580	363	4	hand	hand	NOUN
ejpam-4580	363	5	,	,	PUNCT
ejpam-4580	363	6	for	for	ADP
ejpam-4580	363	7	any	any	DET
ejpam-4580	363	8	x	x	SYM
ejpam-4580	363	9	=	=	SYM
ejpam-4580	363	10	(	(	PUNCT
ejpam-4580	363	11	x1	x1	PROPN
ejpam-4580	363	12	,	,	PUNCT
ejpam-4580	363	13	x2	x2	PROPN
ejpam-4580	363	14	)	)	PUNCT
ejpam-4580	363	15	∈	∈	PROPN
ejpam-4580	363	16	h	h	NOUN
ejpam-4580	363	17	,	,	PUNCT
ejpam-4580	363	18	we	we	PRON
ejpam-4580	363	19	have	have	VERB
ejpam-4580	363	20	⟨ckx2	⟨ckx2	PROPN
ejpam-4580	363	21	,	,	PUNCT
ejpam-4580	363	22	x2⟩	x2⟩	PUNCT
ejpam-4580	364	1	=	=	SYM
ejpam-4580	364	2	⟨t	⟨t	X
ejpam-4580	364	3	k(i	k(i	PROPN
ejpam-4580	364	4	−	−	PROPN
ejpam-4580	364	5	p	p	NOUN
ejpam-4580	364	6	)	)	PUNCT
ejpam-4580	364	7	x	x	NOUN
ejpam-4580	364	8	,	,	PUNCT
ejpam-4580	364	9	(	(	PUNCT
ejpam-4580	364	10	i	i	PRON
ejpam-4580	364	11	−	−	PROPN
ejpam-4580	364	12	p	p	NOUN
ejpam-4580	364	13	)	)	PUNCT
ejpam-4580	364	14	x⟩	x⟩	PUNCT
ejpam-4580	365	1	=	=	SYM
ejpam-4580	365	2	⟨(i	⟨(i	PROPN
ejpam-4580	366	1	−	−	PROPN
ejpam-4580	366	2	p	p	PROPN
ejpam-4580	366	3	)	)	PUNCT
ejpam-4580	366	4	x	x	PROPN
ejpam-4580	366	5	,	,	PUNCT
ejpam-4580	366	6	t	t	PROPN
ejpam-4580	366	7	∗k(i	∗k(i	PROPN
ejpam-4580	366	8	−	−	PROPN
ejpam-4580	366	9	p	p	NOUN
ejpam-4580	366	10	)	)	PUNCT
ejpam-4580	366	11	x⟩	x⟩	PUNCT
ejpam-4580	367	1	=	=	SYM
ejpam-4580	367	2	0	0	PROPN
ejpam-4580	367	3	,	,	PUNCT
ejpam-4580	367	4	which	which	PRON
ejpam-4580	367	5	implies	imply	VERB
ejpam-4580	367	6	ck	ck	PROPN
ejpam-4580	367	7	=	=	SYM
ejpam-4580	367	8	0	0	PROPN
ejpam-4580	367	9	.	.	PUNCT
ejpam-4580	368	1	since	since	SCONJ
ejpam-4580	368	2	σ(a)∪σ(c	σ(a)∪σ(c	NUM
ejpam-4580	368	3	)	)	PUNCT
ejpam-4580	368	4	=	=	SYM
ejpam-4580	368	5	σ(t	σ(t	PROPN
ejpam-4580	368	6	)	)	PUNCT
ejpam-4580	368	7	∪ϑ	∪ϑ	PROPN
ejpam-4580	368	8	,	,	PUNCT
ejpam-4580	368	9	where	where	SCONJ
ejpam-4580	368	10	ϑ	ϑ	PROPN
ejpam-4580	368	11	is	be	AUX
ejpam-4580	368	12	the	the	DET
ejpam-4580	368	13	union	union	NOUN
ejpam-4580	368	14	of	of	ADP
ejpam-4580	368	15	the	the	DET
ejpam-4580	368	16	holes	hole	NOUN
ejpam-4580	368	17	in	in	ADP
ejpam-4580	368	18	σ(t	σ(t	PROPN
ejpam-4580	368	19	)	)	PUNCT
ejpam-4580	368	20	,	,	PUNCT
ejpam-4580	368	21	which	which	PRON
ejpam-4580	368	22	happen	happen	VERB
ejpam-4580	368	23	to	to	PART
