id	sid	tid	token	lemma	pos
ma-222	1	1	2024	2024	NUM
ma-222	1	2	ada	ada	PROPN
ma-222	1	3	academica	academica	PROPN
ma-222	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-222	1	5	.	.	PUNCT
ma-222	2	1	j.	j.	PROPN
ma-222	2	2	math	math	PROPN
ma-222	2	3	.	.	PUNCT
ma-222	3	1	anal	anal	ADJ
ma-222	3	2	.	.	PUNCT
ma-222	4	1	4	4	NUM
ma-222	4	2	(	(	PUNCT
ma-222	4	3	2024	2024	NUM
ma-222	4	4	)	)	PUNCT
ma-222	4	5	6doi	6doi	NOUN
ma-222	4	6	:	:	PUNCT
ma-222	4	7	10.28924	10.28924	NUM
ma-222	4	8	/	/	SYM
ma-222	4	9	ada	ada	PROPN
ma-222	4	10	/	/	SYM
ma-222	4	11	ma.4.6	ma.4.6	VERB
ma-222	4	12	the	the	DET
ma-222	4	13	constants	constant	NOUN
ma-222	4	14	to	to	PART
ma-222	4	15	measure	measure	VERB
ma-222	4	16	the	the	DET
ma-222	4	17	differences	difference	NOUN
ma-222	4	18	between	between	ADP
ma-222	4	19	isosceles	isoscele	NOUN
ma-222	4	20	and	and	CCONJ
ma-222	4	21	α−	α−	ADP
ma-222	4	22	β	β	X
ma-222	4	23	orthogonalities	orthogonalities	PROPN
ma-222	4	24	qichuan	qichuan	PROPN
ma-222	4	25	ni	ni	PROPN
ma-222	4	26	,	,	PUNCT
ma-222	4	27	qi	qi	PROPN
ma-222	4	28	liu∗	liu∗	PROPN
ma-222	4	29	,	,	PUNCT
ma-222	4	30	yin	yin	PROPN
ma-222	4	31	zhou	zhou	PROPN
ma-222	4	32	,	,	PUNCT
ma-222	4	33	qin	qin	PROPN
ma-222	4	34	qian	qian	PROPN
ma-222	4	35	school	school	PROPN
ma-222	4	36	of	of	ADP
ma-222	4	37	mathematics	mathematic	NOUN
ma-222	4	38	and	and	CCONJ
ma-222	4	39	physics	physics	NOUN
ma-222	4	40	,	,	PUNCT
ma-222	4	41	anqing	anqe	VERB
ma-222	4	42	normal	normal	ADJ
ma-222	4	43	university	university	NOUN
ma-222	4	44	,	,	PUNCT
ma-222	4	45	anqing	anqe	VERB
ma-222	4	46	246133	246133	NUM
ma-222	4	47	,	,	PUNCT
ma-222	4	48	p.	p.	PROPN
ma-222	4	49	r.	r.	PROPN
ma-222	4	50	china	china	PROPN
ma-222	4	51	niqichuan111@163.com	niqichuan111@163.com	PROPN
ma-222	4	52	,	,	PUNCT
ma-222	4	53	liuq67@aqnu.edu.cn	liuq67@aqnu.edu.cn	PROPN
ma-222	4	54	,	,	PUNCT
ma-222	4	55	zhouyin0330@163.com	zhouyin0330@163.com	NUM
ma-222	4	56	,	,	PUNCT
ma-222	4	57	15212956918@163.com	15212956918@163.com	NUM
ma-222	4	58	∗correspondence	∗correspondence	NOUN
ma-222	4	59	:	:	PUNCT
ma-222	4	60	liuq67@aqnu.edu.cn	liuq67@aqnu.edu.cn	PROPN
ma-222	4	61	abstract	abstract	NOUN
ma-222	4	62	.	.	PUNCT
ma-222	5	1	in	in	ADP
ma-222	5	2	this	this	DET
ma-222	5	3	paper	paper	NOUN
ma-222	5	4	,	,	PUNCT
ma-222	5	5	by	by	ADP
ma-222	5	6	combining	combine	VERB
