id	sid	tid	token	lemma	pos
iajs-1806	1	1	microsoft	microsoft	PROPN
iajs-1806	1	2	word	word	NOUN
iajs-1806	1	3	337	337	NUM
iajs-1806	1	4	-	-	SYM
iajs-1806	1	5	343	343	NUM
iajs-1806	1	6	ihsciconf	ihsciconf	NOUN
iajs-1806	1	7	2017	2017	NUM
iajs-1806	1	8	special	special	ADJ
iajs-1806	1	9	issue	issue	NOUN
iajs-1806	1	10	ibn	ibn	PROPN
iajs-1806	1	11	al	al	PROPN
iajs-1806	1	12	-	-	PUNCT
iajs-1806	1	13	haitham	haitham	PROPN
iajs-1806	1	14	journal	journal	PROPN
iajs-1806	1	15	for	for	ADP
iajs-1806	1	16	pure	pure	ADJ
iajs-1806	1	17	and	and	CCONJ
iajs-1806	1	18	applied	apply	VERB
iajs-1806	1	19	science	science	NOUN
iajs-1806	1	20	https://doi.org/	https://doi.org/	NOUN
iajs-1806	1	21	10.30526/2017.ihsciconf.1806	10.30526/2017.ihsciconf.1806	NUM
iajs-1806	1	22	for	for	ADP
iajs-1806	1	23	more	more	ADJ
iajs-1806	1	24	information	information	NOUN
iajs-1806	1	25	about	about	ADP
iajs-1806	1	26	the	the	DET
iajs-1806	1	27	conference	conference	NOUN
iajs-1806	1	28	please	please	INTJ
iajs-1806	1	29	visit	visit	VERB
iajs-1806	1	30	the	the	DET
iajs-1806	1	31	websites	website	NOUN
iajs-1806	1	32	:	:	PUNCT
iajs-1806	1	33	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1806	1	34	  	  	SPACE
iajs-1806	1	35	www.ihsciconf.org	www.ihsciconf.org	ADJ
iajs-1806	1	36	   	   	SPACE
iajs-1806	1	37	mathematics	mathematic	NOUN
iajs-1806	1	38	|337	|337	PROPN
iajs-1806	1	39	    	    	SPACE
iajs-1806	1	40	q	q	PROPN
iajs-1806	1	41	uasi	uasi	ADJ
iajs-1806	1	42	-	-	PUNCT
iajs-1806	1	43	inner	inner	ADJ
iajs-1806	1	44	product	product	NOUN
iajs-1806	1	45	spaces	space	NOUN
iajs-1806	1	46	of	of	ADP
iajs-1806	1	47	quasi	quasi	ADJ
iajs-1806	1	48	-	-	ADJ
iajs-1806	1	49	sobolev	sobolev	ADJ
iajs-1806	1	50	spaces	space	NOUN
iajs-1806	1	51	and	and	CCONJ
iajs-1806	1	52	their	their	PRON
iajs-1806	1	53	completeness	completeness	NOUN
iajs-1806	1	54	jawad	jawad	PROPN
iajs-1806	1	55	kadhim	kadhim	PROPN
iajs-1806	1	56	khalaf	khalaf	PROPN
iajs-1806	1	57	al	al	PROPN
iajs-1806	1	58	-	-	PUNCT
iajs-1806	1	59	delfi	delfi	PROPN
iajs-1806	1	60	jawadaldelfi@uomustansiriyah.edu.iq	jawadaldelfi@uomustansiriyah.edu.iq	PROPN
iajs-1806	1	61	dept	dept	NOUN
iajs-1806	1	62	.	.	PROPN
iajs-1806	1	63	of	of	ADP
iajs-1806	1	64	mathematics	mathematics	PROPN
iajs-1806	1	65	/	/	SYM
iajs-1806	1	66	college	college	NOUN
iajs-1806	1	67	of	of	ADP
iajs-1806	1	68	science	science	PROPN
iajs-1806	1	69	/	/	SYM
iajs-1806	1	70	al	al	PROPN
iajs-1806	1	71	-	-	PUNCT
iajs-1806	1	72	mustansiriyah	mustansiriyah	PROPN
iajs-1806	1	73	university	university	NOUN
iajs-1806	1	74	abstract	abstract	ADJ
iajs-1806	1	75	sequences	sequence	NOUN
iajs-1806	1	76	spaces	space	NOUN
iajs-1806	1	77	ℓ	ℓ	PROPN
iajs-1806	1	78	,	,	PUNCT
iajs-1806	1	79	m	m	PROPN
iajs-1806	1	80	∈	∈	PROPN
iajs-1806	1	81	ℝ	ℝ	PROPN
iajs-1806	1	82	,	,	PUNCT
iajs-1806	1	83	p	p	NOUN
iajs-1806	1	84	∈	∈	PROPN
iajs-1806	1	85	ℝ	ℝ	NOUN
iajs-1806	1	86	tha𝑡	tha𝑡	NOUN
iajs-1806	1	87	have	have	AUX
iajs-1806	1	88	called	call	VERB
iajs-1806	1	89	quasi	quasi	ADJ
iajs-1806	1	90	-	-	ADJ
iajs-1806	1	91	sobolev	sobolev	ADJ
iajs-1806	1	92	spaces	space	NOUN
iajs-1806	1	93	were	be	AUX
iajs-1806	1	94	introduced	introduce	VERB
iajs-1806	1	95	by	by	ADP
iajs-1806	1	96	jawad	jawad	PROPN
iajs-1806	1	97	.	.	PUNCT
iajs-1806	2	1	k.	k.	PROPN
iajs-1806	3	1	al	al	PROPN
iajs-1806	3	2	-	-	PUNCT
iajs-1806	3	3	delfi	delfi	PROPN
iajs-1806	3	4	in	in	ADP
iajs-1806	3	5	2013	2013	NUM
iajs-1806	3	6	[	[	PUNCT
iajs-1806	3	7	1	1	NUM
iajs-1806	3	8	[	[	PUNCT
iajs-1806	3	9	.	.	PUNCT
iajs-1806	4	1	in	in	ADP
iajs-1806	4	2	this	this	DET
iajs-1806	4	3	paper	paper	NOUN
iajs-1806	4	4	,	,	PUNCT
iajs-1806	4	5	we	we	PRON
iajs-1806	4	6	deal	deal	VERB
iajs-1806	4	7	with	with	ADP
iajs-1806	4	8	notion	notion	NOUN
iajs-1806	4	9	of	of	ADP
iajs-1806	4	10	quasiinner	quasiinner	NOUN
iajs-1806	4	11	product	product	NOUN
iajs-1806	4	12	space	space	NOUN
iajs-1806	4	13	by	by	ADP
iajs-1806	4	14	using	use	VERB
iajs-1806	4	15	concept	concept	NOUN
iajs-1806	4	16	of	of	ADP
iajs-1806	4	17	quasi	quasi	ADJ
iajs-1806	4	18	-	-	ADJ
iajs-1806	4	19	normed	normed	ADJ
iajs-1806	4	20	space	space	NOUN
iajs-1806	4	21	which	which	PRON
iajs-1806	4	22	is	be	AUX
iajs-1806	4	23	generalized	generalize	VERB
iajs-1806	4	24	to	to	ADP
iajs-1806	4	25	normed	normed	ADJ
iajs-1806	4	26	space	space	NOUN
iajs-1806	4	27	and	and	CCONJ
iajs-1806	4	28	given	give	VERB
iajs-1806	4	29	a	a	DET
iajs-1806	4	30	relationship	relationship	NOUN
iajs-1806	4	31	between	between	ADP
iajs-1806	4	32	pre	pre	ADJ
iajs-1806	4	33	-	-	ADJ
iajs-1806	4	34	hilbert	hilbert	ADJ
iajs-1806	4	35	space	space	NOUN
iajs-1806	4	36	and	and	CCONJ
iajs-1806	4	37	a	a	DET
iajs-1806	4	38	quasi	quasi	ADJ
iajs-1806	4	39	-	-	ADJ
iajs-1806	4	40	inner	inner	ADJ
iajs-1806	4	41	product	product	NOUN
iajs-1806	4	42	space	space	NOUN
iajs-1806	4	43	with	with	ADP
iajs-1806	4	44	important	important	ADJ
iajs-1806	4	45	results	result	NOUN
iajs-1806	4	46	and	and	CCONJ
iajs-1806	4	47	examples	example	NOUN
iajs-1806	4	48	.	.	PUNCT
iajs-1806	5	1	completeness	completeness	NOUN
iajs-1806	5	2	properties	property	NOUN
iajs-1806	5	3	in	in	ADP
iajs-1806	5	4	quasi	quasi	ADJ
iajs-1806	5	5	-	-	ADJ
iajs-1806	5	6	inner	inner	ADJ
iajs-1806	5	7	product	product	NOUN
iajs-1806	5	8	space	space	NOUN
iajs-1806	5	9	gives	give	VERB
iajs-1806	5	10	us	we	PRON
iajs-1806	5	11	concept	concept	NOUN
iajs-1806	5	12	of	of	ADP
iajs-1806	5	13	quasi	quasi	ADJ
iajs-1806	5	14	-	-	ADJ
iajs-1806	5	15	hilbert	hilbert	ADJ
iajs-1806	5	16	space	space	NOUN
iajs-1806	5	17	.	.	PUNCT
iajs-1806	6	1	we	we	PRON
iajs-1806	6	2	show	show	VERB
iajs-1806	6	3	that	that	SCONJ
iajs-1806	6	4	,	,	PUNCT
iajs-1806	6	5	not	not	PART
iajs-1806	6	6	all	all	DET
iajs-1806	6	7	quasisobolev	quasisobolev	NOUN
iajs-1806	6	8	spaces	space	NOUN
iajs-1806	6	9	ℓ	ℓ	PROPN
iajs-1806	6	10	,	,	PUNCT
iajs-1806	6	11	are	be	AUX
iajs-1806	6	12	quasi	quasi	ADJ
iajs-1806	6	13	-	-	ADJ
iajs-1806	6	14	hilbert	hilbert	ADJ
iajs-1806	6	15	spaces	space	NOUN
iajs-1806	6	16	.	.	PUNCT
iajs-1806	7	1	the	the	DET
iajs-1806	7	2	best	good	ADJ
iajs-1806	7	3	examples	example	NOUN
iajs-1806	7	4	which	which	PRON
iajs-1806	7	5	are	be	AUX
iajs-1806	7	6	quasihilbert	quasihilbert	ADJ
iajs-1806	7	7	spaces	space	NOUN
iajs-1806	7	8	and	and	CCONJ
iajs-1806	7	9	hilbert	hilbert	NOUN
iajs-1806	7	10	spaces	space	NOUN
iajs-1806	7	11	are	be	AUX
iajs-1806	7	12	ℓ	ℓ	NOUN
iajs-1806	7	13	,	,	PUNCT
iajs-1806	7	14	where	where	SCONJ
iajs-1806	7	15	m	m	PROPN
iajs-1806	7	16	∈	∈	PROPN
iajs-1806	7	17	ℝ	ℝ	PROPN
iajs-1806	7	18	.	.	PUNCT
iajs-1806	8	1	finally	finally	ADV
iajs-1806	8	2	,	,	PUNCT
iajs-1806	8	3	propositions	proposition	NOUN
iajs-1806	8	4	,	,	PUNCT
iajs-1806	8	5	theorems	theorem	VERB
iajs-1806	8	6	an	an	DET
iajs-1806	8	7	examples	example	NOUN
iajs-1806	8	8	are	be	AUX
iajs-1806	8	9	our	our	PRON
iajs-1806	8	10	own	own	ADJ
iajs-1806	8	11	unless	unless	SCONJ
iajs-1806	8	12	otherwise	otherwise	ADV
iajs-1806	8	13	referred	refer	VERB
iajs-1806	8	14	.	.	PUNCT
iajs-1806	9	1	keywords	keyword	NOUN
iajs-1806	9	2	:	:	PUNCT
iajs-1806	9	3	quasi	quasi	ADJ
iajs-1806	9	4	-	-	ADJ
iajs-1806	9	5	sobolev	sobolev	ADJ
iajs-1806	9	6	space	space	NOUN
iajs-1806	9	7	,	,	PUNCT
iajs-1806	9	8	quasi	quasi	ADJ
iajs-1806	9	9	-	-	ADJ
iajs-1806	9	10	banach	banach	ADJ
iajs-1806	9	11	space	space	NOUN
iajs-1806	9	12	,	,	PUNCT
iajs-1806	9	13	g𝑎teaux	g𝑎teaux	VERB
iajs-1806	9	14	derivative	derivative	ADJ
iajs-1806	9	15	,	,	PUNCT
iajs-1806	9	16	quasi	quasi	ADJ
iajs-1806	9	17	-	-	ADJ
iajs-1806	9	18	inner	inner	ADJ
iajs-1806	9	19	product	product	NOUN
iajs-1806	9	20	space	space	NOUN
iajs-1806	9	21	,	,	PUNCT
iajs-1806	9	22	quasi	quasi	ADJ
iajs-1806	9	23	-	-	ADJ
iajs-1806	9	24	hilbert	hilbert	ADJ
iajs-1806	9	25	space	space	NOUN
iajs-1806	9	26	.	.	PUNCT
iajs-1806	10	1	smooth	smooth	ADJ
iajs-1806	10	2	quasi	quasi	ADJ
iajs-1806	10	3	-	-	ADJ
iajs-1806	10	4	hilbert	hilbert	ADJ
iajs-1806	10	5	space	space	NOUN
iajs-1806	10	6	.	.	PUNCT
iajs-1806	11	1	ihsciconf	ihsciconf	PROPN
iajs-1806	11	2	2017	2017	NUM
iajs-1806	11	3	special	special	ADJ
iajs-1806	11	4	issue	issue	NOUN
iajs-1806	11	5	ibn	ibn	PROPN
iajs-1806	11	6	al	al	PROPN
iajs-1806	11	7	-	-	PUNCT
iajs-1806	11	8	haitham	haitham	PROPN
iajs-1806	11	9	journal	journal	PROPN
iajs-1806	11	10	for	for	ADP
iajs-1806	11	11	pure	pure	ADJ
iajs-1806	11	12	and	and	CCONJ
iajs-1806	11	13	applied	apply	VERB
iajs-1806	11	14	science	science	NOUN
iajs-1806	11	15	https://doi.org/	https://doi.org/	NOUN
iajs-1806	11	16	10.30526/2017.ihsciconf.1806	10.30526/2017.ihsciconf.1806	NUM
iajs-1806	11	17	for	for	ADP
iajs-1806	11	18	more	more	ADJ
iajs-1806	11	19	information	information	NOUN
iajs-1806	11	20	about	about	ADP
iajs-1806	11	21	the	the	DET
iajs-1806	11	22	conference	conference	NOUN
iajs-1806	11	23	please	please	INTJ
iajs-1806	11	24	visit	visit	VERB
iajs-1806	11	25	the	the	DET
iajs-1806	11	26	websites	website	NOUN
iajs-1806	11	27	:	:	PUNCT
iajs-1806	11	28	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1806	11	29	  	  	SPACE
iajs-1806	11	30	www.ihsciconf.org	www.ihsciconf.org	ADJ
iajs-1806	11	31	   	   	SPACE
iajs-1806	11	32	mathematics	mathematic	NOUN
iajs-1806	11	33	|338	|338	NOUN
iajs-1806	11	34	    	    	SPACE
iajs-1806	11	35	1	1	NUM
iajs-1806	11	36	.	.	PUNCT
iajs-1806	12	1	introduction	introduction	NOUN
iajs-1806	12	2	the	the	DET
iajs-1806	12	3	family	family	NOUN
iajs-1806	12	4	of	of	ADP
iajs-1806	12	5	sequence	sequence	NOUN
iajs-1806	12	6	spaces	space	VERB
iajs-1806	12	7	ℓ	ℓ	PROPN
iajs-1806	12	8	,	,	PUNCT
iajs-1806	12	9	1	1	NUM
iajs-1806	12	10	<	<	X
iajs-1806	12	11	p	p	X
iajs-1806	12	12	<	<	X
iajs-1806	12	13	∞	∞	PROPN
iajs-1806	12	14	are	be	AUX
iajs-1806	12	15	normed	normed	ADJ
iajs-1806	12	16	space	space	NOUN
iajs-1806	12	17	where	where	SCONJ
iajs-1806	12	18	,	,	PUNCT
iajs-1806	12	19	ℓ	ℓ	PROPN
iajs-1806	12	20	is	be	AUX
iajs-1806	12	21	the	the	DET
iajs-1806	12	22	only	only	ADJ
iajs-1806	12	23	inner	inner	ADJ
iajs-1806	12	24	product	product	NOUN
iajs-1806	12	25	space	space	NOUN
iajs-1806	12	26	in	in	ADP
iajs-1806	12	27	this	this	DET
iajs-1806	12	28	family	family	NOUN
iajs-1806	12	29	.	.	PUNCT
iajs-1806	13	1	completeness	completeness	NOUN
iajs-1806	13	2	of	of	ADP
iajs-1806	13	3	these	these	DET
iajs-1806	13	4	spaces	space	NOUN
iajs-1806	13	5	can	can	AUX
iajs-1806	13	6	be	be	AUX
iajs-1806	13	7	proved	prove	VERB
iajs-1806	13	8	with	with	ADP
iajs-1806	13	9	respect	respect	NOUN
iajs-1806	13	10	to	to	ADP
iajs-1806	13	11	appropriate	appropriate	ADJ
iajs-1806	13	12	norms	norm	NOUN
iajs-1806	13	13	[	[	X
iajs-1806	13	14	2	2	NUM
iajs-1806	13	15	,	,	PUNCT
iajs-1806	13	16	3	3	NUM
iajs-1806	13	17	]	]	PUNCT
iajs-1806	13	18	.	.	PUNCT
iajs-1806	14	1	since	since	SCONJ
iajs-1806	14	2	the	the	DET
iajs-1806	14	3	triangle	triangle	NOUN
iajs-1806	14	4	inequality	inequality	NOUN
iajs-1806	14	5	fails	fail	VERB
iajs-1806	14	6	in	in	ADP
iajs-1806	14	7	the	the	DET
iajs-1806	14	8	family	family	NOUN
iajs-1806	14	9	of	of	ADP
iajs-1806	14	10	sequence	sequence	NOUN
iajs-1806	14	11	spaces	space	VERB
iajs-1806	14	12	ℓ	ℓ	PROPN
iajs-1806	14	13	,	,	PUNCT
iajs-1806	14	14	0	0	PUNCT
iajs-1806	15	1	<	<	X
iajs-1806	16	1	p	p	X
iajs-1806	16	2	<	<	X
iajs-1806	16	3	1	1	NUM
iajs-1806	16	4	where	where	SCONJ
iajs-1806	16	5	,	,	PUNCT
iajs-1806	16	6	there	there	PRON
iajs-1806	16	7	is	be	VERB
iajs-1806	16	8	no	no	DET
iajs-1806	16	9	norm	norm	NOUN
iajs-1806	16	10	for	for	ADP
iajs-1806	16	11	this	this	DET
iajs-1806	16	12	range	range	NOUN
iajs-1806	16	13	,	,	PUNCT
iajs-1806	16	14	then	then	ADV
iajs-1806	16	15	imply	imply	VERB
iajs-1806	16	16	that	that	SCONJ
iajs-1806	16	17	it	it	PRON
iajs-1806	16	18	is	be	AUX
iajs-1806	16	19	not	not	PART
iajs-1806	16	20	banach	banach	NOUN
iajs-1806	16	21	space	space	NOUN
iajs-1806	16	22	.	.	PUNCT
iajs-1806	17	1	for	for	ADP
iajs-1806	17	2	a	a	DET
iajs-1806	17	3	sequence	sequence	NOUN
iajs-1806	17	4	space	space	NOUN
iajs-1806	17	5	ℓ	ℓ	NOUN
iajs-1806	17	6	,	,	PUNCT
iajs-1806	17	7	where	where	SCONJ
iajs-1806	17	8	0	0	PUNCT
iajs-1806	17	9	<	<	X
iajs-1806	17	10	p	p	X
iajs-1806	17	11	<	<	X
iajs-1806	17	12	1	1	NUM
iajs-1806	17	13	and	and	CCONJ
iajs-1806	17	14	others	other	NOUN
iajs-1806	17	15	,	,	PUNCT
iajs-1806	17	16	many	many	ADJ
iajs-1806	17	17	concepts	concept	NOUN
iajs-1806	17	18	were	be	AUX
iajs-1806	17	19	introduced	introduce	VERB
iajs-1806	17	20	.	.	PUNCT
iajs-1806	18	1	one	one	NUM
iajs-1806	18	2	of	of	ADP
iajs-1806	18	3	these	these	DET
iajs-1806	18	4	concepts	concept	NOUN
iajs-1806	18	5	is	be	AUX
iajs-1806	18	6	a	a	DET
iajs-1806	18	7	quasibanach	quasibanach	NOUN
iajs-1806	18	8	space	space	NOUN
iajs-1806	18	9	which	which	PRON
iajs-1806	18	10	is	be	AUX
iajs-1806	18	11	based	base	VERB
iajs-1806	18	12	on	on	ADP
iajs-1806	18	13	the	the	DET
iajs-1806	18	14	definition	definition	NOUN
iajs-1806	18	15	of	of	ADP
iajs-1806	18	16	a	a	DET
iajs-1806	18	17	quasinorm	quasinorm	NOUN
iajs-1806	18	18	[	[	X
iajs-1806	18	19	4	4	NUM
iajs-1806	18	20	]	]	PUNCT
iajs-1806	18	21	.	.	PUNCT
iajs-1806	19	1	a	a	DET
iajs-1806	19	2	quasibanach	quasibanach	NOUN
iajs-1806	19	3	space	space	NOUN
iajs-1806	19	4	is	be	AUX
iajs-1806	19	5	a	a	DET
iajs-1806	19	6	topological	topological	ADJ
iajs-1806	19	7	linear	linear	ADJ
iajs-1806	19	8	space	space	NOUN
iajs-1806	19	9	[	[	X
iajs-1806	19	10	5	5	NUM
iajs-1806	19	11	]	]	PUNCT
iajs-1806	19	12	.	.	PUNCT
iajs-1806	20	1	in	in	ADP
iajs-1806	20	2	]	]	NUM
iajs-1806	20	3	1	1	NUM
iajs-1806	20	4	[	[	PUNCT
iajs-1806	20	5	,	,	PUNCT
iajs-1806	20	6	we	we	PRON
iajs-1806	20	7	were	be	AUX
iajs-1806	20	8	constructed	construct	VERB
iajs-1806	20	9	a	a	DET
iajs-1806	20	10	set	set	NOUN
iajs-1806	20	11	of	of	ADP
iajs-1806	20	12	all	all	DET
