id	sid	tid	token	lemma	pos
iajs-3473	1	1	287	287	NUM
iajs-3473	1	2	©	©	PROPN
iajs-3473	1	3	2025	2025	NUM
iajs-3473	1	4	the	the	DET
iajs-3473	1	5	author(s	author(s	NOUN
iajs-3473	1	6	)	)	PUNCT
iajs-3473	1	7	.	.	PUNCT
iajs-3473	2	1	published	publish	VERB
iajs-3473	2	2	by	by	ADP
iajs-3473	2	3	college	college	NOUN
iajs-3473	2	4	of	of	ADP
iajs-3473	2	5	education	education	NOUN
iajs-3473	2	6	for	for	ADP
iajs-3473	2	7	pure	pure	ADJ
iajs-3473	2	8	science	science	NOUN
iajs-3473	2	9	(	(	PUNCT
iajs-3473	2	10	ibn	ibn	PROPN
iajs-3473	2	11	al	al	PROPN
iajs-3473	2	12	-	-	PUNCT
iajs-3473	2	13	haitham	haitham	PROPN
iajs-3473	2	14	)	)	PUNCT
iajs-3473	2	15	,	,	PUNCT
iajs-3473	2	16	university	university	NOUN
iajs-3473	2	17	of	of	ADP
iajs-3473	2	18	baghdad	baghdad	PROPN
iajs-3473	2	19	.	.	PUNCT
iajs-3473	3	1	this	this	PRON
iajs-3473	3	2	is	be	AUX
iajs-3473	3	3	an	an	DET
iajs-3473	3	4	open	open	ADJ
iajs-3473	3	5	-	-	PUNCT
iajs-3473	3	6	access	access	NOUN
iajs-3473	3	7	article	article	NOUN
iajs-3473	3	8	distributed	distribute	VERB
iajs-3473	3	9	under	under	ADP
iajs-3473	3	10	the	the	DET
iajs-3473	3	11	terms	term	NOUN
iajs-3473	3	12	of	of	ADP
iajs-3473	3	13	the	the	DET
iajs-3473	3	14	creative	creative	ADJ
iajs-3473	3	15	commons	common	NOUN
iajs-3473	3	16	attribution	attribution	NOUN
iajs-3473	3	17	4.0	4.0	NUM
iajs-3473	3	18	international	international	ADJ
iajs-3473	3	19	license	license	NOUN
iajs-3473	3	20	perturbation	perturbation	NOUN
iajs-3473	3	21	of	of	ADP
iajs-3473	3	22	weyl	weyl	PROPN
iajs-3473	3	23	’s	’s	PART
iajs-3473	3	24	theorems	theorem	NOUN
iajs-3473	3	25	for	for	ADP
iajs-3473	3	26	unbounded	unbounded	ADJ
iajs-3473	3	27	upper	upper	ADJ
iajs-3473	3	28	triangular	triangular	NOUN
iajs-3473	3	29	operator	operator	NOUN
iajs-3473	3	30	matrices	matrix	NOUN
iajs-3473	3	31	dalia	dalia	PROPN
iajs-3473	3	32	s.	s.	PROPN
iajs-3473	3	33	ali	ali	PROPN
iajs-3473	4	1	1	1	NUM
iajs-3473	4	2	*	*	PUNCT
iajs-3473	4	3	and	and	CCONJ
iajs-3473	4	4	buthainah	buthainah	PROPN
iajs-3473	4	5	a.a	a.a	PROPN
iajs-3473	4	6	.	.	PROPN
iajs-3473	4	7	ahmed	ahmed	PROPN
iajs-3473	4	8	2	2	NUM
iajs-3473	4	9	1,2	1,2	NUM
iajs-3473	4	10	mathematics	mathematic	NOUN
iajs-3473	4	11	department	department	NOUN
iajs-3473	4	12	,	,	PUNCT
iajs-3473	4	13	college	college	NOUN
iajs-3473	4	14	of	of	ADP
iajs-3473	4	15	science	science	NOUN
iajs-3473	4	16	,	,	PUNCT
iajs-3473	4	17	university	university	NOUN
iajs-3473	4	18	of	of	ADP
iajs-3473	4	19	baghdad	baghdad	PROPN
iajs-3473	4	20	,	,	PUNCT
iajs-3473	4	21	baghdad	baghdad	PROPN
iajs-3473	4	22	,	,	PUNCT
iajs-3473	4	23	iraq	iraq	PROPN
iajs-3473	4	24	*	*	PUNCT
iajs-3473	4	25	corresponding	correspond	VERB
iajs-3473	4	26	author	author	NOUN
iajs-3473	4	27	.	.	PUNCT
iajs-3473	5	1	received	receive	VERB
iajs-3473	5	2	:	:	PUNCT
iajs-3473	5	3	8	8	NUM
iajs-3473	5	4	may	may	PROPN
iajs-3473	5	5	2023	2023	NUM
iajs-3473	5	6	accepted	accept	VERB
iajs-3473	5	7	:	:	PUNCT
iajs-3473	5	8	11	11	NUM
iajs-3473	5	9	october	october	PROPN
iajs-3473	5	10	2023	2023	NUM
iajs-3473	5	11	published	publish	VERB
iajs-3473	5	12	:	:	PUNCT
iajs-3473	5	13	20	20	NUM
iajs-3473	5	14	october	october	NOUN
iajs-3473	5	15	2025	2025	NUM
iajs-3473	5	16	doi.org/10.30526/38.4.3473	doi.org/10.30526/38.4.3473	NOUN
iajs-3473	5	17	abstract	abstract	ADV
iajs-3473	5	18	let	let	VERB
iajs-3473	5	19	,	,	PUNCT
iajs-3473	5	20	be	be	AUX
iajs-3473	5	21	an	an	DET
iajs-3473	5	22	upper	upper	ADJ
iajs-3473	5	23	triangular	triangular	NOUN
iajs-3473	5	24	operator	operator	NOUN
iajs-3473	5	25	matrix	matrix	NOUN
iajs-3473	5	26	which	which	PRON
iajs-3473	5	27	is	be	AUX
iajs-3473	5	28	unbounded	unbounded	ADJ
iajs-3473	5	29	and	and	CCONJ
iajs-3473	5	30	defined	define	VERB
iajs-3473	5	31	on	on	ADP
iajs-3473	5	32	,	,	PUNCT
iajs-3473	5	33	where	where	SCONJ
iajs-3473	5	34	is	be	AUX
iajs-3473	5	35	infinite	infinite	ADJ
iajs-3473	5	36	dimensional	dimensional	ADJ
iajs-3473	5	37	hilbert	hilbert	NOUN
iajs-3473	5	38	space	space	NOUN
iajs-3473	5	39	.	.	PUNCT
iajs-3473	6	1	this	this	DET
iajs-3473	6	2	paper	paper	NOUN
iajs-3473	6	3	is	be	AUX
iajs-3473	6	4	concerned	concern	VERB
iajs-3473	6	5	with	with	ADP
iajs-3473	6	6	new	new	ADJ
iajs-3473	6	7	spectral	spectral	ADJ
iajs-3473	6	8	properties	property	NOUN
iajs-3473	6	9	which	which	PRON
iajs-3473	6	10	defined	define	VERB
iajs-3473	6	11	to	to	ADP
iajs-3473	6	12	other	other	ADJ
iajs-3473	6	13	bounded	bounded	ADJ
iajs-3473	6	14	operators	operator	NOUN
iajs-3473	6	15	.	.	PUNCT
iajs-3473	7	1	some	some	DET
iajs-3473	7	2	sufficient	sufficient	ADJ
iajs-3473	7	3	and	and	CCONJ
iajs-3473	7	4	necessary	necessary	ADJ
iajs-3473	7	5	conditions	condition	NOUN
iajs-3473	7	6	are	be	AUX
iajs-3473	7	7	given	give	VERB
iajs-3473	7	8	in	in	ADP
iajs-3473	7	9	which	which	PRON
iajs-3473	7	10	these	these	DET
iajs-3473	7	11	properties	property	NOUN
iajs-3473	7	12	are	be	AUX
iajs-3473	7	13	equivalent	equivalent	ADJ
iajs-3473	7	14	.	.	PUNCT
iajs-3473	8	1	we	we	PRON
iajs-3473	8	2	further	far	ADV
iajs-3473	8	3	investigate	investigate	VERB
iajs-3473	8	4	the	the	DET
iajs-3473	8	5	relations	relation	NOUN
iajs-3473	8	6	among	among	ADP
iajs-3473	8	7	weyl	weyl	PROPN
iajs-3473	8	8	’s	’s	PART
iajs-3473	8	9	type	type	NOUN
iajs-3473	8	10	theorems	theorem	NOUN
iajs-3473	8	11	and	and	CCONJ
iajs-3473	8	12	brodwe	brodwe	NOUN
iajs-3473	8	13	’s	’s	PART
iajs-3473	8	14	theorems	theorem	NOUN
iajs-3473	8	15	for	for	ADP
iajs-3473	8	16	this	this	DET
iajs-3473	8	17	type	type	NOUN
iajs-3473	8	18	of	of	ADP
iajs-3473	8	19	operator	operator	NOUN
iajs-3473	8	20	under	under	ADP
iajs-3473	8	21	some	some	DET
iajs-3473	8	22	conditions	condition	NOUN
iajs-3473	8	23	.	.	PUNCT
iajs-3473	9	1	as	as	ADP
iajs-3473	9	2	an	an	DET
iajs-3473	9	3	application	application	NOUN
iajs-3473	9	4	the	the	DET
iajs-3473	9	5	paper	paper	NOUN
iajs-3473	9	6	define	define	VERB
iajs-3473	9	7	the	the	DET
iajs-3473	9	8	plate	plate	NOUN
iajs-3473	9	9	pending	pende	VERB
iajs-3473	9	10	problem	problem	NOUN
iajs-3473	9	11	equation	equation	NOUN
iajs-3473	9	12	with	with	ADP
iajs-3473	9	13	henge	henge	NOUN
iajs-3473	9	14	end	end	NOUN
iajs-3473	9	15	,	,	PUNCT
iajs-3473	9	16	fixed	fix	VERB
iajs-3473	9	17	end	end	NOUN
iajs-3473	9	18	and	and	CCONJ
iajs-3473	9	19	free	free	ADJ
iajs-3473	9	20	end	end	NOUN
iajs-3473	9	21	,	,	PUNCT
iajs-3473	9	22	after	after	ADP
iajs-3473	9	23	transform	transform	VERB
iajs-3473	9	24	it	it	PRON
iajs-3473	9	25	to	to	ADP
iajs-3473	9	26	hamitonian	hamitonian	ADJ
iajs-3473	9	27	matrix	matrix	NOUN
iajs-3473	9	28	then	then	ADV
iajs-3473	9	29	calculate	calculate	VERB
iajs-3473	9	30	the	the	DET
iajs-3473	9	31	spectrum	spectrum	NOUN
iajs-3473	9	32	sets	set	NOUN
iajs-3473	9	33	for	for	ADP
iajs-3473	9	34	this	this	DET
iajs-3473	9	35	matrix	matrix	NOUN
iajs-3473	9	36	which	which	PRON
iajs-3473	9	37	leads	lead	VERB
iajs-3473	9	38	to	to	ADP
iajs-3473	9	39	if	if	SCONJ
iajs-3473	9	40	a	a	PRON
iajs-3473	9	41	has	have	VERB
iajs-3473	9	42	eigenvalues	eigenvalue	NOUN
iajs-3473	9	43	of	of	ADP
iajs-3473	9	44	finite	finite	ADJ
iajs-3473	9	45	multiplicity	multiplicity	NOUN
iajs-3473	9	46	,	,	PUNCT
iajs-3473	9	47	so	so	ADV
iajs-3473	9	48	is	be	AUX
iajs-3473	9	49	m.	m.	NOUN
iajs-3473	9	50	inaddition	inaddition	NOUN
iajs-3473	9	51	if	if	SCONJ
iajs-3473	9	52	has	have	AUX
iajs-3473	9	53	finite	finite	NOUN
iajs-3473	9	54	ascent	ascent	PROPN
iajs-3473	9	55	this	this	PRON
iajs-3473	9	56	implies	imply	VERB
iajs-3473	9	57	that	that	SCONJ
iajs-3473	9	58	the	the	DET
iajs-3473	9	59	hamiltonian	hamiltonian	ADJ
iajs-3473	9	60	operator	operator	NOUN
iajs-3473	9	61	m	m	VERB
iajs-3473	9	62	has	have	VERB
iajs-3473	9	63	finite	finite	PROPN
iajs-3473	9	64	ascent	ascent	NOUN
iajs-3473	9	65	.	.	PUNCT
iajs-3473	10	1	keywords	keyword	NOUN
iajs-3473	10	2	:	:	PUNCT
iajs-3473	10	3	browder	browder	PROPN
iajs-3473	10	4	’s	’s	PART
iajs-3473	10	5	spectrum	spectrum	PROPN
iajs-3473	10	6	,	,	PUNCT
iajs-3473	10	7	spectral	spectral	ADJ
iajs-3473	10	8	properties	property	NOUN
iajs-3473	10	9	,	,	PUNCT
iajs-3473	10	10	upper	upper	ADJ
iajs-3473	10	11	triangular	triangular	NOUN
iajs-3473	10	12	operator	operator	NOUN
iajs-3473	10	13	matrices	matrix	NOUN
iajs-3473	10	14	,	,	PUNCT
iajs-3473	10	15	weyl	weyl	PROPN
iajs-3473	10	16	’s	’s	PART
iajs-3473	10	17	spectrum	spectrum	NOUN
iajs-3473	10	18	,	,	PUNCT
iajs-3473	10	19	weyl	weyl	PROPN
iajs-3473	10	20	’s	’s	PART
iajs-3473	10	21	theorems	theorem	NOUN
iajs-3473	10	22	.	.	PUNCT
iajs-3473	11	1	1	1	X
iajs-3473	11	2	.	.	X
iajs-3473	11	3	introduction	introduction	NOUN
iajs-3473	11	4	the	the	DET
iajs-3473	11	5	conception	conception	NOUN
iajs-3473	11	6	of	of	ADP
iajs-3473	11	7	unbounded	unbounded	ADJ
iajs-3473	11	8	operator	operator	NOUN
iajs-3473	11	9	delivers	deliver	VERB
iajs-3473	11	10	a	a	DET
iajs-3473	11	11	non	non	ADJ
iajs-3473	11	12	-	-	ADJ
iajs-3473	11	13	figurative	figurative	ADJ
iajs-3473	11	14	background	background	NOUN
iajs-3473	11	15	for	for	ADP
iajs-3473	11	16	allocating	allocate	VERB
iajs-3473	11	17	with	with	ADP
iajs-3473	11	18	differential	differential	ADJ
iajs-3473	11	19	operators	operator	NOUN
iajs-3473	11	20	,	,	PUNCT
iajs-3473	11	21	unbounded	unbounded	ADJ
iajs-3473	11	22	perceptible	perceptible	ADJ
iajs-3473	11	23	in	in	ADP
iajs-3473	11	24	quantum	quantum	ADJ
iajs-3473	11	25	mechanics	mechanic	NOUN
iajs-3473	11	26	,	,	PUNCT
iajs-3473	11	27	and	and	CCONJ
iajs-3473	11	28	other	other	ADJ
iajs-3473	11	29	circumstances	circumstance	NOUN
iajs-3473	11	30	.	.	PUNCT
iajs-3473	12	1	the	the	DET
iajs-3473	12	2	weyl	weyl	PROPN
iajs-3473	12	3	’s	’s	PART
iajs-3473	12	4	theorem	theorem	NOUN
iajs-3473	12	5	for	for	ADP
iajs-3473	12	6	bounded	bounded	ADJ
iajs-3473	12	7	hermitian	hermitian	ADJ
iajs-3473	12	8	operators	operator	NOUN
iajs-3473	12	9	was	be	AUX
iajs-3473	12	10	established	establish	VERB
iajs-3473	12	11	by	by	ADP
iajs-3473	12	12	weyl	weyl	PROPN
iajs-3473	12	13	(	(	PUNCT
iajs-3473	12	14	1	1	NUM
iajs-3473	12	15	)	)	PUNCT
iajs-3473	12	16	.	.	PUNCT
iajs-3473	13	1	weyl	weyl	PROPN
iajs-3473	13	2	’s	’s	PART
iajs-3473	13	3	theorem	theorem	NOUN
iajs-3473	13	4	has	have	AUX
iajs-3473	13	5	since	since	ADV
iajs-3473	13	6	been	be	AUX
iajs-3473	13	7	expanded	expand	VERB
iajs-3473	13	8	to	to	PART
iajs-3473	13	9	encompass	encompass	VERB
iajs-3473	13	10	the	the	DET
iajs-3473	13	11	class	class	NOUN
iajs-3473	13	12	of	of	ADP
iajs-3473	13	13	bounded	bounded	ADJ
iajs-3473	13	14	normal	normal	ADJ
iajs-3473	13	15	,	,	PUNCT
iajs-3473	13	16	hyponormal	hyponormal	ADJ
iajs-3473	13	17	,	,	PUNCT
iajs-3473	13	18	and	and	CCONJ
iajs-3473	13	19	toeplitz	toeplitz	NOUN
iajs-3473	13	20	operators	operator	NOUN
iajs-3473	13	21	(	(	PUNCT
iajs-3473	13	22	2	2	X
iajs-3473	13	23	)	)	PUNCT
iajs-3473	13	24	as	as	ADV
iajs-3473	13	25	well	well	ADV
iajs-3473	13	26	as	as	ADP
iajs-3473	13	27	a	a	DET
iajs-3473	13	28	number	number	NOUN
iajs-3473	13	29	of	of	ADP
iajs-3473	13	30	other	other	ADJ
iajs-3473	13	31	non	non	ADJ
iajs-3473	13	32	-	-	ADJ
iajs-3473	13	33	normal	normal	ADJ
iajs-3473	13	34	categories	category	NOUN
iajs-3473	13	35	of	of	ADP
iajs-3473	13	36	bounded	bounded	ADJ
iajs-3473	13	37	operators	operator	NOUN
iajs-3473	13	38	.	.	PUNCT
iajs-3473	14	1	the	the	DET
iajs-3473	14	2	familiar	familiar	ADJ
iajs-3473	14	3	weyl	weyl	PROPN
iajs-3473	14	4	’s	’s	PART
iajs-3473	14	5	theorem	theorem	NOUN
iajs-3473	14	6	is	be	AUX
iajs-3473	14	7	generalized	generalize	VERB
iajs-3473	14	8	in	in	ADP
iajs-3473	14	9	such	such	DET
iajs-3473	14	10	a	a	DET
iajs-3473	14	11	way	way	NOUN
iajs-3473	14	12	.	.	PUNCT
iajs-3473	15	1	furthermore	furthermore	ADV
iajs-3473	15	2	,	,	PUNCT
iajs-3473	15	3	he	he	PRON
iajs-3473	15	4	established	establish	VERB
iajs-3473	15	5	this	this	DET
iajs-3473	15	6	modified	modify	VERB
iajs-3473	15	7	version	version	NOUN
iajs-3473	15	8	of	of	ADP
iajs-3473	15	9	the	the	DET
iajs-3473	15	10	traditional	traditional	ADJ
iajs-3473	15	11	weyl	weyl	PROPN
iajs-3473	15	12	’s	’s	PART
iajs-3473	15	13	theorem	theorem	NOUN
iajs-3473	15	14	for	for	ADP
iajs-3473	15	15	limited	limited	ADJ
iajs-3473	15	16	hyponormal	hyponormal	ADJ
iajs-3473	15	17	operators	operator	NOUN
iajs-3473	15	18	in	in	ADP
iajs-3473	15	19	(	(	PUNCT
iajs-3473	15	20	3	3	NUM
iajs-3473	15	21	)	)	PUNCT
iajs-3473	15	22	.	.	PUNCT
iajs-3473	16	1	the	the	DET
iajs-3473	16	2	works	work	NOUN
iajs-3473	16	3	in	in	ADP
iajs-3473	16	4	this	this	DET
iajs-3473	16	5	direction	direction	NOUN
iajs-3473	16	6	recently	recently	ADV
iajs-3473	16	7	been	be	AUX
iajs-3473	16	8	expanded	expand	VERB
iajs-3473	16	9	to	to	PART
iajs-3473	16	10	include	include	VERB
iajs-3473	16	11	the	the	DET
iajs-3473	16	12	classes	class	NOUN
iajs-3473	16	13	of	of	ADP
iajs-3473	16	14	unbounded	unbounded	ADJ
iajs-3473	16	15	posinormal	posinormal	ADJ
iajs-3473	16	16	operators	operator	NOUN
iajs-3473	16	17	and	and	CCONJ
iajs-3473	16	18	unbounded	unbounded	ADJ
iajs-3473	16	19	hyponormal	hyponormal	ADJ
iajs-3473	16	20	operators	operator	NOUN
iajs-3473	16	21	(	(	PUNCT
iajs-3473	16	22	4	4	NUM
iajs-3473	16	23	)	)	PUNCT
iajs-3473	16	24	.	.	PUNCT
iajs-3473	17	1	for	for	ADP
iajs-3473	17	2	unbounded	unbounded	ADJ
iajs-3473	17	3	operators	operator	NOUN
iajs-3473	17	4	on	on	ADP
iajs-3473	17	5	different	different	ADJ
iajs-3473	17	6	spaces	space	NOUN
iajs-3473	17	7	such	such	ADJ
iajs-3473	17	8	as	as	ADP
iajs-3473	17	9	the	the	DET
iajs-3473	17	10	space	space	NOUN
iajs-3473	17	11	of	of	ADP
iajs-3473	17	12	banach	banach	NOUN
iajs-3473	17	13	with	with	ADP
iajs-3473	17	14	non	non	ADJ
iajs-3473	17	15	-	-	ADJ
iajs-3473	17	16	empty	empty	ADJ
iajs-3473	17	17	resolvent	resolvent	NOUN
iajs-3473	17	18	,	,	PUNCT
iajs-3473	17	19	the	the	DET
iajs-3473	17	20	authors	author	NOUN
iajs-3473	17	21	introduced	introduce	VERB
iajs-3473	17	22	the	the	DET
iajs-3473	17	23	b	b	NOUN
iajs-3473	17	24	-	-	PUNCT
iajs-3473	17	25	fredholm	fredholm	NOUN
iajs-3473	17	26	theory	theory	NOUN
iajs-3473	17	27	in	in	ADP
iajs-3473	17	28	(	(	PUNCT
iajs-3473	17	29	5	5	NUM
iajs-3473	17	30	,	,	PUNCT
iajs-3473	17	31	15	15	NUM
iajs-3473	17	32	)	)	PUNCT
iajs-3473	17	33	.	.	PUNCT
iajs-3473	18	1	weyl	weyl	PROPN
iajs-3473	18	2	’s	’s	PART
iajs-3473	18	3	theorem	theorem	NOUN
iajs-3473	18	4	for	for	ADP
iajs-3473	18	5	the	the	DET
iajs-3473	18	6	category	category	NOUN
iajs-3473	18	7	of	of	ADP
iajs-3473	18	8	paranormal	paranormal	ADJ
iajs-3473	18	9	operators	operator	NOUN
iajs-3473	18	10	on	on	ADP
iajs-3473	18	11	banach	banach	NOUN
iajs-3473	18	12	spaces	space	NOUN
iajs-3473	18	13	was	be	AUX
iajs-3473	18	14	established	establish	VERB
iajs-3473	18	15	by	by	ADP
iajs-3473	18	16	ramanujan(6	ramanujan(6	PROPN
iajs-3473	18	17	)	)	PUNCT
iajs-3473	18	18	,	,	PUNCT
iajs-3473	18	19	and	and	CCONJ
iajs-3473	18	20	it	it	PRON
iajs-3473	18	21	was	be	AUX
iajs-3473	18	22	further	far	ADV
iajs-3473	18	23	developed	develop	VERB
iajs-3473	18	24	by	by	ADP
iajs-3473	18	25	aiena	aiena	PROPN
iajs-3473	18	26	and	and	CCONJ
iajs-3473	18	27	guillen	guillen	PROPN
iajs-3473	18	28	to	to	PART
iajs-3473	18	29	include	include	VERB
iajs-3473	18	30	the	the	DET
iajs-3473	18	31	investigation	investigation	NOUN
iajs-3473	18	32	of	of	ADP
iajs-3473	18	33	weyl	weyl	PROPN
iajs-3473	18	34	’s	’s	PART
iajs-3473	18	35	.	.	PUNCT
iajs-3473	19	1	theorem	theorem	NOUN
iajs-3473	19	2	for	for	ADP
iajs-3473	19	3	the	the	DET
iajs-3473	19	4	perturbation	perturbation	NOUN
iajs-3473	19	5	of	of	ADP
iajs-3473	19	6	paranormal	paranormal	ADJ
iajs-3473	19	7	operators	operator	NOUN
iajs-3473	19	8	by	by	ADP
iajs-3473	19	9	algebraic	algebraic	ADJ
iajs-3473	19	10	operators	operator	NOUN
iajs-3473	19	11	and	and	CCONJ
iajs-3473	19	12	for	for	ADP
iajs-3473	19	13	unbounded	unbounded	ADJ
iajs-3473	19	14	compact	compact	ADJ
iajs-3473	19	15	operators	operator	NOUN
iajs-3473	19	16	defined	define	VERB
iajs-3473	19	17	on	on	ADP
iajs-3473	19	18	a	a	DET
iajs-3473	19	19	banach	banach	NOUN
iajs-3473	19	20	space	space	NOUN
iajs-3473	19	21	are	be	AUX
iajs-3473	19	22	investigated	investigate	VERB
iajs-3473	19	23	by	by	ADP
iajs-3473	19	24	the	the	DET
iajs-3473	19	25	authors	author	NOUN
iajs-3473	19	26	(	(	PUNCT
iajs-3473	19	27	7,16,19	7,16,19	NUM
iajs-3473	19	28	)	)	PUNCT
iajs-3473	19	29	,	,	PUNCT
iajs-3473	19	30	including	include	VERB
iajs-3473	19	31	those	those	PRON
iajs-3473	19	32	by	by	ADP
iajs-3473	19	33	browder	browder	NOUN
iajs-3473	19	34	and	and	CCONJ
iajs-3473	19	35	weyl	weyl	PROPN