ma-222	5	7	the	the	DET
ma-222	5	8	isosceles	isoscele	NOUN
ma-222	5	9	orthogonality	orthogonality	NOUN
ma-222	5	10	and	and	CCONJ
ma-222	5	11	α−β	α−β	PROPN
ma-222	5	12	orthogonality	orthogonality	NOUN
ma-222	5	13	of	of	ADP
ma-222	5	14	banachspaces	banachspace	NOUN
ma-222	5	15	,	,	PUNCT
ma-222	5	16	we	we	PRON
ma-222	5	17	first	first	ADV
ma-222	5	18	introduce	introduce	VERB
ma-222	5	19	a	a	DET
ma-222	5	20	new	new	ADJ
ma-222	5	21	geometric	geometric	ADJ
ma-222	5	22	constant	constant	NOUN
ma-222	5	23	.	.	PUNCT
ma-222	6	1	we	we	PRON
ma-222	6	2	demonstrate	demonstrate	VERB
ma-222	6	3	some	some	DET
ma-222	6	4	basic	basic	ADJ
ma-222	6	5	properties	property	NOUN
ma-222	6	6	aboutit	aboutit	ADJ
ma-222	6	7	,	,	PUNCT
ma-222	6	8	such	such	ADJ
ma-222	6	9	as	as	ADP
ma-222	6	10	calculating	calculate	VERB
ma-222	6	11	its	its	PRON
ma-222	6	12	value	value	NOUN
ma-222	6	13	in	in	ADP
ma-222	6	14	the	the	DET
ma-222	6	15	common	common	ADJ
ma-222	6	16	norm	norm	NOUN
ma-222	6	17	spaces	space	NOUN
ma-222	6	18	.	.	PUNCT
ma-222	7	1	moreover	moreover	ADV
ma-222	7	2	,	,	PUNCT
ma-222	7	3	the	the	DET
ma-222	7	4	necessary	necessary	ADJ
ma-222	7	5	and	and	CCONJ
ma-222	7	6	sufficientconditions	sufficientcondition	NOUN
ma-222	7	7	for	for	ADP
ma-222	7	8	the	the	DET
ma-222	7	9	new	new	ADJ
ma-222	7	10	constant	constant	NOUN
ma-222	7	11	to	to	PART
ma-222	7	12	characterize	characterize	VERB
ma-222	7	13	hilbert	hilbert	NOUN
ma-222	7	14	spaces	space	NOUN
ma-222	7	15	are	be	AUX
ma-222	7	16	given	give	VERB
ma-222	7	17	.	.	PUNCT
ma-222	8	1	finally	finally	ADV
ma-222	8	2	,	,	PUNCT
ma-222	8	3	only	only	ADV
ma-222	8	4	consider	consider	VERB
ma-222	8	5	thepoints	thepoint	NOUN
ma-222	8	6	on	on	ADP
ma-222	8	7	the	the	DET
ma-222	8	8	unit	unit	NOUN
ma-222	8	9	sphere	sphere	ADV
ma-222	8	10	,	,	PUNCT
ma-222	8	11	we	we	PRON
ma-222	8	12	introduce	introduce	VERB
ma-222	8	13	another	another	DET
ma-222	8	14	new	new	ADJ
ma-222	8	15	geometric	geometric	ADJ
ma-222	8	16	constant	constant	ADJ
ma-222	8	17	and	and	CCONJ
ma-222	8	18	some	some	DET
ma-222	8	19	basic	basic	ADJ
ma-222	8	20	propertiesare	propertiesare	NOUN
ma-222	8	21	also	also	ADV
ma-222	8	22	obtained	obtain	VERB
ma-222	8	23	.	.	PUNCT
ma-222	9	1	1	1	X
ma-222	9	2	.	.	X
ma-222	9	3	introduction	introduction	NOUN
ma-222	9	4	traditional	traditional	ADJ