iajs-1806	20	13	sequence	sequence	NOUN
iajs-1806	20	14	spaces	space	NOUN
iajs-1806	20	15	of	of	ADP
iajs-1806	20	16	power	power	NOUN
iajs-1806	20	17	real	real	ADJ
iajs-1806	20	18	number	number	NOUN
iajs-1806	20	19	m	m	PROPN
iajs-1806	20	20	,	,	PUNCT
iajs-1806	20	21	m	m	PROPN
iajs-1806	20	22	∈	∈	PROPN
iajs-1806	20	23	ℝ	ℝ	PROPN
iajs-1806	20	24	.	.	PUNCT
iajs-1806	21	1	the	the	DET
iajs-1806	21	2	new	new	ADJ
iajs-1806	21	3	spaces	space	NOUN
iajs-1806	21	4	have	have	AUX
iajs-1806	21	5	called	call	VERB
iajs-1806	21	6	quasi	quasi	ADJ
iajs-1806	21	7	-	-	ADJ
iajs-1806	21	8	sobolev	sobolev	ADJ
iajs-1806	21	9	spaces	space	NOUN
iajs-1806	21	10	and	and	CCONJ
iajs-1806	21	11	have	have	AUX
iajs-1806	21	12	denoted	denote	VERB
iajs-1806	21	13	by	by	ADP
iajs-1806	21	14	ℓ	ℓ	PROPN
iajs-1806	21	15	.	.	PUNCT
iajs-1806	22	1	we	we	PRON
iajs-1806	22	2	were	be	AUX
iajs-1806	22	3	proved	prove	VERB
iajs-1806	22	4	that	that	SCONJ
iajs-1806	22	5	these	these	DET
iajs-1806	22	6	spaces	space	NOUN
iajs-1806	22	7	are	be	AUX
iajs-1806	22	8	quasi	quasi	ADJ
iajs-1806	22	9	-	-	ADJ
iajs-1806	22	10	banach	banach	ADJ
iajs-1806	22	11	spaces	space	NOUN
iajs-1806	22	12	in	in	ADP
iajs-1806	22	13	case	case	NOUN
iajs-1806	22	14	0	0	PUNCT
iajs-1806	22	15	<	<	X
iajs-1806	22	16	p	p	X
iajs-1806	22	17	<	<	X
iajs-1806	22	18	∞	∞	PROPN
iajs-1806	23	1	and	and	CCONJ
iajs-1806	23	2	they	they	PRON
iajs-1806	23	3	are	be	AUX
iajs-1806	23	4	banach	banach	ADV
iajs-1806	23	5	spaces	space	NOUN
iajs-1806	23	6	for	for	ADP
iajs-1806	23	7	1	1	NUM
iajs-1806	23	8	<	<	X
iajs-1806	23	9	p	p	X
iajs-1806	23	10	<	<	X
iajs-1806	23	11	∞	∞	PROPN
iajs-1806	23	12	.	.	PUNCT
iajs-1806	24	1	in	in	ADP
iajs-1806	24	2	our	our	PRON
iajs-1806	24	3	work	work	NOUN
iajs-1806	24	4	,	,	PUNCT
iajs-1806	24	5	we	we	PRON
iajs-1806	24	6	need	need	VERB
iajs-1806	24	7	study	study	VERB
iajs-1806	24	8	these	these	DET
iajs-1806	24	9	spaces	space	NOUN
iajs-1806	24	10	with	with	ADP
iajs-1806	24	11	other	other	ADJ
iajs-1806	24	12	concepts	concept	NOUN
iajs-1806	24	13	such	such	ADJ
iajs-1806	24	14	as	as	ADP
iajs-1806	24	15	a	a	DET
iajs-1806	24	16	pre	pre	ADJ
iajs-1806	24	17	-	-	ADJ
iajs-1806	24	18	hilbert	hilbert	ADJ
iajs-1806	24	19	space	space	NOUN
iajs-1806	24	20	and	and	CCONJ
iajs-1806	24	21	a	a	DET
iajs-1806	24	22	quasiinner	quasiinner	NOUN
iajs-1806	24	23	product	product	NOUN
iajs-1806	24	24	space	space	NOUN
iajs-1806	24	25	(	(	PUNCT
iajs-1806	24	26	q.	q.	NOUN
iajs-1806	24	27	i	i	PRON
iajs-1806	24	28	.p	.p	PROPN
iajs-1806	24	29	)	)	PUNCT
iajs-1806	24	30	and	and	CCONJ
iajs-1806	24	31	their	their	PRON
iajs-1806	24	32	completeness	completeness	NOUN
iajs-1806	24	33	.	.	PUNCT
iajs-1806	25	1	in	in	ADP
iajs-1806	25	2	normed	normed	ADJ
iajs-1806	25	3	spaces	space	NOUN
iajs-1806	25	4	,	,	PUNCT
iajs-1806	25	5	mathematicians	mathematician	NOUN
iajs-1806	25	6	have	have	AUX
iajs-1806	25	7	used	use	VERB
iajs-1806	25	8	g𝑎teaux	g𝑎teaux	ADJ
iajs-1806	25	9	derivatives	derivative	NOUN
iajs-1806	25	10	to	to	PART
iajs-1806	25	11	introduce	introduce	VERB
iajs-1806	25	12	notion	notion	NOUN
iajs-1806	25	13	of	of	ADP
iajs-1806	25	14	quasiinner	quasiinner	NOUN
iajs-1806	25	15	product	product	NOUN
iajs-1806	25	16	space	space	NOUN
iajs-1806	25	17	and	and	CCONJ
iajs-1806	25	18	have	have	AUX
iajs-1806	25	19	investigated	investigate	VERB
iajs-1806	25	20	properties	property	NOUN
iajs-1806	25	21	of	of	ADP
iajs-1806	25	22	this	this	DET
iajs-1806	25	23	concept	concept	NOUN
iajs-1806	25	24	such	such	ADJ
iajs-1806	25	25	as	as	ADP
iajs-1806	25	26	completeness	completeness	NOUN
iajs-1806	25	27	,	,	PUNCT
iajs-1806	25	28	smoothness	smoothness	ADJ
iajs-1806	25	29	and	and	CCONJ
iajs-1806	25	30	others	other	NOUN
iajs-1806	26	1	[	[	X
iajs-1806	26	2	6,7	6,7	NUM
iajs-1806	26	3	,	,	PUNCT
iajs-1806	26	4	8	8	NUM
iajs-1806	26	5	]	]	PUNCT
iajs-1806	26	6	.	.	PUNCT
iajs-1806	27	1	this	this	DET
iajs-1806	27	2	paper	paper	NOUN
iajs-1806	27	3	is	be	AUX
iajs-1806	27	4	devoted	devoted	ADJ
iajs-1806	27	5	transference	transference	NOUN
iajs-1806	27	6	above	above	ADP
iajs-1806	27	7	ideology	ideology	NOUN
iajs-1806	27	8	on	on	ADP
iajs-1806	27	9	quasi	quasi	ADJ
iajs-1806	27	10	-	-	ADJ
iajs-1806	27	11	normed	normed	ADJ
iajs-1806	27	12	space	space	NOUN
iajs-1806	27	13	to	to	ADP
iajs-1806	27	14	given	give	VERB
iajs-1806	27	15	(	(	PUNCT
iajs-1806	27	16	q.	q.	NOUN
iajs-1806	27	17	i	i	PRON
iajs-1806	27	18	.p	.p	PROPN
iajs-1806	27	19	)	)	PUNCT
iajs-1806	27	20	and	and	CCONJ
iajs-1806	27	21	is	be	AUX
iajs-1806	27	22	studied	study	VERB
iajs-1806	27	23	the	the	DET
iajs-1806	27	24	relationship	relationship	NOUN
iajs-1806	27	25	between	between	ADP
iajs-1806	27	26	this	this	DET
iajs-1806	27	27	notion	notion	NOUN
iajs-1806	27	28	and	and	CCONJ
iajs-1806	27	29	others	other	NOUN
iajs-1806	27	30	,	,	PUNCT
iajs-1806	27	31	in	in	ADP
iajs-1806	27	32	order	order	NOUN
iajs-1806	27	33	to	to	PART
iajs-1806	27	34	study	study	VERB
iajs-1806	27	35	quasi	quasi	ADJ
iajs-1806	27	36	-	-	ADJ
iajs-1806	27	37	inner	inner	ADJ
iajs-1806	27	38	product	product	NOUN
iajs-1806	27	39	spaces	space	VERB
iajs-1806	27	40	for	for	ADP
iajs-1806	27	41	ℓ	ℓ	PROPN
iajs-1806	27	42	and	and	CCONJ
iajs-1806	27	43	their	their	PRON
iajs-1806	27	44	completeness	completeness	NOUN
iajs-1806	27	45	.	.	PUNCT
iajs-1806	28	1	the	the	DET
iajs-1806	28	2	paper	paper	NOUN
iajs-1806	28	3	consists	consist	VERB
iajs-1806	28	4	of	of	ADP
iajs-1806	28	5	two	two	NUM
iajs-1806	28	6	sections	section	NOUN
iajs-1806	28	7	.	.	PUNCT
iajs-1806	29	1	section	section	NOUN
iajs-1806	29	2	one	one	NOUN
iajs-1806	29	3	includes	include	VERB
iajs-1806	29	4	definitions	definition	NOUN
iajs-1806	29	5	of	of	ADP
iajs-1806	29	6	quasinormed	quasinorme	VERB
iajs-1806	29	7	space	space	NOUN
iajs-1806	29	8	and	and	CCONJ
iajs-1806	29	9	quasi	quasi	ADJ
iajs-1806	29	10	-	-	ADJ
iajs-1806	29	11	banach	banach	ADJ
iajs-1806	29	12	space	space	NOUN
iajs-1806	29	13	with	with	ADP
iajs-1806	29	14	some	some	DET
iajs-1806	29	15	useful	useful	ADJ
iajs-1806	29	16	results	result	NOUN
iajs-1806	29	17	which	which	PRON
iajs-1806	29	18	are	be	AUX
iajs-1806	29	19	needed	need	VERB
iajs-1806	29	20	in	in	ADP
iajs-1806	29	21	the	the	DET
iajs-1806	29	22	section	section	NOUN
iajs-1806	29	23	two	two	NUM
iajs-1806	29	24	.	.	PUNCT
iajs-1806	30	1	one	one	NUM
iajs-1806	30	2	of	of	ADP
iajs-1806	30	3	important	important	ADJ
iajs-1806	30	4	theorems	theorem	NOUN
iajs-1806	30	5	which	which	PRON
iajs-1806	30	6	is	be	AUX
iajs-1806	30	7	presented	present	VERB
iajs-1806	30	8	in	in	ADP
iajs-1806	30	9	this	this	DET
iajs-1806	30	10	section	section	NOUN
iajs-1806	30	11	is	be	AUX
iajs-1806	30	12	jordan	jordan	PROPN
iajs-1806	30	13	-	-	PUNCT
iajs-1806	30	14	van	van	PROPN
iajs-1806	30	15	neumann	neumann	PROPN
iajs-1806	30	16	theorem	theorem	PROPN
iajs-1806	30	17	.	.	PUNCT
iajs-1806	31	1	this	this	DET
iajs-1806	31	2	theorem	theorem	NOUN
iajs-1806	31	3	gives	give	VERB
iajs-1806	31	4	necessary	necessary	ADJ
iajs-1806	31	5	and	and	CCONJ
iajs-1806	31	6	sufficient	sufficient	ADJ
iajs-1806	31	7	conditions	condition	NOUN
iajs-1806	31	8	to	to	PART
iajs-1806	31	9	be	be	AUX
iajs-1806	31	10	generated	generate	VERB
iajs-1806	31	11	by	by	ADP
iajs-1806	31	12	an	an	DET
iajs-1806	31	13	inner	inner	ADJ
iajs-1806	31	14	product	product	NOUN
iajs-1806	31	15	space	space	NOUN
iajs-1806	31	16	.	.	PUNCT
iajs-1806	32	1	the	the	DET
iajs-1806	32	2	second	second	ADJ
iajs-1806	32	3	two	two	NUM
iajs-1806	32	4	presents	present	VERB
iajs-1806	32	5	a	a	DET
iajs-1806	32	6	g𝑎teaux	g𝑎teaux	ADJ
iajs-1806	32	7	derivative	derivative	NOUN
iajs-1806	32	8	that	that	PRON
iajs-1806	32	9	has	have	VERB
iajs-1806	32	10	big	big	ADJ
iajs-1806	32	11	role	role	NOUN
iajs-1806	32	12	to	to	PART
iajs-1806	32	13	define	define	VERB
iajs-1806	32	14	many	many	ADJ
iajs-1806	32	15	concepts	concept	NOUN
iajs-1806	32	16	,	,	PUNCT
iajs-1806	32	17	such	such	ADJ
iajs-1806	32	18	as	as	ADP
iajs-1806	32	19	quasiinner	quasiinner	NOUN
iajs-1806	32	20	product	product	NOUN
iajs-1806	32	21	space	space	NOUN
iajs-1806	32	22	with	with	ADP
iajs-1806	32	23	completeness	completeness	NOUN
iajs-1806	32	24	property	property	NOUN
iajs-1806	32	25	of	of	ADP
iajs-1806	32	26	it	it	PRON
iajs-1806	32	27	.	.	PUNCT
iajs-1806	33	1	also	also	ADV
iajs-1806	33	2	,	,	PUNCT
iajs-1806	33	3	this	this	DET
iajs-1806	33	4	section	section	NOUN
iajs-1806	33	5	shows	show	VERB
iajs-1806	33	6	that	that	SCONJ
iajs-1806	33	7	this	this	DET
iajs-1806	33	8	functional	functional	NOUN
iajs-1806	33	9	is	be	AUX
iajs-1806	33	10	an	an	DET
iajs-1806	33	11	inner	inner	ADJ
iajs-1806	33	12	product	product	NOUN
iajs-1806	33	13	function	function	NOUN
iajs-1806	33	14	in	in	ADP
iajs-1806	33	15	pre	pre	ADJ
iajs-1806	33	16	-	-	ADJ
iajs-1806	33	17	hilbert	hilbert	ADJ
iajs-1806	33	18	spaces	space	NOUN
iajs-1806	33	19	.	.	PUNCT
iajs-1806	34	1	a	a	DET
iajs-1806	34	2	space	space	NOUN
iajs-1806	34	3	ℓ	ℓ	NOUN
iajs-1806	34	4	,	,	PUNCT
iajs-1806	34	5	for	for	ADP
iajs-1806	34	6	every	every	DET
iajs-1806	34	7	m	m	NOUN
iajs-1806	34	8	∈	∈	PROPN
iajs-1806	34	9	ℝ	ℝ	PROPN
iajs-1806	34	10	and	and	CCONJ
iajs-1806	34	11	p	p	NOUN
iajs-1806	34	12	∈	∈	NOUN
iajs-1806	35	1	ℝ	ℝ	PROPN
iajs-1806	35	2	is	be	AUX
iajs-1806	35	3	a	a	DET
iajs-1806	35	4	quasi	quasi	ADJ
iajs-1806	35	5	-	-	ADJ
iajs-1806	35	6	hilbert	hilbert	ADJ
iajs-1806	35	7	space	space	NOUN
iajs-1806	35	8	if	if	SCONJ
iajs-1806	35	9	it	it	PRON
iajs-1806	35	10	is	be	AUX
iajs-1806	35	11	a	a	DET
iajs-1806	35	12	quasi	quasi	ADJ
iajs-1806	35	13	-	-	ADJ
iajs-1806	35	14	inner	inner	ADJ
iajs-1806	35	15	product	product	NOUN
iajs-1806	35	16	space	space	NOUN
iajs-1806	35	17	.	.	PUNCT
iajs-1806	36	1	hence	hence	ADV
iajs-1806	36	2	,	,	PUNCT
iajs-1806	36	3	with	with	ADP
iajs-1806	36	4	ℓ	ℓ	PROPN
iajs-1806	36	5	,	,	PUNCT
iajs-1806	36	6	we	we	PRON
iajs-1806	36	7	find	find	VERB
iajs-1806	36	8	spaces	space	NOUN
iajs-1806	36	9	which	which	PRON
iajs-1806	36	10	are	be	AUX
iajs-1806	36	11	quasi	quasi	ADJ
iajs-1806	36	12	-	-	ADJ
iajs-1806	36	13	hilbert	hilbert	ADJ
iajs-1806	36	14	spaces	space	NOUN
iajs-1806	36	15	and	and	CCONJ
iajs-1806	36	16	are	be	AUX
iajs-1806	36	17	not	not	PART
iajs-1806	36	18	hilbert	hilbert	NOUN
iajs-1806	36	19	spaces	space	NOUN
iajs-1806	36	20	,	,	PUNCT
iajs-1806	36	21	spaces	space	VERB
iajs-1806	36	22	neither	neither	CCONJ
iajs-1806	36	23	quasi	quasi	ADJ
iajs-1806	36	24	-	-	ADJ
iajs-1806	36	25	hilbert	hilbert	ADJ
iajs-1806	36	26	spaces	space	NOUN
iajs-1806	36	27	nor	nor	CCONJ
iajs-1806	36	28	hilbert	hilbert	NOUN
iajs-1806	36	29	spaces	space	NOUN
iajs-1806	36	30	and	and	CCONJ
iajs-1806	36	31	spaces	space	NOUN
iajs-1806	36	32	are	be	AUX
iajs-1806	36	33	quasi	quasi	ADJ
iajs-1806	36	34	-	-	ADJ
iajs-1806	36	35	hilbert	hilbert	ADJ
iajs-1806	36	36	spaces	space	NOUN
iajs-1806	36	37	and	and	CCONJ
iajs-1806	36	38	hilbert	hilbert	NOUN
iajs-1806	36	39	space	space	NOUN
iajs-1806	36	40	.	.	PUNCT
iajs-1806	37	1	2	2	X
iajs-1806	37	2	.	.	X
iajs-1806	37	3	quasi	quasi	ADJ
iajs-1806	37	4	-	-	ADJ
iajs-1806	37	5	normed	normed	ADJ
iajs-1806	37	6	spaces	space	NOUN
iajs-1806	37	7	of	of	ADP
iajs-1806	37	8	sequence	sequence	NOUN
iajs-1806	37	9	spaces	space	NOUN
iajs-1806	37	10	.	.	PUNCT
iajs-1806	38	1	this	this	DET
iajs-1806	38	2	section	section	NOUN
iajs-1806	38	3	contains	contain	VERB
iajs-1806	38	4	notions	notion	NOUN
iajs-1806	38	5	such	such	ADJ
iajs-1806	38	6	as	as	ADP
iajs-1806	38	7	quasi	quasi	ADJ
iajs-1806	38	8	-	-	ADJ
iajs-1806	38	9	normed	normed	ADJ
iajs-1806	38	10	space	space	NOUN
iajs-1806	38	11	,	,	PUNCT
iajs-1806	38	12	a	a	DET
iajs-1806	38	13	pre	pre	ADJ
iajs-1806	38	14	-	-	ADJ
iajs-1806	38	15	hilbert	hilbert	ADJ
iajs-1806	38	16	space	space	NOUN
iajs-1806	38	17	and	and	CCONJ
iajs-1806	38	18	others	other	NOUN
iajs-1806	38	19	with	with	ADP
iajs-1806	38	20	the	the	DET
iajs-1806	38	21	relationship	relationship	NOUN
iajs-1806	38	22	between	between	ADP
iajs-1806	38	23	them	they	PRON
iajs-1806	38	24	.	.	PUNCT
iajs-1806	39	1	also	also	ADV
iajs-1806	39	2	,	,	PUNCT
iajs-1806	39	3	theorems	theorem	NOUN
iajs-1806	39	4	and	and	CCONJ
iajs-1806	39	5	equations	equation	NOUN
iajs-1806	39	6	which	which	PRON
iajs-1806	39	7	are	be	AUX
iajs-1806	39	8	useful	useful	ADJ
iajs-1806	39	9	in	in	ADP
iajs-1806	39	10	section	section	NOUN
iajs-1806	39	11	two	two	NUM
iajs-1806	39	12	are	be	AUX
iajs-1806	39	13	introduced	introduce	VERB
iajs-1806	39	14	.	.	PUNCT
iajs-1806	40	1	definition	definition	NOUN
iajs-1806	40	2	1.1	1.1	NUM
iajs-1806	40	3	.	.	PUNCT
iajs-1806	41	1	[	[	X
iajs-1806	41	2	4	4	NUM
iajs-1806	41	3	]	]	X
iajs-1806	41	4	:	:	PUNCT
iajs-1806	41	5	a	a	DET
iajs-1806	41	6	quasi	quasi	NOUN
iajs-1806	41	7	-	-	ADJ
iajs-1806	41	8	norm	norm	ADJ
iajs-1806	41	9	||.||q	||.||q	ADP
iajs-1806	41	10	on	on	ADP
iajs-1806	41	11	vector	vector	NOUN
iajs-1806	41	12	space	space	NOUN
iajs-1806	41	13	v	v	NOUN
iajs-1806	41	14	over	over	ADP
iajs-1806	41	15	the	the	DET
iajs-1806	41	16	field	field	NOUN
iajs-1806	41	17	of	of	ADP
iajs-1806	41	18	real	real	ADJ
iajs-1806	41	19	numbers	number	NOUN
iajs-1806	41	20	ℝ	ℝ	PROPN
iajs-1806	41	21	is	be	AUX
iajs-1806	41	22	a	a	DET
iajs-1806	41	23	function	function	NOUN
iajs-1806	41	24	:	:	PUNCT
iajs-1806	41	25	||.||q	||.||q	ADP
iajs-1806	41	26	v	v	ADP
iajs-1806	41	27			NOUN
iajs-1806	41	28	0	0	NUM
iajs-1806	41	29	,	,	PUNCT
iajs-1806	41	30	∞	∞	PROPN
iajs-1806	41	31	with	with	ADP
iajs-1806	41	32	the	the	DET
iajs-1806	41	33	properties	property	NOUN
iajs-1806	41	34	:	:	PUNCT
iajs-1806	41	35	ihsciconf	ihsciconf	NOUN
iajs-1806	41	36	2017	2017	NUM
iajs-1806	41	37	special	special	ADJ
iajs-1806	41	38	issue	issue	NOUN
iajs-1806	41	39	ibn	ibn	PROPN
iajs-1806	41	40	al	al	PROPN
iajs-1806	41	41	-	-	PUNCT
iajs-1806	41	42	haitham	haitham	PROPN
