id	sid	tid	token	lemma	pos
ejpam-4992	1	1	european	european	PROPN
ejpam-4992	1	2	journal	journal	PROPN
ejpam-4992	1	3	of	of	ADP
ejpam-4992	1	4	pure	pure	ADJ
ejpam-4992	1	5	and	and	CCONJ
ejpam-4992	1	6	applied	apply	VERB
ejpam-4992	1	7	mathematics	mathematic	NOUN
ejpam-4992	1	8	vol	vol	NOUN
ejpam-4992	1	9	.	.	PROPN
ejpam-4992	2	1	17	17	NUM
ejpam-4992	2	2	,	,	PUNCT
ejpam-4992	2	3	no	no	INTJ
ejpam-4992	2	4	.	.	NOUN
ejpam-4992	2	5	1	1	NUM
ejpam-4992	2	6	,	,	PUNCT
ejpam-4992	2	7	2024	2024	NUM
ejpam-4992	2	8	,	,	PUNCT
ejpam-4992	2	9	171	171	NUM
ejpam-4992	2	10	-	-	SYM
ejpam-4992	2	11	179	179	NUM
ejpam-4992	2	12	issn	issn	PROPN
ejpam-4992	2	13	1307	1307	NUM
ejpam-4992	2	14	-	-	SYM
ejpam-4992	2	15	5543	5543	NUM
ejpam-4992	2	16	–	–	PUNCT
ejpam-4992	2	17	ejpam.com	ejpam.com	X
ejpam-4992	2	18	published	publish	VERB
ejpam-4992	2	19	by	by	ADP
ejpam-4992	2	20	new	new	PROPN
ejpam-4992	2	21	york	york	PROPN
ejpam-4992	2	22	business	business	PROPN
ejpam-4992	2	23	global	global	PROPN
ejpam-4992	3	1	köthe	köthe	PROPN
ejpam-4992	3	2	dual	dual	ADV
ejpam-4992	3	3	of	of	ADP
ejpam-4992	3	4	some	some	DET
ejpam-4992	3	5	vector	vector	NOUN
ejpam-4992	3	6	-	-	PUNCT
ejpam-4992	3	7	valued	value	VERB
ejpam-4992	3	8	sequence	sequence	NOUN
ejpam-4992	3	9	spaces	space	NOUN
ejpam-4992	3	10	mohamed	mohamed	PROPN
ejpam-4992	3	11	ahmed	ahmed	AUX
ejpam-4992	4	1	ould	ould	AUX
ejpam-4992	4	2	sidaty1,2	sidaty1,2	PROPN
ejpam-4992	4	3	1	1	NUM
ejpam-4992	4	4	department	department	NOUN
ejpam-4992	4	5	of	of	ADP
ejpam-4992	4	6	mathematics	mathematic	NOUN
ejpam-4992	4	7	and	and	CCONJ
ejpam-4992	4	8	statistics	statistic	NOUN
ejpam-4992	4	9	,	,	PUNCT
ejpam-4992	4	10	college	college	NOUN
ejpam-4992	4	11	of	of	ADP
ejpam-4992	4	12	science	science	NOUN
ejpam-4992	4	13	,	,	PUNCT
ejpam-4992	4	14	imam	imam	PROPN
ejpam-4992	4	15	mohammad	mohammad	PROPN
ejpam-4992	4	16	ibn	ibn	PROPN
ejpam-4992	4	17	saud	saud	PROPN
ejpam-4992	4	18	islamic	islamic	PROPN
ejpam-4992	4	19	university	university	PROPN
ejpam-4992	4	20	,	,	PUNCT
ejpam-4992	4	21	riyadh	riyadh	NOUN
ejpam-4992	4	22	,	,	PUNCT
ejpam-4992	4	23	kingdom	kingdom	NOUN
ejpam-4992	4	24	of	of	ADP
ejpam-4992	4	25	saudi	saudi	PROPN
ejpam-4992	4	26	arabia	arabia	PROPN
ejpam-4992	4	27	2	2	NUM
ejpam-4992	4	28	école	école	ADJ
ejpam-4992	4	29	normale	normale	PROPN
ejpam-4992	4	30	supérieure	supérieure	PROPN
ejpam-4992	4	31	de	de	PROPN
ejpam-4992	4	32	nouakchott	nouakchott	PROPN
ejpam-4992	4	33	,	,	PUNCT
ejpam-4992	4	34	mauritanie	mauritanie	NOUN
ejpam-4992	4	35	abstract	abstract	ADJ
ejpam-4992	4	36	.	.	PUNCT
ejpam-4992	5	1	we	we	PRON
ejpam-4992	5	2	study	study	VERB
ejpam-4992	5	3	some	some	DET
ejpam-4992	5	4	properties	property	NOUN
ejpam-4992	5	5	of	of	ADP
ejpam-4992	5	6	the	the	DET
ejpam-4992	5	7	spaces	space	NOUN
ejpam-4992	5	8	λ(e	λ(e	VERB
ejpam-4992	5	9	)	)	PUNCT
ejpam-4992	5	10	of	of	ADP
ejpam-4992	5	11	weakly	weakly	ADJ
ejpam-4992	5	12	λ	λ	ADJ
ejpam-4992	5	13	-	-	ADJ
ejpam-4992	5	14	summable	summable	ADJ
ejpam-4992	5	15	sequences	sequence	NOUN
ejpam-4992	5	16	and	and	CCONJ
ejpam-4992	5	17	λ⟨e⟩	λ⟨e⟩	PROPN
ejpam-4992	5	18	of	of	ADP
ejpam-4992	5	19	strongly	strongly	ADV
ejpam-4992	5	20	λ	λ	ADJ
ejpam-4992	5	21	-	-	ADJ
ejpam-4992	5	22	summable	summable	ADJ
ejpam-4992	5	23	sequences	sequence	NOUN
ejpam-4992	5	24	of	of	ADP
ejpam-4992	5	25	a	a	DET
ejpam-4992	5	26	locally	locally	ADV
ejpam-4992	5	27	convex	convex	ADJ
ejpam-4992	5	28	space	space	NOUN
ejpam-4992	5	29	e.	e.	PROPN
ejpam-4992	5	30	for	for	ADP
ejpam-4992	5	31	example	example	NOUN
ejpam-4992	5	32	,	,	PUNCT
ejpam-4992	5	33	after	after	ADP
ejpam-4992	5	34	proving	prove	VERB
ejpam-4992	5	35	results	result	NOUN
ejpam-4992	5	36	on	on	ADP
ejpam-4992	5	37	bounded	bounded	ADJ
ejpam-4992	5	38	sets	set	NOUN
ejpam-4992	5	39	of	of	ADP
ejpam-4992	5	40	these	these	DET
ejpam-4992	5	41	spaces	space	NOUN
ejpam-4992	5	42	,	,	PUNCT
ejpam-4992	5	43	we	we	PRON
ejpam-4992	5	44	express	express	VERB
ejpam-4992	5	45	the	the	DET
ejpam-4992	5	46	elements	element	NOUN
ejpam-4992	5	47	of	of	ADP
ejpam-4992	5	48	their	their	PRON
ejpam-4992	5	49	köthe	köthe	ADJ
ejpam-4992	5	50	duals	dual	NOUN
ejpam-4992	5	51	in	in	ADP
ejpam-4992	5	52	terms	term	NOUN
ejpam-4992	5	53	of	of	ADP
ejpam-4992	5	54	sequences	sequence	NOUN
ejpam-4992	5	55	in	in	ADP
ejpam-4992	5	56	the	the	DET
ejpam-4992	5	57	continuous	continuous	ADJ
ejpam-4992	5	58	dual	dual	ADJ
ejpam-4992	5	59	e′	e′	PROPN
ejpam-4992	5	60	of	of	ADP
ejpam-4992	5	61	e	e	PROPN
ejpam-4992	5	62	,	,	PUNCT
ejpam-4992	5	63	then	then	ADV
ejpam-4992	5	64	we	we	PRON
ejpam-4992	5	65	prove	prove	VERB
ejpam-4992	5	66	that	that	SCONJ
ejpam-4992	5	67	these	these	DET
ejpam-4992	5	68	spaces	space	NOUN
ejpam-4992	5	69	possess	possess	VERB
ejpam-4992	5	70	the	the	DET
ejpam-4992	5	71	ak	ak	PROPN
ejpam-4992	5	72	property	property	NOUN
ejpam-4992	5	73	if	if	SCONJ
ejpam-4992	5	74	and	and	CCONJ
ejpam-4992	5	75	only	only	ADV
ejpam-4992	5	76	if	if	SCONJ
ejpam-4992	5	77	the	the	DET
ejpam-4992	5	78	köthe	köthe	NOUN
ejpam-4992	5	79	dual	dual	ADJ
ejpam-4992	5	80	coincides	coincide	VERB
ejpam-4992	5	81	with	with	ADP
ejpam-4992	5	82	the	the	DET
ejpam-4992	5	83	continuous	continuous	ADJ
ejpam-4992	5	84	dual	dual	ADJ
ejpam-4992	5	85	.	.	PUNCT
ejpam-4992	6	1	2020	2020	NUM
ejpam-4992	6	2	mathematics	mathematic	NOUN
ejpam-4992	6	3	subject	subject	NOUN
ejpam-4992	6	4	classifications	classification	NOUN
ejpam-4992	6	5	:	:	PUNCT
ejpam-4992	6	6	46a17	46a17	NUM
ejpam-4992	6	7	,	,	PUNCT
ejpam-4992	6	8	46a45	46a45	NUM
ejpam-4992	6	9	,	,	PUNCT
ejpam-4992	6	10	47b37	47b37	NUM
ejpam-4992	6	11	,	,	PUNCT
ejpam-4992	6	12	46b45	46b45	PRON
ejpam-4992	6	13	key	key	ADJ
ejpam-4992	6	14	words	word	NOUN
ejpam-4992	6	15	and	and	CCONJ
ejpam-4992	6	16	phrases	phrase	NOUN
ejpam-4992	6	17	:	:	PUNCT
ejpam-4992	6	18	sequence	sequence	NOUN
ejpam-4992	6	19	spaces	space	NOUN
ejpam-4992	6	20	,	,	PUNCT
ejpam-4992	6	21	locally	locally	ADV
ejpam-4992	6	22	convex	convex	ADJ
ejpam-4992	6	23	sequence	sequence	NOUN
ejpam-4992	6	24	spaces	space	NOUN
ejpam-4992	6	25	,	,	PUNCT
ejpam-4992	6	26	banach	banach	NOUN
ejpam-4992	6	27	spaces	space	NOUN
ejpam-4992	6	28	,	,	PUNCT
ejpam-4992	6	29	summability	summability	NOUN
ejpam-4992	6	30	introduction	introduction	NOUN
ejpam-4992	6	31	in	in	ADP
ejpam-4992	6	32	order	order	NOUN
ejpam-4992	6	33	to	to	PART
ejpam-4992	6	34	characterize	characterize	VERB
ejpam-4992	6	35	the	the	DET
ejpam-4992	6	36	nuclearity	nuclearity	NOUN
ejpam-4992	6	37	of	of	ADP
ejpam-4992	6	38	a	a	DET
ejpam-4992	6	39	locally	locally	ADV
ejpam-4992	6	40	convex	convex	ADJ
ejpam-4992	6	41	space	space	NOUN
ejpam-4992	6	42	e	e	NOUN
ejpam-4992	6	43	,	,	PUNCT
ejpam-4992	6	44	a.	a.	NOUN
ejpam-4992	6	45	pietsch	pietsch	VERB
ejpam-4992	7	1	[	[	X
ejpam-4992	7	2	9	9	NUM
ejpam-4992	7	3	]	]	PUNCT
ejpam-4992	7	4	introduced	introduce	VERB
ejpam-4992	7	5	the	the	DET
ejpam-4992	7	6	spaces	space	NOUN
ejpam-4992	7	7	ℓp{e	ℓp{e	PROPN
ejpam-4992	7	8	}	}	PUNCT
ejpam-4992	7	9	and	and	CCONJ
ejpam-4992	7	10	ℓp[e	ℓp[e	PROPN
ejpam-4992	7	11	]	]	PUNCT
ejpam-4992	7	12	of	of	ADP
ejpam-4992	7	13	absolutely	absolutely	ADV
ejpam-4992	7	14	ℓp	ℓp	ADJ
ejpam-4992	7	15	-	-	PUNCT
ejpam-4992	7	16	summable	summable	ADJ
ejpam-4992	7	17	and	and	CCONJ
ejpam-4992	7	18	weakly	weakly	ADJ
ejpam-4992	7	19	ℓp	ℓp	ADJ
ejpam-4992	7	20	-	-	PUNCT
ejpam-4992	7	21	summable	summable	ADJ
ejpam-4992	7	22	sequences	sequence	NOUN
ejpam-4992	7	23	in	in	ADP
ejpam-4992	7	24	e	e	NOUN
ejpam-4992	7	25	,	,	PUNCT
ejpam-4992	7	26	respectively	respectively	ADV
ejpam-4992	7	27	.	.	PUNCT
ejpam-4992	8	1	this	this	PRON
ejpam-4992	8	2	allowed	allow	VERB
ejpam-4992	8	3	the	the	DET
ejpam-4992	8	4	author	author	NOUN
ejpam-4992	8	5	also	also	ADV
ejpam-4992	8	6	to	to	PART
ejpam-4992	8	7	introduce	introduce	VERB
ejpam-4992	8	8	and	and	CCONJ
ejpam-4992	8	9	study	study	VERB
ejpam-4992	8	10	the	the	DET
ejpam-4992	8	11	absolutely	absolutely	ADV
ejpam-4992	8	12	p	p	NOUN
ejpam-4992	8	13	-	-	PUNCT
ejpam-4992	8	14	summing	sum	VERB
ejpam-4992	8	15	operators	operator	NOUN
ejpam-4992	8	16	.	.	PUNCT
ejpam-4992	9	1	later	later	ADV
ejpam-4992	9	2	,	,	PUNCT
ejpam-4992	9	3	j.	j.	PROPN
ejpam-4992	9	4	s.	s.	PROPN
ejpam-4992	9	5	cohen	cohen	PROPN
ejpam-4992	10	1	[	[	X
ejpam-4992	10	2	2	2	NUM
ejpam-4992	10	3	]	]	PUNCT
ejpam-4992	10	4	introduced	introduce	VERB
ejpam-4992	10	5	the	the	DET
ejpam-4992	10	6	space	space	NOUN
ejpam-4992	10	7	ℓp⟨e⟩	ℓp⟨e⟩	PROPN
ejpam-4992	10	8	of	of	ADP
ejpam-4992	10	9	strongly	strongly	ADV
ejpam-4992	10	10	p	p	ADJ
ejpam-4992	10	11	-	-	PUNCT
ejpam-4992	10	12	summable	summable	ADJ
ejpam-4992	10	13	sequences	sequence	NOUN
ejpam-4992	10	14	and	and	CCONJ
ejpam-4992	10	15	used	use	VERB
ejpam-4992	10	16	this	this	DET
ejpam-4992	10	17	space	space	NOUN
ejpam-4992	10	18	together	together	ADV
ejpam-4992	10	19	with	with	ADP
ejpam-4992	10	20	the	the	DET
ejpam-4992	10	21	spaces	space	NOUN
ejpam-4992	10	22	ℓp[e	ℓp[e	PROPN
ejpam-4992	10	23	]	]	PUNCT
ejpam-4992	10	24	and	and	CCONJ
ejpam-4992	10	25	ℓp{e	ℓp{e	PROPN
ejpam-4992	10	26	}	}	PUNCT
ejpam-4992	10	27	to	to	PART
ejpam-4992	10	28	define	define	VERB
ejpam-4992	10	29	the	the	DET
ejpam-4992	10	30	strongly	strongly	ADV
ejpam-4992	10	31	and	and	CCONJ
ejpam-4992	10	32	the	the	DET
ejpam-4992	10	33	nuclear	nuclear	ADJ
ejpam-4992	10	34	p	p	NOUN
ejpam-4992	10	35	-	-	PUNCT
ejpam-4992	10	36	summing	sum	VERB
ejpam-4992	10	37	operators	operator	NOUN
ejpam-4992	10	38	.	.	PUNCT
ejpam-4992	11	1	h.	h.	PROPN
ejpam-4992	11	2	apiola	apiola	PROPN
ejpam-4992	12	1	[	[	X
ejpam-4992	12	2	1	1	NUM
ejpam-4992	12	3	]	]	PUNCT
ejpam-4992	12	4	,	,	PUNCT
ejpam-4992	12	5	in	in	ADP
ejpam-4992	12	6	order	order	NOUN
ejpam-4992	12	7	to	to	PART
ejpam-4992	12	8	get	get	VERB
ejpam-4992	12	9	new	new	ADJ
ejpam-4992	12	10	conditions	condition	NOUN
ejpam-4992	12	11	for	for	ADP
ejpam-4992	12	12	the	the	DET
ejpam-4992	12	13	nuclearity	nuclearity	NOUN
ejpam-4992	12	14	of	of	ADP
ejpam-4992	12	15	e	e	PROPN
ejpam-4992	12	16	,	,	PUNCT
ejpam-4992	12	17	generalized	generalize	VERB
ejpam-4992	12	18	to	to	ADP
ejpam-4992	12	19	an	an	DET
ejpam-4992	12	20	arbitrary	arbitrary	ADJ
ejpam-4992	12	21	locally	locally	ADV
ejpam-4992	12	22	convex	convex	ADJ
ejpam-4992	12	23	space	space	NOUN
ejpam-4992	12	24	e	e	NOUN
ejpam-4992	12	25	,	,	PUNCT
ejpam-4992	12	26	the	the	DET
ejpam-4992	12	27	definition	definition	NOUN
ejpam-4992	12	28	of	of	ADP
ejpam-4992	12	29	ℓp⟨e⟩.	ℓp⟨e⟩.	PROPN
ejpam-4992	12	30	on	on	ADP
ejpam-4992	12	31	the	the	DET
ejpam-4992	12	32	other	other	ADJ
ejpam-4992	12	33	hand	hand	NOUN
ejpam-4992	12	34	,	,	PUNCT
ejpam-4992	12	35	a.	a.	NOUN
ejpam-4992	12	36	pietsch	pietsch	VERB
ejpam-4992	13	1	[	[	X
ejpam-4992	13	2	9	9	NUM
ejpam-4992	13	3	]	]	PUNCT
ejpam-4992	13	4	,	,	PUNCT
ejpam-4992	13	5	dealing	deal	VERB
ejpam-4992	13	6	again	again	ADV
ejpam-4992	13	7	with	with	ADP
ejpam-4992	13	8	a	a	DET
ejpam-4992	13	9	perfect	perfect	ADJ
ejpam-4992	13	10	sequence	sequence	NOUN
ejpam-4992	13	11	space	space	NOUN
ejpam-4992	13	12	λ	λ	NOUN
ejpam-4992	13	13	equipped	equip	VERB
ejpam-4992	13	14	with	with	ADP
ejpam-4992	13	15	its	its	PRON
ejpam-4992	13	16	köthe	köthe	PRON
ejpam-4992	13	17	normal	normal	ADJ
ejpam-4992	13	18	topology	topology	NOUN
ejpam-4992	13	19	,	,	PUNCT
ejpam-4992	13	20	introduced	introduce	VERB
ejpam-4992	13	21	the	the	DET
ejpam-4992	13	22	space	space	NOUN
ejpam-4992	13	23	λ(e	λ(e	VERB
ejpam-4992	13	24	)	)	PUNCT
ejpam-4992	13	25	of	of	ADP
ejpam-4992	13	26	weakly	weakly	ADJ
ejpam-4992	13	27	λ	λ	ADJ
ejpam-4992	13	28	-	-	ADJ
ejpam-4992	13	29	summable	summable	ADJ
ejpam-4992	13	30	sequences	sequence	NOUN
ejpam-4992	13	31	in	in	ADP
ejpam-4992	13	32	e.	e.	PROPN
ejpam-4992	13	33	we	we	PRON
ejpam-4992	13	34	note	note	VERB
ejpam-4992	13	35	that	that	SCONJ
ejpam-4992	13	36	,	,	PUNCT
ejpam-4992	13	37	considering	consider	VERB
ejpam-4992	13	38	the	the	DET
ejpam-4992	13	39	general	general	ADJ
ejpam-4992	13	40	case	case	NOUN
ejpam-4992	13	41	where	where	SCONJ
ejpam-4992	13	42	λ	λ	PROPN
ejpam-4992	13	43	is	be	AUX
ejpam-4992	13	44	no	no	ADV
ejpam-4992	13	45	longer	long	ADV
ejpam-4992	13	46	endowed	endow	VERB
ejpam-4992	13	47	with	with	ADP
ejpam-4992	13	48	its	its	PRON
ejpam-4992	13	49	köthe	köthe	PRON
ejpam-4992	13	50	normal	normal	ADJ
ejpam-4992	13	51	topology	topology	NOUN
ejpam-4992	13	52	,	,	PUNCT
ejpam-4992	13	53	but	but	CCONJ
ejpam-4992	13	54	with	with	ADP
ejpam-4992	13	55	a	a	DET
ejpam-4992	13	56	general	general	ADJ
ejpam-4992	13	57	polar	polar	ADJ
ejpam-4992	13	58	topology	topology	NOUN
ejpam-4992	13	59	,	,	PUNCT
ejpam-4992	13	60	m.	m.	NOUN
ejpam-4992	13	61	florencio	florencio	PROPN
ejpam-4992	13	62	and	and	CCONJ
ejpam-4992	13	63	p.	p.	PROPN
ejpam-4992	13	64	j.	j.	PROPN
ejpam-4992	14	1	paúl	paúl	PROPN
ejpam-4992	15	1	[	[	X
ejpam-4992	15	2	3	3	NUM
ejpam-4992	15	3	]	]	PUNCT
ejpam-4992	15	4	studied	study	VERB
ejpam-4992	15	5	λ(e	λ(e	VERB
ejpam-4992	15	6	)	)	PUNCT
ejpam-4992	15	7	and	and	CCONJ
ejpam-4992	15	8	clarified	clarify	VERB
ejpam-4992	15	9	the	the	DET
ejpam-4992	15	10	relationship	relationship	NOUN
ejpam-4992	15	11	between	between	ADP
ejpam-4992	15	12	λ(e	λ(e	NOUN
ejpam-4992	15	13	)	)	PUNCT
ejpam-4992	15	14	and	and	CCONJ
ejpam-4992	15	15	the	the	DET
ejpam-4992	15	16	completion	completion	NOUN
ejpam-4992	15	17	of	of	ADP
ejpam-4992	15	18	the	the	DET
ejpam-4992	15	19	injective	injective	ADJ
ejpam-4992	15	20	tensor	tensor	NOUN
ejpam-4992	15	21	product	product	NOUN
ejpam-4992	15	22	λ⊗ϵe	λ⊗ϵe	NOUN
ejpam-4992	15	23	.	.	PUNCT
ejpam-4992	16	1	they	they	PRON
ejpam-4992	16	2	determined	determine	VERB
ejpam-4992	16	3	conditions	condition	NOUN
ejpam-4992	16	4	on	on	ADP
ejpam-4992	16	5	e	e	NOUN
ejpam-4992	16	6	that	that	PRON
ejpam-4992	16	7	make	make	VERB
ejpam-4992	16	8	λ(e	λ(e	NOUN
ejpam-4992	16	9	)	)	PUNCT
ejpam-4992	16	10	an	an	DET
ejpam-4992	16	11	ak	ak	PROPN
ejpam-4992	16	12	space	space	NOUN
ejpam-4992	16	13	.	.	PUNCT
ejpam-4992	17	1	let	let	VERB
ejpam-4992	17	2	us	we	PRON
ejpam-4992	17	3	mention	mention	VERB
ejpam-4992	17	4	here	here	ADV
ejpam-4992	17	5	that	that	SCONJ
ejpam-4992	17	6	the	the	DET
ejpam-4992	17	7	authors	author	NOUN
ejpam-4992	17	8	,	,	PUNCT
ejpam-4992	17	9	in	in	ADP
ejpam-4992	17	10	[	[	X
ejpam-4992	17	11	7	7	NUM
ejpam-4992	17	12	,	,	PUNCT
ejpam-4992	17	13	8	8	NUM
ejpam-4992	17	14	,	,	PUNCT
ejpam-4992	17	15	10–13	10–13	NUM
ejpam-4992	17	16	]	]	PUNCT
ejpam-4992	17	17	,	,	PUNCT
ejpam-4992	17	18	studied	study	VERB
ejpam-4992	17	19	many	many	ADJ
ejpam-4992	17	20	aspects	aspect	NOUN
ejpam-4992	17	21	of	of	ADP
ejpam-4992	17	22	the	the	DET
ejpam-4992	17	23	space	space	NOUN
ejpam-4992	17	24	λ(e	λ(e	VERB
ejpam-4992	17	25	)	)	PUNCT
ejpam-4992	17	26	such	such	ADJ
ejpam-4992	17	27	as	as	ADP
ejpam-4992	17	28	the	the	DET
ejpam-4992	17	29	reflexivity	reflexivity	NOUN
ejpam-4992	17	30	,	,	PUNCT
ejpam-4992	17	31	the	the	DET
ejpam-4992	17	32	nuclearity	nuclearity	NOUN
ejpam-4992	17	33	and	and	CCONJ
ejpam-4992	17	34	the	the	DET
ejpam-4992	17	35	representation	representation	NOUN
ejpam-4992	17	36	of	of	ADP
ejpam-4992	17	37	the	the	DET
ejpam-4992	17	38	continuous	continuous	ADJ
ejpam-4992	17	39	dual	dual	ADJ
ejpam-4992	17	40	doi	doi	NOUN
ejpam-4992	17	41	:	:	PUNCT
ejpam-4992	18	1	https://doi.org/10.29020/nybg.ejpam.v17i1.4992	https://doi.org/10.29020/nybg.ejpam.v17i1.4992	ADJ
ejpam-4992	18	2	email	email	NOUN
ejpam-4992	18	3	address	address	NOUN
ejpam-4992	18	4	:	:	PUNCT
ejpam-4992	18	5	sidaty1@hotmail.com	sidaty1@hotmail.com	X
ejpam-4992	18	6	(	(	PUNCT
ejpam-4992	18	7	m.	m.	NOUN
ejpam-4992	18	8	a.	a.	NOUN
ejpam-4992	18	9	sidaty	sidaty	PROPN
ejpam-4992	18	10	)	)	PUNCT
ejpam-4992	18	11	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4992	19	1	171	171	NUM
ejpam-4992	19	2	©	©	ADP
ejpam-4992	19	3	2024	2024	NUM
ejpam-4992	19	4	ejpam	ejpam	NOUN
ejpam-4992	19	5	all	all	DET
ejpam-4992	19	6	rights	right	NOUN
ejpam-4992	19	7	reserved	reserve	VERB
ejpam-4992	19	8	.	.	PUNCT
ejpam-4992	20	1	m.	m.	NOUN
ejpam-4992	20	2	a.	a.	PROPN
ejpam-4992	20	3	sidaty	sidaty	PROPN
ejpam-4992	20	4	/	/	SYM
ejpam-4992	20	5	eur	eur	PROPN
ejpam-4992	20	6	.	.	PUNCT
ejpam-4992	21	1	j.	j.	PROPN
ejpam-4992	21	2	pure	pure	PROPN
ejpam-4992	21	3	appl	appl	PROPN
ejpam-4992	21	4	.	.	PROPN
ejpam-4992	21	5	math	math	PROPN
ejpam-4992	21	6	,	,	PUNCT
ejpam-4992	21	7	17	17	NUM
ejpam-4992	21	8	(	(	PUNCT
ejpam-4992	21	9	1	1	NUM
ejpam-4992	21	10	)	)	PUNCT
ejpam-4992	21	11	(	(	PUNCT
ejpam-4992	21	12	2024	2024	NUM
ejpam-4992	21	13	)	)	PUNCT
ejpam-4992	21	14	,	,	PUNCT
ejpam-4992	21	15	171	171	NUM
ejpam-4992	21	16	-	-	SYM
ejpam-4992	21	17	179	179	NUM
ejpam-4992	21	18	172	172	NUM
ejpam-4992	21	19	in	in	ADP
ejpam-4992	21	20	terms	term	NOUN
ejpam-4992	21	21	of	of	ADP
ejpam-4992	21	22	strongly	strongly	ADV
ejpam-4992	21	23	λ∗-summable	λ∗-summable	ADJ
ejpam-4992	21	24	sequences	sequence	NOUN
ejpam-4992	21	25	in	in	ADP
ejpam-4992	21	26	e′	e′	PROPN
ejpam-4992	21	27	,	,	PUNCT
ejpam-4992	21	28	where	where	SCONJ
ejpam-4992	21	29	λ∗	λ∗	PROPN
ejpam-4992	21	30	is	be	AUX
ejpam-4992	21	31	the	the	DET
ejpam-4992	21	32	köthe	köthe	NOUN
ejpam-4992	21	33	dual	dual	ADJ
ejpam-4992	21	34	of	of	ADP
ejpam-4992	21	35	λ	λ	PROPN
ejpam-4992	21	36	and	and	CCONJ
ejpam-4992	21	37	e′	e′	X
ejpam-4992	21	38	the	the	DET
ejpam-4992	21	39	continuous	continuous	ADJ
ejpam-4992	21	40	dual	dual	ADJ
ejpam-4992	21	41	of	of	ADP
ejpam-4992	21	42	e.	e.	PROPN
ejpam-4992	21	43	in	in	ADP
ejpam-4992	21	44	this	this	DET
ejpam-4992	21	45	note	note	NOUN
ejpam-4992	21	46	,	,	PUNCT
ejpam-4992	21	47	we	we	PRON
ejpam-4992	21	48	consider	consider	VERB
ejpam-4992	21	49	on	on	ADP
ejpam-4992	21	50	λ(e	λ(e	NOUN
ejpam-4992	21	51	)	)	PUNCT
ejpam-4992	21	52	and	and	CCONJ
ejpam-4992	21	53	λ⟨e⟩	λ⟨e⟩	PROPN
ejpam-4992	21	54	locally	locally	ADV
ejpam-4992	21	55	convex	convex	NOUN
ejpam-4992	21	56	topologies	topology	NOUN
ejpam-4992	21	57	defined	define	VERB
ejpam-4992	21	58	in	in	ADP
ejpam-4992	21	59	a	a	DET
ejpam-4992	21	60	natural	natural	ADJ