iajs-3473	19	36	.	.	PUNCT
iajs-3473	20	1	the	the	DET
iajs-3473	20	2	theory	theory	NOUN
iajs-3473	20	3	is	be	AUX
iajs-3473	20	4	demonstrated	demonstrate	VERB
iajs-3473	20	5	in	in	ADP
iajs-3473	20	6	the	the	DET
iajs-3473	20	7	final	final	ADJ
iajs-3473	20	8	section	section	NOUN
iajs-3473	20	9	using	use	VERB
iajs-3473	20	10	https://orcid.org/0000-0003-4147-8134	https://orcid.org/0000-0003-4147-8134	NOUN
iajs-3473	20	11	mailto:dalia.sami1103a@sc.uobaghdad.edu.iq	mailto:dalia.sami1103a@sc.uobaghdad.edu.iq	NOUN
iajs-3473	20	12	https://orcid.org/0000-0003-4147-8134	https://orcid.org/0000-0003-4147-8134	NOUN
iajs-3473	20	13	mailto:buthaina.a@sc.uobaghdad.edu.iq	mailto:buthaina.a@sc.uobaghdad.edu.iq	NOUN
iajs-3473	20	14	https://orcid.org/0000-0003-4147-8134	https://orcid.org/0000-0003-4147-8134	NOUN
iajs-3473	20	15	mailto:dalia.sami1103a@sc.uobaghdad.edu.iq	mailto:dalia.sami1103a@sc.uobaghdad.edu.iq	NOUN
iajs-3473	20	16	https://orcid.org/0000-0003-4147-8134	https://orcid.org/0000-0003-4147-8134	NOUN
iajs-3473	20	17	mailto:buthaina.a@sc.uobaghdad.edu.iq	mailto:buthaina.a@sc.uobaghdad.edu.iq	NOUN
iajs-3473	20	18	https://orcid.org/0000-0003-4147-8134	https://orcid.org/0000-0003-4147-8134	NOUN
iajs-3473	20	19	mailto:dalia.sami1103a@sc.uobaghdad.edu.iq	mailto:dalia.sami1103a@sc.uobaghdad.edu.iq	NOUN
iajs-3473	20	20	https://orcid.org/0000-0003-4147-8134	https://orcid.org/0000-0003-4147-8134	NOUN
iajs-3473	20	21	mailto:buthaina.a@sc.uobaghdad.edu.iq	mailto:buthaina.a@sc.uobaghdad.edu.iq	NOUN
iajs-3473	20	22	https://orcid.org/0000-0003-4147-8134	https://orcid.org/0000-0003-4147-8134	NOUN
iajs-3473	20	23	mailto:dalia.sami1103a@sc.uobaghdad.edu.iq	mailto:dalia.sami1103a@sc.uobaghdad.edu.iq	NOUN
iajs-3473	20	24	https://orcid.org/0000-0003-4147-8134	https://orcid.org/0000-0003-4147-8134	NOUN
iajs-3473	20	25	mailto:buthaina.a@sc.uobaghdad.edu.iq	mailto:buthaina.a@sc.uobaghdad.edu.iq	NOUN
iajs-3473	20	26	https://orcid.org/0000-0003-4147-8134	https://orcid.org/0000-0003-4147-8134	NOUN
iajs-3473	20	27	mailto:dalia.sami1103a@sc.uobaghdad.edu.iq	mailto:dalia.sami1103a@sc.uobaghdad.edu.iq	NOUN
iajs-3473	20	28	https://orcid.org/0000-0003-4147-8134	https://orcid.org/0000-0003-4147-8134	NOUN
iajs-3473	20	29	mailto:buthaina.a@sc.uobaghdad.edu.iq	mailto:buthaina.a@sc.uobaghdad.edu.iq	NOUN
iajs-3473	20	30	https://orcid.org/0000-0003-4147-8134	https://orcid.org/0000-0003-4147-8134	NOUN
iajs-3473	20	31	mailto:dalia.sami1103a@sc.uobaghdad.edu.iq	mailto:dalia.sami1103a@sc.uobaghdad.edu.iq	NOUN
iajs-3473	20	32	https://orcid.org/0000-0003-4147-8134	https://orcid.org/0000-0003-4147-8134	NOUN
iajs-3473	20	33	mailto:buthaina.a@sc.uobaghdad.edu.iq	mailto:buthaina.a@sc.uobaghdad.edu.iq	NOUN
iajs-3473	20	34	ihjpas	ihjpa	NOUN
iajs-3473	20	35	.	.	PUNCT
iajs-3473	21	1	2025,38(4	2025,38(4	X
iajs-3473	21	2	)	)	PUNCT
iajs-3473	21	3	288	288	NUM
iajs-3473	21	4	examples	example	NOUN
iajs-3473	21	5	involving	involve	VERB
iajs-3473	21	6	isometrics	isometric	NOUN
iajs-3473	21	7	,	,	PUNCT
iajs-3473	21	8	analytically	analytically	ADV
iajs-3473	21	9	toeplitz	toeplitz	NOUN
iajs-3473	21	10	operators	operator	NOUN
iajs-3473	21	11	,	,	PUNCT
iajs-3473	21	12	semi	semi	ADJ
iajs-3473	21	13	-	-	ADJ
iajs-3473	21	14	shift	shift	ADJ
iajs-3473	21	15	operators	operator	NOUN
iajs-3473	21	16	,	,	PUNCT
iajs-3473	21	17	and	and	CCONJ
iajs-3473	21	18	weighted	weight	VERB
iajs-3473	21	19	right	right	ADJ
iajs-3473	21	20	shifts	shift	NOUN
iajs-3473	21	21	.	.	PUNCT
iajs-3473	22	1	both	both	DET
iajs-3473	22	2	generalized	generalize	VERB
iajs-3473	22	3	weyl	weyl	PROPN
iajs-3473	22	4	’s	’s	PART
iajs-3473	22	5	theorem	theorem	NOUN
iajs-3473	22	6	and	and	CCONJ
iajs-3473	22	7	generalized	generalized	ADJ
iajs-3473	22	8	browder	browder	NOUN
iajs-3473	22	9	’s	’s	PART
iajs-3473	22	10	theorem	theorem	NOUN
iajs-3473	22	11	are	be	AUX
iajs-3473	22	12	susceptible	susceptible	ADJ
iajs-3473	22	13	to	to	ADP
iajs-3473	22	14	failure	failure	NOUN
iajs-3473	22	15	for	for	ADP
iajs-3473	22	16	matrices	matrix	NOUN
iajs-3473	22	17	with	with	ADP
iajs-3473	22	18	two	two	NUM
iajs-3473	22	19	by	by	ADP
iajs-3473	22	20	two	two	NUM
iajs-3473	22	21	operators	operator	NOUN
iajs-3473	22	22	.	.	PUNCT
iajs-3473	23	1	in	in	ADP
iajs-3473	23	2	this	this	DET
iajs-3473	23	3	study	study	NOUN
iajs-3473	23	4	,	,	PUNCT
iajs-3473	23	5	we	we	PRON
iajs-3473	23	6	also	also	ADV
iajs-3473	23	7	investigate	investigate	VERB
iajs-3473	23	8	the	the	DET
iajs-3473	23	9	survival	survival	NOUN
iajs-3473	23	10	of	of	ADP
iajs-3473	23	11	generalized	generalized	ADJ
iajs-3473	23	12	weyl	weyl	PROPN
iajs-3473	23	13	’s	’s	PART
iajs-3473	23	14	,	,	PUNCT
iajs-3473	23	15	generalized	generalized	ADJ
iajs-3473	23	16	browder	browder	NOUN
iajs-3473	23	17	’s	’s	PART
iajs-3473	23	18	,	,	PUNCT
iajs-3473	23	19	generalized	generalize	VERB
iajs-3473	23	20	aweyl	aweyl	VERB
iajs-3473	23	21	’s	’s	PART
iajs-3473	23	22	,	,	PUNCT
iajs-3473	23	23	and	and	CCONJ
iajs-3473	23	24	generalized	generalize	VERB
iajs-3473	23	25	a	a	DET
iajs-3473	23	26	-	-	PUNCT
iajs-3473	23	27	theorems	theorem	NOUN
iajs-3473	23	28	browder	browder	NOUN
iajs-3473	23	29	’s	’s	PART
iajs-3473	23	30	for	for	ADP
iajs-3473	23	31	2dupper	2dupper	NUM
iajs-3473	23	32	triangular	triangular	NOUN
iajs-3473	23	33	operator	operator	NOUN
iajs-3473	23	34	matrices	matrix	NOUN
iajs-3473	23	35	on	on	ADP
iajs-3473	23	36	the	the	DET
iajs-3473	23	37	banach	banach	NOUN
iajs-3473	23	38	space	space	NOUN
iajs-3473	23	39	(	(	PUNCT
iajs-3473	23	40	8	8	NUM
iajs-3473	23	41	,	,	PUNCT
iajs-3473	23	42	20	20	NUM
iajs-3473	23	43	,	,	PUNCT
iajs-3473	23	44	21	21	NUM
iajs-3473	23	45	)	)	PUNCT
iajs-3473	23	46	.	.	PUNCT
iajs-3473	24	1	operator	operator	NOUN
iajs-3473	24	2	matrices	matrix	NOUN
iajs-3473	24	3	are	be	AUX
iajs-3473	24	4	important	important	ADJ
iajs-3473	24	5	to	to	PART
iajs-3473	24	6	determine	determine	VERB
iajs-3473	24	7	the	the	DET
iajs-3473	24	8	solvability	solvability	NOUN
iajs-3473	24	9	and	and	CCONJ
iajs-3473	24	10	stability	stability	NOUN
iajs-3473	24	11	of	of	ADP
iajs-3473	24	12	the	the	DET
iajs-3473	24	13	underlying	underlie	VERB
iajs-3473	24	14	systems	system	NOUN
iajs-3473	24	15	and	and	CCONJ
iajs-3473	24	16	are	be	AUX
iajs-3473	24	17	found	find	VERB
iajs-3473	24	18	in	in	ADP
iajs-3473	24	19	various	various	ADJ
iajs-3473	24	20	areas	area	NOUN
iajs-3473	24	21	of	of	ADP
iajs-3473	24	22	pure	pure	ADJ
iajs-3473	24	23	and	and	CCONJ
iajs-3473	24	24	applied	applied	ADJ
iajs-3473	24	25	mathematics	mathematic	NOUN
iajs-3473	24	26	.	.	PUNCT
iajs-3473	25	1	if	if	SCONJ
iajs-3473	25	2	is	be	AUX
iajs-3473	25	3	a	a	DET
iajs-3473	25	4	bounded	bounded	ADJ
iajs-3473	25	5	linear	linear	ADJ
iajs-3473	25	6	operator	operator	NOUN
iajs-3473	25	7	on	on	ADP
iajs-3473	25	8	a	a	DET
iajs-3473	25	9	hilbert	hilbert	NOUN
iajs-3473	25	10	space	space	NOUN
iajs-3473	25	11	,	,	PUNCT
iajs-3473	25	12	one	one	PRON
iajs-3473	25	13	always	always	ADV
iajs-3473	25	14	has	have	VERB
iajs-3473	25	15	the	the	DET
iajs-3473	25	16	following	follow	VERB
iajs-3473	25	17	block	block	NOUN
iajs-3473	25	18	representation	representation	NOUN
iajs-3473	25	19	.	.	PUNCT
iajs-3473	26	1	(	(	PUNCT
iajs-3473	26	2	)	)	PUNCT
iajs-3473	26	3	in	in	ADP
iajs-3473	26	4	addition	addition	NOUN
iajs-3473	26	5	,	,	PUNCT
iajs-3473	26	6	if	if	SCONJ
iajs-3473	26	7	,	,	PUNCT
iajs-3473	26	8	then	then	ADV
iajs-3473	26	9	is	be	AUX
iajs-3473	26	10	an	an	DET
iajs-3473	26	11	upper	upper	ADJ
iajs-3473	26	12	triangular	triangular	NOUN
iajs-3473	26	13	operator	operator	NOUN
iajs-3473	26	14	matrix	matrix	NOUN
iajs-3473	26	15	.	.	PUNCT
iajs-3473	27	1	there	there	PRON
iajs-3473	27	2	are	be	VERB
iajs-3473	27	3	many	many	ADJ
iajs-3473	27	4	publications	publication	NOUN
iajs-3473	27	5	looking	look	VERB
iajs-3473	27	6	at	at	ADP
iajs-3473	27	7	the	the	DET
iajs-3473	27	8	spectral	spectral	ADJ
iajs-3473	27	9	properties	property	NOUN
iajs-3473	27	10	of	of	ADP
iajs-3473	27	11	upper	upper	ADJ
iajs-3473	27	12	triangular	triangular	NOUN
iajs-3473	27	13	operator	operator	NOUN
iajs-3473	27	14	matrices	matrix	NOUN
iajs-3473	27	15	.	.	PUNCT
iajs-3473	28	1	it	it	PRON
iajs-3473	28	2	's	be	AUX
iajs-3473	28	3	worth	worth	ADJ
iajs-3473	28	4	mentioning	mention	VERB
iajs-3473	28	5	that	that	SCONJ
iajs-3473	28	6	some	some	DET
iajs-3473	28	7	authors	author	NOUN
iajs-3473	28	8	estimate	estimate	VERB
iajs-3473	28	9	the	the	DET
iajs-3473	28	10	set	set	NOUN
iajs-3473	28	11	(	(	PUNCT
iajs-3473	28	12	(	(	PUNCT
iajs-3473	28	13	)	)	PUNCT
iajs-3473	28	14	(	(	PUNCT
iajs-3473	28	15	)	)	PUNCT
iajs-3473	28	16	)	)	PUNCT
iajs-3473	28	17	(	(	PUNCT
iajs-3473	28	18	)	)	PUNCT
iajs-3473	28	19	and	and	CCONJ
iajs-3473	28	20	obtain	obtain	VERB
iajs-3473	28	21	some	some	DET
iajs-3473	28	22	sufficient	sufficient	ADJ
iajs-3473	28	23	conditions	condition	NOUN
iajs-3473	28	24	of	of	ADP
iajs-3473	28	25	(	(	PUNCT
iajs-3473	28	26	)	)	PUNCT
iajs-3473	28	27	(	(	PUNCT
iajs-3473	28	28	)	)	PUNCT
iajs-3473	28	29	(	(	PUNCT
iajs-3473	28	30	)	)	PUNCT
iajs-3473	28	31	where	where	SCONJ
iajs-3473	28	32	the	the	DET
iajs-3473	28	33	upper	upper	ADJ
iajs-3473	28	34	triangular	triangular	NOUN
iajs-3473	28	35	operator	operator	NOUN
iajs-3473	28	36	matrix	matrix	NOUN
iajs-3473	28	37	is	be	AUX
iajs-3473	28	38	acting	act	VERB
iajs-3473	28	39	in	in	ADP
iajs-3473	28	40	a	a	DET
iajs-3473	28	41	banach	banach	NOUN
iajs-3473	28	42	space	space	NOUN
iajs-3473	28	43	,	,	PUNCT
iajs-3473	28	44	and	and	CCONJ
iajs-3473	28	45	*	*	PUNCT
iajs-3473	28	46	,	,	PUNCT
iajs-3473	28	47	+	+	PROPN
iajs-3473	28	48	.	.	PUNCT
iajs-3473	28	49	block	block	NOUN
iajs-3473	28	50	operator	operator	NOUN
iajs-3473	28	51	matrices	matrix	NOUN
iajs-3473	28	52	play	play	VERB
iajs-3473	28	53	a	a	DET
iajs-3473	28	54	significant	significant	ADJ
iajs-3473	28	55	role	role	NOUN
iajs-3473	28	56	in	in	ADP
iajs-3473	28	57	coupled	couple	VERB
iajs-3473	28	58	systems	system	NOUN
iajs-3473	28	59	of	of	ADP
iajs-3473	28	60	partial	partial	ADJ
iajs-3473	28	61	differential	differential	ADJ
iajs-3473	28	62	equations	equation	NOUN
iajs-3473	28	63	of	of	ADP
iajs-3473	28	64	mixed	mixed	ADJ
iajs-3473	28	65	order	order	NOUN
iajs-3473	28	66	.	.	PUNCT
iajs-3473	29	1	the	the	DET
iajs-3473	29	2	study	study	NOUN
iajs-3473	29	3	of	of	ADP
iajs-3473	29	4	upper	upper	ADJ
iajs-3473	29	5	triangular	triangular	NOUN
iajs-3473	29	6	operator	operator	NOUN
iajs-3473	29	7	matrices	matrix	NOUN
iajs-3473	29	8	and	and	CCONJ
iajs-3473	29	9	related	related	ADJ
iajs-3473	29	10	topics	topic	NOUN
iajs-3473	29	11	is	be	AUX
iajs-3473	29	12	one	one	NUM
iajs-3473	29	13	of	of	ADP
iajs-3473	29	14	the	the	DET
iajs-3473	29	15	hottest	hot	ADJ
iajs-3473	29	16	areas	area	NOUN
iajs-3473	29	17	in	in	ADP
iajs-3473	29	18	operator	operator	NOUN
iajs-3473	29	19	theory	theory	NOUN
iajs-3473	29	20	.	.	PUNCT
iajs-3473	30	1	a	a	DET
iajs-3473	30	2	number	number	NOUN
iajs-3473	30	3	of	of	ADP
iajs-3473	30	4	mathematicians	mathematician	NOUN
iajs-3473	30	5	have	have	AUX
iajs-3473	30	6	studied	study	VERB
iajs-3473	30	7	upper	upper	ADJ
iajs-3473	30	8	triangular	triangular	NOUN
iajs-3473	30	9	operator	operator	NOUN
iajs-3473	30	10	matrices	matrix	NOUN
iajs-3473	30	11	in	in	ADP
iajs-3473	30	12	the	the	DET
iajs-3473	30	13	past	past	NOUN
iajs-3473	30	14	.	.	PUNCT
iajs-3473	31	1	2	2	X
iajs-3473	31	2	.	.	X
iajs-3473	31	3	preliminaries	preliminary	NOUN
iajs-3473	31	4	in	in	ADP
iajs-3473	31	5	this	this	DET
iajs-3473	31	6	section	section	NOUN
iajs-3473	31	7	,	,	PUNCT
iajs-3473	31	8	we	we	PRON
iajs-3473	31	9	recall	recall	VERB
iajs-3473	31	10	the	the	DET
iajs-3473	31	11	following	follow	VERB
iajs-3473	31	12	concepts	concept	NOUN
iajs-3473	31	13	,	,	PUNCT
iajs-3473	31	14	which	which	PRON
iajs-3473	31	15	are	be	AUX
iajs-3473	31	16	used	use	VERB
iajs-3473	31	17	later	later	ADV
iajs-3473	31	18	.	.	PUNCT
iajs-3473	32	1	all	all	ADV
iajs-3473	32	2	through	through	ADP
iajs-3473	32	3	this	this	DET
iajs-3473	32	4	work	work	NOUN
iajs-3473	32	5	,	,	PUNCT
iajs-3473	32	6	denotes	denote	VERB
iajs-3473	32	7	to	to	PART
iajs-3473	32	8	infinite	infinite	VERB
iajs-3473	32	9	dimensional	dimensional	ADJ
iajs-3473	32	10	complex	complex	ADJ
iajs-3473	32	11	hilbert	hilbert	NOUN
iajs-3473	32	12	space	space	NOUN
iajs-3473	32	13	,	,	PUNCT
iajs-3473	32	14	(	(	PUNCT
iajs-3473	32	15	)	)	PUNCT
iajs-3473	32	16	is	be	AUX
iajs-3473	32	17	the	the	DET
iajs-3473	32	18	set	set	NOUN
iajs-3473	32	19	of	of	ADP
iajs-3473	32	20	all	all	DET
iajs-3473	32	21	closed	close	VERB
iajs-3473	32	22	linear	linear	ADJ
iajs-3473	32	23	operators	operator	NOUN
iajs-3473	32	24	defined	define	VERB
iajs-3473	32	25	on	on	ADP
iajs-3473	32	26	.	.	PUNCT
iajs-3473	33	1	for	for	ADP
iajs-3473	33	2	an	an	DET
iajs-3473	33	3	operator	operator	NOUN
iajs-3473	33	4	(	(	PUNCT
iajs-3473	33	5	)	)	PUNCT
iajs-3473	33	6	,	,	PUNCT
iajs-3473	33	7	we	we	PRON
iajs-3473	33	8	define	define	VERB
iajs-3473	33	9	(	(	PUNCT
iajs-3473	33	10	)	)	PUNCT
iajs-3473	33	11	as	as	ADP
iajs-3473	33	12	the	the	DET
iajs-3473	33	13	kernel	kernel	NOUN
iajs-3473	33	14	of	of	ADP
iajs-3473	33	15	,	,	PUNCT
iajs-3473	33	16	while	while	SCONJ
iajs-3473	33	17	(	(	PUNCT
iajs-3473	33	18	)	)	PUNCT
iajs-3473	33	19	represents	represent	VERB
iajs-3473	33	20	the	the	DET
iajs-3473	33	21	domain	domain	NOUN
iajs-3473	33	22	,	,	PUNCT
iajs-3473	33	23	and	and	CCONJ
iajs-3473	33	24	(	(	PUNCT
iajs-3473	33	25	)	)	PUNCT
iajs-3473	33	26	denotes	denote	VERB
iajs-3473	33	27	the	the	DET
iajs-3473	33	28	range	range	NOUN
iajs-3473	33	29	of	of	ADP
iajs-3473	33	30	.	.	PUNCT
iajs-3473	34	1	the	the	DET
iajs-3473	34	2	upper	upper	ADJ
iajs-3473	34	3	semi	semi	ADJ
iajs-3473	34	4	fredholm	fredholm	NOUN
iajs-3473	34	5	operator	operator	NOUN
iajs-3473	34	6	is	be	AUX
iajs-3473	34	7	define	define	VERB
iajs-3473	34	8	if	if	SCONJ
iajs-3473	34	9	(	(	PUNCT
iajs-3473	34	10	)	)	PUNCT
iajs-3473	34	11	is	be	AUX
iajs-3473	34	12	closed	close	VERB
iajs-3473	34	13	and	and	CCONJ
iajs-3473	34	14	(	(	PUNCT
iajs-3473	34	15	)	)	PUNCT
iajs-3473	34	16	(	(	PUNCT
iajs-3473	34	17	)	)	PUNCT
iajs-3473	34	18	is	be	AUX
iajs-3473	34	19	finite	finite	ADJ
iajs-3473	34	20	while	while	SCONJ
iajs-3473	34	21	we	we	PRON
iajs-3473	34	22	say	say	VERB
iajs-3473	34	23	that	that	PRON
iajs-3473	34	24	is	be	AUX
iajs-3473	34	25	lower	low	ADJ
iajs-3473	34	26	semi	semi	ADJ
iajs-3473	34	27	fredholm	fredholm	NOUN
iajs-3473	34	28	operator	operator	NOUN
iajs-3473	34	29	if	if	SCONJ
iajs-3473	34	30	(	(	PUNCT
iajs-3473	34	31	)	)	PUNCT
iajs-3473	34	32	(	(	PUNCT
iajs-3473	34	33	)	)	PUNCT
iajs-3473	34	34	is	be	AUX
iajs-3473	34	35	finite	finite	PROPN
iajs-3473	34	36	.	.	PUNCT
iajs-3473	35	1	a	a	DET
iajs-3473	35	2	fredholm	fredholm	NOUN
iajs-3473	35	3	operator	operator	NOUN
iajs-3473	35	4	is	be	AUX
iajs-3473	35	5	upper	upper	ADJ
iajs-3473	35	6	and	and	CCONJ
iajs-3473	35	7	lower	low	ADJ
iajs-3473	35	8	semi	semi	ADJ
iajs-3473	35	9	fredholm	fredholm	NOUN
iajs-3473	35	10	operator	operator	NOUN
iajs-3473	35	11	.	.	PUNCT
iajs-3473	36	1	(	(	PUNCT
iajs-3473	36	2	)	)	PUNCT
iajs-3473	36	3	*	*	PUNCT
iajs-3473	36	4	(	(	PUNCT
iajs-3473	36	5	)	)	PUNCT
iajs-3473	36	6	+	+	CCONJ
iajs-3473	36	7	(	(	PUNCT
iajs-3473	36	8	)	)	PUNCT
iajs-3473	36	9	*	*	PUNCT
iajs-3473	36	10	(	(	PUNCT
iajs-3473	36	11	)	)	PUNCT
iajs-3473	37	1	+	+	X
iajs-3473	37	2	.	.	PUNCT
iajs-3473	38	1	the	the	DET
iajs-3473	38	2	of	of	ADP
iajs-3473	38	3	is	be	AUX
iajs-3473	38	4	defined	define	VERB
iajs-3473	38	5	as	as	ADP
iajs-3473	38	6	(	(	PUNCT
iajs-3473	38	7	)	)	PUNCT
iajs-3473	38	8	(	(	PUNCT
iajs-3473	38	9	)	)	PUNCT
iajs-3473	38	10	(	(	PUNCT
iajs-3473	38	11	)	)	PUNCT
iajs-3473	38	12	an	an	DET
iajs-3473	38	13	operator	operator	NOUN
iajs-3473	38	14	(	(	PUNCT
iajs-3473	38	15	)	)	PUNCT
iajs-3473	38	16	which	which	PRON
iajs-3473	38	17	is	be	AUX
iajs-3473	38	18	fredholm	fredholm	NOUN
iajs-3473	38	19	operator	operator	NOUN
iajs-3473	38	20	of	of	ADP
iajs-3473	38	21	index	index	NOUN
iajs-3473	38	22	is	be	AUX
iajs-3473	38	23	defined	define	VERB
iajs-3473	38	24	as	as	ADP
iajs-3473	38	25	weyl	weyl	VERB
iajs-3473	38	26	operator	operator	NOUN
iajs-3473	38	27	,	,	PUNCT
iajs-3473	38	28	while	while	SCONJ
iajs-3473	38	29	(	(	PUNCT
iajs-3473	38	30	)	)	PUNCT
iajs-3473	38	31	*	*	PUNCT
iajs-3473	38	32	is	be	AUX
iajs-3473	38	33	not	not	PART
iajs-3473	38	34	weyl	weyl	VERB
iajs-3473	38	35	}	}	PUNCT