iajs-1806	41	43	journal	journal	PROPN
iajs-1806	41	44	for	for	ADP
iajs-1806	41	45	pure	pure	ADJ
iajs-1806	41	46	and	and	CCONJ
iajs-1806	41	47	applied	apply	VERB
iajs-1806	41	48	science	science	NOUN
iajs-1806	41	49	https://doi.org/	https://doi.org/	NOUN
iajs-1806	41	50	10.30526/2017.ihsciconf.1806	10.30526/2017.ihsciconf.1806	NUM
iajs-1806	41	51	for	for	ADP
iajs-1806	41	52	more	more	ADJ
iajs-1806	41	53	information	information	NOUN
iajs-1806	41	54	about	about	ADP
iajs-1806	41	55	the	the	DET
iajs-1806	41	56	conference	conference	NOUN
iajs-1806	41	57	please	please	INTJ
iajs-1806	41	58	visit	visit	VERB
iajs-1806	41	59	the	the	DET
iajs-1806	41	60	websites	website	NOUN
iajs-1806	41	61	:	:	PUNCT
iajs-1806	41	62	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1806	41	63	  	  	SPACE
iajs-1806	41	64	www.ihsciconf.org	www.ihsciconf.org	ADJ
iajs-1806	41	65	   	   	SPACE
iajs-1806	41	66	mathematics	mathematic	NOUN
iajs-1806	41	67	|339	|339	NOUN
iajs-1806	41	68	    	    	SPACE
iajs-1806	41	69	(	(	PUNCT
iajs-1806	41	70	1	1	NUM
iajs-1806	41	71	)	)	PUNCT
iajs-1806	41	72	0||||,,0||||	0||||,,0||||	NOUN
iajs-1806	41	73			PROPN
iajs-1806	41	74	vvvv	vvvv	VERB
iajs-1806	41	75	qq	qq	PROPN
iajs-1806	41	76	↔	↔	PROPN
iajs-1806	41	77	v=	v=	NOUN
iajs-1806	41	78	0	0	NUM
iajs-1806	41	79	.	.	PUNCT
iajs-1806	42	1	(	(	PUNCT
iajs-1806	42	2	2	2	NUM
iajs-1806	42	3	)	)	PUNCT
iajs-1806	42	4	||||||||||	||||||||||	NOUN
iajs-1806	42	5	vv	vv	NOUN
iajs-1806	42	6	qq	qq	X
iajs-1806	43	1			VERB
iajs-1806	43	2			PROPN
iajs-1806	43	3	,	,	PUNCT
iajs-1806	43	4			PROPN
iajs-1806	43	5	,vv	,vv	NOUN
iajs-1806	43	6	ℝ.	ℝ.	PROPN
iajs-1806	43	7	(	(	PUNCT
iajs-1806	43	8	3	3	NUM
iajs-1806	43	9	)	)	PUNCT
iajs-1806	43	10			NOUN
iajs-1806	43	11	||||||||||||	||||||||||||	VERB
iajs-1806	43	12	wvcwv	wvcwv	ADJ
iajs-1806	43	13	qqq	qqq	NOUN
iajs-1806	43	14			PROPN
iajs-1806	43	15			NOUN
iajs-1806	43	16	v	v	ADP
iajs-1806	43	17	,	,	PUNCT
iajs-1806	43	18	w	w	PROPN
iajs-1806	43	19	,	,	PUNCT
iajs-1806	43	20	∊	∊	PROPN
iajs-1806	43	21	v	v	NOUN
iajs-1806	43	22	,	,	PUNCT
iajs-1806	43	23	where	where	SCONJ
iajs-1806	43	24	c	c	NOUN
iajs-1806	43	25	1	1	NUM
iajs-1806	43	26	is	be	AUX
iajs-1806	43	27	a	a	DET
iajs-1806	43	28	constant	constant	ADJ
iajs-1806	43	29	independent	independent	NOUN
iajs-1806	43	30	of	of	ADP
iajs-1806	43	31	v	v	NUM
iajs-1806	43	32	,	,	PUNCT
iajs-1806	43	33	w.	w.	PROPN
iajs-1806	43	34	a	a	DET
iajs-1806	43	35	quasi	quasi	ADJ
iajs-1806	43	36	-	-	ADJ
iajs-1806	43	37	normed	normed	ADJ
iajs-1806	43	38	space	space	NOUN
iajs-1806	43	39	is	be	AUX
iajs-1806	43	40	denoted	denote	VERB
iajs-1806	43	41	by	by	ADP
iajs-1806	43	42			NOUN
iajs-1806	43	43	||.||	||.||	PROPN
iajs-1806	43	44	,	,	PUNCT
iajs-1806	43	45	qv	qv	ADV
iajs-1806	43	46	or	or	CCONJ
iajs-1806	43	47	simply	simply	ADV
iajs-1806	43	48	v.	v.	ADP
iajs-1806	43	49	a	a	DET
iajs-1806	43	50	function	function	NOUN
iajs-1806	43	51	||.||q	||.||q	PART
iajs-1806	43	52	be	be	AUX
iajs-1806	43	53	a	a	DET
iajs-1806	43	54	norm	norm	NOUN
iajs-1806	43	55	if	if	SCONJ
iajs-1806	43	56	c	c	NOUN
iajs-1806	43	57	=	=	SYM
iajs-1806	43	58	1	1	NUM
iajs-1806	43	59	,	,	PUNCT
iajs-1806	43	60	thus	thus	ADV
iajs-1806	43	61	it	it	PRON
iajs-1806	43	62	is	be	AUX
iajs-1806	43	63	generalization	generalization	NOUN
iajs-1806	43	64	of	of	ADP
iajs-1806	43	65	norm	norm	NOUN
iajs-1806	43	66	.	.	PUNCT
iajs-1806	44	1	every	every	DET
iajs-1806	44	2	norm	norm	NOUN
iajs-1806	44	3	function	function	NOUN
iajs-1806	44	4	is	be	AUX
iajs-1806	44	5	quasi	quasi	ADJ
iajs-1806	44	6	-	-	NOUN
iajs-1806	44	7	norm	norm	ADJ
iajs-1806	44	8	.	.	PUNCT
iajs-1806	45	1	the	the	DET
iajs-1806	45	2	converse	converse	NOUN
iajs-1806	45	3	does	do	AUX
iajs-1806	45	4	not	not	PART
iajs-1806	45	5	hold	hold	VERB
iajs-1806	45	6	,	,	PUNCT
iajs-1806	45	7	in	in	ADP
iajs-1806	45	8	general	general	ADJ
iajs-1806	45	9	.	.	PUNCT
iajs-1806	46	1	since	since	SCONJ
iajs-1806	46	2	every	every	DET
iajs-1806	46	3	quasi	quasi	ADJ
iajs-1806	46	4	-	-	ADJ
iajs-1806	46	5	normed	normed	ADJ
iajs-1806	46	6	space	space	NOUN
iajs-1806	46	7	v	v	NOUN
iajs-1806	46	8	is	be	AUX
iajs-1806	46	9	a	a	DET
iajs-1806	46	10	metric	metric	ADJ
iajs-1806	46	11	space	space	NOUN
iajs-1806	46	12	by	by	ADP
iajs-1806	46	13	d(v	d(v	PROPN
iajs-1806	46	14	,	,	PUNCT
iajs-1806	46	15	w	w	NOUN
iajs-1806	46	16	)	)	PUNCT
iajs-1806	46	17	=	=	VERB
iajs-1806	46	18	||||	||||	X
iajs-1806	46	19	wvq	wvq	PROPN
iajs-1806	46	20			NOUN
iajs-1806	46	21	,	,	PUNCT
iajs-1806	46	22	then	then	ADV
iajs-1806	46	23	it	it	PRON
iajs-1806	46	24	is	be	AUX
iajs-1806	46	25	atopological	atopological	ADJ
iajs-1806	46	26	linear	linear	ADJ
iajs-1806	46	27	space	space	NOUN
iajs-1806	46	28	and	and	CCONJ
iajs-1806	46	29	the	the	DET
iajs-1806	46	30	concepts	concept	NOUN
iajs-1806	46	31	of	of	ADP
iajs-1806	46	32	fundamental	fundamental	ADJ
iajs-1806	46	33	sequences	sequence	NOUN
iajs-1806	46	34	and	and	CCONJ
iajs-1806	46	35	completeness	completeness	NOUN
iajs-1806	46	36	in	in	ADP
iajs-1806	46	37	quasi	quasi	ADJ
iajs-1806	46	38	-	-	ADJ
iajs-1806	46	39	normed	normed	ADJ
iajs-1806	46	40	spaces	space	NOUN
iajs-1806	46	41	are	be	AUX
iajs-1806	46	42	given	give	VERB
iajs-1806	46	43	[	[	PUNCT
iajs-1806	46	44	5	5	NUM
iajs-1806	46	45	]	]	PUNCT
iajs-1806	46	46	.	.	PUNCT
iajs-1806	47	1	a	a	DET
iajs-1806	47	2	quasibanach	quasibanach	NOUN
iajs-1806	47	3	space	space	NOUN
iajs-1806	47	4	is	be	AUX
iajs-1806	47	5	a	a	DET
iajs-1806	47	6	complete	complete	ADJ
iajs-1806	47	7	quasi	quasi	ADJ
iajs-1806	47	8	-	-	ADJ
iajs-1806	47	9	normed	normed	ADJ
iajs-1806	47	10	space	space	NOUN
iajs-1806	47	11	.	.	PUNCT
iajs-1806	48	1	definition	definition	NOUN
iajs-1806	48	2	1.2	1.2	NUM
iajs-1806	48	3	.	.	PUNCT
iajs-1806	49	1	a	a	DET
iajs-1806	49	2	symmetric	symmetric	ADJ
iajs-1806	49	3	linear	linear	ADJ
iajs-1806	49	4	functional	functional	ADJ
iajs-1806	49	5	on	on	ADP
iajs-1806	49	6	2v	2v	PROPN
iajs-1806	49	7	is	be	AUX
iajs-1806	49	8	a	a	DET
iajs-1806	49	9	functional	functional	ADJ
iajs-1806	49	10	l	l	NOUN
iajs-1806	49	11	such	such	ADJ
iajs-1806	49	12	that	that	SCONJ
iajs-1806	49	13	:	:	PUNCT
iajs-1806	49	14	(	(	PUNCT
iajs-1806	49	15	1	1	X
iajs-1806	49	16	)	)	PUNCT
iajs-1806	49	17	l(𝛽	l(𝛽	NOUN
iajs-1806	49	18	v	v	NOUN
iajs-1806	49	19	+	+	X
iajs-1806	49	20	𝜇	𝜇	X
iajs-1806	49	21	w	w	PROPN
iajs-1806	49	22	,	,	PUNCT
iajs-1806	49	23	u	u	NOUN
iajs-1806	49	24	)	)	PUNCT
iajs-1806	49	25	=	=	SYM
iajs-1806	49	26	𝛽	𝛽	PROPN
iajs-1806	49	27	l(v	l(v	NOUN
iajs-1806	49	28	,	,	PUNCT
iajs-1806	49	29	u	u	NOUN
iajs-1806	49	30	)	)	PUNCT
iajs-1806	49	31	+	+	NOUN
iajs-1806	49	32	𝜇l(w	𝜇l(w	NOUN
iajs-1806	49	33	,	,	PUNCT
iajs-1806	49	34	u	u	NOUN
iajs-1806	49	35	)	)	PUNCT
iajs-1806	49	36	;	;	PUNCT
iajs-1806	49	37	(	(	PUNCT
iajs-1806	49	38	2	2	X
iajs-1806	49	39	)	)	PUNCT
iajs-1806	49	40	l(v	l(v	NOUN
iajs-1806	49	41	,	,	PUNCT
iajs-1806	49	42	w	w	NOUN
iajs-1806	49	43	)	)	PUNCT
iajs-1806	50	1	=	=	SYM
iajs-1806	50	2	l(w	l(w	PROPN
iajs-1806	50	3	,	,	PUNCT
iajs-1806	50	4	v	v	NOUN
iajs-1806	50	5	)	)	PUNCT
iajs-1806	50	6	,	,	PUNCT
iajs-1806	50	7	𝛽	𝛽	PROPN
iajs-1806	50	8	,	,	PUNCT
iajs-1806	50	9	𝜇	𝜇	ADP
iajs-1806	50	10	∊	∊	PROPN
iajs-1806	50	11	ℝ.	ℝ.	PROPN
iajs-1806	50	12	,	,	PUNCT
iajs-1806	50	13			NOUN
iajs-1806	50	14	𝑣	𝑣	ADP
iajs-1806	50	15	,	,	PUNCT
iajs-1806	50	16	𝑤	𝑤	ADP
iajs-1806	50	17	,	,	PUNCT
iajs-1806	50	18	𝑢	𝑢	PROPN
iajs-1806	50	19	∈	∈	PROPN
iajs-1806	50	20	𝑉.	𝑉.	NOUN
iajs-1806	50	21	remark	remark	NOUN
iajs-1806	50	22	1.3	1.3	NUM
iajs-1806	50	23	.	.	PUNCT
iajs-1806	51	1	it	it	PRON
iajs-1806	51	2	is	be	AUX
iajs-1806	51	3	obvious	obvious	ADJ
iajs-1806	51	4	,	,	PUNCT
iajs-1806	51	5	any	any	DET
iajs-1806	51	6	inner	inner	ADJ
iajs-1806	51	7	product	product	NOUN
iajs-1806	51	8	function	function	NOUN
iajs-1806	51	9	satisfies	satisfy	VERB
iajs-1806	51	10	definition	definition	NOUN
iajs-1806	51	11	1.2	1.2	NUM
iajs-1806	51	12	and	and	CCONJ
iajs-1806	51	13	generates	generate	VERB
iajs-1806	51	14	a	a	DET
iajs-1806	51	15	quasi	quasi	ADJ
iajs-1806	51	16	norm	norm	NOUN
iajs-1806	51	17	which	which	PRON
iajs-1806	51	18	is	be	AUX
iajs-1806	51	19	||||	||||	ADJ
iajs-1806	51	20	vq	vq	NOUN
iajs-1806	51	21	=	=	SYM
iajs-1806	51	22	𝑣	𝑣	NOUN
iajs-1806	51	23	,	,	PUNCT
iajs-1806	51	24	𝑣	𝑣	NOUN
iajs-1806	51	25	/	/	SYM
iajs-1806	51	26			PROPN
iajs-1806	51	27	v	v	ADP
iajs-1806	51	28	∊	∊	NUM
iajs-1806	51	29	v	v	NOUN
iajs-1806	51	30	lemma	lemma	PROPN
iajs-1806	51	31	1.4	1.4	NUM
iajs-1806	51	32	.	.	PUNCT
iajs-1806	52	1	in	in	ADP
iajs-1806	52	2	a	a	DET
iajs-1806	52	3	pre	pre	ADJ
iajs-1806	52	4	-	-	ADJ
iajs-1806	52	5	hilbert	hilbert	ADJ
iajs-1806	52	6	space	space	NOUN
iajs-1806	52	7	v	v	NOUN
iajs-1806	52	8	,	,	PUNCT
iajs-1806	52	9	one	one	PRON
iajs-1806	52	10	has	have	VERB
iajs-1806	52	11	the	the	DET
iajs-1806	52	12	equality	equality	NOUN
iajs-1806	52	13	:	:	PUNCT
iajs-1806	52	14			NOUN
iajs-1806	52	15	4||||	4||||	NUM
iajs-1806	52	16	wvq	wvq	NOUN
iajs-1806	52	17	4||||	4||||	NUM
iajs-1806	52	18	wvq	wvq	NOUN
iajs-1806	52	19			NOUN
iajs-1806	52	20	=	=	SYM
iajs-1806	52	21	)	)	PUNCT
iajs-1806	52	22	||||||||(8	||||||||(8	PROPN
iajs-1806	52	23	22	22	NUM
iajs-1806	52	24	wv	wv	PROPN
iajs-1806	52	25	qq	qq	PROPN
iajs-1806	52	26			PROPN
iajs-1806	52	27	v	v	ADP
iajs-1806	52	28	,	,	PUNCT
iajs-1806	52	29	w	w	PROPN
iajs-1806	52	30			NOUN
iajs-1806	52	31	v	v	ADP
iajs-1806	52	32	,	,	PUNCT
iajs-1806	52	33	w	w	PROPN
iajs-1806	52	34	,	,	PUNCT
iajs-1806	52	35	∊	∊	PROPN
iajs-1806	52	36	v	v	NOUN
iajs-1806	52	37	(	(	PUNCT
iajs-1806	52	38	1	1	NUM
iajs-1806	52	39	)	)	PUNCT
iajs-1806	52	40	proof	proof	NOUN
iajs-1806	52	41	:	:	PUNCT
iajs-1806	52	42	using	use	VERB
iajs-1806	52	43	remark	remark	NOUN
iajs-1806	52	44	1.3	1.3	NUM
iajs-1806	52	45	,	,	PUNCT
iajs-1806	52	46	we	we	PRON
iajs-1806	52	47	get	get	VERB
iajs-1806	52	48			NOUN
iajs-1806	52	49	2||||	2||||	NUM
iajs-1806	52	50	wvq	wvq	NOUN
iajs-1806	52	51	<	<	X
iajs-1806	52	52	v+	v+	X
iajs-1806	52	53	w	w	PROPN
iajs-1806	52	54	,	,	PUNCT
iajs-1806	52	55	v	v	NOUN
iajs-1806	52	56	+	+	CCONJ
iajs-1806	52	57	w	w	NOUN
iajs-1806	52	58	>	>	X
iajs-1806	52	59	=	=	PUNCT
iajs-1806	53	1	2||||	2||||	PROPN
iajs-1806	53	2	vq	vq	ADP
iajs-1806	53	3	2	2	NUM
iajs-1806	53	4	<	<	X
iajs-1806	53	5	v	v	NOUN
iajs-1806	53	6	,	,	PUNCT
iajs-1806	53	7	w	w	PROPN
iajs-1806	53	8	>	>	X
iajs-1806	53	9	+	+	NUM
iajs-1806	53	10	2||||	2||||	NUM
iajs-1806	53	11	wq	wq	NOUN
iajs-1806	53	12	⇒	⇒	PROPN
iajs-1806	53	13	2||||	2||||	NUM
iajs-1806	53	14	wvq	wvq	NOUN
iajs-1806	53	15			ADV
iajs-1806	53	16	=	=	X
iajs-1806	53	17	22	22	NUM
iajs-1806	53	18	||||||||	||||||||	X
iajs-1806	53	19	wv	wv	PROPN
iajs-1806	53	20	qq	qq	PROPN
iajs-1806	53	21			PUNCT
iajs-1806	53	22	+	+	CCONJ
iajs-1806	53	23	4	4	NUM
iajs-1806	53	24	v	v	NOUN
iajs-1806	53	25	,	,	PUNCT
iajs-1806	53	26	w	w	PROPN
iajs-1806	53	27	22	22	NUM
iajs-1806	53	28	||||||||	||||||||	X
iajs-1806	53	29	wv	wv	PROPN
iajs-1806	53	30	qq	qq	PROPN
iajs-1806	53	31			PUNCT
iajs-1806	53	32	+	+	CCONJ
iajs-1806	53	33	4	4	NUM
iajs-1806	53	34	𝑣	𝑣	NOUN
iajs-1806	53	35	,	,	PUNCT
iajs-1806	53	36	𝑤	𝑤	X
iajs-1806	53	37	.	.	PUNCT
iajs-1806	54	1	also	also	ADV
iajs-1806	54	2	,	,	PUNCT
iajs-1806	54	3			PROPN
iajs-1806	54	4	2||||	2||||	NUM
iajs-1806	54	5	wvq	wvq	NOUN
iajs-1806	54	6	2||||	2||||	NOUN
iajs-1806	54	7	vq	vq	ADP
iajs-1806	54	8	2	2	NUM
iajs-1806	54	9	<	<	X
iajs-1806	54	10	v	v	NOUN
iajs-1806	54	11	,	,	PUNCT
iajs-1806	54	12	w	w	PROPN
iajs-1806	54	13	>	>	X
iajs-1806	54	14	+	+	NUM
iajs-1806	54	15	2||||	2||||	NUM
iajs-1806	54	16	wq	wq	NOUN
iajs-1806	54	17	⇒	⇒	NOUN
iajs-1806	54	18	4||||	4||||	NUM
iajs-1806	54	19	wvq	wvq	PROPN
iajs-1806	54	20			NOUN
iajs-1806	54	21	=	=	SYM
iajs-1806	54	22	22	22	NUM
iajs-1806	54	23	||||||||	||||||||	X
iajs-1806	54	24	wv	wv	PROPN
iajs-1806	54	25	qq	qq	PROPN
iajs-1806	54	26			VERB
iajs-1806	54	27	4	4	NUM
iajs-1806	54	28	v	v	NOUN
iajs-1806	54	29	,	,	PUNCT
iajs-1806	54	30	w	w	PROPN
iajs-1806	54	31	22	22	NUM
iajs-1806	54	32	||||||||	||||||||	X
iajs-1806	54	33	wv	wv	PROPN
iajs-1806	54	34	qq	qq	PROPN
iajs-1806	54	35			PUNCT
iajs-1806	54	36	+	+	CCONJ
iajs-1806	54	37	4	4	NUM
iajs-1806	54	38	𝑣	𝑣	NOUN
iajs-1806	54	39	,	,	PUNCT
iajs-1806	54	40	𝑤	𝑤	X
iajs-1806	54	41	.	.	PUNCT
iajs-1806	55	1	thus	thus	ADV
iajs-1806	55	2	,	,	PUNCT
iajs-1806	55	3			PROPN
iajs-1806	55	4	4||||	4||||	NUM
iajs-1806	55	5	wvq	wvq	NOUN
iajs-1806	55	6	4||||	4||||	NUM
iajs-1806	55	7	wvq	wvq	NOUN
iajs-1806	55	8			NOUN
iajs-1806	55	9	=	=	SYM
iajs-1806	55	10	)	)	PUNCT
iajs-1806	55	11	||||||||(8	||||||||(8	PROPN
iajs-1806	55	12	22	22	NUM
iajs-1806	55	13	wv	wv	PROPN
iajs-1806	55	14	qq	qq	PROPN
iajs-1806	55	15			PROPN
iajs-1806	55	16	v	v	ADP
iajs-1806	55	17	,	,	PUNCT
iajs-1806	55	18	w	w	PROPN
iajs-1806	55	19	and	and	CCONJ
iajs-1806	55	20	this	this	PRON
iajs-1806	55	21	is	be	AUX
iajs-1806	55	22	the	the	DET
iajs-1806	55	23	desired	desire	VERB
iajs-1806	55	24	result	result	NOUN
iajs-1806	55	25	.	.	PUNCT
iajs-1806	56	1	definition	definition	NOUN
iajs-1806	56	2	1.5	1.5	NUM
iajs-1806	56	3	.	.	PUNCT
iajs-1806	57	1	[	[	X
iajs-1806	57	2	1	1	NUM
iajs-1806	57	3	]	]	PUNCT
iajs-1806	57	4	:	:	PUNCT
iajs-1806	57	5	let	let	VERB
iajs-1806	57	6	λ	λ	PROPN
iajs-1806	57	7	⊂ℝ	⊂ℝ	PROPN
iajs-1806	57	8	is	be	AUX
iajs-1806	57	9	monotonically	monotonically	ADV
iajs-1806	57	10	increasing	increase	VERB
iajs-1806	57	11	sequence	sequence	NOUN
iajs-1806	57	12	such	such	ADJ
iajs-1806	57	13	that	that	SCONJ
iajs-1806	57	14	lim	lim	PROPN
iajs-1806	57	15	→	→	SYM
iajs-1806	57	16	λ	λ	PROPN
iajs-1806	57	17	=	=	SYM
iajs-1806	58	1	+	+	NUM
iajs-1806	58	2	∞	∞	PROPN
iajs-1806	58	3	,	,	PUNCT
iajs-1806	58	4	quasisobolev	quasisobolev	NOUN
iajs-1806	58	5	spaces	space	NOUN
iajs-1806	58	6	are	be	AUX