ejpam-4992	21	61	way	way	NOUN
ejpam-4992	21	62	as	as	ADP
ejpam-4992	21	63	bellow	bellow	ADJ
ejpam-4992	21	64	,	,	PUNCT
ejpam-4992	21	65	and	and	CCONJ
ejpam-4992	21	66	then	then	ADV
ejpam-4992	21	67	,	,	PUNCT
ejpam-4992	21	68	we	we	PRON
ejpam-4992	21	69	study	study	VERB
ejpam-4992	21	70	some	some	DET
ejpam-4992	21	71	aspects	aspect	NOUN
ejpam-4992	21	72	of	of	ADP
ejpam-4992	21	73	their	their	PRON
ejpam-4992	21	74	properties	property	NOUN
ejpam-4992	21	75	such	such	ADJ
ejpam-4992	21	76	as	as	ADP
ejpam-4992	21	77	,	,	PUNCT
ejpam-4992	21	78	bounded	bound	VERB
ejpam-4992	21	79	sets	set	NOUN
ejpam-4992	21	80	and	and	CCONJ
ejpam-4992	21	81	the	the	DET
ejpam-4992	21	82	generalized	generalized	ADJ
ejpam-4992	21	83	köthe	köthe	NOUN
ejpam-4992	21	84	dual	dual	ADJ
ejpam-4992	21	85	.	.	PUNCT
ejpam-4992	22	1	we	we	PRON
ejpam-4992	22	2	introduce	introduce	VERB
ejpam-4992	22	3	,	,	PUNCT
ejpam-4992	22	4	in	in	ADP
ejpam-4992	22	5	the	the	DET
ejpam-4992	22	6	preliminary	preliminary	ADJ
ejpam-4992	22	7	section	section	NOUN
ejpam-4992	22	8	,	,	PUNCT
ejpam-4992	22	9	the	the	DET
ejpam-4992	22	10	notations	notation	NOUN
ejpam-4992	22	11	and	and	CCONJ
ejpam-4992	22	12	background	background	NOUN
ejpam-4992	22	13	that	that	PRON
ejpam-4992	22	14	will	will	AUX
ejpam-4992	22	15	be	be	AUX
ejpam-4992	22	16	needed	need	VERB
ejpam-4992	22	17	in	in	ADP
ejpam-4992	22	18	the	the	DET
ejpam-4992	22	19	sequel	sequel	NOUN
ejpam-4992	22	20	.	.	PUNCT
ejpam-4992	23	1	in	in	ADP
ejpam-4992	23	2	section	section	NOUN
ejpam-4992	23	3	2	2	NUM
ejpam-4992	23	4	,	,	PUNCT
ejpam-4992	23	5	a	a	DET
ejpam-4992	23	6	fundamental	fundamental	ADJ
ejpam-4992	23	7	family	family	NOUN
ejpam-4992	23	8	of	of	ADP
ejpam-4992	23	9	bounded	bounded	ADJ
ejpam-4992	23	10	sets	set	NOUN
ejpam-4992	23	11	in	in	ADP
ejpam-4992	23	12	λ(e	λ(e	ADJ
ejpam-4992	23	13	)	)	PUNCT
ejpam-4992	23	14	and	and	CCONJ
ejpam-4992	23	15	some	some	DET
ejpam-4992	23	16	bounded	bounded	ADJ
ejpam-4992	23	17	sets	set	NOUN
ejpam-4992	23	18	of	of	ADP
ejpam-4992	23	19	λ⟨e⟩	λ⟨e⟩	PROPN
ejpam-4992	23	20	are	be	AUX
ejpam-4992	23	21	exhibited	exhibit	VERB
ejpam-4992	23	22	.	.	PUNCT
ejpam-4992	24	1	section	section	NOUN
ejpam-4992	24	2	3	3	NUM
ejpam-4992	24	3	is	be	AUX
ejpam-4992	24	4	devoted	devote	VERB
ejpam-4992	24	5	to	to	ADP
ejpam-4992	24	6	the	the	DET
ejpam-4992	24	7	determination	determination	NOUN
ejpam-4992	24	8	of	of	ADP
ejpam-4992	24	9	the	the	DET
ejpam-4992	24	10	köthe	köthe	NOUN
ejpam-4992	24	11	dual	dual	ADJ
ejpam-4992	24	12	of	of	ADP
ejpam-4992	24	13	λ(e	λ(e	ADJ
ejpam-4992	24	14	)	)	PUNCT
ejpam-4992	24	15	and	and	CCONJ
ejpam-4992	24	16	λ⟨e⟩	λ⟨e⟩	PROPN
ejpam-4992	24	17	in	in	ADP
ejpam-4992	24	18	terms	term	NOUN
ejpam-4992	24	19	of	of	ADP
ejpam-4992	24	20	sequences	sequence	NOUN
ejpam-4992	24	21	of	of	ADP
ejpam-4992	24	22	continuous	continuous	ADJ
ejpam-4992	24	23	linear	linear	NOUN
ejpam-4992	24	24	forms	form	NOUN
ejpam-4992	24	25	on	on	ADP
ejpam-4992	24	26	e.	e.	PROPN
ejpam-4992	24	27	in	in	ADP
ejpam-4992	24	28	particular	particular	ADJ
ejpam-4992	24	29	,	,	PUNCT
ejpam-4992	24	30	we	we	PRON
ejpam-4992	24	31	extend	extend	VERB
ejpam-4992	24	32	to	to	ADP
ejpam-4992	24	33	these	these	DET
ejpam-4992	24	34	spaces	space	NOUN
ejpam-4992	24	35	the	the	DET
ejpam-4992	24	36	well	well	ADV
ejpam-4992	24	37	known	know	VERB
ejpam-4992	24	38	result	result	NOUN
ejpam-4992	24	39	that	that	SCONJ
ejpam-4992	24	40	,	,	PUNCT
ejpam-4992	24	41	the	the	DET
ejpam-4992	24	42	continuous	continuous	ADJ
ejpam-4992	24	43	dual	dual	ADJ
ejpam-4992	24	44	of	of	ADP
ejpam-4992	24	45	a	a	DET
ejpam-4992	24	46	scalar	scalar	ADJ
ejpam-4992	24	47	sequence	sequence	NOUN
ejpam-4992	24	48	space	space	NOUN
ejpam-4992	24	49	λ	λ	NOUN
ejpam-4992	24	50	with	with	ADP
ejpam-4992	24	51	respect	respect	NOUN
ejpam-4992	24	52	to	to	ADP
ejpam-4992	24	53	a	a	DET
ejpam-4992	24	54	polar	polar	ADJ
ejpam-4992	24	55	topology	topology	NOUN
ejpam-4992	24	56	,	,	PUNCT
ejpam-4992	24	57	coincides	coincide	VERB
ejpam-4992	24	58	with	with	ADP
ejpam-4992	24	59	its	its	PRON
ejpam-4992	24	60	köthe	köthe	NOUN
ejpam-4992	24	61	dual	dual	ADJ
ejpam-4992	24	62	,	,	PUNCT
ejpam-4992	24	63	if	if	SCONJ
ejpam-4992	24	64	and	and	CCONJ
ejpam-4992	24	65	only	only	ADV
ejpam-4992	24	66	if	if	SCONJ
ejpam-4992	24	67	λ	λ	PROPN
ejpam-4992	24	68	has	have	VERB
ejpam-4992	24	69	the	the	DET
ejpam-4992	24	70	ak	ak	PROPN
ejpam-4992	24	71	property	property	NOUN
ejpam-4992	24	72	.	.	PUNCT
ejpam-4992	25	1	1	1	X
ejpam-4992	25	2	.	.	NUM
ejpam-4992	25	3	notations	notation	NOUN
ejpam-4992	25	4	and	and	CCONJ
ejpam-4992	25	5	background	background	NOUN
ejpam-4992	25	6	throughout	throughout	ADP
ejpam-4992	25	7	this	this	DET
ejpam-4992	25	8	note	note	NOUN
ejpam-4992	25	9	,	,	PUNCT
ejpam-4992	25	10	if	if	SCONJ
ejpam-4992	25	11	v	v	NOUN
ejpam-4992	25	12	is	be	AUX
ejpam-4992	25	13	a	a	DET
ejpam-4992	25	14	normed	normed	ADJ
ejpam-4992	25	15	space	space	NOUN
ejpam-4992	25	16	then	then	ADV
ejpam-4992	25	17	v	v	NOUN
ejpam-4992	25	18	′	′	NUM
ejpam-4992	25	19	,	,	PUNCT
ejpam-4992	25	20	∥	∥	X
ejpam-4992	25	21	·	·	PUNCT
ejpam-4992	26	1	∥v	∥v	NOUN
ejpam-4992	26	2	and	and	CCONJ
ejpam-4992	26	3	bv	bv	PROPN
ejpam-4992	26	4	will	will	AUX
ejpam-4992	26	5	denote	denote	VERB
ejpam-4992	26	6	the	the	DET
ejpam-4992	26	7	continuous	continuous	ADJ
ejpam-4992	26	8	dual	dual	ADJ
ejpam-4992	26	9	,	,	PUNCT
ejpam-4992	26	10	the	the	DET
ejpam-4992	26	11	norm	norm	NOUN
ejpam-4992	26	12	and	and	CCONJ
ejpam-4992	26	13	the	the	DET
ejpam-4992	26	14	closed	closed	ADJ
ejpam-4992	26	15	unit	unit	NOUN
ejpam-4992	26	16	ball	ball	NOUN
ejpam-4992	26	17	of	of	ADP
ejpam-4992	26	18	v	v	NOUN
ejpam-4992	26	19	,	,	PUNCT
ejpam-4992	26	20	respectively	respectively	ADV
ejpam-4992	26	21	.	.	PUNCT
ejpam-4992	27	1	we	we	PRON
ejpam-4992	27	2	will	will	AUX
ejpam-4992	27	3	stand	stand	VERB
ejpam-4992	27	4	by	by	ADP
ejpam-4992	27	5	λ	λ	PROPN
ejpam-4992	27	6	a	a	DET
ejpam-4992	27	7	perfect	perfect	ADJ
ejpam-4992	27	8	banach	banach	NOUN
ejpam-4992	27	9	sequence	sequence	NOUN
ejpam-4992	27	10	space	space	NOUN
ejpam-4992	27	11	and	and	CCONJ
ejpam-4992	27	12	by	by	ADP
ejpam-4992	27	13	λ∗	λ∗	NOUN
ejpam-4992	27	14	its	its	PRON
ejpam-4992	27	15	köthe	köthe	NOUN
ejpam-4992	27	16	dual	dual	ADJ
ejpam-4992	27	17	.	.	PUNCT
ejpam-4992	28	1	although	although	SCONJ
ejpam-4992	28	2	many	many	ADJ
ejpam-4992	28	3	of	of	ADP
ejpam-4992	28	4	results	result	NOUN
ejpam-4992	28	5	presented	present	VERB
ejpam-4992	28	6	here	here	ADV
ejpam-4992	28	7	are	be	AUX
ejpam-4992	28	8	valid	valid	ADJ
ejpam-4992	28	9	for	for	ADP
ejpam-4992	28	10	more	more	ADV
ejpam-4992	28	11	general	general	ADJ
ejpam-4992	28	12	setting	setting	NOUN
ejpam-4992	28	13	,	,	PUNCT
ejpam-4992	28	14	we	we	PRON
ejpam-4992	28	15	will	will	AUX
ejpam-4992	28	16	assume	assume	VERB
ejpam-4992	28	17	that	that	SCONJ
ejpam-4992	28	18	the	the	DET
ejpam-4992	28	19	norm	norm	NOUN
ejpam-4992	28	20	of	of	ADP
ejpam-4992	28	21	λ	λ	PROPN
ejpam-4992	28	22	satisfies	satisfy	VERB
ejpam-4992	28	23	the	the	DET
ejpam-4992	28	24	conditions	condition	NOUN
ejpam-4992	28	25	:	:	PUNCT
ejpam-4992	28	26	(	(	PUNCT
ejpam-4992	28	27	1	1	X
ejpam-4992	28	28	)	)	PUNCT
ejpam-4992	28	29	if	if	SCONJ
ejpam-4992	28	30	α	α	X
ejpam-4992	28	31	,	,	PUNCT
ejpam-4992	28	32	β	β	X
ejpam-4992	28	33	∈	∈	PROPN
ejpam-4992	28	34	λ	λ	PROPN
ejpam-4992	28	35	,	,	PUNCT
ejpam-4992	28	36	with	with	ADP
ejpam-4992	28	37	α	α	NOUN
ejpam-4992	28	38	≤	≤	NUM
ejpam-4992	28	39	β	β	NOUN
ejpam-4992	28	40	,	,	PUNCT
ejpam-4992	28	41	then	then	ADV
ejpam-4992	28	42	∥α∥λ	∥α∥λ	VERB
ejpam-4992	28	43	≤	≤	NOUN
ejpam-4992	28	44	∥β∥λ	∥β∥λ	ADV
ejpam-4992	28	45	,	,	PUNCT
ejpam-4992	28	46	and	and	CCONJ
ejpam-4992	28	47	(	(	PUNCT
ejpam-4992	28	48	2	2	NUM
ejpam-4992	28	49	)	)	PUNCT
ejpam-4992	28	50	(	(	PUNCT
ejpam-4992	28	51	λ	λ	X
ejpam-4992	28	52	,	,	PUNCT
ejpam-4992	28	53	∥	∥	X
ejpam-4992	28	54	·	·	PUNCT
ejpam-4992	28	55	∥λ	∥λ	PROPN
ejpam-4992	28	56	)	)	PUNCT
ejpam-4992	28	57	is	be	AUX
ejpam-4992	28	58	an	an	DET
ejpam-4992	28	59	ak	ak	PROPN
ejpam-4992	28	60	space	space	NOUN
ejpam-4992	28	61	,	,	PUNCT
ejpam-4992	28	62	i.e.	i.e.	X
ejpam-4992	28	63	,	,	PUNCT
ejpam-4992	28	64	every	every	DET
ejpam-4992	28	65	α	α	NOUN
ejpam-4992	28	66	=	=	PUNCT
ejpam-4992	28	67	(	(	PUNCT
ejpam-4992	28	68	αn)n	αn)n	NOUN
ejpam-4992	28	69	∈	∈	NOUN
ejpam-4992	28	70	λ	λ	NOUN
ejpam-4992	28	71	is	be	AUX
ejpam-4992	28	72	the	the	DET
ejpam-4992	28	73	∥	∥	X
ejpam-4992	28	74	·	·	PUNCT
ejpam-4992	28	75	∥λ	∥λ	NOUN
ejpam-4992	28	76	-	-	PUNCT
ejpam-4992	28	77	limit	limit	NOUN
ejpam-4992	28	78	of	of	ADP
ejpam-4992	28	79	its	its	PRON
ejpam-4992	28	80	sections	section	NOUN
ejpam-4992	28	81	(	(	PUNCT
ejpam-4992	28	82	α1	α1	PROPN
ejpam-4992	28	83	,	,	PUNCT
ejpam-4992	28	84	.	.	PUNCT
ejpam-4992	28	85	.	.	PUNCT
ejpam-4992	29	1	.	.	PUNCT
ejpam-4992	30	1	,	,	PUNCT
ejpam-4992	30	2	αn	αn	NOUN
ejpam-4992	30	3	,	,	PUNCT
ejpam-4992	30	4	0	0	NUM
ejpam-4992	30	5	,	,	PUNCT
ejpam-4992	30	6	.	.	PUNCT
ejpam-4992	30	7	.	.	PUNCT
ejpam-4992	31	1	.	.	PUNCT
ejpam-4992	31	2	)	)	PUNCT
ejpam-4992	32	1	,	,	PUNCT
ejpam-4992	32	2	n	n	PROPN
ejpam-4992	32	3	∈	∈	PROPN
ejpam-4992	32	4	n.	n.	NOUN
ejpam-4992	32	5	this	this	DET
ejpam-4992	32	6	condition	condition	NOUN
ejpam-4992	32	7	is	be	AUX
ejpam-4992	32	8	satisfied	satisfied	ADJ
ejpam-4992	32	9	if	if	SCONJ
ejpam-4992	32	10	and	and	CCONJ
ejpam-4992	32	11	only	only	ADV
ejpam-4992	32	12	if	if	SCONJ
ejpam-4992	32	13	λ∗	λ∗	NOUN
ejpam-4992	32	14	=	=	PUNCT
ejpam-4992	32	15	λ′.	λ′.	AUX
ejpam-4992	32	16	so	so	ADV
ejpam-4992	32	17	,	,	PUNCT
ejpam-4992	32	18	λ	λ	PROPN
ejpam-4992	32	19	will	will	AUX
ejpam-4992	32	20	be	be	AUX
ejpam-4992	32	21	reflexive	reflexive	ADJ
ejpam-4992	32	22	whenever	whenever	SCONJ
ejpam-4992	32	23	(	(	PUNCT
ejpam-4992	32	24	λ∗	λ∗	NOUN
ejpam-4992	32	25	,	,	PUNCT
ejpam-4992	32	26	∥·∥λ∗	∥·∥λ∗	NOUN
ejpam-4992	32	27	)	)	PUNCT
ejpam-4992	32	28	is	be	AUX
ejpam-4992	32	29	also	also	ADV
ejpam-4992	32	30	an	an	DET
ejpam-4992	32	31	ak	ak	PROPN
ejpam-4992	32	32	space	space	NOUN
ejpam-4992	32	33	.	.	PUNCT
ejpam-4992	33	1	the	the	DET
ejpam-4992	33	2	results	result	NOUN
ejpam-4992	33	3	proved	prove	VERB
ejpam-4992	33	4	here	here	ADV
ejpam-4992	33	5	are	be	AUX
ejpam-4992	33	6	then	then	ADV
ejpam-4992	33	7	applicable	applicable	ADJ
ejpam-4992	33	8	to	to	ADP
ejpam-4992	33	9	many	many	ADJ
ejpam-4992	33	10	cases	case	NOUN
ejpam-4992	33	11	of	of	ADP
ejpam-4992	33	12	the	the	DET
ejpam-4992	33	13	orlicz	orlicz	ADJ
ejpam-4992	33	14	sequence	sequence	NOUN
ejpam-4992	33	15	spaces	space	VERB
ejpam-4992	33	16	ℓm	ℓm	ADP
ejpam-4992	33	17	(	(	PUNCT
ejpam-4992	33	18	see	see	VERB
ejpam-4992	33	19	for	for	ADP
ejpam-4992	33	20	example	example	NOUN
ejpam-4992	34	1	[	[	X
ejpam-4992	34	2	12	12	NUM
ejpam-4992	34	3	]	]	PUNCT
ejpam-4992	34	4	)	)	PUNCT
ejpam-4992	34	5	and	and	CCONJ
ejpam-4992	34	6	,	,	PUNCT
ejpam-4992	34	7	in	in	ADP
ejpam-4992	34	8	particular	particular	ADJ
ejpam-4992	34	9	,	,	PUNCT
ejpam-4992	34	10	to	to	ADP
ejpam-4992	34	11	the	the	DET
ejpam-4992	34	12	ℓp	ℓp	ADJ
ejpam-4992	34	13	spaces	space	NOUN
ejpam-4992	34	14	.	.	PUNCT
ejpam-4992	35	1	further	far	ADV
ejpam-4992	35	2	,	,	PUNCT
ejpam-4992	35	3	we	we	PRON
ejpam-4992	35	4	mean	mean	VERB
ejpam-4992	35	5	by	by	ADP
ejpam-4992	35	6	e	e	PROPN
ejpam-4992	35	7	a	a	DET
ejpam-4992	35	8	sequentially	sequentially	ADV
ejpam-4992	35	9	complete	complete	ADJ
ejpam-4992	35	10	hausdorff	hausdorff	NOUN
ejpam-4992	35	11	locally	locally	ADV
ejpam-4992	35	12	convex	convex	ADJ
ejpam-4992	35	13	space	space	NOUN
ejpam-4992	35	14	,	,	PUNCT
ejpam-4992	35	15	e′	e′	X
ejpam-4992	35	16	its	its	PRON
ejpam-4992	35	17	continuous	continuous	ADJ
ejpam-4992	35	18	dual	dual	ADJ
ejpam-4992	35	19	and	and	CCONJ
ejpam-4992	35	20	by	by	ADP
ejpam-4992	35	21	m	m	DET
ejpam-4992	36	1	the	the	DET
ejpam-4992	36	2	collection	collection	NOUN
ejpam-4992	36	3	of	of	ADP
ejpam-4992	36	4	all	all	DET
ejpam-4992	36	5	absolutely	absolutely	ADV
ejpam-4992	36	6	convex	convex	ADJ
ejpam-4992	36	7	,	,	PUNCT
ejpam-4992	36	8	σ(e′	σ(e′	PROPN
ejpam-4992	36	9	,	,	PUNCT
ejpam-4992	36	10	e)-closed	e)-closed	ADJ
ejpam-4992	36	11	and	and	CCONJ
ejpam-4992	36	12	equicontinuous	equicontinuous	ADJ
ejpam-4992	36	13	subsets	subset	NOUN
ejpam-4992	36	14	of	of	ADP
ejpam-4992	36	15	e′.	e′.	NUM
ejpam-4992	36	16	the	the	DET
ejpam-4992	36	17	topology	topology	NOUN
ejpam-4992	36	18	of	of	ADP
ejpam-4992	36	19	e	e	PROPN
ejpam-4992	36	20	is	be	AUX
ejpam-4992	36	21	then	then	ADV
ejpam-4992	36	22	defined	define	VERB
ejpam-4992	36	23	by	by	ADP
ejpam-4992	36	24	the	the	DET
ejpam-4992	36	25	family	family	NOUN
ejpam-4992	36	26	of	of	ADP
ejpam-4992	36	27	seminorms	seminorm	NOUN
ejpam-4992	36	28	(	(	PUNCT
ejpam-4992	36	29	pm	pm	NOUN
ejpam-4992	36	30	)	)	PUNCT
ejpam-4992	36	31	m∈m	m∈m	NOUN
ejpam-4992	36	32	such	such	ADJ
ejpam-4992	36	33	that	that	SCONJ
ejpam-4992	36	34	,	,	PUNCT
ejpam-4992	36	35	for	for	ADP
ejpam-4992	36	36	all	all	DET
ejpam-4992	36	37	x	x	SYM
ejpam-4992	36	38	∈	∈	PROPN
ejpam-4992	36	39	e	e	NOUN
ejpam-4992	36	40	,	,	PUNCT
ejpam-4992	36	41	pm	pm	INTJ
ejpam-4992	36	42	(	(	PUNCT
ejpam-4992	36	43	x	x	NOUN
ejpam-4992	36	44	)	)	PUNCT
ejpam-4992	36	45	=	=	VERB
ejpam-4992	37	1	sup{|a(x)|	sup{|a(x)|	NOUN
ejpam-4992	37	2	:	:	PUNCT
ejpam-4992	37	3	a	a	DET
ejpam-4992	37	4	∈	∈	PROPN
ejpam-4992	37	5	m	m	PRON
ejpam-4992	37	6	}	}	PUNCT
ejpam-4992	37	7	,	,	PUNCT
ejpam-4992	37	8	for	for	ADP
ejpam-4992	37	9	all	all	DET
ejpam-4992	37	10	m	m	PROPN
ejpam-4992	37	11	∈	∈	NOUN
ejpam-4992	37	12	m.	m.	NOUN
ejpam-4992	37	13	define	define	VERB
ejpam-4992	37	14	the	the	DET
ejpam-4992	37	15	following	follow	VERB
ejpam-4992	37	16	space	space	NOUN
ejpam-4992	37	17	λ(e	λ(e	ADJ
ejpam-4992	37	18	)	)	PUNCT
ejpam-4992	37	19	=	=	PRON
ejpam-4992	37	20	{	{	PUNCT
ejpam-4992	37	21	x	x	SYM
ejpam-4992	37	22	=	=	SYM
ejpam-4992	37	23	(	(	PUNCT
ejpam-4992	37	24	xn)n	xn)n	PROPN
ejpam-4992	37	25	⊂	⊂	PROPN
ejpam-4992	37	26	e	e	NOUN
ejpam-4992	37	27	:	:	PUNCT
ejpam-4992	37	28	∑	∑	PUNCT
ejpam-4992	37	29	αnxn	αnxn	VERB
ejpam-4992	37	30	converges	converge	NOUN
ejpam-4992	37	31	in	in	ADP
ejpam-4992	37	32	e	e	NOUN
ejpam-4992	37	33	,	,	PUNCT
ejpam-4992	37	34	for	for	ADP
ejpam-4992	37	35	all	all	PRON
ejpam-4992	37	36	(	(	PUNCT
ejpam-4992	37	37	αn)n	αn)n	PROPN
ejpam-4992	37	38	∈	∈	PROPN
ejpam-4992	37	39	λ∗	λ∗	NOUN
ejpam-4992	37	40	}	}	PUNCT
ejpam-4992	37	41	.	.	PUNCT
ejpam-4992	38	1	following	follow	VERB
ejpam-4992	38	2	[	[	X
ejpam-4992	38	3	3	3	NUM
ejpam-4992	38	4	]	]	PUNCT
ejpam-4992	38	5	,	,	PUNCT
ejpam-4992	38	6	a	a	DET
ejpam-4992	38	7	locally	locally	ADV
ejpam-4992	38	8	convex	convex	ADJ
ejpam-4992	38	9	topology	topology	NOUN
ejpam-4992	38	10	on	on	ADP
ejpam-4992	38	11	λ(e	λ(e	NOUN
ejpam-4992	38	12	)	)	PUNCT
ejpam-4992	38	13	is	be	AUX
ejpam-4992	38	14	defined	define	VERB
ejpam-4992	38	15	by	by	ADP
ejpam-4992	38	16	the	the	DET
ejpam-4992	38	17	family	family	NOUN
ejpam-4992	38	18	of	of	ADP
ejpam-4992	38	19	seminorms	seminorm	NOUN
ejpam-4992	38	20	(	(	PUNCT
ejpam-4992	38	21	ϵm	ϵm	NOUN
ejpam-4992	38	22	)	)	PUNCT
ejpam-4992	38	23	m∈m	m∈m	NOUN
ejpam-4992	38	24	,	,	PUNCT
ejpam-4992	38	25	where	where	SCONJ
ejpam-4992	38	26	ϵm	ϵm	PROPN
ejpam-4992	38	27	(	(	PUNCT
ejpam-4992	38	28	x	x	NOUN
ejpam-4992	38	29	)	)	PUNCT
ejpam-4992	38	30	:	:	PUNCT
ejpam-4992	39	1	=	=	SYM
ejpam-4992	39	2	sup	sup	NOUN
ejpam-4992	39	3	{	{	PUNCT
ejpam-4992	39	4	∞∑	∞∑	NUM
ejpam-4992	39	5	n=1	n=1	PROPN
ejpam-4992	39	6	|αna(xn)|	|αna(xn)|	NOUN
ejpam-4992	39	7	:	:	PUNCT
ejpam-4992	39	8	a	a	DET
ejpam-4992	39	9	∈	∈	PROPN
ejpam-4992	39	10	m	m	NOUN
ejpam-4992	39	11	,	,	PUNCT
ejpam-4992	39	12	α	α	PROPN
ejpam-4992	39	13	∈	∈	PROPN
ejpam-4992	39	14	bλ∗	bλ∗	NOUN
ejpam-4992	39	15	}	}	PUNCT
ejpam-4992	39	16	,	,	PUNCT
ejpam-4992	39	17	for	for	ADP
ejpam-4992	39	18	all	all	PRON
ejpam-4992	39	19	x	x	PUNCT
ejpam-4992	39	20	=	=	SYM
ejpam-4992	39	21	(	(	PUNCT
ejpam-4992	39	22	xn)n	xn)n	PROPN
ejpam-4992	39	23	∈	∈	PROPN
ejpam-4992	39	24	λ(e	λ(e	PROPN
ejpam-4992	39	25	)	)	PUNCT
ejpam-4992	39	26	.	.	PUNCT
ejpam-4992	40	1	these	these	DET
ejpam-4992	40	2	seminorms	seminorm	NOUN
ejpam-4992	40	3	turn	turn	VERB
ejpam-4992	40	4	out	out	ADP
ejpam-4992	40	5	to	to	PART
ejpam-4992	40	6	be	be	AUX
ejpam-4992	40	7	defined	define	VERB
ejpam-4992	40	8	also	also	ADV
ejpam-4992	40	9	on	on	ADP
ejpam-4992	40	10	the	the	DET
ejpam-4992	40	11	space	space	NOUN
ejpam-4992	40	12	λ[e	λ[e	X
ejpam-4992	40	13	]	]	X
ejpam-4992	40	14	=	=	X
ejpam-4992	40	15	{	{	PUNCT
ejpam-4992	40	16	x	x	SYM
ejpam-4992	40	17	=	=	SYM
ejpam-4992	40	18	(	(	PUNCT
ejpam-4992	40	19	xn)n	xn)n	PROPN
ejpam-4992	40	20	⊂	⊂	PROPN
ejpam-4992	40	21	e	e	NOUN
ejpam-4992	40	22	:	:	PUNCT
ejpam-4992	40	23	(	(	PUNCT
ejpam-4992	40	24	a(xn))n	a(xn))n	PROPN
ejpam-4992	40	25	∈	∈	PROPN
ejpam-4992	40	26	λ∗	λ∗	PROPN
ejpam-4992	40	27	,	,	PUNCT
ejpam-4992	40	28	for	for	ADP
ejpam-4992	40	29	all	all	DET
ejpam-4992	40	30	a	a	DET
ejpam-4992	40	31	∈	∈	NOUN
ejpam-4992	40	32	e′	e′	NOUN
ejpam-4992	40	33	}	}	PUNCT
ejpam-4992	40	34	.	.	PUNCT
ejpam-4992	41	1	m.	m.	NOUN
ejpam-4992	41	2	a.	a.	PROPN
ejpam-4992	41	3	sidaty	sidaty	PROPN
ejpam-4992	41	4	/	/	SYM
ejpam-4992	41	5	eur	eur	PROPN
ejpam-4992	41	6	.	.	PUNCT
ejpam-4992	42	1	j.	j.	PROPN
ejpam-4992	42	2	pure	pure	PROPN
ejpam-4992	42	3	appl	appl	PROPN
ejpam-4992	42	4	.	.	PROPN
ejpam-4992	42	5	math	math	PROPN
ejpam-4992	42	6	,	,	PUNCT
ejpam-4992	42	7	17	17	NUM
ejpam-4992	42	8	(	(	PUNCT
ejpam-4992	42	9	1	1	NUM
ejpam-4992	42	10	)	)	PUNCT
ejpam-4992	42	11	(	(	PUNCT
ejpam-4992	42	12	2024	2024	NUM
ejpam-4992	42	13	)	)	PUNCT
ejpam-4992	42	14	,	,	PUNCT
ejpam-4992	42	15	171	171	NUM
ejpam-4992	42	16	-	-	SYM
ejpam-4992	42	17	179	179	NUM
ejpam-4992	42	18	173	173	NUM
ejpam-4992	42	19	following	follow	VERB
ejpam-4992	42	20	[	[	X
ejpam-4992	42	21	2	2	NUM
ejpam-4992	42	22	]	]	PUNCT
ejpam-4992	42	23	and	and	CCONJ
ejpam-4992	42	24	[	[	X
ejpam-4992	42	25	7	7	NUM
ejpam-4992	42	26	]	]	PUNCT