iajs-3473	38	36	is	be	AUX
iajs-3473	38	37	used	use	VERB
iajs-3473	38	38	to	to	PART
iajs-3473	38	39	define	define	VERB
iajs-3473	38	40	the	the	DET
iajs-3473	38	41	weyl	weyl	ADJ
iajs-3473	38	42	spectrum	spectrum	NOUN
iajs-3473	38	43	of	of	ADP
iajs-3473	38	44	.	.	PUNCT
iajs-3473	39	1	in	in	ADP
iajs-3473	39	2	addition	addition	NOUN
iajs-3473	39	3	we	we	PRON
iajs-3473	39	4	can	can	AUX
iajs-3473	39	5	assign	assign	VERB
iajs-3473	39	6	the	the	DET
iajs-3473	39	7	following	following	ADJ
iajs-3473	39	8	notations	notation	NOUN
iajs-3473	39	9	:	:	PUNCT
iajs-3473	39	10	(	(	PUNCT
iajs-3473	39	11	)	)	PUNCT
iajs-3473	39	12	*	*	PUNCT
iajs-3473	39	13	(	(	PUNCT
iajs-3473	39	14	)	)	PUNCT
iajs-3473	39	15	(	(	PUNCT
iajs-3473	39	16	)	)	PUNCT
iajs-3473	39	17	,	,	PUNCT
iajs-3473	39	18	(	(	PUNCT
iajs-3473	39	19	)	)	PUNCT
iajs-3473	39	20	}	}	PUNCT
iajs-3473	39	21	(	(	PUNCT
iajs-3473	39	22	)	)	PUNCT
iajs-3473	39	23	*	*	PUNCT
iajs-3473	39	24	(	(	PUNCT
iajs-3473	39	25	)	)	PUNCT
iajs-3473	39	26	(	(	PUNCT
iajs-3473	39	27	)	)	PUNCT
iajs-3473	39	28	,	,	PUNCT
iajs-3473	39	29	(	(	PUNCT
iajs-3473	39	30	)	)	PUNCT
iajs-3473	39	31	+	+	CCONJ
iajs-3473	39	32	in	in	ADP
iajs-3473	39	33	(	(	PUNCT
iajs-3473	39	34	4	4	NUM
iajs-3473	39	35	)	)	PUNCT
iajs-3473	39	36	,	,	PUNCT
iajs-3473	39	37	berkani	berkani	NOUN
iajs-3473	39	38	generalized	generalize	VERB
iajs-3473	39	39	the	the	DET
iajs-3473	39	40	concept	concept	NOUN
iajs-3473	39	41	of	of	ADP
iajs-3473	39	42	fredholm	fredholm	NOUN
iajs-3473	39	43	operators	operator	NOUN
iajs-3473	39	44	to	to	ADP
iajs-3473	39	45	b	b	X
iajs-3473	39	46	-	-	PUNCT
iajs-3473	39	47	fredholm	fredholm	NOUN
iajs-3473	39	48	operators	operator	NOUN
iajs-3473	39	49	as	as	SCONJ
iajs-3473	39	50	follows	follow	VERB
iajs-3473	39	51	(	(	PUNCT
iajs-3473	39	52	)	)	PUNCT
iajs-3473	39	53	{	{	PUNCT
iajs-3473	39	54	(	(	PUNCT
iajs-3473	39	55	)	)	PUNCT
iajs-3473	39	56	(	(	PUNCT
iajs-3473	39	57	)	)	PUNCT
iajs-3473	39	58	(	(	PUNCT
iajs-3473	39	59	)	)	PUNCT
iajs-3473	39	60	(	(	PUNCT
iajs-3473	39	61	)	)	PUNCT
iajs-3473	39	62	}	}	PUNCT
iajs-3473	39	63	the	the	DET
iajs-3473	39	64	degree	degree	NOUN
iajs-3473	39	65	of	of	ADP
iajs-3473	39	66	stable	stable	ADJ
iajs-3473	39	67	iteration	iteration	NOUN
iajs-3473	39	68	of	of	ADP
iajs-3473	39	69	is	be	AUX
iajs-3473	39	70	denoted	denote	VERB
iajs-3473	39	71	by	by	ADP
iajs-3473	39	72	(	(	PUNCT
iajs-3473	39	73	)	)	PUNCT
iajs-3473	39	74	and	and	CCONJ
iajs-3473	39	75	defined	define	VERB
iajs-3473	39	76	by	by	ADP
iajs-3473	39	77	(	(	PUNCT
iajs-3473	39	78	)	)	PUNCT
iajs-3473	39	79	(	(	PUNCT
iajs-3473	39	80	)	)	PUNCT
iajs-3473	39	81	and	and	CCONJ
iajs-3473	39	82	(	(	PUNCT
iajs-3473	39	83	)	)	PUNCT
iajs-3473	40	1	when	when	SCONJ
iajs-3473	40	2	(	(	PUNCT
iajs-3473	40	3	)	)	PUNCT
iajs-3473	40	4	.	.	PUNCT
iajs-3473	41	1	furthermore	furthermore	ADV
iajs-3473	41	2	,	,	PUNCT
iajs-3473	41	3	for	for	ADP
iajs-3473	41	4	(	(	PUNCT
iajs-3473	41	5	)	)	PUNCT
iajs-3473	41	6	the	the	DET
iajs-3473	41	7	operator	operator	NOUN
iajs-3473	41	8	is	be	AUX
iajs-3473	41	9	upper	upper	ADJ
iajs-3473	41	10	and	and	CCONJ
iajs-3473	41	11	lower	low	ADJ
iajs-3473	41	12	semi	semi	ADJ
iajs-3473	41	13	operator	operator	NOUN
iajs-3473	41	14	,	,	PUNCT
iajs-3473	41	15	where	where	SCONJ
iajs-3473	41	16	is	be	AUX
iajs-3473	41	17	(	(	PUNCT
iajs-3473	41	18	resp	resp	NOUN
iajs-3473	41	19	.	.	PUNCT
iajs-3473	41	20	,	,	PUNCT
iajs-3473	41	21	)	)	PUNCT
iajs-3473	41	22	semi	semi	ADV
iajs-3473	41	23	operator	operator	NOUN
iajs-3473	41	24	if	if	SCONJ
iajs-3473	41	25	ihjpas	ihjpa	NOUN
iajs-3473	41	26	.	.	PUNCT
iajs-3473	42	1	2025,38(4	2025,38(4	NOUN
iajs-3473	42	2	)	)	PUNCT
iajs-3473	43	1	289	289	NUM
iajs-3473	43	2	(	(	PUNCT
iajs-3473	43	3	)	)	PUNCT
iajs-3473	43	4	*	*	PUNCT
iajs-3473	44	1	(	(	PUNCT
iajs-3473	44	2	)	)	PUNCT
iajs-3473	44	3	(	(	PUNCT
iajs-3473	44	4	)	)	PUNCT
iajs-3473	44	5	+	+	CCONJ
iajs-3473	44	6	is	be	AUX
iajs-3473	44	7	finite	finite	ADJ
iajs-3473	44	8	and	and	CCONJ
iajs-3473	44	9	(	(	PUNCT
iajs-3473	44	10	)	)	PUNCT
iajs-3473	44	11	closed	closed	ADJ
iajs-3473	44	12	and	and	CCONJ
iajs-3473	44	13	(	(	PUNCT
iajs-3473	44	14	resp	resp	NOUN
iajs-3473	44	15	.	.	PUNCT
iajs-3473	44	16	,	,	PUNCT
iajs-3473	45	1	*	*	PUNCT
iajs-3473	45	2	(	(	PUNCT
iajs-3473	45	3	)	)	PUNCT
iajs-3473	45	4	(	(	PUNCT
iajs-3473	45	5	)	)	PUNCT
iajs-3473	45	6	+	+	CCONJ
iajs-3473	45	7	is	be	AUX
iajs-3473	45	8	finite	finite	ADJ
iajs-3473	45	9	)	)	PUNCT
iajs-3473	45	10	,	,	PUNCT
iajs-3473	45	11	and	and	CCONJ
iajs-3473	45	12	the	the	DET
iajs-3473	45	13	index	index	NOUN
iajs-3473	45	14	of	of	ADP
iajs-3473	45	15	is	be	AUX
iajs-3473	45	16	(	(	PUNCT
iajs-3473	45	17	)	)	PUNCT
iajs-3473	45	18	*	*	PUNCT
iajs-3473	45	19	(	(	PUNCT
iajs-3473	45	20	)	)	PUNCT
iajs-3473	45	21	(	(	PUNCT
iajs-3473	45	22	)	)	PUNCT
iajs-3473	45	23	+	+	NUM
iajs-3473	45	24	*	*	PUNCT
iajs-3473	45	25	(	(	PUNCT
iajs-3473	45	26	)	)	PUNCT
iajs-3473	45	27	(	(	PUNCT
iajs-3473	45	28	)	)	PUNCT
iajs-3473	45	29	+	+	CCONJ
iajs-3473	45	30	we	we	PRON
iajs-3473	45	31	call	call	VERB
iajs-3473	45	32	(	(	PUNCT
iajs-3473	45	33	)	)	PUNCT
iajs-3473	45	34	as	as	SCONJ
iajs-3473	45	35	if	if	SCONJ
iajs-3473	45	36	it	it	PRON
iajs-3473	45	37	’s	’	VERB
iajs-3473	45	38	operator	operator	NOUN
iajs-3473	45	39	with	with	ADP
iajs-3473	45	40	and	and	CCONJ
iajs-3473	45	41	(	(	PUNCT
iajs-3473	45	42	)	)	PUNCT
iajs-3473	45	43	is	be	AUX
iajs-3473	45	44	used	use	VERB
iajs-3473	45	45	to	to	PART
iajs-3473	45	46	symbolize	symbolize	VERB
iajs-3473	45	47	the	the	DET
iajs-3473	45	48	spectrum	spectrum	NOUN
iajs-3473	45	49	of	of	ADP
iajs-3473	45	50	and	and	CCONJ
iajs-3473	45	51	defined	define	VERB
iajs-3473	45	52	by	by	ADP
iajs-3473	45	53	(	(	PUNCT
iajs-3473	45	54	)	)	PUNCT
iajs-3473	45	55	*	*	PUNCT
iajs-3473	45	56	is	be	AUX
iajs-3473	45	57	not	not	PART
iajs-3473	45	58	-weyl	-weyl	ADJ
iajs-3473	45	59	+	+	CCONJ
iajs-3473	45	60	moreover	moreover	ADV
iajs-3473	45	61	,	,	PUNCT
iajs-3473	45	62	the	the	DET
iajs-3473	45	63	ascent	ascent	NOUN
iajs-3473	45	64	(	(	PUNCT
iajs-3473	45	65	)	)	PUNCT
iajs-3473	45	66	and	and	CCONJ
iajs-3473	45	67	descent	descent	NOUN
iajs-3473	45	68	(	(	PUNCT
iajs-3473	45	69	)	)	PUNCT
iajs-3473	45	70	for	for	ADP
iajs-3473	45	71	(	(	PUNCT
iajs-3473	45	72	)	)	PUNCT
iajs-3473	45	73	are	be	AUX
iajs-3473	45	74	defined	define	VERB
iajs-3473	45	75	as	as	ADP
iajs-3473	45	76	:	:	PUNCT
iajs-3473	45	77	(	(	PUNCT
iajs-3473	45	78	)	)	PUNCT
iajs-3473	45	79	{	{	PUNCT
iajs-3473	45	80	.	.	PUNCT
iajs-3473	46	1	/	/	PUNCT
iajs-3473	46	2	.	.	PUNCT
iajs-3473	46	3	/	/	PUNCT
iajs-3473	46	4	}	}	PUNCT
iajs-3473	46	5	(	(	PUNCT
iajs-3473	46	6	)	)	PUNCT
iajs-3473	46	7	{	{	PUNCT
iajs-3473	46	8	.	.	PUNCT
iajs-3473	46	9	/	/	PUNCT
iajs-3473	46	10	.	.	PUNCT
iajs-3473	47	1	/	/	PUNCT
iajs-3473	47	2	}	}	PUNCT
iajs-3473	47	3	an	an	DET
iajs-3473	47	4	operator	operator	NOUN
iajs-3473	47	5	(	(	PUNCT
iajs-3473	47	6	)	)	PUNCT
iajs-3473	47	7	is	be	AUX
iajs-3473	47	8	called	call	VERB
iajs-3473	47	9	browder	browder	NOUN
iajs-3473	47	10	if	if	SCONJ
iajs-3473	47	11	it	it	PRON
iajs-3473	47	12	’s	’	VERB
iajs-3473	47	13	both	both	PRON
iajs-3473	47	14	and	and	CCONJ
iajs-3473	47	15	semi	semi	ADV
iajs-3473	47	16	browder	browder	NOUN
iajs-3473	47	17	,	,	PUNCT
iajs-3473	47	18	where	where	SCONJ
iajs-3473	47	19	(	(	PUNCT
iajs-3473	47	20	)	)	PUNCT
iajs-3473	47	21	is	be	AUX
iajs-3473	47	22	semibrowder	semibrowd	ADJ
iajs-3473	47	23	if	if	SCONJ
iajs-3473	47	24	(	(	PUNCT
iajs-3473	47	25	)	)	PUNCT
iajs-3473	47	26	with	with	SCONJ
iajs-3473	47	27	is	be	AUX
iajs-3473	47	28	semifredholm	semifredholm	ADJ
iajs-3473	47	29	and	and	CCONJ
iajs-3473	47	30	it	it	PRON
iajs-3473	47	31	is	be	AUX
iajs-3473	47	32	semi	semi	ADJ
iajs-3473	47	33	-	-	NOUN
iajs-3473	47	34	browder	browder	NOUN
iajs-3473	47	35	if	if	SCONJ
iajs-3473	47	36	(	(	PUNCT
iajs-3473	47	37	)	)	PUNCT
iajs-3473	47	38	with	with	SCONJ
iajs-3473	47	39	is	be	AUX
iajs-3473	47	40	semi	semi	ADJ
iajs-3473	47	41	–	–	PUNCT
iajs-3473	47	42	fredholm	fredholm	NOUN
iajs-3473	47	43	.	.	PUNCT
iajs-3473	48	1	now	now	ADV
iajs-3473	48	2	,	,	PUNCT
iajs-3473	48	3	we	we	PRON
iajs-3473	48	4	can	can	AUX
iajs-3473	48	5	define	define	VERB
iajs-3473	48	6	the	the	DET
iajs-3473	48	7	following	follow	VERB
iajs-3473	48	8	spectrum	spectrum	NOUN
iajs-3473	48	9	for	for	ADP
iajs-3473	48	10	an	an	DET
iajs-3473	48	11	operator	operator	NOUN
iajs-3473	48	12	as	as	ADP
iajs-3473	48	13	:	:	PUNCT
iajs-3473	48	14	(	(	PUNCT
iajs-3473	48	15	)	)	PUNCT
iajs-3473	48	16	*	*	PUNCT
iajs-3473	48	17	not	not	PART
iajs-3473	48	18	upper	upper	ADJ
iajs-3473	48	19	semi	semi	ADJ
iajs-3473	48	20	fredholm+	fredholm+	PROPN
iajs-3473	48	21	,	,	PUNCT
iajs-3473	48	22	(	(	PUNCT
iajs-3473	48	23	)	)	PUNCT
iajs-3473	48	24	*	*	PUNCT
iajs-3473	48	25	not	not	PART
iajs-3473	48	26	lower	low	ADJ
iajs-3473	48	27	semi	semi	ADV
iajs-3473	48	28	fredholm+	fredholm+	NOUN
iajs-3473	48	29	,	,	PUNCT
iajs-3473	48	30	(	(	PUNCT
iajs-3473	48	31	)	)	PUNCT
iajs-3473	48	32	*	*	PUNCT
iajs-3473	48	33	not	not	PART
iajs-3473	48	34	fredholm+	fredholm+	VERB
iajs-3473	48	35	,	,	PUNCT
iajs-3473	48	36	(	(	PUNCT
iajs-3473	48	37	)	)	PUNCT
iajs-3473	48	38	*	*	PUNCT
iajs-3473	48	39	(	(	PUNCT
iajs-3473	48	40	)	)	PUNCT
iajs-3473	49	1	+	+	ADJ
iajs-3473	49	2	,	,	PUNCT
iajs-3473	49	3	(	(	PUNCT
iajs-3473	49	4	)	)	PUNCT
iajs-3473	49	5	*	*	PUNCT
iajs-3473	49	6	not	not	PART
iajs-3473	49	7	upper	upper	ADJ
iajs-3473	49	8	semi	semi	ADJ
iajs-3473	49	9	-	-	NOUN
iajs-3473	49	10	browder	browder	NOUN
iajs-3473	49	11	+	+	NOUN
iajs-3473	49	12	,	,	PUNCT
iajs-3473	49	13	(	(	PUNCT
iajs-3473	49	14	)	)	PUNCT
iajs-3473	49	15	*	*	PUNCT
iajs-3473	49	16	not	not	PART
iajs-3473	49	17	lower	low	ADJ
iajs-3473	49	18	semi	semi	NOUN
iajs-3473	49	19	-	-	ADJ
iajs-3473	49	20	browder+	browder+	ADV
iajs-3473	49	21	and	and	CCONJ
iajs-3473	49	22	(	(	PUNCT
iajs-3473	49	23	)	)	PUNCT
iajs-3473	49	24	*	*	PUNCT
iajs-3473	49	25	not	not	PART
iajs-3473	49	26	browder	browder	NOUN
iajs-3473	49	27	+	+	ADV
iajs-3473	49	28	,	,	PUNCT
iajs-3473	49	29	respectively	respectively	ADV
iajs-3473	49	30	.	.	PUNCT
iajs-3473	50	1	evidently	evidently	ADV
iajs-3473	50	2	(	(	PUNCT
iajs-3473	50	3	)	)	PUNCT
iajs-3473	50	4	(	(	PUNCT
iajs-3473	50	5	)	)	PUNCT
iajs-3473	50	6	(	(	PUNCT
iajs-3473	50	7	)	)	PUNCT
iajs-3473	50	8	(	(	PUNCT
iajs-3473	50	9	)	)	PUNCT
iajs-3473	50	10	(	(	PUNCT
iajs-3473	50	11	)	)	PUNCT
iajs-3473	50	12	where	where	SCONJ
iajs-3473	50	13	(	(	PUNCT
iajs-3473	50	14	)	)	PUNCT
iajs-3473	50	15	denotes	denote	VERB
iajs-3473	50	16	the	the	DET
iajs-3473	50	17	set	set	NOUN
iajs-3473	50	18	of	of	ADP
iajs-3473	50	19	accumulation	accumulation	NOUN
iajs-3473	50	20	points	point	NOUN
iajs-3473	50	21	of	of	ADP
iajs-3473	50	22	the	the	DET
iajs-3473	50	23	spectrum	spectrum	NOUN
iajs-3473	50	24	(	(	PUNCT
iajs-3473	50	25	)	)	PUNCT
iajs-3473	50	26	of	of	ADP
iajs-3473	50	27	.	.	PUNCT
iajs-3473	50	28	approximate	approximate	ADJ
iajs-3473	50	29	point	point	NOUN
iajs-3473	50	30	spectrum	spectrum	NOUN
iajs-3473	50	31	of	of	ADP
iajs-3473	50	32	.	.	PUNCT
iajs-3473	51	1	weyl	weyl	PROPN
iajs-3473	51	2	claims	claim	VERB
iajs-3473	51	3	that	that	SCONJ
iajs-3473	51	4	the	the	DET
iajs-3473	51	5	wey’l	wey’l	ADJ
iajs-3473	51	6	spectrum	spectrum	NOUN
iajs-3473	51	7	of	of	ADP
iajs-3473	51	8	a	a	DET
iajs-3473	51	9	hermition	hermition	NOUN
iajs-3473	51	10	operator	operator	NOUN
iajs-3473	51	11	contains	contain	VERB
iajs-3473	51	12	exactly	exactly	ADV
iajs-3473	51	13	all	all	PRON
iajs-3473	51	14	of	of	ADP
iajs-3473	51	15	the	the	DET
iajs-3473	51	16	points	point	NOUN
iajs-3473	51	17	in	in	ADP
iajs-3473	51	18	the	the	DET
iajs-3473	51	19	spectrum	spectrum	NOUN
iajs-3473	51	20	of	of	ADP
iajs-3473	51	21	with	with	ADP
iajs-3473	51	22	the	the	DET
iajs-3473	51	23	exception	exception	NOUN
iajs-3473	51	24	of	of	ADP
iajs-3473	51	25	those	those	DET
iajs-3473	51	26	points	point	NOUN
iajs-3473	51	27	,	,	PUNCT
iajs-3473	51	28	which	which	PRON
iajs-3473	51	29	are	be	AUX
iajs-3473	51	30	isolate	isolate	VERB
iajs-3473	51	31	eigenvalues	eigenvalue	NOUN
iajs-3473	51	32	of	of	ADP
iajs-3473	51	33	restricted	restricted	ADJ
iajs-3473	51	34	pluralism	pluralism	NOUN
iajs-3473	51	35	,	,	PUNCT
iajs-3473	51	36	in	in	ADP
iajs-3473	51	37	(	(	PUNCT
iajs-3473	51	38	9	9	NUM
iajs-3473	51	39	)	)	PUNCT
iajs-3473	51	40	,	,	PUNCT
iajs-3473	51	41	where	where	SCONJ
iajs-3473	51	42	he	he	PRON
iajs-3473	51	43	proved	prove	VERB
iajs-3473	51	44	the	the	DET
iajs-3473	51	45	weyl	weyl	PROPN
iajs-3473	51	46	’s	’s	PART
iajs-3473	51	47	theorems	theorem	NOUN
iajs-3473	51	48	for	for	ADP
iajs-3473	51	49	bounded	bounded	ADJ
iajs-3473	51	50	hermition	hermition	NOUN
iajs-3473	51	51	operators	operator	NOUN
iajs-3473	51	52	.	.	PUNCT
iajs-3473	52	1	weyl	weyl	PROPN
iajs-3473	52	2	’s	’s	PART
iajs-3473	52	3	theorem	theorem	NOUN
iajs-3473	52	4	has	have	AUX
iajs-3473	52	5	now	now	ADV
iajs-3473	52	6	been	be	AUX
iajs-3473	52	7	extended	extend	VERB
iajs-3473	52	8	to	to	ADP
iajs-3473	52	9	other	other	ADJ
iajs-3473	52	10	types	type	NOUN
iajs-3473	52	11	of	of	ADP
iajs-3473	52	12	bounded	bounded	ADJ
iajs-3473	52	13	operators	operator	NOUN
iajs-3473	52	14	(	(	PUNCT
iajs-3473	52	15	10	10	NUM
iajs-3473	52	16	)	)	PUNCT
iajs-3473	52	17	.	.	PUNCT
iajs-3473	53	1	recall	recall	VERB
iajs-3473	53	2	that	that	PRON
iajs-3473	53	3	one	one	NOUN
iajs-3473	53	4	says	say	VERB
iajs-3473	53	5	that	that	SCONJ
iajs-3473	53	6	obeys	obey	VERB
iajs-3473	53	7	weyl	weyl	PROPN
iajs-3473	53	8	's	's	PART
iajs-3473	53	9	theorem	theorem	NOUN
iajs-3473	53	10	if	if	SCONJ
iajs-3473	53	11	(	(	PUNCT
iajs-3473	53	12	)	)	PUNCT
iajs-3473	53	13	(	(	PUNCT
iajs-3473	53	14	)	)	PUNCT
iajs-3473	53	15	(	(	PUNCT
iajs-3473	53	16	)	)	PUNCT
iajs-3473	53	17	where	where	SCONJ
iajs-3473	53	18	(	(	PUNCT
iajs-3473	53	19	)	)	PUNCT
iajs-3473	53	20	is	be	AUX
iajs-3473	53	21	the	the	DET
iajs-3473	53	22	set	set	NOUN
iajs-3473	53	23	of	of	ADP
iajs-3473	53	24	isolated	isolated	ADJ
iajs-3473	53	25	points	point	NOUN
iajs-3473	53	26	of	of	ADP
iajs-3473	53	27	(	(	PUNCT
iajs-3473	53	28	)	)	PUNCT
iajs-3473	53	29	which	which	PRON
iajs-3473	53	30	are	be	AUX
iajs-3473	53	31	eigenvalues	eigenvalue	NOUN
iajs-3473	53	32	of	of	ADP
iajs-3473	53	33	finite	finite	ADJ
iajs-3473	53	34	multiplicity	multiplicity	NOUN
iajs-3473	53	35	,	,	PUNCT
iajs-3473	53	36	and	and	CCONJ
iajs-3473	53	37	that	that	DET
iajs-3473	53	38	one	one	NOUN
iajs-3473	53	39	says	say	VERB
iajs-3473	53	40	that	that	SCONJ
iajs-3473	53	41	obeys	obey	VERB
iajs-3473	53	42	browder	browder	PROPN
iajs-3473	53	43	's	's	PART
iajs-3473	53	44	theorem	theorem	NOUN
iajs-3473	53	45	if	if	SCONJ
iajs-3473	53	46	(	(	PUNCT
iajs-3473	53	47	)	)	PUNCT
iajs-3473	53	48	(	(	PUNCT
iajs-3473	53	49	)	)	PUNCT
iajs-3473	53	50	.	.	PUNCT
iajs-3473	54	1	we	we	PRON
iajs-3473	54	2	say	say	VERB
iajs-3473	54	3	that	that	PRON
iajs-3473	54	4	obeys	obey	VERB
iajs-3473	54	5	a	a	DET
iajs-3473	54	6	-	-	PUNCT
iajs-3473	54	7	weyl	weyl	NOUN
iajs-3473	54	8	's	's	PART
iajs-3473	54	9	theorem	theorem	NOUN
iajs-3473	54	10	if	if	SCONJ
iajs-3473	54	11	(	(	PUNCT
iajs-3473	54	12	)	)	PUNCT
iajs-3473	54	13	(	(	PUNCT
iajs-3473	54	14	)	)	PUNCT
iajs-3473	54	15	(	(	PUNCT
iajs-3473	54	16	)	)	PUNCT
iajs-3473	54	17	where	where	SCONJ
iajs-3473	54	18	(	(	PUNCT
iajs-3473	54	19	)	)	PUNCT
iajs-3473	54	20	is	be	AUX
iajs-3473	54	21	the	the	DET
iajs-3473	54	22	set	set	NOUN
iajs-3473	54	23	of	of	ADP
iajs-3473	54	24	isolated	isolated	ADJ
iajs-3473	54	25	points	point	NOUN
iajs-3473	54	26	of	of	ADP
iajs-3473	54	27	(	(	PUNCT
iajs-3473	54	28	)	)	PUNCT
iajs-3473	54	29	which	which	PRON
iajs-3473	54	30	are	be	AUX
iajs-3473	54	31	eigenvalues	eigenvalue	NOUN
iajs-3473	54	32	of	of	ADP
iajs-3473	54	33	finite	finite	ADJ
iajs-3473	54	34	multiplicity	multiplicity	NOUN
iajs-3473	54	35	,	,	PUNCT
iajs-3473	54	36	and	and	CCONJ
iajs-3473	54	37	that	that	PRON
iajs-3473	54	38	obeys	obey	VERB
iajs-3473	54	39	a	a	DET
iajs-3473	54	40	-	-	PUNCT
iajs-3473	54	41	browder	browder	NOUN
iajs-3473	54	42	's	's	PART
iajs-3473	54	43	theorem	theorem	NOUN
iajs-3473	54	44	if	if	SCONJ
iajs-3473	54	45	(	(	PUNCT
iajs-3473	54	46	)	)	PUNCT
iajs-3473	54	47	(	(	PUNCT
iajs-3473	54	48	)	)	PUNCT
iajs-3473	54	49	.	.	PUNCT
iajs-3473	55	1	let	let	AUX
iajs-3473	55	2	be	be	AUX
iajs-3473	55	3	an	an	DET
iajs-3473	55	4	infinite	infinite	ADJ
iajs-3473	55	5	dimensional	dimensional	ADJ