ejpam-4580	368	24	be	be	AUX
ejpam-4580	368	25	a	a	DET
ejpam-4580	368	26	subset	subset	NOUN
ejpam-4580	368	27	of	of	ADP
ejpam-4580	368	28	σ(a	σ(a	PROPN
ejpam-4580	368	29	)	)	PUNCT
ejpam-4580	368	30	∩	∩	NOUN
ejpam-4580	368	31	σ(c	σ(c	PROPN
ejpam-4580	368	32	)	)	PUNCT
ejpam-4580	368	33	by	by	ADP
ejpam-4580	368	34	[	[	X
ejpam-4580	368	35	3	3	NUM
ejpam-4580	368	36	,	,	PUNCT
ejpam-4580	368	37	corollary	corollary	ADJ
ejpam-4580	368	38	7	7	NUM
ejpam-4580	368	39	]	]	PUNCT
ejpam-4580	368	40	and	and	CCONJ
ejpam-4580	368	41	σ(a	σ(a	PROPN
ejpam-4580	368	42	)	)	PUNCT
ejpam-4580	368	43	∩	∩	NOUN
ejpam-4580	368	44	σ(c	σ(c	PROPN
ejpam-4580	368	45	)	)	PUNCT
ejpam-4580	368	46	has	have	VERB
ejpam-4580	368	47	no	no	DET
ejpam-4580	368	48	interior	interior	ADJ
ejpam-4580	368	49	points	point	NOUN
ejpam-4580	368	50	,	,	PUNCT
ejpam-4580	368	51	then	then	ADV
ejpam-4580	368	52	σ(t	σ(t	X
ejpam-4580	368	53	)	)	PUNCT
ejpam-4580	369	1	=	=	SYM
ejpam-4580	369	2	σ(a	σ(a	PROPN
ejpam-4580	369	3	)	)	PUNCT
ejpam-4580	369	4	∪	∪	ADP
ejpam-4580	369	5	σ(c	σ(c	PROPN
ejpam-4580	369	6	)	)	PUNCT
ejpam-4580	369	7	=	=	SYM
ejpam-4580	370	1	σ(a	σ(a	PROPN
ejpam-4580	370	2	)	)	PUNCT
ejpam-4580	370	3	∪	∪	NOUN
ejpam-4580	370	4	{	{	PUNCT
ejpam-4580	370	5	0	0	NUM
ejpam-4580	370	6	}	}	PUNCT
ejpam-4580	370	7	.	.	PUNCT
ejpam-4580	371	1	references	reference	NOUN
ejpam-4580	371	2	1853	1853	NUM
ejpam-4580	371	3	corollary	corollary	ADJ
ejpam-4580	371	4	1	1	NUM
ejpam-4580	371	5	.	.	PUNCT
ejpam-4580	372	1	let	let	VERB
ejpam-4580	372	2	t	t	PROPN
ejpam-4580	372	3	∈	∈	PROPN
ejpam-4580	372	4	l(h	l(h	PROPN
ejpam-4580	372	5	)	)	PUNCT
ejpam-4580	372	6	be	be	AUX
ejpam-4580	372	7	a	a	DET
ejpam-4580	372	8	k−quasi	k−quasi	NOUN
ejpam-4580	372	9	class	class	NOUN
ejpam-4580	372	10	q∗(n	q∗(n	NOUN
ejpam-4580	372	11	)	)	PUNCT
ejpam-4580	372	12	operator	operator	NOUN
ejpam-4580	372	13	,	,	PUNCT
ejpam-4580	372	14	the	the	DET
ejpam-4580	372	15	range	range	NOUN
ejpam-4580	372	16	of	of	ADP
ejpam-4580	372	17	t	t	PROPN
ejpam-4580	372	18	k	k	PROPN
ejpam-4580	372	19	not	not	PART
ejpam-4580	372	20	to	to	PART
ejpam-4580	372	21	be	be	AUX
ejpam-4580	372	22	dense	dense	ADJ
ejpam-4580	372	23	,	,	PUNCT
ejpam-4580	372	24	then	then	ADV
ejpam-4580	372	25	t	t	PROPN
ejpam-4580	372	26	=	=	PUNCT