ma-222	9	5	orthogonality	orthogonality	NOUN
ma-222	9	6	plays	play	VERB
ma-222	9	7	a	a	DET
ma-222	9	8	key	key	ADJ
ma-222	9	9	role	role	NOUN
ma-222	9	10	in	in	ADP
ma-222	9	11	the	the	DET
ma-222	9	12	geometry	geometry	NOUN
ma-222	9	13	of	of	ADP
ma-222	9	14	banach	banach	NOUN
ma-222	9	15	spaces	space	NOUN
ma-222	9	16	and	and	CCONJ
ma-222	9	17	is	be	AUX
ma-222	9	18	a	a	DET
ma-222	9	19	geometricfeature	geometricfeature	NOUN
ma-222	9	20	of	of	ADP
ma-222	9	21	hilbert	hilbert	PROPN
ma-222	9	22	spaces	space	NOUN
ma-222	9	23	.	.	PUNCT
ma-222	10	1	we	we	PRON
ma-222	10	2	repeat	repeat	VERB
ma-222	10	3	the	the	DET
ma-222	10	4	definitions	definition	NOUN
ma-222	10	5	of	of	ADP
ma-222	10	6	the	the	DET
ma-222	10	7	next	next	ADJ
ma-222	10	8	three	three	NUM
ma-222	10	9	orthogonality	orthogonality	NOUN
ma-222	10	10	types	type	NOUN
ma-222	10	11	.	.	PUNCT
ma-222	11	1	in	in	ADP
ma-222	11	2	1945,james	1945,james	NUM
ma-222	11	3	[	[	SYM
ma-222	11	4	8	8	NUM
ma-222	11	5	]	]	PUNCT
ma-222	11	6	introduced	introduce	VERB
ma-222	11	7	isosceles	isoscele	NOUN
ma-222	11	8	orthogonality	orthogonality	NOUN
ma-222	11	9	as	as	SCONJ
ma-222	11	10	follows	follow	VERB
ma-222	11	11	:	:	PUNCT
ma-222	11	12	x	x	PROPN
ma-222	11	13	⊥i	⊥i	PROPN
ma-222	11	14	y	y	PROPN
ma-222	11	15	if	if	SCONJ
ma-222	11	16	and	and	CCONJ
ma-222	11	17	only	only	ADV
ma-222	11	18	if	if	SCONJ
ma-222	11	19	‖x	‖x	PROPN
ma-222	11	20	+	+	NUM
ma-222	11	21	y‖	y‖	X
ma-222	11	22	=	=	PUNCT
ma-222	11	23	‖x	‖x	PRON
ma-222	11	24	−	−	PROPN
ma-222	11	25	y‖.	y‖.	PROPN
ma-222	11	26	balestro	balestro	VERB
ma-222	11	27	[	[	X
ma-222	11	28	4	4	NUM
ma-222	11	29	]	]	PUNCT
ma-222	11	30	introduced	introduce	VERB
ma-222	11	31	the	the	DET
ma-222	11	32	orthogonality	orthogonality	NOUN
ma-222	11	33	of	of	ADP
ma-222	11	34	pythagoras	pythagoras	PROPN
ma-222	11	35	as	as	SCONJ
ma-222	11	36	follows	follow	VERB
ma-222	11	37	:	:	PUNCT
ma-222	11	38	x	x	X
ma-222	11	39	⊥p	⊥p	ADP
ma-222	11	40	y	y	PROPN
ma-222	11	41	if	if	SCONJ
ma-222	11	42	and	and	CCONJ
ma-222	11	43	only	only	ADV
ma-222	11	44	if	if	SCONJ
ma-222	11	45	‖x	‖x	PRON
ma-222	11	46	−	−	PROPN
ma-222	11	47	y‖2	y‖2	X
ma-222	11	48	=	=	SYM
ma-222	11	49	‖x‖2	‖x‖2	VERB
ma-222	12	1	+	+	CCONJ
ma-222	12	2	‖y‖2	‖y‖2	PROPN
ma-222	12	3	.	.	PUNCT
ma-222	12	4	birkhoff	birkhoff	PROPN
ma-222	12	5	defined	define	VERB
ma-222	12	6	the	the	DET