ejpam-4992	42	27	,	,	PUNCT
ejpam-4992	42	28	a	a	DET
ejpam-4992	42	29	sequence	sequence	NOUN
ejpam-4992	42	30	(	(	PUNCT
ejpam-4992	42	31	xn)n	xn)n	PROPN
ejpam-4992	42	32	⊂	⊂	PROPN
ejpam-4992	42	33	e	e	PROPN
ejpam-4992	42	34	is	be	AUX
ejpam-4992	42	35	said	say	VERB
ejpam-4992	42	36	to	to	PART
ejpam-4992	42	37	be	be	AUX
ejpam-4992	42	38	strongly	strongly	ADV
ejpam-4992	42	39	λ	λ	NOUN
ejpam-4992	42	40	-	-	ADJ
ejpam-4992	42	41	summable	summable	ADJ
ejpam-4992	42	42	if	if	SCONJ
ejpam-4992	42	43	,	,	PUNCT
ejpam-4992	42	44	for	for	ADP
ejpam-4992	42	45	every	every	DET
ejpam-4992	42	46	m	m	NOUN
ejpam-4992	42	47	∈	∈	NOUN
ejpam-4992	42	48	m	m	NOUN
ejpam-4992	42	49	and	and	CCONJ
ejpam-4992	42	50	(	(	PUNCT
ejpam-4992	42	51	an)n	an)n	PROPN
ejpam-4992	42	52	∈	∈	PROPN
ejpam-4992	42	53	λ∗[e′	λ∗[e′	X
ejpam-4992	42	54	m	m	VERB
ejpam-4992	42	55	]	]	X
ejpam-4992	42	56	,	,	PUNCT
ejpam-4992	42	57	the	the	DET
ejpam-4992	42	58	series	series	NOUN
ejpam-4992	42	59	σ|an(xn)|	σ|an(xn)|	PROPN
ejpam-4992	42	60	converges	converge	VERB
ejpam-4992	42	61	.	.	PUNCT
ejpam-4992	43	1	we	we	PRON
ejpam-4992	43	2	mean	mean	VERB
ejpam-4992	43	3	by	by	ADP
ejpam-4992	43	4	e′	e′	PROPN
ejpam-4992	43	5	m	m	VERB
ejpam-4992	43	6	the	the	DET
ejpam-4992	43	7	linear	linear	ADJ
ejpam-4992	43	8	subspace	subspace	NOUN
ejpam-4992	43	9	of	of	ADP
ejpam-4992	43	10	e′	e′	PROPN
ejpam-4992	43	11	spanned	span	VERB
ejpam-4992	43	12	by	by	ADP
ejpam-4992	43	13	m	m	NOUN
ejpam-4992	43	14	and	and	CCONJ
ejpam-4992	43	15	equipped	equip	VERB
ejpam-4992	43	16	with	with	ADP
ejpam-4992	43	17	the	the	DET
ejpam-4992	43	18	gauge	gauge	NOUN
ejpam-4992	43	19	∥	∥	X
ejpam-4992	43	20	·	·	PUNCT
ejpam-4992	43	21	∥m	∥m	PROPN
ejpam-4992	43	22	of	of	ADP
ejpam-4992	43	23	m	m	PROPN
ejpam-4992	43	24	.	.	PUNCT
ejpam-4992	44	1	denote	denote	VERB
ejpam-4992	44	2	by	by	ADP
ejpam-4992	44	3	λ	λ	PROPN
ejpam-4992	44	4	⟨e⟩	⟨e⟩	PROPN
ejpam-4992	44	5	the	the	DET
ejpam-4992	44	6	space	space	NOUN
ejpam-4992	44	7	of	of	ADP
ejpam-4992	44	8	all	all	DET
ejpam-4992	44	9	strongly	strongly	ADV
ejpam-4992	44	10	λ−summable	λ−summable	ADJ
ejpam-4992	44	11	sequences	sequence	NOUN
ejpam-4992	44	12	in	in	ADP
ejpam-4992	44	13	e.	e.	PROPN
ejpam-4992	44	14	we	we	PRON
ejpam-4992	44	15	will	will	AUX
ejpam-4992	44	16	endow	endow	VERB
ejpam-4992	44	17	λ⟨e⟩	λ⟨e⟩	PROPN
ejpam-4992	44	18	with	with	ADP
ejpam-4992	44	19	the	the	DET
ejpam-4992	44	20	locally	locally	ADV
ejpam-4992	44	21	convex	convex	ADJ
ejpam-4992	44	22	topology	topology	NOUN
ejpam-4992	44	23	introduced	introduce	VERB
ejpam-4992	44	24	in	in	ADP
ejpam-4992	44	25	[	[	X
ejpam-4992	44	26	8	8	NUM
ejpam-4992	44	27	]	]	PUNCT
ejpam-4992	44	28	and	and	CCONJ
ejpam-4992	44	29	defined	define	VERB
ejpam-4992	44	30	by	by	ADP
ejpam-4992	44	31	the	the	DET
ejpam-4992	44	32	family	family	NOUN
ejpam-4992	44	33	of	of	ADP
ejpam-4992	44	34	seminorms	seminorm	NOUN
ejpam-4992	44	35	(	(	PUNCT
ejpam-4992	44	36	σm	σm	INTJ
ejpam-4992	44	37	)	)	PUNCT
ejpam-4992	44	38	m∈m	m∈m	NOUN
ejpam-4992	44	39	,	,	PUNCT
ejpam-4992	44	40	where	where	SCONJ
ejpam-4992	44	41	σm	σm	INTJ
ejpam-4992	44	42	(	(	PUNCT
ejpam-4992	44	43	x	x	X
ejpam-4992	44	44	)	)	PUNCT
ejpam-4992	44	45	=	=	SYM
ejpam-4992	44	46	sup	sup	NOUN
ejpam-4992	44	47	{	{	PUNCT
ejpam-4992	44	48	∞∑	∞∑	NUM
ejpam-4992	44	49	n=1	n=1	PROPN
ejpam-4992	44	50	|an(xn)|	|an(xn)|	NOUN
ejpam-4992	44	51	:	:	PUNCT
ejpam-4992	44	52	a	a	PRON
ejpam-4992	44	53	=	=	X
ejpam-4992	44	54	(	(	PUNCT
ejpam-4992	44	55	an)n	an)n	PROPN
ejpam-4992	44	56	∈	∈	PROPN
ejpam-4992	44	57	bλ∗(e′	bλ∗(e′	NOUN
ejpam-4992	44	58	m	m	PROPN
ejpam-4992	44	59	)	)	PUNCT
ejpam-4992	44	60	}	}	PUNCT
ejpam-4992	44	61	,	,	PUNCT
ejpam-4992	44	62	for	for	ADP
ejpam-4992	44	63	all	all	PRON
ejpam-4992	44	64	x	x	PUNCT
ejpam-4992	44	65	=	=	SYM
ejpam-4992	44	66	(	(	PUNCT
ejpam-4992	44	67	xn)n	xn)n	PROPN
ejpam-4992	44	68	∈	∈	PROPN
ejpam-4992	44	69	λ⟨e⟩.	λ⟨e⟩.	PRON
ejpam-4992	44	70	notice	notice	VERB
ejpam-4992	44	71	that	that	SCONJ
ejpam-4992	44	72	,	,	PUNCT
ejpam-4992	44	73	since	since	SCONJ
ejpam-4992	44	74	λ	λ	PROPN
ejpam-4992	44	75	is	be	AUX
ejpam-4992	44	76	perfect	perfect	ADJ
ejpam-4992	44	77	,	,	PUNCT
ejpam-4992	44	78	we	we	PRON
ejpam-4992	44	79	have	have	VERB
ejpam-4992	44	80	λ	λ	PROPN
ejpam-4992	45	1	⟨e⟩	⟨e⟩	PROPN
ejpam-4992	45	2	⊂	⊂	PROPN
ejpam-4992	45	3	λ(e	λ(e	PROPN
ejpam-4992	45	4	)	)	PUNCT
ejpam-4992	45	5	⊂	⊂	X
ejpam-4992	45	6	λ[e	λ[e	X
ejpam-4992	45	7	]	]	X
ejpam-4992	45	8	.	.	PUNCT
ejpam-4992	46	1	the	the	DET
ejpam-4992	46	2	spaces	space	NOUN
ejpam-4992	46	3	λ	λ	X
ejpam-4992	46	4	⟨e⟩	⟨e⟩	PROPN
ejpam-4992	46	5	,	,	PUNCT
ejpam-4992	46	6	λ(e	λ(e	ADJ
ejpam-4992	46	7	)	)	PUNCT
ejpam-4992	46	8	and	and	CCONJ
ejpam-4992	46	9	λ[e	λ[e	X
ejpam-4992	46	10	]	]	X
ejpam-4992	46	11	are	be	AUX
ejpam-4992	46	12	sequentially	sequentially	ADV
ejpam-4992	46	13	complete	complete	ADJ
ejpam-4992	46	14	,	,	PUNCT
ejpam-4992	46	15	in	in	ADP
ejpam-4992	46	16	particular	particular	ADJ
ejpam-4992	46	17	,	,	PUNCT
ejpam-4992	46	18	banach	banach	NOUN
ejpam-4992	46	19	spaces	space	VERB
ejpam-4992	46	20	whenever	whenever	SCONJ
ejpam-4992	46	21	λ	λ	PROPN
ejpam-4992	46	22	and	and	CCONJ
ejpam-4992	46	23	e	e	NOUN
ejpam-4992	46	24	are	be	AUX
ejpam-4992	46	25	.	.	PUNCT
ejpam-4992	47	1	on	on	ADP
ejpam-4992	47	2	the	the	DET
ejpam-4992	47	3	other	other	ADJ
ejpam-4992	47	4	hand	hand	NOUN
ejpam-4992	47	5	,	,	PUNCT
ejpam-4992	47	6	since	since	SCONJ
ejpam-4992	47	7	λ′	λ′	PROPN
ejpam-4992	47	8	coincides	coincide	VERB
ejpam-4992	47	9	with	with	ADP
ejpam-4992	47	10	λ∗	λ∗	PROPN
ejpam-4992	47	11	,	,	PUNCT
ejpam-4992	47	12	one	one	NUM
ejpam-4992	47	13	deduces	deduce	VERB
ejpam-4992	47	14	from	from	ADP
ejpam-4992	47	15	[	[	X
ejpam-4992	47	16	5	5	NUM
ejpam-4992	47	17	,	,	PUNCT
ejpam-4992	47	18	theorem	theorem	VERB
ejpam-4992	47	19	1	1	NUM
ejpam-4992	47	20	]	]	PUNCT
ejpam-4992	47	21	that	that	SCONJ
ejpam-4992	47	22	λ(e	λ(e	ADJ
ejpam-4992	47	23	)	)	PUNCT
ejpam-4992	47	24	=	=	PUNCT
ejpam-4992	48	1	λ[e	λ[e	X
ejpam-4992	48	2	]	]	X
ejpam-4992	48	3	.	.	PUNCT
ejpam-4992	49	1	for	for	ADP
ejpam-4992	49	2	any	any	DET
ejpam-4992	49	3	sequence	sequence	NOUN
ejpam-4992	49	4	x	x	PUNCT
ejpam-4992	49	5	=	=	SYM
ejpam-4992	49	6	(	(	PUNCT
ejpam-4992	49	7	xn)n	xn)n	PROPN
ejpam-4992	49	8	in	in	ADP
ejpam-4992	49	9	e	e	PROPN
ejpam-4992	49	10	and	and	CCONJ
ejpam-4992	49	11	p	p	PROPN
ejpam-4992	49	12	∈	∈	PROPN
ejpam-4992	49	13	n	n	CCONJ
ejpam-4992	49	14	,	,	PUNCT
ejpam-4992	49	15	denote	denote	VERB
ejpam-4992	49	16	by	by	ADP
ejpam-4992	49	17	x(p	x(p	PROPN
ejpam-4992	49	18	)	)	PUNCT
ejpam-4992	49	19	=	=	PUNCT
ejpam-4992	49	20	(	(	PUNCT
ejpam-4992	49	21	x1	x1	PROPN
ejpam-4992	49	22	,	,	PUNCT
ejpam-4992	49	23	x2	x2	PROPN
ejpam-4992	49	24	,	,	PUNCT
ejpam-4992	49	25	.	.	PUNCT
ejpam-4992	49	26	.	.	PUNCT
ejpam-4992	49	27	.	.	PUNCT
ejpam-4992	50	1	,	,	PUNCT
ejpam-4992	50	2	xp	xp	INTJ
ejpam-4992	50	3	,	,	PUNCT
ejpam-4992	50	4	0	0	NUM
ejpam-4992	50	5	,	,	PUNCT
ejpam-4992	50	6	0	0	NUM
ejpam-4992	50	7	,	,	PUNCT
ejpam-4992	50	8	.	.	PUNCT
ejpam-4992	50	9	.	.	PUNCT
ejpam-4992	50	10	.	.	PUNCT
ejpam-4992	50	11	)	)	PUNCT
ejpam-4992	51	1	the	the	DET
ejpam-4992	51	2	pth	pth	NOUN
ejpam-4992	51	3	finite	finite	NOUN
ejpam-4992	51	4	section	section	NOUN
ejpam-4992	51	5	of	of	ADP
ejpam-4992	51	6	x.	x.	NOUN
ejpam-4992	51	7	let	let	VERB
ejpam-4992	51	8	x	x	X
ejpam-4992	51	9	<	<	X
ejpam-4992	51	10	p	p	X
ejpam-4992	51	11	>	>	X
ejpam-4992	51	12	=	=	PUNCT
ejpam-4992	51	13	x−	x−	PROPN
ejpam-4992	51	14	x(p	x(p	PROPN
ejpam-4992	51	15	)	)	PUNCT
ejpam-4992	52	1	=	=	PRON
ejpam-4992	52	2	(	(	PUNCT
ejpam-4992	52	3	0	0	NUM
ejpam-4992	52	4	,	,	PUNCT
ejpam-4992	52	5	0	0	NUM
ejpam-4992	52	6	,	,	PUNCT
ejpam-4992	52	7	.	.	PUNCT
ejpam-4992	52	8	.	.	PUNCT
ejpam-4992	53	1	.	.	PUNCT
ejpam-4992	54	1	,	,	PUNCT
ejpam-4992	54	2	0	0	NUM
ejpam-4992	54	3	,	,	PUNCT
ejpam-4992	54	4	xp+1	xp+1	NUM
ejpam-4992	54	5	,	,	PUNCT
ejpam-4992	54	6	xp+2	xp+2	PROPN
ejpam-4992	54	7	,	,	PUNCT
ejpam-4992	54	8	.	.	PUNCT
ejpam-4992	54	9	.	.	PUNCT
ejpam-4992	54	10	.	.	PUNCT
ejpam-4992	54	11	)	)	PUNCT
ejpam-4992	54	12	.	.	PUNCT
ejpam-4992	55	1	if	if	SCONJ
ejpam-4992	55	2	en	en	X
ejpam-4992	55	3	is	be	AUX
ejpam-4992	55	4	the	the	DET
ejpam-4992	55	5	nth	nth	NOUN
ejpam-4992	55	6	unit	unit	NOUN
ejpam-4992	55	7	coordinate	coordinate	NOUN
ejpam-4992	55	8	vector	vector	NOUN
ejpam-4992	55	9	of	of	ADP
ejpam-4992	55	10	cn	cn	PROPN
ejpam-4992	55	11	,	,	PUNCT
ejpam-4992	55	12	then	then	ADV
ejpam-4992	55	13	x(p	x(p	PROPN
ejpam-4992	55	14	)	)	PUNCT
ejpam-4992	56	1	=	=	SYM
ejpam-4992	56	2	∑p	∑p	ADJ
ejpam-4992	56	3	n=1	n=1	PROPN
ejpam-4992	56	4	xnen	xnen	PROPN
ejpam-4992	56	5	.	.	PUNCT
ejpam-4992	57	1	we	we	PRON
ejpam-4992	57	2	will	will	AUX
ejpam-4992	57	3	denote	denote	VERB
ejpam-4992	57	4	by	by	ADP
ejpam-4992	57	5	λ(e)r	λ(e)r	PROPN
ejpam-4992	57	6	(	(	PUNCT
ejpam-4992	57	7	resp	resp	NOUN
ejpam-4992	57	8	.	.	PUNCT
ejpam-4992	58	1	λ⟨e⟩r	λ⟨e⟩r	NUM
ejpam-4992	58	2	)	)	PUNCT
ejpam-4992	59	1	,	,	PUNCT
ejpam-4992	59	2	the	the	DET
ejpam-4992	59	3	subspace	subspace	NOUN
ejpam-4992	59	4	of	of	ADP
ejpam-4992	59	5	λ(e	λ(e	PROPN
ejpam-4992	59	6	)	)	PUNCT
ejpam-4992	59	7	(	(	PUNCT
ejpam-4992	59	8	rep	rep	PROPN
ejpam-4992	59	9	.	.	PROPN
ejpam-4992	59	10	λ⟨e⟩	λ⟨e⟩	PROPN
ejpam-4992	59	11	)	)	PUNCT
ejpam-4992	59	12	consisting	consist	VERB
ejpam-4992	59	13	of	of	ADP
ejpam-4992	59	14	all	all	DET
ejpam-4992	59	15	the	the	DET
ejpam-4992	59	16	sequences	sequence	NOUN
ejpam-4992	59	17	x	x	PUNCT
ejpam-4992	59	18	=	=	SYM
ejpam-4992	59	19	(	(	PUNCT
ejpam-4992	59	20	xn)n	xn)n	PROPN
ejpam-4992	59	21	which	which	PRON
ejpam-4992	59	22	are	be	AUX
ejpam-4992	59	23	limits	limit	NOUN
ejpam-4992	59	24	of	of	ADP
ejpam-4992	59	25	their	their	PRON
ejpam-4992	59	26	finite	finite	ADJ
ejpam-4992	59	27	sections	section	NOUN
ejpam-4992	59	28	x(p	x(p	PROPN
ejpam-4992	59	29	)	)	PUNCT
ejpam-4992	59	30	.	.	PUNCT
ejpam-4992	60	1	the	the	DET
ejpam-4992	60	2	reader	reader	NOUN
ejpam-4992	60	3	is	be	AUX
ejpam-4992	60	4	referred	refer	VERB
ejpam-4992	60	5	to	to	ADP
ejpam-4992	60	6	[	[	X
ejpam-4992	60	7	6	6	NUM
ejpam-4992	60	8	,	,	PUNCT
ejpam-4992	60	9	14	14	NUM
ejpam-4992	60	10	]	]	PUNCT
ejpam-4992	60	11	for	for	ADP
ejpam-4992	60	12	notations	notation	NOUN
ejpam-4992	60	13	and	and	CCONJ
ejpam-4992	60	14	concepts	concept	NOUN
ejpam-4992	60	15	related	relate	VERB
ejpam-4992	60	16	to	to	ADP
ejpam-4992	60	17	the	the	DET
ejpam-4992	60	18	köthe	köthe	PROPN
ejpam-4992	60	19	theory	theory	NOUN
ejpam-4992	60	20	of	of	ADP
ejpam-4992	60	21	sequence	sequence	NOUN
ejpam-4992	60	22	spaces	space	NOUN
ejpam-4992	60	23	and	and	CCONJ
ejpam-4992	60	24	the	the	DET
ejpam-4992	60	25	general	general	ADJ
ejpam-4992	60	26	theory	theory	NOUN
ejpam-4992	60	27	of	of	ADP
ejpam-4992	60	28	locally	locally	ADV
ejpam-4992	60	29	convex	convex	ADJ
ejpam-4992	60	30	spaces	space	NOUN
ejpam-4992	60	31	.	.	PUNCT
ejpam-4992	61	1	2	2	X
ejpam-4992	61	2	.	.	X
ejpam-4992	61	3	bounded	bound	VERB
ejpam-4992	61	4	sets	set	NOUN
ejpam-4992	61	5	of	of	ADP
ejpam-4992	61	6	λ(e	λ(e	NOUN
ejpam-4992	61	7	)	)	PUNCT
ejpam-4992	61	8	if	if	SCONJ
ejpam-4992	61	9	b	b	PROPN
ejpam-4992	61	10	is	be	AUX
ejpam-4992	61	11	a	a	DET
ejpam-4992	61	12	closed	closed	ADJ
ejpam-4992	61	13	,	,	PUNCT
ejpam-4992	61	14	absolutely	absolutely	ADV
ejpam-4992	61	15	convex	convex	ADJ
ejpam-4992	61	16	and	and	CCONJ
ejpam-4992	61	17	bounded	bound	VERB
ejpam-4992	61	18	subset	subset	NOUN
ejpam-4992	61	19	of	of	ADP
ejpam-4992	61	20	e	e	NOUN
ejpam-4992	61	21	,	,	PUNCT
ejpam-4992	61	22	and	and	CCONJ
ejpam-4992	61	23	s	s	NOUN
ejpam-4992	61	24	=	=	NOUN
ejpam-4992	61	25	bλ∗	bλ∗	NOUN
ejpam-4992	61	26	,	,	PUNCT
ejpam-4992	61	27	let	let	VERB
ejpam-4992	61	28	b̃	b̃	PROPN
ejpam-4992	61	29	=	=	PRON
ejpam-4992	61	30	{	{	PUNCT
ejpam-4992	61	31	(	(	PUNCT
ejpam-4992	61	32	xn)n	xn)n	PROPN
ejpam-4992	61	33	∈	∈	PROPN
ejpam-4992	61	34	λ(e	λ(e	PROPN
ejpam-4992	61	35	)	)	PUNCT
ejpam-4992	61	36	:	:	PUNCT
ejpam-4992	61	37	∀α	∀α	X
ejpam-4992	61	38	=	=	SYM
ejpam-4992	61	39	(	(	PUNCT
ejpam-4992	61	40	αn)n	αn)n	PROPN
ejpam-4992	61	41	∈	∈	NOUN
ejpam-4992	61	42	s	s	NOUN
ejpam-4992	61	43	,	,	PUNCT
ejpam-4992	61	44	∑	∑	ADP
ejpam-4992	61	45	n	n	PRON
ejpam-4992	61	46	αnxn	αnxn	VERB
ejpam-4992	61	47	∈	∈	PROPN
ejpam-4992	61	48	b	b	PROPN
ejpam-4992	61	49	}	}	PUNCT
ejpam-4992	61	50	.	.	PUNCT
ejpam-4992	62	1	(	(	PUNCT
ejpam-4992	62	2	1	1	X
ejpam-4992	62	3	)	)	PUNCT
ejpam-4992	62	4	we	we	PRON
ejpam-4992	62	5	have	have	VERB
ejpam-4992	62	6	the	the	DET
ejpam-4992	62	7	following	follow	VERB
ejpam-4992	62	8	result	result	NOUN
ejpam-4992	62	9	.	.	PUNCT
ejpam-4992	63	1	proposition	proposition	NOUN
ejpam-4992	63	2	1	1	NUM
ejpam-4992	63	3	.	.	PUNCT
ejpam-4992	64	1	the	the	DET
ejpam-4992	64	2	collection	collection	NOUN
ejpam-4992	64	3	{	{	PUNCT
ejpam-4992	64	4	b̃	b̃	NOUN
ejpam-4992	64	5	:	:	PUNCT
ejpam-4992	64	6	b	b	X
ejpam-4992	64	7	bounded	bound	VERB
ejpam-4992	64	8	in	in	ADP
ejpam-4992	64	9	e	e	PROPN
ejpam-4992	64	10	}	}	PUNCT
ejpam-4992	64	11	constitutes	constitute	VERB
ejpam-4992	64	12	a	a	DET
ejpam-4992	64	13	fundamental	fundamental	ADJ
ejpam-4992	64	14	system	system	NOUN
ejpam-4992	64	15	of	of	ADP
ejpam-4992	64	16	bounded	bounded	ADJ
ejpam-4992	64	17	sets	set	NOUN
ejpam-4992	64	18	for	for	ADP
ejpam-4992	64	19	λ(e	λ(e	NOUN
ejpam-4992	64	20	)	)	PUNCT
ejpam-4992	64	21	.	.	PUNCT
ejpam-4992	65	1	proof	proof	NOUN
ejpam-4992	65	2	.	.	PUNCT
ejpam-4992	66	1	if	if	SCONJ
ejpam-4992	66	2	b	b	PROPN
ejpam-4992	66	3	is	be	AUX
ejpam-4992	66	4	a	a	DET
ejpam-4992	66	5	bounded	bound	VERB
ejpam-4992	66	6	set	set	NOUN
ejpam-4992	66	7	in	in	ADP
ejpam-4992	66	8	e	e	NOUN
ejpam-4992	66	9	,	,	PUNCT
ejpam-4992	66	10	then	then	ADV
ejpam-4992	66	11	the	the	DET
ejpam-4992	66	12	corresponding	corresponding	ADJ
ejpam-4992	66	13	set	set	VERB
ejpam-4992	66	14	b̃	b̃	PROPN
ejpam-4992	66	15	in	in	ADP
ejpam-4992	66	16	(	(	PUNCT
ejpam-4992	66	17	1	1	X
ejpam-4992	66	18	)	)	PUNCT
ejpam-4992	66	19	is	be	AUX
ejpam-4992	66	20	bounded	bound	VERB
ejpam-4992	66	21	in	in	ADP
ejpam-4992	66	22	λ(e	λ(e	NOUN
ejpam-4992	66	23	)	)	PUNCT
ejpam-4992	66	24	,	,	PUNCT
ejpam-4992	66	25	by	by	ADP
ejpam-4992	66	26	[	[	X
ejpam-4992	66	27	8	8	NUM
ejpam-4992	66	28	,	,	PUNCT
ejpam-4992	66	29	proposition	proposition	NOUN
ejpam-4992	66	30	1	1	NUM
ejpam-4992	66	31	]	]	PUNCT
ejpam-4992	66	32	.	.	PUNCT
ejpam-4992	67	1	now	now	ADV
ejpam-4992	67	2	,	,	PUNCT
ejpam-4992	67	3	let	let	VERB
ejpam-4992	67	4	b	b	X
ejpam-4992	67	5	be	be	AUX
ejpam-4992	67	6	a	a	DET
ejpam-4992	67	7	bounded	bounded	ADJ
ejpam-4992	67	8	set	set	NOUN
ejpam-4992	67	9	of	of	ADP
ejpam-4992	67	10	λ(e	λ(e	PROPN
ejpam-4992	67	11	)	)	PUNCT
ejpam-4992	67	12	and	and	CCONJ
ejpam-4992	67	13	s	s	VERB
ejpam-4992	67	14	the	the	DET
ejpam-4992	67	15	unit	unit	NOUN
ejpam-4992	67	16	ball	ball	NOUN
ejpam-4992	67	17	of	of	ADP
ejpam-4992	67	18	λ∗.	λ∗.	PART
ejpam-4992	67	19	consider	consider	VERB
ejpam-4992	67	20	the	the	DET
ejpam-4992	67	21	subset	subset	NOUN
ejpam-4992	67	22	b	b	PROPN
ejpam-4992	67	23	of	of	ADP
ejpam-4992	67	24	e	e	NOUN
ejpam-4992	67	25	defined	define	VERB
ejpam-4992	67	26	by	by	ADP
ejpam-4992	67	27	b	b	PROPN
ejpam-4992	67	28	=	=	SYM
ejpam-4992	67	29	{	{	PUNCT
ejpam-4992	67	30	y	y	PROPN
ejpam-4992	67	31	∈	∈	PROPN
ejpam-4992	67	32	λ(e	λ(e	PROPN
ejpam-4992	67	33	)	)	PUNCT
ejpam-4992	67	34	:	:	PUNCT
ejpam-4992	68	1	y	y	NOUN
ejpam-4992	68	2	=	=	PUNCT
ejpam-4992	68	3	∞∑	∞∑	NUM
ejpam-4992	68	4	n=1	n=1	PROPN
ejpam-4992	68	5	αnxn	αnxn	NOUN
ejpam-4992	68	6	,	,	PUNCT
ejpam-4992	68	7	for	for	ADP
ejpam-4992	68	8	some	some	DET
ejpam-4992	68	9	α	α	NOUN
ejpam-4992	68	10	∈	∈	NOUN
ejpam-4992	68	11	s	s	PART
ejpam-4992	68	12	and	and	CCONJ
ejpam-4992	68	13	x	x	SYM
ejpam-4992	68	14	=	=	SYM
ejpam-4992	68	15	(	(	PUNCT
ejpam-4992	68	16	xn)n	xn)n	PROPN
ejpam-4992	68	17	∈	∈	PROPN
ejpam-4992	68	18	b	b	PROPN
ejpam-4992	68	19	}	}	PUNCT
ejpam-4992	68	20	.	.	PUNCT
ejpam-4992	69	1	m.	m.	NOUN
ejpam-4992	69	2	a.	a.	PROPN
ejpam-4992	69	3	sidaty	sidaty	PROPN
ejpam-4992	69	4	/	/	SYM
ejpam-4992	69	5	eur	eur	PROPN
ejpam-4992	69	6	.	.	PUNCT
ejpam-4992	70	1	j.	j.	PROPN
ejpam-4992	70	2	pure	pure	PROPN
ejpam-4992	70	3	appl	appl	PROPN
ejpam-4992	70	4	.	.	PROPN
ejpam-4992	70	5	math	math	PROPN
ejpam-4992	70	6	,	,	PUNCT
ejpam-4992	70	7	17	17	NUM
ejpam-4992	70	8	(	(	PUNCT
ejpam-4992	70	9	1	1	NUM
ejpam-4992	70	10	)	)	PUNCT
ejpam-4992	70	11	(	(	PUNCT
ejpam-4992	70	12	2024	2024	NUM
ejpam-4992	70	13	)	)	PUNCT
ejpam-4992	70	14	,	,	PUNCT
ejpam-4992	70	15	171	171	NUM
ejpam-4992	70	16	-	-	SYM
ejpam-4992	70	17	179	179	NUM
ejpam-4992	70	18	174	174	NUM
ejpam-4992	70	19	let	let	VERB
ejpam-4992	70	20	a	a	DET
ejpam-4992	70	21	∈	∈	NOUN
ejpam-4992	70	22	e′	e′	NOUN
ejpam-4992	70	23	,	,	PUNCT
ejpam-4992	70	24	m	m	VERB
ejpam-4992	70	25	∈	∈	NOUN
ejpam-4992	70	26	m	m	VERB
ejpam-4992	70	27	with	with	ADP
ejpam-4992	70	28	a	a	DET
ejpam-4992	70	29	∈	∈	NOUN
ejpam-4992	70	30	m	m	NOUN
ejpam-4992	70	31	and	and	CCONJ
ejpam-4992	70	32	x	x	SYM
ejpam-4992	70	33	=	=	SYM
ejpam-4992	70	34	(	(	PUNCT
ejpam-4992	70	35	xn)n	xn)n	PROPN
ejpam-4992	70	36	∈	∈	PROPN
ejpam-4992	70	37	b.	b.	PROPN
ejpam-4992	70	38	then,∣∣∣∣∣	then,∣∣∣∣∣	PROPN
ejpam-4992	71	1	〈	〈	PROPN
ejpam-4992	71	2	a	a	PRON
ejpam-4992	71	3	,	,	PUNCT
ejpam-4992	71	4	∞∑	∞∑	NUM
ejpam-4992	71	5	n=1	n=1	PROPN
ejpam-4992	71	6	αnxn	αnxn	NOUN
ejpam-4992	71	7	〉	〉	NOUN
ejpam-4992	71	8	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-4992	71	9	=	=	SYM
ejpam-4992	72	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-4992	72	2	∞∑	∞∑	NUM
ejpam-4992	72	3	n=1	n=1	PROPN
ejpam-4992	72	4	αna(xn	αna(xn	NUM
ejpam-4992	72	5	)	)	PUNCT
ejpam-4992	72	6	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-4992	72	7	≤	≤	NOUN
ejpam-4992	73	1	∞∑	∞∑	NUM
ejpam-4992	73	2	n=1	n=1	PROPN
ejpam-4992	73	3	|αna(xn)|	|αna(xn)|	ADJ
ejpam-4992	73	4	≤	≤	NUM
ejpam-4992	73	5	εm	εm	NOUN
ejpam-4992	73	6	(	(	PUNCT
ejpam-4992	73	7	x	x	NOUN
ejpam-4992	73	8	)	)	PUNCT
ejpam-4992	73	9	.	.	PUNCT