iajs-1806	58	7	sequence	sequence	NOUN
iajs-1806	58	8	spaces	space	NOUN
iajs-1806	58	9	ℓ	ℓ	NOUN
iajs-1806	58	10	,	,	PUNCT
iajs-1806	58	11	where	where	SCONJ
iajs-1806	58	12	0	0	PUNCT
iajs-1806	58	13	<	<	X
iajs-1806	58	14	p	p	X
iajs-1806	58	15	<	<	X
iajs-1806	58	16	∞	∞	PROPN
iajs-1806	58	17	and	and	CCONJ
iajs-1806	58	18	m	m	PROPN
iajs-1806	58	19	∈	∈	PROPN
iajs-1806	58	20	ℝ	ℝ	PROPN
iajs-1806	58	21	which	which	PRON
iajs-1806	58	22	are	be	AUX
iajs-1806	58	23	defined	define	VERB
iajs-1806	58	24	as	as	ADP
iajs-1806	58	25	:	:	PUNCT
iajs-1806	58	26	ℓ	ℓ	X
iajs-1806	58	27	=	=	PUNCT
iajs-1806	58	28	{	{	PUNCT
iajs-1806	58	29	𝑣	𝑣	PART
iajs-1806	58	30	𝑣	𝑣	ADP
iajs-1806	58	31	∶	∶	NOUN
iajs-1806	58	32			X
iajs-1806	58	33			VERB
iajs-1806	58	34	1k	1k	VERB
iajs-1806	58	35	𝜆	𝜆	DET
iajs-1806	58	36	|𝑣	|𝑣	NOUN
iajs-1806	58	37	|	|	ADV
iajs-1806	58	38	∞	∞	PROPN
iajs-1806	58	39	.	.	PUNCT
iajs-1806	59	1	ihsciconf	ihsciconf	PROPN
iajs-1806	59	2	2017	2017	NUM
iajs-1806	59	3	special	special	ADJ
iajs-1806	59	4	issue	issue	NOUN
iajs-1806	59	5	ibn	ibn	PROPN
iajs-1806	59	6	al	al	PROPN
iajs-1806	59	7	-	-	PUNCT
iajs-1806	59	8	haitham	haitham	PROPN
iajs-1806	59	9	journal	journal	PROPN
iajs-1806	59	10	for	for	ADP
iajs-1806	59	11	pure	pure	ADJ
iajs-1806	59	12	and	and	CCONJ
iajs-1806	59	13	applied	apply	VERB
iajs-1806	59	14	science	science	NOUN
iajs-1806	59	15	https://doi.org/	https://doi.org/	NOUN
iajs-1806	59	16	10.30526/2017.ihsciconf.1806	10.30526/2017.ihsciconf.1806	NUM
iajs-1806	59	17	for	for	ADP
iajs-1806	59	18	more	more	ADJ
iajs-1806	59	19	information	information	NOUN
iajs-1806	59	20	about	about	ADP
iajs-1806	59	21	the	the	DET
iajs-1806	59	22	conference	conference	NOUN
iajs-1806	59	23	please	please	INTJ
iajs-1806	59	24	visit	visit	VERB
iajs-1806	59	25	the	the	DET
iajs-1806	59	26	websites	website	NOUN
iajs-1806	59	27	:	:	PUNCT
iajs-1806	59	28	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1806	59	29	  	  	SPACE
iajs-1806	59	30	www.ihsciconf.org	www.ihsciconf.org	ADJ
iajs-1806	59	31	   	   	SPACE
iajs-1806	59	32	mathematics	mathematic	NOUN
iajs-1806	59	33	|340	|340	NOUN
iajs-1806	59	34	    	    	SPACE
iajs-1806	59	35	when	when	SCONJ
iajs-1806	59	36	m	m	VERB
iajs-1806	59	37	=	=	VERB
iajs-1806	59	38	0	0	PUNCT
iajs-1806	60	1	then	then	ADV
iajs-1806	60	2	ℓ	ℓ	PROPN
iajs-1806	60	3	=	=	SYM
iajs-1806	60	4	ℓ	ℓ	PROPN
iajs-1806	60	5	,	,	PUNCT
iajs-1806	60	6	0	0	PUNCT
iajs-1806	60	7	<	<	X
iajs-1806	61	1	p	p	X
iajs-1806	61	2	<	<	X
iajs-1806	61	3	∞	∞	PROPN
iajs-1806	61	4	.	.	PUNCT
iajs-1806	62	1	theorem	theorem	VERB
iajs-1806	62	2	1.6	1.6	NUM
iajs-1806	62	3	.	.	PUNCT
iajs-1806	63	1	[	[	X
iajs-1806	63	2	1	1	NUM
iajs-1806	63	3	]	]	X
iajs-1806	63	4	:	:	PUNCT
iajs-1806	63	5	for	for	ADP
iajs-1806	63	6	every	every	DET
iajs-1806	63	7	m	m	NOUN
iajs-1806	63	8	∈	∈	PROPN
iajs-1806	63	9	ℝ	ℝ	PROPN
iajs-1806	63	10	and	and	CCONJ
iajs-1806	63	11	p	p	NOUN
iajs-1806	63	12	∈	∈	NOUN
iajs-1806	63	13	ℝ	ℝ	PROPN
iajs-1806	63	14	a	a	DET
iajs-1806	63	15	space	space	NOUN
iajs-1806	63	16	ℓ	ℓ	NOUN
iajs-1806	63	17	,	,	PUNCT
iajs-1806	63	18	is	be	AUX
iajs-1806	63	19	a	a	DET
iajs-1806	63	20	quasi	quasi	ADJ
iajs-1806	63	21	-	-	ADJ
iajs-1806	63	22	banach	banach	ADJ
iajs-1806	63	23	space	space	NOUN
iajs-1806	63	24	with	with	ADP
iajs-1806	63	25	the	the	DET
iajs-1806	63	26	function	function	NOUN
iajs-1806	63	27	:	:	PUNCT
iajs-1806	63	28	||||	||||	X
iajs-1806	63	29	vq	vq	ADP
iajs-1806	63	30			X
iajs-1806	63	31			VERB
iajs-1806	63	32	1k	1k	VERB
iajs-1806	63	33	𝜆𝑘	𝜆𝑘	ADP
iajs-1806	63	34	𝑚𝑝	𝑚𝑝	PUNCT
iajs-1806	63	35	2	2	NUM
iajs-1806	63	36	|𝑣𝑘|p	|𝑣𝑘|p	PROPN
iajs-1806	63	37	1/𝑝	1/𝑝	NUM
iajs-1806	63	38	.	.	PUNCT
iajs-1806	64	1	we	we	PRON
iajs-1806	64	2	note	note	VERB
iajs-1806	64	3	that	that	SCONJ
iajs-1806	64	4	the	the	DET
iajs-1806	64	5	constant	constant	ADJ
iajs-1806	64	6	c	c	NOUN
iajs-1806	64	7	=	=	SYM
iajs-1806	64	8	p12	p12	NOUN
iajs-1806	64	9	/	/	PUNCT
iajs-1806	64	10	for	for	ADP
iajs-1806	64	11	p	p	PROPN
iajs-1806	64	12	∊	∊	PROPN
iajs-1806	64	13	(	(	PUNCT
iajs-1806	64	14	0	0	NUM
iajs-1806	64	15	,	,	PUNCT
iajs-1806	64	16	1	1	NUM
iajs-1806	64	17	)	)	PUNCT
iajs-1806	64	18	,	,	PUNCT
iajs-1806	64	19	and	and	CCONJ
iajs-1806	64	20	c	c	X
iajs-1806	64	21	=	=	SYM
iajs-1806	64	22	1	1	NUM
iajs-1806	64	23	for	for	ADP
iajs-1806	64	24	p	p	PROPN
iajs-1806	64	25	∊	∊	PROPN
iajs-1806	64	26	[	[	X
iajs-1806	64	27	1	1	NUM
iajs-1806	64	28	,	,	PUNCT
iajs-1806	64	29	+	+	CCONJ
iajs-1806	64	30	∞	∞	NUM
iajs-1806	64	31	)	)	PUNCT
iajs-1806	64	32	.	.	PUNCT
iajs-1806	65	1	theorem	theorem	VERB
iajs-1806	65	2	1.7	1.7	NUM
iajs-1806	65	3	.	.	PUNCT
iajs-1806	66	1	(	(	PUNCT
iajs-1806	66	2	parallelogram	parallelogram	NOUN
iajs-1806	66	3	equality	equality	NOUN
iajs-1806	66	4	)	)	PUNCT
iajs-1806	66	5	let	let	VERB
iajs-1806	66	6	v	v	PART
iajs-1806	66	7	be	be	AUX
iajs-1806	66	8	a	a	DET
iajs-1806	66	9	pre	pre	ADJ
iajs-1806	66	10	-	-	ADJ
iajs-1806	66	11	hilbert	hilbert	ADJ
iajs-1806	66	12	space	space	NOUN
iajs-1806	66	13	.	.	PUNCT
iajs-1806	67	1	then	then	ADV
iajs-1806	67	2	∀	∀	NOUN
iajs-1806	67	3	v	v	NOUN
iajs-1806	67	4	,	,	PUNCT
iajs-1806	67	5	w	w	PROPN
iajs-1806	67	6	∊	∊	NUM
iajs-1806	67	7	v	v	NOUN
iajs-1806	67	8	,	,	PUNCT
iajs-1806	67	9	2||||	2||||	NUM
iajs-1806	67	10	wvq	wvq	NOUN
iajs-1806	67	11			ADV
iajs-1806	67	12	+	+	CCONJ
iajs-1806	67	13	2||||	2||||	NUM
iajs-1806	67	14	wvq	wvq	PROPN
iajs-1806	67	15			NOUN
iajs-1806	67	16	=	=	SYM
iajs-1806	67	17	2||||2	2||||2	NUM
iajs-1806	67	18	vq	vq	PROPN
iajs-1806	68	1	+	+	CCONJ
iajs-1806	68	2	2||||2	2||||2	PROPN
iajs-1806	68	3	wq	wq	PROPN
iajs-1806	68	4	(	(	PUNCT
iajs-1806	68	5	2	2	X
iajs-1806	68	6	)	)	PUNCT
iajs-1806	68	7	proof	proof	NOUN
iajs-1806	68	8	:	:	PUNCT
iajs-1806	68	9	since	since	SCONJ
iajs-1806	68	10	v	v	NUM
iajs-1806	68	11	be	be	AUX
iajs-1806	68	12	a	a	DET
iajs-1806	68	13	pre	pre	ADJ
iajs-1806	68	14	-	-	ADJ
iajs-1806	68	15	hilbert	hilbert	ADJ
iajs-1806	68	16	space	space	NOUN
iajs-1806	68	17	and	and	CCONJ
iajs-1806	68	18	𝑣	𝑣	NOUN
iajs-1806	68	19	,	,	PUNCT
iajs-1806	68	20	𝑤	𝑤	ADP
iajs-1806	68	21	=	=	SYM
iajs-1806	68	22	1	1	NUM
iajs-1806	68	23	4	4	NUM
iajs-1806	68	24	2||||	2||||	NUM
iajs-1806	68	25	wvq	wvq	NOUN
iajs-1806	68	26			ADJ
iajs-1806	68	27	1	1	NUM
iajs-1806	68	28	4	4	NUM
iajs-1806	68	29	2||||	2||||	NUM
iajs-1806	68	30	wvq	wvq	PROPN
iajs-1806	68	31			NOUN
iajs-1806	68	32	from	from	ADP
iajs-1806	68	33	remark	remark	NOUN
iajs-1806	68	34	1.3	1.3	NUM
iajs-1806	68	35	and	and	CCONJ
iajs-1806	68	36	proof	proof	NOUN
iajs-1806	68	37	of	of	ADP
iajs-1806	68	38	lemma	lemma	PROPN
iajs-1806	68	39	1.4	1.4	NUM
iajs-1806	68	40	,	,	PUNCT
iajs-1806	68	41	then	then	ADV
iajs-1806	68	42	putting	put	VERB
iajs-1806	68	43	this	this	DET
iajs-1806	68	44	function	function	NOUN
iajs-1806	68	45	in	in	ADP
iajs-1806	68	46	equation	equation	NOUN
iajs-1806	68	47	(	(	PUNCT
iajs-1806	68	48	1	1	X
iajs-1806	68	49	)	)	PUNCT
iajs-1806	68	50	we	we	PRON
iajs-1806	68	51	obtain	obtain	VERB
iajs-1806	68	52	the	the	DET
iajs-1806	68	53	desired	desire	VERB
iajs-1806	68	54	result	result	NOUN
iajs-1806	68	55	.	.	PUNCT
iajs-1806	69	1	now	now	ADV
iajs-1806	69	2	,	,	PUNCT
iajs-1806	69	3	we	we	PRON
iajs-1806	69	4	introduce	introduce	VERB
iajs-1806	69	5	jordan	jordan	PROPN
iajs-1806	69	6	-	-	PUNCT
iajs-1806	69	7	van	van	PROPN
iajs-1806	69	8	neumann	neumann	PROPN
iajs-1806	69	9	theorem	theorem	VERB
iajs-1806	69	10	in	in	ADP
iajs-1806	69	11	quasinormed	quasinorme	VERB
iajs-1806	69	12	spaces	space	NOUN
iajs-1806	69	13	.	.	PUNCT
iajs-1806	70	1	theorem	theorem	VERB
iajs-1806	70	2	1.8	1.8	NUM
iajs-1806	70	3	.	.	PUNCT
iajs-1806	71	1	(	(	PUNCT
iajs-1806	71	2	jordan	jordan	PROPN
iajs-1806	71	3	–	–	PUNCT
iajs-1806	71	4	van	van	PROPN
iajs-1806	71	5	neumann	neumann	PROPN
iajs-1806	71	6	)	)	PUNCT
iajs-1806	71	7	a	a	DET
iajs-1806	71	8	quasi	quasi	ADJ
iajs-1806	71	9	-	-	ADJ
iajs-1806	71	10	normed	normed	ADJ
iajs-1806	71	11	space	space	NOUN
iajs-1806	71	12	v	v	NOUN
iajs-1806	71	13	is	be	AUX
iajs-1806	71	14	a	a	DET
iajs-1806	71	15	pre	pre	ADJ
iajs-1806	71	16	-	-	ADJ
iajs-1806	71	17	hilbert	hilbert	ADJ
iajs-1806	71	18	space	space	NOUN
iajs-1806	71	19	iff	iff	PROPN
iajs-1806	71	20	equality	equality	NOUN
iajs-1806	71	21	(	(	PUNCT
iajs-1806	71	22	2	2	NUM
iajs-1806	71	23	)	)	PUNCT
iajs-1806	71	24	is	be	AUX
iajs-1806	71	25	satisfied	satisfied	ADJ
iajs-1806	71	26	by	by	ADP
iajs-1806	71	27	the	the	DET
iajs-1806	71	28	quasinorm	quasinorm	NOUN
iajs-1806	71	29	of	of	ADP
iajs-1806	71	30	v.	v.	ADP
iajs-1806	71	31	proof	proof	NOUN
iajs-1806	71	32	:	:	PUNCT
iajs-1806	71	33	the	the	DET
iajs-1806	71	34	proof	proof	NOUN
iajs-1806	71	35	of	of	ADP
iajs-1806	71	36	this	this	DET
iajs-1806	71	37	theorem	theorem	NOUN
iajs-1806	71	38	is	be	AUX
iajs-1806	71	39	very	very	ADV
iajs-1806	71	40	technical	technical	ADJ
iajs-1806	71	41	and	and	CCONJ
iajs-1806	71	42	proceeds	proceed	NOUN
iajs-1806	71	43	in	in	ADP
iajs-1806	71	44	a	a	DET
iajs-1806	71	45	way	way	NOUN
iajs-1806	71	46	similar	similar	ADJ
iajs-1806	71	47	to	to	ADP
iajs-1806	71	48	its	its	PRON
iajs-1806	71	49	version	version	NOUN
iajs-1806	71	50	in	in	ADP
iajs-1806	71	51	normed	normed	ADJ
iajs-1806	71	52	space	space	NOUN
iajs-1806	71	53	(	(	PUNCT
iajs-1806	71	54	see	see	VERB
iajs-1806	71	55	[	[	X
iajs-1806	71	56	3	3	NUM
iajs-1806	71	57	]	]	NUM
iajs-1806	71	58	)	)	PUNCT
iajs-1806	71	59	.	.	PUNCT
iajs-1806	72	1	the	the	DET
iajs-1806	72	2	next	next	ADJ
iajs-1806	72	3	example	example	NOUN
iajs-1806	72	4	shows	show	VERB
iajs-1806	72	5	the	the	DET
iajs-1806	72	6	importance	importance	NOUN
iajs-1806	72	7	of	of	ADP
iajs-1806	72	8	the	the	DET
iajs-1806	72	9	parallelogram	parallelogram	NOUN
iajs-1806	72	10	equality	equality	NOUN
iajs-1806	72	11	mentioned	mention	VERB
iajs-1806	72	12	in	in	ADP
iajs-1806	72	13	the	the	DET
iajs-1806	72	14	previous	previous	ADJ
iajs-1806	72	15	theorem	theorem	PROPN
iajs-1806	72	16	.	.	PROPN
iajs-1806	72	17	example	example	NOUN
iajs-1806	72	18	1.9	1.9	NUM
iajs-1806	72	19	:	:	PUNCT
iajs-1806	72	20	let	let	VERB
iajs-1806	72	21	v	v	NOUN
iajs-1806	72	22	and	and	CCONJ
iajs-1806	72	23	w	w	VERB
iajs-1806	72	24	belong	belong	VERB
iajs-1806	72	25	to	to	ADP
iajs-1806	72	26	the	the	DET
iajs-1806	72	27	quasi	quasi	ADJ
iajs-1806	72	28	-	-	ADJ
iajs-1806	72	29	normed	normed	ADJ
iajs-1806	72	30	space	space	NOUN
iajs-1806	72	31	ℓ	ℓ	PROPN
iajs-1806	72	32	/	/	PUNCT
iajs-1806	72	33	,	,	PUNCT
iajs-1806	72	34	where	where	SCONJ
iajs-1806	72	35	v	v	NOUN
iajs-1806	72	36	=	=	SYM
iajs-1806	72	37	{	{	PUNCT
iajs-1806	72	38	vk}={0.1,0	vk}={0.1,0	ADJ
iajs-1806	72	39	,	,	PUNCT
iajs-1806	72	40	0	0	NUM
iajs-1806	72	41	,	,	PUNCT
iajs-1806	72	42	0	0	NUM
iajs-1806	72	43	,	,	PUNCT
iajs-1806	72	44	…	…	PUNCT
iajs-1806	72	45	}	}	PUNCT
iajs-1806	72	46	,	,	PUNCT
iajs-1806	72	47	w	w	X
iajs-1806	72	48	=	=	SYM
iajs-1806	72	49	{	{	PUNCT
iajs-1806	72	50	wk	wk	NOUN
iajs-1806	72	51	}	}	PUNCT
iajs-1806	72	52	=	=	PUNCT
iajs-1806	72	53	{	{	PUNCT
iajs-1806	72	54	0	0	NUM
iajs-1806	72	55	,	,	PUNCT
iajs-1806	72	56	0.2	0.2	NUM
iajs-1806	72	57	,	,	PUNCT
iajs-1806	72	58	0	0	NUM
iajs-1806	72	59	,	,	PUNCT
iajs-1806	72	60	0	0	NUM
iajs-1806	72	61	,	,	PUNCT
iajs-1806	72	62	…	…	PUNCT
iajs-1806	72	63	}	}	PUNCT
iajs-1806	72	64	and	and	CCONJ
iajs-1806	72	65	take	take	VERB
iajs-1806	72	66	{	{	PUNCT
iajs-1806	72	67	𝞴k	𝞴k	NOUN
iajs-1806	72	68	}	}	PUNCT
iajs-1806	72	69	=	=	SYM
iajs-1806	72	70	{	{	PUNCT
iajs-1806	72	71	k	k	NOUN
iajs-1806	72	72	}	}	PUNCT
iajs-1806	72	73	,	,	PUNCT
iajs-1806	72	74	𝑘	𝑘	DET
iajs-1806	72	75	∈ℕ.	∈ℕ.	PROPN
iajs-1806	72	76	then	then	ADV
iajs-1806	72	77	we	we	PRON
iajs-1806	72	78	have	have	VERB
iajs-1806	72	79	:	:	PUNCT
iajs-1806	72	80	2||||	2||||	NUM
iajs-1806	72	81	wv	wv	PROPN
iajs-1806	72	82			PROPN
iajs-1806	72	83	½	½	X
iajs-1806	72	84			X
iajs-1806	72	85			VERB
iajs-1806	72	86	1k	1k	VERB
iajs-1806	72	87	𝜆	𝜆	DET
iajs-1806	72	88	|x	|x	NOUN
iajs-1806	72	89	𝑦	𝑦	NOUN
iajs-1806	72	90	|	|	NOUN
iajs-1806	72	91	/	/	SYM
iajs-1806	72	92	=	=	NOUN
iajs-1806	72	93	0.4792627792275938	0.4792627792275938	NUM
iajs-1806	72	94	=	=	SYM
iajs-1806	72	95	2||||	2||||	NUM
iajs-1806	72	96	wv	wv	PROPN
iajs-1806	72	97			PROPN
iajs-1806	72	98	½	½	NOUN
iajs-1806	72	99	,	,	PUNCT
iajs-1806	72	100	so	so	SCONJ
iajs-1806	72	101	2||||	2||||	NUM
iajs-1806	72	102	wv	wv	PROPN
iajs-1806	72	103			PROPN
iajs-1806	72	104	½	½	PROPN
iajs-1806	72	105	+	+	CCONJ
iajs-1806	72	106	2||||	2||||	NUM
iajs-1806	72	107	wv	wv	PROPN
iajs-1806	72	108			PROPN
iajs-1806	72	109	½	½	NOUN
iajs-1806	72	110	=	=	PUNCT
iajs-1806	72	111	0.9585255584551875	0.9585255584551875	NUM
iajs-1806	72	112	,	,	PUNCT
iajs-1806	72	113	and	and	CCONJ
iajs-1806	72	114	,	,	PUNCT
iajs-1806	72	115	2	2	NUM
iajs-1806	72	116	2||||	2||||	NUM
iajs-1806	72	117	v	v	ADP
iajs-1806	72	118	½	½	NOUN
iajs-1806	72	119	+	+	CCONJ
iajs-1806	72	120	2	2	NUM
iajs-1806	72	121	2||||	2||||	NUM
iajs-1806	72	122	w	w	NOUN
iajs-1806	72	123	½	½	NOUN
iajs-1806	72	124	=	=	PUNCT
iajs-1806	72	125	0.482842712474619	0.482842712474619	NUM
iajs-1806	72	126	.	.	PUNCT
iajs-1806	73	1	it	it	PRON
iajs-1806	73	2	is	be	AUX
iajs-1806	73	3	clear	clear	ADJ
iajs-1806	73	4	that	that	SCONJ
iajs-1806	73	5	two	two	NUM
iajs-1806	73	6	sides	side	NOUN
iajs-1806	73	7	of	of	ADP
iajs-1806	73	8	the	the	DET
iajs-1806	73	9	equation	equation	NOUN
iajs-1806	73	10	(	(	PUNCT
iajs-1806	73	11	2	2	X
iajs-1806	73	12	)	)	PUNCT
iajs-1806	73	13	do	do	AUX
iajs-1806	73	14	not	not	PART
iajs-1806	73	15	hold	hold	VERB
iajs-1806	73	16	.	.	PUNCT
iajs-1806	74	1	thus	thus	ADV
iajs-1806	74	2	,	,	PUNCT
iajs-1806	74	3	ℓ	ℓ	PROPN
iajs-1806	74	4	/	/	PUNCT
iajs-1806	74	5	is	be	AUX
iajs-1806	74	6	not	not	PART
iajs-1806	74	7	pre	pre	ADJ
iajs-1806	74	8	-	-	ADJ
iajs-1806	74	9	hilbert	hilbert	ADJ