ma-222	12	7	following	follow	VERB
ma-222	12	8	birkhoff	birkhoff	NOUN
ma-222	12	9	orthogonality	orthogonality	NOUN
ma-222	12	10	[	[	X
ma-222	12	11	5	5	NUM
ma-222	12	12	]	]	PUNCT
ma-222	12	13	in	in	ADP
ma-222	12	14	linear	linear	PROPN
ma-222	12	15	metric	metric	ADJ
ma-222	12	16	spaces	space	NOUN
ma-222	12	17	:	:	PUNCT
ma-222	12	18	x	x	X
ma-222	12	19	⊥b	⊥b	PRON
ma-222	12	20	y	y	NOUN
ma-222	12	21	if	if	SCONJ
ma-222	12	22	and	and	CCONJ
ma-222	12	23	only	only	ADV
ma-222	12	24	if	if	SCONJ
ma-222	12	25	‖x	‖x	PROPN
ma-222	12	26	+	+	CCONJ
ma-222	12	27	αy‖	αy‖	X
ma-222	12	28	≥	≥	NOUN
ma-222	12	29	‖x‖	‖x‖	PROPN
ma-222	12	30	for	for	ADP
ma-222	12	31	all	all	DET
ma-222	12	32	α	α	PROPN
ma-222	12	33	∈	∈	PROPN
ma-222	12	34	r.	r.	NOUN
ma-222	12	35	these	these	DET
ma-222	12	36	three	three	NUM
ma-222	12	37	orthogonalities	orthogonality	NOUN
ma-222	12	38	have	have	AUX
ma-222	12	39	been	be	AUX
ma-222	12	40	investigated	investigate	VERB
ma-222	12	41	in	in	ADP
ma-222	12	42	several	several	ADJ
ma-222	12	43	papers	paper	NOUN
ma-222	12	44	(	(	PUNCT
ma-222	12	45	see	see	VERB
ma-222	12	46	[	[	X
ma-222	12	47	2	2	NUM
ma-222	12	48	]	]	PUNCT
ma-222	12	49	,	,	PUNCT
ma-222	13	1	[	[	X
ma-222	13	2	9	9	NUM
ma-222	13	3	]	]	PUNCT
ma-222	13	4	and	and	CCONJ
ma-222	13	5	so	so	ADV
ma-222	13	6	on).over	on).over	ADV
ma-222	13	7	the	the	DET
ma-222	13	8	years	year	NOUN
ma-222	13	9	,	,	PUNCT
ma-222	13	10	many	many	ADJ
ma-222	13	11	scholars	scholar	NOUN
ma-222	13	12	have	have	AUX
ma-222	13	13	introduced	introduce	VERB
ma-222	13	14	the	the	DET
ma-222	13	15	concept	concept	NOUN
ma-222	13	16	of	of	ADP
ma-222	13	17	extended	extended	ADJ
ma-222	13	18	orthogonality	orthogonality	NOUN
ma-222	13	19	.	.	PUNCT
ma-222	14	1	the	the	DET
ma-222	14	2	familyof	familyof	ADJ
ma-222	14	3	orthogonalities	orthogonality	NOUN
ma-222	14	4	introduced	introduce	VERB
ma-222	14	5	by	by	ADP
ma-222	14	6	carlson	carlson	PROPN
ma-222	15	1	[	[	X
ma-222	15	2	6	6	NUM
ma-222	15	3	]	]	PUNCT
ma-222	15	4	in	in	ADP
ma-222	15	5	1961	1961	NUM
ma-222	15	6	,	,	PUNCT
ma-222	15	7	covering	cover	VERB
ma-222	15	8	isosceles	isoscele	NOUN
ma-222	15	9	and	and	CCONJ
ma-222	15	10	pythagorean	pythagorean	PROPN
ma-222	15	11	orthogo	orthogo	PROPN
ma-222	15	12	-	-	PUNCT
ma-222	15	13	nalities	nalitie	NOUN
ma-222	15	14	,	,	PUNCT
ma-222	15	15	is	be	AUX
ma-222	15	16	known	know	VERB