ejpam-4992	74	1	since	since	SCONJ
ejpam-4992	74	2	s	s	PROPN
ejpam-4992	74	3	is	be	AUX
ejpam-4992	74	4	a	a	DET
ejpam-4992	74	5	normal	normal	ADJ
ejpam-4992	74	6	disk	disk	NOUN
ejpam-4992	74	7	in	in	ADP
ejpam-4992	74	8	λ∗	λ∗	PROPN
ejpam-4992	74	9	and	and	CCONJ
ejpam-4992	74	10	b	b	PROPN
ejpam-4992	74	11	is	be	AUX
ejpam-4992	74	12	bounded	bound	VERB
ejpam-4992	74	13	in	in	ADP
ejpam-4992	74	14	λ(e	λ(e	PROPN
ejpam-4992	74	15	)	)	PUNCT
ejpam-4992	74	16	,	,	PUNCT
ejpam-4992	74	17	then	then	ADV
ejpam-4992	74	18	b	b	PROPN
ejpam-4992	74	19	is	be	AUX
ejpam-4992	74	20	a	a	DET
ejpam-4992	74	21	bounded	bounded	ADJ
ejpam-4992	74	22	disk	disk	NOUN
ejpam-4992	74	23	in	in	ADP
ejpam-4992	74	24	e.	e.	PROPN
ejpam-4992	74	25	moreover	moreover	ADV
ejpam-4992	74	26	,	,	PUNCT
ejpam-4992	74	27	by	by	ADP
ejpam-4992	74	28	the	the	DET
ejpam-4992	74	29	definition	definition	NOUN
ejpam-4992	74	30	of	of	ADP
ejpam-4992	74	31	b	b	PROPN
ejpam-4992	74	32	,	,	PUNCT
ejpam-4992	74	33	we	we	PRON
ejpam-4992	74	34	see	see	VERB
ejpam-4992	74	35	that	that	PRON
ejpam-4992	74	36	b	b	NOUN
ejpam-4992	74	37	⊂	⊂	ADJ
ejpam-4992	74	38	b̃.	b̃.	PROPN
ejpam-4992	74	39	■	■	PUNCT
ejpam-4992	74	40	lemma	lemma	PROPN
ejpam-4992	74	41	2	2	NUM
ejpam-4992	74	42	.	.	PUNCT
ejpam-4992	75	1	for	for	ADP
ejpam-4992	75	2	every	every	DET
ejpam-4992	75	3	t	t	NOUN
ejpam-4992	75	4	∈	∈	PROPN
ejpam-4992	75	5	e	e	NOUN
ejpam-4992	75	6	and	and	CCONJ
ejpam-4992	75	7	β	β	X
ejpam-4992	75	8	=	=	SYM
ejpam-4992	75	9	(	(	PUNCT
ejpam-4992	75	10	βn)n	βn)n	PROPN
ejpam-4992	75	11	∈	∈	PROPN
ejpam-4992	75	12	λ	λ	PROPN
ejpam-4992	75	13	,	,	PUNCT
ejpam-4992	75	14	we	we	PRON
ejpam-4992	75	15	have	have	VERB
ejpam-4992	75	16	(	(	PUNCT
ejpam-4992	75	17	βnt)n	βnt)n	NOUN
ejpam-4992	75	18	∈	∈	PROPN
ejpam-4992	75	19	λ⟨e⟩.	λ⟨e⟩.	X
ejpam-4992	75	20	proof	proof	NOUN
ejpam-4992	75	21	.	.	PUNCT
ejpam-4992	76	1	for	for	ADP
ejpam-4992	76	2	t	t	PROPN
ejpam-4992	76	3	∈	∈	PROPN
ejpam-4992	76	4	e	e	NOUN
ejpam-4992	76	5	,	,	PUNCT
ejpam-4992	76	6	let	let	VERB
ejpam-4992	76	7	δt	δt	PART
ejpam-4992	76	8	denote	denote	VERB
ejpam-4992	76	9	the	the	DET
ejpam-4992	76	10	evaluation	evaluation	NOUN
ejpam-4992	76	11	defined	define	VERB
ejpam-4992	76	12	on	on	ADP
ejpam-4992	76	13	e′	e′	PROPN
ejpam-4992	76	14	by	by	ADP
ejpam-4992	76	15	δt(x	δt(x	PROPN
ejpam-4992	76	16	′	′	NUM
ejpam-4992	76	17	)	)	PUNCT
ejpam-4992	76	18	=	=	PUNCT
ejpam-4992	77	1	x′(t	x′(t	PROPN
ejpam-4992	77	2	)	)	PUNCT
ejpam-4992	77	3	.	.	PUNCT
ejpam-4992	78	1	we	we	PRON
ejpam-4992	78	2	have	have	VERB
ejpam-4992	78	3	,	,	PUNCT
ejpam-4992	78	4	if	if	SCONJ
ejpam-4992	78	5	m	m	VERB
ejpam-4992	78	6	∈	∈	PROPN
ejpam-4992	78	7	m	m	NOUN
ejpam-4992	78	8	,	,	PUNCT
ejpam-4992	78	9	then	then	ADV
ejpam-4992	78	10	|δt(x′)|	|δt(x′)|	ADJ
ejpam-4992	78	11	≤	≤	NUM
ejpam-4992	78	12	pm	pm	NOUN
ejpam-4992	78	13	(	(	PUNCT
ejpam-4992	78	14	t)∥x′∥m	t)∥x′∥m	NOUN
ejpam-4992	78	15	for	for	ADP
ejpam-4992	78	16	every	every	DET
ejpam-4992	78	17	x′	x′	PROPN
ejpam-4992	78	18	∈	∈	PROPN
ejpam-4992	78	19	e′	e′	NOUN
ejpam-4992	78	20	m	m	PROPN
ejpam-4992	78	21	.	.	PUNCT
ejpam-4992	79	1	this	this	PRON
ejpam-4992	79	2	means	mean	VERB
ejpam-4992	79	3	that	that	SCONJ
ejpam-4992	79	4	δt	δt	ADP
ejpam-4992	79	5	∈	∈	PROPN
ejpam-4992	79	6	(	(	PUNCT
ejpam-4992	79	7	e′	e′	NOUN
ejpam-4992	79	8	m	m	PROPN
ejpam-4992	79	9	)	)	PUNCT
ejpam-4992	79	10	′	′	NUM
ejpam-4992	79	11	and	and	CCONJ
ejpam-4992	79	12	that	that	PRON
ejpam-4992	79	13	∥δt∥	∥δt∥	PRON
ejpam-4992	79	14	≤	≤	NUM
ejpam-4992	79	15	pm	pm	NOUN
ejpam-4992	79	16	(	(	PUNCT
ejpam-4992	79	17	t	t	PROPN
ejpam-4992	79	18	)	)	PUNCT
ejpam-4992	79	19	.	.	PUNCT
ejpam-4992	80	1	let	let	VERB
ejpam-4992	80	2	β	β	X
ejpam-4992	80	3	=	=	SYM
ejpam-4992	80	4	(	(	PUNCT
ejpam-4992	80	5	βn)n	βn)n	PROPN
ejpam-4992	80	6	∈	∈	PROPN
ejpam-4992	80	7	λ	λ	PROPN
ejpam-4992	80	8	and	and	CCONJ
ejpam-4992	80	9	(	(	PUNCT
ejpam-4992	80	10	an)n	an)n	PROPN
ejpam-4992	80	11	∈	∈	PROPN
ejpam-4992	80	12	λ∗[e′	λ∗[e′	X
ejpam-4992	80	13	m	m	VERB
ejpam-4992	80	14	]	]	X
ejpam-4992	80	15	.	.	PUNCT
ejpam-4992	81	1	by	by	ADP
ejpam-4992	81	2	the	the	DET
ejpam-4992	81	3	definition	definition	NOUN
ejpam-4992	81	4	of	of	ADP
ejpam-4992	81	5	λ∗[e′	λ∗[e′	PROPN
ejpam-4992	81	6	m	m	VERB
ejpam-4992	81	7	]	]	X
ejpam-4992	81	8	,	,	PUNCT
ejpam-4992	81	9	(	(	PUNCT
ejpam-4992	81	10	an(t))n	an(t))n	X
ejpam-4992	81	11	=	=	SYM
ejpam-4992	81	12	(	(	PUNCT
ejpam-4992	81	13	δt(an	δt(an	ADJ
ejpam-4992	81	14	)	)	PUNCT
ejpam-4992	81	15	)	)	PUNCT
ejpam-4992	82	1	∈	∈	PROPN
ejpam-4992	82	2	λ∗	λ∗	PROPN
ejpam-4992	82	3	,	,	PUNCT
ejpam-4992	82	4	and	and	CCONJ
ejpam-4992	82	5	then	then	ADV
ejpam-4992	82	6	∞∑	∞∑	NUM
ejpam-4992	82	7	n=1	n=1	PROPN
ejpam-4992	82	8	|an(βnt)|	|an(βnt)|	VERB
ejpam-4992	82	9	=	=	SYM
ejpam-4992	82	10	∞∑	∞∑	NUM
ejpam-4992	82	11	n=1	n=1	ADJ
ejpam-4992	82	12	|an(t)βn|	|an(t)βn|	NOUN
ejpam-4992	82	13	<	<	X
ejpam-4992	82	14	∞.	∞.	PROPN
ejpam-4992	82	15	thus	thus	ADV
ejpam-4992	82	16	,	,	PUNCT
ejpam-4992	82	17	(	(	PUNCT
ejpam-4992	82	18	βnt)n	βnt)n	SYM
ejpam-4992	82	19	∈	∈	PROPN
ejpam-4992	83	1	λ⟨e⟩.	λ⟨e⟩.	X
ejpam-4992	83	2	■	■	X
ejpam-4992	83	3	now	now	ADV
ejpam-4992	83	4	,	,	PUNCT
ejpam-4992	83	5	for	for	ADP
ejpam-4992	83	6	s	s	NOUN
ejpam-4992	83	7	=	=	SYM
ejpam-4992	83	8	bλ	bλ	PROPN
ejpam-4992	83	9	and	and	CCONJ
ejpam-4992	83	10	a	a	DET
ejpam-4992	83	11	closed	closed	ADJ
ejpam-4992	83	12	absolutely	absolutely	ADV
ejpam-4992	83	13	convex	convex	ADJ
ejpam-4992	83	14	bounded	bound	VERB
ejpam-4992	83	15	subset	subset	PROPN
ejpam-4992	83	16	b	b	PROPN
ejpam-4992	83	17	of	of	ADP
ejpam-4992	83	18	e	e	NOUN
ejpam-4992	83	19	,	,	PUNCT
ejpam-4992	83	20	define	define	VERB
ejpam-4992	83	21	b̄	b̄	NOUN
ejpam-4992	83	22	=	=	PUNCT
ejpam-4992	83	23	{	{	PUNCT
ejpam-4992	83	24	∞∑	∞∑	NUM
ejpam-4992	83	25	k=1	k=1	AUX
ejpam-4992	83	26	ξkβ	ξkβ	VERB
ejpam-4992	83	27	kxk	kxk	NOUN
ejpam-4992	83	28	:	:	PUNCT
ejpam-4992	83	29	βk	βk	ADP
ejpam-4992	83	30	=	=	PUNCT
ejpam-4992	83	31	(	(	PUNCT
ejpam-4992	83	32	βk	βk	ADP
ejpam-4992	83	33	n)n	n)n	NOUN
ejpam-4992	83	34	∈	∈	PROPN
ejpam-4992	83	35	bλ	bλ	PROPN
ejpam-4992	83	36	,	,	PUNCT
ejpam-4992	83	37	xk	xk	PROPN
ejpam-4992	83	38	∈	∈	PROPN
ejpam-4992	83	39	b	b	PROPN
ejpam-4992	83	40	,	,	PUNCT
ejpam-4992	83	41	and	and	CCONJ
ejpam-4992	83	42	∞∑	∞∑	PRON
ejpam-4992	83	43	k=1	k=1	ADP
ejpam-4992	83	44	|ξk|	|ξk|	VERB
ejpam-4992	83	45	≤	≤	NUM
ejpam-4992	83	46	1	1	NUM
ejpam-4992	83	47	}	}	PUNCT
ejpam-4992	83	48	.	.	PUNCT
ejpam-4992	84	1	(	(	PUNCT
ejpam-4992	84	2	2	2	X
ejpam-4992	84	3	)	)	PUNCT
ejpam-4992	84	4	proposition	proposition	NOUN
ejpam-4992	84	5	3	3	NUM
ejpam-4992	84	6	.	.	PUNCT
ejpam-4992	85	1	the	the	DET
ejpam-4992	85	2	set	set	NOUN
ejpam-4992	85	3	b̄	b̄	NOUN
ejpam-4992	85	4	is	be	AUX
ejpam-4992	85	5	a	a	DET
ejpam-4992	85	6	bounded	bounded	ADJ
ejpam-4992	85	7	subset	subset	NOUN
ejpam-4992	85	8	of	of	ADP
ejpam-4992	85	9	λ⟨e⟩.	λ⟨e⟩.	PROPN
ejpam-4992	85	10	proof	proof	NOUN
ejpam-4992	85	11	.	.	PUNCT
ejpam-4992	86	1	let	let	VERB
ejpam-4992	86	2	{	{	PUNCT
ejpam-4992	86	3	βk	βk	VERB
ejpam-4992	86	4	=	=	PUNCT
ejpam-4992	86	5	(	(	PUNCT
ejpam-4992	86	6	βk	βk	ADP
ejpam-4992	86	7	n)n}∞k	n)n}∞k	PROPN
ejpam-4992	86	8	and	and	CCONJ
ejpam-4992	86	9	{	{	PUNCT
ejpam-4992	86	10	xk}∞k	xk}∞k	NOUN
ejpam-4992	86	11	be	be	VERB
ejpam-4992	86	12	sequences	sequence	NOUN
ejpam-4992	86	13	in	in	ADP
ejpam-4992	86	14	bλ	bλ	NOUN
ejpam-4992	86	15	and	and	CCONJ
ejpam-4992	86	16	b	b	NOUN
ejpam-4992	86	17	respectively	respectively	ADV
ejpam-4992	86	18	.	.	PUNCT
ejpam-4992	87	1	fix	fix	VERB
ejpam-4992	87	2	k	k	PROPN
ejpam-4992	87	3	∈	∈	PROPN
ejpam-4992	87	4	n	n	CCONJ
ejpam-4992	87	5	,	,	PUNCT
ejpam-4992	87	6	m	m	VERB
ejpam-4992	87	7	∈	∈	NOUN
ejpam-4992	87	8	m	m	NOUN
ejpam-4992	87	9	and	and	CCONJ
ejpam-4992	87	10	a	a	PRON
ejpam-4992	87	11	=	=	X
ejpam-4992	87	12	(	(	PUNCT
ejpam-4992	87	13	an)n	an)n	PROPN
ejpam-4992	87	14	∈	∈	PROPN
ejpam-4992	87	15	λ∗[e′	λ∗[e′	X
ejpam-4992	87	16	m	m	NOUN
ejpam-4992	87	17	]	]	X
ejpam-4992	87	18	=	=	PUNCT
ejpam-4992	87	19	λ∗(e′	λ∗(e′	ADJ
ejpam-4992	87	20	m	m	VERB
ejpam-4992	87	21	)	)	PUNCT
ejpam-4992	87	22	,	,	PUNCT
ejpam-4992	87	23	with	with	ADP
ejpam-4992	87	24	∥a∥λ∗(e′	∥a∥λ∗(e′	PROPN
ejpam-4992	87	25	m	m	PROPN
ejpam-4992	87	26	)	)	PUNCT
ejpam-4992	87	27	≤	≤	NUM
ejpam-4992	87	28	1	1	NUM
ejpam-4992	87	29	.	.	PUNCT
ejpam-4992	88	1	as	as	ADP
ejpam-4992	88	2	in	in	ADP
ejpam-4992	88	3	the	the	DET
ejpam-4992	88	4	proof	proof	NOUN
ejpam-4992	88	5	of	of	ADP
ejpam-4992	88	6	the	the	DET
ejpam-4992	88	7	previous	previous	ADJ
ejpam-4992	88	8	lemma	lemma	PROPN
ejpam-4992	88	9	,	,	PUNCT
ejpam-4992	88	10	δxk	δxk	PROPN
ejpam-4992	88	11	denotes	denote	VERB
ejpam-4992	88	12	the	the	DET
ejpam-4992	88	13	evaluation	evaluation	NOUN
ejpam-4992	88	14	defined	define	VERB
ejpam-4992	88	15	on	on	ADP
ejpam-4992	88	16	e′	e′	X
ejpam-4992	88	17	m	m	VERB
ejpam-4992	88	18	.	.	PUNCT
ejpam-4992	89	1	we	we	PRON
ejpam-4992	89	2	have	have	VERB
ejpam-4992	89	3	∞∑	∞∑	NUM
ejpam-4992	89	4	n=1	n=1	NUM
ejpam-4992	89	5	∣∣∣an(βk	∣∣∣an(βk	PROPN
ejpam-4992	89	6	nxk	nxk	NOUN
ejpam-4992	89	7	)	)	PUNCT
ejpam-4992	89	8	∣∣∣	∣∣∣	NOUN
ejpam-4992	90	1	=	=	PUNCT
ejpam-4992	90	2	∞∑	∞∑	NUM
ejpam-4992	90	3	n=1	n=1	PROPN
ejpam-4992	90	4	∣∣∣βk	∣∣∣βk	PROPN
ejpam-4992	90	5	nan(xk	nan(xk	X
ejpam-4992	90	6	)	)	PUNCT
ejpam-4992	90	7	∣∣∣	∣∣∣	NOUN
ejpam-4992	91	1	=	=	SYM
ejpam-4992	91	2	∞∑	∞∑	NUM
ejpam-4992	91	3	n=1	n=1	PROPN
ejpam-4992	91	4	∣∣∣βk	∣∣∣βk	PROPN
ejpam-4992	91	5	nδxk	nδxk	NOUN
ejpam-4992	91	6	(	(	PUNCT
ejpam-4992	91	7	an	an	NOUN
ejpam-4992	91	8	)	)	PUNCT
ejpam-4992	91	9	∣∣∣	∣∣∣	NOUN
ejpam-4992	91	10	=	=	SYM
ejpam-4992	91	11	∥βk∥λpm	∥βk∥λpm	X
ejpam-4992	91	12	(	(	PUNCT
ejpam-4992	91	13	xk	xk	NOUN
ejpam-4992	91	14	)	)	PUNCT
ejpam-4992	91	15	∞∑	∞∑	PROPN
ejpam-4992	91	16	n=1	n=1	ADP
ejpam-4992	91	17	∣∣∣∣	∣∣∣∣	NOUN
ejpam-4992	91	18	βk	βk	NOUN
ejpam-4992	91	19	n	n	PRON
ejpam-4992	91	20	∥βk∥λ	∥βk∥λ	NOUN
ejpam-4992	91	21	δxk	δxk	NOUN
ejpam-4992	91	22	pm	pm	NOUN
ejpam-4992	91	23	(	(	PUNCT
ejpam-4992	91	24	xk	xk	PROPN
ejpam-4992	91	25	)	)	PUNCT
ejpam-4992	91	26	(	(	PUNCT
ejpam-4992	91	27	an	an	X
ejpam-4992	91	28	)	)	PUNCT
ejpam-4992	91	29	∣∣∣∣	∣∣∣∣	NOUN
ejpam-4992	91	30	≤	≤	NOUN
ejpam-4992	91	31	∥βk∥λpm	∥βk∥λpm	VERB
ejpam-4992	91	32	(	(	PUNCT
ejpam-4992	91	33	xk)∥a∥λ∗(e′	xk)∥a∥λ∗(e′	PROPN
ejpam-4992	91	34	m	m	AUX
ejpam-4992	91	35	)	)	PUNCT
ejpam-4992	91	36	≤	≤	NOUN
ejpam-4992	91	37	∥βk∥λpm	∥βk∥λpm	VERB
ejpam-4992	92	1	(	(	PUNCT
ejpam-4992	92	2	xk	xk	NOUN
ejpam-4992	92	3	)	)	PUNCT
ejpam-4992	92	4	≤	≤	NUM
ejpam-4992	92	5	pm	pm	NOUN
ejpam-4992	92	6	(	(	PUNCT
ejpam-4992	92	7	xk	xk	NOUN
ejpam-4992	92	8	)	)	PUNCT
ejpam-4992	92	9	.	.	PUNCT
ejpam-4992	93	1	since	since	SCONJ
ejpam-4992	93	2	b	b	PROPN
ejpam-4992	93	3	is	be	AUX
ejpam-4992	93	4	bounded	bound	VERB
ejpam-4992	93	5	in	in	ADP
ejpam-4992	93	6	e	e	NOUN
ejpam-4992	93	7	,	,	PUNCT
ejpam-4992	93	8	then	then	ADV
ejpam-4992	93	9	there	there	PRON
ejpam-4992	93	10	exists	exist	VERB
ejpam-4992	93	11	ρ	ρ	PROPN
ejpam-4992	93	12	>	>	X
ejpam-4992	93	13	0	0	NUM
ejpam-4992	93	14	,	,	PUNCT
ejpam-4992	93	15	so	so	SCONJ
ejpam-4992	93	16	that	that	SCONJ
ejpam-4992	93	17	pm	pm	NOUN
ejpam-4992	93	18	(	(	PUNCT
ejpam-4992	93	19	xk	xk	NOUN
ejpam-4992	93	20	)	)	PUNCT
ejpam-4992	93	21	≤	≤	NOUN
ejpam-4992	93	22	ρ	ρ	NOUN
ejpam-4992	93	23	for	for	ADP
ejpam-4992	93	24	every	every	DET
ejpam-4992	93	25	k	k	PROPN
ejpam-4992	93	26	∈	∈	PROPN
ejpam-4992	93	27	n	n	CCONJ
ejpam-4992	93	28	;	;	PUNCT
ejpam-4992	93	29	and	and	CCONJ
ejpam-4992	93	30	,	,	PUNCT
ejpam-4992	93	31	by	by	ADP
ejpam-4992	93	32	the	the	DET
ejpam-4992	93	33	definition	definition	NOUN
ejpam-4992	93	34	of	of	ADP
ejpam-4992	93	35	σm	σm	X
ejpam-4992	93	36	,	,	PUNCT
ejpam-4992	93	37	one	one	PRON
ejpam-4992	93	38	has	have	VERB
ejpam-4992	93	39	σm	σm	X
ejpam-4992	93	40	(	(	PUNCT
ejpam-4992	93	41	βkxk	βkxk	ADJ
ejpam-4992	93	42	)	)	PUNCT
ejpam-4992	93	43	≤	≤	NOUN
ejpam-4992	93	44	ρ	ρ	PROPN
ejpam-4992	93	45	,	,	PUNCT
ejpam-4992	93	46	for	for	ADP
ejpam-4992	93	47	every	every	DET
ejpam-4992	93	48	k	k	PROPN
ejpam-4992	93	49	∈	∈	PROPN
ejpam-4992	93	50	n.	n.	NOUN
ejpam-4992	93	51	moreover	moreover	ADV
ejpam-4992	93	52	,	,	PUNCT
ejpam-4992	93	53	if	if	SCONJ
ejpam-4992	93	54	(	(	PUNCT
ejpam-4992	93	55	ξk)k	ξk)k	NOUN
ejpam-4992	93	56	satisfies	satisfy	VERB
ejpam-4992	93	57	∑∞	∑∞	X
ejpam-4992	93	58	k=1	k=1	X
ejpam-4992	93	59	|ξk|	|ξk|	VERB
ejpam-4992	93	60	≤	≤	NUM
ejpam-4992	93	61	1	1	NUM
ejpam-4992	93	62	then	then	ADV
ejpam-4992	93	63	,	,	PUNCT
ejpam-4992	93	64	∞∑	∞∑	ADJ
ejpam-4992	93	65	k=1	k=1	PUNCT
ejpam-4992	93	66	σm	σm	INTJ
ejpam-4992	93	67	(	(	PUNCT
ejpam-4992	93	68	ξkβ	ξkβ	VERB
ejpam-4992	93	69	kxk	kxk	PROPN
ejpam-4992	93	70	)	)	PUNCT
ejpam-4992	93	71	≤	≤	NOUN
ejpam-4992	94	1	∞∑	∞∑	NUM
ejpam-4992	94	2	k=1	k=1	ADJ
ejpam-4992	94	3	|ξk|∥βk∥λpm	|ξk|∥βk∥λpm	X
ejpam-4992	94	4	(	(	PUNCT
ejpam-4992	94	5	xk	xk	NOUN
ejpam-4992	94	6	)	)	PUNCT
ejpam-4992	94	7	≤	≤	NOUN
ejpam-4992	94	8	ρ	ρ	NUM
ejpam-4992	94	9	∞∑	∞∑	NUM
ejpam-4992	94	10	k=1	k=1	ADP
ejpam-4992	94	11	|ξk|	|ξk|	NOUN
ejpam-4992	94	12	≤	≤	NUM
ejpam-4992	94	13	ρ	ρ	NOUN
ejpam-4992	94	14	.	.	PUNCT
ejpam-4992	95	1	(	(	PUNCT
ejpam-4992	95	2	3	3	X
ejpam-4992	95	3	)	)	PUNCT
ejpam-4992	95	4	by	by	ADP
ejpam-4992	95	5	lemma	lemma	PROPN
ejpam-4992	95	6	2	2	NUM
ejpam-4992	95	7	,	,	PUNCT
ejpam-4992	95	8	the	the	DET
ejpam-4992	95	9	terms	term	NOUN
ejpam-4992	95	10	of	of	ADP
ejpam-4992	95	11	the	the	DET
ejpam-4992	95	12	series	series	NOUN
ejpam-4992	95	13	∑∞	∑∞	PROPN
ejpam-4992	95	14	k=1	k=1	X
ejpam-4992	95	15	ξkβ	ξkβ	VERB
ejpam-4992	95	16	kxk	kxk	PROPN
ejpam-4992	95	17	belong	belong	VERB
ejpam-4992	95	18	to	to	ADP
ejpam-4992	95	19	λ⟨e⟩.	λ⟨e⟩.	PROPN
ejpam-4992	95	20	since	since	SCONJ
ejpam-4992	95	21	λ⟨e⟩	λ⟨e⟩	PROPN
ejpam-4992	95	22	is	be	AUX
ejpam-4992	95	23	sequentially	sequentially	ADV
ejpam-4992	95	24	complete	complete	ADJ
ejpam-4992	95	25	,	,	PUNCT
ejpam-4992	95	26	we	we	PRON
ejpam-4992	95	27	derive	derive	VERB
ejpam-4992	95	28	from	from	ADP
ejpam-4992	95	29	(	(	PUNCT
ejpam-4992	95	30	3	3	NUM
ejpam-4992	95	31	)	)	PUNCT
ejpam-4992	95	32	that	that	SCONJ
ejpam-4992	95	33	this	this	DET
ejpam-4992	95	34	series	series	NOUN
ejpam-4992	95	35	is	be	AUX
ejpam-4992	95	36	convergent	convergent	ADJ
ejpam-4992	95	37	in	in	ADP
ejpam-4992	95	38	λ⟨e⟩	λ⟨e⟩	PROPN
ejpam-4992	95	39	and	and	CCONJ
ejpam-4992	95	40	that	that	SCONJ
ejpam-4992	95	41	the	the	DET
ejpam-4992	95	42	corresponding	correspond	VERB
ejpam-4992	95	43	set	set	NOUN
ejpam-4992	95	44	b̄	b̄	NOUN
ejpam-4992	95	45	in	in	ADP
ejpam-4992	95	46	(	(	PUNCT
ejpam-4992	95	47	2	2	NUM
ejpam-4992	95	48	)	)	PUNCT
ejpam-4992	95	49	is	be	AUX
ejpam-4992	95	50	well	well	ADV
ejpam-4992	95	51	defined	define	VERB
ejpam-4992	95	52	,	,	PUNCT
ejpam-4992	95	53	contained	contain	VERB
ejpam-4992	95	54	and	and	CCONJ
ejpam-4992	95	55	bounded	bound	VERB
ejpam-4992	95	56	in	in	ADP
ejpam-4992	95	57	λ⟨e⟩.	λ⟨e⟩.	PROPN
ejpam-4992	95	58	■	■	PUNCT
ejpam-4992	95	59	m.	m.	NOUN
ejpam-4992	95	60	a.	a.	NOUN
ejpam-4992	95	61	sidaty	sidaty	PROPN
ejpam-4992	95	62	/	/	SYM
ejpam-4992	95	63	eur	eur	PROPN
ejpam-4992	95	64	.	.	PUNCT
ejpam-4992	96	1	j.	j.	PROPN
ejpam-4992	96	2	pure	pure	PROPN
ejpam-4992	96	3	appl	appl	PROPN
ejpam-4992	96	4	.	.	PROPN
ejpam-4992	96	5	math	math	PROPN
ejpam-4992	96	6	,	,	PUNCT
ejpam-4992	96	7	17	17	NUM
ejpam-4992	96	8	(	(	PUNCT
ejpam-4992	96	9	1	1	NUM
ejpam-4992	96	10	)	)	PUNCT
ejpam-4992	96	11	(	(	PUNCT
ejpam-4992	96	12	2024	2024	NUM
ejpam-4992	96	13	)	)	PUNCT
ejpam-4992	96	14	,	,	PUNCT
ejpam-4992	96	15	171	171	NUM
ejpam-4992	96	16	-	-	SYM
ejpam-4992	96	17	179	179	NUM
ejpam-4992	96	18	175	175	NUM
ejpam-4992	96	19	3	3	NUM
ejpam-4992	96	20	.	.	PUNCT
ejpam-4992	97	1	köthe	köthe	DET
ejpam-4992	97	2	duals	dual	NOUN
ejpam-4992	97	3	of	of	ADP
ejpam-4992	97	4	λ(e	λ(e	NOUN
ejpam-4992	97	5	)	)	PUNCT
ejpam-4992	97	6	and	and	CCONJ
ejpam-4992	97	7	λ⟨e⟩	λ⟨e⟩	PROPN
ejpam-4992	97	8	following	follow	VERB
ejpam-4992	97	9	[	[	X
ejpam-4992	97	10	4	4	NUM
ejpam-4992	97	11	]	]	PUNCT
ejpam-4992	97	12	,	,	PUNCT
ejpam-4992	97	13	if	if	SCONJ
ejpam-4992	97	14	f	f	PROPN
ejpam-4992	97	15	is	be	AUX
ejpam-4992	97	16	a	a	DET
ejpam-4992	97	17	linear	linear	ADJ
ejpam-4992	97	18	subspace	subspace	NOUN
ejpam-4992	97	19	of	of	ADP
ejpam-4992	97	20	en	en	X
ejpam-4992	97	21	,	,	PUNCT
ejpam-4992	97	22	the	the	DET
ejpam-4992	97	23	generalized	generalize	VERB
ejpam-4992	97	24	köthe	köthe	NOUN
ejpam-4992	97	25	dual	dual	ADJ
ejpam-4992	97	26	of	of	ADP
ejpam-4992	97	27	f	f	PROPN
ejpam-4992	97	28	is	be	AUX
ejpam-4992	97	29	defined	define	VERB
ejpam-4992	97	30	by	by	ADP
ejpam-4992	97	31	f	f	PROPN
ejpam-4992	97	32	∗	∗	NOUN
ejpam-4992	97	33	=	=	SYM
ejpam-4992	97	34	{	{	PUNCT
ejpam-4992	97	35	(	(	PUNCT
ejpam-4992	97	36	an)n	an)n	PROPN
ejpam-4992	97	37	⊂	⊂	PROPN
ejpam-4992	97	38	e′	e′	PROPN
ejpam-4992	97	39	:	:	PUNCT
ejpam-4992	97	40	∑	∑	PUNCT
ejpam-4992	97	41	|an(xn)|	|an(xn)|	NOUN
ejpam-4992	97	42	converges	converge	VERB
ejpam-4992	97	43	for	for	ADP
ejpam-4992	97	44	all	all	PRON
ejpam-4992	97	45	x	x	PUNCT
ejpam-4992	97	46	=	=	SYM
ejpam-4992	97	47	(	(	PUNCT
ejpam-4992	97	48	xn)n	xn)n	PROPN
ejpam-4992	97	49	∈	∈	PROPN
ejpam-4992	97	50	f	f	PROPN
ejpam-4992	97	51	}	}	PUNCT
ejpam-4992	97	52	.	.	PUNCT
ejpam-4992	98	1	for	for	ADP
ejpam-4992	98	2	every	every	DET
ejpam-4992	98	3	x	x	SYM
ejpam-4992	98	4	∈	∈	PROPN
ejpam-4992	98	5	e	e	NOUN
ejpam-4992	98	6	,	,	PUNCT
ejpam-4992	98	7	denote	denote	VERB
ejpam-4992	98	8	by	by	ADP
ejpam-4992	98	9	δx	δx	ADP
ejpam-4992	98	10	the	the	DET
ejpam-4992	98	11	evaluation	evaluation	NOUN
ejpam-4992	98	12	defined	define	VERB
ejpam-4992	98	13	,	,	PUNCT
ejpam-4992	98	14	as	as	ADP
ejpam-4992	98	15	in	in	ADP
ejpam-4992	98	16	the	the	DET
ejpam-4992	98	17	proof	proof	NOUN
ejpam-4992	98	18	of	of	ADP
ejpam-4992	98	19	lemma	lemma	PROPN
ejpam-4992	98	20	2	2	NUM
ejpam-4992	98	21	,	,	PUNCT
ejpam-4992	98	22	by	by	ADP
ejpam-4992	98	23	δx(x	δx(x	NUM
ejpam-4992	98	24	′	′	NUM