iajs-1806	74	10	space	space	NOUN
iajs-1806	74	11	.	.	PUNCT
iajs-1806	75	1	3.quasi	3.quasi	NUM
iajs-1806	75	2	-	-	ADJ
iajs-1806	75	3	inner	inner	ADJ
iajs-1806	75	4	product	product	NOUN
iajs-1806	75	5	spaces	space	NOUN
iajs-1806	75	6	of	of	ADP
iajs-1806	75	7	sequence	sequence	NOUN
iajs-1806	75	8	spaces	space	VERB
iajs-1806	75	9	a	a	DET
iajs-1806	75	10	g𝑎teaux	g𝑎teaux	ADJ
iajs-1806	75	11	derivative	derivative	NOUN
iajs-1806	75	12	is	be	AUX
iajs-1806	75	13	used	use	VERB
iajs-1806	75	14	to	to	PART
iajs-1806	75	15	define	define	VERB
iajs-1806	75	16	many	many	ADJ
iajs-1806	75	17	concepts	concept	NOUN
iajs-1806	75	18	,	,	PUNCT
iajs-1806	75	19	such	such	ADJ
iajs-1806	75	20	as	as	ADP
iajs-1806	75	21	quasiinner	quasiinner	NOUN
iajs-1806	75	22	product	product	NOUN
iajs-1806	75	23	function	function	NOUN
iajs-1806	75	24	,	,	PUNCT
iajs-1806	75	25	and	and	CCONJ
iajs-1806	75	26	smooth	smooth	ADJ
iajs-1806	75	27	quasi	quasi	ADJ
iajs-1806	75	28	-	-	ADJ
iajs-1806	75	29	hilbert	hilbert	ADJ
iajs-1806	75	30	space	space	NOUN
iajs-1806	75	31	with	with	ADP
iajs-1806	75	32	some	some	DET
iajs-1806	75	33	important	important	ADJ
iajs-1806	75	34	results	result	NOUN
iajs-1806	75	35	and	and	CCONJ
iajs-1806	75	36	examples	example	NOUN
iajs-1806	75	37	.	.	PUNCT
iajs-1806	76	1	definition	definition	NOUN
iajs-1806	76	2	2.1	2.1	NUM
iajs-1806	76	3	.	.	PUNCT
iajs-1806	77	1	ihsciconf	ihsciconf	PROPN
iajs-1806	77	2	2017	2017	NUM
iajs-1806	77	3	special	special	ADJ
iajs-1806	77	4	issue	issue	NOUN
iajs-1806	77	5	ibn	ibn	PROPN
iajs-1806	77	6	al	al	PROPN
iajs-1806	77	7	-	-	PUNCT
iajs-1806	77	8	haitham	haitham	PROPN
iajs-1806	77	9	journal	journal	PROPN
iajs-1806	77	10	for	for	ADP
iajs-1806	77	11	pure	pure	ADJ
iajs-1806	77	12	and	and	CCONJ
iajs-1806	77	13	applied	apply	VERB
iajs-1806	77	14	science	science	NOUN
iajs-1806	77	15	https://doi.org/	https://doi.org/	NOUN
iajs-1806	77	16	10.30526/2017.ihsciconf.1806	10.30526/2017.ihsciconf.1806	NUM
iajs-1806	77	17	for	for	ADP
iajs-1806	77	18	more	more	ADJ
iajs-1806	77	19	information	information	NOUN
iajs-1806	77	20	about	about	ADP
iajs-1806	77	21	the	the	DET
iajs-1806	77	22	conference	conference	NOUN
iajs-1806	77	23	please	please	INTJ
iajs-1806	77	24	visit	visit	VERB
iajs-1806	77	25	the	the	DET
iajs-1806	77	26	websites	website	NOUN
iajs-1806	77	27	:	:	PUNCT
iajs-1806	77	28	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1806	77	29	  	  	SPACE
iajs-1806	77	30	www.ihsciconf.org	www.ihsciconf.org	ADJ
iajs-1806	77	31	   	   	SPACE
iajs-1806	77	32	mathematics	mathematic	NOUN
iajs-1806	77	33	|341	|341	NOUN
iajs-1806	77	34	    	    	SPACE
iajs-1806	77	35	let	let	VERB
iajs-1806	77	36	v	v	PART
iajs-1806	77	37	be	be	AUX
iajs-1806	77	38	a	a	DET
iajs-1806	77	39	vector	vector	NOUN
iajs-1806	77	40	space	space	NOUN
iajs-1806	77	41	over	over	ADP
iajs-1806	77	42	the	the	DET
iajs-1806	77	43	field	field	NOUN
iajs-1806	77	44	ℝ	ℝ	PROPN
iajs-1806	77	45	equipped	equip	VERB
iajs-1806	77	46	with	with	ADP
iajs-1806	77	47	||.||q	||.||q	PROPN
iajs-1806	77	48	.	.	PUNCT
iajs-1806	78	1	a	a	DET
iajs-1806	78	2	g𝑎teaux	g𝑎teaux	ADJ
iajs-1806	78	3	derivative	derivative	NOUN
iajs-1806	78	4	of	of	ADP
iajs-1806	78	5	||||	||||	X
iajs-1806	78	6	vq	vq	NOUN
iajs-1806	78	7	is	be	AUX
iajs-1806	78	8	a	a	DET
iajs-1806	78	9	functional	functional	ADJ
iajs-1806	78	10	𝛿	𝛿	ADJ
iajs-1806	78	11	(	(	PUNCT
iajs-1806	78	12	v	v	NOUN
iajs-1806	78	13	,	,	PUNCT
iajs-1806	78	14	w	w	NOUN
iajs-1806	78	15	)	)	PUNCT
iajs-1806	78	16	at	at	ADP
iajs-1806	78	17	v	v	NUM
iajs-1806	78	18	∈	∈	NOUN
iajs-1806	78	19	v	v	NOUN
iajs-1806	78	20	in	in	ADP
iajs-1806	78	21	the	the	DET
iajs-1806	78	22	direction	direction	NOUN
iajs-1806	78	23	w	w	PROPN
iajs-1806	78	24	∈	∈	PROPN
iajs-1806	78	25	v	v	NOUN
iajs-1806	78	26	which	which	PRON
iajs-1806	78	27	is	be	AUX
iajs-1806	78	28	defined	define	VERB
iajs-1806	78	29	as	as	ADP
iajs-1806	78	30	:	:	PUNCT
iajs-1806	78	31	𝛿(v	𝛿(v	NOUN
iajs-1806	78	32	,	,	PUNCT
iajs-1806	78	33	w	w	NOUN
iajs-1806	78	34	)	)	PUNCT
iajs-1806	78	35	=	=	SYM
iajs-1806	78	36	(	(	PUNCT
iajs-1806	78	37	δ	δ	NOUN
iajs-1806	78	38	𝑣	𝑣	NOUN
iajs-1806	78	39	,	,	PUNCT
iajs-1806	78	40	𝑤	𝑤	ADP
iajs-1806	78	41	+	+	NUM
iajs-1806	79	1	δ	δ	PROPN
iajs-1806	79	2	𝑣	𝑣	NOUN
iajs-1806	79	3	,	,	PUNCT
iajs-1806	79	4	𝑤	𝑤	ADP
iajs-1806	79	5	)	)	PUNCT
iajs-1806	79	6	such	such	ADJ
iajs-1806	79	7	that	that	SCONJ
iajs-1806	79	8	:	:	PUNCT
iajs-1806	79	9	𝛿	𝛿	PRON
iajs-1806	79	10	𝑣	𝑣	NOUN
iajs-1806	79	11	,	,	PUNCT
iajs-1806	79	12	𝑤	𝑤	ADP
iajs-1806	79	13	=	=	SYM
iajs-1806	79	14	lim	lim	PROPN
iajs-1806	79	15	→	→	SYM
iajs-1806	79	16	ℎ	ℎ	X
iajs-1806	79	17	||||	||||	ADV
iajs-1806	79	18	hwvq	hwvq	PROPN
iajs-1806	79	19			SYM
iajs-1806	79	20	||||	||||	X
iajs-1806	79	21	vq	vq	NOUN
iajs-1806	79	22	,	,	PUNCT
iajs-1806	79	23	and	and	CCONJ
iajs-1806	79	24	δ	δ	PROPN
iajs-1806	79	25	𝑥	𝑥	PROPN
iajs-1806	79	26	,	,	PUNCT
iajs-1806	79	27	𝑦	𝑦	PROPN
iajs-1806	79	28	=	=	SYM
iajs-1806	79	29	lim	lim	PROPN
iajs-1806	79	30	→	→	SYM
iajs-1806	79	31	ℎ	ℎ	X
iajs-1806	79	32	||||	||||	ADV
iajs-1806	79	33	hwvq	hwvq	PROPN
iajs-1806	79	34			SYM
iajs-1806	79	35	||||	||||	X
iajs-1806	79	36	vq	vq	NOUN
iajs-1806	79	37	,	,	PUNCT
iajs-1806	79	38	where	where	SCONJ
iajs-1806	79	39	h	h	NOUN
iajs-1806	79	40	∊	∊	NOUN
iajs-1806	79	41	ℝ	ℝ	NOUN
iajs-1806	79	42	\	\	X
iajs-1806	79	43	0	0	NUM
iajs-1806	79	44	.	.	PUNCT
iajs-1806	80	1	in	in	ADP
iajs-1806	80	2	similar	similar	ADJ
iajs-1806	80	3	way	way	NOUN
iajs-1806	80	4	,	,	PUNCT
iajs-1806	80	5	we	we	PRON
iajs-1806	80	6	define	define	VERB
iajs-1806	80	7	𝛿	𝛿	PROPN
iajs-1806	80	8	(	(	PUNCT
iajs-1806	80	9	w	w	PROPN
iajs-1806	80	10	,	,	PUNCT
iajs-1806	80	11	v	v	NOUN
iajs-1806	80	12	)	)	PUNCT
iajs-1806	80	13	.	.	PUNCT
iajs-1806	81	1	g𝑎teaux	g𝑎teaux	ADJ
iajs-1806	81	2	derivatives	derivative	NOUN
iajs-1806	81	3	𝛿(v	𝛿(v	PROPN
iajs-1806	81	4	,	,	PUNCT
iajs-1806	81	5	w	w	NOUN
iajs-1806	81	6	)	)	PUNCT
iajs-1806	81	7	and	and	CCONJ
iajs-1806	81	8	𝛿(w	𝛿(w	VERB
iajs-1806	81	9	,	,	PUNCT
iajs-1806	81	10	v	v	NOUN
iajs-1806	81	11	)	)	PUNCT
iajs-1806	81	12	inspires	inspire	VERB
iajs-1806	81	13	the	the	DET
iajs-1806	81	14	functionals	functional	NOUN
iajs-1806	81	15	𝜏(v	𝜏(v	NOUN
iajs-1806	81	16	,	,	PUNCT
iajs-1806	81	17	w	w	NOUN
iajs-1806	81	18	)	)	PUNCT
iajs-1806	81	19	=	=	VERB
iajs-1806	82	1	||||	||||	X
iajs-1806	82	2	vq	vq	ADP
iajs-1806	82	3	𝛿(v	𝛿(v	PROPN
iajs-1806	82	4	,	,	PUNCT
iajs-1806	82	5	w	w	NOUN
iajs-1806	82	6	)	)	PUNCT
iajs-1806	82	7	and	and	CCONJ
iajs-1806	82	8	𝜏	𝜏	X
iajs-1806	82	9	(	(	PUNCT
iajs-1806	82	10	w	w	PROPN
iajs-1806	82	11	,	,	PUNCT
iajs-1806	82	12	v	v	NOUN
iajs-1806	82	13	)	)	PUNCT
iajs-1806	82	14	=	=	VERB
iajs-1806	83	1	||||	||||	X
iajs-1806	83	2	wq	wq	X
iajs-1806	83	3	𝛿	𝛿	ADJ
iajs-1806	83	4	(	(	PUNCT
iajs-1806	83	5	w	w	PROPN
iajs-1806	83	6	,	,	PUNCT
iajs-1806	83	7	v	v	NOUN
iajs-1806	83	8	)	)	PUNCT
iajs-1806	83	9	sequentially	sequentially	ADV
iajs-1806	83	10	.	.	PUNCT
iajs-1806	84	1	definition	definition	NOUN
iajs-1806	84	2	2.2	2.2	NUM
iajs-1806	84	3	a	a	DET
iajs-1806	84	4	g𝑎teaux	g𝑎teaux	ADJ
iajs-1806	84	5	derivative	derivative	ADJ
iajs-1806	84	6	𝜏	𝜏	X
iajs-1806	84	7	(	(	PUNCT
iajs-1806	84	8	v	v	NOUN
iajs-1806	84	9	,	,	PUNCT
iajs-1806	84	10	w	w	NOUN
iajs-1806	84	11	)	)	PUNCT
iajs-1806	84	12	is	be	AUX
iajs-1806	84	13	said	say	VERB
iajs-1806	84	14	to	to	PART
iajs-1806	84	15	be	be	AUX
iajs-1806	84	16	quasi	quasi	ADJ
iajs-1806	84	17	-	-	ADJ
iajs-1806	84	18	inner	inner	ADJ
iajs-1806	84	19	product	product	NOUN
iajs-1806	84	20	function	function	NOUN
iajs-1806	84	21	if	if	SCONJ
iajs-1806	84	22	𝜏	𝜏	PROPN
iajs-1806	84	23	(	(	PUNCT
iajs-1806	84	24	w	w	PROPN
iajs-1806	84	25	,	,	PUNCT
iajs-1806	84	26	v	v	NOUN
iajs-1806	84	27	)	)	PUNCT
iajs-1806	84	28	exists	exist	VERB
iajs-1806	84	29	and	and	CCONJ
iajs-1806	84	30	the	the	DET
iajs-1806	84	31	next	next	ADJ
iajs-1806	84	32	equality	equality	NOUN
iajs-1806	84	33	is	be	AUX
iajs-1806	84	34	satisfied	satisfied	ADJ
iajs-1806	84	35	:	:	PUNCT
iajs-1806	85	1			NOUN
iajs-1806	85	2	4||||	4||||	NUM
iajs-1806	85	3	wvq	wvq	NOUN
iajs-1806	85	4	4||||	4||||	NUM
iajs-1806	85	5	wvq	wvq	NOUN
iajs-1806	85	6			NOUN
iajs-1806	85	7	=	=	SYM
iajs-1806	85	8	8	8	NUM
iajs-1806	85	9	(	(	PUNCT
iajs-1806	85	10	2||||	2||||	NUM
iajs-1806	85	11	vq	vq	ADP
iajs-1806	85	12	𝜏	𝜏	X
iajs-1806	85	13	(	(	PUNCT
iajs-1806	85	14	v	v	NOUN
iajs-1806	85	15	,	,	PUNCT
iajs-1806	85	16	w	w	NOUN
iajs-1806	85	17	)	)	PUNCT
iajs-1806	85	18	+	+	CCONJ
iajs-1806	85	19	2||||	2||||	NUM
iajs-1806	85	20	wq	wq	NOUN
iajs-1806	85	21	𝜏	𝜏	X
iajs-1806	85	22	(	(	PUNCT
iajs-1806	85	23	w	w	PROPN
iajs-1806	85	24	,	,	PUNCT
iajs-1806	85	25	v	v	NOUN
iajs-1806	85	26	)	)	PUNCT
iajs-1806	85	27	)	)	PUNCT
iajs-1806	85	28	,	,	PUNCT
iajs-1806	85	29			NOUN
iajs-1806	85	30	v	v	NOUN
iajs-1806	85	31	,	,	PUNCT
iajs-1806	85	32	w	w	PROPN
iajs-1806	85	33	∊	∊	NUM
iajs-1806	85	34	v	v	NOUN
iajs-1806	85	35	(	(	PUNCT
iajs-1806	85	36	3	3	NUM
iajs-1806	85	37	)	)	PUNCT
iajs-1806	85	38	similarly	similarly	ADV
iajs-1806	85	39	,	,	PUNCT
iajs-1806	85	40	𝜏	𝜏	PROPN
iajs-1806	85	41	(	(	PUNCT
iajs-1806	85	42	w	w	PROPN
iajs-1806	85	43	,	,	PUNCT
iajs-1806	85	44	v	v	NOUN
iajs-1806	85	45	)	)	PUNCT
iajs-1806	85	46	.	.	PUNCT
iajs-1806	86	1	a	a	DET
iajs-1806	86	2	space	space	NOUN
iajs-1806	86	3	v	v	NOUN
iajs-1806	86	4	is	be	AUX
iajs-1806	86	5	said	say	VERB
iajs-1806	86	6	to	to	PART
iajs-1806	86	7	be	be	AUX
iajs-1806	86	8	a	a	DET
iajs-1806	86	9	quasi	quasi	ADJ
iajs-1806	86	10	-	-	ADJ
iajs-1806	86	11	inner	inner	ADJ
iajs-1806	86	12	product	product	NOUN
iajs-1806	86	13	if	if	SCONJ
iajs-1806	86	14	both	both	PRON
iajs-1806	86	15	𝜏	𝜏	X
iajs-1806	86	16	(	(	PUNCT
iajs-1806	86	17	v	v	NOUN
iajs-1806	86	18	,	,	PUNCT
iajs-1806	86	19	w	w	NOUN
iajs-1806	86	20	)	)	PUNCT
iajs-1806	86	21	and	and	CCONJ
iajs-1806	86	22	𝜏	𝜏	X
iajs-1806	86	23	(	(	PUNCT
iajs-1806	86	24	w	w	PROPN
iajs-1806	86	25	,	,	PUNCT
iajs-1806	86	26	v	v	NOUN
iajs-1806	86	27	)	)	PUNCT
iajs-1806	86	28	are	be	AUX
iajs-1806	86	29	quasi	quasi	ADJ
iajs-1806	86	30	-	-	ADJ
iajs-1806	86	31	inner	inner	ADJ
iajs-1806	86	32	product	product	NOUN
iajs-1806	86	33	functions	function	NOUN
iajs-1806	86	34	.	.	PUNCT
iajs-1806	87	1	lemma	lemma	PROPN
iajs-1806	87	2	2.3	2.3	NUM
iajs-1806	87	3	for	for	ADP
iajs-1806	87	4	every	every	DET
iajs-1806	87	5	positive	positive	ADJ
iajs-1806	87	6	integer	integer	NOUN
iajs-1806	87	7	p	p	PROPN
iajs-1806	87	8	≥	≥	NUM
iajs-1806	87	9	1	1	NUM
iajs-1806	87	10	and	and	CCONJ
iajs-1806	87	11	m	m	PROPN
iajs-1806	87	12	∈	∈	PROPN
iajs-1806	87	13	ℝ	ℝ	PROPN
iajs-1806	87	14	,	,	PUNCT
iajs-1806	87	15	the	the	DET
iajs-1806	87	16	functional	functional	ADJ
iajs-1806	87	17	𝜏	𝜏	X
iajs-1806	87	18	(	(	PUNCT
iajs-1806	87	19	v	v	NOUN
iajs-1806	87	20	,	,	PUNCT
iajs-1806	87	21	w	w	NOUN
iajs-1806	87	22	)	)	PUNCT
iajs-1806	87	23	in	in	ADP
iajs-1806	87	24	quasi	quasi	ADJ
iajs-1806	87	25	-	-	ADJ
iajs-1806	87	26	sobolev	sobolev	ADJ
iajs-1806	87	27	spaces	space	NOUN
iajs-1806	87	28	ℓ	ℓ	PROPN
iajs-1806	87	29	exists	exist	VERB
iajs-1806	87	30	and	and	CCONJ
iajs-1806	87	31	is	be	AUX
iajs-1806	87	32	defined	define	VERB
iajs-1806	87	33	as	as	ADP
iajs-1806	87	34	:	:	PUNCT
iajs-1806	87	35	𝜏	𝜏	X
iajs-1806	87	36	(	(	PUNCT
iajs-1806	87	37	v	v	NOUN
iajs-1806	87	38	,	,	PUNCT
iajs-1806	87	39	w	w	NOUN
iajs-1806	87	40	)	)	PUNCT
iajs-1806	87	41	=	=	PUNCT
iajs-1806	88	1	p	p	X
iajs-1806	88	2	q	q	NOUN
iajs-1806	88	3	v	v	NOUN
iajs-1806	88	4	2||||	2||||	NOUN
iajs-1806	88	5			X
iajs-1806	89	1	k	k	NOUN
iajs-1806	89	2	𝜆𝑘	𝜆𝑘	ADJ
iajs-1806	89	3	|𝑣𝑘|p	|𝑣𝑘|p	PROPN
iajs-1806	89	4	1	1	NUM
iajs-1806	89	5	sng	sng	NOUN
iajs-1806	89	6	𝑣𝑘	𝑣𝑘	INTJ
iajs-1806	89	7	𝑤𝑘	𝑤𝑘	INTJ
iajs-1806	89	8	,	,	PUNCT
iajs-1806	89	9			NOUN
iajs-1806	89	10	v	v	ADP
iajs-1806	89	11	∊	∊	PROPN
iajs-1806	89	12	ℓ	ℓ	PROPN
iajs-1806	89	13	s.t	s.t	PROPN
iajs-1806	89	14	.	.	PROPN
iajs-1806	89	15	||||	||||	PROPN
iajs-1806	89	16	vq	vq	PROPN
iajs-1806	89	17	∊	∊	PROPN
iajs-1806	89	18	e	e	PROPN
iajs-1806	89	19	,	,	PUNCT
iajs-1806	89	20	where	where	SCONJ
iajs-1806	89	21	,	,	PUNCT
iajs-1806	89	22	e	e	NOUN
iajs-1806	89	23	=	=	PUNCT
iajs-1806	89	24	||||	||||	X
iajs-1806	89	25	vq	vq	NOUN
iajs-1806	89	26	:	:	PUNCT
iajs-1806	89	27	||||	||||	X
iajs-1806	89	28	vq	vq	PROPN
iajs-1806	89	29	0	0	NUM
iajs-1806	89	30	,	,	PUNCT
iajs-1806	89	31	𝑃	𝑃	PROPN
iajs-1806	89	32	1	1	NUM
iajs-1806	89	33	||||	||||	NOUN
iajs-1806	89	34	vq	vq	NOUN
iajs-1806	89	35	0	0	NUM
iajs-1806	89	36	,	,	PUNCT
iajs-1806	89	37	𝑃	𝑃	PROPN
iajs-1806	89	38	2	2	NUM
iajs-1806	89	39	and	and	CCONJ
iajs-1806	89	40	sng	sng	NOUN
iajs-1806	89	41	𝑣	𝑣	ADP
iajs-1806	89	42	=	=	SYM
iajs-1806	89	43	1	1	NUM
iajs-1806	89	44	,	,	PUNCT
iajs-1806	89	45	𝑣	𝑣	PRON
iajs-1806	89	46	0	0	NUM
iajs-1806	89	47	0	0	NUM
iajs-1806	89	48	,	,	PUNCT
iajs-1806	89	49	𝑣	𝑣	PRON
iajs-1806	89	50	0	0	NUM
iajs-1806	89	51	1	1	NUM
iajs-1806	89	52	,	,	PUNCT
iajs-1806	89	53	𝑣	𝑣	PRON
iajs-1806	89	54	0	0	NUM
iajs-1806	89	55	.	.	PUNCT
iajs-1806	90	1	(	(	PUNCT
iajs-1806	90	2	4	4	X
iajs-1806	90	3	)	)	PUNCT
iajs-1806	90	4	similarly	similarly	ADV
iajs-1806	90	5	,	,	PUNCT
iajs-1806	90	6	we	we	PRON
iajs-1806	90	7	define	define	VERB
iajs-1806	90	8	𝜏	𝜏	PRON
iajs-1806	90	9	𝑤	𝑤	PROPN
iajs-1806	90	10	,	,	PUNCT
iajs-1806	90	11	𝑣	𝑣	X
iajs-1806	90	12	.	.	PUNCT
iajs-1806	91	1	proof	proof	NOUN
iajs-1806	91	2	:	:	PUNCT
iajs-1806	91	3	in	in	ADP
iajs-1806	91	4	definition	definition	NOUN
iajs-1806	91	5	2.1	2.1	NUM
iajs-1806	91	6	,	,	PUNCT
iajs-1806	91	7	we	we	PRON
iajs-1806	91	8	use	use	VERB
iajs-1806	91	9	properties	property	NOUN
iajs-1806	91	10	of	of	ADP
iajs-1806	91	11	limits	limit	NOUN
iajs-1806	91	12	of	of	ADP
iajs-1806	91	13	functions	function	NOUN
iajs-1806	91	14	and	and	CCONJ
iajs-1806	91	15	applying	apply	VERB