ejpam-4580	372	27	(	(	PUNCT
ejpam-4580	372	28	a	a	DET
ejpam-4580	372	29	b	b	X
ejpam-4580	372	30	o	o	X
ejpam-4580	372	31	c	c	NOUN
ejpam-4580	372	32	)	)	PUNCT
ejpam-4580	372	33	on	on	ADP
ejpam-4580	372	34	h	h	NOUN
ejpam-4580	372	35	=	=	PROPN
ejpam-4580	372	36	t	t	PROPN
ejpam-4580	372	37	k(h)⊕	k(h)⊕	PROPN
ejpam-4580	372	38	kert	kert	PROPN
ejpam-4580	372	39	∗k	∗k	PROPN
ejpam-4580	372	40	.	.	PUNCT
ejpam-4580	373	1	where	where	SCONJ
ejpam-4580	373	2	a	a	PRON
ejpam-4580	373	3	is	be	AUX
ejpam-4580	373	4	an	an	DET
ejpam-4580	373	5	operator	operator	NOUN
ejpam-4580	373	6	of	of	ADP
ejpam-4580	373	7	the	the	DET
ejpam-4580	373	8	class	class	NOUN
ejpam-4580	373	9	q∗(n	q∗(n	PROPN
ejpam-4580	373	10	)	)	PUNCT
ejpam-4580	373	11	on	on	ADP
ejpam-4580	373	12	t	t	PROPN
ejpam-4580	373	13	k(h	k(h	PROPN
ejpam-4580	373	14	)	)	PUNCT
ejpam-4580	373	15	,	,	PUNCT
ejpam-4580	373	16	ck	ck	NOUN
ejpam-4580	373	17	=	=	NOUN
ejpam-4580	373	18	o.	o.	NOUN
ejpam-4580	373	19	references	reference	NOUN
ejpam-4580	374	1	[	[	X
ejpam-4580	374	2	1	1	NUM
ejpam-4580	374	3	]	]	PUNCT
ejpam-4580	374	4	a.	a.	NOUN
ejpam-4580	374	5	aluthge	aluthge	PROPN
ejpam-4580	374	6	.	.	PUNCT
ejpam-4580	375	1	on	on	ADP
ejpam-4580	375	2	p	p	PROPN
ejpam-4580	375	3	-	-	PUNCT
ejpam-4580	375	4	hyponormal	hyponormal	ADJ
ejpam-4580	375	5	operators	operator	NOUN
ejpam-4580	375	6	for	for	ADP
ejpam-4580	375	7	0	0	NUM
ejpam-4580	375	8	<	<	X
ejpam-4580	375	9	p	p	X
ejpam-4580	375	10	<	<	X
ejpam-4580	375	11	1	1	NUM
ejpam-4580	375	12	,	,	PUNCT
ejpam-4580	375	13	integral	integral	ADJ
ejpam-4580	375	14	equations	equation	NOUN
ejpam-4580	375	15	operator	operator	NOUN
ejpam-4580	375	16	theory	theory	NOUN
ejpam-4580	375	17	.	.	PUNCT
ejpam-4580	376	1	springer	springer	PROPN
ejpam-4580	376	2	link	link	PROPN
ejpam-4580	376	3	,	,	PUNCT
ejpam-4580	376	4	13:307–315	13:307–315	NUM
ejpam-4580	376	5	,	,	PUNCT
ejpam-4580	376	6	1990	1990	NUM
ejpam-4580	376	7	.	.	PUNCT
ejpam-4580	377	1	[	[	X
ejpam-4580	377	2	2	2	X
ejpam-4580	377	3	]	]	PUNCT
ejpam-4580	377	4	f.	f.	PROPN
ejpam-4580	377	5	gao	gao	PROPN
ejpam-4580	377	6	and	and	CCONJ
ejpam-4580	377	7	x.	x.	NOUN
ejpam-4580	377	8	fang	fang	PROPN
ejpam-4580	377	9	.	.	PUNCT
ejpam-4580	378	1	on	on	ADP
ejpam-4580	378	2	k−quasi	k−quasi	PROPN
ejpam-4580	378	3	-	-	PUNCT