ma-222	15	17	as	as	ADP
ma-222	15	18	carlson	carlson	PROPN
ma-222	15	19	orthogonality	orthogonality	PROPN
ma-222	15	20	:	:	PUNCT
ma-222	15	21	x	x	X
ma-222	15	22	⊥c	⊥c	VERB
ma-222	15	23	y	y	NOUN
ma-222	15	24	if	if	SCONJ
ma-222	15	25	and	and	CCONJ
ma-222	16	1	only	only	ADV
ma-222	16	2	if	if	SCONJ
ma-222	16	3	n∑	n∑	PROPN
ma-222	16	4	i=1	i=1	PROPN
ma-222	16	5	ai‖bix	ai‖bix	X
ma-222	16	6	+	+	CCONJ
ma-222	16	7	ciy‖2	ciy‖2	NOUN
ma-222	16	8	=	=	SYM
ma-222	16	9	0	0	X
ma-222	16	10	.	.	PUNCT
ma-222	16	11	received	receive	VERB
ma-222	16	12	:	:	PUNCT
ma-222	16	13	22	22	NUM
ma-222	16	14	jan	jan	PROPN
ma-222	16	15	2024	2024	NUM
ma-222	16	16	.	.	PUNCT
ma-222	17	1	key	key	ADJ
ma-222	17	2	words	word	NOUN
ma-222	17	3	and	and	CCONJ
ma-222	17	4	phrases	phrase	NOUN
ma-222	17	5	.	.	PUNCT
ma-222	18	1	isosceles	isoscele	NOUN
ma-222	18	2	orthogonality	orthogonality	NOUN
ma-222	18	3	;	;	PUNCT
ma-222	18	4	α−	α−	ADP
ma-222	18	5	β	β	X
ma-222	18	6	orthogonality	orthogonality	NOUN
ma-222	18	7	;	;	PUNCT
ma-222	18	8	geometric	geometric	ADJ
ma-222	18	9	constant	constant	ADJ
ma-222	18	10	;	;	PUNCT
ma-222	18	11	hilbert	hilbert	PROPN
ma-222	18	12	spaces.1	spaces.1	PROPN
ma-222	18	13	https://adac.ee	https://adac.ee	PROPN
ma-222	18	14	https://doi.org/10.28924/ada/ma.4.6	https://doi.org/10.28924/ada/ma.4.6	PROPN
ma-222	18	15	eur	eur	PROPN
ma-222	18	16	.	.	PUNCT
ma-222	19	1	j.	j.	PROPN
ma-222	19	2	math	math	PROPN
ma-222	19	3	.	.	PUNCT
ma-222	20	1	anal	anal	PROPN
ma-222	20	2	.	.	PUNCT
ma-222	21	1	10.28924	10.28924	NUM
ma-222	21	2	/	/	SYM
ma-222	21	3	ada	ada	PROPN
ma-222	21	4	/	/	SYM
ma-222	21	5	ma.4.6	ma.4.6	NOUN
ma-222	21	6	2a	2a	NUM
ma-222	21	7	further	further	ADJ
ma-222	21	8	special	special	ADJ
ma-222	21	9	case	case	NOUN
ma-222	21	10	of	of	ADP
ma-222	21	11	carlson	carlson	PROPN
ma-222	21	12	orthogonality	orthogonality	NOUN
ma-222	21	13	was	be	AUX
ma-222	21	14	introduced	introduce	VERB
ma-222	21	15	by	by	ADP
ma-222	21	16	dimitini	dimitini	PROPN
ma-222	21	17	et	et	PROPN
ma-222	21	18	al	al	PROPN
ma-222	21	19	.	.	PUNCT
ma-222	22	1	[	[	X
ma-222	22	2	7	7	X
ma-222	22	3	]	]	PUNCT
ma-222	22	4	in	in	ADP
ma-222	22	5	1983	1983	NUM
ma-222	22	6	asfollows	asfollow	VERB
ma-222	22	7	:	:	PUNCT
ma-222	22	8	x	x	PROPN
ma-222	22	9	⊥α	⊥α	PROPN
ma-222	22	10	y	y	PROPN
ma-222	22	11	if	if	SCONJ
ma-222	22	12	and	and	CCONJ