iajs-3473	55	6	hilbert	hilbert	NOUN
iajs-3473	55	7	space	space	NOUN
iajs-3473	55	8	.	.	PUNCT
iajs-3473	56	1	hamiltonian	hamiltonian	ADJ
iajs-3473	56	2	operator	operator	NOUN
iajs-3473	56	3	can	can	AUX
iajs-3473	56	4	be	be	AUX
iajs-3473	56	5	defined	define	VERB
iajs-3473	56	6	as	as	ADP
iajs-3473	56	7	densely	densely	ADV
iajs-3473	56	8	closed	close	VERB
iajs-3473	56	9	operator	operator	NOUN
iajs-3473	56	10	matrix	matrix	NOUN
iajs-3473	56	11	(	(	PUNCT
iajs-3473	56	12	)	)	PUNCT
iajs-3473	56	13	(	(	PUNCT
iajs-3473	56	14	(	(	PUNCT
iajs-3473	56	15	)	)	PUNCT
iajs-3473	56	16	(	(	PUNCT
iajs-3473	56	17	)	)	PUNCT
iajs-3473	56	18	)	)	PUNCT
iajs-3473	57	1	(	(	PUNCT
iajs-3473	57	2	(	(	PUNCT
iajs-3473	57	3	)	)	PUNCT
iajs-3473	57	4	(	(	PUNCT
iajs-3473	57	5	)	)	PUNCT
iajs-3473	57	6	)	)	PUNCT
iajs-3473	57	7	where	where	SCONJ
iajs-3473	57	8	is	be	AUX
iajs-3473	57	9	a	a	DET
iajs-3473	57	10	densely	densely	ADV
iajs-3473	57	11	defined	define	VERB
iajs-3473	57	12	closed	closed	ADJ
iajs-3473	57	13	operator	operator	NOUN
iajs-3473	57	14	,	,	PUNCT
iajs-3473	57	15	and	and	CCONJ
iajs-3473	57	16	are	be	AUX
iajs-3473	57	17	self	self	NOUN
iajs-3473	57	18	adjoint	adjoint	NOUN
iajs-3473	57	19	operators.(see	operators.(see	PROPN
iajs-3473	57	20	(	(	PUNCT
iajs-3473	57	21	4	4	NUM
iajs-3473	57	22	)	)	PUNCT
iajs-3473	57	23	)	)	PUNCT
iajs-3473	57	24	.	.	PUNCT
iajs-3473	58	1	for	for	ADP
iajs-3473	58	2	the	the	DET
iajs-3473	58	3	proof	proof	NOUN
iajs-3473	58	4	of	of	ADP
iajs-3473	58	5	the	the	DET
iajs-3473	58	6	main	main	ADJ
iajs-3473	58	7	results	result	NOUN
iajs-3473	58	8	in	in	ADP
iajs-3473	58	9	the	the	DET
iajs-3473	58	10	next	next	ADJ
iajs-3473	58	11	section	section	NOUN
iajs-3473	58	12	,	,	PUNCT
iajs-3473	58	13	we	we	PRON
iajs-3473	58	14	need	need	VERB
iajs-3473	58	15	the	the	DET
iajs-3473	58	16	following	follow	VERB
iajs-3473	58	17	auxiliary	auxiliary	ADJ
iajs-3473	58	18	lemmas	lemmas	NOUN
iajs-3473	58	19	.	.	PUNCT
iajs-3473	59	1	2.1	2.1	NUM
iajs-3473	59	2	.	.	PUNCT
iajs-3473	60	1	lemma	lemma	PROPN
iajs-3473	60	2	1	1	NUM
iajs-3473	60	3	.	.	PUNCT
iajs-3473	60	4	is	be	AUX
iajs-3473	60	5	upper	upper	ADJ
iajs-3473	60	6	semib	semib	NOUN
iajs-3473	60	7	-	-	PUNCT
iajs-3473	60	8	fredholm	fredholm	NOUN
iajs-3473	60	9	and	and	CCONJ
iajs-3473	60	10	(	(	PUNCT
iajs-3473	60	11	)	)	PUNCT
iajs-3473	60	12	if	if	SCONJ
iajs-3473	60	13	and	and	CCONJ
iajs-3473	60	14	only	only	ADV
iajs-3473	60	15	if	if	SCONJ
iajs-3473	60	16	is	be	AUX
iajs-3473	60	17	left	leave	VERB
iajs-3473	60	18	fredholm	fredholm	NOUN
iajs-3473	60	19	.	.	PUNCT
iajs-3473	61	1	2	2	X
iajs-3473	61	2	.	.	X
iajs-3473	61	3	is	be	AUX
iajs-3473	61	4	lower	low	ADJ
iajs-3473	61	5	semib	semib	NOUN
iajs-3473	61	6	-	-	PUNCT
iajs-3473	61	7	fredholm	fredholm	NOUN
iajs-3473	61	8	and	and	CCONJ
iajs-3473	61	9	(	(	PUNCT
iajs-3473	61	10	)	)	PUNCT
iajs-3473	61	11	if	if	SCONJ
iajs-3473	61	12	and	and	CCONJ
iajs-3473	61	13	only	only	ADV
iajs-3473	61	14	if	if	SCONJ
iajs-3473	61	15	is	be	AUX
iajs-3473	61	16	right	right	ADJ
iajs-3473	61	17	fredholm	fredholm	NOUN
iajs-3473	61	18	.	.	PUNCT
iajs-3473	62	1	proof	proof	NOUN
iajs-3473	62	2	.	.	PUNCT
iajs-3473	63	1	the	the	DET
iajs-3473	63	2	proof	proof	NOUN
iajs-3473	63	3	of	of	ADP
iajs-3473	63	4	this	this	DET
iajs-3473	63	5	lemma	lemma	PROPN
iajs-3473	63	6	is	be	AUX
iajs-3473	63	7	similar	similar	ADJ
iajs-3473	63	8	to	to	ADP
iajs-3473	63	9	the	the	DET
iajs-3473	63	10	proof	proof	NOUN
iajs-3473	63	11	in	in	ADP
iajs-3473	63	12	bounded	bounded	ADJ
iajs-3473	63	13	case	case	NOUN
iajs-3473	63	14	.	.	PUNCT
iajs-3473	64	1	ihjpas	ihjpas	PROPN
iajs-3473	64	2	.	.	PUNCT
iajs-3473	65	1	2025,38(4	2025,38(4	NOUN
iajs-3473	65	2	)	)	PUNCT
iajs-3473	66	1	290	290	NUM
iajs-3473	66	2	2.2	2.2	NUM
iajs-3473	66	3	.	.	PUNCT
iajs-3473	67	1	lemma	lemma	PROPN
iajs-3473	67	2	(	(	PUNCT
iajs-3473	67	3	see	see	VERB
iajs-3473	67	4	(	(	PUNCT
iajs-3473	67	5	13	13	NUM
iajs-3473	67	6	)	)	PUNCT
iajs-3473	67	7	)	)	PUNCT
iajs-3473	67	8	let	let	VERB
iajs-3473	67	9	(	(	PUNCT
iajs-3473	67	10	)	)	PUNCT
iajs-3473	67	11	(	(	PUNCT
iajs-3473	67	12	)	)	PUNCT
iajs-3473	67	13	(	(	PUNCT
iajs-3473	67	14	)	)	PUNCT
iajs-3473	67	15	be	be	AUX
iajs-3473	67	16	a	a	DET
iajs-3473	67	17	closed	closed	ADJ
iajs-3473	67	18	operator	operator	NOUN
iajs-3473	67	19	matrix	matrix	NOUN
iajs-3473	67	20	such	such	ADJ
iajs-3473	67	21	that	that	PRON
iajs-3473	67	22	are	be	AUX
iajs-3473	67	23	closed	close	VERB
iajs-3473	67	24	operators	operator	NOUN
iajs-3473	67	25	with	with	ADP
iajs-3473	67	26	dense	dense	ADJ
iajs-3473	67	27	domains	domain	NOUN
iajs-3473	67	28	and	and	CCONJ
iajs-3473	67	29	is	be	AUX
iajs-3473	67	30	a	a	DET
iajs-3473	67	31	closable	closable	ADJ
iajs-3473	67	32	operator	operator	NOUN
iajs-3473	67	33	.	.	PUNCT
iajs-3473	68	1	then	then	ADV
iajs-3473	68	2	(	(	PUNCT
iajs-3473	68	3	1	1	X
iajs-3473	68	4	)	)	PUNCT
iajs-3473	68	5	if	if	SCONJ
iajs-3473	68	6	and	and	CCONJ
iajs-3473	68	7	are	be	AUX
iajs-3473	68	8	right	right	ADJ
iajs-3473	68	9	fredholm	fredholm	NOUN
iajs-3473	68	10	,	,	PUNCT
iajs-3473	68	11	then	then	ADV
iajs-3473	68	12	is	be	AUX
iajs-3473	68	13	right	right	ADJ
iajs-3473	68	14	fredholm	fredholm	NOUN
iajs-3473	68	15	.	.	PUNCT
iajs-3473	69	1	(	(	PUNCT
iajs-3473	69	2	2	2	X
iajs-3473	69	3	)	)	PUNCT
iajs-3473	69	4	if	if	SCONJ
iajs-3473	69	5	and	and	CCONJ
iajs-3473	69	6	are	be	AUX
iajs-3473	69	7	left	leave	VERB
iajs-3473	69	8	fredholm	fredholm	NOUN
iajs-3473	69	9	,	,	PUNCT
iajs-3473	69	10	then	then	ADV
iajs-3473	69	11	is	be	AUX
iajs-3473	69	12	left	leave	VERB
iajs-3473	69	13	fredholm	fredholm	NOUN
iajs-3473	69	14	.	.	PUNCT
iajs-3473	70	1	(	(	PUNCT
iajs-3473	70	2	3	3	X
iajs-3473	70	3	)	)	PUNCT
iajs-3473	70	4	if	if	SCONJ
iajs-3473	70	5	(	(	PUNCT
iajs-3473	70	6	resp	resp	NOUN
iajs-3473	70	7	.	.	PUNCT
iajs-3473	70	8	,	,	PUNCT
iajs-3473	71	1	d	d	X
iajs-3473	71	2	)	)	PUNCT
iajs-3473	71	3	and	and	CCONJ
iajs-3473	71	4	are	be	AUX
iajs-3473	71	5	fredholm	fredholm	NOUN
iajs-3473	71	6	,	,	PUNCT
iajs-3473	71	7	then	then	ADV
iajs-3473	71	8	(	(	PUNCT
iajs-3473	71	9	resp	resp	NOUN
iajs-3473	71	10	.	.	PUNCT
iajs-3473	71	11	,	,	PUNCT
iajs-3473	71	12	)	)	PUNCT
iajs-3473	71	13	is	be	AUX
iajs-3473	71	14	fredholm	fredholm	NOUN
iajs-3473	71	15	.	.	PUNCT
iajs-3473	72	1	(	(	PUNCT
iajs-3473	72	2	4	4	X
iajs-3473	72	3	)	)	PUNCT
iajs-3473	72	4	if	if	SCONJ
iajs-3473	72	5	a	a	DET
iajs-3473	72	6	(	(	PUNCT
iajs-3473	72	7	resp	resp	NOUN
iajs-3473	72	8	.	.	PUNCT
iajs-3473	72	9	,	,	PUNCT
iajs-3473	73	1	d	d	X
iajs-3473	73	2	)	)	PUNCT
iajs-3473	73	3	and	and	CCONJ
iajs-3473	73	4	are	be	AUX
iajs-3473	73	5	weyl	weyl	VERB
iajs-3473	73	6	,	,	PUNCT
iajs-3473	73	7	then	then	ADV
iajs-3473	73	8	d	d	X
iajs-3473	73	9	(	(	PUNCT
iajs-3473	73	10	resp	resp	PROPN
iajs-3473	73	11	.	.	PUNCT
iajs-3473	73	12	,	,	PUNCT
iajs-3473	73	13	a	a	PRON
iajs-3473	73	14	)	)	PUNCT
iajs-3473	73	15	is	be	AUX
iajs-3473	73	16	weyl	weyl	VERB
iajs-3473	73	17	.	.	PUNCT
iajs-3473	74	1	2.3	2.3	NUM
iajs-3473	74	2	.	.	PUNCT
iajs-3473	75	1	lemma	lemma	PROPN
iajs-3473	75	2	(	(	PUNCT
iajs-3473	75	3	see	see	VERB
iajs-3473	75	4	(	(	PUNCT
iajs-3473	75	5	14	14	NUM
iajs-3473	75	6	)	)	PUNCT
iajs-3473	75	7	)	)	PUNCT
iajs-3473	75	8	suppose	suppose	VERB
iajs-3473	75	9	that	that	SCONJ
iajs-3473	75	10	either	either	ADV
iajs-3473	75	11	(	(	PUNCT
iajs-3473	75	12	)	)	PUNCT
iajs-3473	75	13	or	or	CCONJ
iajs-3473	75	14	(	(	PUNCT
iajs-3473	75	15	)	)	PUNCT
iajs-3473	75	16	is	be	AUX
iajs-3473	75	17	finite	finite	ADJ
iajs-3473	75	18	,	,	PUNCT
iajs-3473	75	19	and	and	CCONJ
iajs-3473	75	20	that	that	SCONJ
iajs-3473	75	21	(	(	PUNCT
iajs-3473	75	22	)	)	PUNCT
iajs-3473	75	23	is	be	AUX
iajs-3473	75	24	finite	finite	ADJ
iajs-3473	75	25	then	then	ADV
iajs-3473	75	26	(	(	PUNCT
iajs-3473	75	27	)	)	PUNCT
iajs-3473	75	28	(	(	PUNCT
iajs-3473	75	29	)	)	PUNCT
iajs-3473	75	30	.	.	PUNCT
iajs-3473	76	1	2.4	2.4	NUM
iajs-3473	76	2	.	.	PUNCT
iajs-3473	77	1	lemma	lemma	PROPN
iajs-3473	77	2	(	(	PUNCT
iajs-3473	77	3	see	see	VERB
iajs-3473	77	4	(	(	PUNCT
iajs-3473	77	5	14	14	NUM
iajs-3473	77	6	)	)	PUNCT
iajs-3473	77	7	)	)	PUNCT
iajs-3473	77	8	suppose	suppose	VERB
iajs-3473	77	9	that	that	SCONJ
iajs-3473	77	10	either	either	ADV
iajs-3473	77	11	(	(	PUNCT
iajs-3473	77	12	)	)	PUNCT
iajs-3473	77	13	or	or	CCONJ
iajs-3473	77	14	(	(	PUNCT
iajs-3473	77	15	)	)	PUNCT
iajs-3473	77	16	is	be	AUX
iajs-3473	77	17	finite	finite	ADJ
iajs-3473	77	18	,	,	PUNCT
iajs-3473	77	19	and	and	CCONJ
iajs-3473	77	20	that	that	SCONJ
iajs-3473	77	21	(	(	PUNCT
iajs-3473	77	22	)	)	PUNCT
iajs-3473	77	23	is	be	AUX
iajs-3473	77	24	finite	finite	ADJ
iajs-3473	77	25	then	then	ADV
iajs-3473	77	26	(	(	PUNCT
iajs-3473	77	27	)	)	PUNCT
iajs-3473	77	28	(	(	PUNCT
iajs-3473	77	29	)	)	PUNCT
iajs-3473	77	30	(	(	PUNCT
iajs-3473	77	31	)	)	PUNCT
iajs-3473	77	32	.	.	PUNCT
iajs-3473	78	1	in	in	ADP
iajs-3473	78	2	particular	particular	ADJ
iajs-3473	78	3	,	,	PUNCT
iajs-3473	78	4	(	(	PUNCT
iajs-3473	78	5	)	)	PUNCT
iajs-3473	78	6	(	(	PUNCT
iajs-3473	78	7	)	)	PUNCT
iajs-3473	78	8	if	if	SCONJ
iajs-3473	78	9	(	(	PUNCT
iajs-3473	78	10	)	)	PUNCT
iajs-3473	78	11	.	.	PUNCT
iajs-3473	78	12	2.5	2.5	NUM
iajs-3473	78	13	.	.	PUNCT
iajs-3473	79	1	lemma	lemma	PROPN
iajs-3473	79	2	(	(	PUNCT
iajs-3473	79	3	see	see	VERB
iajs-3473	79	4	(	(	PUNCT
iajs-3473	79	5	14	14	NUM
iajs-3473	79	6	)	)	PUNCT
iajs-3473	79	7	)	)	PUNCT
iajs-3473	80	1	a	a	X
iajs-3473	80	2	)	)	PUNCT
iajs-3473	80	3	if	if	SCONJ
iajs-3473	80	4	(	(	PUNCT
iajs-3473	80	5	)	)	PUNCT
iajs-3473	80	6	and	and	CCONJ
iajs-3473	80	7	(	(	PUNCT
iajs-3473	80	8	)	)	PUNCT
iajs-3473	80	9	are	be	AUX
iajs-3473	80	10	finite	finite	ADJ
iajs-3473	80	11	,	,	PUNCT
iajs-3473	80	12	then	then	ADV
iajs-3473	80	13	(	(	PUNCT
iajs-3473	80	14	)	)	PUNCT
iajs-3473	80	15	(	(	PUNCT
iajs-3473	80	16	)	)	PUNCT
iajs-3473	80	17	.	.	PUNCT
iajs-3473	81	1	if	if	SCONJ
iajs-3473	81	2	also	also	ADV
iajs-3473	81	3	(	(	PUNCT
iajs-3473	81	4	)	)	PUNCT
iajs-3473	81	5	,	,	PUNCT
iajs-3473	81	6	then	then	ADV
iajs-3473	81	7	(	(	PUNCT
iajs-3473	81	8	)	)	PUNCT
iajs-3473	81	9	(	(	PUNCT
iajs-3473	81	10	)	)	PUNCT
iajs-3473	81	11	.	.	PUNCT
iajs-3473	82	1	b	b	X
iajs-3473	82	2	)	)	PUNCT
iajs-3473	82	3	suppose	suppose	VERB
iajs-3473	82	4	that	that	SCONJ
iajs-3473	82	5	(	(	PUNCT
iajs-3473	82	6	)	)	PUNCT
iajs-3473	82	7	is	be	AUX
iajs-3473	82	8	finite	finite	ADJ
iajs-3473	82	9	and	and	CCONJ
iajs-3473	82	10	that	that	SCONJ
iajs-3473	82	11	(	(	PUNCT
iajs-3473	82	12	)	)	PUNCT
iajs-3473	82	13	(	(	PUNCT
iajs-3473	82	14	)	)	PUNCT
iajs-3473	82	15	.	.	PUNCT
iajs-3473	83	1	then	then	ADV
iajs-3473	84	1	(	(	PUNCT
iajs-3473	84	2	)	)	PUNCT
iajs-3473	84	3	(	(	PUNCT
iajs-3473	84	4	)	)	PUNCT
iajs-3473	84	5	.	.	PUNCT
iajs-3473	85	1	c	c	X
iajs-3473	85	2	)	)	PUNCT
iajs-3473	85	3	suppose	suppose	VERB
iajs-3473	85	4	that	that	SCONJ
iajs-3473	85	5	(	(	PUNCT
iajs-3473	85	6	)	)	PUNCT
iajs-3473	85	7	,	,	PUNCT
iajs-3473	85	8	that	that	SCONJ
iajs-3473	85	9	(	(	PUNCT
iajs-3473	85	10	)	)	PUNCT
iajs-3473	85	11	is	be	AUX
iajs-3473	85	12	finite	finite	ADJ
iajs-3473	85	13	,	,	PUNCT
iajs-3473	85	14	and	and	CCONJ
iajs-3473	85	15	that	that	SCONJ
iajs-3473	85	16	(	(	PUNCT
iajs-3473	85	17	)	)	PUNCT
iajs-3473	85	18	(	(	PUNCT
iajs-3473	85	19	)	)	PUNCT
iajs-3473	85	20	.	.	PUNCT
iajs-3473	86	1	then	then	ADV
iajs-3473	86	2	(	(	PUNCT
iajs-3473	86	3	)	)	PUNCT
iajs-3473	86	4	(	(	PUNCT
iajs-3473	86	5	)	)	PUNCT
iajs-3473	86	6	.	.	PUNCT
iajs-3473	87	1	2.6	2.6	NUM
iajs-3473	87	2	.	.	PUNCT
iajs-3473	88	1	lemma	lemma	PROPN
iajs-3473	88	2	(	(	PUNCT
iajs-3473	88	3	see	see	VERB
iajs-3473	88	4	(	(	PUNCT
iajs-3473	88	5	11	11	NUM
iajs-3473	88	6	)	)	PUNCT
iajs-3473	88	7	)	)	PUNCT
iajs-3473	89	1	if	if	SCONJ
iajs-3473	89	2	is	be	AUX
iajs-3473	89	3	linear	linear	ADJ
iajs-3473	89	4	operator	operator	NOUN
iajs-3473	89	5	on	on	ADP
iajs-3473	89	6	a	a	DET
iajs-3473	89	7	vector	vector	NOUN
iajs-3473	89	8	space	space	NOUN
iajs-3473	89	9	then	then	ADV
iajs-3473	89	10	the	the	DET
iajs-3473	89	11	following	follow	VERB
iajs-3473	89	12	hold	hold	NOUN
iajs-3473	89	13	:	:	PUNCT
iajs-3473	89	14	1	1	X
iajs-3473	89	15	.	.	X
iajs-3473	90	1	if	if	SCONJ
iajs-3473	90	2	(	(	PUNCT
iajs-3473	90	3	)	)	PUNCT
iajs-3473	90	4	then	then	ADV
iajs-3473	90	5	(	(	PUNCT
iajs-3473	90	6	)	)	PUNCT
iajs-3473	90	7	(	(	PUNCT
iajs-3473	90	8	)	)	PUNCT
iajs-3473	90	9	2	2	X
iajs-3473	90	10	.	.	X
iajs-3473	90	11	if	if	SCONJ
iajs-3473	90	12	(	(	PUNCT
iajs-3473	90	13	)	)	PUNCT
iajs-3473	90	14	then	then	ADV
iajs-3473	90	15	(	(	PUNCT
iajs-3473	90	16	)	)	PUNCT
iajs-3473	90	17	(	(	PUNCT
iajs-3473	90	18	)	)	PUNCT
iajs-3473	90	19	3	3	X
iajs-3473	90	20	.	.	X
iajs-3473	90	21	results	result	NOUN
iajs-3473	90	22	in	in	ADP
iajs-3473	90	23	this	this	DET
iajs-3473	90	24	part	part	NOUN
iajs-3473	90	25	of	of	ADP
iajs-3473	90	26	paper	paper	NOUN
iajs-3473	90	27	,	,	PUNCT
iajs-3473	90	28	we	we	PRON
iajs-3473	90	29	define	define	VERB
iajs-3473	90	30	some	some	DET
iajs-3473	90	31	spectral	spectral	ADJ
iajs-3473	90	32	properties	property	NOUN
iajs-3473	90	33	for	for	ADP
iajs-3473	90	34	unbounded	unbounded	ADJ
iajs-3473	90	35	upper	upper	ADJ
iajs-3473	90	36	triangular	triangular	NOUN
iajs-3473	90	37	operator	operator	NOUN
iajs-3473	90	38	matrices	matrix	NOUN
iajs-3473	90	39	,	,	PUNCT
iajs-3473	90	40	these	these	DET
iajs-3473	90	41	properties	property	NOUN
iajs-3473	90	42	are	be	AUX
iajs-3473	90	43	defined	define	VERB
iajs-3473	90	44	for	for	ADP
iajs-3473	90	45	operators	operator	NOUN
iajs-3473	90	46	in	in	ADP
iajs-3473	90	47	bounded	bounded	ADJ
iajs-3473	90	48	case	case	NOUN
iajs-3473	90	49	(	(	PUNCT
iajs-3473	90	50	see	see	VERB
iajs-3473	90	51	(	(	PUNCT
iajs-3473	90	52	4	4	NUM
iajs-3473	90	53	)	)	PUNCT
iajs-3473	90	54	,	,	PUNCT
iajs-3473	90	55	(	(	PUNCT
iajs-3473	90	56	5	5	NUM
iajs-3473	90	57	)	)	PUNCT
iajs-3473	90	58	,	,	PUNCT
iajs-3473	90	59	(	(	PUNCT
iajs-3473	90	60	12	12	NUM
iajs-3473	90	61	)	)	PUNCT
iajs-3473	90	62	and	and	CCONJ
iajs-3473	90	63	(	(	PUNCT
iajs-3473	90	64	13	13	NUM
iajs-3473	90	65	)	)	PUNCT
iajs-3473	90	66	)	)	PUNCT
iajs-3473	90	67	.	.	PUNCT
iajs-3473	91	1	furthermore	furthermore	ADV
iajs-3473	91	2	,	,	PUNCT
iajs-3473	91	3	we	we	PRON
iajs-3473	91	4	effort	effort	VERB
iajs-3473	91	5	some	some	DET
iajs-3473	91	6	necessary	necessary	ADJ
iajs-3473	91	7	and	and	CCONJ
iajs-3473	91	8	sufficient	sufficient	ADJ
iajs-3473	91	9	conditions	condition	NOUN
iajs-3473	91	10	to	to	PART
iajs-3473	91	11	obtain	obtain	VERB
iajs-3473	91	12	the	the	DET
iajs-3473	91	13	equivalence	equivalence	NOUN
iajs-3473	91	14	among	among	ADP
iajs-3473	91	15	them	they	PRON
iajs-3473	91	16	and	and	CCONJ
iajs-3473	91	17	among	among	ADP
iajs-3473	91	18	the	the	DET
iajs-3473	91	19	weyl	weyl	VERB
iajs-3473	91	20	type	type	NOUN
iajs-3473	91	21	theorems	theorem	NOUN
iajs-3473	91	22	such	such	ADJ
iajs-3473	91	23	as	as	ADP
iajs-3473	91	24	weyl	weyl	PROPN
iajs-3473	91	25	’s	’s	PART
iajs-3473	91	26	,	,	PUNCT
iajs-3473	91	27	a	a	DET
iajs-3473	91	28	-	-	PUNCT
iajs-3473	91	29	weyl	weyl	VERB
iajs-3473	91	30	’s	’s	NOUN
iajs-3473	91	31	,	,	PUNCT
iajs-3473	91	32	browder	browder	NOUN
iajs-3473	91	33	’s	’s	PART
iajs-3473	91	34	and	and	CCONJ
iajs-3473	91	35	a	a	DET
iajs-3473	91	36	-	-	PUNCT
iajs-3473	91	37	browder	browder	NOUN
iajs-3473	91	38	’s	’s	NOUN
iajs-3473	91	39	.	.	PUNCT
iajs-3473	92	1	before	before	SCONJ
iajs-3473	92	2	we	we	PRON
iajs-3473	92	3	proceed	proceed	VERB
iajs-3473	92	4	,	,	PUNCT
iajs-3473	92	5	we	we	PRON
iajs-3473	92	6	need	need	VERB
iajs-3473	92	7	to	to	PART
iajs-3473	92	8	define	define	VERB
iajs-3473	92	9	the	the	DET
iajs-3473	92	10	following	follow	VERB
iajs-3473	92	11	spectrums	spectrum	NOUN
iajs-3473	92	12	:	:	PUNCT
iajs-3473	92	13	(	(	PUNCT
iajs-3473	92	14	)	)	PUNCT
iajs-3473	92	15	{	{	PUNCT
iajs-3473	92	16	(	(	PUNCT
iajs-3473	92	17	)	)	PUNCT
iajs-3473	92	18	(	(	PUNCT
iajs-3473	92	19	)	)	PUNCT
iajs-3473	92	20	}	}	PUNCT
iajs-3473	92	21	;	;	PUNCT
iajs-3473	92	22	(	(	PUNCT
iajs-3473	92	23	)	)	PUNCT
iajs-3473	92	24	{	{	PUNCT
iajs-3473	92	25	(	(	PUNCT
iajs-3473	92	26	)	)	PUNCT
iajs-3473	92	27	}	}	PUNCT
iajs-3473	92	28	;	;	PUNCT
iajs-3473	92	29	(	(	PUNCT
iajs-3473	92	30	)	)	PUNCT
iajs-3473	92	31	{	{	PUNCT
iajs-3473	92	32	(	(	PUNCT
iajs-3473	92	33	)	)	PUNCT
iajs-3473	92	34	(	(	PUNCT
iajs-3473	92	35	)	)	PUNCT
iajs-3473	92	36	(	(	PUNCT
iajs-3473	92	37	)	)	PUNCT
iajs-3473	92	38	}	}	PUNCT
iajs-3473	92	39	for	for	ADP
iajs-3473	92	40	an	an	DET