ejpam-4580	378	4	class	class	NOUN
ejpam-4580	378	5	a	a	DET
ejpam-4580	378	6	operators	operator	NOUN
ejpam-4580	378	7	.	.	PUNCT
ejpam-4580	379	1	journal	journal	PROPN
ejpam-4580	379	2	of	of	ADP
ejpam-4580	379	3	inequalities	inequality	NOUN
ejpam-4580	379	4	and	and	CCONJ
ejpam-4580	379	5	applications	application	NOUN
ejpam-4580	379	6	,	,	PUNCT
ejpam-4580	379	7	pages	page	NOUN
ejpam-4580	379	8	1–10	1–10	NOUN
ejpam-4580	379	9	,	,	PUNCT
ejpam-4580	379	10	2009	2009	NUM
ejpam-4580	379	11	.	.	PUNCT
ejpam-4580	380	1	[	[	X
ejpam-4580	380	2	3	3	X
ejpam-4580	380	3	]	]	PUNCT
ejpam-4580	380	4	j.	j.	PROPN
ejpam-4580	380	5	k.	k.	PROPN
ejpam-4580	380	6	han	han	PROPN
ejpam-4580	380	7	h.	h.	PROPN
ejpam-4580	380	8	y.	y.	PROPN
ejpam-4580	380	9	lee	lee	PROPN
ejpam-4580	380	10	and	and	CCONJ
ejpam-4580	380	11	w.	w.	PROPN
ejpam-4580	380	12	y.	y.	PROPN
ejpam-4580	380	13	lee	lee	PROPN
ejpam-4580	380	14	.	.	PUNCT
ejpam-4580	380	15	invertible	invertible	ADJ
ejpam-4580	380	16	completions	completion	NOUN
ejpam-4580	380	17	of	of	ADP
ejpam-4580	380	18	2x2	2x2	NUM
ejpam-4580	380	19	upper	upper	ADJ
ejpam-4580	380	20	triangular	triangular	NOUN
ejpam-4580	380	21	operator	operator	NOUN
ejpam-4580	380	22	matrices	matrix	NOUN
ejpam-4580	380	23	.	.	PUNCT
ejpam-4580	381	1	proc	proc	PROPN
ejpam-4580	381	2	.	.	PUNCT
ejpam-4580	382	1	amer	amer	PROPN
ejpam-4580	382	2	.	.	PUNCT
ejpam-4580	382	3	math	math	PROPN
ejpam-4580	382	4	.	.	PUNCT
ejpam-4580	383	1	soc	soc	PROPN
ejpam-4580	383	2	.	.	PUNCT
ejpam-4580	383	3	,	,	PUNCT
ejpam-4580	383	4	128:119–123	128:119–123	NUM
ejpam-4580	383	5	,	,	PUNCT
ejpam-4580	383	6	2000	2000	NUM
ejpam-4580	383	7	.	.	PUNCT
ejpam-4580	384	1	[	[	X
ejpam-4580	384	2	4	4	NUM
ejpam-4580	384	3	]	]	X
ejpam-4580	384	4	v.r	v.r	PROPN
ejpam-4580	384	5	.	.	PROPN
ejpam-4580	384	6	hamiti	hamiti	PROPN
ejpam-4580	384	7	.	.	PUNCT
ejpam-4580	385	1	on	on	ADP
ejpam-4580	385	2	k−quasi	k−quasi	PROPN
ejpam-4580	385	3	class	class	NOUN
ejpam-4580	385	4	q	q	PROPN
ejpam-4580	385	5	operators	operator	NOUN
ejpam-4580	385	6	.	.	PUNCT
ejpam-4580	386	1	bulletin	bulletin	NOUN
ejpam-4580	386	2	of	of	ADP
ejpam-4580	386	3	mathematical	mathematical	ADJ
ejpam-4580	386	4	analysis	analysis	NOUN
ejpam-4580	386	5	and	and	CCONJ
ejpam-4580	386	6	applications	application	NOUN