iajs-1806	91	16	definition	definition	NOUN
iajs-1806	91	17	of	of	ADP
iajs-1806	91	18	a	a	DET
iajs-1806	91	19	quasi	quasi	ADJ
iajs-1806	91	20	-	-	ADJ
iajs-1806	91	21	norm	norm	ADJ
iajs-1806	91	22	function	function	NOUN
iajs-1806	91	23	of	of	ADP
iajs-1806	91	24	ℓ	ℓ	PROPN
iajs-1806	91	25	which	which	PRON
iajs-1806	91	26	is	be	AUX
iajs-1806	91	27	in	in	ADP
iajs-1806	91	28	theorem	theorem	ADJ
iajs-1806	91	29	1.6	1.6	NUM
iajs-1806	91	30	with	with	ADP
iajs-1806	91	31	help	help	NOUN
iajs-1806	91	32	of	of	ADP
iajs-1806	91	33	the	the	DET
iajs-1806	91	34	binomial	binomial	ADJ
iajs-1806	91	35	theorem	theorem	NOUN
iajs-1806	91	36	,	,	PUNCT
iajs-1806	91	37	which	which	PRON
iajs-1806	91	38	is	be	AUX
iajs-1806	91	39	for	for	ADP
iajs-1806	91	40	every	every	DET
iajs-1806	91	41	positive	positive	ADJ
iajs-1806	91	42	integer	integer	NOUN
iajs-1806	91	43	p	p	NOUN
iajs-1806	91	44	,	,	PUNCT
iajs-1806	91	45	𝑣	𝑣	PART
iajs-1806	91	46	𝑤	𝑤	ADP
iajs-1806	91	47	𝑣	𝑣	ADP
iajs-1806	91	48	𝑤	𝑤	INTJ
iajs-1806	91	49	,	,	PUNCT
iajs-1806	91	50	we	we	PRON
iajs-1806	91	51	get	get	VERB
iajs-1806	91	52	eq	eq	ADJ
iajs-1806	91	53	.	.	PUNCT
iajs-1806	92	1	(	(	PUNCT
iajs-1806	92	2	4	4	NUM
iajs-1806	92	3	)	)	PUNCT
iajs-1806	92	4	.	.	PUNCT
iajs-1806	93	1	proposition	proposition	NOUN
iajs-1806	93	2	2.4	2.4	NUM
iajs-1806	93	3	.	.	PUNCT
iajs-1806	94	1	ihsciconf	ihsciconf	PROPN
iajs-1806	94	2	2017	2017	NUM
iajs-1806	94	3	special	special	ADJ
iajs-1806	94	4	issue	issue	NOUN
iajs-1806	94	5	ibn	ibn	PROPN
iajs-1806	94	6	al	al	PROPN
iajs-1806	94	7	-	-	PUNCT
iajs-1806	94	8	haitham	haitham	PROPN
iajs-1806	94	9	journal	journal	PROPN
iajs-1806	94	10	for	for	ADP
iajs-1806	94	11	pure	pure	ADJ
iajs-1806	94	12	and	and	CCONJ
iajs-1806	94	13	applied	apply	VERB
iajs-1806	94	14	science	science	NOUN
iajs-1806	94	15	https://doi.org/	https://doi.org/	NOUN
iajs-1806	94	16	10.30526/2017.ihsciconf.1806	10.30526/2017.ihsciconf.1806	NUM
iajs-1806	94	17	for	for	ADP
iajs-1806	94	18	more	more	ADJ
iajs-1806	94	19	information	information	NOUN
iajs-1806	94	20	about	about	ADP
iajs-1806	94	21	the	the	DET
iajs-1806	94	22	conference	conference	NOUN
iajs-1806	94	23	please	please	INTJ
iajs-1806	94	24	visit	visit	VERB
iajs-1806	94	25	the	the	DET
iajs-1806	94	26	websites	website	NOUN
iajs-1806	94	27	:	:	PUNCT
iajs-1806	94	28	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1806	94	29	  	  	SPACE
iajs-1806	94	30	www.ihsciconf.org	www.ihsciconf.org	ADJ
iajs-1806	94	31	   	   	SPACE
iajs-1806	94	32	mathematics	mathematic	NOUN
iajs-1806	94	33	|342	|342	NOUN
iajs-1806	94	34	    	    	SPACE
iajs-1806	94	35	the	the	DET
iajs-1806	94	36	existence	existence	NOUN
iajs-1806	94	37	of	of	ADP
iajs-1806	94	38	the	the	DET
iajs-1806	94	39	limit	limit	NOUN
iajs-1806	94	40	in	in	ADP
iajs-1806	94	41	definition	definition	NOUN
iajs-1806	94	42	of	of	ADP
iajs-1806	94	43	g𝑎teaux	g𝑎teaux	ADJ
iajs-1806	94	44	functions	function	NOUN
iajs-1806	94	45	is	be	AUX
iajs-1806	94	46	necessary	necessary	ADJ
iajs-1806	94	47	condition	condition	NOUN
iajs-1806	94	48	,	,	PUNCT
iajs-1806	94	49	not	not	PART
iajs-1806	94	50	sufficient	sufficient	ADJ
iajs-1806	94	51	,	,	PUNCT
iajs-1806	94	52	in	in	ADP
iajs-1806	94	53	order	order	NOUN
iajs-1806	94	54	that	that	SCONJ
iajs-1806	94	55	any	any	DET
iajs-1806	94	56	quasi	quasi	ADJ
iajs-1806	94	57	-	-	ADJ
iajs-1806	94	58	normed	normed	ADJ
iajs-1806	94	59	space	space	NOUN
iajs-1806	94	60	be	be	AUX
iajs-1806	94	61	a	a	DET
iajs-1806	94	62	quasi	quasi	ADJ
iajs-1806	94	63	-	-	ADJ
iajs-1806	94	64	inner	inner	ADJ
iajs-1806	94	65	product	product	NOUN
iajs-1806	94	66	space	space	NOUN
iajs-1806	94	67	.	.	PUNCT
iajs-1806	95	1	proof	proof	NOUN
iajs-1806	95	2	suppose	suppose	VERB
iajs-1806	95	3	v	v	NOUN
iajs-1806	95	4	is	be	AUX
iajs-1806	95	5	a	a	DET
iajs-1806	95	6	quasi	quasi	ADJ
iajs-1806	95	7	-	-	ADJ
iajs-1806	95	8	normed	normed	ADJ
iajs-1806	95	9	space	space	NOUN
iajs-1806	95	10	.	.	PUNCT
iajs-1806	96	1	from	from	ADP
iajs-1806	96	2	definition	definition	NOUN
iajs-1806	96	3	2.1	2.1	NUM
iajs-1806	96	4	,	,	PUNCT
iajs-1806	96	5	we	we	PRON
iajs-1806	96	6	observe	observe	VERB
iajs-1806	96	7	that	that	DET
iajs-1806	96	8	existence	existence	NOUN
iajs-1806	96	9	of	of	ADP
iajs-1806	96	10	δ	δ	PROPN
iajs-1806	96	11	(	(	PUNCT
iajs-1806	96	12	v	v	PROPN
iajs-1806	96	13	,	,	PUNCT
iajs-1806	96	14	w	w	NOUN
iajs-1806	96	15	)	)	PUNCT
iajs-1806	96	16	and	and	CCONJ
iajs-1806	96	17	δ	δ	PROPN
iajs-1806	96	18	(	(	PUNCT
iajs-1806	96	19	v	v	PROPN
iajs-1806	96	20	,	,	PUNCT
iajs-1806	96	21	w	w	NOUN
iajs-1806	96	22	)	)	PUNCT
iajs-1806	96	23	are	be	AUX
iajs-1806	96	24	connected	connect	VERB
iajs-1806	96	25	by	by	ADP
iajs-1806	96	26	the	the	DET
iajs-1806	96	27	limit	limit	NOUN
iajs-1806	96	28	on	on	ADP
iajs-1806	96	29	behavior	behavior	NOUN
iajs-1806	96	30	of	of	ADP
iajs-1806	96	31	the	the	DET
iajs-1806	96	32	quasi	quasi	NOUN
iajs-1806	96	33	-	-	NOUN
iajs-1806	96	34	norm	norm	NOUN
iajs-1806	96	35	as	as	ADP
iajs-1806	96	36	h	h	NOUN
iajs-1806	96	37	→	→	SYM
iajs-1806	96	38	±0	±0	NOUN
iajs-1806	96	39	.	.	PUNCT
iajs-1806	97	1	hence	hence	ADV
iajs-1806	97	2	,	,	PUNCT
iajs-1806	97	3	𝜏	𝜏	X
iajs-1806	97	4	(	(	PUNCT
iajs-1806	97	5	v	v	NOUN
iajs-1806	97	6	,	,	PUNCT
iajs-1806	97	7	w	w	NOUN
iajs-1806	97	8	)	)	PUNCT
iajs-1806	97	9	is	be	AUX
iajs-1806	97	10	exist	exist	ADJ
iajs-1806	97	11	if	if	SCONJ
iajs-1806	97	12	this	this	DET
iajs-1806	97	13	limit	limit	NOUN
iajs-1806	97	14	is	be	AUX
iajs-1806	97	15	exist	exist	NOUN
iajs-1806	97	16	.	.	PUNCT
iajs-1806	98	1	also	also	ADV
iajs-1806	98	2	,	,	PUNCT
iajs-1806	98	3	with	with	ADP
iajs-1806	98	4	𝜏	𝜏	PROPN
iajs-1806	98	5	(	(	PUNCT
iajs-1806	98	6	w	w	PROPN
iajs-1806	98	7	,	,	PUNCT
iajs-1806	98	8	v	v	NOUN
iajs-1806	98	9	)	)	PUNCT
iajs-1806	98	10	similarly	similarly	ADV
iajs-1806	98	11	.	.	PUNCT
iajs-1806	99	1	to	to	PART
iajs-1806	99	2	explains	explain	VERB
iajs-1806	99	3	above	above	ADP
iajs-1806	99	4	condition	condition	NOUN
iajs-1806	99	5	is	be	AUX
iajs-1806	99	6	not	not	PART
iajs-1806	99	7	sufficiently	sufficiently	ADV
iajs-1806	99	8	,	,	PUNCT
iajs-1806	99	9	we	we	PRON
iajs-1806	99	10	take	take	VERB
iajs-1806	99	11	the	the	DET
iajs-1806	99	12	example	example	NOUN
iajs-1806	99	13	:	:	PUNCT
iajs-1806	99	14	example	example	NOUN
iajs-1806	99	15	2.5	2.5	NUM
iajs-1806	99	16	:	:	PUNCT
iajs-1806	99	17	suppose	suppose	VERB
iajs-1806	99	18	v	v	X
iajs-1806	99	19	,	,	PUNCT
iajs-1806	99	20	w	w	PROPN
iajs-1806	99	21	∈	∈	PROPN
iajs-1806	99	22	ℓ	ℓ	PROPN
iajs-1806	99	23	,	,	PUNCT
iajs-1806	99	24	where	where	SCONJ
iajs-1806	99	25	v	v	NOUN
iajs-1806	99	26	=	=	SYM
iajs-1806	99	27	{	{	PUNCT
iajs-1806	99	28	vk	vk	NOUN
iajs-1806	99	29	}	}	PUNCT
iajs-1806	99	30	=	=	PUNCT
iajs-1806	99	31	{	{	PUNCT
iajs-1806	99	32	1,0	1,0	NUM
iajs-1806	99	33	,	,	PUNCT
iajs-1806	99	34	0	0	NUM
iajs-1806	99	35	,	,	PUNCT
iajs-1806	99	36	0	0	NUM
iajs-1806	99	37	,	,	PUNCT
iajs-1806	99	38	…	…	PUNCT
iajs-1806	99	39	}	}	PUNCT
iajs-1806	99	40	,	,	PUNCT
iajs-1806	100	1	w	w	X
iajs-1806	100	2	=	=	SYM
iajs-1806	100	3	{	{	PUNCT
iajs-1806	100	4	wk	wk	NOUN
iajs-1806	100	5	}	}	PUNCT
iajs-1806	100	6	=	=	PUNCT
iajs-1806	100	7	{	{	PUNCT
iajs-1806	100	8	1	1	NUM
iajs-1806	100	9	,	,	PUNCT
iajs-1806	100	10	1	1	NUM
iajs-1806	100	11	,	,	PUNCT
iajs-1806	100	12	0	0	NUM
iajs-1806	100	13	,	,	PUNCT
iajs-1806	100	14	0	0	NUM
iajs-1806	100	15	,	,	PUNCT
iajs-1806	100	16	…	…	PUNCT
iajs-1806	100	17	}	}	PUNCT
iajs-1806	100	18	and	and	CCONJ
iajs-1806	100	19	take	take	VERB
iajs-1806	100	20	{	{	PUNCT
iajs-1806	100	21	𝜆k	𝜆k	NOUN
iajs-1806	100	22	}	}	PUNCT
iajs-1806	100	23	=	=	SYM
iajs-1806	100	24	{	{	PUNCT
iajs-1806	100	25	√𝑘	√𝑘	NOUN
iajs-1806	100	26	}	}	PUNCT
iajs-1806	100	27	,	,	PUNCT
iajs-1806	100	28	𝑘	𝑘	PROPN
iajs-1806	100	29	∈	∈	PROPN
iajs-1806	100	30	ℕ.	ℕ.	PROPN
iajs-1806	100	31	then	then	ADV
iajs-1806	100	32	,	,	PUNCT
iajs-1806	100	33	using	use	VERB
iajs-1806	100	34	lemma	lemma	PROPN
iajs-1806	100	35	2.3,we	2.3,we	PROPN
iajs-1806	100	36	get	get	NOUN
iajs-1806	100	37	𝜏(v	𝜏(v	NOUN
iajs-1806	100	38	,	,	PUNCT
iajs-1806	100	39	w)=	w)=	NOUN
iajs-1806	100	40	1	1	NUM
iajs-1806	100	41	,	,	PUNCT
iajs-1806	100	42	𝜏	𝜏	X
iajs-1806	100	43	(	(	PUNCT
iajs-1806	100	44	w	w	PROPN
iajs-1806	100	45	,	,	PUNCT
iajs-1806	100	46	v)=	v)=	NOUN
iajs-1806	100	47	0.372884880824589	0.372884880824589	NUM
iajs-1806	100	48	.	.	PUNCT
iajs-1806	101	1	thus	thus	ADV
iajs-1806	101	2	,	,	PUNCT
iajs-1806	101	3	𝜏(v	𝜏(v	NOUN
iajs-1806	101	4	,	,	PUNCT
iajs-1806	101	5	w	w	PROPN
iajs-1806	101	6	)	)	PUNCT
iajs-1806	101	7	and	and	CCONJ
iajs-1806	101	8	𝜏	𝜏	X
iajs-1806	101	9	(	(	PUNCT
iajs-1806	101	10	w	w	PROPN
iajs-1806	101	11	,	,	PUNCT
iajs-1806	101	12	v	v	NOUN
iajs-1806	101	13	)	)	PUNCT
iajs-1806	101	14	are	be	AUX
iajs-1806	101	15	exist	exist	ADJ
iajs-1806	101	16	.	.	PUNCT
iajs-1806	102	1	however	however	ADV
iajs-1806	102	2	,	,	PUNCT
iajs-1806	102	3	equation	equation	NOUN
iajs-1806	102	4	(	(	PUNCT
iajs-1806	102	5	3	3	X
iajs-1806	102	6	)	)	PUNCT
iajs-1806	102	7	is	be	AUX
iajs-1806	102	8	not	not	PART
iajs-1806	102	9	satisfied	satisfied	ADJ
iajs-1806	102	10	.	.	PUNCT
iajs-1806	103	1	therefore	therefore	ADV
iajs-1806	103	2	,	,	PUNCT
iajs-1806	103	3	the	the	DET
iajs-1806	103	4	space	space	NOUN
iajs-1806	103	5	ℓ	ℓ	PROPN
iajs-1806	103	6	is	be	AUX
iajs-1806	103	7	not	not	PART
iajs-1806	103	8	quasi	quasi	ADJ
iajs-1806	103	9	-	-	ADJ
iajs-1806	103	10	inner	inner	ADJ
iajs-1806	103	11	product	product	NOUN
iajs-1806	103	12	space	space	NOUN
iajs-1806	103	13	.	.	PUNCT
iajs-1806	104	1	remark	remark	VERB
iajs-1806	104	2	2.6	2.6	NUM
iajs-1806	104	3	.	.	PUNCT
iajs-1806	105	1	if	if	SCONJ
iajs-1806	105	2	cases	case	VERB
iajs-1806	105	3	the	the	DET
iajs-1806	105	4	values	value	NOUN
iajs-1806	105	5	of	of	ADP
iajs-1806	105	6	p	p	PRON
iajs-1806	105	7	differ	differ	VERB
iajs-1806	105	8	from	from	ADP
iajs-1806	105	9	those	those	DET
iajs-1806	105	10	values	value	NOUN
iajs-1806	105	11	considered	consider	VERB
iajs-1806	105	12	in	in	ADP
iajs-1806	105	13	lemma	lemma	PROPN
iajs-1806	105	14	2.3	2.3	NUM
iajs-1806	105	15	,	,	PUNCT
iajs-1806	105	16	we	we	PRON
iajs-1806	105	17	have	have	VERB
iajs-1806	105	18	quasisobolev	quasisobolev	NOUN
iajs-1806	105	19	spaces	space	NOUN
iajs-1806	105	20	ℓ	ℓ	NOUN
iajs-1806	105	21	which	which	PRON
iajs-1806	105	22	are	be	AUX
iajs-1806	105	23	not	not	PART
iajs-1806	105	24	quasiinner	quasiinner	NOUN
iajs-1806	105	25	product	product	NOUN
iajs-1806	105	26	.	.	PUNCT
iajs-1806	106	1	for	for	ADP
iajs-1806	106	2	instance	instance	NOUN
iajs-1806	106	3	,	,	PUNCT
iajs-1806	106	4	in	in	ADP
iajs-1806	106	5	case	case	NOUN
iajs-1806	106	6	p	p	X
iajs-1806	106	7	∊	∊	NUM
iajs-1806	106	8	0,1	0,1	NUM
iajs-1806	106	9	,	,	PUNCT
iajs-1806	106	10	as	as	SCONJ
iajs-1806	106	11	it	it	PRON
iajs-1806	106	12	is	be	AUX
iajs-1806	106	13	shown	show	VERB
iajs-1806	106	14	in	in	ADP
iajs-1806	106	15	the	the	DET
iajs-1806	106	16	example	example	NOUN
iajs-1806	106	17	1.9	1.9	NUM
iajs-1806	106	18	.	.	PUNCT
iajs-1806	107	1	indeed	indeed	ADV
iajs-1806	107	2	,	,	PUNCT
iajs-1806	107	3	with	with	ADP
iajs-1806	107	4	the	the	DET
iajs-1806	107	5	space	space	NOUN
iajs-1806	107	6	ℓ	ℓ	PROPN
iajs-1806	107	7	/	/	SYM
iajs-1806	107	8	,	,	PUNCT
iajs-1806	107	9	𝛿	𝛿	PROPN
iajs-1806	107	10	(	(	PUNCT
iajs-1806	107	11	v	v	NOUN
iajs-1806	107	12	,	,	PUNCT
iajs-1806	107	13	w	w	NOUN
iajs-1806	107	14	)	)	PUNCT
iajs-1806	107	15	and	and	CCONJ
iajs-1806	107	16	𝛿	𝛿	X
iajs-1806	107	17	(	(	PUNCT
iajs-1806	107	18	w	w	PROPN
iajs-1806	107	19	,	,	PUNCT
iajs-1806	107	20	v	v	NOUN
iajs-1806	107	21	)	)	PUNCT
iajs-1806	107	22	do	do	AUX
iajs-1806	107	23	not	not	PART
iajs-1806	107	24	exist	exist	VERB
iajs-1806	107	25	,	,	PUNCT
iajs-1806	107	26	since	since	SCONJ
iajs-1806	107	27	there	there	PRON
iajs-1806	107	28	is	be	VERB
iajs-1806	107	29	no	no	DET
iajs-1806	107	30	limit	limit	NOUN
iajs-1806	107	31	as	as	ADP
iajs-1806	107	32	h	h	NOUN
iajs-1806	107	33	→	→	PUNCT
iajs-1806	107	34	±0	±0	NOUN
iajs-1806	107	35	from	from	ADP
iajs-1806	107	36	definition	definition	NOUN
iajs-1806	107	37	2.1	2.1	NUM
iajs-1806	107	38	.	.	PUNCT
iajs-1806	108	1	then	then	ADV
iajs-1806	108	2	right	right	ADJ
iajs-1806	108	3	hand	hand	NOUN
iajs-1806	108	4	in	in	ADP
iajs-1806	108	5	eq	eq	ADP
iajs-1806	108	6	.	.	PUNCT
iajs-1806	109	1	(	(	PUNCT
iajs-1806	109	2	3	3	X
iajs-1806	109	3	)	)	PUNCT
iajs-1806	109	4	is	be	AUX
iajs-1806	109	5	not	not	PART
iajs-1806	109	6	finite	finite	ADJ
iajs-1806	109	7	,	,	PUNCT
iajs-1806	109	8	while	while	SCONJ
iajs-1806	109	9	left	leave	VERB
iajs-1806	109	10	hand	hand	NOUN
iajs-1806	109	11	equal	equal	ADJ
iajs-1806	109	12	zero	zero	NUM
iajs-1806	109	13	.	.	PUNCT
iajs-1806	110	1	definition	definition	NOUN
iajs-1806	110	2	2.7	2.7	NUM
iajs-1806	110	3	a	a	DET
iajs-1806	110	4	quasi	quasi	ADJ
iajs-1806	110	5	-	-	ADJ
iajs-1806	110	6	normed	normed	ADJ
iajs-1806	110	7	space	space	NOUN
iajs-1806	110	8	v	v	NOUN
iajs-1806	110	9	is	be	AUX
iajs-1806	110	10	smooth	smooth	ADJ
iajs-1806	110	11	if	if	SCONJ
iajs-1806	110	12	𝛿	𝛿	ADJ
iajs-1806	110	13	𝑣	𝑣	NOUN
iajs-1806	110	14	,	,	PUNCT
iajs-1806	110	15	𝑤	𝑤	ADP
iajs-1806	110	16	and	and	CCONJ
iajs-1806	110	17	𝛿	𝛿	DET
iajs-1806	110	18	𝑣	𝑣	NOUN
iajs-1806	110	19	,	,	PUNCT
iajs-1806	110	20	𝑤	𝑤	PART
iajs-1806	110	21	have	have	AUX
iajs-1806	110	22	one	one	NUM
iajs-1806	110	23	value	value	NOUN
iajs-1806	110	24	.	.	PUNCT
iajs-1806	111	1	when	when	SCONJ
iajs-1806	111	2	v	v	NOUN
iajs-1806	111	3	is	be	AUX
iajs-1806	111	4	smooth	smooth	ADJ
iajs-1806	111	5	quasi	quasi	ADJ
iajs-1806	111	6	-	-	ADJ
iajs-1806	111	7	normed	normed	ADJ
iajs-1806	111	8	space	space	NOUN
iajs-1806	111	9	,	,	PUNCT
iajs-1806	111	10	then	then	ADV
iajs-1806	111	11	𝜏	𝜏	X
iajs-1806	111	12	(	(	PUNCT