ma-222	22	13	only	only	ADV
ma-222	22	14	if	if	SCONJ
ma-222	22	15	(	(	PUNCT
ma-222	22	16	1	1	NUM
ma-222	22	17	+	+	CCONJ
ma-222	22	18	α2)‖x	α2)‖x	ADJ
ma-222	22	19	−	−	NUM
ma-222	22	20	y‖2	y‖2	X
ma-222	22	21	=	=	SYM
ma-222	22	22	‖x	‖x	PROPN
ma-222	22	23	−	−	PROPN
ma-222	22	24	αy‖2	αy‖2	PROPN
ma-222	22	25	+	+	CCONJ
ma-222	22	26	‖y	‖y	SYM
ma-222	22	27	−	−	PROPN
ma-222	23	1	αx‖2,where	αx‖2,where	PROPN
ma-222	23	2	fixed	fix	VERB
ma-222	23	3	α	α	PROPN
ma-222	23	4	6=	6=	PROPN
ma-222	23	5	1	1	NUM
ma-222	23	6	.	.	PUNCT
ma-222	23	7	two	two	NUM
ma-222	23	8	years	year	NOUN
ma-222	23	9	later	later	ADV
ma-222	23	10	,	,	PUNCT
ma-222	23	11	this	this	DET
ma-222	23	12	orthogonality	orthogonality	NOUN
ma-222	23	13	was	be	AUX
ma-222	23	14	generalized	generalize	VERB
ma-222	23	15	by	by	ADP
ma-222	23	16	the	the	DET
ma-222	23	17	same	same	ADJ
ma-222	23	18	author	author	NOUN
ma-222	23	19	[	[	X
ma-222	23	20	3	3	NUM
ma-222	23	21	]	]	PUNCT
ma-222	23	22	as	as	ADP
ma-222	23	23	:	:	PUNCT
ma-222	23	24	x	x	X
ma-222	23	25	⊥αβ	⊥αβ	VERB
ma-222	23	26	y	y	NOUN
ma-222	23	27	if	if	SCONJ
ma-222	24	1	and	and	CCONJ
ma-222	24	2	only	only	ADV
ma-222	24	3	if	if	SCONJ
ma-222	24	4	‖x	‖x	PRON
ma-222	24	5	−	−	PROPN
ma-222	24	6	y‖2	y‖2	X
ma-222	24	7	+	+	CCONJ
ma-222	25	1	‖αx	‖αx	PROPN
ma-222	25	2	−	−	NOUN
ma-222	26	1	βy‖2	βy‖2	NOUN
ma-222	26	2	=	=	SYM
ma-222	26	3	‖x	‖x	NOUN
ma-222	26	4	−	−	PROPN
ma-222	27	1	βy‖2	βy‖2	PROPN
ma-222	27	2	+	+	CCONJ
ma-222	27	3	‖y	‖y	NUM
ma-222	28	1	−	−	PROPN
ma-222	28	2	αx‖2	αx‖2	ADJ
ma-222	28	3	.	.	PUNCT
ma-222	29	1	it	it	PRON
ma-222	29	2	is	be	AUX
ma-222	29	3	well	well	ADV
ma-222	29	4	known	know	VERB
ma-222	29	5	that	that	SCONJ
ma-222	29	6	in	in	ADP
ma-222	29	7	the	the	DET
ma-222	29	8	general	general	ADJ
ma-222	29	9	banach	banach	NOUN
ma-222	29	10	spaces	space	VERB
ma-222	29	11	,	,	PUNCT
ma-222	29	12	these	these	DET
ma-222	29	13	orthogonalities	orthogonality	NOUN
ma-222	29	14	are	be	AUX
ma-222	29	15	not	not	PART
ma-222	29	16	the	the	DET
ma-222	29	17	same	same	ADJ
ma-222	29	18	.	.	PUNCT
ma-222	30	1	forexample	forexample	NOUN
ma-222	30	2	,	,	PUNCT
ma-222	30	3	isosceles	isoscele	NOUN
ma-222	30	4	orthogonality	orthogonality	NOUN
ma-222	30	5	has	have	VERB
ma-222	30	6	symmetry	symmetry	NOUN
ma-222	30	7	,	,	PUNCT
ma-222	30	8	but	but	CCONJ
ma-222	30	9	birkhoff	birkhoff	NOUN