iajs-3473	92	41	operator	operator	NOUN
iajs-3473	92	42	(	(	PUNCT
iajs-3473	92	43	)	)	PUNCT
iajs-3473	92	44	and	and	CCONJ
iajs-3473	92	45	(	(	PUNCT
iajs-3473	92	46	)	)	PUNCT
iajs-3473	92	47	*	*	PUNCT
iajs-3473	92	48	(	(	PUNCT
iajs-3473	92	49	)	)	PUNCT
iajs-3473	92	50	is	be	AUX
iajs-3473	92	51	not	not	PART
iajs-3473	92	52	closed	close	VERB
iajs-3473	92	53	+	+	PROPN
iajs-3473	92	54	.	.	PROPN
iajs-3473	92	55	3.1	3.1	NUM
iajs-3473	92	56	.	.	PUNCT
iajs-3473	92	57	theorem	theorem	VERB
iajs-3473	92	58	if	if	SCONJ
iajs-3473	92	59	(	(	PUNCT
iajs-3473	92	60	)	)	PUNCT
iajs-3473	92	61	(	(	PUNCT
iajs-3473	92	62	)	)	PUNCT
iajs-3473	92	63	(	(	PUNCT
iajs-3473	92	64	)	)	PUNCT
iajs-3473	92	65	(	(	PUNCT
iajs-3473	92	66	)	)	PUNCT
iajs-3473	92	67	and	and	CCONJ
iajs-3473	92	68	(	(	PUNCT
iajs-3473	92	69	)	)	PUNCT
iajs-3473	92	70	(	(	PUNCT
iajs-3473	92	71	)	)	PUNCT
iajs-3473	92	72	(	(	PUNCT
iajs-3473	92	73	)	)	PUNCT
iajs-3473	92	74	(	(	PUNCT
iajs-3473	92	75	)	)	PUNCT
iajs-3473	92	76	with	with	ADP
iajs-3473	92	77	(	(	PUNCT
iajs-3473	92	78	)	)	PUNCT
iajs-3473	92	79	(	(	PUNCT
iajs-3473	92	80	)	)	PUNCT
iajs-3473	92	81	then	then	ADV
iajs-3473	92	82	obeys	obey	VERB
iajs-3473	92	83	weyl	weyl	PROPN
iajs-3473	92	84	’s	’s	PART
iajs-3473	92	85	theorem	theorem	ADJ
iajs-3473	92	86	if	if	SCONJ
iajs-3473	92	87	and	and	CCONJ
iajs-3473	92	88	only	only	ADV
iajs-3473	92	89	if	if	SCONJ
iajs-3473	92	90	obeys	obey	NOUN
iajs-3473	92	91	-weyl	-weyl	PROPN
iajs-3473	92	92	’s	’s	PART
iajs-3473	92	93	theorem	theorem	ADJ
iajs-3473	92	94	.	.	PUNCT
iajs-3473	93	1	proof	proof	NOUN
iajs-3473	93	2	.	.	PUNCT
iajs-3473	94	1	since	since	SCONJ
iajs-3473	94	2	(	(	PUNCT
iajs-3473	94	3	)	)	PUNCT
iajs-3473	94	4	(	(	PUNCT
iajs-3473	94	5	)	)	PUNCT
iajs-3473	94	6	this	this	PRON
iajs-3473	94	7	would	would	AUX
iajs-3473	94	8	imply	imply	VERB
iajs-3473	94	9	that	that	PRON
iajs-3473	94	10	(	(	PUNCT
iajs-3473	94	11	)	)	PUNCT
iajs-3473	94	12	(	(	PUNCT
iajs-3473	94	13	)	)	PUNCT
iajs-3473	94	14	.to	.to	PUNCT
iajs-3473	94	15	prove	prove	VERB
iajs-3473	94	16	the	the	DET
iajs-3473	94	17	equivalence	equivalence	NOUN
iajs-3473	94	18	,	,	PUNCT
iajs-3473	94	19	it	it	PRON
iajs-3473	94	20	sufficient	sufficient	ADJ
iajs-3473	94	21	to	to	PART
iajs-3473	94	22	show	show	VERB
iajs-3473	94	23	that	that	SCONJ
iajs-3473	94	24	(	(	PUNCT
iajs-3473	94	25	)	)	PUNCT
iajs-3473	94	26	(	(	PUNCT
iajs-3473	94	27	)	)	PUNCT
iajs-3473	94	28	.	.	PUNCT
iajs-3473	95	1	let	let	VERB
iajs-3473	95	2	(	(	PUNCT
iajs-3473	95	3	)	)	PUNCT
iajs-3473	95	4	,	,	PUNCT
iajs-3473	95	5	to	to	PART
iajs-3473	95	6	prove	prove	VERB
iajs-3473	95	7	(	(	PUNCT
iajs-3473	95	8	)	)	PUNCT
iajs-3473	95	9	i.e.	i.e.	X
iajs-3473	95	10	,	,	PUNCT
iajs-3473	95	11	is	be	AUX
iajs-3473	95	12	weyl	weyl	VERB
iajs-3473	95	13	operator	operator	NOUN
iajs-3473	95	14	.	.	PUNCT
iajs-3473	96	1	since	since	SCONJ
iajs-3473	96	2	(	(	PUNCT
iajs-3473	96	3	)	)	PUNCT
iajs-3473	96	4	(	(	PUNCT
iajs-3473	96	5	)	)	PUNCT
iajs-3473	96	6	(	(	PUNCT
iajs-3473	96	7	)	)	PUNCT
iajs-3473	96	8	(	(	PUNCT
iajs-3473	96	9	)	)	PUNCT
iajs-3473	96	10	these	these	DET
iajs-3473	96	11	conditions	condition	NOUN
iajs-3473	96	12	imply	imply	VERB
iajs-3473	96	13	that	that	PRON
iajs-3473	96	14	and	and	CCONJ
iajs-3473	96	15	are	be	AUX
iajs-3473	96	16	fredholm	fredholm	NOUN
iajs-3473	96	17	operators	operator	NOUN
iajs-3473	96	18	,	,	PUNCT
iajs-3473	96	19	by	by	ADP
iajs-3473	96	20	lemma	lemma	PROPN
iajs-3473	96	21	(	(	PUNCT
iajs-3473	96	22	1	1	NUM
iajs-3473	96	23	)	)	PUNCT
iajs-3473	96	24	and	and	CCONJ
iajs-3473	96	25	(	(	PUNCT
iajs-3473	96	26	2	2	NUM
iajs-3473	96	27	)	)	PUNCT
iajs-3473	96	28	,	,	PUNCT
iajs-3473	96	29	we	we	PRON
iajs-3473	96	30	get	get	VERB
iajs-3473	96	31	is	be	AUX
iajs-3473	96	32	fredholm	fredholm	NOUN
iajs-3473	96	33	operator	operator	NOUN
iajs-3473	96	34	.	.	PUNCT
iajs-3473	97	1	clearly	clearly	ADV
iajs-3473	97	2	(	(	PUNCT
iajs-3473	97	3	)	)	PUNCT
iajs-3473	97	4	,	,	PUNCT
iajs-3473	97	5	(	(	PUNCT
iajs-3473	97	6	)	)	PUNCT
iajs-3473	97	7	since	since	SCONJ
iajs-3473	97	8	(	(	PUNCT
iajs-3473	97	9	)	)	PUNCT
iajs-3473	97	10	(	(	PUNCT
iajs-3473	97	11	)	)	PUNCT
iajs-3473	97	12	and	and	CCONJ
iajs-3473	97	13	(	(	PUNCT
iajs-3473	97	14	)	)	PUNCT
iajs-3473	97	15	(	(	PUNCT
iajs-3473	97	16	)	)	PUNCT
iajs-3473	97	17	,	,	PUNCT
iajs-3473	97	18	thus	thus	ADV
iajs-3473	97	19	(	(	PUNCT
iajs-3473	97	20	)	)	PUNCT
iajs-3473	97	21	(	(	PUNCT
iajs-3473	97	22	)	)	PUNCT
iajs-3473	97	23	(	(	PUNCT
iajs-3473	97	24	)	)	PUNCT
iajs-3473	97	25	,	,	PUNCT
iajs-3473	97	26	but	but	CCONJ
iajs-3473	97	27	(	(	PUNCT
iajs-3473	97	28	)	)	PUNCT
iajs-3473	97	29	then	then	ADV
iajs-3473	97	30	(	(	PUNCT
iajs-3473	97	31	)	)	PUNCT
iajs-3473	97	32	which	which	PRON
iajs-3473	97	33	leads	lead	VERB
iajs-3473	97	34	to	to	ADP
iajs-3473	97	35	(	(	PUNCT
iajs-3473	97	36	)	)	PUNCT
iajs-3473	97	37	.	.	PUNCT
iajs-3473	98	1	the	the	DET
iajs-3473	98	2	proof	proof	NOUN
iajs-3473	98	3	is	be	AUX
iajs-3473	98	4	completed	complete	VERB
iajs-3473	98	5	.	.	PUNCT
iajs-3473	99	1	3.2	3.2	NUM
iajs-3473	99	2	.	.	PUNCT
iajs-3473	100	1	theorem	theorem	NOUN
iajs-3473	100	2	obeys	obey	NOUN
iajs-3473	100	3	a	a	PROPN
iajs-3473	100	4	-	-	PUNCT
iajs-3473	100	5	weyl	weyl	NOUN
iajs-3473	100	6	's	's	PART
iajs-3473	100	7	theorem	theorem	NOUN
iajs-3473	100	8	if	if	SCONJ
iajs-3473	100	9	and	and	CCONJ
iajs-3473	100	10	only	only	ADV
iajs-3473	100	11	if	if	SCONJ
iajs-3473	100	12	obeys	obey	NOUN
iajs-3473	100	13	a	a	DET
iajs-3473	100	14	-	-	PUNCT
iajs-3473	100	15	browder	browder	NOUN
iajs-3473	100	16	's	's	PART
iajs-3473	100	17	theorem	theorem	NOUN
iajs-3473	100	18	,	,	PUNCT
iajs-3473	100	19	and	and	CCONJ
iajs-3473	100	20	(	(	PUNCT
iajs-3473	100	21	)	)	PUNCT
iajs-3473	100	22	(	(	PUNCT
iajs-3473	100	23	)	)	PUNCT
iajs-3473	100	24	(	(	PUNCT
iajs-3473	100	25	)	)	PUNCT
iajs-3473	100	26	(	(	PUNCT
iajs-3473	100	27	)	)	PUNCT
iajs-3473	100	28	ihjpas	ihjpas	PROPN
iajs-3473	100	29	.	.	PUNCT
iajs-3473	101	1	2025,38(4	2025,38(4	X
iajs-3473	101	2	)	)	PUNCT
iajs-3473	101	3	291	291	NUM
iajs-3473	101	4	proof	proof	NOUN
iajs-3473	101	5	.	.	PUNCT
iajs-3473	102	1	the	the	DET
iajs-3473	102	2	proof	proof	NOUN
iajs-3473	102	3	is	be	AUX
iajs-3473	102	4	similar	similar	ADJ
iajs-3473	102	5	to	to	ADP
iajs-3473	102	6	the	the	DET
iajs-3473	102	7	proof	proof	NOUN
iajs-3473	102	8	in	in	ADP
iajs-3473	102	9	bounded	bounded	ADJ
iajs-3473	102	10	case	case	NOUN
iajs-3473	102	11	(	(	PUNCT
iajs-3473	102	12	see	see	VERB
iajs-3473	102	13	(	(	PUNCT
iajs-3473	102	14	16	16	NUM
iajs-3473	102	15	)	)	PUNCT
iajs-3473	102	16	)	)	PUNCT
iajs-3473	102	17	.	.	PUNCT
iajs-3473	103	1	3.3	3.3	NUM
iajs-3473	103	2	.	.	PUNCT
iajs-3473	103	3	theorem	theorem	VERB
iajs-3473	103	4	m	m	PROPN
iajs-3473	103	5	obeys	obey	NOUN
iajs-3473	103	6	weyl	weyl	PROPN
iajs-3473	103	7	's	's	PART
iajs-3473	103	8	theorem	theorem	ADJ
iajs-3473	103	9	if	if	SCONJ
iajs-3473	104	1	and	and	CCONJ
iajs-3473	104	2	only	only	ADV
iajs-3473	104	3	if	if	SCONJ
iajs-3473	104	4	obeys	obey	NOUN
iajs-3473	104	5	browder	browder	PROPN
iajs-3473	104	6	's	's	PART
iajs-3473	104	7	theorem	theorem	NOUN
iajs-3473	104	8	,	,	PUNCT
iajs-3473	104	9	and	and	CCONJ
iajs-3473	104	10	(	(	PUNCT
iajs-3473	104	11	)	)	PUNCT
iajs-3473	104	12	(	(	PUNCT
iajs-3473	104	13	)	)	PUNCT
iajs-3473	104	14	proof	proof	NOUN
iajs-3473	104	15	.	.	PUNCT
iajs-3473	105	1	the	the	DET
iajs-3473	105	2	proof	proof	NOUN
iajs-3473	105	3	is	be	AUX
iajs-3473	105	4	similar	similar	ADJ
iajs-3473	105	5	to	to	ADP
iajs-3473	105	6	the	the	DET
iajs-3473	105	7	proof	proof	NOUN
iajs-3473	105	8	in	in	ADP
iajs-3473	105	9	bounded	bounded	ADJ
iajs-3473	105	10	case	case	NOUN
iajs-3473	105	11	(	(	PUNCT
iajs-3473	105	12	see	see	VERB
iajs-3473	105	13	(	(	PUNCT
iajs-3473	105	14	16	16	NUM
iajs-3473	105	15	)	)	PUNCT
iajs-3473	105	16	)	)	PUNCT
iajs-3473	105	17	.	.	PUNCT
iajs-3473	106	1	3.4	3.4	NUM
iajs-3473	106	2	.	.	PUNCT
iajs-3473	106	3	definition	definition	NOUN
iajs-3473	106	4	(	(	PUNCT
iajs-3473	106	5	6	6	NUM
iajs-3473	106	6	)	)	PUNCT
iajs-3473	106	7	for	for	ADP
iajs-3473	106	8	(	(	PUNCT
iajs-3473	106	9	)	)	PUNCT
iajs-3473	106	10	we	we	PRON
iajs-3473	106	11	say	say	VERB
iajs-3473	106	12	obeys	obey	NOUN
iajs-3473	106	13	1	1	NUM
iajs-3473	106	14	.	.	PUNCT
iajs-3473	107	1	(	(	PUNCT
iajs-3473	107	2	)	)	PUNCT
iajs-3473	107	3	if	if	SCONJ
iajs-3473	107	4	(	(	PUNCT
iajs-3473	107	5	)	)	PUNCT
iajs-3473	107	6	(	(	PUNCT
iajs-3473	107	7	)	)	PUNCT
iajs-3473	107	8	(	(	PUNCT
iajs-3473	107	9	)	)	PUNCT
iajs-3473	107	10	2	2	X
iajs-3473	107	11	.	.	X
iajs-3473	107	12	property	property	NOUN
iajs-3473	107	13	(	(	PUNCT
iajs-3473	107	14	)	)	PUNCT
iajs-3473	107	15	if	if	SCONJ
iajs-3473	107	16	(	(	PUNCT
iajs-3473	107	17	)	)	PUNCT
iajs-3473	107	18	(	(	PUNCT
iajs-3473	107	19	)	)	PUNCT
iajs-3473	107	20	(	(	PUNCT
iajs-3473	107	21	)	)	PUNCT
iajs-3473	107	22	3	3	X
iajs-3473	107	23	.	.	X
iajs-3473	107	24	property	property	NOUN
iajs-3473	107	25	(	(	PUNCT
iajs-3473	107	26	b	b	NOUN
iajs-3473	107	27	)	)	PUNCT
iajs-3473	107	28	if	if	SCONJ
iajs-3473	107	29	(	(	PUNCT
iajs-3473	107	30	)	)	PUNCT
iajs-3473	107	31	(	(	PUNCT
iajs-3473	107	32	)	)	PUNCT
iajs-3473	107	33	(	(	PUNCT
iajs-3473	107	34	)	)	PUNCT
iajs-3473	107	35	(	(	PUNCT
iajs-3473	107	36	)	)	PUNCT
iajs-3473	107	37	4	4	X
iajs-3473	107	38	.	.	X
iajs-3473	107	39	property	property	NOUN
iajs-3473	107	40	(	(	PUNCT
iajs-3473	107	41	)	)	PUNCT
iajs-3473	107	42	if	if	SCONJ
iajs-3473	107	43	(	(	PUNCT
iajs-3473	107	44	)	)	PUNCT
iajs-3473	107	45	(	(	PUNCT
iajs-3473	107	46	)	)	PUNCT
iajs-3473	107	47	(	(	PUNCT
iajs-3473	107	48	)	)	PUNCT
iajs-3473	107	49	3.5	3.5	NUM
iajs-3473	107	50	.	.	PUNCT
iajs-3473	108	1	definition	definition	NOUN
iajs-3473	108	2	.	.	PUNCT
iajs-3473	109	1	for	for	ADP
iajs-3473	109	2	(	(	PUNCT
iajs-3473	109	3	)	)	PUNCT
iajs-3473	109	4	,	,	PUNCT
iajs-3473	109	5	we	we	PRON
iajs-3473	109	6	say	say	VERB
iajs-3473	109	7	obeys	obey	NOUN
iajs-3473	109	8	1	1	NUM
iajs-3473	109	9	.	.	PUNCT
iajs-3473	110	1	(	(	PUNCT
iajs-3473	110	2	)	)	PUNCT
iajs-3473	110	3	if	if	SCONJ
iajs-3473	110	4	(	(	PUNCT
iajs-3473	110	5	)	)	PUNCT
iajs-3473	110	6	(	(	PUNCT
iajs-3473	110	7	)	)	PUNCT
iajs-3473	110	8	(	(	PUNCT
iajs-3473	110	9	)	)	PUNCT
iajs-3473	110	10	2	2	X
iajs-3473	110	11	.	.	X
iajs-3473	110	12	property	property	NOUN
iajs-3473	110	13	(	(	PUNCT
iajs-3473	110	14	)	)	PUNCT
iajs-3473	110	15	if	if	SCONJ
iajs-3473	110	16	(	(	PUNCT
iajs-3473	110	17	)	)	PUNCT
iajs-3473	110	18	(	(	PUNCT
iajs-3473	110	19	)	)	PUNCT
iajs-3473	110	20	(	(	PUNCT
iajs-3473	110	21	)	)	PUNCT
iajs-3473	110	22	3	3	X
iajs-3473	110	23	.	.	X
iajs-3473	110	24	property	property	NOUN
iajs-3473	110	25	(	(	PUNCT
iajs-3473	110	26	)	)	PUNCT
iajs-3473	110	27	if	if	SCONJ
iajs-3473	110	28	(	(	PUNCT
iajs-3473	110	29	)	)	PUNCT
iajs-3473	110	30	(	(	PUNCT
iajs-3473	110	31	)	)	PUNCT
iajs-3473	110	32	(	(	PUNCT
iajs-3473	110	33	)	)	PUNCT
iajs-3473	110	34	3.6	3.6	NUM
iajs-3473	110	35	.	.	PUNCT
iajs-3473	111	1	theorem	theorem	NOUN
iajs-3473	111	2	let	let	VERB
iajs-3473	111	3	obeys	obey	NOUN
iajs-3473	111	4	property	property	NOUN
iajs-3473	111	5	(	(	PUNCT
iajs-3473	111	6	gw	gw	PROPN
iajs-3473	111	7	)	)	PUNCT
iajs-3473	111	8	with	with	ADP
iajs-3473	111	9	(	(	PUNCT
iajs-3473	111	10	)	)	PUNCT
iajs-3473	111	11	(	(	PUNCT
iajs-3473	111	12	)	)	PUNCT
iajs-3473	111	13	and	and	CCONJ
iajs-3473	111	14	(	(	PUNCT
iajs-3473	111	15	)	)	PUNCT
iajs-3473	111	16	(	(	PUNCT
iajs-3473	111	17	)	)	PUNCT
iajs-3473	111	18	then	then	ADV
iajs-3473	111	19	obeys	obey	VERB
iajs-3473	111	20	(	(	PUNCT
iajs-3473	111	21	sz	sz	NOUN
iajs-3473	111	22	)	)	PUNCT
iajs-3473	111	23	property	property	NOUN
iajs-3473	111	24	.	.	PUNCT
iajs-3473	112	1	proof	proof	NOUN
iajs-3473	112	2	.	.	PUNCT
iajs-3473	113	1	let	let	VERB
iajs-3473	113	2	(	(	PUNCT
iajs-3473	113	3	)	)	PUNCT
iajs-3473	113	4	(	(	PUNCT
iajs-3473	113	5	)	)	PUNCT
iajs-3473	113	6	,	,	PUNCT
iajs-3473	113	7	then	then	ADV
iajs-3473	113	8	(	(	PUNCT
iajs-3473	113	9	)	)	PUNCT
iajs-3473	113	10	and	and	CCONJ
iajs-3473	113	11	(	(	PUNCT
iajs-3473	113	12	)	)	PUNCT
iajs-3473	113	13	,	,	PUNCT
iajs-3473	113	14	by	by	ADP
iajs-3473	113	15	lemma	lemma	PROPN
iajs-3473	113	16	2.1.(1	2.1.(1	NUM
iajs-3473	113	17	)	)	PUNCT
iajs-3473	113	18	,	,	PUNCT
iajs-3473	113	19	we	we	PRON
iajs-3473	113	20	have	have	VERB
iajs-3473	113	21	is	be	AUX
iajs-3473	113	22	upper	upper	ADJ
iajs-3473	113	23	semi	semi	ADJ
iajs-3473	113	24	b	b	NOUN
iajs-3473	113	25	-	-	PUNCT
iajs-3473	113	26	fredholm	fredholm	NOUN
iajs-3473	113	27	with	with	ADP
iajs-3473	113	28	(	(	PUNCT
iajs-3473	113	29	)	)	PUNCT
iajs-3473	113	30	,	,	PUNCT
iajs-3473	113	31	since	since	SCONJ
iajs-3473	113	32	by	by	ADP
iajs-3473	113	33	assumption	assumption	NOUN
iajs-3473	113	34	(	(	PUNCT
iajs-3473	113	35	)	)	PUNCT
iajs-3473	113	36	(	(	PUNCT
iajs-3473	113	37	)	)	PUNCT
iajs-3473	113	38	,	,	PUNCT
iajs-3473	113	39	then	then	ADV
iajs-3473	113	40	(	(	PUNCT
iajs-3473	113	41	(	(	PUNCT
iajs-3473	113	42	)	)	PUNCT
iajs-3473	113	43	,	,	PUNCT
iajs-3473	113	44	but	but	CCONJ
iajs-3473	113	45	obeys	obey	NOUN
iajs-3473	113	46	(	(	PUNCT
iajs-3473	113	47	gw	gw	NOUN
iajs-3473	113	48	)	)	PUNCT
iajs-3473	113	49	property	property	NOUN
iajs-3473	113	50	,	,	PUNCT
iajs-3473	113	51	thus	thus	ADV
iajs-3473	113	52	(	(	PUNCT
iajs-3473	113	53	)	)	PUNCT
iajs-3473	113	54	.	.	PUNCT
iajs-3473	114	1	for	for	ADP
iajs-3473	114	2	the	the	DET
iajs-3473	114	3	reverse	reverse	ADJ
iajs-3473	114	4	inclusion	inclusion	NOUN
iajs-3473	114	5	,	,	PUNCT
iajs-3473	114	6	let	let	VERB
iajs-3473	114	7	(	(	PUNCT
iajs-3473	114	8	)	)	PUNCT
iajs-3473	114	9	,	,	PUNCT
iajs-3473	114	10	then	then	ADV
iajs-3473	114	11	(	(	PUNCT
iajs-3473	114	12	)	)	PUNCT
iajs-3473	114	13	,	,	PUNCT
iajs-3473	114	14	by	by	ADP
iajs-3473	114	15	assumption	assumption	NOUN
iajs-3473	114	16	:	:	PUNCT
iajs-3473	114	17	(	(	PUNCT
iajs-3473	114	18	)	)	PUNCT
iajs-3473	114	19	(	(	PUNCT
iajs-3473	114	20	)	)	PUNCT
iajs-3473	114	21	and	and	CCONJ
iajs-3473	114	22	(	(	PUNCT
iajs-3473	114	23	)	)	PUNCT
iajs-3473	114	24	are	be	AUX
iajs-3473	114	25	right	right	ADJ
iajs-3473	114	26	fredholm	fredholm	NOUN
iajs-3473	114	27	with	with	ADP
iajs-3473	114	28	(	(	PUNCT
iajs-3473	114	29	)	)	PUNCT
iajs-3473	114	30	+	+	CCONJ
iajs-3473	114	31	(	(	PUNCT
iajs-3473	114	32	)	)	PUNCT
iajs-3473	114	33	,	,	PUNCT
iajs-3473	114	34	then	then	ADV
iajs-3473	114	35	by	by	ADP
iajs-3473	114	36	lemma	lemma	PROPN
iajs-3473	114	37	(	(	PUNCT
iajs-3473	114	38	)	)	PUNCT
iajs-3473	114	39	,	,	PUNCT
iajs-3473	114	40	we	we	PRON
iajs-3473	114	41	have	have	AUX
iajs-3473	114	42	(	(	PUNCT
iajs-3473	114	43	)	)	PUNCT
iajs-3473	114	44	is	be	AUX
iajs-3473	114	45	right	right	ADJ
iajs-3473	114	46	fredholm	fredholm	NOUN
iajs-3473	114	47	with	with	ADP
iajs-3473	114	48	(	(	PUNCT
iajs-3473	114	49	)	)	PUNCT
iajs-3473	114	50	(	(	PUNCT
iajs-3473	114	51	)	)	PUNCT
iajs-3473	114	52	(	(	PUNCT
iajs-3473	114	53	)	)	PUNCT
iajs-3473	114	54	,	,	PUNCT
iajs-3473	114	55	then	then	ADV
iajs-3473	114	56	(	(	PUNCT
iajs-3473	114	57	)	)	PUNCT
iajs-3473	114	58	thus	thus	ADV
iajs-3473	114	59	,	,	PUNCT
iajs-3473	114	60	(	(	PUNCT
iajs-3473	114	61	)	)	PUNCT
iajs-3473	114	62	(	(	PUNCT
iajs-3473	114	63	)	)	PUNCT
iajs-3473	114	64	.	.	PUNCT
iajs-3473	115	1	then	then	ADV
iajs-3473	115	2	obeys	obey	VERB
iajs-3473	115	3	property	property	NOUN
iajs-3473	115	4	(	(	PUNCT
iajs-3473	115	5	sz	sz	NOUN
iajs-3473	115	6	)	)	PUNCT
iajs-3473	115	7	.	.	PUNCT
iajs-3473	116	1	3.7	3.7	NUM
iajs-3473	116	2	.	.	PUNCT
iajs-3473	116	3	theorem	theorem	NOUN
iajs-3473	116	4	let	let	VERB
iajs-3473	116	5	m	m	PRON
iajs-3473	116	6	obeys	obey	NOUN
iajs-3473	116	7	property	property	NOUN
iajs-3473	116	8	(	(	PUNCT
iajs-3473	116	9	gb	gb	NOUN
iajs-3473	116	10	)	)	PUNCT
iajs-3473	116	11	with	with	ADP
iajs-3473	116	12	(	(	PUNCT
iajs-3473	116	13	)	)	PUNCT
iajs-3473	116	14	(	(	PUNCT
iajs-3473	116	15	)	)	PUNCT
iajs-3473	116	16	and	and	CCONJ
iajs-3473	116	17	(	(	PUNCT
iajs-3473	116	18	)	)	PUNCT
iajs-3473	116	19	(	(	PUNCT
iajs-3473	116	20	)	)	PUNCT
iajs-3473	116	21	,	,	PUNCT
iajs-3473	116	22	then	then	ADV
iajs-3473	116	23	obeys	obey	VERB
iajs-3473	116	24	property	property	NOUN
iajs-3473	116	25	(	(	PUNCT
iajs-3473	116	26	asz	asz	NOUN
iajs-3473	116	27	)	)	PUNCT
iajs-3473	116	28	.	.	PUNCT
iajs-3473	117	1	proof	proof	NOUN
iajs-3473	117	2	.	.	PUNCT
iajs-3473	118	1	the	the	DET
iajs-3473	118	2	proof	proof	NOUN