iajs-1806	111	13	v	v	NOUN
iajs-1806	111	14	,	,	PUNCT
iajs-1806	111	15	w	w	NOUN
iajs-1806	111	16	)	)	PUNCT
iajs-1806	111	17	||||	||||	NOUN
iajs-1806	111	18	vq	vq	PROPN
iajs-1806	111	19	lim	lim	PROPN
iajs-1806	111	20	→	→	PUNCT
iajs-1806	111	21	ℎ	ℎ	X
iajs-1806	111	22	||||	||||	ADV
iajs-1806	111	23	hwvq	hwvq	PROPN
iajs-1806	111	24			SYM
iajs-1806	111	25	||||	||||	X
iajs-1806	111	26	vq	vq	NOUN
iajs-1806	111	27	.	.	PUNCT
iajs-1806	112	1	similarly	similarly	ADV
iajs-1806	112	2	,	,	PUNCT
iajs-1806	112	3	𝜏	𝜏	PROPN
iajs-1806	112	4	(	(	PUNCT
iajs-1806	112	5	w	w	PROPN
iajs-1806	112	6	,	,	PUNCT
iajs-1806	112	7	v	v	NOUN
iajs-1806	112	8	)	)	PUNCT
iajs-1806	112	9	.	.	PUNCT
iajs-1806	113	1	proposition	proposition	NOUN
iajs-1806	113	2	2.8	2.8	NUM
iajs-1806	113	3	.	.	PUNCT
iajs-1806	114	1	every	every	DET
iajs-1806	114	2	pre	pre	NOUN
iajs-1806	114	3	-	-	ADJ
iajs-1806	114	4	hilbert	hilbert	ADJ
iajs-1806	114	5	space.is	space.is	PROPN
iajs-1806	114	6	a	a	DET
iajs-1806	114	7	quasi	quasi	ADJ
iajs-1806	114	8	-	-	ADJ
iajs-1806	114	9	inner	inner	ADJ
iajs-1806	114	10	product	product	NOUN
iajs-1806	114	11	space	space	NOUN
iajs-1806	114	12	.	.	PUNCT
iajs-1806	115	1	proof	proof	NOUN
iajs-1806	115	2	:	:	PUNCT
iajs-1806	115	3	let	let	VERB
iajs-1806	115	4	v	v	NOUN
iajs-1806	115	5	is	be	AUX
iajs-1806	115	6	a	a	DET
iajs-1806	115	7	pre	pre	ADJ
iajs-1806	115	8	-	-	ADJ
iajs-1806	115	9	hilbert	hilbert	ADJ
iajs-1806	115	10	space	space	NOUN
iajs-1806	115	11	.	.	PUNCT
iajs-1806	116	1	according	accord	VERB
iajs-1806	116	2	to	to	ADP
iajs-1806	116	3	lemma	lemma	PROPN
iajs-1806	116	4	1.4	1.4	NUM
iajs-1806	116	5	,	,	PUNCT
iajs-1806	116	6	an	an	DET
iajs-1806	116	7	inner	inner	ADJ
iajs-1806	116	8	product	product	NOUN
iajs-1806	116	9	function	function	NOUN
iajs-1806	116	10	gives	give	VERB
iajs-1806	116	11	eq	eq	NOUN
iajs-1806	116	12	.	.	PUNCT
iajs-1806	117	1	(	(	PUNCT
iajs-1806	117	2	1	1	NUM
iajs-1806	117	3	)	)	PUNCT
iajs-1806	117	4	.	.	PUNCT
iajs-1806	118	1	also	also	ADV
iajs-1806	118	2	,	,	PUNCT
iajs-1806	118	3	by	by	ADP
iajs-1806	118	4	remark	remark	NOUN
iajs-1806	118	5	1.3	1.3	NUM
iajs-1806	118	6	and	and	CCONJ
iajs-1806	118	7	definition	definition	NOUN
iajs-1806	118	8	2.1	2.1	NUM
iajs-1806	118	9	,	,	PUNCT
iajs-1806	118	10	we	we	PRON
iajs-1806	118	11	obtain	obtain	VERB
iajs-1806	118	12	𝜏(v	𝜏(v	NOUN
iajs-1806	118	13	,	,	PUNCT
iajs-1806	118	14	w	w	NOUN
iajs-1806	118	15	)	)	PUNCT
iajs-1806	118	16	=	=	SYM
iajs-1806	118	17	<	<	X
iajs-1806	118	18	v	v	PROPN
iajs-1806	118	19	,	,	PUNCT
iajs-1806	118	20	w	w	NOUN
iajs-1806	118	21	>	>	X
iajs-1806	118	22	and	and	CCONJ
iajs-1806	118	23	𝜏(w	𝜏(w	NOUN
iajs-1806	118	24	,	,	PUNCT
iajs-1806	118	25	v	v	NOUN
iajs-1806	118	26	)	)	PUNCT
iajs-1806	118	27	=	=	PUNCT
iajs-1806	119	1	<	<	X
iajs-1806	119	2	w	w	PROPN
iajs-1806	119	3	,	,	PUNCT
iajs-1806	119	4	v	v	ADP
iajs-1806	119	5	>	>	X
iajs-1806	119	6	.	.	PUNCT
iajs-1806	120	1	hence	hence	ADV
iajs-1806	120	2	,	,	PUNCT
iajs-1806	120	3	we	we	PRON
iajs-1806	120	4	have	have	VERB
iajs-1806	120	5	equation	equation	NOUN
iajs-1806	120	6	(	(	PUNCT
iajs-1806	120	7	3	3	NUM
iajs-1806	120	8	)	)	PUNCT
iajs-1806	120	9	,	,	PUNCT
iajs-1806	120	10	and	and	CCONJ
iajs-1806	120	11	the	the	DET
iajs-1806	120	12	definition	definition	NOUN
iajs-1806	120	13	2.2	2.2	NUM
iajs-1806	120	14	is	be	AUX
iajs-1806	120	15	hold	hold	NOUN
iajs-1806	120	16	.	.	PUNCT
iajs-1806	121	1	thus	thus	ADV
iajs-1806	121	2	,	,	PUNCT
iajs-1806	121	3	v	v	NOUN
iajs-1806	121	4	is	be	AUX
iajs-1806	121	5	an	an	DET
iajs-1806	121	6	quasi	quasi	ADJ
iajs-1806	121	7	-	-	ADJ
iajs-1806	121	8	inner	inner	ADJ
iajs-1806	121	9	product	product	NOUN
iajs-1806	121	10	space	space	NOUN
iajs-1806	121	11	.	.	PUNCT
iajs-1806	122	1	the	the	DET
iajs-1806	122	2	converse	converse	NOUN
iajs-1806	122	3	of	of	ADP
iajs-1806	122	4	proposition	proposition	NOUN
iajs-1806	122	5	does	do	AUX
iajs-1806	122	6	not	not	PART
iajs-1806	122	7	hold	hold	VERB
iajs-1806	122	8	,	,	PUNCT
iajs-1806	122	9	consider	consider	VERB
iajs-1806	122	10	the	the	DET
iajs-1806	122	11	following	follow	VERB
iajs-1806	122	12	example	example	NOUN
iajs-1806	122	13	:	:	PUNCT
iajs-1806	122	14	example	example	NOUN
iajs-1806	122	15	2.9	2.9	NUM
iajs-1806	122	16	:	:	PUNCT
iajs-1806	122	17	take	take	VERB
iajs-1806	122	18	example	example	NOUN
iajs-1806	122	19	2.5	2.5	NUM
iajs-1806	122	20	with	with	ADP
iajs-1806	122	21	replace	replace	NOUN
iajs-1806	122	22	space	space	NOUN
iajs-1806	122	23	ℓ	ℓ	NOUN
iajs-1806	122	24	by	by	ADP
iajs-1806	122	25	ℓ	ℓ	PROPN
iajs-1806	122	26	.	.	PUNCT
iajs-1806	123	1	since	since	SCONJ
iajs-1806	123	2	eq	eq	NUM
iajs-1806	123	3	.	.	PUNCT
iajs-1806	123	4	(	(	PUNCT
iajs-1806	123	5	3	3	X
iajs-1806	123	6	)	)	PUNCT
iajs-1806	123	7	is	be	AUX
iajs-1806	123	8	satisfied	satisfied	ADJ
iajs-1806	123	9	with	with	ADP
iajs-1806	123	10	quasinormed	quasinorme	VERB
iajs-1806	123	11	space	space	NOUN
iajs-1806	123	12	ℓ	ℓ	PROPN
iajs-1806	123	13	,	,	PUNCT
iajs-1806	123	14	where	where	SCONJ
iajs-1806	123	15	the	the	DET
iajs-1806	123	16	left	left	ADJ
iajs-1806	123	17	and	and	CCONJ
iajs-1806	123	18	right	right	ADJ
iajs-1806	123	19	hand	hand	NOUN
iajs-1806	123	20	of	of	ADP
iajs-1806	123	21	eq	eq	PROPN
iajs-1806	123	22	.	.	PUNCT
iajs-1806	124	1	(	(	PUNCT
iajs-1806	124	2	3	3	X
iajs-1806	124	3	)	)	PUNCT
iajs-1806	124	4	are	be	AUX
iajs-1806	124	5	equal	equal	ADJ
iajs-1806	124	6	to	to	ADP
iajs-1806	124	7	16	16	NUM
iajs-1806	124	8	,	,	PUNCT
iajs-1806	124	9	so	so	CCONJ
iajs-1806	124	10	it	it	PRON
iajs-1806	124	11	is	be	AUX
iajs-1806	124	12	quasi	quasi	ADJ
iajs-1806	124	13	-	-	ADJ
iajs-1806	124	14	inner	inner	ADJ
iajs-1806	124	15	product	product	NOUN
iajs-1806	124	16	space	space	NOUN
iajs-1806	124	17	.	.	PUNCT
iajs-1806	125	1	but	but	CCONJ
iajs-1806	125	2	the	the	DET
iajs-1806	125	3	left	left	ADJ
iajs-1806	125	4	and	and	CCONJ
iajs-1806	125	5	right	right	ADJ
iajs-1806	125	6	hand	hand	NOUN
iajs-1806	125	7	of	of	ADP
iajs-1806	125	8	eq	eq	PROPN
iajs-1806	125	9	.	.	PUNCT
iajs-1806	126	1	(	(	PUNCT
iajs-1806	126	2	2	2	X
iajs-1806	126	3	)	)	PUNCT
iajs-1806	126	4	are	be	AUX
iajs-1806	126	5	not	not	PART
iajs-1806	126	6	equal	equal	ADJ
iajs-1806	126	7	,	,	PUNCT
iajs-1806	126	8	hence	hence	ADV
iajs-1806	126	9	this	this	DET
iajs-1806	126	10	space	space	NOUN
iajs-1806	126	11	is	be	AUX
iajs-1806	126	12	not	not	PART
iajs-1806	126	13	a	a	DET
iajs-1806	126	14	pre	pre	ADJ
iajs-1806	126	15	-	-	ADJ
iajs-1806	126	16	hilbert	hilbert	ADJ
iajs-1806	126	17	space	space	NOUN
iajs-1806	126	18	.	.	PUNCT
iajs-1806	127	1	definition	definition	NOUN
iajs-1806	127	2	2.10	2.10	NUM
iajs-1806	127	3	.	.	PUNCT
iajs-1806	128	1	a	a	DET
iajs-1806	128	2	complete	complete	ADJ
iajs-1806	128	3	quasiinner	quasiinner	NOUN
iajs-1806	128	4	product	product	NOUN
iajs-1806	128	5	space	space	NOUN
iajs-1806	128	6	is	be	AUX
iajs-1806	128	7	called	call	VERB
iajs-1806	128	8	a	a	DET
iajs-1806	128	9	quasi	quasi	ADJ
iajs-1806	128	10	-	-	ADJ
iajs-1806	128	11	hilbert	hilbert	ADJ
iajs-1806	128	12	space	space	NOUN
iajs-1806	128	13	.	.	PUNCT
iajs-1806	129	1	if	if	SCONJ
iajs-1806	129	2	a	a	DET
iajs-1806	129	3	quasi	quasi	ADJ
iajs-1806	129	4	-	-	ADJ
iajs-1806	129	5	hilbert	hilbert	ADJ
iajs-1806	129	6	space	space	NOUN
iajs-1806	129	7	is	be	AUX
iajs-1806	129	8	smooth	smooth	ADJ
iajs-1806	129	9	,	,	PUNCT
iajs-1806	129	10	then	then	ADV
iajs-1806	129	11	it	it	PRON
iajs-1806	129	12	is	be	AUX
iajs-1806	129	13	called	call	VERB
iajs-1806	129	14	a	a	DET
iajs-1806	129	15	smooth	smooth	ADJ
iajs-1806	129	16	quasi	quasi	ADJ
iajs-1806	129	17	-	-	ADJ
iajs-1806	129	18	hilbert	hilbert	ADJ
iajs-1806	129	19	space	space	NOUN
iajs-1806	129	20	.	.	PUNCT
iajs-1806	130	1	we	we	PRON
iajs-1806	130	2	recall	recall	VERB
iajs-1806	130	3	that	that	SCONJ
iajs-1806	130	4	completeness	completeness	NOUN
iajs-1806	130	5	property	property	NOUN
iajs-1806	130	6	is	be	AUX
iajs-1806	130	7	coming	come	VERB
iajs-1806	130	8	from	from	ADP
iajs-1806	130	9	this	this	DET
iajs-1806	130	10	property	property	NOUN
iajs-1806	130	11	of	of	ADP
iajs-1806	130	12	quasi	quasi	ADJ
iajs-1806	130	13	-	-	ADJ
iajs-1806	130	14	normed	normed	ADJ
iajs-1806	130	15	space	space	NOUN
iajs-1806	130	16	.	.	PUNCT
iajs-1806	131	1	theorem	theorem	VERB
iajs-1806	131	2	2.11	2.11	NUM
iajs-1806	131	3	.	.	PUNCT
iajs-1806	132	1	ihsciconf	ihsciconf	PROPN
iajs-1806	132	2	2017	2017	NUM
iajs-1806	132	3	special	special	ADJ
iajs-1806	132	4	issue	issue	NOUN
iajs-1806	132	5	ibn	ibn	PROPN
iajs-1806	132	6	al	al	PROPN
iajs-1806	132	7	-	-	PUNCT
iajs-1806	132	8	haitham	haitham	PROPN
iajs-1806	132	9	journal	journal	PROPN
iajs-1806	132	10	for	for	ADP
iajs-1806	132	11	pure	pure	ADJ
iajs-1806	132	12	and	and	CCONJ
iajs-1806	132	13	applied	apply	VERB
iajs-1806	132	14	science	science	NOUN
iajs-1806	132	15	https://doi.org/	https://doi.org/	NOUN
iajs-1806	132	16	10.30526/2017.ihsciconf.1806	10.30526/2017.ihsciconf.1806	NUM
iajs-1806	132	17	for	for	ADP
iajs-1806	132	18	more	more	ADJ
iajs-1806	132	19	information	information	NOUN
iajs-1806	132	20	about	about	ADP
iajs-1806	132	21	the	the	DET
iajs-1806	132	22	conference	conference	NOUN
iajs-1806	132	23	please	please	INTJ
iajs-1806	132	24	visit	visit	VERB
iajs-1806	132	25	the	the	DET
iajs-1806	132	26	websites	website	NOUN
iajs-1806	132	27	:	:	PUNCT
iajs-1806	132	28	http://www.ihsciconf.org/conf/	http://www.ihsciconf.org/conf/	VERB
iajs-1806	132	29	  	  	SPACE
iajs-1806	132	30	www.ihsciconf.org	www.ihsciconf.org	ADJ
iajs-1806	132	31	   	   	SPACE
iajs-1806	132	32	mathematics	mathematic	NOUN
iajs-1806	132	33	|343	|343	PROPN
iajs-1806	132	34	    	    	SPACE
iajs-1806	132	35	for	for	ADP
iajs-1806	132	36	every	every	DET
iajs-1806	132	37	𝑚	𝑚	PROPN
iajs-1806	132	38	∈	∈	PROPN
iajs-1806	132	39	ℝ	ℝ	PROPN
iajs-1806	132	40	,	,	PUNCT
iajs-1806	132	41	ℓ	ℓ	PROPN
iajs-1806	132	42	is	be	AUX
iajs-1806	132	43	a	a	DET
iajs-1806	132	44	smooth	smooth	ADJ
iajs-1806	132	45	quasi	quasi	ADJ
iajs-1806	132	46	-	-	ADJ
iajs-1806	132	47	hilbert	hilbert	ADJ
iajs-1806	132	48	space	space	NOUN
iajs-1806	132	49	and	and	CCONJ
iajs-1806	132	50	hilbert	hilbert	NOUN
iajs-1806	132	51	space	space	NOUN
iajs-1806	132	52	.	.	PUNCT
iajs-1806	133	1	proof	proof	NOUN
iajs-1806	133	2	:	:	PUNCT
iajs-1806	133	3	according	accord	VERB
iajs-1806	133	4	to	to	ADP
iajs-1806	133	5	lemma	lemma	PROPN
iajs-1806	133	6	2.3	2.3	NUM
iajs-1806	133	7	,	,	PUNCT
iajs-1806	133	8	we	we	PRON
iajs-1806	133	9	get	get	VERB
iajs-1806	133	10	𝜏	𝜏	PRON
iajs-1806	133	11	(	(	PUNCT
iajs-1806	133	12	v	v	NOUN
iajs-1806	133	13	,	,	PUNCT
iajs-1806	133	14	w	w	NOUN
iajs-1806	133	15	)	)	PUNCT
iajs-1806	134	1	=	=	NOUN
iajs-1806	134	2			X
iajs-1806	135	1	k	k	X
iajs-1806	135	2	𝜆𝑘	𝜆𝑘	NOUN
iajs-1806	135	3	|𝑣𝑘|	|𝑣𝑘|	PROPN
iajs-1806	135	4	𝑠𝑛𝑔	𝑠𝑛𝑔	NOUN
iajs-1806	135	5	𝑣𝑘	𝑣𝑘	ADP
iajs-1806	135	6	𝑤𝑘,and	𝑤𝑘,and	NUM
iajs-1806	135	7	𝜏(w	𝜏(w	NOUN
iajs-1806	135	8	,	,	PUNCT
iajs-1806	135	9	v	v	NOUN
iajs-1806	135	10	)	)	PUNCT
iajs-1806	135	11	=	=	NOUN
iajs-1806	135	12			X
iajs-1806	135	13	k	k	X
iajs-1806	135	14	𝜆	𝜆	X
iajs-1806	135	15	𝑚|𝑤	𝑚|𝑤	PROPN
iajs-1806	136	1	|	|	ADV
iajs-1806	136	2	𝑠𝑛𝑔	𝑠𝑛𝑔	NOUN
iajs-1806	136	3	𝑤	𝑤	ADP
iajs-1806	136	4	𝑣	𝑣	PRON
iajs-1806	136	5	which	which	PRON
iajs-1806	136	6	are	be	AUX
iajs-1806	136	7	linear	linear	ADJ
iajs-1806	136	8	by	by	ADP
iajs-1806	136	9	definition	definition	NOUN
iajs-1806	136	10	1.2	1.2	NUM
iajs-1806	136	11	,	,	PUNCT
iajs-1806	136	12	with	with	ADP
iajs-1806	136	13	definition	definition	NOUN
iajs-1806	136	14	of	of	ADP
iajs-1806	136	15	𝜏	𝜏	PROPN
iajs-1806	136	16	(	(	PUNCT
iajs-1806	136	17	v	v	NOUN
iajs-1806	136	18	,	,	PUNCT
iajs-1806	136	19	w	w	NOUN
iajs-1806	136	20	)	)	PUNCT
iajs-1806	136	21	and	and	CCONJ
iajs-1806	136	22	𝜏(w	𝜏(w	NUM
iajs-1806	136	23	,	,	PUNCT
iajs-1806	136	24	v	v	NOUN
iajs-1806	136	25	)	)	PUNCT
iajs-1806	136	26	as	as	ADP
iajs-1806	136	27	above	above	ADV
iajs-1806	136	28	,	,	PUNCT
iajs-1806	136	29	then	then	ADV
iajs-1806	136	30	they	they	PRON
iajs-1806	136	31	are	be	AUX
iajs-1806	136	32	symmetric	symmetric	ADJ
iajs-1806	136	33	,	,	PUNCT
iajs-1806	136	34	that	that	ADV
iajs-1806	136	35	is	is	ADV
iajs-1806	136	36	,	,	PUNCT
iajs-1806	136	37	𝜏(v	𝜏(v	PROPN
iajs-1806	136	38	,	,	PUNCT
iajs-1806	136	39	w	w	NOUN
iajs-1806	136	40	)	)	PUNCT
iajs-1806	137	1	=	=	SYM
iajs-1806	137	2	𝜏(w	𝜏(w	NOUN
iajs-1806	137	3	,	,	PUNCT
iajs-1806	137	4	v	v	NOUN
iajs-1806	137	5	)	)	PUNCT
iajs-1806	137	6	,	,	PUNCT
iajs-1806	137	7	and	and	CCONJ
iajs-1806	137	8	𝜏(v	𝜏(v	PROPN
iajs-1806	137	9	,	,	PUNCT
iajs-1806	137	10	v	v	NOUN
iajs-1806	137	11	)	)	PUNCT
iajs-1806	137	12	=	=	SYM
iajs-1806	137	13	2||||	2||||	NUM
iajs-1806	137	14	vq	vq	PROPN
iajs-1806	137	15	0	0	NUM
iajs-1806	137	16	,	,	PUNCT
iajs-1806	137	17	with	with	ADP
iajs-1806	137	18	equality	equality	NOUN
iajs-1806	137	19	iff	iff	VERB
iajs-1806	137	20	v	v	ADP
iajs-1806	137	21	=	=	SYM
iajs-1806	137	22	0	0	NUM
iajs-1806	137	23	.	.	PUNCT
iajs-1806	138	1	hence	hence	ADV
iajs-1806	138	2	,	,	PUNCT
iajs-1806	138	3	ℓ	ℓ	PROPN
iajs-1806	138	4	is	be	AUX
iajs-1806	138	5	a	a	DET
iajs-1806	138	6	pre	pre	ADJ
iajs-1806	138	7	-	-	ADJ
iajs-1806	138	8	hilbert	hilbert	ADJ
iajs-1806	138	9	space	space	NOUN
iajs-1806	138	10	.	.	PUNCT
iajs-1806	139	1	by	by	ADP
iajs-1806	139	2	proposition	proposition	NOUN
iajs-1806	139	3	2.8	2.8	NUM
iajs-1806	139	4	,	,	PUNCT
iajs-1806	139	5	it	it	PRON
iajs-1806	139	6	is	be	AUX
iajs-1806	139	7	a	a	DET
iajs-1806	139	8	quasi	quasi	ADJ
iajs-1806	139	9	-	-	ADJ
iajs-1806	139	10	inner	inner	ADJ
iajs-1806	139	11	product	product	NOUN
iajs-1806	139	12	space	space	NOUN
iajs-1806	139	13	,	,	PUNCT
iajs-1806	139	14	where	where	SCONJ
iajs-1806	140	1	8	8	NUM
iajs-1806	140	2	k	k	PROPN
iajs-1806	141	1	𝜆	𝜆	X
iajs-1806	141	2	2𝑚|𝑣	2𝑚|𝑣	ADJ