ejpam-4580	386	7	,	,	PUNCT
ejpam-4580	386	8	6:31–37	6:31–37	NOUN
ejpam-4580	386	9	,	,	PUNCT
ejpam-4580	386	10	2014	2014	NUM
ejpam-4580	386	11	.	.	PUNCT
ejpam-4580	387	1	[	[	X
ejpam-4580	387	2	5	5	NUM
ejpam-4580	387	3	]	]	PUNCT
ejpam-4580	387	4	i.	i.	PROPN
ejpam-4580	387	5	hoxha	hoxha	PROPN
ejpam-4580	387	6	and	and	CCONJ
ejpam-4580	387	7	n.	n.	PROPN
ejpam-4580	387	8	l.	l.	PROPN
ejpam-4580	387	9	braha	braha	PROPN
ejpam-4580	387	10	.	.	PUNCT
ejpam-4580	388	1	a	a	DET
ejpam-4580	388	2	note	note	NOUN
ejpam-4580	388	3	on	on	ADP
ejpam-4580	388	4	k−quasi∗−paranormal	k−quasi∗−paranormal	PROPN
ejpam-4580	388	5	operators	operator	NOUN
ejpam-4580	388	6	.	.	PUNCT
ejpam-4580	389	1	journal	journal	PROPN
ejpam-4580	389	2	of	of	ADP
ejpam-4580	389	3	inequalities	inequality	NOUN
ejpam-4580	389	4	and	and	CCONJ
ejpam-4580	389	5	applications	application	NOUN
ejpam-4580	389	6	,	,	PUNCT
ejpam-4580	389	7	1(350	1(350	NUM
ejpam-4580	389	8	)	)	PUNCT
ejpam-4580	389	9	,	,	PUNCT
ejpam-4580	389	10	2013	2013	NUM
ejpam-4580	389	11	.	.	PUNCT
ejpam-4580	390	1	[	[	X
ejpam-4580	390	2	6	6	NUM
ejpam-4580	390	3	]	]	X
ejpam-4580	390	4	sh	sh	PROPN
ejpam-4580	390	5	.	.	PROPN
ejpam-4580	390	6	lohaj	lohaj	PROPN
ejpam-4580	390	7	and	and	CCONJ
ejpam-4580	390	8	v.	v.	PROPN
ejpam-4580	390	9	r.	r.	PROPN
ejpam-4580	390	10	hamiti	hamiti	PROPN
ejpam-4580	390	11	.	.	PUNCT
ejpam-4580	391	1	some	some	DET
ejpam-4580	391	2	properties	property	NOUN
ejpam-4580	391	3	k−quasi	k−quasi	PROPN
ejpam-4580	391	4	class	class	NOUN
ejpam-4580	391	5	q∗	q∗	NOUN
ejpam-4580	391	6	operators	operator	NOUN
ejpam-4580	391	7	.	.	PUNCT
ejpam-4580	392	1	the	the	DET
ejpam-4580	392	2	australian	australian	ADJ
ejpam-4580	392	3	journal	journal	NOUN
ejpam-4580	392	4	of	of	ADP
ejpam-4580	392	5	mathematical	mathematical	ADJ
ejpam-4580	392	6	analysis	analysis	NOUN
ejpam-4580	392	7	and	and	CCONJ
ejpam-4580	392	8	applications	application	NOUN
ejpam-4580	392	9	,	,	PUNCT
ejpam-4580	392	10	14:1–10	14:1–10	NUM
ejpam-4580	392	11	,	,	PUNCT
ejpam-4580	392	12	2017	2017	NUM
ejpam-4580	392	13	.	.	PUNCT
ejpam-4580	393	1	[	[	X
ejpam-4580	393	2	7	7	X
ejpam-4580	393	3	]	]	X
ejpam-4580	393	4	sh	sh	PROPN
ejpam-4580	393	5	.	.	PROPN
ejpam-4580	393	6	lohaj	lohaj	PROPN
ejpam-4580	393	7	and	and	CCONJ
ejpam-4580	393	8	v.	v.	PROPN