iajs-3473	118	3	of	of	ADP
iajs-3473	118	4	this	this	DET
iajs-3473	118	5	theorem	theorem	NOUN
iajs-3473	118	6	is	be	AUX
iajs-3473	118	7	similar	similar	ADJ
iajs-3473	118	8	to	to	ADP
iajs-3473	118	9	the	the	DET
iajs-3473	118	10	proof	proof	NOUN
iajs-3473	118	11	of	of	ADP
iajs-3473	118	12	theorem	theorem	ADJ
iajs-3473	118	13	3.6	3.6	NUM
iajs-3473	118	14	.	.	PUNCT
iajs-3473	119	1	3.8	3.8	NUM
iajs-3473	119	2	.	.	PUNCT
iajs-3473	119	3	theorem	theorem	VERB
iajs-3473	119	4	if	if	SCONJ
iajs-3473	119	5	(	(	PUNCT
iajs-3473	119	6	)	)	PUNCT
iajs-3473	119	7	(	(	PUNCT
iajs-3473	119	8	)	)	PUNCT
iajs-3473	119	9	and	and	CCONJ
iajs-3473	119	10	(	(	PUNCT
iajs-3473	119	11	)	)	PUNCT
iajs-3473	119	12	,	,	PUNCT
iajs-3473	119	13	then	then	ADV
iajs-3473	119	14	obeys	obey	VERB
iajs-3473	119	15	(	(	PUNCT
iajs-3473	119	16	w	w	NOUN
iajs-3473	119	17	)	)	PUNCT
iajs-3473	119	18	property	property	NOUN
iajs-3473	119	19	with	with	ADP
iajs-3473	119	20	(	(	PUNCT
iajs-3473	119	21	)	)	PUNCT
iajs-3473	119	22	(	(	PUNCT
iajs-3473	119	23	)	)	PUNCT
iajs-3473	119	24	and	and	CCONJ
iajs-3473	119	25	(	(	PUNCT
iajs-3473	119	26	)	)	PUNCT
iajs-3473	119	27	(	(	PUNCT
iajs-3473	119	28	)	)	PUNCT
iajs-3473	119	29	if	if	SCONJ
iajs-3473	120	1	and	and	CCONJ
iajs-3473	120	2	only	only	ADV
iajs-3473	120	3	if	if	SCONJ
iajs-3473	120	4	obeys	obey	NOUN
iajs-3473	120	5	property	property	NOUN
iajs-3473	120	6	(	(	PUNCT
iajs-3473	120	7	)	)	PUNCT
iajs-3473	120	8	with	with	ADP
iajs-3473	120	9	(	(	PUNCT
iajs-3473	120	10	)	)	PUNCT
iajs-3473	120	11	(	(	PUNCT
iajs-3473	120	12	)	)	PUNCT
iajs-3473	120	13	proof	proof	NOUN
iajs-3473	120	14	.	.	PUNCT
iajs-3473	121	1	to	to	PART
iajs-3473	121	2	prove	prove	VERB
iajs-3473	121	3	(	(	PUNCT
iajs-3473	121	4	)	)	PUNCT
iajs-3473	121	5	obeys	obey	VERB
iajs-3473	121	6	property	property	NOUN
iajs-3473	121	7	(	(	PUNCT
iajs-3473	121	8	)	)	PUNCT
iajs-3473	121	9	with	with	ADP
iajs-3473	121	10	(	(	PUNCT
iajs-3473	121	11	)	)	PUNCT
iajs-3473	121	12	(	(	PUNCT
iajs-3473	121	13	)	)	PUNCT
iajs-3473	121	14	we	we	PRON
iajs-3473	121	15	need	need	VERB
iajs-3473	121	16	to	to	PART
iajs-3473	121	17	proof	proof	NOUN
iajs-3473	121	18	(	(	PUNCT
iajs-3473	121	19	)	)	PUNCT
iajs-3473	121	20	(	(	PUNCT
iajs-3473	121	21	)	)	PUNCT
iajs-3473	121	22	(	(	PUNCT
iajs-3473	121	23	)	)	PUNCT
iajs-3473	121	24	(	(	PUNCT
iajs-3473	121	25	)	)	PUNCT
iajs-3473	121	26	.	.	PUNCT
iajs-3473	122	1	let	let	VERB
iajs-3473	122	2	(	(	PUNCT
iajs-3473	122	3	)	)	PUNCT
iajs-3473	122	4	(	(	PUNCT
iajs-3473	122	5	)	)	PUNCT
iajs-3473	122	6	,	,	PUNCT
iajs-3473	122	7	then	then	ADV
iajs-3473	122	8	(	(	PUNCT
iajs-3473	122	9	)	)	PUNCT
iajs-3473	122	10	(	(	PUNCT
iajs-3473	122	11	)	)	PUNCT
iajs-3473	122	12	and	and	CCONJ
iajs-3473	122	13	(	(	PUNCT
iajs-3473	122	14	)	)	PUNCT
iajs-3473	122	15	is	be	AUX
iajs-3473	122	16	upper	upper	ADJ
iajs-3473	122	17	semi	semi	ADJ
iajs-3473	122	18	fredholm	fredholm	NOUN
iajs-3473	122	19	with	with	ADP
iajs-3473	122	20	(	(	PUNCT
iajs-3473	122	21	)	)	PUNCT
iajs-3473	122	22	,	,	PUNCT
iajs-3473	122	23	to	to	PART
iajs-3473	122	24	prove	prove	VERB
iajs-3473	122	25	(	(	PUNCT
iajs-3473	122	26	)	)	PUNCT
iajs-3473	122	27	,	,	PUNCT
iajs-3473	122	28	i.e.	i.e.	X
iajs-3473	122	29	,	,	PUNCT
iajs-3473	122	30	(	(	PUNCT
iajs-3473	122	31	)	)	PUNCT
iajs-3473	122	32	is	be	AUX
iajs-3473	122	33	browder	browder	NOUN
iajs-3473	122	34	operator	operator	NOUN
iajs-3473	122	35	.	.	PUNCT
iajs-3473	123	1	since	since	SCONJ
iajs-3473	123	2	by	by	ADP
iajs-3473	123	3	assumption	assumption	NOUN
iajs-3473	123	4	(	(	PUNCT
iajs-3473	123	5	)	)	PUNCT
iajs-3473	123	6	(	(	PUNCT
iajs-3473	123	7	)	)	PUNCT
iajs-3473	123	8	and	and	CCONJ
iajs-3473	123	9	(	(	PUNCT
iajs-3473	123	10	)	)	PUNCT
iajs-3473	123	11	(	(	PUNCT
iajs-3473	123	12	)	)	PUNCT
iajs-3473	123	13	then	then	ADV
iajs-3473	123	14	(	(	PUNCT
iajs-3473	123	15	)	)	PUNCT
iajs-3473	123	16	and	and	CCONJ
iajs-3473	123	17	(	(	PUNCT
iajs-3473	123	18	)	)	PUNCT
iajs-3473	123	19	,	,	PUNCT
iajs-3473	123	20	by	by	ADP
iajs-3473	123	21	lemma	lemma	PROPN
iajs-3473	123	22	2.4	2.4	NUM
iajs-3473	123	23	.	.	PUNCT
iajs-3473	124	1	we	we	PRON
iajs-3473	124	2	get	get	VERB
iajs-3473	124	3	(	(	PUNCT
iajs-3473	124	4	)	)	PUNCT
iajs-3473	124	5	(	(	PUNCT
iajs-3473	124	6	)	)	PUNCT
iajs-3473	124	7	,	,	PUNCT
iajs-3473	124	8	thus	thus	ADV
iajs-3473	124	9	(	(	PUNCT
iajs-3473	124	10	)	)	PUNCT
iajs-3473	124	11	then	then	ADV
iajs-3473	124	12	(	(	PUNCT
iajs-3473	124	13	)	)	PUNCT
iajs-3473	124	14	(	(	PUNCT
iajs-3473	124	15	)	)	PUNCT
iajs-3473	124	16	,	,	PUNCT
iajs-3473	124	17	thus	thus	ADV
iajs-3473	124	18	(	(	PUNCT
iajs-3473	124	19	)	)	PUNCT
iajs-3473	124	20	(	(	PUNCT
iajs-3473	124	21	)	)	PUNCT
iajs-3473	124	22	(	(	PUNCT
iajs-3473	124	23	)	)	PUNCT
iajs-3473	124	24	(	(	PUNCT
iajs-3473	124	25	)	)	PUNCT
iajs-3473	124	26	but	but	CCONJ
iajs-3473	124	27	obeys	obey	NOUN
iajs-3473	124	28	property	property	NOUN
iajs-3473	124	29	(	(	PUNCT
iajs-3473	124	30	w	w	NOUN
iajs-3473	124	31	)	)	PUNCT
iajs-3473	124	32	,	,	PUNCT
iajs-3473	124	33	i.e.	i.e.	X
iajs-3473	124	34	,	,	PUNCT
iajs-3473	124	35	(	(	PUNCT
iajs-3473	124	36	)	)	PUNCT
iajs-3473	124	37	then	then	ADV
iajs-3473	124	38	(	(	PUNCT
iajs-3473	124	39	)	)	PUNCT
iajs-3473	124	40	(	(	PUNCT
iajs-3473	124	41	)	)	PUNCT
iajs-3473	124	42	.	.	PUNCT
iajs-3473	125	1	now	now	ADV
iajs-3473	125	2	,	,	PUNCT
iajs-3473	125	3	let	let	VERB
iajs-3473	125	4	(	(	PUNCT
iajs-3473	125	5	)	)	PUNCT
iajs-3473	125	6	(	(	PUNCT
iajs-3473	125	7	)	)	PUNCT
iajs-3473	125	8	,	,	PUNCT
iajs-3473	125	9	then	then	ADV
iajs-3473	125	10	(	(	PUNCT
iajs-3473	125	11	)	)	PUNCT
iajs-3473	125	12	(	(	PUNCT
iajs-3473	125	13	)	)	PUNCT
iajs-3473	125	14	and	and	CCONJ
iajs-3473	125	15	is	be	AUX
iajs-3473	125	16	browder	browder	NOUN
iajs-3473	125	17	i.e.	i.e.	X
iajs-3473	125	18	,	,	PUNCT
iajs-3473	125	19	(	(	PUNCT
iajs-3473	125	20	)	)	PUNCT
iajs-3473	125	21	is	be	AUX
iajs-3473	125	22	fredholm	fredholm	NOUN
iajs-3473	125	23	operator	operator	NOUN
iajs-3473	125	24	with	with	ADP
iajs-3473	125	25	finite	finite	PROPN
iajs-3473	125	26	ascent	ascent	PROPN
iajs-3473	125	27	and	and	CCONJ
iajs-3473	125	28	finite	finite	ADJ
iajs-3473	125	29	descent	descent	NOUN
iajs-3473	125	30	,	,	PUNCT
iajs-3473	125	31	then	then	ADV
iajs-3473	125	32	by	by	ADP
iajs-3473	125	33	definition	definition	NOUN
iajs-3473	125	34	of	of	ADP
iajs-3473	125	35	fredholm	fredholm	NOUN
iajs-3473	125	36	operator	operator	NOUN
iajs-3473	125	37	:	:	PUNCT
iajs-3473	125	38	is	be	AUX
iajs-3473	125	39	upper	upper	ADJ
iajs-3473	125	40	and	and	CCONJ
iajs-3473	125	41	lower	low	ADJ
iajs-3473	125	42	semi	semi	ADJ
iajs-3473	125	43	fredholm	fredholm	NOUN
iajs-3473	125	44	operator	operator	NOUN
iajs-3473	125	45	.	.	PUNCT
iajs-3473	126	1	since	since	SCONJ
iajs-3473	126	2	(	(	PUNCT
iajs-3473	126	3	)	)	PUNCT
iajs-3473	126	4	and	and	CCONJ
iajs-3473	126	5	(	(	PUNCT
iajs-3473	126	6	)	)	PUNCT
iajs-3473	126	7	,	,	PUNCT
iajs-3473	126	8	then	then	ADV
iajs-3473	126	9	by	by	ADP
iajs-3473	126	10	lemma	lemma	PROPN
iajs-3473	126	11	2.3	2.3	NUM
iajs-3473	126	12	and	and	CCONJ
iajs-3473	126	13	lemma	lemma	PROPN
iajs-3473	126	14	2.4	2.4	NUM
iajs-3473	126	15	we	we	PRON
iajs-3473	126	16	get	get	VERB
iajs-3473	126	17	(	(	PUNCT
iajs-3473	126	18	)	)	PUNCT
iajs-3473	126	19	(	(	PUNCT
iajs-3473	126	20	)	)	PUNCT
iajs-3473	126	21	thus	thus	ADV
iajs-3473	126	22	is	be	AUX
iajs-3473	126	23	belong	belong	ADJ
iajs-3473	126	24	to	to	ADP
iajs-3473	126	25	(	(	PUNCT
iajs-3473	126	26	)	)	PUNCT
iajs-3473	126	27	,	,	PUNCT
iajs-3473	126	28	thus	thus	ADV
iajs-3473	126	29	(	(	PUNCT
iajs-3473	126	30	)	)	PUNCT
iajs-3473	126	31	,	,	PUNCT
iajs-3473	126	32	from	from	ADP
iajs-3473	126	33	all	all	PRON
iajs-3473	126	34	of	of	ADP
iajs-3473	126	35	that	that	PRON
iajs-3473	126	36	we	we	PRON
iajs-3473	126	37	get	get	VERB
iajs-3473	126	38	(	(	PUNCT
iajs-3473	126	39	)	)	PUNCT
iajs-3473	126	40	(	(	PUNCT
iajs-3473	126	41	)	)	PUNCT
iajs-3473	126	42	then	then	ADV
iajs-3473	126	43	(	(	PUNCT
iajs-3473	126	44	)	)	PUNCT
iajs-3473	126	45	obeys	obey	VERB
iajs-3473	126	46	property	property	NOUN
iajs-3473	126	47	(	(	PUNCT
iajs-3473	126	48	b	b	NOUN
iajs-3473	126	49	)	)	PUNCT
iajs-3473	126	50	.	.	PUNCT
iajs-3473	127	1	ihjpas	ihjpas	PROPN
iajs-3473	127	2	.	.	PUNCT
iajs-3473	128	1	2025,38(4	2025,38(4	X
iajs-3473	128	2	)	)	PUNCT
iajs-3473	129	1	292	292	NUM
iajs-3473	129	2	to	to	PART
iajs-3473	129	3	proof	proof	VERB
iajs-3473	129	4	the	the	DET
iajs-3473	129	5	reverse	reverse	ADJ
iajs-3473	129	6	direction	direction	NOUN
iajs-3473	129	7	,	,	PUNCT
iajs-3473	129	8	i.e.	i.e.	X
iajs-3473	129	9	,	,	PUNCT
iajs-3473	129	10	to	to	ADP
iajs-3473	129	11	proof	proof	NOUN
iajs-3473	129	12	m	m	NOUN
iajs-3473	129	13	obeys	obey	NOUN
iajs-3473	129	14	property	property	NOUN
iajs-3473	129	15	(	(	PUNCT
iajs-3473	129	16	w	w	NOUN
iajs-3473	129	17	)	)	PUNCT
iajs-3473	129	18	we	we	PRON
iajs-3473	129	19	need	need	VERB
iajs-3473	129	20	to	to	PART
iajs-3473	129	21	show	show	VERB
iajs-3473	129	22	that	that	PRON
iajs-3473	129	23	(	(	PUNCT
iajs-3473	129	24	)	)	PUNCT
iajs-3473	129	25	(	(	PUNCT
iajs-3473	129	26	)	)	PUNCT
iajs-3473	129	27	(	(	PUNCT
iajs-3473	129	28	)	)	PUNCT
iajs-3473	129	29	let	let	VERB
iajs-3473	129	30	(	(	PUNCT
iajs-3473	129	31	)	)	PUNCT
iajs-3473	129	32	(	(	PUNCT
iajs-3473	129	33	)	)	PUNCT
iajs-3473	129	34	,	,	PUNCT
iajs-3473	129	35	since	since	SCONJ
iajs-3473	129	36	obeys	obey	NOUN
iajs-3473	129	37	(	(	PUNCT
iajs-3473	129	38	w	w	NOUN
iajs-3473	129	39	)	)	PUNCT
iajs-3473	129	40	property	property	NOUN
iajs-3473	129	41	then	then	ADV
iajs-3473	129	42	(	(	PUNCT
iajs-3473	129	43	)	)	PUNCT
iajs-3473	129	44	(	(	PUNCT
iajs-3473	129	45	)	)	PUNCT
iajs-3473	129	46	(	(	PUNCT
iajs-3473	129	47	)	)	PUNCT
iajs-3473	129	48	*	*	PUNCT
iajs-3473	129	49	(	(	PUNCT
iajs-3473	129	50	)	)	PUNCT
iajs-3473	129	51	(	(	PUNCT
iajs-3473	129	52	)	)	PUNCT
iajs-3473	130	1	+	+	ADV
iajs-3473	130	2	,	,	PUNCT
iajs-3473	130	3	then	then	ADV
iajs-3473	130	4	iso	iso	NOUN
iajs-3473	130	5	(	(	PUNCT
iajs-3473	130	6	)	)	PUNCT
iajs-3473	130	7	.	.	PUNCT
iajs-3473	131	1	since	since	SCONJ
iajs-3473	131	2	is	be	AUX
iajs-3473	131	3	upper	upper	ADJ
iajs-3473	131	4	semi	semi	ADJ
iajs-3473	131	5	fredholm	fredholm	NOUN
iajs-3473	131	6	operator	operator	NOUN
iajs-3473	131	7	with	with	ADP
iajs-3473	131	8	(	(	PUNCT
iajs-3473	131	9	)	)	PUNCT
iajs-3473	131	10	and	and	CCONJ
iajs-3473	131	11	(	(	PUNCT
iajs-3473	131	12	)	)	PUNCT
iajs-3473	131	13	and	and	CCONJ
iajs-3473	131	14	(	(	PUNCT
iajs-3473	131	15	)	)	PUNCT
iajs-3473	131	16	with	with	ADP
iajs-3473	131	17	(	(	PUNCT
iajs-3473	131	18	)	)	PUNCT
iajs-3473	131	19	.	.	PUNCT
iajs-3473	132	1	then	then	ADV
iajs-3473	132	2	(	(	PUNCT
iajs-3473	132	3	)	)	PUNCT
iajs-3473	132	4	(	(	PUNCT
iajs-3473	132	5	)	)	PUNCT
iajs-3473	132	6	,	,	PUNCT
iajs-3473	132	7	also	also	ADV
iajs-3473	132	8	(	(	PUNCT
iajs-3473	132	9	)	)	PUNCT
iajs-3473	132	10	(	(	PUNCT
iajs-3473	132	11	)	)	PUNCT
iajs-3473	132	12	must	must	AUX
iajs-3473	132	13	be	be	AUX
iajs-3473	132	14	larger	large	ADJ
iajs-3473	132	15	than	than	ADP
iajs-3473	132	16	zero	zero	NUM
iajs-3473	132	17	,	,	PUNCT
iajs-3473	132	18	if	if	SCONJ
iajs-3473	132	19	(	(	PUNCT
iajs-3473	132	20	)	)	PUNCT
iajs-3473	132	21	(	(	PUNCT
iajs-3473	132	22	)	)	PUNCT
iajs-3473	132	23	then	then	ADV
iajs-3473	132	24	is	be	AUX
iajs-3473	132	25	one	one	NUM
iajs-3473	132	26	-	-	PUNCT
iajs-3473	132	27	one	one	NUM
iajs-3473	132	28	mapping	mapping	NOUN
iajs-3473	132	29	of	of	ADP
iajs-3473	132	30	(	(	PUNCT
iajs-3473	132	31	)	)	PUNCT
iajs-3473	132	32	onto	onto	ADP
iajs-3473	132	33	all	all	PRON
iajs-3473	132	34	of	of	ADP
iajs-3473	132	35	.	.	PUNCT
iajs-3473	133	1	the	the	DET
iajs-3473	133	2	inverse	inverse	NOUN
iajs-3473	133	3	(	(	PUNCT
iajs-3473	133	4	)	)	PUNCT
iajs-3473	133	5	is	be	AUX
iajs-3473	133	6	then	then	ADV
iajs-3473	133	7	closed	closed	ADJ
iajs-3473	133	8	and	and	CCONJ
iajs-3473	133	9	hence	hence	ADV
iajs-3473	133	10	bounded	bound	VERB
iajs-3473	133	11	,	,	PUNCT
iajs-3473	133	12	thus	thus	ADV
iajs-3473	133	13	(	(	PUNCT
iajs-3473	133	14	)	)	PUNCT
iajs-3473	133	15	,	,	PUNCT
iajs-3473	133	16	which	which	PRON
iajs-3473	133	17	is	be	AUX
iajs-3473	133	18	contradiction	contradiction	NOUN
iajs-3473	133	19	.	.	PUNCT
iajs-3473	134	1	hence	hence	ADV
iajs-3473	134	2	(	(	PUNCT
iajs-3473	134	3	)	)	PUNCT
iajs-3473	134	4	,	,	PUNCT
iajs-3473	134	5	then	then	ADV
iajs-3473	134	6	(	(	PUNCT
iajs-3473	134	7	)	)	PUNCT
iajs-3473	134	8	.	.	PUNCT
iajs-3473	135	1	now	now	ADV
iajs-3473	135	2	,	,	PUNCT
iajs-3473	135	3	assume	assume	VERB
iajs-3473	135	4	(	(	PUNCT
iajs-3473	135	5	)	)	PUNCT
iajs-3473	135	6	,	,	PUNCT
iajs-3473	135	7	to	to	PART
iajs-3473	135	8	prove	prove	VERB
iajs-3473	135	9	(	(	PUNCT
iajs-3473	135	10	)	)	PUNCT
iajs-3473	135	11	(	(	PUNCT
iajs-3473	135	12	)	)	PUNCT
iajs-3473	135	13	since	since	SCONJ
iajs-3473	135	14	(	(	PUNCT
iajs-3473	135	15	)	)	PUNCT
iajs-3473	135	16	then	then	ADV
iajs-3473	135	17	iso	iso	NOUN
iajs-3473	135	18	(	(	PUNCT
iajs-3473	135	19	)	)	PUNCT
iajs-3473	135	20	which	which	PRON
iajs-3473	135	21	imply	imply	VERB
iajs-3473	135	22	(	(	PUNCT
iajs-3473	135	23	)	)	PUNCT
iajs-3473	135	24	(	(	PUNCT
iajs-3473	135	25	)	)	PUNCT
iajs-3473	135	26	.	.	PUNCT
iajs-3473	136	1	to	to	PART
iajs-3473	136	2	prove	prove	VERB
iajs-3473	136	3	is	be	AUX
iajs-3473	136	4	belong	belong	ADJ
iajs-3473	136	5	to	to	ADP
iajs-3473	136	6	(	(	PUNCT
iajs-3473	136	7	)	)	PUNCT
iajs-3473	136	8	since	since	SCONJ
iajs-3473	136	9	obeys	obey	NOUN
iajs-3473	136	10	(	(	PUNCT
iajs-3473	136	11	b	b	NOUN
iajs-3473	136	12	)	)	PUNCT
iajs-3473	136	13	property	property	NOUN
iajs-3473	136	14	with	with	ADP
iajs-3473	136	15	(	(	PUNCT
iajs-3473	136	16	)	)	PUNCT
iajs-3473	136	17	(	(	PUNCT
iajs-3473	136	18	)	)	PUNCT
iajs-3473	136	19	and	and	CCONJ
iajs-3473	136	20	(	(	PUNCT
iajs-3473	136	21	)	)	PUNCT
iajs-3473	136	22	,	,	PUNCT
iajs-3473	136	23	then	then	ADV
iajs-3473	136	24	(	(	PUNCT
iajs-3473	136	25	)	)	PUNCT
iajs-3473	136	26	and	and	CCONJ
iajs-3473	136	27	(	(	PUNCT
iajs-3473	136	28	)	)	PUNCT
iajs-3473	136	29	is	be	AUX
iajs-3473	136	30	closed	close	VERB
iajs-3473	136	31	with	with	ADP
iajs-3473	136	32	is	be	AUX
iajs-3473	136	33	browder	browder	NOUN
iajs-3473	136	34	operator	operator	NOUN
iajs-3473	136	35	i.e.	i.e.	ADV
iajs-3473	136	36	,	,	PUNCT
iajs-3473	136	37	(	(	PUNCT
iajs-3473	136	38	)	)	PUNCT
iajs-3473	136	39	and	and	CCONJ
iajs-3473	136	40	(	(	PUNCT
iajs-3473	136	41	)	)	PUNCT
iajs-3473	136	42	(	(	PUNCT
iajs-3473	136	43	)	)	PUNCT
iajs-3473	136	44	and	and	CCONJ
iajs-3473	136	45	(	(	PUNCT
iajs-3473	136	46	)	)	PUNCT
iajs-3473	136	47	(	(	PUNCT
iajs-3473	136	48	)	)	PUNCT
iajs-3473	136	49	.	.	PUNCT
iajs-3473	137	1	the	the	DET
iajs-3473	137	2	proof	proof	NOUN
iajs-3473	137	3	is	be	AUX
iajs-3473	137	4	completed	complete	VERB
iajs-3473	137	5	.	.	PUNCT
iajs-3473	138	1	3.9	3.9	NUM
iajs-3473	138	2	.	.	PUNCT
iajs-3473	138	3	theorem	theorem	NOUN
iajs-3473	138	4	if	if	SCONJ
iajs-3473	138	5	is	be	AUX
iajs-3473	138	6	upper	upper	ADJ
iajs-3473	138	7	triangular	triangular	NOUN
iajs-3473	138	8	unbounded	unbounded	ADJ
iajs-3473	138	9	operator	operator	NOUN
iajs-3473	138	10	matrix	matrix	NOUN
iajs-3473	138	11	with	with	ADP
iajs-3473	138	12	(	(	PUNCT
iajs-3473	138	13	)	)	PUNCT
iajs-3473	138	14	(	(	PUNCT
iajs-3473	138	15	)	)	PUNCT
iajs-3473	138	16	and	and	CCONJ
iajs-3473	138	17	(	(	PUNCT
iajs-3473	138	18	)	)	PUNCT
iajs-3473	138	19	(	(	PUNCT
iajs-3473	138	20	)	)	PUNCT
iajs-3473	138	21	,	,	PUNCT
iajs-3473	138	22	(	(	PUNCT
iajs-3473	138	23	)	)	PUNCT
iajs-3473	138	24	(	(	PUNCT
iajs-3473	138	25	)	)	PUNCT
iajs-3473	138	26	(	(	PUNCT
iajs-3473	138	27	)	)	PUNCT
iajs-3473	138	28	(	(	PUNCT
iajs-3473	138	29	)	)	PUNCT
iajs-3473	138	30	,	,	PUNCT
iajs-3473	138	31	then	then	ADV
iajs-3473	138	32	obeys	obey	VERB
iajs-3473	138	33	property	property	NOUN
iajs-3473	138	34	(	(	PUNCT
iajs-3473	138	35	am	am	NOUN
iajs-3473	138	36	)	)	PUNCT
iajs-3473	138	37	.	.	PUNCT
iajs-3473	139	1	proof	proof	NOUN
iajs-3473	139	2	.	.	PUNCT
iajs-3473	140	1	let	let	VERB
iajs-3473	140	2	(	(	PUNCT
iajs-3473	140	3	)	)	PUNCT
iajs-3473	140	4	(	(	PUNCT
iajs-3473	140	5	)	)	PUNCT
iajs-3473	140	6	,	,	PUNCT
iajs-3473	140	7	to	to	PART
iajs-3473	140	8	prove	prove	VERB
iajs-3473	140	9	(	(	PUNCT
iajs-3473	140	10	)	)	PUNCT
iajs-3473	140	11	i.e.	i.e.	X
iajs-3473	140	12	,	,	PUNCT
iajs-3473	140	13	to	to	PART
iajs-3473	140	14	prove	prove	VERB