iajs-1806	142	1	|	|	NOUN
iajs-1806	142	2	sng	sng	NOUN
iajs-1806	142	3	v	v	NOUN
iajs-1806	142	4	w	w	NOUN
iajs-1806	142	5	+	+	NUM
iajs-1806	142	6	8	8	NUM
iajs-1806	142	7			X
iajs-1806	143	1	k	k	PROPN
iajs-1806	143	2	𝜆	𝜆	PROPN
iajs-1806	143	3	|𝑤	|𝑤	X
iajs-1806	143	4	|	|	ADV
iajs-1806	143	5	𝑠𝑛𝑔	𝑠𝑛𝑔	NOUN
iajs-1806	143	6	𝑤	𝑤	ADP
iajs-1806	143	7	𝑣	𝑣	PROPN
iajs-1806	143	8	is	be	AUX
iajs-1806	143	9	value	value	NOUN
iajs-1806	143	10	to	to	ADP
iajs-1806	143	11	both	both	DET
iajs-1806	143	12	sides	side	NOUN
iajs-1806	143	13	of	of	ADP
iajs-1806	143	14	equation	equation	NOUN
iajs-1806	143	15	(	(	PUNCT
iajs-1806	143	16	3	3	NUM
iajs-1806	143	17	)	)	PUNCT
iajs-1806	143	18	.	.	PUNCT
iajs-1806	144	1	if	if	SCONJ
iajs-1806	144	2	we	we	PRON
iajs-1806	144	3	apply	apply	VERB
iajs-1806	144	4	quasi	quasi	ADJ
iajs-1806	144	5	-	-	ADJ
iajs-1806	144	6	norm	norm	ADJ
iajs-1806	144	7	function	function	NOUN
iajs-1806	144	8	of	of	ADP
iajs-1806	144	9	ℓ	ℓ	PROPN
iajs-1806	144	10	in	in	ADP
iajs-1806	144	11	definition	definition	NOUN
iajs-1806	144	12	2.1	2.1	NUM
iajs-1806	144	13	,	,	PUNCT
iajs-1806	144	14	we	we	PRON
iajs-1806	144	15	obtain	obtain	VERB
iajs-1806	144	16	𝛿	𝛿	DET
iajs-1806	144	17	𝑣	𝑣	NOUN
iajs-1806	144	18	,	,	PUNCT
iajs-1806	144	19	𝑤	𝑤	ADP
iajs-1806	144	20	=	=	SYM
iajs-1806	144	21	𝛿	𝛿	PROPN
iajs-1806	144	22	𝑣	𝑣	NOUN
iajs-1806	144	23	,	,	PUNCT
iajs-1806	144	24	𝑤	𝑤	VERB
iajs-1806	144	25	since	since	SCONJ
iajs-1806	144	26	the	the	DET
iajs-1806	144	27	limit	limit	NOUN
iajs-1806	144	28	in	in	ADP
iajs-1806	144	29	𝛿	𝛿	PRON
iajs-1806	144	30	𝑣	𝑣	NOUN
iajs-1806	144	31	,	,	PUNCT
iajs-1806	144	32	𝑤	𝑤	ADP
iajs-1806	144	33	itself	itself	PRON
iajs-1806	144	34	one	one	NUM
iajs-1806	144	35	𝛿	𝛿	DET
iajs-1806	144	36	𝑣	𝑣	NOUN
iajs-1806	144	37	,	,	PUNCT
iajs-1806	144	38	𝑤	𝑤	PART
iajs-1806	144	39	.	.	PUNCT
iajs-1806	145	1	then	then	ADV
iajs-1806	145	2	ℓ	ℓ	PROPN
iajs-1806	145	3	is	be	AUX
iajs-1806	145	4	smooth	smooth	ADJ
iajs-1806	145	5	.	.	PUNCT
iajs-1806	146	1	now	now	ADV
iajs-1806	146	2	,	,	PUNCT
iajs-1806	146	3	since	since	SCONJ
iajs-1806	146	4	ℓ	ℓ	PROPN
iajs-1806	146	5	is	be	AUX
iajs-1806	146	6	a	a	DET
iajs-1806	146	7	quasi	quasi	ADJ
iajs-1806	146	8	-	-	ADJ
iajs-1806	146	9	banach	banach	ADJ
iajs-1806	146	10	space	space	NOUN
iajs-1806	146	11	for	for	ADP
iajs-1806	146	12	every	every	DET
iajs-1806	146	13	𝑚	𝑚	PROPN
iajs-1806	146	14	∈	∈	PROPN
iajs-1806	146	15	ℝ	ℝ	NOUN
iajs-1806	146	16	by	by	ADP
iajs-1806	146	17	theorem	theorem	NOUN
iajs-1806	146	18	1.6	1.6	NUM
iajs-1806	146	19	,	,	PUNCT
iajs-1806	146	20	then	then	ADV
iajs-1806	146	21	it	it	PRON
iajs-1806	146	22	is	be	AUX
iajs-1806	146	23	complete	complete	ADJ
iajs-1806	146	24	under	under	ADP
iajs-1806	146	25	||||	||||	NOUN
iajs-1806	146	26	vq	vq	NOUN
iajs-1806	147	1	=	=	SYM
iajs-1806	147	2	𝜏	𝜏	X
iajs-1806	147	3	𝑣	𝑣	NOUN
iajs-1806	147	4	,	,	PUNCT
iajs-1806	147	5	𝑣	𝑣	X
iajs-1806	147	6	/	/	SYM
iajs-1806	147	7	,	,	PUNCT
iajs-1806	147	8	i.e.	i.e.	X
iajs-1806	147	9	every	every	DET
iajs-1806	147	10	fundamental	fundamental	ADJ
iajs-1806	147	11	sequence	sequence	NOUN
iajs-1806	147	12	{	{	PUNCT
iajs-1806	147	13	vk	vk	PROPN
iajs-1806	147	14	}	}	PUNCT
iajs-1806	147	15	,	,	PUNCT
iajs-1806	147	16	𝑘	𝑘	DET
iajs-1806	147	17	∈	∈	PROPN
iajs-1806	147	18	ℕ	ℕ	PROPN
iajs-1806	147	19	is	be	AUX
iajs-1806	147	20	convergent	convergent	NOUN
iajs-1806	147	21	in	in	ADP
iajs-1806	147	22	it	it	PRON
iajs-1806	147	23	.	.	PUNCT
iajs-1806	148	1	therefore	therefore	ADV
iajs-1806	148	2	,	,	PUNCT
iajs-1806	148	3	theorem	theorem	VERB
iajs-1806	148	4	is	be	AUX
iajs-1806	148	5	proved	prove	VERB
iajs-1806	148	6	.	.	PUNCT
iajs-1806	149	1	remark	remark	VERB
iajs-1806	149	2	2.12	2.12	NUM
iajs-1806	149	3	.	.	PUNCT
iajs-1806	150	1	since	since	SCONJ
iajs-1806	150	2	a	a	DET
iajs-1806	150	3	space	space	NOUN
iajs-1806	150	4	ℓ	ℓ	NOUN
iajs-1806	150	5	,	,	PUNCT
iajs-1806	150	6	for	for	ADP
iajs-1806	150	7	every	every	DET
iajs-1806	150	8	m	m	NOUN
iajs-1806	150	9	∈	∈	PROPN
iajs-1806	150	10	ℝ	ℝ	PROPN
iajs-1806	150	11	and	and	CCONJ
iajs-1806	150	12	p	p	NOUN
iajs-1806	150	13	∈	∈	NOUN
iajs-1806	150	14	ℝ	ℝ	PROPN
iajs-1806	150	15	is	be	AUX
iajs-1806	150	16	a	a	DET
iajs-1806	150	17	quasi	quasi	ADJ
iajs-1806	150	18	-	-	ADJ
iajs-1806	150	19	banach	banach	ADJ
iajs-1806	150	20	space	space	NOUN
iajs-1806	150	21	,	,	PUNCT
iajs-1806	150	22	then	then	ADV
iajs-1806	150	23	ℓ	ℓ	PROPN
iajs-1806	150	24	is	be	AUX
iajs-1806	150	25	a	a	DET
iajs-1806	150	26	quasi	quasi	ADJ
iajs-1806	150	27	-	-	ADJ
iajs-1806	150	28	hilbert	hilbert	ADJ
iajs-1806	150	29	space	space	NOUN
iajs-1806	150	30	if	if	SCONJ
iajs-1806	150	31	it	it	PRON
iajs-1806	150	32	is	be	AUX
iajs-1806	150	33	a	a	DET
iajs-1806	150	34	quasi	quasi	ADJ
iajs-1806	150	35	-	-	ADJ
iajs-1806	150	36	inner	inner	ADJ
iajs-1806	150	37	product	product	NOUN
iajs-1806	150	38	space	space	NOUN
iajs-1806	150	39	.	.	PUNCT
iajs-1806	151	1	references	reference	NOUN
iajs-1806	151	2	[	[	X
iajs-1806	151	3	1	1	X
iajs-1806	151	4	]	]	X
iajs-1806	151	5	j.k	j.k	PROPN
iajs-1806	151	6	.	.	PUNCT
iajs-1806	151	7	al	al	PROPN
iajs-1806	151	8	-	-	PUNCT
iajs-1806	151	9	delfi	delfi	PROPN
iajs-1806	151	10	.	.	PUNCT
iajs-1806	152	1	,	,	PUNCT
iajs-1806	152	2	quasi	quasi	ADJ
iajs-1806	152	3	-	-	ADJ
iajs-1806	152	4	sobolev	sobolev	ADJ
iajs-1806	152	5	spaces	space	NOUN
iajs-1806	152	6	ℓ	ℓ	INTJ
iajs-1806	152	7	.	.	PUNCT
iajs-1806	152	8	,	,	PUNCT
iajs-1806	152	9	bulletin	bulletin	NOUN
iajs-1806	152	10	of	of	ADP
iajs-1806	152	11	south	south	ADJ
iajs-1806	152	12	ural	ural	PROPN
iajs-1806	152	13	state	state	PROPN
iajs-1806	152	14	university	university	PROPN
iajs-1806	152	15	,	,	PUNCT
iajs-1806	152	16	series	series	NOUN
iajs-1806	152	17	of	of	ADP
iajs-1806	152	18	“	"	PUNCT
iajs-1806	152	19	mathematics.mechanics	mathematics.mechanic	NOUN
iajs-1806	152	20	.	.	PUNCT
iajs-1806	153	1	physics	physics	PROPN
iajs-1806	153	2	”	"	PUNCT
iajs-1806	153	3	,	,	PUNCT
iajs-1806	153	4	5	5	NUM
iajs-1806	153	5	,	,	PUNCT
iajs-1806	153	6	1	1	NUM
iajs-1806	153	7	.	.	NUM
iajs-1806	153	8	,	,	PUNCT
iajs-1806	153	9	107–109	107–109	NUM
iajs-1806	153	10	.	.	PUNCT
iajs-1806	154	1	(	(	PUNCT
iajs-1806	154	2	in	in	ADP
iajs-1806	154	3	russian	russian	NOUN
iajs-1806	154	4	)	)	PUNCT
iajs-1806	154	5	.	.	PUNCT
iajs-1806	155	1	2013	2013	NUM
iajs-1806	155	2	.	.	PUNCT
iajs-1806	156	1	[	[	X
iajs-1806	156	2	2	2	X
iajs-1806	156	3	]	]	PUNCT
iajs-1806	156	4	w.	w.	PROPN
iajs-1806	156	5	rudin	rudin	PROPN
iajs-1806	156	6	,	,	PUNCT
iajs-1806	156	7	functional	functional	ADJ
iajs-1806	156	8	analysis	analysis	NOUN
iajs-1806	156	9	.	.	PUNCT
iajs-1806	156	10	,	,	PUNCT
iajs-1806	156	11	mcgraw	mcgraw	PROPN
iajs-1806	156	12	-	-	PUNCT
iajs-1806	156	13	hill	hill	PROPN
iajs-1806	156	14	,	,	PUNCT
iajs-1806	156	15	inc	inc	PROPN
iajs-1806	156	16	.	.	PROPN
iajs-1806	156	17	,	,	PUNCT
iajs-1806	156	18	new	new	PROPN
iajs-1806	156	19	york	york	PROPN
iajs-1806	156	20	,	,	PUNCT
iajs-1806	156	21	1991	1991	NUM
iajs-1806	156	22	.	.	PUNCT
iajs-1806	157	1	[	[	X
iajs-1806	157	2	3	3	NUM
iajs-1806	157	3	]	]	PUNCT
iajs-1806	157	4	a.	a.	NOUN
iajs-1806	157	5	h.	h.	PROPN
iajs-1806	157	6	siddiqi	siddiqi	PROPN
iajs-1806	157	7	,	,	PUNCT
iajs-1806	157	8	functional	functional	ADJ
iajs-1806	157	9	analysis	analysis	NOUN
iajs-1806	157	10	with	with	ADP
iajs-1806	157	11	applications	application	NOUN
iajs-1806	157	12	.	.	PUNCT
iajs-1806	157	13	,	,	PUNCT
iajs-1806	157	14	tata	tata	PROPN
iajs-1806	157	15	mcgraw	mcgraw	PROPN
iajs-1806	157	16	-	-	PUNCT
iajs-1806	157	17	hill	hill	NOUN
iajs-1806	157	18	publishing	publishing	NOUN
iajs-1806	157	19	company	company	NOUN
iajs-1806	157	20	,	,	PUNCT
iajs-1806	157	21	ltd	ltd	PROPN
iajs-1806	157	22	,	,	PUNCT
iajs-1806	157	23	new	new	ADJ
iajs-1806	157	24	delhi	delhi	PROPN
iajs-1806	157	25	,	,	PUNCT
iajs-1806	157	26	india	india	PROPN
iajs-1806	157	27	,	,	PUNCT
iajs-1806	157	28	1986	1986	NUM
iajs-1806	157	29	.	.	PUNCT
iajs-1806	158	1	[	[	X
iajs-1806	158	2	4	4	NUM
iajs-1806	158	3	]	]	X
iajs-1806	158	4	n.	n.	PROPN
iajs-1806	158	5	kalton	kalton	PROPN
iajs-1806	158	6	,	,	PUNCT
iajs-1806	158	7	quasi	quasi	ADJ
iajs-1806	158	8	-	-	NOUN
iajs-1806	158	9	banach	banach	NOUN
iajs-1806	158	10	spaces	space	NOUN
iajs-1806	158	11	.	.	PUNCT
iajs-1806	158	12	,	,	PUNCT
iajs-1806	158	13	handbook	handbook	NOUN
iajs-1806	158	14	of	of	ADP
iajs-1806	158	15	the	the	DET
iajs-1806	158	16	geometry	geometry	NOUN
iajs-1806	158	17	of	of	ADP
iajs-1806	158	18	banach	banach	NOUN
iajs-1806	158	19	spaces	space	NOUN
iajs-1806	158	20	,	,	PUNCT
iajs-1806	158	21	vol	vol	NOUN
iajs-1806	158	22	.	.	PUNCT
iajs-1806	158	23	edit	edit	PROPN
iajs-1806	158	24	.	.	PUNCT
iajs-1806	159	1	by	by	ADP
iajs-1806	159	2	.	.	PUNCT
iajs-1806	160	1	johnson	johnson	PROPN
iajs-1806	160	2	w.b	w.b	PROPN
iajs-1806	160	3	and	and	CCONJ
iajs-1806	160	4	.	.	PUNCT
iajs-1806	161	1	lindenstrauss	lindenstrauss	PROPN
iajs-1806	161	2	.	.	PUNCT
iajs-1806	162	1	j	j	PROPN
iajs-1806	162	2	–	–	PUNCT
iajs-1806	162	3	amsterdam	amsterdam	PROPN
iajs-1806	162	4	etc	etc	X
iajs-1806	162	5	.	.	PUNCT
iajs-1806	162	6	:	:	PUNCT
iajs-1806	163	1	elsevier	elsevier	NOUN
iajs-1806	163	2	,	,	PUNCT
iajs-1806	163	3	1099–1130	1099–1130	NUM
iajs-1806	163	4	.	.	PUNCT
iajs-1806	163	5	2003	2003	NUM
iajs-1806	164	1	[	[	X
iajs-1806	164	2	5	5	X
iajs-1806	164	3	]	]	PUNCT
iajs-1806	164	4	j.	j.	PROPN
iajs-1806	164	5	bergh	bergh	PROPN
iajs-1806	164	6	;	;	PUNCT
iajs-1806	164	7	j.	j.	PROPN
iajs-1806	164	8	löfström	löfström	PROPN
iajs-1806	164	9	,	,	PUNCT
iajs-1806	164	10	interpolation	interpolation	NOUN
iajs-1806	164	11	spaces	space	NOUN
iajs-1806	164	12	.	.	PUNCT
iajs-1806	165	1	an	an	DET
iajs-1806	165	2	introduction	introduction	NOUN
iajs-1806	165	3	.	.	PUNCT
iajs-1806	166	1	,	,	PUNCT
iajs-1806	166	2	berlin	berlin	PROPN
iajs-1806	166	3	–	–	PUNCT
iajs-1806	166	4	heidelberg	heidelberg	PROPN
iajs-1806	166	5	–	–	PUNCT
iajs-1806	166	6	new	new	PROPN
iajs-1806	166	7	york	york	PROPN
iajs-1806	166	8	,	,	PUNCT
iajs-1806	166	9	springer	springer	NOUN
iajs-1806	166	10	-	-	PUNCT
iajs-1806	166	11	verlag	verlag	PROPN
iajs-1806	166	12	,	,	PUNCT
iajs-1806	166	13	1976	1976	NUM
iajs-1806	166	14	.	.	PUNCT
iajs-1806	167	1	[	[	X
iajs-1806	167	2	6	6	NUM
iajs-1806	167	3	]	]	SYM
iajs-1806	167	4	p.m.	p.m.	NOUN
iajs-1806	167	5	milicic	milicic	PROPN
iajs-1806	167	6	,	,	PUNCT
iajs-1806	167	7	on	on	ADP
iajs-1806	167	8	the	the	DET
iajs-1806	167	9	g	g	NOUN
iajs-1806	167	10	-	-	PUNCT
iajs-1806	167	11	orthogonal	orthogonal	ADJ
iajs-1806	167	12	projection	projection	NOUN
iajs-1806	167	13	and	and	CCONJ
iajs-1806	167	14	the	the	DET
iajs-1806	167	15	best	good	ADJ
iajs-1806	167	16	approximation	approximation	NOUN
iajs-1806	167	17	of	of	ADP
iajs-1806	167	18	vector	vector	NOUN
iajs-1806	167	19	in	in	ADP
iajs-1806	167	20	a	a	DET
iajs-1806	167	21	quasiinner	quasiinner	NOUN
iajs-1806	167	22	product	product	NOUN
iajs-1806	167	23	spaces	space	VERB
iajs-1806	167	24	.	.	PUNCT
iajs-1806	167	25	,	,	PUNCT
iajs-1806	167	26	scientiae	scientiae	PROPN
iajs-1806	167	27	mathematicae	mathematicae	PROPN
iajs-1806	167	28	japonicae	japonicae	PROPN
iajs-1806	167	29	,	,	PUNCT
iajs-1806	167	30	4	4	NUM
iajs-1806	167	31	,	,	PUNCT
iajs-1806	167	32	3	3	NUM
iajs-1806	167	33	,	,	PUNCT
iajs-1806	167	34	941	941	NUM
iajs-1806	167	35	-	-	SYM
iajs-1806	167	36	944	944	NUM
iajs-1806	167	37	.	.	NUM
iajs-1806	167	38	2001	2001	NUM
iajs-1806	167	39	.	.	PUNCT
iajs-1806	168	1	[	[	X
iajs-1806	168	2	7	7	X
iajs-1806	168	3	]	]	X
iajs-1806	168	4	r	r	NOUN
iajs-1806	168	5	.a	.a	NOUN
iajs-1806	168	6	.	.	PUNCT
iajs-1806	169	1	tapia	tapia	PROPN
iajs-1806	169	2	.	.	PROPN
iajs-1806	169	3	,	,	PUNCT
iajs-1806	169	4	a	a	DET
iajs-1806	169	5	characterization	characterization	NOUN
iajs-1806	169	6	of	of	ADP
iajs-1806	169	7	inner	inner	ADJ
iajs-1806	169	8	product	product	NOUN
iajs-1806	169	9	spaces	space	VERB
iajs-1806	169	10	.	.	PUNCT
iajs-1806	169	11	,	,	PUNCT
iajs-1806	169	12	proc	proc	PROPN
iajs-1806	169	13	.	.	PUNCT
iajs-1806	170	1	amer	amer	PROPN
iajs-1806	170	2	.	.	PUNCT
iajs-1806	170	3	math	math	PROPN
iajs-1806	170	4	.	.	PUNCT
iajs-1806	171	1	soc	soc	PROPN
iajs-1806	171	2	.	.	PROPN
iajs-1806	171	3	,	,	PUNCT
iajs-1806	171	4	41	41	NUM
iajs-1806	171	5	,	,	PUNCT
iajs-1806	171	6	569	569	NUM
iajs-1806	171	7	-	-	SYM
iajs-1806	171	8	574	574	NUM
iajs-1806	171	9	.	.	PUNCT
iajs-1806	172	1	1973	1973	NUM
iajs-1806	172	2	[	[	X
iajs-1806	172	3	8	8	NUM
iajs-1806	172	4	]	]	PUNCT
iajs-1806	172	5	a.	a.	NOUN
iajs-1806	172	6	sahovi	sahovi	NOUN
iajs-1806	172	7	;	;	PUNCT
iajs-1806	172	8	f.vajzovi	f.vajzovi	VERB
iajs-1806	172	9	and	and	CCONJ
iajs-1806	172	10	peco	peco	PROPN
iajs-1806	172	11	.	.	PUNCT
iajs-1806	173	1	s.	s.	PROPN
iajs-1806	173	2	,	,	PUNCT
iajs-1806	173	3	continuity	continuity	NOUN
iajs-1806	173	4	conditions	condition	NOUN
iajs-1806	173	5	for	for	ADP
iajs-1806	173	6	the	the	DET
iajs-1806	173	7	hilbert	hilbert	PROPN
iajs-1806	173	8	transform	transform	NOUN
iajs-1806	173	9	on	on	ADP
iajs-1806	173	10	quasi	quasi	ADJ
iajs-1806	173	11	-	-	ADJ
iajs-1806	173	12	hilbert	hilbert	ADJ
iajs-1806	173	13	spaces	space	NOUN
iajs-1806	173	14	.	.	PUNCT
iajs-1806	173	15	,	,	PUNCT
iajs-1806	173	16	sarajevo	sarajevo	PROPN
iajs-1806	173	17	journal	journal	PROPN
iajs-1806	173	18	of	of	ADP
iajs-1806	173	19	mathematics	mathematic	NOUN
iajs-1806	173	20	,	,	PUNCT
iajs-1806	173	21	(	(	PUNCT
iajs-1806	173	22	2014	2014	NUM
iajs-1806	173	23	)	)	PUNCT
iajs-1806	173	24	,	,	PUNCT
iajs-1806	173	25	vol.10	vol.10	NOUN
iajs-1806	173	26	,	,	PUNCT
iajs-1806	173	27	no	no	INTJ
iajs-1806	173	28	.	.	NOUN
iajs-1806	173	29	22	22	NUM
iajs-1806	173	30	,	,	PUNCT
iajs-1806	173	31	pp	pp	ADP
iajs-1806	173	32	111–120	111–120	NUM
iajs-1806	173	33	.	.	PUNCT
iajs-1806	173	34	  	  	SPACE