ejpam-4580	393	9	r.	r.	PROPN
ejpam-4580	393	10	hamiti	hamiti	PROPN
ejpam-4580	393	11	.	.	PUNCT
ejpam-4580	394	1	a	a	DET
ejpam-4580	394	2	note	note	NOUN
ejpam-4580	394	3	on	on	ADP
ejpam-4580	394	4	class	class	NOUN
ejpam-4580	394	5	q(n	q(n	PROPN
ejpam-4580	394	6	)	)	PUNCT
ejpam-4580	394	7	operators	operator	NOUN
ejpam-4580	394	8	.	.	PUNCT
ejpam-4580	395	1	missouri	missouri	PROPN
ejpam-4580	395	2	journal	journal	PROPN
ejpam-4580	395	3	of	of	ADP
ejpam-4580	395	4	math	math	NOUN
ejpam-4580	395	5	.	.	PUNCT
ejpam-4580	396	1	sci	sci	PROPN
ejpam-4580	396	2	.	.	PROPN
ejpam-4580	396	3	,	,	PUNCT
ejpam-4580	396	4	2:185–196	2:185–196	NUM
ejpam-4580	396	5	,	,	PUNCT
ejpam-4580	396	6	2018	2018	NUM
ejpam-4580	396	7	.	.	PUNCT
ejpam-4580	397	1	[	[	X
ejpam-4580	397	2	8	8	NUM
ejpam-4580	397	3	]	]	X
ejpam-4580	397	4	n.l	n.l	PROPN
ejpam-4580	397	5	.	.	PROPN
ejpam-4580	397	6	braha	braha	PROPN
ejpam-4580	397	7	m.	m.	PROPN
ejpam-4580	397	8	lohaj	lohaj	PROPN
ejpam-4580	397	9	f.	f.	PROPN
ejpam-4580	397	10	marevci	marevci	PROPN
ejpam-4580	397	11	sh	sh	PROPN
ejpam-4580	397	12	.	.	PROPN
ejpam-4580	397	13	lohaj	lohaj	PROPN
ejpam-4580	397	14	.	.	PUNCT
ejpam-4580	398	1	some	some	DET
ejpam-4580	398	2	properties	property	NOUN
ejpam-4580	398	3	of	of	ADP
ejpam-4580	398	4	paranormal	paranormal	ADJ
ejpam-4580	398	5	and	and	CCONJ
ejpam-4580	398	6	hyponormal	hyponormal	ADJ
ejpam-4580	398	7	operators	operator	NOUN
ejpam-4580	398	8	.	.	PUNCT
ejpam-4580	399	1	bulletin	bulletin	NOUN
ejpam-4580	399	2	of	of	ADP
ejpam-4580	399	3	mathematical	mathematical	ADJ
ejpam-4580	399	4	analysis	analysis	NOUN
ejpam-4580	399	5	and	and	CCONJ
ejpam-4580	399	6	applications	application	NOUN
ejpam-4580	399	7	,	,	PUNCT
ejpam-4580	399	8	1:23–35	1:23–35	NUM
ejpam-4580	399	9	,	,	PUNCT
ejpam-4580	399	10	2009	2009	NUM
ejpam-4580	399	11	.	.	PUNCT
ejpam-4580	400	1	[	[	X
ejpam-4580	400	2	9	9	NUM
ejpam-4580	400	3	]	]	SYM
ejpam-4580	400	4	salah	salah	PROPN
ejpam-4580	400	5	mecheri	mecheri	PROPN
ejpam-4580	400	6	.	.	PUNCT
ejpam-4580	401	1	bishop	bishop	PROPN
ejpam-4580	401	2	s	s	PART
ejpam-4580	401	3	property	property	NOUN
ejpam-4580	401	4	b	b	PROPN
ejpam-4580	401	5	and	and	CCONJ
ejpam-4580	401	6	riesz	riesz	VERB
ejpam-4580	401	7	idempotent	idempotent	NOUN
ejpam-4580	401	8	for	for	ADP