ma-222	30	10	orthogonality	orthogonality	NOUN
ma-222	30	11	does	do	AUX
ma-222	30	12	not	not	PART
ma-222	30	13	have	have	VERB
ma-222	30	14	symmetry	symmetry	NOUN
ma-222	30	15	,	,	PUNCT
ma-222	30	16	which	which	PRON
ma-222	30	17	means	mean	VERB
ma-222	30	18	that	that	SCONJ
ma-222	30	19	x	x	PUNCT
ma-222	30	20	⊥b	⊥b	PRON
ma-222	30	21	y	y	PROPN
ma-222	30	22	can	can	AUX
ma-222	30	23	not	not	PART
ma-222	30	24	show	show	VERB
ma-222	30	25	that	that	SCONJ
ma-222	30	26	y	y	PROPN
ma-222	30	27	⊥b	⊥b	ADP
ma-222	30	28	x	x	PROPN
ma-222	30	29	.	.	PUNCT
ma-222	31	1	because	because	SCONJ
ma-222	31	2	of	of	ADP
ma-222	31	3	this	this	DET
ma-222	31	4	difference	difference	NOUN
ma-222	31	5	,	,	PUNCT
ma-222	31	6	measuring	measure	VERB
ma-222	31	7	thedifference	thedifference	NOUN
ma-222	31	8	between	between	ADP
ma-222	31	9	the	the	DET
ma-222	31	10	two	two	NUM
ma-222	31	11	types	type	NOUN
ma-222	31	12	of	of	ADP
ma-222	31	13	orthogonality	orthogonality	NOUN
ma-222	31	14	is	be	AUX
ma-222	31	15	of	of	ADP
ma-222	31	16	great	great	ADJ
ma-222	31	17	significance	significance	NOUN
ma-222	31	18	.	.	PUNCT
ma-222	32	1	many	many	ADJ
ma-222	32	2	scholars	scholar	NOUN
ma-222	32	3	havedefined	havedefine	VERB
ma-222	32	4	and	and	CCONJ
ma-222	32	5	studied	study	VERB
ma-222	32	6	many	many	ADJ
ma-222	32	7	novel	novel	ADJ
ma-222	32	8	orthogonality	orthogonality	NOUN
ma-222	32	9	geometric	geometric	ADJ
ma-222	32	10	constants	constant	NOUN
ma-222	32	11	and	and	CCONJ
ma-222	32	12	given	give	VERB
ma-222	32	13	a	a	DET
ma-222	32	14	large	large	ADJ
ma-222	32	15	number	number	NOUN
ma-222	32	16	ofresults	ofresult	NOUN
ma-222	32	17	,	,	PUNCT
ma-222	32	18	including	include	VERB
ma-222	32	19	well	well	ADV
ma-222	32	20	-	-	PUNCT
ma-222	32	21	known	know	VERB
ma-222	32	22	constants	constant	NOUN
ma-222	32	23	(	(	PUNCT
ma-222	32	24	see	see	VERB
ma-222	32	25	[	[	X
ma-222	32	26	11	11	NUM
ma-222	32	27	]	]	PUNCT
ma-222	32	28	,	,	PUNCT
ma-222	32	29	[	[	X
ma-222	32	30	12	12	NUM
ma-222	32	31	]	]	SYM
ma-222	32	32	):	):	PUNCT
ma-222	32	33	bi(x	bi(x	NUM
ma-222	32	34	)	)	PUNCT
ma-222	33	1	=	=	SYM
ma-222	33	2	sup	sup	NOUN
ma-222	33	3	{	{	PUNCT
ma-222	33	4	‖x	‖x	NOUN
ma-222	33	5	+	+	NUM
ma-222	33	6	y‖	y‖	PROPN
ma-222	33	7	−	−	PROPN
ma-222	33	8	‖x	‖x	NOUN
ma-222	34	1	−	−	PROPN
ma-222	34	2	y‖	y‖	PROPN
ma-222	34	3	‖x‖	‖x‖	PROPN
ma-222	34	4	:	:	PUNCT