ejpam-4992	98	25	)	)	PUNCT
ejpam-4992	98	26	=	=	SYM
ejpam-4992	99	1	x′(x	x′(x	X
ejpam-4992	99	2	)	)	PUNCT
ejpam-4992	99	3	,	,	PUNCT
ejpam-4992	99	4	for	for	ADP
ejpam-4992	99	5	x′	x′	PROPN
ejpam-4992	99	6	∈	∈	PROPN
ejpam-4992	99	7	e′.	e′.	ADJ
ejpam-4992	99	8	thanks	thank	NOUN
ejpam-4992	99	9	to	to	ADP
ejpam-4992	99	10	the	the	DET
ejpam-4992	99	11	linear	linear	ADJ
ejpam-4992	99	12	and	and	CCONJ
ejpam-4992	99	13	isometric	isometric	ADJ
ejpam-4992	99	14	map	map	NOUN
ejpam-4992	99	15	δ	δ	NOUN
ejpam-4992	99	16	:	:	PUNCT
ejpam-4992	99	17	x	x	X
ejpam-4992	99	18	→	→	SYM
ejpam-4992	99	19	δx	δx	NOUN
ejpam-4992	99	20	from	from	ADP
ejpam-4992	99	21	e	e	PROPN
ejpam-4992	99	22	to	to	ADP
ejpam-4992	99	23	e′′	e′′	PROPN
ejpam-4992	99	24	,	,	PUNCT
ejpam-4992	99	25	we	we	PRON
ejpam-4992	99	26	always	always	ADV
ejpam-4992	99	27	have	have	VERB
ejpam-4992	99	28	f	f	PROPN
ejpam-4992	99	29	⊂	⊂	PROPN
ejpam-4992	99	30	f	f	PROPN
ejpam-4992	99	31	∗∗.	∗∗.	VERB
ejpam-4992	99	32	the	the	DET
ejpam-4992	99	33	sequence	sequence	NOUN
ejpam-4992	99	34	space	space	NOUN
ejpam-4992	99	35	f	f	PROPN
ejpam-4992	99	36	is	be	AUX
ejpam-4992	99	37	said	say	VERB
ejpam-4992	99	38	to	to	PART
ejpam-4992	99	39	be	be	AUX
ejpam-4992	99	40	perfect	perfect	ADJ
ejpam-4992	99	41	if	if	SCONJ
ejpam-4992	99	42	f	f	PROPN
ejpam-4992	99	43	∗∗	∗∗	PROPN
ejpam-4992	99	44	=	=	SYM
ejpam-4992	99	45	f	f	PROPN
ejpam-4992	99	46	.	.	PUNCT
ejpam-4992	100	1	proposition	proposition	NOUN
ejpam-4992	100	2	4	4	NUM
ejpam-4992	100	3	.	.	PUNCT
ejpam-4992	101	1	let	let	VERB
ejpam-4992	101	2	λ	λ	PRON
ejpam-4992	101	3	be	be	AUX
ejpam-4992	101	4	a	a	DET
ejpam-4992	101	5	perfect	perfect	ADJ
ejpam-4992	101	6	normed	normed	ADJ
ejpam-4992	101	7	sequence	sequence	NOUN
ejpam-4992	101	8	space	space	NOUN
ejpam-4992	101	9	with	with	ADP
ejpam-4992	101	10	dual	dual	ADJ
ejpam-4992	101	11	space	space	NOUN
ejpam-4992	101	12	λ∗	λ∗	NOUN
ejpam-4992	101	13	and	and	CCONJ
ejpam-4992	101	14	e	e	X
ejpam-4992	101	15	a	a	DET
ejpam-4992	101	16	locally	locally	ADV
ejpam-4992	101	17	convex	convex	ADJ
ejpam-4992	101	18	space	space	NOUN
ejpam-4992	101	19	.	.	PUNCT
ejpam-4992	102	1	then	then	ADV
ejpam-4992	102	2	(	(	PUNCT
ejpam-4992	102	3	λ(e)r	λ(e)r	ADJ
ejpam-4992	102	4	)	)	PUNCT
ejpam-4992	102	5	∗	∗	NOUN
ejpam-4992	102	6	=	=	SYM
ejpam-4992	102	7	(	(	PUNCT
ejpam-4992	102	8	λ(e))∗	λ(e))∗	PROPN
ejpam-4992	102	9	and	and	CCONJ
ejpam-4992	102	10	(	(	PUNCT
ejpam-4992	102	11	λ⟨e⟩r)∗	λ⟨e⟩r)∗	PUNCT
ejpam-4992	102	12	=	=	SYM
ejpam-4992	102	13	(	(	PUNCT
ejpam-4992	102	14	λ⟨e⟩)∗.	λ⟨e⟩)∗.	NOUN
ejpam-4992	102	15	proof	proof	NOUN
ejpam-4992	102	16	.	.	PUNCT
ejpam-4992	103	1	we	we	PRON
ejpam-4992	103	2	prove	prove	VERB
ejpam-4992	103	3	that	that	SCONJ
ejpam-4992	103	4	(	(	PUNCT
ejpam-4992	103	5	λ(e)r	λ(e)r	ADJ
ejpam-4992	103	6	)	)	PUNCT
ejpam-4992	103	7	∗	∗	NOUN
ejpam-4992	103	8	=	=	SYM
ejpam-4992	103	9	(	(	PUNCT
ejpam-4992	103	10	λ(e))∗	λ(e))∗	PROPN
ejpam-4992	103	11	,	,	PUNCT
ejpam-4992	103	12	the	the	DET
ejpam-4992	103	13	same	same	ADJ
ejpam-4992	103	14	argument	argument	NOUN
ejpam-4992	103	15	applies	apply	VERB
ejpam-4992	103	16	for	for	ADP
ejpam-4992	103	17	the	the	DET
ejpam-4992	103	18	second	second	ADJ
ejpam-4992	103	19	equality	equality	NOUN
ejpam-4992	103	20	.	.	PUNCT
ejpam-4992	104	1	it	it	PRON
ejpam-4992	104	2	is	be	AUX
ejpam-4992	104	3	clear	clear	ADJ
ejpam-4992	104	4	that	that	SCONJ
ejpam-4992	104	5	(	(	PUNCT
ejpam-4992	104	6	λ(e))∗	λ(e))∗	PROPN
ejpam-4992	104	7	⊂	⊂	PROPN
ejpam-4992	104	8	(	(	PUNCT
ejpam-4992	104	9	λ(e)r	λ(e)r	PROPN
ejpam-4992	104	10	)	)	PUNCT
ejpam-4992	104	11	∗.	∗.	PROPN
ejpam-4992	104	12	let	let	VERB
ejpam-4992	104	13	a	a	DET
ejpam-4992	104	14	=	=	PUNCT
ejpam-4992	104	15	(	(	PUNCT
ejpam-4992	104	16	an)n	an)n	PROPN
ejpam-4992	104	17	∈	∈	PROPN
ejpam-4992	104	18	(	(	PUNCT
ejpam-4992	104	19	λ(e)r	λ(e)r	ADJ
ejpam-4992	104	20	)	)	PUNCT
ejpam-4992	104	21	∗	∗	NOUN
ejpam-4992	104	22	and	and	CCONJ
ejpam-4992	104	23	x	x	SYM
ejpam-4992	104	24	=	=	SYM
ejpam-4992	104	25	(	(	PUNCT
ejpam-4992	104	26	xn)n	xn)n	PROPN
ejpam-4992	104	27	∈	∈	PROPN
ejpam-4992	104	28	λ(e	λ(e	PROPN
ejpam-4992	104	29	)	)	PUNCT
ejpam-4992	104	30	.	.	PUNCT
ejpam-4992	105	1	to	to	PART
ejpam-4992	105	2	prove	prove	VERB
ejpam-4992	105	3	that	that	DET
ejpam-4992	105	4	∑∞	∑∞	NOUN
ejpam-4992	105	5	n=1	n=1	SCONJ
ejpam-4992	105	6	|an(xn)|	|an(xn)|	NOUN
ejpam-4992	105	7	converges	converge	VERB
ejpam-4992	105	8	,	,	PUNCT
ejpam-4992	105	9	it	it	PRON
ejpam-4992	105	10	is	be	AUX
ejpam-4992	105	11	enough	enough	ADJ
ejpam-4992	105	12	to	to	PART
ejpam-4992	105	13	prove	prove	VERB
ejpam-4992	105	14	that	that	SCONJ
ejpam-4992	105	15	,	,	PUNCT
ejpam-4992	105	16	for	for	ADP
ejpam-4992	105	17	every	every	DET
ejpam-4992	105	18	(	(	PUNCT
ejpam-4992	105	19	γn)n	γn)n	PROPN
ejpam-4992	105	20	∈	∈	PROPN
ejpam-4992	105	21	c0	c0	NOUN
ejpam-4992	105	22	,	,	PUNCT
ejpam-4992	105	23	the	the	DET
ejpam-4992	105	24	series	series	PROPN
ejpam-4992	105	25	∑∞	∑∞	PROPN
ejpam-4992	105	26	n=1	n=1	ADP
ejpam-4992	105	27	|γnan(xn)|	|γnan(xn)|	NOUN
ejpam-4992	105	28	converges	converge	VERB
ejpam-4992	105	29	.	.	PUNCT
ejpam-4992	106	1	set	set	VERB
ejpam-4992	106	2	y	y	PROPN
ejpam-4992	106	3	=	=	PUNCT
ejpam-4992	106	4	(	(	PUNCT
ejpam-4992	106	5	yn)n	yn)n	PROPN
ejpam-4992	106	6	where	where	SCONJ
ejpam-4992	106	7	yn	yn	PROPN
ejpam-4992	106	8	=	=	SYM
ejpam-4992	106	9	γnxn	γnxn	PROPN
ejpam-4992	106	10	,	,	PUNCT
ejpam-4992	106	11	for	for	ADP
ejpam-4992	106	12	all	all	PRON
ejpam-4992	106	13	n	n	DET
ejpam-4992	106	14	∈	∈	PROPN
ejpam-4992	106	15	n.	n.	NOUN
ejpam-4992	106	16	we	we	PRON
ejpam-4992	106	17	see	see	VERB
ejpam-4992	106	18	that	that	SCONJ
ejpam-4992	106	19	y	y	PROPN
ejpam-4992	106	20	∈	∈	PROPN
ejpam-4992	106	21	λ(e	λ(e	PROPN
ejpam-4992	106	22	)	)	PUNCT
ejpam-4992	106	23	.	.	PUNCT
ejpam-4992	107	1	in	in	ADP
ejpam-4992	107	2	the	the	DET
ejpam-4992	107	3	other	other	ADJ
ejpam-4992	107	4	hand	hand	NOUN
ejpam-4992	107	5	,	,	PUNCT
ejpam-4992	107	6	for	for	ADP
ejpam-4992	107	7	m	m	PROPN
ejpam-4992	107	8	∈	∈	PROPN
ejpam-4992	107	9	m	m	PROPN
ejpam-4992	107	10	,	,	PUNCT
ejpam-4992	107	11	a	a	DET
ejpam-4992	107	12	∈	∈	NOUN
ejpam-4992	107	13	m	m	NOUN
ejpam-4992	107	14	,	,	PUNCT
ejpam-4992	107	15	α	α	X
ejpam-4992	107	16	=	=	PUNCT
ejpam-4992	107	17	(	(	PUNCT
ejpam-4992	107	18	αn)n	αn)n	NOUN
ejpam-4992	107	19	∈	∈	NOUN
ejpam-4992	107	20	bλ∗	bλ∗	NOUN
ejpam-4992	107	21	and	and	CCONJ
ejpam-4992	107	22	p	p	NOUN
ejpam-4992	107	23	∈	∈	PROPN
ejpam-4992	107	24	n	n	CCONJ
ejpam-4992	107	25	,	,	PUNCT
ejpam-4992	107	26	one	one	PRON
ejpam-4992	107	27	has	have	VERB
ejpam-4992	107	28	∞∑	∞∑	NUM
ejpam-4992	107	29	n	n	CCONJ
ejpam-4992	107	30	=	=	NOUN
ejpam-4992	107	31	p+1	p+1	PRON
ejpam-4992	107	32	|αna	|αna	PROPN
ejpam-4992	107	33	(	(	PUNCT
ejpam-4992	107	34	γnxn)|	γnxn)|	X
ejpam-4992	107	35	≤	≤	NUM
ejpam-4992	107	36	sup	sup	NOUN
ejpam-4992	107	37	n≥p+1	n≥p+1	NOUN
ejpam-4992	107	38	|γn|	|γn|	NOUN
ejpam-4992	108	1	∞∑	∞∑	NUM
ejpam-4992	108	2	n	n	CCONJ
ejpam-4992	108	3	=	=	PROPN
ejpam-4992	108	4	p+1	p+1	PRON
ejpam-4992	108	5	|αna	|αna	PROPN
ejpam-4992	108	6	(	(	PUNCT
ejpam-4992	108	7	xn)|	xn)|	PROPN
ejpam-4992	108	8	≤	≤	PROPN
ejpam-4992	108	9	∥γ	∥γ	PROPN
ejpam-4992	108	10	<	<	X
ejpam-4992	108	11	p>∥c0ϵm	p>∥c0ϵm	NOUN
ejpam-4992	108	12	(	(	PUNCT
ejpam-4992	108	13	x	x	NOUN
ejpam-4992	108	14	)	)	PUNCT
ejpam-4992	108	15	.	.	PUNCT
ejpam-4992	109	1	this	this	PRON
ejpam-4992	109	2	shows	show	VERB
ejpam-4992	109	3	that	that	SCONJ
ejpam-4992	109	4	ϵm	ϵm	PROPN
ejpam-4992	110	1	(	(	PUNCT
ejpam-4992	110	2	y	y	X
ejpam-4992	110	3	<	<	X
ejpam-4992	110	4	p	p	X
ejpam-4992	110	5	>	>	NOUN
ejpam-4992	110	6	)	)	PUNCT
ejpam-4992	110	7	≤	≤	PUNCT
ejpam-4992	111	1	∥γ	∥γ	PROPN
ejpam-4992	111	2	<	<	X
ejpam-4992	111	3	p>∥c0ϵm	p>∥c0ϵm	NOUN
ejpam-4992	111	4	(	(	PUNCT
ejpam-4992	111	5	x	x	NOUN
ejpam-4992	111	6	)	)	PUNCT
ejpam-4992	111	7	,	,	PUNCT
ejpam-4992	111	8	and	and	CCONJ
ejpam-4992	111	9	then	then	ADV
ejpam-4992	111	10	y	y	PROPN
ejpam-4992	111	11	∈	∈	PROPN
ejpam-4992	111	12	λ(e)r	λ(e)r	PROPN
ejpam-4992	111	13	since	since	SCONJ
ejpam-4992	111	14	(	(	PUNCT
ejpam-4992	111	15	γ	γ	X
ejpam-4992	111	16	<	<	X
ejpam-4992	111	17	p>)p	p>)p	PROPN
ejpam-4992	111	18	converges	converge	VERB
ejpam-4992	111	19	to	to	ADP
ejpam-4992	111	20	0	0	NUM
ejpam-4992	111	21	.	.	PUNCT
ejpam-4992	112	1	now	now	ADV
ejpam-4992	112	2	,	,	PUNCT
ejpam-4992	112	3	we	we	PRON
ejpam-4992	112	4	have	have	VERB
ejpam-4992	112	5	∞∑	∞∑	NUM
ejpam-4992	112	6	n=1	n=1	PROPN
ejpam-4992	112	7	|γnan(xn)|	|γnan(xn)|	NOUN
ejpam-4992	112	8	=	=	SYM
ejpam-4992	113	1	∞∑	∞∑	NUM
ejpam-4992	113	2	n=1	n=1	ADJ
ejpam-4992	113	3	|an(γnxn)|	|an(γnxn)|	NOUN
ejpam-4992	113	4	=	=	PUNCT
ejpam-4992	113	5	∞∑	∞∑	NUM
ejpam-4992	113	6	n=1	n=1	PROPN
ejpam-4992	113	7	|an(yn)|	|an(yn)|	VERB
ejpam-4992	113	8	<	<	X
ejpam-4992	113	9	∞.	∞.	PROPN
ejpam-4992	113	10	this	this	PRON
ejpam-4992	113	11	completes	complete	VERB
ejpam-4992	113	12	the	the	DET
ejpam-4992	113	13	proof	proof	NOUN
ejpam-4992	113	14	.	.	PUNCT
ejpam-4992	114	1	■	■	PUNCT
ejpam-4992	114	2	according	accord	VERB
ejpam-4992	114	3	to	to	ADP
ejpam-4992	114	4	[	[	X
ejpam-4992	114	5	7	7	NUM
ejpam-4992	114	6	,	,	PUNCT
ejpam-4992	114	7	theorem	theorem	VERB
ejpam-4992	114	8	7	7	NUM
ejpam-4992	114	9	]	]	PUNCT
ejpam-4992	114	10	,	,	PUNCT
ejpam-4992	114	11	the	the	DET
ejpam-4992	114	12	continuous	continuous	ADJ
ejpam-4992	114	13	dual	dual	ADJ
ejpam-4992	114	14	λ(e)r	λ(e)r	PROPN
ejpam-4992	114	15	of	of	ADP
ejpam-4992	114	16	(	(	PUNCT
ejpam-4992	114	17	λ(e)r	λ(e)r	ADJ
ejpam-4992	114	18	)	)	PUNCT
ejpam-4992	114	19	′	′	NUM
ejpam-4992	114	20	is	be	AUX
ejpam-4992	114	21	given	give	VERB
ejpam-4992	114	22	by	by	ADP
ejpam-4992	114	23	(	(	PUNCT
ejpam-4992	114	24	λ(e)r	λ(e)r	ADJ
ejpam-4992	114	25	)	)	PUNCT
ejpam-4992	114	26	′	′	NOUN
ejpam-4992	115	1	=	=	PUNCT
ejpam-4992	115	2	⋃	⋃	NOUN
ejpam-4992	115	3	m∈m	m∈m	NOUN
ejpam-4992	115	4	λ∗⟨e′	λ∗⟨e′	PROPN
ejpam-4992	115	5	m	m	NOUN
ejpam-4992	115	6	⟩.	⟩.	PROPN
ejpam-4992	115	7	in	in	ADP
ejpam-4992	115	8	particular	particular	ADJ
ejpam-4992	115	9	,	,	PUNCT
ejpam-4992	115	10	if	if	SCONJ
ejpam-4992	115	11	λ	λ	PROPN
ejpam-4992	115	12	and	and	CCONJ
ejpam-4992	115	13	e	e	NOUN
ejpam-4992	115	14	are	be	AUX
ejpam-4992	115	15	banach	banach	NOUN
ejpam-4992	115	16	spaces	space	NOUN
ejpam-4992	115	17	then	then	ADV
ejpam-4992	115	18	(	(	PUNCT
ejpam-4992	115	19	λ(e)r	λ(e)r	ADJ
ejpam-4992	115	20	)	)	PUNCT
ejpam-4992	115	21	′	′	NOUN
ejpam-4992	116	1	=	=	PUNCT
ejpam-4992	116	2	λ∗⟨e′⟩.	λ∗⟨e′⟩.	NOUN
ejpam-4992	116	3	(	(	PUNCT
ejpam-4992	116	4	4	4	X
ejpam-4992	116	5	)	)	PUNCT
ejpam-4992	116	6	the	the	DET
ejpam-4992	116	7	last	last	ADJ
ejpam-4992	116	8	equality	equality	NOUN
ejpam-4992	116	9	is	be	AUX
ejpam-4992	116	10	actually	actually	ADV
ejpam-4992	116	11	topological	topological	ADJ
ejpam-4992	116	12	,	,	PUNCT
ejpam-4992	116	13	by	by	ADP
ejpam-4992	116	14	(	(	PUNCT
ejpam-4992	116	15	[	[	X
ejpam-4992	116	16	6	6	NUM
ejpam-4992	116	17	,	,	PUNCT
ejpam-4992	116	18	15.12(2	15.12(2	NUM
ejpam-4992	116	19	)	)	PUNCT
ejpam-4992	116	20	]	]	PUNCT
ejpam-4992	116	21	)	)	PUNCT
ejpam-4992	116	22	.	.	PUNCT
ejpam-4992	117	1	proposition	proposition	NOUN
ejpam-4992	117	2	5	5	NUM
ejpam-4992	117	3	.	.	PUNCT
ejpam-4992	118	1	for	for	ADP
ejpam-4992	118	2	every	every	DET
ejpam-4992	118	3	banach	banach	NOUN
ejpam-4992	118	4	space	space	NOUN
ejpam-4992	118	5	e	e	NOUN
ejpam-4992	118	6	,	,	PUNCT
ejpam-4992	118	7	we	we	PRON
ejpam-4992	118	8	have	have	VERB
ejpam-4992	118	9	(	(	PUNCT
ejpam-4992	118	10	a	a	X
ejpam-4992	118	11	)	)	PUNCT
ejpam-4992	118	12	the	the	DET
ejpam-4992	118	13	köthe	köthe	PROPN
ejpam-4992	118	14	dual	dual	ADJ
ejpam-4992	118	15	of	of	ADP
ejpam-4992	118	16	(	(	PUNCT
ejpam-4992	118	17	λ(e))∗	λ(e))∗	PROPN
ejpam-4992	118	18	satisfies	satisfy	VERB
ejpam-4992	118	19	(	(	PUNCT
ejpam-4992	118	20	λ(e))∗	λ(e))∗	PROPN
ejpam-4992	118	21	=	=	SYM
ejpam-4992	118	22	λ∗⟨e′⟩	λ∗⟨e′⟩	PROPN
ejpam-4992	118	23	=	=	SYM
ejpam-4992	118	24	(	(	PUNCT
ejpam-4992	118	25	λ(e)r	λ(e)r	ADJ
ejpam-4992	118	26	)	)	PUNCT
ejpam-4992	118	27	′	′	NOUN
ejpam-4992	118	28	,	,	PUNCT
ejpam-4992	118	29	(	(	PUNCT
ejpam-4992	118	30	b	b	X
ejpam-4992	118	31	)	)	PUNCT
ejpam-4992	118	32	the	the	DET
ejpam-4992	118	33	köthe	köthe	PROPN
ejpam-4992	118	34	dual	dual	ADJ
ejpam-4992	118	35	of	of	ADP
ejpam-4992	118	36	(	(	PUNCT
ejpam-4992	118	37	λ(e))∗	λ(e))∗	PROPN
ejpam-4992	118	38	satisfies	satisfie	NOUN
ejpam-4992	118	39	(	(	PUNCT
ejpam-4992	118	40	λ(e))∗∗	λ(e))∗∗	X
ejpam-4992	118	41	=	=	SYM
ejpam-4992	118	42	λ(e′′	λ(e′′	PROPN
ejpam-4992	118	43	)	)	PUNCT
ejpam-4992	118	44	.	.	PUNCT
ejpam-4992	119	1	in	in	ADP
ejpam-4992	119	2	particular	particular	ADJ
ejpam-4992	119	3	,	,	PUNCT
ejpam-4992	119	4	if	if	SCONJ
ejpam-4992	119	5	e	e	NOUN
ejpam-4992	119	6	is	be	AUX
ejpam-4992	119	7	reflexive	reflexive	ADJ
ejpam-4992	119	8	then	then	ADV
ejpam-4992	119	9	(	(	PUNCT
ejpam-4992	119	10	λ(e))∗∗	λ(e))∗∗	X
ejpam-4992	119	11	=	=	SYM
ejpam-4992	119	12	λ(e	λ(e	PROPN
ejpam-4992	119	13	)	)	PUNCT
ejpam-4992	119	14	.	.	PUNCT
ejpam-4992	120	1	m.	m.	NOUN
ejpam-4992	120	2	a.	a.	PROPN
ejpam-4992	120	3	sidaty	sidaty	PROPN
ejpam-4992	120	4	/	/	SYM
ejpam-4992	120	5	eur	eur	PROPN
ejpam-4992	120	6	.	.	PUNCT
ejpam-4992	121	1	j.	j.	PROPN
ejpam-4992	121	2	pure	pure	PROPN
ejpam-4992	121	3	appl	appl	PROPN
ejpam-4992	121	4	.	.	PROPN
ejpam-4992	121	5	math	math	PROPN
ejpam-4992	121	6	,	,	PUNCT
ejpam-4992	121	7	17	17	NUM
ejpam-4992	121	8	(	(	PUNCT
ejpam-4992	121	9	1	1	NUM
ejpam-4992	121	10	)	)	PUNCT
ejpam-4992	121	11	(	(	PUNCT
ejpam-4992	121	12	2024	2024	NUM
ejpam-4992	121	13	)	)	PUNCT
ejpam-4992	121	14	,	,	PUNCT
ejpam-4992	121	15	171	171	NUM
ejpam-4992	121	16	-	-	SYM
ejpam-4992	121	17	179	179	NUM
ejpam-4992	122	1	176	176	NUM
ejpam-4992	122	2	proof	proof	NOUN
ejpam-4992	122	3	.	.	PUNCT
ejpam-4992	123	1	by	by	ADP
ejpam-4992	123	2	the	the	DET
ejpam-4992	123	3	definition	definition	NOUN
ejpam-4992	123	4	of	of	ADP
ejpam-4992	123	5	the	the	DET
ejpam-4992	123	6	spaces	space	NOUN
ejpam-4992	123	7	λ∗⟨e′⟩	λ∗⟨e′⟩	PROPN
ejpam-4992	123	8	and	and	CCONJ
ejpam-4992	123	9	(	(	PUNCT
ejpam-4992	123	10	λ(e))∗	λ(e))∗	PROPN
ejpam-4992	123	11	,	,	PUNCT
ejpam-4992	123	12	we	we	PRON
ejpam-4992	123	13	have	have	VERB
ejpam-4992	123	14	λ∗⟨e′⟩	λ∗⟨e′⟩	PROPN
ejpam-4992	123	15	⊂	⊂	X
ejpam-4992	123	16	(	(	PUNCT
ejpam-4992	123	17	λ(e))∗.	λ(e))∗.	NOUN
ejpam-4992	123	18	let	let	VERB
ejpam-4992	123	19	a	a	PRON
ejpam-4992	123	20	=	=	PUNCT
ejpam-4992	123	21	(	(	PUNCT
ejpam-4992	123	22	an)n	an)n	PROPN
ejpam-4992	123	23	∈	∈	PROPN
ejpam-4992	123	24	(	(	PUNCT
ejpam-4992	123	25	λ(e))∗.	λ(e))∗.	NOUN
ejpam-4992	123	26	using	use	VERB
ejpam-4992	123	27	the	the	DET
ejpam-4992	123	28	closed	closed	ADJ
ejpam-4992	123	29	graph	graph	NOUN
ejpam-4992	123	30	theorem	theorem	ADJ
ejpam-4992	123	31	(	(	PUNCT
ejpam-4992	123	32	[	[	X
ejpam-4992	123	33	6	6	NUM
ejpam-4992	123	34	,	,	PUNCT
ejpam-4992	123	35	15.12(3	15.12(3	NOUN
ejpam-4992	123	36	)	)	PUNCT
ejpam-4992	123	37	]	]	PUNCT
ejpam-4992	123	38	)	)	PUNCT
ejpam-4992	123	39	,	,	PUNCT
ejpam-4992	123	40	we	we	PRON
ejpam-4992	123	41	can	can	AUX
ejpam-4992	123	42	prove	prove	VERB
ejpam-4992	123	43	that	that	SCONJ
ejpam-4992	123	44	the	the	DET
ejpam-4992	123	45	mapping	mapping	NOUN
ejpam-4992	123	46	fa	fa	INTJ
ejpam-4992	123	47	:	:	PUNCT
ejpam-4992	123	48	λ(e)r	λ(e)r	PROPN
ejpam-4992	123	49	→	→	SYM
ejpam-4992	123	50	ℓ1	ℓ1	NOUN
ejpam-4992	123	51	defined	define	VERB
ejpam-4992	123	52	by	by	ADP
ejpam-4992	123	53	fa(x	fa(x	NOUN
ejpam-4992	123	54	)	)	PUNCT
ejpam-4992	123	55	=	=	SYM
ejpam-4992	123	56	(	(	PUNCT
ejpam-4992	123	57	an(xn))n	an(xn))n	NOUN
ejpam-4992	123	58	is	be	AUX
ejpam-4992	123	59	continuous	continuous	ADJ
ejpam-4992	123	60	,	,	PUNCT
ejpam-4992	123	61	and	and	CCONJ
ejpam-4992	123	62	then	then	ADV
ejpam-4992	123	63	a	a	DET
ejpam-4992	123	64	∈	∈	PROPN
ejpam-4992	123	65	(	(	PUNCT
ejpam-4992	123	66	λ(e)r	λ(e)r	ADJ
ejpam-4992	123	67	)	)	PUNCT
ejpam-4992	123	68	′.	′.	NOUN
ejpam-4992	123	69	so	so	ADV
ejpam-4992	123	70	,	,	PUNCT
ejpam-4992	123	71	(	(	PUNCT
ejpam-4992	123	72	λ(e))∗	λ(e))∗	PROPN
ejpam-4992	123	73	⊂	⊂	PROPN
ejpam-4992	123	74	(	(	PUNCT
ejpam-4992	123	75	λ(e)r	λ(e)r	ADJ
ejpam-4992	123	76	)	)	PUNCT
ejpam-4992	123	77	′.	′.	NOUN
ejpam-4992	123	78	the	the	DET
ejpam-4992	123	79	part	part	NOUN
ejpam-4992	123	80	(	(	PUNCT
ejpam-4992	123	81	a	a	PRON
ejpam-4992	123	82	)	)	PUNCT
ejpam-4992	123	83	follows	follow	VERB
ejpam-4992	123	84	from	from	ADP
ejpam-4992	123	85	(	(	PUNCT
ejpam-4992	123	86	4	4	NUM
ejpam-4992	123	87	)	)	PUNCT
ejpam-4992	123	88	.	.	PUNCT
ejpam-4992	124	1	for	for	ADP
ejpam-4992	124	2	(	(	PUNCT
ejpam-4992	124	3	b	b	NOUN
ejpam-4992	124	4	)	)	PUNCT
ejpam-4992	124	5	,	,	PUNCT
ejpam-4992	124	6	we	we	PRON
ejpam-4992	124	7	have	have	VERB
ejpam-4992	124	8	(	(	PUNCT
ejpam-4992	124	9	λ(e))∗	λ(e))∗	PROPN
ejpam-4992	124	10	=	=	SYM
ejpam-4992	124	11	(	(	PUNCT
ejpam-4992	124	12	λ(e)r	λ(e)r	ADJ
ejpam-4992	124	13	)	)	PUNCT
ejpam-4992	124	14	∗	∗	NOUN
ejpam-4992	124	15	,	,	PUNCT
ejpam-4992	124	16	(	(	PUNCT
ejpam-4992	124	17	by	by	ADP
ejpam-4992	124	18	proposition	proposition	NOUN
ejpam-4992	124	19	4	4	NUM
ejpam-4992	124	20	)	)	PUNCT
ejpam-4992	124	21	=	=	PRON
ejpam-4992	124	22	(	(	PUNCT
ejpam-4992	124	23	λ(e)r	λ(e)r	ADJ
ejpam-4992	124	24	)	)	PUNCT
ejpam-4992	124	25	′	′	NOUN
ejpam-4992	124	26	,	,	PUNCT
ejpam-4992	124	27	(	(	PUNCT
ejpam-4992	124	28	by	by	ADP
ejpam-4992	124	29	(	(	PUNCT
ejpam-4992	124	30	a	a	NOUN
ejpam-4992	124	31	)	)	PUNCT
ejpam-4992	124	32	)	)	PUNCT
ejpam-4992	125	1	=	=	SYM
ejpam-4992	125	2	(	(	PUNCT
ejpam-4992	125	3	λ⊗̃εe)′	λ⊗̃εe)′	PROPN
ejpam-4992	125	4	,	,	PUNCT
ejpam-4992	125	5	(	(	PUNCT
ejpam-4992	125	6	by	by	ADP
ejpam-4992	125	7	[	[	X
ejpam-4992	125	8	3	3	NUM
ejpam-4992	125	9	,	,	PUNCT
ejpam-4992	125	10	prop	prop	NOUN
ejpam-4992	125	11	.	.	PUNCT
ejpam-4992	126	1	2	2	NUM
ejpam-4992	126	2	]	]	NUM
ejpam-4992	126	3	)	)	PUNCT