ejpam-4580	401	9	k−quasi	k−quasi	ADJ
ejpam-4580	401	10	-	-	ADJ
ejpam-4580	401	11	paranormal	paranormal	ADJ
ejpam-4580	401	12	operators	operator	NOUN
ejpam-4580	401	13	.	.	PUNCT
ejpam-4580	402	1	banach	banach	PROPN
ejpam-4580	402	2	j.	j.	PROPN
ejpam-4580	402	3	math	math	PROPN
ejpam-4580	402	4	.	.	PUNCT
ejpam-4580	403	1	anal	anal	PROPN
ejpam-4580	403	2	.	.	PUNCT
ejpam-4580	403	3	,	,	PUNCT
ejpam-4580	403	4	6(1):147	6(1):147	NUM
ejpam-4580	403	5	–	–	PUNCT
ejpam-4580	403	6	154	154	NUM
ejpam-4580	403	7	,	,	PUNCT
ejpam-4580	403	8	2012	2012	NUM
ejpam-4580	403	9	.	.	PUNCT
ejpam-4580	404	1	[	[	X
ejpam-4580	404	2	10	10	NUM
ejpam-4580	404	3	]	]	X
ejpam-4580	404	4	salah	salah	PROPN
ejpam-4580	404	5	mecheri	mecheri	PROPN
ejpam-4580	404	6	.	.	PUNCT
ejpam-4580	405	1	isolated	isolated	ADJ
ejpam-4580	405	2	points	point	NOUN
ejpam-4580	405	3	of	of	ADP
ejpam-4580	405	4	spectrum	spectrum	NOUN
ejpam-4580	405	5	of	of	ADP
ejpam-4580	405	6	k−	k−	PROPN
ejpam-4580	405	7	quasi∗−class	quasi∗−class	PROPN
ejpam-4580	405	8	a	a	DET
ejpam-4580	405	9	operators	operator	NOUN
ejpam-4580	405	10	.	.	PUNCT
ejpam-4580	406	1	studia	studia	PROPN
ejpam-4580	406	2	mathematica	mathematica	PROPN
ejpam-4580	406	3	,	,	PUNCT
ejpam-4580	406	4	1(208):87–96	1(208):87–96	PROPN
ejpam-4580	406	5	,	,	PUNCT
ejpam-4580	406	6	2012	2012	NUM
ejpam-4580	406	7	.	.	PUNCT
ejpam-4580	407	1	[	[	X
ejpam-4580	407	2	11	11	NUM
ejpam-4580	407	3	]	]	PUNCT
ejpam-4580	407	4	t.	t.	PROPN
ejpam-4580	407	5	yamazaki	yamazaki	PROPN
ejpam-4580	407	6	.	.	PUNCT
ejpam-4580	408	1	parallelisms	parallelism	NOUN
ejpam-4580	408	2	between	between	ADP
ejpam-4580	408	3	aluthge	aluthge	ADJ
ejpam-4580	408	4	transformation	transformation	NOUN
ejpam-4580	408	5	and	and	CCONJ
ejpam-4580	408	6	powers	power	NOUN
ejpam-4580	408	7	of	of	ADP
ejpam-4580	408	8	operators	operator	NOUN
ejpam-4580	408	9	.	.	PUNCT
ejpam-4580	409	1	acta	acta	PROPN
ejpam-4580	409	2	sci	sci	PROPN
ejpam-4580	409	3	.	.	PROPN
ejpam-4580	409	4	math	math	PROPN
ejpam-4580	409	5	.	.	PUNCT
ejpam-4580	410	1	(	(	PUNCT
ejpam-4580	410	2	szeged	szeged	PROPN
ejpam-4580	410	3	)	)	PUNCT
ejpam-4580	410	4	,	,	PUNCT
ejpam-4580	410	5	67:809–820	67:809–820	PROPN
ejpam-4580	410	6	,	,	PUNCT
ejpam-4580	410	7	2001	2001	NUM
ejpam-4580	410	8	.	.	PUNCT