iajs-3473	140	15	(	(	PUNCT
iajs-3473	140	16	)	)	PUNCT
iajs-3473	140	17	*	*	PUNCT
iajs-3473	140	18	(	(	PUNCT
iajs-3473	140	19	)	)	PUNCT
iajs-3473	140	20	(	(	PUNCT
iajs-3473	140	21	)	)	PUNCT
iajs-3473	141	1	+	+	X
iajs-3473	141	2	.	.	PUNCT
iajs-3473	142	1	since	since	SCONJ
iajs-3473	142	2	(	(	PUNCT
iajs-3473	142	3	)	)	PUNCT
iajs-3473	142	4	(	(	PUNCT
iajs-3473	142	5	)	)	PUNCT
iajs-3473	142	6	(	(	PUNCT
iajs-3473	142	7	)	)	PUNCT
iajs-3473	142	8	(	(	PUNCT
iajs-3473	142	9	(	(	PUNCT
iajs-3473	142	10	)	)	PUNCT
iajs-3473	142	11	(	(	PUNCT
iajs-3473	142	12	)	)	PUNCT
iajs-3473	142	13	)	)	PUNCT
iajs-3473	142	14	(	(	PUNCT
iajs-3473	142	15	)	)	PUNCT
iajs-3473	142	16	(	(	PUNCT
iajs-3473	142	17	)	)	PUNCT
iajs-3473	142	18	(	(	PUNCT
iajs-3473	142	19	)	)	PUNCT
iajs-3473	142	20	,	,	PUNCT
iajs-3473	142	21	since	since	SCONJ
iajs-3473	142	22	(	(	PUNCT
iajs-3473	142	23	)	)	PUNCT
iajs-3473	142	24	then	then	ADV
iajs-3473	142	25	we	we	PRON
iajs-3473	142	26	get	get	VERB
iajs-3473	142	27	(	(	PUNCT
iajs-3473	142	28	)	)	PUNCT
iajs-3473	142	29	(	(	PUNCT
iajs-3473	142	30	)	)	PUNCT
iajs-3473	142	31	thus	thus	ADV
iajs-3473	142	32	(	(	PUNCT
iajs-3473	142	33	)	)	PUNCT
iajs-3473	142	34	.	.	PUNCT
iajs-3473	143	1	let	let	VERB
iajs-3473	143	2	(	(	PUNCT
iajs-3473	143	3	)	)	PUNCT
iajs-3473	143	4	,	,	PUNCT
iajs-3473	143	5	to	to	PART
iajs-3473	143	6	prove	prove	VERB
iajs-3473	143	7	(	(	PUNCT
iajs-3473	143	8	)	)	PUNCT
iajs-3473	143	9	(	(	PUNCT
iajs-3473	143	10	)	)	PUNCT
iajs-3473	143	11	since	since	SCONJ
iajs-3473	143	12	(	(	PUNCT
iajs-3473	143	13	)	)	PUNCT
iajs-3473	143	14	,	,	PUNCT
iajs-3473	143	15	then	then	ADV
iajs-3473	143	16	(	(	PUNCT
iajs-3473	143	17	)	)	PUNCT
iajs-3473	143	18	,	,	PUNCT
iajs-3473	143	19	it	it	PRON
iajs-3473	143	20	remains	remain	VERB
iajs-3473	143	21	to	to	PART
iajs-3473	143	22	prove	prove	VERB
iajs-3473	143	23	(	(	PUNCT
iajs-3473	143	24	)	)	PUNCT
iajs-3473	143	25	,	,	PUNCT
iajs-3473	143	26	since	since	SCONJ
iajs-3473	143	27	(	(	PUNCT
iajs-3473	143	28	)	)	PUNCT
iajs-3473	143	29	(	(	PUNCT
iajs-3473	143	30	)	)	PUNCT
iajs-3473	143	31	then	then	ADV
iajs-3473	143	32	(	(	PUNCT
iajs-3473	143	33	)	)	PUNCT
iajs-3473	143	34	.	.	PUNCT
iajs-3473	144	1	from	from	ADP
iajs-3473	144	2	lemma	lemma	PROPN
iajs-3473	144	3	4	4	NUM
iajs-3473	144	4	(	(	PUNCT
iajs-3473	144	5	see	see	VERB
iajs-3473	144	6	(	(	PUNCT
iajs-3473	144	7	9	9	NUM
iajs-3473	144	8	)	)	PUNCT
iajs-3473	144	9	)	)	PUNCT
iajs-3473	144	10	and	and	CCONJ
iajs-3473	144	11	(	(	PUNCT
iajs-3473	144	12	)	)	PUNCT
iajs-3473	144	13	(	(	PUNCT
iajs-3473	144	14	)	)	PUNCT
iajs-3473	144	15	we	we	PRON
iajs-3473	144	16	see	see	VERB
iajs-3473	144	17	that	that	PRON
iajs-3473	144	18	(	(	PUNCT
iajs-3473	144	19	)	)	PUNCT
iajs-3473	144	20	(	(	PUNCT
iajs-3473	144	21	)	)	PUNCT
iajs-3473	144	22	,	,	PUNCT
iajs-3473	144	23	and	and	CCONJ
iajs-3473	144	24	since	since	SCONJ
iajs-3473	144	25	(	(	PUNCT
iajs-3473	144	26	)	)	PUNCT
iajs-3473	144	27	(	(	PUNCT
iajs-3473	144	28	)	)	PUNCT
iajs-3473	144	29	(	(	PUNCT
iajs-3473	144	30	)	)	PUNCT
iajs-3473	144	31	(	(	PUNCT
iajs-3473	144	32	)	)	PUNCT
iajs-3473	144	33	,	,	PUNCT
iajs-3473	144	34	we	we	PRON
iajs-3473	144	35	have	have	VERB
iajs-3473	144	36	(	(	PUNCT
iajs-3473	144	37	)	)	PUNCT
iajs-3473	144	38	and	and	CCONJ
iajs-3473	144	39	(	(	PUNCT
iajs-3473	144	40	)	)	PUNCT
iajs-3473	144	41	hence	hence	ADV
iajs-3473	144	42	(	(	PUNCT
iajs-3473	144	43	)	)	PUNCT
iajs-3473	144	44	then	then	ADV
iajs-3473	144	45	by	by	ADP
iajs-3473	144	46	lemma	lemma	PROPN
iajs-3473	144	47	(	(	PUNCT
iajs-3473	144	48	)	)	PUNCT
iajs-3473	144	49	,	,	PUNCT
iajs-3473	144	50	we	we	PRON
iajs-3473	144	51	get	get	VERB
iajs-3473	144	52	(	(	PUNCT
iajs-3473	144	53	)	)	PUNCT
iajs-3473	144	54	(	(	PUNCT
iajs-3473	144	55	)	)	PUNCT
iajs-3473	144	56	,	,	PUNCT
iajs-3473	144	57	thus	thus	ADV
iajs-3473	144	58	(	(	PUNCT
iajs-3473	144	59	)	)	PUNCT
iajs-3473	144	60	.	.	PUNCT
iajs-3473	145	1	then	then	ADV
iajs-3473	145	2	obeys	obey	VERB
iajs-3473	145	3	(	(	PUNCT
iajs-3473	145	4	am	am	NOUN
iajs-3473	145	5	)	)	PUNCT
iajs-3473	145	6	property	property	NOUN
iajs-3473	145	7	.	.	PUNCT
iajs-3473	146	1	3.10	3.10	NUM
iajs-3473	146	2	.	.	PUNCT
iajs-3473	146	3	theorem	theorem	VERB
iajs-3473	146	4	if	if	SCONJ
iajs-3473	146	5	obeys	obey	NOUN
iajs-3473	146	6	weyl	weyl	PROPN
iajs-3473	146	7	’s	’s	PART
iajs-3473	146	8	theorem	theorem	PROPN
iajs-3473	146	9	and	and	CCONJ
iajs-3473	146	10	(	(	PUNCT
iajs-3473	146	11	)	)	PUNCT
iajs-3473	146	12	with	with	ADP
iajs-3473	146	13	(	(	PUNCT
iajs-3473	146	14	)	)	PUNCT
iajs-3473	146	15	(	(	PUNCT
iajs-3473	146	16	)	)	PUNCT
iajs-3473	146	17	and	and	CCONJ
iajs-3473	146	18	(	(	PUNCT
iajs-3473	146	19	)	)	PUNCT
iajs-3473	146	20	(	(	PUNCT
iajs-3473	146	21	)	)	PUNCT
iajs-3473	146	22	then	then	ADV
iajs-3473	146	23	obeys	obey	VERB
iajs-3473	146	24	(	(	PUNCT
iajs-3473	146	25	am	am	NOUN
iajs-3473	146	26	)	)	PUNCT
iajs-3473	146	27	property	property	NOUN
iajs-3473	146	28	.	.	PUNCT
iajs-3473	147	1	proof	proof	NOUN
iajs-3473	147	2	.	.	PUNCT
iajs-3473	148	1	by	by	ADP
iajs-3473	148	2	using	use	VERB
iajs-3473	148	3	the	the	DET
iajs-3473	148	4	same	same	ADJ
iajs-3473	148	5	steps	step	NOUN
iajs-3473	148	6	in	in	ADP
iajs-3473	148	7	theorem	theorem	ADJ
iajs-3473	148	8	3.9	3.9	NUM
iajs-3473	148	9	one	one	NUM
iajs-3473	148	10	can	can	AUX
iajs-3473	148	11	show	show	VERB
iajs-3473	148	12	(	(	PUNCT
iajs-3473	148	13	)	)	PUNCT
iajs-3473	148	14	(	(	PUNCT
iajs-3473	148	15	)	)	PUNCT
iajs-3473	148	16	.	.	PUNCT
iajs-3473	149	1	it	it	PRON
iajs-3473	149	2	remains	remain	VERB
iajs-3473	149	3	to	to	ADP
iajs-3473	149	4	proof	proof	NOUN
iajs-3473	149	5	(	(	PUNCT
iajs-3473	149	6	)	)	PUNCT
iajs-3473	149	7	(	(	PUNCT
iajs-3473	149	8	)	)	PUNCT
iajs-3473	149	9	(	(	PUNCT
iajs-3473	149	10	)	)	PUNCT
iajs-3473	149	11	.let	.let	NOUN
iajs-3473	150	1	(	(	PUNCT
iajs-3473	150	2	)	)	PUNCT
iajs-3473	150	3	then	then	ADV
iajs-3473	150	4	(	(	PUNCT
iajs-3473	150	5	)	)	PUNCT
iajs-3473	150	6	also	also	ADV
iajs-3473	150	7	(	(	PUNCT
iajs-3473	150	8	)	)	PUNCT
iajs-3473	150	9	but	but	CCONJ
iajs-3473	150	10	obeys	obey	NOUN
iajs-3473	150	11	weyl	weyl	PROPN
iajs-3473	150	12	's	's	PART
iajs-3473	150	13	theorem	theorem	NOUN
iajs-3473	150	14	then	then	ADV
iajs-3473	150	15	(	(	PUNCT
iajs-3473	150	16	)	)	PUNCT
iajs-3473	150	17	(	(	PUNCT
iajs-3473	150	18	)	)	PUNCT
iajs-3473	150	19	(	(	PUNCT
iajs-3473	150	20	)	)	PUNCT
iajs-3473	150	21	i.e.	i.e.	X
iajs-3473	150	22	,	,	PUNCT
iajs-3473	150	23	is	be	AUX
iajs-3473	150	24	weyl	weyl	VERB
iajs-3473	150	25	theorem	theorem	VERB
iajs-3473	150	26	.	.	PUNCT
iajs-3473	151	1	by	by	ADP
iajs-3473	151	2	assumptions	assumption	NOUN
iajs-3473	151	3	we	we	PRON
iajs-3473	151	4	have	have	VERB
iajs-3473	151	5	(	(	PUNCT
iajs-3473	151	6	)	)	PUNCT
iajs-3473	151	7	(	(	PUNCT
iajs-3473	151	8	)	)	PUNCT
iajs-3473	151	9	and	and	CCONJ
iajs-3473	151	10	(	(	PUNCT
iajs-3473	151	11	)	)	PUNCT
iajs-3473	151	12	(	(	PUNCT
iajs-3473	151	13	)	)	PUNCT
iajs-3473	151	14	these	these	PRON
iajs-3473	151	15	would	would	AUX
iajs-3473	151	16	imply	imply	VERB
iajs-3473	151	17	that	that	PRON
iajs-3473	151	18	(	(	PUNCT
iajs-3473	151	19	)	)	PUNCT
iajs-3473	151	20	and	and	CCONJ
iajs-3473	151	21	(	(	PUNCT
iajs-3473	151	22	)	)	PUNCT
iajs-3473	151	23	are	be	AUX
iajs-3473	151	24	finite	finite	ADJ
iajs-3473	151	25	then	then	ADV
iajs-3473	151	26	(	(	PUNCT
iajs-3473	151	27	)	)	PUNCT
iajs-3473	151	28	is	be	AUX
iajs-3473	151	29	browder	browder	NOUN
iajs-3473	151	30	operator	operator	NOUN
iajs-3473	151	31	.	.	PUNCT
iajs-3473	152	1	then	then	ADV
iajs-3473	152	2	the	the	DET
iajs-3473	152	3	proof	proof	NOUN
iajs-3473	152	4	is	be	AUX
iajs-3473	152	5	completed	complete	VERB
iajs-3473	152	6	.	.	PUNCT
iajs-3473	153	1	3.11	3.11	NUM
iajs-3473	153	2	.	.	PUNCT
iajs-3473	153	3	example	example	NOUN
iajs-3473	153	4	in	in	ADP
iajs-3473	153	5	this	this	DET
iajs-3473	153	6	example	example	NOUN
iajs-3473	153	7	,	,	PUNCT
iajs-3473	153	8	we	we	PRON
iajs-3473	153	9	tried	try	VERB
iajs-3473	153	10	to	to	PART
iajs-3473	153	11	apply	apply	VERB
iajs-3473	153	12	the	the	DET
iajs-3473	153	13	results	result	NOUN
iajs-3473	153	14	in	in	ADP
iajs-3473	153	15	(	(	PUNCT
iajs-3473	153	16	16	16	NUM
iajs-3473	153	17	)	)	PUNCT
iajs-3473	153	18	and	and	CCONJ
iajs-3473	153	19	(	(	PUNCT
iajs-3473	153	20	17	17	NUM
iajs-3473	153	21	)	)	PUNCT
iajs-3473	153	22	and	and	CCONJ
iajs-3473	153	23	some	some	DET
iajs-3473	153	24	results	result	NOUN
iajs-3473	153	25	in	in	ADP
iajs-3473	153	26	this	this	DET
iajs-3473	153	27	paper	paper	NOUN
iajs-3473	153	28	to	to	ADP
iajs-3473	153	29	the	the	DET
iajs-3473	153	30	hamiltonian	hamiltonian	ADJ
iajs-3473	153	31	operator	operator	NOUN
iajs-3473	153	32	matrix	matrix	NOUN
iajs-3473	153	33	by	by	ADP
iajs-3473	153	34	applying	apply	VERB
iajs-3473	153	35	the	the	DET
iajs-3473	153	36	plate	plate	NOUN
iajs-3473	153	37	bending	bending	NOUN
iajs-3473	153	38	problem	problem	NOUN
iajs-3473	153	39	.	.	PUNCT
iajs-3473	154	1	assume	assume	VERB
iajs-3473	154	2	the	the	DET
iajs-3473	154	3	plate	plate	NOUN
iajs-3473	154	4	bending	bend	VERB
iajs-3473	154	5	problem	problem	NOUN
iajs-3473	154	6	(	(	PUNCT
iajs-3473	154	7	)	)	PUNCT
iajs-3473	154	8	with	with	ADP
iajs-3473	154	9	from	from	ADP
iajs-3473	154	10	0	0	NUM
iajs-3473	154	11	to	to	ADP
iajs-3473	154	12	1	1	NUM
iajs-3473	154	13	.	.	PUNCT
iajs-3473	155	1	for	for	ADP
iajs-3473	155	2	the	the	DET
iajs-3473	155	3	y	y	NOUN
iajs-3473	155	4	-	-	PUNCT
iajs-3473	155	5	direction	direction	NOUN
iajs-3473	155	6	:	:	PUNCT
iajs-3473	155	7	at	at	SCONJ
iajs-3473	155	8	we	we	PRON
iajs-3473	155	9	have	have	VERB
iajs-3473	155	10	(	(	PUNCT
iajs-3473	155	11	hinge	hinge	NOUN
iajs-3473	155	12	end	end	NOUN
iajs-3473	155	13	)	)	PUNCT
iajs-3473	155	14	at	at	SCONJ
iajs-3473	155	15	we	we	PRON
iajs-3473	155	16	have	have	VERB
iajs-3473	155	17	=	=	NOUN
iajs-3473	155	18	0	0	NUM
iajs-3473	155	19	(	(	PUNCT
iajs-3473	155	20	fixed	fix	VERB
iajs-3473	155	21	end	end	NOUN
iajs-3473	155	22	)	)	PUNCT
iajs-3473	155	23	at	at	ADP
iajs-3473	155	24	we	we	PRON
iajs-3473	155	25	have	have	AUX
iajs-3473	155	26	given	give	VERB
iajs-3473	155	27	function	function	NOUN
iajs-3473	155	28	and	and	CCONJ
iajs-3473	155	29	(	(	PUNCT
iajs-3473	155	30	free	free	ADJ
iajs-3473	155	31	end	end	NOUN
iajs-3473	155	32	)	)	PUNCT
iajs-3473	155	33	ihjpas	ihjpas	PROPN
iajs-3473	155	34	.	.	PUNCT
iajs-3473	156	1	2025,38(4	2025,38(4	NOUN
iajs-3473	156	2	)	)	PUNCT
iajs-3473	156	3	293	293	NUM
iajs-3473	156	4	for	for	ADP
iajs-3473	156	5	the	the	DET
iajs-3473	156	6	x	x	NOUN
iajs-3473	156	7	-	-	NOUN
iajs-3473	156	8	direction	direction	NOUN
iajs-3473	156	9	:	:	PUNCT
iajs-3473	156	10	are	be	AUX
iajs-3473	156	11	given	give	VERB
iajs-3473	156	12	function	function	NOUN
iajs-3473	156	13	at	at	ADP
iajs-3473	156	14	to	to	ADP
iajs-3473	156	15	.	.	PUNCT
iajs-3473	157	1	the	the	DET
iajs-3473	157	2	problem	problem	NOUN
iajs-3473	157	3	can	can	AUX
iajs-3473	157	4	be	be	AUX
iajs-3473	157	5	described	describe	VERB
iajs-3473	157	6	by	by	ADP
iajs-3473	157	7	the	the	DET
iajs-3473	157	8	following	follow	VERB
iajs-3473	157	9	hamiltonian	hamiltonian	ADJ
iajs-3473	157	10	system	system	NOUN
iajs-3473	157	11	(	(	PUNCT
iajs-3473	157	12	18	18	NUM
iajs-3473	157	13	)	)	PUNCT
iajs-3473	157	14	(	(	PUNCT
iajs-3473	157	15	)	)	PUNCT
iajs-3473	157	16	(	(	PUNCT
iajs-3473	157	17	)	)	PUNCT
iajs-3473	157	18	(	(	PUNCT
iajs-3473	157	19	)	)	PUNCT
iajs-3473	157	20	and	and	CCONJ
iajs-3473	157	21	the	the	DET
iajs-3473	157	22	corresponding	corresponding	ADJ
iajs-3473	157	23	hamiltonian	hamiltonian	ADJ
iajs-3473	157	24	operator	operator	NOUN
iajs-3473	157	25	matrix	matrix	NOUN
iajs-3473	157	26	is	be	AUX
iajs-3473	157	27	given	give	VERB
iajs-3473	157	28	by	by	ADP
iajs-3473	157	29	(	(	PUNCT
iajs-3473	157	30	)	)	PUNCT
iajs-3473	157	31	(	(	PUNCT
iajs-3473	157	32	)	)	PUNCT
iajs-3473	157	33	with	with	ADP
iajs-3473	157	34	domain	domain	NOUN
iajs-3473	157	35	is	be	AUX
iajs-3473	157	36	(	(	PUNCT
iajs-3473	157	37	)	)	PUNCT
iajs-3473	157	38	(	(	PUNCT
iajs-3473	157	39	)	)	PUNCT
iajs-3473	157	40	(	(	PUNCT
iajs-3473	157	41	)	)	PUNCT
iajs-3473	157	42	(	(	PUNCT
iajs-3473	157	43	)	)	PUNCT
iajs-3473	157	44	,	,	PUNCT
iajs-3473	157	45	-	-	PUNCT
iajs-3473	157	46	,	,	PUNCT
iajs-3473	157	47	and	and	CCONJ
iajs-3473	157	48	(	(	PUNCT
iajs-3473	157	49	)	)	PUNCT
iajs-3473	157	50	(	(	PUNCT
iajs-3473	157	51	)	)	PUNCT
iajs-3473	157	52	(	(	PUNCT
iajs-3473	157	53	)	)	PUNCT
iajs-3473	157	54	{	{	PUNCT
iajs-3473	157	55	(	(	PUNCT
iajs-3473	157	56	)	)	PUNCT
iajs-3473	157	57	(	(	PUNCT
iajs-3473	157	58	)	)	PUNCT
iajs-3473	157	59	}	}	PUNCT
iajs-3473	157	60	with	with	ADP
iajs-3473	157	61	some	some	DET
iajs-3473	157	62	simple	simple	ADJ
iajs-3473	157	63	calculation	calculation	NOUN
iajs-3473	157	64	,	,	PUNCT
iajs-3473	157	65	we	we	PRON
iajs-3473	157	66	have	have	VERB
iajs-3473	157	67	(	(	PUNCT
iajs-3473	157	68	)	)	PUNCT
iajs-3473	157	69	(	(	PUNCT
iajs-3473	157	70	)	)	PUNCT
iajs-3473	157	71	(	(	PUNCT
iajs-3473	157	72	)	)	PUNCT
iajs-3473	157	73	(	(	PUNCT
iajs-3473	157	74	)	)	PUNCT
iajs-3473	157	75	(	(	PUNCT
iajs-3473	157	76	)	)	PUNCT
iajs-3473	157	77	,	,	PUNCT
iajs-3473	157	78	(	(	PUNCT
iajs-3473	157	79	)	)	PUNCT
iajs-3473	157	80	(	(	PUNCT
iajs-3473	157	81	)	)	PUNCT
iajs-3473	157	82	and	and	CCONJ
iajs-3473	157	83	(	(	PUNCT
iajs-3473	157	84	)	)	PUNCT
iajs-3473	157	85	.	.	PUNCT
iajs-3473	158	1	then	then	ADV
iajs-3473	158	2	from	from	ADP
iajs-3473	158	3	propositions	proposition	NOUN
iajs-3473	158	4	4.1	4.1	NUM
iajs-3473	158	5	,	,	PUNCT
iajs-3473	158	6	4.2	4.2	NUM
iajs-3473	158	7	and	and	CCONJ
iajs-3473	158	8	4.3	4.3	NUM
iajs-3473	158	9	in	in	ADP
iajs-3473	158	10	(	(	PUNCT
iajs-3473	158	11	5	5	NUM
iajs-3473	158	12	)	)	PUNCT
iajs-3473	158	13	,	,	PUNCT
iajs-3473	158	14	and	and	CCONJ
iajs-3473	158	15	from	from	ADP
iajs-3473	158	16	propositions	proposition	NOUN
iajs-3473	158	17	10	10	NUM
iajs-3473	158	18	and	and	CCONJ
iajs-3473	158	19	11	11	NUM
iajs-3473	158	20	in	in	ADP
iajs-3473	158	21	(	(	PUNCT
iajs-3473	158	22	10	10	NUM
iajs-3473	158	23	)	)	PUNCT
iajs-3473	158	24	,	,	PUNCT
iajs-3473	158	25	we	we	PRON
iajs-3473	158	26	have	have	VERB
iajs-3473	158	27	(	(	PUNCT
iajs-3473	158	28	)	)	PUNCT
iajs-3473	158	29	(	(	PUNCT
iajs-3473	158	30	)	)	PUNCT
iajs-3473	158	31	(	(	PUNCT
iajs-3473	158	32	)	)	PUNCT
iajs-3473	159	1	where	where	SCONJ
iajs-3473	159	2	{	{	PUNCT
iajs-3473	159	3	}	}	PUNCT
iajs-3473	159	4	.	.	PUNCT
iajs-3473	160	1	now	now	ADV
iajs-3473	160	2	,	,	PUNCT
iajs-3473	160	3	by	by	ADP
iajs-3473	160	4	theorem	theorem	NOUN
iajs-3473	160	5	3.1	3.1	NUM
iajs-3473	160	6	we	we	PRON
iajs-3473	160	7	found	find	VERB
iajs-3473	160	8	that	that	SCONJ
iajs-3473	160	9	(	(	PUNCT
iajs-3473	160	10	)	)	PUNCT
iajs-3473	160	11	(	(	PUNCT
iajs-3473	160	12	)	)	PUNCT
iajs-3473	160	13	if	if	SCONJ
iajs-3473	160	14	(	(	PUNCT
iajs-3473	160	15	)	)	PUNCT
iajs-3473	160	16	(	(	PUNCT
iajs-3473	160	17	)	)	PUNCT
iajs-3473	160	18	.	.	PUNCT
iajs-3473	161	1	4	4	X
iajs-3473	161	2	.	.	X
iajs-3473	161	3	conclusion	conclusion	NOUN
iajs-3473	161	4	in	in	ADP
iajs-3473	161	5	this	this	DET
iajs-3473	161	6	paper	paper	NOUN
iajs-3473	161	7	,	,	PUNCT
iajs-3473	161	8	other	other	ADJ
iajs-3473	161	9	spectral	spectral	ADJ
iajs-3473	161	10	properties	property	NOUN
iajs-3473	161	11	are	be	AUX
iajs-3473	161	12	introduced	introduce	VERB
iajs-3473	161	13	and	and	CCONJ
iajs-3473	161	14	studied	study	VERB
iajs-3473	161	15	for	for	ADP
iajs-3473	161	16	the	the	DET
iajs-3473	161	17	upper	upper	ADJ
iajs-3473	161	18	triangular	triangular	NOUN
iajs-3473	161	19	operator	operator	NOUN
iajs-3473	161	20	matrices	matrix	NOUN
iajs-3473	161	21	.	.	PUNCT
iajs-3473	162	1	furthermore	furthermore	ADV
iajs-3473	162	2	,	,	PUNCT
iajs-3473	162	3	weyl	weyl	PROPN
iajs-3473	162	4	’s	’s	PART
iajs-3473	162	5	type	type	NOUN
iajs-3473	162	6	theorems	theorem	NOUN
iajs-3473	162	7	and	and	CCONJ
iajs-3473	162	8	browder	browder	NOUN
iajs-3473	162	9	’s	’s	PART
iajs-3473	162	10	theorems	theorem	NOUN
iajs-3473	162	11	are	be	AUX
iajs-3473	162	12	also	also	ADV
iajs-3473	162	13	proved	prove	VERB
iajs-3473	162	14	under	under	ADP
iajs-3473	162	15	certain	certain	ADJ
iajs-3473	162	16	conditions	condition	NOUN
iajs-3473	162	17	.	.	PUNCT
iajs-3473	163	1	finally	finally	ADV
iajs-3473	163	2	,	,	PUNCT
iajs-3473	163	3	as	as	ADP
iajs-3473	163	4	an	an	DET
iajs-3473	163	5	application	application	NOUN