ejpam-4992	127	1	=	=	SYM
ejpam-4992	128	1	λ∗⊗̃πe	λ∗⊗̃πe	PUNCT
ejpam-4992	128	2	′	′	NUM
ejpam-4992	128	3	,	,	PUNCT
ejpam-4992	128	4	(	(	PUNCT
ejpam-4992	128	5	by	by	ADP
ejpam-4992	128	6	[	[	X
ejpam-4992	128	7	6	6	NUM
ejpam-4992	128	8	,	,	PUNCT
ejpam-4992	128	9	45.6(5	45.6(5	NOUN
ejpam-4992	128	10	)	)	PUNCT
ejpam-4992	128	11	]	]	PUNCT
ejpam-4992	128	12	)	)	PUNCT
ejpam-4992	128	13	.	.	PUNCT
ejpam-4992	129	1	on	on	ADP
ejpam-4992	129	2	the	the	DET
ejpam-4992	129	3	other	other	ADJ
ejpam-4992	129	4	hand	hand	NOUN
ejpam-4992	129	5	,	,	PUNCT
ejpam-4992	129	6	since	since	SCONJ
ejpam-4992	129	7	(	(	PUNCT
ejpam-4992	129	8	λ∗⟨e′⟩)′	λ∗⟨e′⟩)′	NOUN
ejpam-4992	129	9	=	=	SYM
ejpam-4992	129	10	(	(	PUNCT
ejpam-4992	129	11	λ⊗̃εe)′′	λ⊗̃εe)′′	X
ejpam-4992	129	12	=	=	SYM
ejpam-4992	129	13	(	(	PUNCT
ejpam-4992	129	14	λ∗⊗̃πe	λ∗⊗̃πe	PUNCT
ejpam-4992	129	15	′)′	′)′	PROPN
ejpam-4992	129	16	=	=	PUNCT
ejpam-4992	129	17	l(λ∗	l(λ∗	ADJ
ejpam-4992	129	18	,	,	PUNCT
ejpam-4992	129	19	e′′	e′′	PROPN
ejpam-4992	129	20	)	)	PUNCT
ejpam-4992	129	21	,	,	PUNCT
ejpam-4992	129	22	(	(	PUNCT
ejpam-4992	129	23	by	by	ADP
ejpam-4992	129	24	[	[	PUNCT
ejpam-4992	129	25	6	6	NUM
ejpam-4992	129	26	,	,	PUNCT
ejpam-4992	129	27	41.3(6	41.3(6	NOUN
ejpam-4992	129	28	)	)	PUNCT
ejpam-4992	129	29	]	]	PUNCT
ejpam-4992	129	30	)	)	PUNCT
ejpam-4992	129	31	=	=	SYM
ejpam-4992	129	32	λ(e′′	λ(e′′	X
ejpam-4992	129	33	)	)	PUNCT
ejpam-4992	129	34	,	,	PUNCT
ejpam-4992	129	35	(	(	PUNCT
ejpam-4992	129	36	by	by	ADP
ejpam-4992	129	37	[	[	X
ejpam-4992	129	38	10	10	NUM
ejpam-4992	129	39	,	,	PUNCT
ejpam-4992	129	40	propoition	propoition	NOUN
ejpam-4992	129	41	2	2	NUM
ejpam-4992	129	42	]	]	PUNCT
ejpam-4992	129	43	)	)	PUNCT
ejpam-4992	129	44	then	then	ADV
ejpam-4992	129	45	,	,	PUNCT
ejpam-4992	129	46	(	(	PUNCT
ejpam-4992	129	47	λ(e))∗∗	λ(e))∗∗	X
ejpam-4992	129	48	=	=	SYM
ejpam-4992	129	49	λ(e′′	λ(e′′	PROPN
ejpam-4992	129	50	)	)	PUNCT
ejpam-4992	129	51	.	.	PUNCT
ejpam-4992	130	1	■	■	PUNCT
ejpam-4992	130	2	now	now	ADV
ejpam-4992	130	3	,	,	PUNCT
ejpam-4992	130	4	by	by	ADP
ejpam-4992	130	5	[	[	X
ejpam-4992	130	6	8	8	NUM
ejpam-4992	130	7	,	,	PUNCT
ejpam-4992	130	8	theorem	theorem	VERB
ejpam-4992	130	9	1	1	NUM
ejpam-4992	130	10	]	]	PUNCT
ejpam-4992	130	11	,	,	PUNCT
ejpam-4992	130	12	the	the	DET
ejpam-4992	130	13	continuous	continuous	ADJ
ejpam-4992	130	14	dual	dual	ADJ
ejpam-4992	130	15	(	(	PUNCT
ejpam-4992	130	16	λ⟨e⟩r)′	λ⟨e⟩r)′	NOUN
ejpam-4992	130	17	of	of	ADP
ejpam-4992	130	18	λ⟨e⟩r	λ⟨e⟩r	NOUN
ejpam-4992	130	19	is	be	AUX
ejpam-4992	130	20	given	give	VERB
ejpam-4992	130	21	by	by	ADP
ejpam-4992	130	22	the	the	DET
ejpam-4992	130	23	algebraic	algebraic	ADJ
ejpam-4992	130	24	equality	equality	NOUN
ejpam-4992	130	25	(	(	PUNCT
ejpam-4992	130	26	λ⟨e⟩r)′	λ⟨e⟩r)′	NOUN
ejpam-4992	130	27	=	=	SYM
ejpam-4992	130	28	⋃	⋃	NOUN
ejpam-4992	130	29	m∈m	m∈m	NOUN
ejpam-4992	130	30	λ∗(e′	λ∗(e′	NOUN
ejpam-4992	130	31	m	m	NOUN
ejpam-4992	130	32	)	)	PUNCT
ejpam-4992	130	33	.	.	PUNCT
ejpam-4992	131	1	if	if	SCONJ
ejpam-4992	131	2	λ	λ	PROPN
ejpam-4992	131	3	and	and	CCONJ
ejpam-4992	131	4	e	e	NOUN
ejpam-4992	131	5	are	be	AUX
ejpam-4992	131	6	banach	banach	NOUN
ejpam-4992	131	7	spaces	space	NOUN
ejpam-4992	131	8	then	then	ADV
ejpam-4992	131	9	(	(	PUNCT
ejpam-4992	131	10	λ⟨e⟩r)′	λ⟨e⟩r)′	NOUN
ejpam-4992	131	11	=	=	SYM
ejpam-4992	131	12	λ∗(e′	λ∗(e′	ADJ
ejpam-4992	131	13	)	)	PUNCT
ejpam-4992	131	14	.	.	PUNCT
ejpam-4992	132	1	(	(	PUNCT
ejpam-4992	132	2	5	5	X
ejpam-4992	132	3	)	)	PUNCT
ejpam-4992	132	4	this	this	DET
ejpam-4992	132	5	equality	equality	NOUN
ejpam-4992	132	6	is	be	AUX
ejpam-4992	132	7	topological	topological	ADJ
ejpam-4992	132	8	,	,	PUNCT
ejpam-4992	132	9	by	by	ADP
ejpam-4992	132	10	(	(	PUNCT
ejpam-4992	132	11	[	[	X
ejpam-4992	132	12	6	6	NUM
ejpam-4992	132	13	,	,	PUNCT
ejpam-4992	132	14	15.12(2	15.12(2	NUM
ejpam-4992	132	15	)	)	PUNCT
ejpam-4992	132	16	]	]	PUNCT
ejpam-4992	132	17	)	)	PUNCT
ejpam-4992	132	18	.	.	PUNCT
ejpam-4992	133	1	similarly	similarly	ADV
ejpam-4992	133	2	,	,	PUNCT
ejpam-4992	133	3	we	we	PRON
ejpam-4992	133	4	have	have	VERB
ejpam-4992	133	5	proposition	proposition	NOUN
ejpam-4992	133	6	6	6	NUM
ejpam-4992	133	7	.	.	PUNCT
ejpam-4992	134	1	for	for	ADP
ejpam-4992	134	2	every	every	DET
ejpam-4992	134	3	banach	banach	NOUN
ejpam-4992	134	4	space	space	NOUN
ejpam-4992	134	5	e	e	NOUN
ejpam-4992	134	6	,	,	PUNCT
ejpam-4992	134	7	the	the	DET
ejpam-4992	134	8	following	follow	VERB
ejpam-4992	134	9	equalities	equality	NOUN
ejpam-4992	134	10	hold	hold	VERB
ejpam-4992	134	11	(	(	PUNCT
ejpam-4992	134	12	a	a	NOUN
ejpam-4992	134	13	)	)	PUNCT
ejpam-4992	134	14	(	(	PUNCT
ejpam-4992	134	15	λ⟨e⟩)∗	λ⟨e⟩)∗	NOUN
ejpam-4992	134	16	=	=	SYM
ejpam-4992	134	17	λ∗(e′	λ∗(e′	ADJ
ejpam-4992	134	18	)	)	PUNCT
ejpam-4992	134	19	=	=	SYM
ejpam-4992	134	20	(	(	PUNCT
ejpam-4992	134	21	λ⟨e⟩r)′	λ⟨e⟩r)′	PROPN
ejpam-4992	134	22	,	,	PUNCT
ejpam-4992	134	23	(	(	PUNCT
ejpam-4992	134	24	b	b	X
ejpam-4992	134	25	)	)	PUNCT
ejpam-4992	134	26	(	(	PUNCT
ejpam-4992	134	27	λ⟨e⟩)∗∗	λ⟨e⟩)∗∗	NOUN
ejpam-4992	134	28	=	=	PRON
ejpam-4992	134	29	λ⟨e′′⟩.	λ⟨e′′⟩.	NOUN
ejpam-4992	134	30	in	in	ADP
ejpam-4992	134	31	particular	particular	ADJ
ejpam-4992	134	32	,	,	PUNCT
ejpam-4992	134	33	if	if	SCONJ
ejpam-4992	134	34	e	e	NOUN
ejpam-4992	134	35	is	be	AUX
ejpam-4992	134	36	reflexive	reflexive	ADJ
ejpam-4992	134	37	then	then	ADV
ejpam-4992	134	38	(	(	PUNCT
ejpam-4992	134	39	λ⟨e⟩)∗∗	λ⟨e⟩)∗∗	NOUN
ejpam-4992	134	40	=	=	PUNCT
ejpam-4992	135	1	λ⟨e⟩.	λ⟨e⟩.	X
ejpam-4992	135	2	proof	proof	NOUN
ejpam-4992	135	3	.	.	PUNCT
ejpam-4992	136	1	the	the	DET
ejpam-4992	136	2	proof	proof	NOUN
ejpam-4992	136	3	is	be	AUX
ejpam-4992	136	4	similar	similar	ADJ
ejpam-4992	136	5	to	to	ADP
ejpam-4992	136	6	that	that	PRON
ejpam-4992	136	7	of	of	ADP
ejpam-4992	136	8	proposition	proposition	NOUN
ejpam-4992	136	9	5	5	NUM
ejpam-4992	136	10	,	,	PUNCT
ejpam-4992	136	11	but	but	CCONJ
ejpam-4992	136	12	we	we	PRON
ejpam-4992	136	13	present	present	VERB
ejpam-4992	136	14	it	it	PRON
ejpam-4992	136	15	for	for	ADP
ejpam-4992	136	16	the	the	DET
ejpam-4992	136	17	sake	sake	NOUN
ejpam-4992	136	18	of	of	ADP
ejpam-4992	136	19	completeness	completeness	NOUN
ejpam-4992	136	20	.	.	PUNCT
ejpam-4992	137	1	by	by	ADP
ejpam-4992	137	2	[	[	X
ejpam-4992	137	3	5	5	NUM
ejpam-4992	137	4	,	,	PUNCT
ejpam-4992	137	5	theorem	theorem	VERB
ejpam-4992	137	6	1	1	NUM
ejpam-4992	137	7	]	]	PUNCT
ejpam-4992	137	8	,	,	PUNCT
ejpam-4992	137	9	λ∗(e′	λ∗(e′	ADJ
ejpam-4992	137	10	)	)	PUNCT
ejpam-4992	137	11	=	=	PUNCT
ejpam-4992	138	1	λ∗[e′	λ∗[e′	NOUN
ejpam-4992	138	2	]	]	X
ejpam-4992	138	3	,	,	PUNCT
ejpam-4992	138	4	and	and	CCONJ
ejpam-4992	138	5	then	then	ADV
ejpam-4992	138	6	,	,	PUNCT
ejpam-4992	138	7	by	by	ADP
ejpam-4992	138	8	the	the	DET
ejpam-4992	138	9	definition	definition	NOUN
ejpam-4992	138	10	of	of	ADP
ejpam-4992	138	11	the	the	DET
ejpam-4992	138	12	space	space	NOUN
ejpam-4992	138	13	λ⟨e⟩	λ⟨e⟩	PROPN
ejpam-4992	138	14	,	,	PUNCT
ejpam-4992	138	15	we	we	PRON
ejpam-4992	138	16	have	have	VERB
ejpam-4992	138	17	λ∗(e′	λ∗(e′	ADJ
ejpam-4992	138	18	)	)	PUNCT
ejpam-4992	139	1	⊂	⊂	PRON
ejpam-4992	139	2	(	(	PUNCT
ejpam-4992	139	3	λ⟨e⟩)∗.	λ⟨e⟩)∗.	X
ejpam-4992	139	4	on	on	ADP
ejpam-4992	139	5	the	the	DET
ejpam-4992	139	6	other	other	ADJ
ejpam-4992	139	7	hand	hand	NOUN
ejpam-4992	139	8	,	,	PUNCT
ejpam-4992	139	9	in	in	ADP
ejpam-4992	139	10	view	view	NOUN
ejpam-4992	139	11	of	of	ADP
ejpam-4992	139	12	the	the	DET
ejpam-4992	139	13	closed	closed	ADJ
ejpam-4992	139	14	graph	graph	NOUN
ejpam-4992	139	15	theorem	theorem	ADJ
ejpam-4992	139	16	(	(	PUNCT
ejpam-4992	139	17	[	[	X
ejpam-4992	139	18	6	6	NUM
ejpam-4992	139	19	,	,	PUNCT
ejpam-4992	139	20	15.12(3	15.12(3	NOUN
ejpam-4992	139	21	)	)	PUNCT
ejpam-4992	139	22	]	]	PUNCT
ejpam-4992	139	23	)	)	PUNCT
ejpam-4992	139	24	,	,	PUNCT
ejpam-4992	139	25	we	we	PRON
ejpam-4992	139	26	deduce	deduce	VERB
ejpam-4992	139	27	that	that	SCONJ
ejpam-4992	139	28	every	every	DET
ejpam-4992	139	29	a	a	X
ejpam-4992	139	30	=	=	X
ejpam-4992	139	31	(	(	PUNCT
ejpam-4992	139	32	an)n	an)n	PROPN
ejpam-4992	139	33	∈	∈	PROPN
ejpam-4992	139	34	(	(	PUNCT
ejpam-4992	139	35	λ⟨e⟩)∗	λ⟨e⟩)∗	NOUN
ejpam-4992	139	36	corresponds	correspond	VERB
ejpam-4992	139	37	to	to	ADP
ejpam-4992	139	38	a	a	DET
ejpam-4992	139	39	continuous	continuous	ADJ
ejpam-4992	139	40	linear	linear	NOUN
ejpam-4992	139	41	form	form	NOUN
ejpam-4992	139	42	on	on	ADP
ejpam-4992	139	43	λ⟨e⟩r	λ⟨e⟩r	NOUN
ejpam-4992	139	44	by	by	ADP
ejpam-4992	139	45	setting	set	VERB
ejpam-4992	139	46	fa(x	fa(x	NOUN
ejpam-4992	139	47	)	)	PUNCT
ejpam-4992	139	48	=	=	SYM
ejpam-4992	139	49	∑∞	∑∞	NOUN
ejpam-4992	139	50	n=1	n=1	PROPN
ejpam-4992	139	51	an(xn	an(xn	PROPN
ejpam-4992	139	52	)	)	PUNCT
ejpam-4992	139	53	.	.	PUNCT
ejpam-4992	140	1	thus	thus	ADV
ejpam-4992	140	2	,	,	PUNCT
ejpam-4992	140	3	(	(	PUNCT
ejpam-4992	140	4	λ⟨e⟩)∗	λ⟨e⟩)∗	PUNCT
ejpam-4992	140	5	⊂	⊂	X
ejpam-4992	140	6	(	(	PUNCT
ejpam-4992	140	7	λ⟨e⟩r)′.	λ⟨e⟩r)′.	NOUN
ejpam-4992	140	8	the	the	DET
ejpam-4992	140	9	part	part	NOUN
ejpam-4992	140	10	(	(	PUNCT
ejpam-4992	140	11	a	a	PRON
ejpam-4992	140	12	)	)	PUNCT
ejpam-4992	140	13	follows	follow	VERB
ejpam-4992	140	14	from	from	ADP
ejpam-4992	140	15	(	(	PUNCT
ejpam-4992	140	16	5	5	NUM
ejpam-4992	140	17	)	)	PUNCT
ejpam-4992	140	18	.	.	PUNCT
ejpam-4992	141	1	regarding	regard	VERB
ejpam-4992	141	2	(	(	PUNCT
ejpam-4992	141	3	b	b	NOUN
ejpam-4992	141	4	)	)	PUNCT
ejpam-4992	141	5	,	,	PUNCT
ejpam-4992	141	6	we	we	PRON
ejpam-4992	141	7	have	have	VERB
ejpam-4992	141	8	(	(	PUNCT
ejpam-4992	141	9	λ⟨e⟩)∗	λ⟨e⟩)∗	PUNCT
ejpam-4992	141	10	=	=	SYM
ejpam-4992	141	11	(	(	PUNCT
ejpam-4992	141	12	λ⟨e⟩r)∗	λ⟨e⟩r)∗	PROPN
ejpam-4992	141	13	,	,	PUNCT
ejpam-4992	141	14	(	(	PUNCT
ejpam-4992	141	15	by	by	ADP
ejpam-4992	141	16	proposition	proposition	NOUN
ejpam-4992	141	17	4	4	NUM
ejpam-4992	141	18	)	)	PUNCT
ejpam-4992	141	19	=	=	SYM
ejpam-4992	141	20	(	(	PUNCT
ejpam-4992	141	21	λ⟨e⟩r)′	λ⟨e⟩r)′	PROPN
ejpam-4992	141	22	,	,	PUNCT
ejpam-4992	141	23	(	(	PUNCT
ejpam-4992	141	24	by	by	ADP
ejpam-4992	141	25	(	(	PUNCT
ejpam-4992	141	26	a	a	NOUN
ejpam-4992	141	27	)	)	PUNCT
ejpam-4992	141	28	)	)	PUNCT
ejpam-4992	141	29	=	=	PUNCT
ejpam-4992	141	30	λ∗(e′	λ∗(e′	ADJ
ejpam-4992	141	31	)	)	PUNCT
ejpam-4992	141	32	,	,	PUNCT
ejpam-4992	141	33	(	(	PUNCT
ejpam-4992	141	34	by	by	ADP
ejpam-4992	141	35	[	[	X
ejpam-4992	141	36	8	8	NUM
ejpam-4992	141	37	,	,	PUNCT
ejpam-4992	141	38	theorem	theorem	VERB
ejpam-4992	141	39	1	1	NUM
ejpam-4992	141	40	]	]	PUNCT
ejpam-4992	141	41	)	)	PUNCT
ejpam-4992	141	42	.	.	PUNCT
ejpam-4992	142	1	this	this	PRON
ejpam-4992	142	2	leads	lead	VERB
ejpam-4992	142	3	to	to	ADP
ejpam-4992	142	4	(	(	PUNCT
ejpam-4992	142	5	λ⟨e⟩)∗∗	λ⟨e⟩)∗∗	NOUN
ejpam-4992	142	6	=	=	SYM
ejpam-4992	142	7	(	(	PUNCT
ejpam-4992	142	8	λ∗(e′))∗	λ∗(e′))∗	X
ejpam-4992	142	9	=	=	SYM
ejpam-4992	142	10	λ∗∗⟨e′′⟩	λ∗∗⟨e′′⟩	PROPN
ejpam-4992	142	11	=	=	SYM
ejpam-4992	142	12	λ⟨e′′⟩	λ⟨e′′⟩	PROPN
ejpam-4992	142	13	,	,	PUNCT
ejpam-4992	142	14	(	(	PUNCT
ejpam-4992	142	15	by	by	ADP
ejpam-4992	142	16	(	(	PUNCT
ejpam-4992	142	17	a	a	NOUN
ejpam-4992	142	18	)	)	PUNCT
ejpam-4992	142	19	of	of	ADP
ejpam-4992	142	20	proposition	proposition	NOUN
ejpam-4992	142	21	5	5	NUM
ejpam-4992	142	22	)	)	PUNCT
ejpam-4992	142	23	.	.	PUNCT
ejpam-4992	143	1	this	this	PRON
ejpam-4992	143	2	ends	end	VERB
ejpam-4992	143	3	the	the	DET
ejpam-4992	143	4	proof	proof	NOUN
ejpam-4992	143	5	.	.	PUNCT
ejpam-4992	144	1	■	■	PUNCT
ejpam-4992	144	2	m.	m.	NOUN
ejpam-4992	144	3	a.	a.	NOUN
ejpam-4992	144	4	sidaty	sidaty	PROPN
ejpam-4992	144	5	/	/	SYM
ejpam-4992	144	6	eur	eur	PROPN
ejpam-4992	144	7	.	.	PUNCT
ejpam-4992	145	1	j.	j.	PROPN
ejpam-4992	145	2	pure	pure	PROPN
ejpam-4992	145	3	appl	appl	PROPN
ejpam-4992	145	4	.	.	PROPN
ejpam-4992	145	5	math	math	PROPN
ejpam-4992	145	6	,	,	PUNCT
ejpam-4992	145	7	17	17	NUM
ejpam-4992	145	8	(	(	PUNCT
ejpam-4992	145	9	1	1	NUM
ejpam-4992	145	10	)	)	PUNCT
ejpam-4992	145	11	(	(	PUNCT
ejpam-4992	145	12	2024	2024	NUM
ejpam-4992	145	13	)	)	PUNCT
ejpam-4992	145	14	,	,	PUNCT
ejpam-4992	145	15	171	171	NUM
ejpam-4992	145	16	-	-	SYM
ejpam-4992	145	17	179	179	NUM
ejpam-4992	145	18	177	177	NUM
ejpam-4992	145	19	proposition	proposition	NOUN
ejpam-4992	145	20	7	7	NUM
ejpam-4992	145	21	.	.	PUNCT
ejpam-4992	145	22	suppose	suppose	VERB
ejpam-4992	145	23	that	that	SCONJ
ejpam-4992	145	24	e	e	PROPN
ejpam-4992	145	25	and	and	CCONJ
ejpam-4992	145	26	λ	λ	PROPN
ejpam-4992	145	27	are	be	AUX
ejpam-4992	145	28	banach	banach	ADV
ejpam-4992	145	29	spaces	space	NOUN
ejpam-4992	145	30	with	with	ADP
ejpam-4992	145	31	λ	λ	NOUN
ejpam-4992	145	32	reflexive	reflexive	ADJ
ejpam-4992	145	33	.	.	PUNCT
ejpam-4992	146	1	then	then	ADV
ejpam-4992	146	2	,	,	PUNCT
ejpam-4992	146	3	λ∗⟨e′⟩r	λ∗⟨e′⟩r	ADJ
ejpam-4992	146	4	=	=	SYM
ejpam-4992	146	5	λ∗⟨e′⟩.	λ∗⟨e′⟩.	NOUN
ejpam-4992	146	6	proof	proof	NOUN
ejpam-4992	146	7	.	.	PUNCT
ejpam-4992	147	1	let	let	VERB
ejpam-4992	147	2	a	a	PRON
ejpam-4992	147	3	=	=	PUNCT
ejpam-4992	147	4	(	(	PUNCT
ejpam-4992	147	5	an)n	an)n	PROPN
ejpam-4992	147	6	∈	∈	PROPN
ejpam-4992	147	7	λ∗⟨e′⟩	λ∗⟨e′⟩	PROPN
ejpam-4992	147	8	,	,	PUNCT
ejpam-4992	147	9	and	and	CCONJ
ejpam-4992	147	10	consider	consider	VERB
ejpam-4992	147	11	φa	φa	X
ejpam-4992	147	12	:	:	PUNCT
ejpam-4992	147	13	λ(e′′	λ(e′′	X
ejpam-4992	147	14	)	)	PUNCT
ejpam-4992	147	15	→	→	SYM
ejpam-4992	147	16	ℓ1	ℓ1	NOUN
ejpam-4992	147	17	,	,	PUNCT
ejpam-4992	147	18	φa((x	φa((x	VERB
ejpam-4992	147	19	′′	′′	PROPN
ejpam-4992	147	20	n)n	n)n	NOUN
ejpam-4992	147	21	)	)	PUNCT
ejpam-4992	147	22	=	=	SYM
ejpam-4992	147	23	(	(	PUNCT
ejpam-4992	147	24	x′′n(an))n	x′′n(an))n	PROPN
ejpam-4992	147	25	.	.	PUNCT
ejpam-4992	148	1	the	the	DET
ejpam-4992	148	2	linear	linear	PROPN
ejpam-4992	148	3	mapping	mapping	NOUN
ejpam-4992	148	4	φa	φa	NOUN
ejpam-4992	148	5	is	be	AUX
ejpam-4992	148	6	well	well	ADV
ejpam-4992	148	7	defined	define	VERB
ejpam-4992	148	8	,	,	PUNCT
ejpam-4992	148	9	since	since	SCONJ
ejpam-4992	148	10	λ(e′′	λ(e′′	PROPN
ejpam-4992	148	11	)	)	PUNCT
ejpam-4992	149	1	=	=	PUNCT
ejpam-4992	149	2	λ[e′′	λ[e′′	PROPN
ejpam-4992	149	3	]	]	PUNCT
ejpam-4992	149	4	by	by	ADP
ejpam-4992	149	5	[	[	X
ejpam-4992	149	6	5	5	NUM
ejpam-4992	149	7	,	,	PUNCT
ejpam-4992	149	8	theorem	theorem	VERB
ejpam-4992	149	9	1	1	NUM
ejpam-4992	149	10	]	]	PUNCT
ejpam-4992	149	11	.	.	PUNCT
ejpam-4992	150	1	let	let	VERB
ejpam-4992	150	2	us	we	PRON
ejpam-4992	150	3	show	show	VERB
ejpam-4992	150	4	that	that	SCONJ
ejpam-4992	150	5	φa	φa	INTJ
ejpam-4992	150	6	is	be	AUX
ejpam-4992	150	7	weak	weak	ADJ
ejpam-4992	150	8	to	to	ADP
ejpam-4992	150	9	weak	weak	ADJ
ejpam-4992	150	10	continuous	continuous	ADJ
ejpam-4992	150	11	.	.	PUNCT
ejpam-4992	151	1	if	if	SCONJ
ejpam-4992	151	2	(	(	PUNCT
ejpam-4992	151	3	αn)n	αn)n	PROPN
ejpam-4992	151	4	∈	∈	PROPN
ejpam-4992	151	5	ℓ∞	ℓ∞	PROPN
ejpam-4992	151	6	then	then	ADV
ejpam-4992	151	7	(	(	PUNCT
ejpam-4992	151	8	αnan)n	αnan)n	PROPN
ejpam-4992	151	9	∈	∈	PROPN
ejpam-4992	151	10	λ∗⟨e′⟩	λ∗⟨e′⟩	PROPN
ejpam-4992	151	11	and	and	CCONJ
ejpam-4992	151	12	for	for	ADP
ejpam-4992	151	13	all	all	PRON
ejpam-4992	151	14	(	(	PUNCT
ejpam-4992	151	15	x′′n)n	x′′n)n	PROPN
ejpam-4992	151	16	∈	∈	PROPN
ejpam-4992	151	17	λ(e′′	λ(e′′	PROPN
ejpam-4992	151	18	)	)	PUNCT
ejpam-4992	151	19	,	,	PUNCT
ejpam-4992	151	20	we	we	PRON
ejpam-4992	151	21	have	have	VERB
ejpam-4992	151	22	〈	〈	PROPN
ejpam-4992	151	23	(	(	PUNCT
ejpam-4992	151	24	αn)n	αn)n	NOUN
ejpam-4992	151	25	,	,	PUNCT
ejpam-4992	151	26	(	(	PUNCT
ejpam-4992	151	27	x′′n(an))n	x′′n(an))n	X
ejpam-4992	151	28	〉	〉	NOUN
ejpam-4992	151	29	=	=	SYM
ejpam-4992	151	30	〈	〈	PROPN
ejpam-4992	151	31	(	(	PUNCT
ejpam-4992	151	32	αnan)n	αnan)n	NUM
ejpam-4992	151	33	,	,	PUNCT
ejpam-4992	151	34	(	(	PUNCT
ejpam-4992	151	35	x	x	X
ejpam-4992	151	36	′′	′′	PROPN
ejpam-4992	151	37	n)n	n)n	NOUN
ejpam-4992	151	38	〉	〉	NOUN
ejpam-4992	151	39	.	.	PUNCT
ejpam-4992	152	1	let	let	VERB
ejpam-4992	152	2	b	b	X
ejpam-4992	152	3	be	be	AUX
ejpam-4992	152	4	a	a	DET
ejpam-4992	152	5	bounded	bound	VERB
ejpam-4992	152	6	set	set	NOUN
ejpam-4992	152	7	in	in	ADP
ejpam-4992	152	8	λ(e)r	λ(e)r	PROPN
ejpam-4992	152	9	.	.	PUNCT
ejpam-4992	153	1	the	the	DET
ejpam-4992	153	2	alaoglu	alaoglu	NOUN
ejpam-4992	153	3	-	-	PUNCT
ejpam-4992	153	4	bourbaki	bourbaki	NOUN
ejpam-4992	153	5	theorem	theorem	NOUN
ejpam-4992	153	6	(	(	PUNCT
ejpam-4992	153	7	[	[	X
ejpam-4992	153	8	6	6	NUM
ejpam-4992	153	9	,	,	PUNCT
ejpam-4992	153	10	20.9(4	20.9(4	PROPN
ejpam-4992	153	11	)	)	PUNCT
ejpam-4992	153	12	]	]	PUNCT
ejpam-4992	153	13	)	)	PUNCT
ejpam-4992	153	14	asserts	assert	VERB
ejpam-4992	153	15	that	that	SCONJ
ejpam-4992	153	16	b	b	NOUN
ejpam-4992	153	17	is	be	AUX
ejpam-4992	153	18	relatively	relatively	ADV
ejpam-4992	153	19	weak∗	weak∗	NOUN
ejpam-4992	153	20	compact	compact	NOUN
ejpam-4992	153	21	.	.	PUNCT
ejpam-4992	154	1	we	we	PRON
ejpam-4992	154	2	derive	derive	VERB
ejpam-4992	154	3	from	from	ADP
ejpam-4992	154	4	[	[	X
ejpam-4992	154	5	6	6	NUM
ejpam-4992	154	6	,	,	PUNCT
ejpam-4992	154	7	22.4(3	22.4(3	NUM
ejpam-4992	154	8	)	)	PUNCT
ejpam-4992	154	9	]	]	PUNCT
ejpam-4992	154	10	that	that	SCONJ
ejpam-4992	154	11	{	{	PUNCT
ejpam-4992	154	12	(	(	PUNCT
ejpam-4992	154	13	an(xn))n	an(xn))n	NOUN
ejpam-4992	154	14	:	:	PUNCT
ejpam-4992	154	15	(	(	PUNCT
ejpam-4992	154	16	xn)n	xn)n	PROPN
ejpam-4992	154	17	∈	∈	PROPN
ejpam-4992	154	18	b	b	PROPN
ejpam-4992	154	19	}	}	PUNCT
ejpam-4992	154	20	is	be	AUX
ejpam-4992	154	21	relatively	relatively	ADV
ejpam-4992	154	22	compact	compact	ADJ
ejpam-4992	154	23	in	in	ADP
ejpam-4992	154	24	ℓ1	ℓ1	NOUN
ejpam-4992	154	25	and	and	CCONJ
ejpam-4992	154	26	then	then	ADV
ejpam-4992	154	27	lim	lim	PROPN
ejpam-4992	154	28	p→∞	p→∞	ADJ
ejpam-4992	154	29	sup	sup	NOUN
ejpam-4992	154	30			PUNCT
ejpam-4992	154	31	∞∑	∞∑	NUM
ejpam-4992	154	32	n	n	CCONJ
ejpam-4992	154	33	=	=	NOUN
ejpam-4992	154	34	p+1	p+1	NOUN
ejpam-4992	154	35	|an(xn)|	|an(xn)|	NOUN
ejpam-4992	154	36	:	:	PUNCT
ejpam-4992	154	37	(	(	PUNCT
ejpam-4992	154	38	xn)n	xn)n	PROPN
ejpam-4992	154	39	∈	∈	PROPN
ejpam-4992	154	40	b	b	X
ejpam-4992	154	41			NOUN
ejpam-4992	154	42	=	=	NOUN
ejpam-4992	155	1	0	0	X
ejpam-4992	155	2	.	.	PUNCT
ejpam-4992	156	1	this	this	PRON
ejpam-4992	156	2	means	mean	VERB
ejpam-4992	156	3	that	that	SCONJ
ejpam-4992	156	4	(	(	PUNCT
ejpam-4992	156	5	a	a	DET
ejpam-4992	156	6	<	<	X
ejpam-4992	156	7	p>)p	p>)p	PROPN
ejpam-4992	156	8	is	be	AUX
ejpam-4992	156	9	a	a	DET
ejpam-4992	156	10	null	null	ADJ
ejpam-4992	156	11	sequence	sequence	NOUN
ejpam-4992	156	12	in	in	ADP
ejpam-4992	156	13	λ∗⟨e′⟩.	λ∗⟨e′⟩.	NOUN
ejpam-4992	156	14	this	this	PRON
ejpam-4992	156	15	completes	complete	VERB
ejpam-4992	156	16	the	the	DET
ejpam-4992	156	17	proof	proof	NOUN
ejpam-4992	156	18	.	.	PUNCT
ejpam-4992	157	1	■	■	PUNCT
ejpam-4992	157	2	proposition	proposition	NOUN
ejpam-4992	157	3	8	8	NUM
ejpam-4992	157	4	.	.	PUNCT
ejpam-4992	158	1	let	let	VERB
ejpam-4992	158	2	e	e	PRON
ejpam-4992	158	3	be	be	AUX
ejpam-4992	158	4	a	a	DET
ejpam-4992	158	5	banach	banach	NOUN
ejpam-4992	158	6	and	and	CCONJ
ejpam-4992	158	7	λ	λ	X
ejpam-4992	158	8	a	a	DET
ejpam-4992	158	9	reflexive	reflexive	ADJ
ejpam-4992	158	10	banach	banach	NOUN
ejpam-4992	158	11	sequence	sequence	NOUN
ejpam-4992	158	12	space	space	NOUN
ejpam-4992	158	13	.	.	PUNCT
ejpam-4992	159	1	then	then	ADV
ejpam-4992	159	2	,	,	PUNCT
ejpam-4992	159	3	the	the	DET
ejpam-4992	159	4	elements	element	NOUN
ejpam-4992	159	5	of	of	ADP
ejpam-4992	159	6	λ∗⟨e′⟩	λ∗⟨e′⟩	PROPN
ejpam-4992	159	7	are	be	AUX
ejpam-4992	159	8	the	the	DET
ejpam-4992	159	9	sequences	sequence	NOUN
ejpam-4992	159	10	a	a	DET
ejpam-4992	159	11	=	=	X
ejpam-4992	159	12	(	(	PUNCT
ejpam-4992	159	13	an)n	an)n	PROPN
ejpam-4992	159	14	⊂	⊂	PROPN
ejpam-4992	159	15	e′	e′	PROPN
ejpam-4992	159	16	that	that	PRON
ejpam-4992	159	17	have	have	VERB
ejpam-4992	159	18	the	the	DET
ejpam-4992	159	19	form	form	NOUN
ejpam-4992	159	20	a	a	DET
ejpam-4992	159	21	=	=	SYM
ejpam-4992	159	22	∞∑	∞∑	NUM
ejpam-4992	159	23	k=1	k=1	PROPN
ejpam-4992	159	24	λkβ	λkβ	PROPN
ejpam-4992	159	25	kx′k	kx′k	PROPN
ejpam-4992	159	26	,	,	PUNCT
ejpam-4992	159	27	where	where	SCONJ
ejpam-4992	159	28	(	(	PUNCT
ejpam-4992	159	29	λk)k	λk)k	PROPN
ejpam-4992	159	30	∈	∈	NOUN
ejpam-4992	159	31	ℓ1	ℓ1	NOUN
ejpam-4992	159	32	and	and	CCONJ
ejpam-4992	159	33	,	,	PUNCT
ejpam-4992	159	34	for	for	ADP
ejpam-4992	159	35	every	every	DET
ejpam-4992	159	36	k	k	PROPN
ejpam-4992	159	37	∈	∈	PROPN
ejpam-4992	159	38	n	n	CCONJ
ejpam-4992	159	39	,	,	PUNCT
ejpam-4992	159	40	βk	βk	ADP
ejpam-4992	159	41	=	=	PUNCT
ejpam-4992	159	42	(	(	PUNCT
ejpam-4992	159	43	βk	βk	ADP
ejpam-4992	159	44	n)n	n)n	NOUN
ejpam-4992	159	45	∈	∈	NOUN
ejpam-4992	159	46	bλ	bλ	NOUN
ejpam-4992	159	47	and	and	CCONJ
ejpam-4992	159	48	x′k	x′k	PROPN
ejpam-4992	159	49	∈	∈	PROPN
ejpam-4992	159	50	be′.	be′.	NOUN
ejpam-4992	159	51	proof	proof	NOUN
ejpam-4992	159	52	.	.	PUNCT
ejpam-4992	160	1	as	as	ADP
ejpam-4992	160	2	in	in	ADP
ejpam-4992	160	3	proposition	proposition	NOUN
ejpam-4992	160	4	7	7	NUM
ejpam-4992	160	5	,	,	PUNCT
ejpam-4992	160	6	we	we	PRON
ejpam-4992	160	7	have	have	VERB
ejpam-4992	160	8	λ∗⟨e′⟩	λ∗⟨e′⟩	PROPN
ejpam-4992	160	9	=	=	SYM
ejpam-4992	160	10	(	(	PUNCT
ejpam-4992	160	11	λ(e)r	λ(e)r	ADJ
ejpam-4992	160	12	)	)	PUNCT
ejpam-4992	160	13	′	′	NOUN
ejpam-4992	160	14	,	,	PUNCT
ejpam-4992	160	15	by	by	ADP
ejpam-4992	160	16	[	[	X
ejpam-4992	160	17	7	7	NUM
ejpam-4992	160	18	,	,	PUNCT
ejpam-4992	160	19	theorem	theorem	VERB
ejpam-4992	160	20	7	7	NUM
ejpam-4992	160	21	]	]	X
ejpam-4992	160	22	=	=	SYM
ejpam-4992	160	23	(	(	PUNCT
ejpam-4992	160	24	λ⊗̃εe)′	λ⊗̃εe)′	PROPN
ejpam-4992	160	25	,	,	PUNCT
ejpam-4992	160	26	by	by	ADP
ejpam-4992	160	27	[	[	X
ejpam-4992	160	28	3	3	NUM
ejpam-4992	160	29	,	,	PUNCT
ejpam-4992	160	30	prop	prop	NOUN
ejpam-4992	160	31	.	.	PUNCT
ejpam-4992	161	1	2	2	NUM
ejpam-4992	161	2	]	]	PUNCT
ejpam-4992	161	3	=	=	PUNCT
ejpam-4992	161	4	i(λ×	i(λ×	NOUN
ejpam-4992	161	5	e	e	NOUN
ejpam-4992	161	6	)	)	PUNCT
ejpam-4992	161	7	,	,	PUNCT
ejpam-4992	161	8	integral	integral	ADJ
ejpam-4992	161	9	bilinear	bilinear	NOUN
ejpam-4992	161	10	forms	form	NOUN
ejpam-4992	161	11	on	on	ADP
ejpam-4992	161	12	λ×	λ×	PROPN
ejpam-4992	161	13	e	e	PROPN
ejpam-4992	161	14	,	,	PUNCT
ejpam-4992	161	15	by	by	ADP
ejpam-4992	161	16	[	[	X
ejpam-4992	161	17	6	6	NUM
ejpam-4992	161	18	,	,	PUNCT
ejpam-4992	161	19	45.1(2	45.1(2	NUM
ejpam-4992	161	20	)	)	PUNCT
ejpam-4992	161	21	]	]	PUNCT
ejpam-4992	162	1	=	=	SYM
ejpam-4992	162	2	li(λ	li(λ	X
ejpam-4992	162	3	,	,	PUNCT
ejpam-4992	162	4	e′	e′	ADJ
ejpam-4992	162	5	)	)	PUNCT
ejpam-4992	162	6	,	,	PUNCT
ejpam-4992	162	7	integral	integral	ADJ
ejpam-4992	162	8	mappings	mapping	NOUN
ejpam-4992	162	9	of	of	ADP
ejpam-4992	162	10	λ	λ	PROPN
ejpam-4992	162	11	in	in	ADP
ejpam-4992	162	12	e′	e′	PROPN
ejpam-4992	162	13	,	,	PUNCT
ejpam-4992	162	14	by	by	ADP
ejpam-4992	162	15	[	[	X
ejpam-4992	162	16	6	6	NUM
ejpam-4992	162	17	,	,	PUNCT
ejpam-4992	162	18	45.4(1	45.4(1	NOUN
ejpam-4992	162	19	)	)	PUNCT
ejpam-4992	162	20	]	]	PUNCT
ejpam-4992	163	1	=	=	SYM
ejpam-4992	163	2	n	n	X
ejpam-4992	163	3	(	(	PUNCT
ejpam-4992	163	4	λ	λ	PROPN
ejpam-4992	163	5	,	,	PUNCT
ejpam-4992	163	6	e′	e′	NOUN
ejpam-4992	163	7	)	)	PUNCT
ejpam-4992	163	8	.	.	PUNCT
ejpam-4992	164	1	nuclear	nuclear	ADJ
ejpam-4992	164	2	operators	operator	NOUN
ejpam-4992	164	3	from	from	ADP
ejpam-4992	164	4	λ	λ	PROPN
ejpam-4992	164	5	in	in	ADP
ejpam-4992	164	6	e′	e′	NOUN
ejpam-4992	164	7	by	by	ADP
ejpam-4992	164	8	[	[	X
ejpam-4992	164	9	6	6	NUM
ejpam-4992	164	10	,	,	PUNCT
ejpam-4992	164	11	45.6(1	45.6(1	NUM
ejpam-4992	164	12	)	)	PUNCT
ejpam-4992	164	13	and	and	CCONJ
ejpam-4992	164	14	45.6(4	45.6(4	PROPN
ejpam-4992	164	15	)	)	PUNCT
ejpam-4992	164	16	]	]	PUNCT
ejpam-4992	164	17	for	for	ADP
ejpam-4992	164	18	a	a	DET
ejpam-4992	164	19	=	=	PUNCT
ejpam-4992	164	20	(	(	PUNCT
ejpam-4992	164	21	an)n	an)n	PROPN
ejpam-4992	164	22	∈	∈	PROPN
ejpam-4992	164	23	λ∗⟨e′⟩	λ∗⟨e′⟩	PROPN
ejpam-4992	164	24	,	,	PUNCT
ejpam-4992	164	25	the	the	DET
ejpam-4992	164	26	corresponding	correspond	VERB
ejpam-4992	164	27	fa	fa	PROPN
ejpam-4992	164	28	∈	∈	PROPN
ejpam-4992	164	29	li(λ	li(λ	NOUN
ejpam-4992	164	30	,	,	PUNCT
ejpam-4992	164	31	e′	e′	X
ejpam-4992	164	32	)	)	PUNCT
ejpam-4992	164	33	is	be	AUX
ejpam-4992	164	34	defined	define	VERB
ejpam-4992	164	35	by	by	ADP
ejpam-4992	164	36	fa(α	fa(α	NOUN
ejpam-4992	164	37	)	)	PUNCT
ejpam-4992	164	38	∈	∈	PROPN
ejpam-4992	164	39	e′	e′	NOUN
ejpam-4992	164	40	such	such	ADJ
ejpam-4992	164	41	that	that	DET
ejpam-4992	164	42	fa(α)(t	fa(α)(t	X
ejpam-4992	164	43	)	)	PUNCT
ejpam-4992	164	44	=	=	SYM
ejpam-4992	164	45	b(α	b(α	PROPN
ejpam-4992	164	46	,	,	PUNCT
ejpam-4992	164	47	t	t	PROPN
ejpam-4992	164	48	)	)	PUNCT
ejpam-4992	164	49	=	=	SYM
ejpam-4992	164	50	⟨a	⟨a	PROPN
ejpam-4992	164	51	,	,	PUNCT
ejpam-4992	164	52	αt⟩	αt⟩	NUM
ejpam-4992	164	53	,	,	PUNCT
ejpam-4992	164	54	for	for	ADP
ejpam-4992	164	55	α	α	NOUN
ejpam-4992	164	56	=	=	SYM
ejpam-4992	164	57	(	(	PUNCT
ejpam-4992	164	58	αn)n	αn)n	NOUN
ejpam-4992	164	59	∈	∈	PROPN
ejpam-4992	164	60	λ	λ	PROPN
ejpam-4992	164	61	and	and	CCONJ
ejpam-4992	164	62	t	t	PROPN
ejpam-4992	164	63	∈	∈	PROPN
ejpam-4992	164	64	e	e	NOUN
ejpam-4992	164	65	,	,	PUNCT
ejpam-4992	164	66	where	where	SCONJ
ejpam-4992	164	67	b	b	X
ejpam-4992	164	68	∈	∈	PROPN
ejpam-4992	164	69	i(λ	i(λ	PROPN
ejpam-4992	164	70	×	×	NOUN
ejpam-4992	164	71	e	e	NOUN
ejpam-4992	164	72	)	)	PUNCT
ejpam-4992	164	73	is	be	AUX
ejpam-4992	164	74	the	the	DET
ejpam-4992	164	75	integral	integral	ADJ
ejpam-4992	164	76	bilinear	bilinear	NOUN
ejpam-4992	164	77	form	form	NOUN
ejpam-4992	164	78	on	on	ADP
ejpam-4992	164	79	λ×	λ×	PROPN
ejpam-4992	164	80	e	e	PROPN
ejpam-4992	164	81	corresponding	correspond	VERB
ejpam-4992	164	82	to	to	ADP
ejpam-4992	164	83	fa	fa	PROPN
ejpam-4992	164	84	.	.	PUNCT
ejpam-4992	165	1	now	now	ADV
ejpam-4992	165	2	,	,	PUNCT
ejpam-4992	165	3	since	since	SCONJ
ejpam-4992	165	4	fa	fa	PROPN
ejpam-4992	165	5	∈	∈	PROPN
ejpam-4992	165	6	n	n	CCONJ
ejpam-4992	165	7	(	(	PUNCT
ejpam-4992	165	8	λ	λ	PROPN
ejpam-4992	165	9	,	,	PUNCT
ejpam-4992	165	10	e′	e′	ADJ
ejpam-4992	165	11	)	)	PUNCT
ejpam-4992	165	12	,	,	PUNCT
ejpam-4992	165	13	then	then	ADV
ejpam-4992	165	14	by	by	ADP
ejpam-4992	165	15	[	[	X
ejpam-4992	165	16	6	6	NUM
ejpam-4992	165	17	,	,	PUNCT
ejpam-4992	165	18	42.5(5)-(6	42.5(5)-(6	NUM
ejpam-4992	165	19	)	)	PUNCT
ejpam-4992	165	20	]	]	PUNCT
ejpam-4992	165	21	,	,	PUNCT
ejpam-4992	165	22	there	there	PRON
ejpam-4992	165	23	are	be	VERB
ejpam-4992	165	24	(	(	PUNCT
ejpam-4992	165	25	λk)k	λk)k	PROPN
ejpam-4992	165	26	∈	∈	NOUN
ejpam-4992	165	27	ℓ1	ℓ1	NOUN
ejpam-4992	165	28	,	,	PUNCT
ejpam-4992	165	29	a	a	DET
ejpam-4992	165	30	sequence	sequence	NOUN
ejpam-4992	165	31	m.	m.	NOUN
ejpam-4992	165	32	a.	a.	NOUN
ejpam-4992	165	33	sidaty	sidaty	PROPN
ejpam-4992	165	34	/	/	SYM
ejpam-4992	165	35	eur	eur	PROPN
ejpam-4992	165	36	.	.	PUNCT
ejpam-4992	166	1	j.	j.	PROPN
ejpam-4992	166	2	pure	pure	PROPN
ejpam-4992	166	3	appl	appl	PROPN
ejpam-4992	166	4	.	.	PROPN
ejpam-4992	166	5	math	math	PROPN
ejpam-4992	166	6	,	,	PUNCT
ejpam-4992	166	7	17	17	NUM
ejpam-4992	166	8	(	(	PUNCT
ejpam-4992	166	9	1	1	NUM
ejpam-4992	166	10	)	)	PUNCT
ejpam-4992	166	11	(	(	PUNCT
ejpam-4992	166	12	2024	2024	NUM
ejpam-4992	166	13	)	)	PUNCT
ejpam-4992	166	14	,	,	PUNCT
ejpam-4992	166	15	171	171	NUM
ejpam-4992	166	16	-	-	SYM
ejpam-4992	166	17	179	179	NUM
ejpam-4992	166	18	178	178	NUM
ejpam-4992	166	19	{	{	PUNCT
ejpam-4992	166	20	βk	βk	NOUN
ejpam-4992	166	21	=	=	PUNCT
ejpam-4992	166	22	(	(	PUNCT
ejpam-4992	166	23	βk	βk	ADP
ejpam-4992	166	24	n)n	n)n	NOUN
ejpam-4992	166	25	:	:	PUNCT
ejpam-4992	166	26	k	k	PROPN
ejpam-4992	166	27	∈	∈	PROPN
ejpam-4992	166	28	n	n	CCONJ
ejpam-4992	166	29	}	}	PUNCT
ejpam-4992	166	30	in	in	ADP
ejpam-4992	166	31	bλ	bλ	NOUN
ejpam-4992	166	32	and	and	CCONJ
ejpam-4992	166	33	a	a	DET
ejpam-4992	166	34	sequence	sequence	NOUN
ejpam-4992	166	35	(	(	PUNCT
ejpam-4992	166	36	x′k)k	x′k)k	NUM
ejpam-4992	166	37	in	in	ADP
ejpam-4992	166	38	be′	be′	ADP
ejpam-4992	166	39	such	such	ADJ
ejpam-4992	166	40	that	that	PRON
ejpam-4992	166	41	,	,	PUNCT
ejpam-4992	166	42	for	for	ADP
ejpam-4992	166	43	every	every	DET
ejpam-4992	166	44	α	α	NOUN
ejpam-4992	166	45	∈	∈	PROPN
ejpam-4992	166	46	λ	λ	PROPN
ejpam-4992	166	47	and	and	CCONJ
ejpam-4992	166	48	t	t	PROPN
ejpam-4992	166	49	∈	∈	PROPN
ejpam-4992	166	50	e	e	X
ejpam-4992	166	51	,	,	PUNCT
ejpam-4992	166	52	we	we	PRON
ejpam-4992	166	53	have	have	AUX
ejpam-4992	166	54	⟨a	⟨a	NOUN
ejpam-4992	166	55	,	,	PUNCT
ejpam-4992	166	56	αt⟩	αt⟩	NUM
ejpam-4992	166	57	=	=	SYM
ejpam-4992	166	58	fa(α)(t	fa(α)(t	X
ejpam-4992	166	59	)	)	PUNCT
ejpam-4992	166	60	=	=	NOUN
ejpam-4992	167	1	∞∑	∞∑	NUM
ejpam-4992	167	2	k=1	k=1	PUNCT
ejpam-4992	167	3	λk⟨βk	λk⟨βk	NOUN
ejpam-4992	167	4	,	,	PUNCT
ejpam-4992	167	5	α⟩x′k(t	α⟩x′k(t	NOUN
ejpam-4992	167	6	)	)	PUNCT
ejpam-4992	167	7	.	.	PUNCT
ejpam-4992	168	1	this	this	PRON
ejpam-4992	168	2	implies	imply	VERB
ejpam-4992	168	3	that	that	SCONJ
ejpam-4992	168	4	an	an	DET
ejpam-4992	168	5	=	=	NOUN
ejpam-4992	168	6	∑∞	∑∞	NOUN
ejpam-4992	168	7	k=1	k=1	X
ejpam-4992	168	8	λkβ	λkβ	VERB
ejpam-4992	169	1	k	k	X
ejpam-4992	170	1	nx	nx	INTJ
ejpam-4992	170	2	′	′	NUM
ejpam-4992	170	3	k	k	PROPN
ejpam-4992	170	4	for	for	ADP
ejpam-4992	170	5	every	every	DET
ejpam-4992	170	6	n	n	PRON
ejpam-4992	170	7	∈	∈	NOUN
ejpam-4992	170	8	n	n	NOUN
ejpam-4992	170	9	and	and	CCONJ
ejpam-4992	170	10	that	that	SCONJ
ejpam-4992	170	11	a	a	DET
ejpam-4992	170	12	=	=	NOUN
ejpam-4992	170	13	∑∞	∑∞	NOUN
ejpam-4992	171	1	k=1	k=1	X
ejpam-4992	171	2	λkβ	λkβ	X
ejpam-4992	171	3	kx′k	kx′k	PROPN
ejpam-4992	171	4	.	.	PUNCT
ejpam-4992	172	1	by	by	ADP
ejpam-4992	172	2	ascending	ascend	VERB
ejpam-4992	172	3	the	the	DET
ejpam-4992	172	4	previous	previous	ADJ
ejpam-4992	172	5	chain	chain	NOUN
ejpam-4992	172	6	of	of	ADP
ejpam-4992	172	7	equalities	equality	NOUN
ejpam-4992	172	8	,	,	PUNCT
ejpam-4992	172	9	we	we	PRON
ejpam-4992	172	10	easily	easily	ADV
ejpam-4992	172	11	see	see	VERB
ejpam-4992	172	12	that	that	SCONJ
ejpam-4992	172	13	the	the	DET
ejpam-4992	172	14	inverse	inverse	NOUN
ejpam-4992	172	15	is	be	AUX
ejpam-4992	172	16	true	true	ADJ
ejpam-4992	172	17	.	.	PUNCT
ejpam-4992	173	1	■	■	PUNCT
ejpam-4992	173	2	proposition	proposition	NOUN
ejpam-4992	173	3	9	9	NUM
ejpam-4992	173	4	.	.	PUNCT
ejpam-4992	174	1	(	(	PUNCT
ejpam-4992	174	2	λ(e))∗	λ(e))∗	X
ejpam-4992	174	3	=	=	SYM
ejpam-4992	174	4	(	(	PUNCT
ejpam-4992	174	5	λ(e))′	λ(e))′	X
ejpam-4992	174	6	if	if	SCONJ
ejpam-4992	174	7	and	and	CCONJ
ejpam-4992	174	8	only	only	ADV
ejpam-4992	174	9	if	if	SCONJ
ejpam-4992	174	10	λ(e)r	λ(e)r	PROPN
ejpam-4992	174	11	=	=	SYM
ejpam-4992	174	12	λ(e	λ(e	PROPN
ejpam-4992	174	13	)	)	PUNCT
ejpam-4992	174	14	.	.	PUNCT
ejpam-4992	175	1	proof	proof	NOUN
ejpam-4992	175	2	.	.	PUNCT
ejpam-4992	176	1	by	by	ADP
ejpam-4992	176	2	(	(	PUNCT
ejpam-4992	176	3	a	a	NOUN
ejpam-4992	176	4	)	)	PUNCT
ejpam-4992	176	5	of	of	ADP
ejpam-4992	176	6	proposition	proposition	NOUN
ejpam-4992	176	7	5	5	NUM
ejpam-4992	176	8	,	,	PUNCT
ejpam-4992	176	9	if	if	SCONJ
ejpam-4992	176	10	λ(e)r	λ(e)r	PROPN
ejpam-4992	176	11	=	=	SYM
ejpam-4992	176	12	λ(e	λ(e	PROPN
ejpam-4992	176	13	)	)	PUNCT
ejpam-4992	176	14	then	then	ADV
ejpam-4992	176	15	(	(	PUNCT
ejpam-4992	176	16	λ(e))∗	λ(e))∗	PROPN
ejpam-4992	176	17	=	=	SYM
ejpam-4992	176	18	(	(	PUNCT
ejpam-4992	176	19	λ(e)r	λ(e)r	ADJ
ejpam-4992	176	20	)	)	PUNCT
ejpam-4992	176	21	′	′	NUM
ejpam-4992	177	1	=	=	PUNCT
ejpam-4992	177	2	(	(	PUNCT
ejpam-4992	177	3	λ(e))′.	λ(e))′.	PROPN
ejpam-4992	177	4	inversely	inversely	ADV
ejpam-4992	177	5	,	,	PUNCT
ejpam-4992	177	6	suppose	suppose	VERB
ejpam-4992	177	7	that	that	SCONJ
ejpam-4992	177	8	(	(	PUNCT
ejpam-4992	177	9	λ(e))∗	λ(e))∗	X
ejpam-4992	177	10	=	=	SYM
ejpam-4992	177	11	(	(	PUNCT
ejpam-4992	177	12	λ(e))′.	λ(e))′.	PROPN
ejpam-4992	177	13	as	as	ADP
ejpam-4992	177	14	in	in	ADP
ejpam-4992	177	15	the	the	DET
ejpam-4992	177	16	proof	proof	NOUN
ejpam-4992	177	17	of	of	ADP
ejpam-4992	177	18	proposition	proposition	NOUN
ejpam-4992	177	19	7	7	NUM
ejpam-4992	177	20	,	,	PUNCT
ejpam-4992	177	21	for	for	ADP
ejpam-4992	177	22	every	every	PRON
ejpam-4992	177	23	x	x	SYM
ejpam-4992	177	24	=	=	SYM
ejpam-4992	177	25	(	(	PUNCT
ejpam-4992	177	26	xn)n	xn)n	PROPN
ejpam-4992	177	27	∈	∈	PROPN
ejpam-4992	177	28	λ(e	λ(e	PROPN
ejpam-4992	177	29	)	)	PUNCT
ejpam-4992	177	30	,	,	PUNCT
ejpam-4992	177	31	φx	φx	X
ejpam-4992	177	32	:	:	PUNCT
ejpam-4992	177	33	(	(	PUNCT
ejpam-4992	177	34	λ(e))′	λ(e))′	PROPN
ejpam-4992	177	35	→	→	SYM
ejpam-4992	177	36	ℓ1	ℓ1	NOUN
ejpam-4992	177	37	,	,	PUNCT
ejpam-4992	177	38	φx((an)n	φx((an)n	NOUN
ejpam-4992	177	39	)	)	PUNCT
ejpam-4992	177	40	=	=	SYM
ejpam-4992	177	41	(	(	PUNCT
ejpam-4992	177	42	an(x))n	an(x))n	PROPN
ejpam-4992	177	43	,	,	PUNCT
ejpam-4992	177	44	is	be	AUX
ejpam-4992	177	45	well	well	ADV
ejpam-4992	177	46	defined	define	VERB
ejpam-4992	177	47	,	,	PUNCT
ejpam-4992	177	48	linear	linear	ADJ
ejpam-4992	177	49	and	and	CCONJ
ejpam-4992	177	50	weak	weak	ADJ
ejpam-4992	177	51	to	to	ADP
ejpam-4992	177	52	weak	weak	ADJ
ejpam-4992	177	53	continuous	continuous	ADJ
ejpam-4992	177	54	.	.	PUNCT
ejpam-4992	178	1	denote	denote	VERB
ejpam-4992	178	2	by	by	ADP
ejpam-4992	178	3	h	h	PROPN
ejpam-4992	178	4	the	the	DET
ejpam-4992	178	5	closed	closed	ADJ
ejpam-4992	178	6	unit	unit	NOUN
ejpam-4992	178	7	ball	ball	NOUN
ejpam-4992	178	8	of	of	ADP
ejpam-4992	178	9	(	(	PUNCT
ejpam-4992	178	10	λ(e))∗.	λ(e))∗.	PROPN
ejpam-4992	178	11	here	here	ADV
ejpam-4992	178	12	also	also	ADV
ejpam-4992	178	13	,	,	PUNCT
ejpam-4992	178	14	the	the	DET
ejpam-4992	178	15	alaoglu	alaoglu	NOUN
ejpam-4992	178	16	-	-	PUNCT
ejpam-4992	178	17	bourbaki	bourbaki	NOUN
ejpam-4992	178	18	theorem	theorem	NOUN
ejpam-4992	178	19	(	(	PUNCT
ejpam-4992	178	20	[	[	X
ejpam-4992	178	21	6	6	NUM
ejpam-4992	178	22	,	,	PUNCT
ejpam-4992	178	23	20.9(4	20.9(4	PROPN
ejpam-4992	178	24	)	)	PUNCT
ejpam-4992	178	25	]	]	PUNCT
ejpam-4992	178	26	)	)	PUNCT
ejpam-4992	178	27	guarantees	guarantee	VERB
ejpam-4992	178	28	that	that	SCONJ
ejpam-4992	178	29	h	h	NOUN
ejpam-4992	178	30	is	be	AUX
ejpam-4992	178	31	relatively	relatively	ADV
ejpam-4992	178	32	weak∗	weak∗	NOUN
ejpam-4992	178	33	compact	compact	NOUN
ejpam-4992	178	34	.	.	PUNCT
ejpam-4992	179	1	we	we	PRON
ejpam-4992	179	2	derive	derive	VERB
ejpam-4992	179	3	from	from	ADP
ejpam-4992	179	4	[	[	X
ejpam-4992	179	5	6	6	NUM
ejpam-4992	179	6	,	,	PUNCT
ejpam-4992	179	7	22.4(3	22.4(3	NUM
ejpam-4992	179	8	)	)	PUNCT
ejpam-4992	179	9	]	]	PUNCT
ejpam-4992	179	10	,	,	PUNCT
ejpam-4992	179	11	that	that	SCONJ
ejpam-4992	179	12	{	{	PUNCT
ejpam-4992	179	13	(	(	PUNCT
ejpam-4992	179	14	an(xn))n	an(xn))n	NOUN
ejpam-4992	179	15	:	:	PUNCT
ejpam-4992	179	16	(	(	PUNCT
ejpam-4992	179	17	an)n	an)n	PROPN
ejpam-4992	179	18	∈	∈	PROPN
ejpam-4992	179	19	h	h	NOUN
ejpam-4992	179	20	}	}	PUNCT
ejpam-4992	179	21	is	be	AUX
ejpam-4992	179	22	relatively	relatively	ADV
ejpam-4992	179	23	compact	compact	ADJ
ejpam-4992	179	24	in	in	ADP
ejpam-4992	179	25	ℓ1	ℓ1	NOUN
ejpam-4992	179	26	and	and	CCONJ
ejpam-4992	179	27	then	then	ADV
ejpam-4992	179	28	lim	lim	PROPN
ejpam-4992	179	29	p→∞	p→∞	ADJ
ejpam-4992	179	30	εm	εm	PROPN
ejpam-4992	179	31	(	(	PUNCT
ejpam-4992	179	32	x	x	X
ejpam-4992	179	33	<	<	X
ejpam-4992	179	34	p	p	X
ejpam-4992	179	35	>	>	PUNCT
ejpam-4992	179	36	)	)	PUNCT
ejpam-4992	180	1	=	=	SYM
ejpam-4992	180	2	lim	lim	PROPN
ejpam-4992	180	3	p→∞	p→∞	ADJ
ejpam-4992	180	4	sup	sup	NOUN
ejpam-4992	180	5			PUNCT
ejpam-4992	180	6	∞∑	∞∑	NUM
ejpam-4992	180	7	n	n	CCONJ
ejpam-4992	180	8	=	=	NOUN
ejpam-4992	180	9	p+1	p+1	NOUN
ejpam-4992	180	10	|an(xn)|	|an(xn)|	NOUN
ejpam-4992	180	11	:	:	PUNCT
ejpam-4992	180	12	(	(	PUNCT
ejpam-4992	180	13	an)n	an)n	PROPN
ejpam-4992	180	14	∈	∈	PROPN
ejpam-4992	180	15	h	h	NOUN
ejpam-4992	180	16			NOUN
ejpam-4992	180	17	=	=	NOUN
ejpam-4992	180	18	0	0	X