iajs-3473	163	6	the	the	DET
iajs-3473	163	7	paper	paper	NOUN
iajs-3473	163	8	study	study	NOUN
iajs-3473	163	9	the	the	DET
iajs-3473	163	10	plate	plate	NOUN
iajs-3473	163	11	bending	bend	VERB
iajs-3473	163	12	problem	problem	NOUN
iajs-3473	163	13	and	and	CCONJ
iajs-3473	163	14	calculate	calculate	VERB
iajs-3473	163	15	the	the	DET
iajs-3473	163	16	spectrum	spectrum	NOUN
iajs-3473	163	17	sets	set	NOUN
iajs-3473	163	18	denoted	denote	VERB
iajs-3473	163	19	by	by	ADP
iajs-3473	163	20	where	where	SCONJ
iajs-3473	163	21	{	{	PUNCT
iajs-3473	163	22	}	}	PUNCT
iajs-3473	163	23	.	.	PUNCT
iajs-3473	164	1	acknowledgment	acknowledgment	NOUN
iajs-3473	164	2	our	our	PRON
iajs-3473	164	3	researcher	researcher	NOUN
iajs-3473	164	4	extends	extend	VERB
iajs-3473	164	5	his	his	PRON
iajs-3473	164	6	sincere	sincere	ADJ
iajs-3473	164	7	thanks	thank	NOUN
iajs-3473	164	8	to	to	ADP
iajs-3473	164	9	the	the	DET
iajs-3473	164	10	editor	editor	NOUN
iajs-3473	164	11	and	and	CCONJ
iajs-3473	164	12	members	member	NOUN
iajs-3473	164	13	of	of	ADP
iajs-3473	164	14	the	the	DET
iajs-3473	164	15	preparatory	preparatory	PROPN
iajs-3473	164	16	committee	committee	NOUN
iajs-3473	164	17	of	of	ADP
iajs-3473	164	18	the	the	DET
iajs-3473	164	19	ibn	ibn	PROPN
iajs-3473	164	20	al	al	PROPN
iajs-3473	164	21	-	-	PUNCT
iajs-3473	164	22	haitham	haitham	PROPN
iajs-3473	164	23	journal	journal	PROPN
iajs-3473	164	24	of	of	ADP
iajs-3473	164	25	pure	pure	ADJ
iajs-3473	164	26	and	and	CCONJ
iajs-3473	164	27	applied	applied	ADJ
iajs-3473	164	28	sciences	science	NOUN
iajs-3473	164	29	.	.	PUNCT
iajs-3473	165	1	conflict	conflict	NOUN
iajs-3473	165	2	of	of	ADP
iajs-3473	165	3	interest	interest	NOUN
iajs-3473	165	4	there	there	PRON
iajs-3473	165	5	are	be	VERB
iajs-3473	165	6	no	no	DET
iajs-3473	165	7	conflicts	conflict	NOUN
iajs-3473	165	8	of	of	ADP
iajs-3473	165	9	interest	interest	NOUN
iajs-3473	165	10	.	.	PUNCT
iajs-3473	166	1	funding	funding	NOUN
iajs-3473	166	2	there	there	PRON
iajs-3473	166	3	is	be	VERB
iajs-3473	166	4	no	no	DET
iajs-3473	166	5	funding	funding	NOUN
iajs-3473	166	6	for	for	ADP
iajs-3473	166	7	the	the	DET
iajs-3473	166	8	article	article	NOUN
iajs-3473	166	9	.	.	PUNCT
iajs-3473	167	1	references	reference	NOUN
iajs-3473	167	2	1	1	NUM
iajs-3473	167	3	.	.	PUNCT
iajs-3473	168	1	weyl	weyl	PROPN
iajs-3473	168	2	h.	h.	PROPN
iajs-3473	168	3	überbeschränkte	überbeschränkte	PROPN
iajs-3473	168	4	quadratische	quadratische	PROPN
iajs-3473	168	5	formen	formen	PROPN
iajs-3473	168	6	,	,	PUNCT
iajs-3473	168	7	deren	deren	PROPN
iajs-3473	168	8	differenz	differenz	PROPN
iajs-3473	168	9	vollstetig	vollstetig	NOUN
iajs-3473	168	10	ist	ist	NOUN
iajs-3473	168	11	.	.	PUNCT
iajs-3473	169	1	rend	rend	VERB
iajs-3473	169	2	circ	circ	PROPN
iajs-3473	169	3	mat	mat	NOUN
iajs-3473	169	4	palermo	palermo	NOUN
iajs-3473	169	5	.	.	PUNCT
iajs-3473	170	1	1909	1909	NUM
iajs-3473	170	2	;	;	PUNCT
iajs-3473	170	3	27(1	27(1	NUM
iajs-3473	170	4	)	)	PUNCT
iajs-3473	170	5	:	:	PUNCT
iajs-3473	171	1	373–392	373–392	X
iajs-3473	171	2	.	.	PUNCT
iajs-3473	171	3	https://link.springer.com/article/10.1007/bf03019655	https://link.springer.com/article/10.1007/bf03019655	NOUN
iajs-3473	171	4	.	.	PUNCT
iajs-3473	172	1	2	2	X
iajs-3473	172	2	.	.	X
iajs-3473	172	3	coburn	coburn	PROPN
iajs-3473	172	4	la	la	PROPN
iajs-3473	172	5	.	.	PUNCT
iajs-3473	173	1	weyl	weyl	PROPN
iajs-3473	173	2	's	's	PART
iajs-3473	173	3	theorem	theorem	NOUN
iajs-3473	173	4	for	for	ADP
iajs-3473	173	5	nonnormal	nonnormal	ADJ
iajs-3473	173	6	operators	operator	NOUN
iajs-3473	173	7	.	.	PUNCT
iajs-3473	174	1	michigan	michigan	PROPN
iajs-3473	174	2	math	math	PROPN
iajs-3473	174	3	j.	j.	PROPN
iajs-3473	174	4	1966	1966	NUM
iajs-3473	174	5	;	;	PUNCT
iajs-3473	174	6	13(3):285–288	13(3):285–288	NUM
iajs-3473	174	7	.	.	PUNCT
iajs-3473	175	1	http://dx.doi.org/10.1307/mmj/1031732778	http://dx.doi.org/10.1307/mmj/1031732778	NOUN
iajs-3473	175	2	.	.	PROPN
iajs-3473	176	1	3	3	X
iajs-3473	176	2	.	.	X
iajs-3473	176	3	berkani	berkani	PROPN
iajs-3473	176	4	m	m	PROPN
iajs-3473	176	5	,	,	PUNCT
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iajs-3473	176	9	weyl	weyl	PROPN
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iajs-3473	177	1	j	j	PROPN
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iajs-3473	177	5	.	.	PUNCT
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iajs-3473	178	2	;	;	PUNCT
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iajs-3473	178	8	.	.	X
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iajs-3473	182	2	.	.	X
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iajs-3473	182	16	.	.	PUNCT
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iajs-3473	187	2	.	.	X
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iajs-3473	188	1	bull	bull	PROPN
iajs-3473	188	2	aust	aust	PROPN
iajs-3473	188	3	math	math	PROPN
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iajs-3473	188	5	.	.	PUNCT
iajs-3473	189	1	1980	1980	NUM
iajs-3473	189	2	;	;	PUNCT
iajs-3473	189	3	21(2):161–168	21(2):161–168	NUM
iajs-3473	189	4	.	.	PUNCT
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iajs-3473	190	2	.	.	PUNCT
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iajs-3473	191	2	http://dx.doi.org/10.1307/mmj/1031732778	http://dx.doi.org/10.1307/mmj/1031732778	PROPN
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iajs-3473	191	8	.	.	PUNCT
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iajs-3473	194	1	mediterr	mediterr	PROPN
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iajs-3473	195	2	.	.	PUNCT
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iajs-3473	197	2	.	.	PUNCT
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iajs-3473	199	1	acta	acta	PROPN
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iajs-3473	200	2	;	;	PUNCT
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iajs-3473	201	2	.	.	NOUN
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iajs-3473	201	4	.	.	PUNCT
iajs-3473	202	1	9	9	X
iajs-3473	202	2	.	.	X
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iajs-3473	202	9	-	-	PUNCT
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iajs-3473	202	16	.	.	PUNCT
iajs-3473	203	1	j	j	PROPN
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iajs-3473	203	5	.	.	PUNCT
iajs-3473	204	1	2017	2017	NUM
iajs-3473	204	2	;	;	PUNCT
iajs-3473	204	3	52(4):191–197	52(4):191–197	NUM
iajs-3473	204	4	.	.	PUNCT
iajs-3473	205	1	https://doi.org/10.3103/s1068362317040057	https://doi.org/10.3103/s1068362317040057	NUM
iajs-3473	205	2	.	.	PUNCT
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iajs-3473	206	2	.	.	PUNCT
iajs-3473	207	1	finch	finch	PROPN
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iajs-3473	207	6	extension	extension	NOUN
iajs-3473	207	7	property	property	NOUN
iajs-3473	207	8	on	on	ADP
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iajs-3473	207	12	.	.	PUNCT
iajs-3473	208	1	pac	pac	PROPN
iajs-3473	209	1	j	j	PROPN
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iajs-3473	210	2	.	.	PUNCT
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iajs-3473	210	4	.	.	PUNCT
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iajs-3473	211	2	.	.	PUNCT
iajs-3473	212	1	aiena	aiena	PROPN
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iajs-3473	212	8	.	.	PUNCT
iajs-3473	213	1	berlin	berlin	ADJ
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iajs-3473	213	4	;	;	PUNCT
iajs-3473	213	5	2004	2004	NUM
iajs-3473	213	6	.	.	PUNCT
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iajs-3473	214	2	.	.	PUNCT
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iajs-3473	215	14	-	-	PUNCT
iajs-3473	215	15	s	s	PART
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iajs-3473	217	7	.	.	PUNCT
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iajs-3473	219	2	.	.	X
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iajs-3473	221	7	;	;	PUNCT
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iajs-3473	221	9	.	.	PUNCT
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iajs-3473	222	3	-	-	SYM
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iajs-3473	228	2	.	.	X
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iajs-3473	228	12	al	al	PROPN
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iajs-3473	229	9	:	:	PUNCT
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iajs-3473	233	11	and	and	CCONJ
iajs-3473	233	12	hypercyclicity	hypercyclicity	NOUN
iajs-3473	233	13	.	.	PUNCT
iajs-3473	234	1	monatshefte	monatshefte	PROPN
iajs-3473	234	2	für	für	PROPN
iajs-3473	234	3	mathematik	mathematik	PROPN
iajs-3473	234	4	.	.	PUNCT
iajs-3473	234	5	2024	2024	NUM
iajs-3473	234	6	;	;	PUNCT
iajs-3473	234	7	204:107	204:107	NUM
iajs-3473	234	8	–	–	PUNCT
iajs-3473	234	9	125	125	NUM
iajs-3473	234	10	.	.	PUNCT
iajs-3473	235	1	https://doi.org/10.1007/s00605-024-01951-5	https://doi.org/10.1007/s00605-024-01951-5	PROPN
iajs-3473	235	2	.	.	PUNCT
iajs-3473	236	1	17	17	NUM
iajs-3473	236	2	.	.	PUNCT
iajs-3473	237	1	xu	xu	PROPN
iajs-3473	238	1	w	w	PROPN
iajs-3473	238	2	,	,	PUNCT
iajs-3473	238	3	aponte	aponte	PROPN
iajs-3473	238	4	e	e	PROPN
iajs-3473	238	5	,	,	PUNCT
iajs-3473	238	6	vasanthakumar	vasanthakumar	PROPN
iajs-3473	238	7	p.	p.	PROPN
iajs-3473	239	1	the	the	DET
iajs-3473	239	2	property	property	NOUN
iajs-3473	239	3	(	(	PUNCT
iajs-3473	239	4	ω	ω	NOUN
iajs-3473	239	5	 	 	SPACE
iajs-3473	239	6	π	π	NOUN
iajs-3473	239	7	)	)	PUNCT
iajs-3473	239	8	as	as	ADP
iajs-3473	239	9	a	a	DET
iajs-3473	239	10	generalization	generalization	NOUN
iajs-3473	239	11	of	of	ADP
iajs-3473	239	12	the	the	DET
iajs-3473	239	13	a	a	PRON
iajs-3473	239	14	-	-	PUNCT
iajs-3473	239	15	weyl	weyl	VERB
iajs-3473	239	16	theorem	theorem	NOUN
iajs-3473	239	17	.	.	PUNCT
iajs-3473	239	18	aims	aim	VERB
iajs-3473	239	19	math	math	NOUN
iajs-3473	239	20	.	.	PUNCT
iajs-3473	240	1	2024	2024	NUM
iajs-3473	240	2	;	;	PUNCT
iajs-3473	240	3	9(9):25646–25658	9(9):25646–25658	NOUN
iajs-3473	240	4	.	.	PUNCT
iajs-3473	241	1	https://doi.org/10.3934/math.20241567	https://doi.org/10.3934/math.20241567	X
iajs-3473	241	2	.	.	PUNCT
iajs-3473	242	1	18	18	NUM
iajs-3473	242	2	.	.	X
iajs-3473	243	1	sun	sun	PROPN
iajs-3473	243	2	y	y	PROPN
iajs-3473	243	3	,	,	PUNCT
iajs-3473	243	4	cao	cao	PROPN
iajs-3473	243	5	x.	x.	NOUN
iajs-3473	243	6	criteria	criteria	PROPN
iajs-3473	243	7	for	for	ADP
iajs-3473	243	8	the	the	DET
iajs-3473	243	9	property	property	NOUN
iajs-3473	243	10	(	(	PUNCT
iajs-3473	243	11	uwe	uwe	PROPN
iajs-3473	243	12	)	)	PUNCT
iajs-3473	243	13	and	and	CCONJ
iajs-3473	243	14	the	the	DET
iajs-3473	243	15	a	a	PRON
iajs-3473	243	16	-	-	PUNCT
iajs-3473	243	17	weyl	weyl	VERB
iajs-3473	243	18	theorem	theorem	VERB
iajs-3473	243	19	.	.	PROPN
iajs-3473	243	20	funct	funct	PROPN
iajs-3473	243	21	anal	anal	ADJ
iajs-3473	243	22	appl	appl	NOUN
iajs-3473	243	23	.	.	PUNCT
iajs-3473	243	24	2023	2023	NUM
iajs-3473	243	25	;	;	PUNCT
iajs-3473	243	26	56(3):216–224	56(3):216–224	NUM
iajs-3473	243	27	.	.	PUNCT
iajs-3473	244	1	https://doi.org/10.1134/s0016266322030054	https://doi.org/10.1134/s0016266322030054	NUM
iajs-3473	244	2	.	.	PUNCT
iajs-3473	245	1	19	19	NUM
iajs-3473	245	2	.	.	PUNCT
iajs-3473	246	1	li	li	PROPN
iajs-3473	246	2	s	s	PROPN
iajs-3473	246	3	,	,	PUNCT
iajs-3473	246	4	zhang	zhang	PROPN
iajs-3473	246	5	y	y	PROPN
iajs-3473	246	6	,	,	PUNCT
iajs-3473	246	7	cao	cao	PROPN
iajs-3473	246	8	x.	x.	PROPN
iajs-3473	246	9	fa	fa	PROPN
iajs-3473	246	10	-	-	PUNCT
iajs-3473	246	11	weyl	weyl	PROPN
iajs-3473	246	12	’s	’s	PART
iajs-3473	246	13	theorem	theorem	NOUN
iajs-3473	246	14	and	and	CCONJ
iajs-3473	246	15	a	a	DET
iajs-3473	246	16	-	-	PUNCT
iajs-3473	246	17	weyl	weyl	VERB
iajs-3473	246	18	’s	’s	PART
iajs-3473	246	19	theorem	theorem	NOUN
iajs-3473	246	20	for	for	ADP
iajs-3473	246	21	bounded	bounded	ADJ
iajs-3473	246	22	linear	linear	PROPN
iajs-3473	246	23	operators	operator	NOUN
iajs-3473	246	24	.	.	PUNCT
iajs-3473	247	1	ecnu	ecnu	PROPN
iajs-3473	247	2	j	j	PROPN
iajs-3473	247	3	math	math	PROPN
iajs-3473	247	4	.	.	PUNCT
iajs-3473	248	1	2025	2025	NUM
iajs-3473	248	2	;	;	PUNCT
iajs-3473	248	3	2025(1):13–27	2025(1):13–27	NUM
iajs-3473	248	4	.	.	PUNCT
iajs-3473	249	1	https://doi.org/10.3969/j.issn.1000-5641.2025.01.002	https://doi.org/10.3969/j.issn.1000-5641.2025.01.002	X
iajs-3473	249	2	.	.	PROPN
iajs-3473	249	3	20	20	NUM
iajs-3473	249	4	.	.	PUNCT
iajs-3473	250	1	kong	kong	PROPN
iajs-3473	250	2	y	y	PROPN
iajs-3473	250	3	,	,	PUNCT
iajs-3473	250	4	ren	ren	PROPN
iajs-3473	250	5	y	y	PROPN
iajs-3473	250	6	,	,	PUNCT
iajs-3473	250	7	jiang	jiang	PROPN
iajs-3473	250	8	l.	l.	PROPN
iajs-3473	250	9	spectral	spectral	PROPN
iajs-3473	250	10	theory	theory	NOUN
iajs-3473	250	11	of	of	ADP
iajs-3473	250	12	b	b	NOUN
iajs-3473	250	13	-	-	PUNCT
iajs-3473	250	14	weyl	weyl	VERB
iajs-3473	250	15	elements	element	NOUN
iajs-3473	250	16	and	and	CCONJ
iajs-3473	250	17	the	the	DET
iajs-3473	250	18	generalized	generalize	VERB
iajs-3473	250	19	weyl	weyl	PROPN
iajs-3473	250	20	’s	’s	PART
iajs-3473	250	21	theorem	theorem	NOUN
iajs-3473	250	22	in	in	ADP
iajs-3473	250	23	primitive	primitive	ADJ
iajs-3473	250	24	c*-algebra	c*-algebra	PROPN
iajs-3473	250	25	.	.	PUNCT
iajs-3473	251	1	turk	turk	PROPN
iajs-3473	251	2	j	j	PROPN
iajs-3473	251	3	math	math	PROPN
iajs-3473	251	4	.	.	PUNCT
iajs-3473	252	1	2022	2022	NUM
iajs-3473	252	2	;	;	PUNCT
iajs-3473	253	1	46(5):1927–1944	46(5):1927–1944	NUM
iajs-3473	253	2	.	.	PUNCT
iajs-3473	253	3	https://doi.org/10.55730/13000098.3242	https://doi.org/10.55730/13000098.3242	NOUN
iajs-3473	253	4	.	.	PUNCT
iajs-3473	254	1	21	21	NUM
iajs-3473	254	2	.	.	PUNCT
iajs-3473	255	1	zhou	zhou	PROPN
iajs-3473	255	2	d	d	PROPN
iajs-3473	255	3	,	,	PUNCT
iajs-3473	255	4	chen	chen	PROPN
iajs-3473	255	5	j.	j.	PROPN
iajs-3473	255	6	further	further	PROPN
iajs-3473	255	7	results	result	NOUN
iajs-3473	255	8	on	on	ADP
iajs-3473	255	9	two	two	NUM
iajs-3473	255	10	stronger	strong	ADJ
iajs-3473	255	11	variants	variant	NOUN
iajs-3473	255	12	of	of	ADP
iajs-3473	255	13	weyl	weyl	PROPN
iajs-3473	255	14	’s	’s	PART
iajs-3473	255	15	theorem	theorem	PROPN
iajs-3473	255	16	.	.	PROPN
iajs-3473	256	1	mediterr	mediterr	PROPN
iajs-3473	256	2	j	j	PROPN
iajs-3473	256	3	math	math	PROPN
iajs-3473	256	4	.	.	PUNCT
iajs-3473	257	1	2025	2025	NUM
iajs-3473	257	2	;	;	PUNCT
iajs-3473	257	3	22:68	22:68	NUM
iajs-3473	257	4	.	.	PUNCT
iajs-3473	258	1	https://doi.org/10.1007/s00009-025-02816-3	https://doi.org/10.1007/s00009-025-02816-3	NOUN
iajs-3473	258	2	.	.	PUNCT
iajs-3473	259	1	http://doi.org/10.1007/s00009-018-1176-y	http://doi.org/10.1007/s00009-018-1176-y	NOUN
iajs-3473	259	2	http://doi.org/10.1007/s40306-021-00431-4	http://doi.org/10.1007/s40306-021-00431-4	NUM
iajs-3473	259	3	https://doi.org/10.3103/s1068362317040057	https://doi.org/10.3103/s1068362317040057	NUM
iajs-3473	259	4	http://dx.doi.org/10.2140/pjm.1975.58.61	http://dx.doi.org/10.2140/pjm.1975.58.61	NOUN
iajs-3473	259	5	http://dx.doi.org/10.21474/ijar01/520	http://dx.doi.org/10.21474/ijar01/520	NOUN
iajs-3473	259	6	http://dx.doi.org/10.21474/ijar01/520	http://dx.doi.org/10.21474/ijar01/520	NOUN
iajs-3473	259	7	http://dx.doi.org/10.1088/1742-6596/1530/1/012107	http://dx.doi.org/10.1088/1742-6596/1530/1/012107	PROPN
iajs-3473	259	8	https://doi.org/10.52866/2788-7421.1198	https://doi.org/10.52866/2788-7421.1198	ADJ
iajs-3473	259	9	https://doi.org/10.52866/2788-7421.1198	https://doi.org/10.52866/2788-7421.1198	ADJ
iajs-3473	259	10	http://dx.doi.org/10.5269/bspm.70929	http://dx.doi.org/10.5269/bspm.70929	NOUN
iajs-3473	260	1	http://dx.doi.org/10.5269/bspm.70929	http://dx.doi.org/10.5269/bspm.70929	NOUN
iajs-3473	261	1	https://doi.org/10.1007/s00605-024-01951-5	https://doi.org/10.1007/s00605-024-01951-5	NUM
iajs-3473	261	2	https://doi.org/10.3934/math.20241567	https://doi.org/10.3934/math.20241567	ADJ
iajs-3473	262	1	http://dx.doi.org/10.1134/s0016266322030054	http://dx.doi.org/10.1134/s0016266322030054	PROPN
iajs-3473	262	2	https://doi.org/10.55730/1300-0098.3242	https://doi.org/10.55730/1300-0098.3242	PROPN
iajs-3473	262	3	https://doi.org/10.55730/1300-0098.3242	https://doi.org/10.55730/1300-0098.3242	PROPN
iajs-3473	262	4	https://doi.org/10.1007/s00009-025-02816-3	https://doi.org/10.1007/s00009-025-02816-3	NUM