ejpam-4992	180	19	.	.	PUNCT
ejpam-4992	181	1	thus	thus	ADV
ejpam-4992	181	2	,	,	PUNCT
ejpam-4992	181	3	x	x	PROPN
ejpam-4992	181	4	∈	∈	PROPN
ejpam-4992	181	5	λ(e)r	λ(e)r	NOUN
ejpam-4992	181	6	.	.	PUNCT
ejpam-4992	182	1	■	■	PUNCT
ejpam-4992	182	2	proposition	proposition	NOUN
ejpam-4992	182	3	10	10	NUM
ejpam-4992	182	4	.	.	PUNCT
ejpam-4992	183	1	(	(	PUNCT
ejpam-4992	183	2	λ⟨e⟩)∗	λ⟨e⟩)∗	PUNCT
ejpam-4992	183	3	=	=	SYM
ejpam-4992	183	4	(	(	PUNCT
ejpam-4992	183	5	λ⟨e⟩)′	λ⟨e⟩)′	PROPN
ejpam-4992	183	6	if	if	SCONJ
ejpam-4992	183	7	and	and	CCONJ
ejpam-4992	183	8	only	only	ADV
ejpam-4992	183	9	if	if	SCONJ
ejpam-4992	183	10	λ⟨e⟩r	λ⟨e⟩r	NOUN
ejpam-4992	183	11	=	=	PUNCT
ejpam-4992	183	12	λ⟨e⟩.	λ⟨e⟩.	X
ejpam-4992	183	13	proof	proof	NOUN
ejpam-4992	183	14	.	.	PUNCT
ejpam-4992	184	1	the	the	DET
ejpam-4992	184	2	proof	proof	NOUN
ejpam-4992	184	3	is	be	AUX
ejpam-4992	184	4	similar	similar	ADJ
ejpam-4992	184	5	to	to	ADP
ejpam-4992	184	6	that	that	PRON
ejpam-4992	184	7	of	of	ADP
ejpam-4992	184	8	proposition	proposition	NOUN
ejpam-4992	184	9	9	9	NUM
ejpam-4992	184	10	when	when	SCONJ
ejpam-4992	184	11	interchanging	interchange	VERB
ejpam-4992	184	12	the	the	DET
ejpam-4992	184	13	roles	role	NOUN
ejpam-4992	184	14	of	of	ADP
ejpam-4992	184	15	λ(e	λ(e	NOUN
ejpam-4992	184	16	)	)	PUNCT
ejpam-4992	184	17	and	and	CCONJ
ejpam-4992	184	18	(	(	PUNCT
ejpam-4992	184	19	λ(e))′	λ(e))′	PROPN
ejpam-4992	184	20	by	by	ADP
ejpam-4992	184	21	those	those	PRON
ejpam-4992	184	22	of	of	ADP
ejpam-4992	184	23	λ⟨e⟩	λ⟨e⟩	PROPN
ejpam-4992	184	24	and	and	CCONJ
ejpam-4992	184	25	(	(	PUNCT
ejpam-4992	184	26	λ⟨e⟩)′	λ⟨e⟩)′	PROPN
ejpam-4992	184	27	,	,	PUNCT
ejpam-4992	184	28	respectively	respectively	ADV
ejpam-4992	184	29	.	.	PUNCT
ejpam-4992	185	1	■	■	PUNCT
ejpam-4992	185	2	conclusion	conclusion	NOUN
ejpam-4992	185	3	let	let	VERB
ejpam-4992	185	4	e	e	PRON
ejpam-4992	185	5	be	be	AUX
ejpam-4992	185	6	a	a	DET
ejpam-4992	185	7	banach	banach	NOUN
ejpam-4992	185	8	space	space	NOUN
ejpam-4992	185	9	and	and	CCONJ
ejpam-4992	185	10	λ	λ	X
ejpam-4992	185	11	a	a	DET
ejpam-4992	185	12	perfect	perfect	ADJ
ejpam-4992	185	13	banach	banach	NOUN
ejpam-4992	185	14	sequence	sequence	NOUN
ejpam-4992	185	15	space	space	NOUN
ejpam-4992	185	16	which	which	PRON
ejpam-4992	185	17	is	be	AUX
ejpam-4992	185	18	reflexive	reflexive	ADJ
ejpam-4992	185	19	.	.	PUNCT
ejpam-4992	186	1	we	we	PRON
ejpam-4992	186	2	prove	prove	VERB
ejpam-4992	186	3	that	that	SCONJ
ejpam-4992	186	4	λ(e	λ(e	VERB
ejpam-4992	186	5	)	)	PUNCT
ejpam-4992	186	6	and	and	CCONJ
ejpam-4992	186	7	λ⟨e⟩	λ⟨e⟩	PROPN
ejpam-4992	186	8	have	have	VERB
ejpam-4992	186	9	the	the	DET
ejpam-4992	186	10	ak	ak	PROPN
ejpam-4992	186	11	property	property	NOUN
ejpam-4992	186	12	if	if	SCONJ
ejpam-4992	186	13	and	and	CCONJ
ejpam-4992	186	14	only	only	ADV
ejpam-4992	186	15	if	if	SCONJ
ejpam-4992	186	16	the	the	DET
ejpam-4992	186	17	köthe	köthe	NOUN
ejpam-4992	186	18	dual	dual	ADJ
ejpam-4992	186	19	and	and	CCONJ
ejpam-4992	186	20	the	the	DET
ejpam-4992	186	21	continuous	continuous	ADJ
ejpam-4992	186	22	dual	dual	NOUN
ejpam-4992	186	23	are	be	AUX
ejpam-4992	186	24	equal	equal	ADJ
ejpam-4992	186	25	.	.	PUNCT
ejpam-4992	187	1	if	if	SCONJ
ejpam-4992	187	2	,	,	PUNCT
ejpam-4992	187	3	moreover	moreover	ADV
ejpam-4992	187	4	e	e	NOUN
ejpam-4992	187	5	is	be	AUX
ejpam-4992	187	6	reflexive	reflexive	ADJ
ejpam-4992	187	7	,	,	PUNCT
ejpam-4992	187	8	these	these	DET
ejpam-4992	187	9	spaces	space	NOUN
ejpam-4992	187	10	become	become	VERB
ejpam-4992	187	11	perfect	perfect	ADJ
ejpam-4992	187	12	.	.	PUNCT
ejpam-4992	188	1	acknowledgements	acknowledgement	NOUN
ejpam-4992	188	2	i	i	PRON
ejpam-4992	188	3	wish	wish	VERB
ejpam-4992	188	4	to	to	PART
ejpam-4992	188	5	thank	thank	VERB
ejpam-4992	188	6	the	the	DET
ejpam-4992	188	7	reviewers	reviewer	NOUN
ejpam-4992	188	8	for	for	ADP
ejpam-4992	188	9	their	their	PRON
ejpam-4992	188	10	remarks	remark	NOUN
ejpam-4992	188	11	and	and	CCONJ
ejpam-4992	188	12	suggestions	suggestion	NOUN
ejpam-4992	188	13	which	which	PRON
ejpam-4992	188	14	improved	improve	VERB
ejpam-4992	188	15	the	the	DET
ejpam-4992	188	16	presentation	presentation	NOUN
ejpam-4992	188	17	of	of	ADP
ejpam-4992	188	18	the	the	DET
ejpam-4992	188	19	paper	paper	NOUN
ejpam-4992	188	20	.	.	PUNCT
ejpam-4992	189	1	references	reference	NOUN
ejpam-4992	189	2	179	179	NUM
ejpam-4992	189	3	references	reference	NOUN
ejpam-4992	189	4	[	[	X
ejpam-4992	189	5	1	1	NUM
ejpam-4992	189	6	]	]	PUNCT
ejpam-4992	189	7	h.	h.	PROPN
ejpam-4992	189	8	apiola	apiola	PROPN
ejpam-4992	189	9	.	.	PUNCT
ejpam-4992	190	1	duality	duality	NOUN
ejpam-4992	190	2	between	between	ADP
ejpam-4992	190	3	spaces	space	NOUN
ejpam-4992	190	4	of	of	ADP
ejpam-4992	190	5	p	p	NOUN
ejpam-4992	190	6	-	-	PUNCT
ejpam-4992	190	7	summing	sum	VERB
ejpam-4992	190	8	operators	operator	NOUN
ejpam-4992	190	9	and	and	CCONJ
ejpam-4992	190	10	characterization	characterization	NOUN
ejpam-4992	190	11	of	of	ADP
ejpam-4992	190	12	nuclearity	nuclearity	NOUN
ejpam-4992	190	13	.	.	PUNCT
ejpam-4992	190	14	math	math	NOUN
ejpam-4992	190	15	.	.	PUNCT
ejpam-4992	191	1	ann	ann	PROPN
ejpam-4992	191	2	.	.	PROPN
ejpam-4992	191	3	,	,	PUNCT
ejpam-4992	191	4	219:53–64	219:53–64	PROPN
ejpam-4992	191	5	,	,	PUNCT
ejpam-4992	191	6	1974	1974	NUM
ejpam-4992	191	7	.	.	PUNCT
ejpam-4992	192	1	[	[	X
ejpam-4992	192	2	2	2	X
ejpam-4992	192	3	]	]	PUNCT
ejpam-4992	192	4	j.	j.	PROPN
ejpam-4992	192	5	s.	s.	PROPN
ejpam-4992	192	6	cohen	cohen	PROPN
ejpam-4992	192	7	.	.	PUNCT
ejpam-4992	193	1	absolutely	absolutely	ADV
ejpam-4992	193	2	p	p	ADV
ejpam-4992	193	3	-	-	PUNCT
ejpam-4992	193	4	summing	sum	VERB
ejpam-4992	193	5	,	,	PUNCT
ejpam-4992	193	6	p	p	NOUN
ejpam-4992	193	7	-	-	PUNCT
ejpam-4992	193	8	nuclearoperators	nuclearoperator	NOUN
ejpam-4992	193	9	and	and	CCONJ
ejpam-4992	193	10	their	their	PRON
ejpam-4992	193	11	conjugates	conjugate	NOUN
ejpam-4992	193	12	.	.	PUNCT
ejpam-4992	194	1	math	math	NOUN
ejpam-4992	194	2	.	.	PUNCT
ejpam-4992	195	1	ann	ann	PROPN
ejpam-4992	195	2	.	.	PROPN
ejpam-4992	195	3	,	,	PUNCT
ejpam-4992	195	4	201:177–200	201:177–200	NUM
ejpam-4992	195	5	,	,	PUNCT
ejpam-4992	195	6	1973	1973	NUM
ejpam-4992	195	7	.	.	PUNCT
ejpam-4992	196	1	[	[	X
ejpam-4992	196	2	3	3	X
ejpam-4992	196	3	]	]	X
ejpam-4992	196	4	m.	m.	NOUN
ejpam-4992	196	5	florencio	florencio	NOUN
ejpam-4992	196	6	and	and	CCONJ
ejpam-4992	196	7	pedro	pedro	PROPN
ejpam-4992	196	8	j.	j.	PROPN
ejpam-4992	196	9	paúl	paúl	PROPN
ejpam-4992	196	10	.	.	PROPN
ejpam-4992	196	11	una	una	PROPN
ejpam-4992	196	12	representación	representación	PROPN
ejpam-4992	196	13	de	de	X
ejpam-4992	196	14	cietros	cietros	PROPN
ejpam-4992	196	15	ϵ-productos	ϵ-producto	NOUN
ejpam-4992	196	16	tensoriales	tensoriale	NOUN
ejpam-4992	196	17	.	.	PUNCT
ejpam-4992	197	1	in	in	ADP
ejpam-4992	197	2	actas	actas	PROPN
ejpam-4992	197	3	de	de	PROPN
ejpam-4992	197	4	las	las	PROPN
ejpam-4992	197	5	jornadas	jornadas	PROPN
ejpam-4992	197	6	matematicas	matematicas	PROPN
ejpam-4992	197	7	hispano	hispano	PROPN
ejpam-4992	197	8	lusas	lusas	PROPN
ejpam-4992	197	9	,	,	PUNCT
ejpam-4992	197	10	murcia	murcia	PROPN
ejpam-4992	197	11	,	,	PUNCT
ejpam-4992	197	12	pages	page	NOUN
ejpam-4992	197	13	191–203	191–203	NUM
ejpam-4992	197	14	,	,	PUNCT
ejpam-4992	197	15	murcia	murcia	PROPN
ejpam-4992	197	16	,	,	PUNCT
ejpam-4992	197	17	spain	spain	PROPN
ejpam-4992	197	18	,	,	PUNCT
ejpam-4992	197	19	1985	1985	NUM
ejpam-4992	197	20	.	.	PUNCT
ejpam-4992	198	1	universidad	universidad	PROPN
ejpam-4992	198	2	de	de	PROPN
ejpam-4992	198	3	murcia	murcia	PROPN
ejpam-4992	198	4	.	.	PUNCT
ejpam-4992	199	1	[	[	X
ejpam-4992	199	2	4	4	NUM
ejpam-4992	199	3	]	]	PUNCT
ejpam-4992	199	4	m.	m.	NOUN
ejpam-4992	199	5	florencio	florencio	PROPN
ejpam-4992	199	6	and	and	CCONJ
ejpam-4992	199	7	pedro	pedro	PROPN
ejpam-4992	199	8	j.	j.	PROPN
ejpam-4992	199	9	paúl	paúl	PROPN
ejpam-4992	199	10	.	.	PUNCT
ejpam-4992	199	11	barrelledness	barrelledness	NOUN
ejpam-4992	199	12	conditions	condition	NOUN
ejpam-4992	199	13	on	on	ADP
ejpam-4992	199	14	vector	vector	NOUN
ejpam-4992	199	15	valued	value	VERB
ejpam-4992	199	16	sequence	sequence	NOUN
ejpam-4992	199	17	spaces	space	VERB
ejpam-4992	199	18	.	.	PUNCT
ejpam-4992	200	1	arch	arch	NOUN
ejpam-4992	200	2	.	.	PUNCT
ejpam-4992	201	1	math	math	NOUN
ejpam-4992	201	2	.	.	PUNCT
ejpam-4992	201	3	,	,	PUNCT
ejpam-4992	201	4	48:153–164	48:153–164	NOUN
ejpam-4992	201	5	,	,	PUNCT
ejpam-4992	201	6	1987	1987	NUM
ejpam-4992	201	7	.	.	PUNCT
ejpam-4992	202	1	[	[	X
ejpam-4992	202	2	5	5	NUM
ejpam-4992	202	3	]	]	PUNCT
ejpam-4992	202	4	m.	m.	NOUN
ejpam-4992	202	5	florencio	florencio	NOUN
ejpam-4992	202	6	and	and	CCONJ
ejpam-4992	202	7	pedro	pedro	PROPN
ejpam-4992	202	8	j.	j.	PROPN
ejpam-4992	202	9	paúl	paúl	PROPN
ejpam-4992	202	10	.	.	PUNCT
ejpam-4992	203	1	a	a	DET
ejpam-4992	203	2	note	note	NOUN
ejpam-4992	203	3	on	on	ADP
ejpam-4992	203	4	λ	λ	NOUN
ejpam-4992	203	5	-	-	ADJ
ejpam-4992	203	6	multiplier	multipli	ADJ
ejpam-4992	203	7	convergent	convergent	NOUN
ejpam-4992	203	8	series	series	NOUN
ejpam-4992	203	9	.	.	PUNCT
ejpam-4992	204	1	časopis	časopis	PROPN
ejpam-4992	204	2	p̌est	p̌est	X
ejpam-4992	204	3	.	.	PUNCT
ejpam-4992	205	1	mat	mat	NOUN
ejpam-4992	205	2	.	.	PROPN
ejpam-4992	205	3	,	,	PUNCT
ejpam-4992	205	4	113:421–428	113:421–428	NUM
ejpam-4992	205	5	,	,	PUNCT
ejpam-4992	205	6	1988	1988	NUM
ejpam-4992	205	7	.	.	PUNCT
ejpam-4992	206	1	[	[	X
ejpam-4992	206	2	6	6	NUM
ejpam-4992	206	3	]	]	PUNCT
ejpam-4992	206	4	g.	g.	PROPN
ejpam-4992	206	5	köthe	köthe	PROPN
ejpam-4992	206	6	.	.	PUNCT
ejpam-4992	207	1	topological	topological	ADJ
ejpam-4992	207	2	vector	vector	NOUN
ejpam-4992	207	3	spaces	space	NOUN
ejpam-4992	207	4	i	i	PRON
ejpam-4992	207	5	and	and	CCONJ
ejpam-4992	207	6	ii	ii	PROPN
ejpam-4992	207	7	.	.	PROPN
ejpam-4992	208	1	springer	springer	NOUN
ejpam-4992	208	2	-	-	PUNCT
ejpam-4992	208	3	verlag	verlag	PROPN
ejpam-4992	208	4	,	,	PUNCT
ejpam-4992	208	5	berlin	berlin	PROPN
ejpam-4992	208	6	,	,	PUNCT
ejpam-4992	208	7	heidelberg	heidelberg	PROPN
ejpam-4992	208	8	,	,	PUNCT
ejpam-4992	208	9	new	new	PROPN
ejpam-4992	208	10	york	york	PROPN
ejpam-4992	208	11	,	,	PUNCT
ejpam-4992	208	12	1979	1979	NUM
ejpam-4992	208	13	.	.	PUNCT
ejpam-4992	209	1	[	[	X
ejpam-4992	209	2	7	7	X
ejpam-4992	209	3	]	]	X
ejpam-4992	209	4	l.	l.	PROPN
ejpam-4992	209	5	oubbi	oubbi	PROPN
ejpam-4992	209	6	and	and	CCONJ
ejpam-4992	209	7	m.	m.	PROPN
ejpam-4992	209	8	a.	a.	PROPN
ejpam-4992	209	9	ould	ould	AUX
ejpam-4992	209	10	sidaty	sidaty	VERB
ejpam-4992	209	11	.	.	PUNCT
ejpam-4992	210	1	dual	dual	ADJ
ejpam-4992	210	2	space	space	NOUN
ejpam-4992	210	3	of	of	ADP
ejpam-4992	210	4	certain	certain	ADJ
ejpam-4992	210	5	locally	locally	ADV
ejpam-4992	210	6	convex	convex	ADJ
ejpam-4992	210	7	sequence	sequence	NOUN
ejpam-4992	210	8	spaces	space	VERB
ejpam-4992	210	9	.	.	PUNCT
ejpam-4992	211	1	revista	revista	PROPN
ejpam-4992	211	2	de	de	X
ejpam-4992	211	3	la	la	PROPN
ejpam-4992	211	4	real	real	PROPN
ejpam-4992	211	5	academia	academia	PROPN
ejpam-4992	211	6	de	de	PROPN
ejpam-4992	211	7	ciencias	ciencias	PROPN
ejpam-4992	211	8	de	de	PROPN
ejpam-4992	211	9	zargoza	zargoza	PROPN
ejpam-4992	211	10	,	,	PUNCT
ejpam-4992	211	11	59:79–88	59:79–88	NUM
ejpam-4992	211	12	,	,	PUNCT
ejpam-4992	211	13	2004	2004	NUM
ejpam-4992	211	14	.	.	PUNCT
ejpam-4992	212	1	[	[	X
ejpam-4992	212	2	8	8	NUM
ejpam-4992	212	3	]	]	X
ejpam-4992	212	4	l.	l.	PROPN
ejpam-4992	212	5	oubbi	oubbi	PROPN
ejpam-4992	212	6	and	and	CCONJ
ejpam-4992	212	7	m.	m.	PROPN
ejpam-4992	212	8	a.	a.	PROPN
ejpam-4992	212	9	ould	ould	AUX
ejpam-4992	212	10	sidaty	sidaty	VERB
ejpam-4992	212	11	.	.	PUNCT
ejpam-4992	213	1	reflexivity	reflexivity	NOUN
ejpam-4992	213	2	of	of	ADP
ejpam-4992	213	3	spaces	space	NOUN
ejpam-4992	213	4	of	of	ADP
ejpam-4992	213	5	weakly	weakly	ADJ
ejpam-4992	213	6	summable	summable	ADJ
ejpam-4992	213	7	sequences	sequence	NOUN
ejpam-4992	213	8	.	.	PUNCT
ejpam-4992	214	1	rev	rev	PROPN
ejpam-4992	214	2	.	.	PROPN
ejpam-4992	214	3	r.	r.	PROPN
ejpam-4992	214	4	acad	acad	PROPN
ejpam-4992	214	5	.	.	PUNCT
ejpam-4992	215	1	cien	cien	NOUN
ejpam-4992	215	2	.	.	PUNCT
ejpam-4992	216	1	serie	serie	PROPN
ejpam-4992	216	2	a.	a.	PROPN
ejpam-4992	216	3	mat	mat	PROPN
ejpam-4992	216	4	.	.	PROPN
ejpam-4992	216	5	,	,	PUNCT
ejpam-4992	216	6	101(1):51–62	101(1):51–62	NUM
ejpam-4992	216	7	,	,	PUNCT
ejpam-4992	216	8	2007	2007	NUM
ejpam-4992	216	9	.	.	PUNCT
ejpam-4992	217	1	[	[	X
ejpam-4992	217	2	9	9	NUM
ejpam-4992	217	3	]	]	X
ejpam-4992	217	4	e.	e.	PROPN
ejpam-4992	217	5	pietsch	pietsch	PROPN
ejpam-4992	217	6	.	.	PUNCT
ejpam-4992	218	1	nuclear	nuclear	ADJ
ejpam-4992	218	2	locally	locally	ADV
ejpam-4992	218	3	convex	convex	PROPN
ejpam-4992	218	4	spaces	space	NOUN
ejpam-4992	218	5	.	.	PUNCT
ejpam-4992	219	1	springer	springer	NOUN
ejpam-4992	219	2	-	-	PUNCT
ejpam-4992	219	3	verlag	verlag	PROPN
ejpam-4992	219	4	,	,	PUNCT
ejpam-4992	219	5	berlin	berlin	PROPN
ejpam-4992	219	6	,	,	PUNCT
ejpam-4992	219	7	heidelberg	heidelberg	PROPN
ejpam-4992	219	8	,	,	PUNCT
ejpam-4992	219	9	new	new	PROPN
ejpam-4992	219	10	york	york	PROPN
ejpam-4992	219	11	,	,	PUNCT
ejpam-4992	219	12	1972	1972	NUM
ejpam-4992	219	13	.	.	PUNCT
ejpam-4992	220	1	[	[	X
ejpam-4992	220	2	10	10	NUM
ejpam-4992	220	3	]	]	X
ejpam-4992	220	4	m.	m.	NOUN
ejpam-4992	220	5	a.	a.	NOUN
ejpam-4992	220	6	ould	ould	AUX
ejpam-4992	220	7	sidaty	sidaty	VERB
ejpam-4992	220	8	.	.	PUNCT
ejpam-4992	221	1	reflexivity	reflexivity	NOUN
ejpam-4992	221	2	and	and	CCONJ
ejpam-4992	221	3	ak	ak	NOUN
ejpam-4992	221	4	-	-	PUNCT
ejpam-4992	221	5	property	property	NOUN
ejpam-4992	221	6	of	of	ADP
ejpam-4992	221	7	certain	certain	ADJ
ejpam-4992	221	8	vector	vector	NOUN
ejpam-4992	221	9	sequence	sequence	NOUN
ejpam-4992	221	10	spaces	space	VERB
ejpam-4992	221	11	.	.	PUNCT
ejpam-4992	222	1	bull	bull	NOUN
ejpam-4992	222	2	.	.	PUNCT
ejpam-4992	223	1	belg	belg	PROPN
ejpam-4992	223	2	.	.	PUNCT
ejpam-4992	224	1	math	math	NOUN
ejpam-4992	224	2	.	.	PUNCT
ejpam-4992	225	1	soc	soc	PROPN
ejpam-4992	225	2	.	.	PUNCT
ejpam-4992	225	3	,	,	PUNCT
ejpam-4992	225	4	10(4):579–583	10(4):579–583	PROPN
ejpam-4992	225	5	,	,	PUNCT
ejpam-4992	225	6	2003	2003	NUM
ejpam-4992	225	7	.	.	PUNCT
ejpam-4992	226	1	[	[	X
ejpam-4992	226	2	11	11	NUM
ejpam-4992	226	3	]	]	PUNCT
ejpam-4992	226	4	m.	m.	NOUN
ejpam-4992	226	5	a.	a.	NOUN
ejpam-4992	226	6	ould	ould	AUX
ejpam-4992	226	7	sidaty	sidaty	VERB
ejpam-4992	226	8	.	.	PUNCT
ejpam-4992	227	1	nuclearity	nuclearity	NOUN
ejpam-4992	227	2	of	of	ADP
ejpam-4992	227	3	certain	certain	ADJ
ejpam-4992	227	4	vector	vector	NOUN
ejpam-4992	227	5	-	-	PUNCT
ejpam-4992	227	6	valued	value	VERB
ejpam-4992	227	7	sequence	sequence	NOUN
ejpam-4992	227	8	spaces	space	VERB
ejpam-4992	227	9	.	.	PUNCT
ejpam-4992	228	1	rev	rev	PROPN
ejpam-4992	228	2	.	.	PUNCT
ejpam-4992	229	1	real	real	PROPN
ejpam-4992	229	2	academia	academia	PROPN
ejpam-4992	229	3	de	de	PROPN
ejpam-4992	229	4	ciencias	ciencias	PROPN
ejpam-4992	229	5	.	.	PUNCT
ejpam-4992	230	1	zaragoza	zaragoza	PROPN
ejpam-4992	230	2	.	.	PROPN
ejpam-4992	230	3	,	,	PUNCT
ejpam-4992	230	4	62:81–89	62:81–89	PROPN
ejpam-4992	230	5	,	,	PUNCT
ejpam-4992	230	6	2007	2007	NUM
ejpam-4992	230	7	.	.	PUNCT
ejpam-4992	231	1	[	[	X
ejpam-4992	231	2	12	12	NUM
ejpam-4992	231	3	]	]	PUNCT
ejpam-4992	231	4	m.	m.	NOUN
ejpam-4992	231	5	a.	a.	NOUN
ejpam-4992	231	6	ould	ould	AUX
ejpam-4992	231	7	sidaty	sidaty	VERB
ejpam-4992	231	8	.	.	PUNCT
ejpam-4992	232	1	reflexivity	reflexivity	NOUN
ejpam-4992	232	2	of	of	ADP
ejpam-4992	232	3	vector	vector	NOUN
ejpam-4992	232	4	-	-	PUNCT
ejpam-4992	232	5	valued	value	VERB
ejpam-4992	232	6	köthe	köthe	PROPN
ejpam-4992	232	7	-	-	PUNCT
ejpam-4992	232	8	orlicz	orlicz	ADJ
ejpam-4992	232	9	sequence	sequence	NOUN
ejpam-4992	232	10	spaces	space	NOUN
ejpam-4992	232	11	.	.	PUNCT
ejpam-4992	233	1	turk	turk	PROPN
ejpam-4992	233	2	.	.	PUNCT
ejpam-4992	234	1	j.	j.	PROPN
ejpam-4992	234	2	math	math	PROPN
ejpam-4992	234	3	.	.	PUNCT
ejpam-4992	234	4	,	,	PUNCT
ejpam-4992	234	5	42(3):911–923	42(3):911–923	PROPN
ejpam-4992	234	6	,	,	PUNCT
ejpam-4992	234	7	2018	2018	NUM
ejpam-4992	234	8	.	.	PUNCT
ejpam-4992	235	1	[	[	X
ejpam-4992	235	2	13	13	NUM
ejpam-4992	235	3	]	]	PUNCT
ejpam-4992	235	4	m.	m.	NOUN
ejpam-4992	235	5	a.	a.	NOUN
ejpam-4992	235	6	ould	ould	AUX
ejpam-4992	235	7	sidaty	sidaty	VERB
ejpam-4992	235	8	.	.	PUNCT
ejpam-4992	236	1	nuclearity	nuclearity	NOUN
ejpam-4992	236	2	of	of	ADP
ejpam-4992	236	3	a	a	DET
ejpam-4992	236	4	class	class	NOUN
ejpam-4992	236	5	of	of	ADP
ejpam-4992	236	6	vector	vector	NOUN
ejpam-4992	236	7	-	-	PUNCT
ejpam-4992	236	8	valued	value	VERB
ejpam-4992	236	9	sequence	sequence	NOUN
ejpam-4992	236	10	spaces	space	VERB
ejpam-4992	236	11	.	.	PUNCT
ejpam-4992	237	1	eur	eur	PROPN
ejpam-4992	237	2	.	.	PUNCT
ejpam-4992	238	1	j.	j.	PROPN
ejpam-4992	238	2	pure	pure	PROPN
ejpam-4992	238	3	appl	appl	PROPN
ejpam-4992	238	4	.	.	PUNCT
ejpam-4992	238	5	math	math	PROPN
ejpam-4992	238	6	.	.	PUNCT
ejpam-4992	238	7	,	,	PUNCT
ejpam-4992	238	8	16(3):1762–1771	16(3):1762–1771	NUM
ejpam-4992	238	9	,	,	PUNCT
ejpam-4992	238	10	2023	2023	NUM
ejpam-4992	238	11	.	.	PUNCT
ejpam-4992	239	1	[	[	X
ejpam-4992	239	2	14	14	NUM
ejpam-4992	239	3	]	]	X
ejpam-4992	239	4	m.	m.	NOUN
ejpam-4992	239	5	valdivia	valdivia	PROPN
ejpam-4992	239	6	.	.	PUNCT
ejpam-4992	240	1	topics	topic	NOUN
ejpam-4992	240	2	on	on	ADP
ejpam-4992	240	3	locally	locally	ADV
ejpam-4992	240	4	convex	convex	ADJ
ejpam-4992	240	5	spaces	space	NOUN
ejpam-4992	240	6	.	.	PUNCT
ejpam-4992	241	1	north	north	NOUN
ejpam-4992	241	2	-	-	PUNCT
ejpam-4992	241	3	holland	holland	PROPN
ejpam-4992	241	4	,	,	PUNCT
ejpam-4992	241	5	amsterdam	amsterdam	PROPN
ejpam-4992	241	6	,	,	PUNCT
ejpam-4992	241	7	new	new	PROPN
ejpam-4992	241	8	york	york	PROPN
ejpam-4992	241	9	,	,	PUNCT
ejpam-4992	241	10	oxford	oxford	PROPN
ejpam-4992	241	11	,	,	PUNCT
ejpam-4992	241	12	1982	1982	NUM
ejpam-4992	241	13	.	.	PUNCT