ma-222	34	5	x	x	X
ma-222	34	6	,	,	PUNCT
ma-222	34	7	y	y	PROPN
ma-222	34	8	∈	∈	PROPN
ma-222	34	9	sx	sx	PROPN
ma-222	34	10	,	,	PUNCT
ma-222	34	11	x	x	PROPN
ma-222	34	12	,	,	PUNCT
ma-222	34	13	y	y	PROPN
ma-222	34	14	6=	6=	PROPN
ma-222	34	15	0	0	NUM
ma-222	34	16	,	,	PUNCT
ma-222	34	17	x	x	PUNCT
ma-222	34	18	⊥b	⊥b	PRON
ma-222	34	19	y	y	PROPN
ma-222	34	20	}	}	PUNCT
ma-222	34	21	and	and	CCONJ
ma-222	34	22	br(x	br(x	PUNCT
ma-222	34	23	)	)	PUNCT
ma-222	35	1	=	=	SYM
ma-222	35	2	sup	sup	NUM
ma-222	35	3	α>0	α>0	NOUN
ma-222	35	4	{	{	PUNCT
ma-222	35	5	‖x	‖x	NOUN
ma-222	35	6	+	+	CCONJ
ma-222	35	7	αy‖	αy‖	PROPN
ma-222	35	8	−	−	PROPN
ma-222	35	9	‖x	‖x	NOUN
ma-222	36	1	−	−	PROPN
ma-222	36	2	αy‖	αy‖	PROPN
ma-222	36	3	α	α	NOUN
ma-222	36	4	:	:	PUNCT
ma-222	36	5	x	x	X
ma-222	36	6	,	,	PUNCT
ma-222	36	7	y	y	PROPN
ma-222	36	8	∈	∈	PROPN
ma-222	36	9	sx	sx	PROPN
ma-222	36	10	,	,	PUNCT
ma-222	36	11	x	x	PROPN
ma-222	36	12	⊥b	⊥b	SYM
ma-222	36	13	y	y	PROPN
ma-222	36	14	}	}	PUNCT
ma-222	36	15	.	.	PUNCT
ma-222	37	1	for	for	ADP
ma-222	37	2	more	more	ADJ
ma-222	37	3	information	information	NOUN
ma-222	37	4	,	,	PUNCT
ma-222	37	5	refer	refer	VERB
ma-222	37	6	to	to	ADP
ma-222	37	7	references	reference	NOUN
ma-222	37	8	[	[	X
ma-222	37	9	1	1	NUM
ma-222	37	10	]	]	PUNCT
ma-222	37	11	,	,	PUNCT
ma-222	38	1	[	[	X
ma-222	38	2	13	13	NUM
ma-222	38	3	-	-	SYM
ma-222	38	4	15	15	NUM
ma-222	38	5	]	]	PUNCT
ma-222	38	6	.	.	PUNCT
ma-222	39	1	throughout	throughout	ADP
ma-222	39	2	the	the	DET
ma-222	39	3	article	article	NOUN
ma-222	39	4	,	,	PUNCT
ma-222	39	5	we	we	PRON
ma-222	39	6	use	use	VERB
ma-222	39	7	x	x	X
ma-222	39	8	torepresent	torepresent	NOUN
ma-222	39	9	a	a	DET
ma-222	39	10	real	real	ADJ
ma-222	39	11	banach	banach	NOUN
ma-222	39	12	space	space	NOUN
ma-222	39	13	with	with	ADP
ma-222	39	14	norm	norm	NOUN
ma-222	39	15	‖	‖	PROPN
ma-222	39	16	·	·	PUNCT
ma-222	39	17	‖	‖	PROPN
ma-222	39	18	,	,	PUNCT
ma-222	39	19	the	the	DET
ma-222	39	20	unit	unit	NOUN
ma-222	39	21	ball	ball	NOUN
ma-222	39	22	is	be	AUX
ma-222	39	23	denoted	denote	VERB
ma-222	39	24	as	as	ADP
ma-222	39	25	bx	bx	NOUN
ma-222	39	26	=	=	NOUN
ma-222	39	27	{	{	PUNCT
ma-222	39	28	x	x	PUNCT
ma-222	39	29	∈	∈	NOUN
ma-222	39	30	x	x	X
ma-222	39	31	:	:	PUNCT
ma-222	39	32	‖x‖	‖x‖	VERB
ma-222	39	33	≤	≤	NOUN
ma-222	39	34	1}and	1}and	NUM
ma-222	40	1	the	the	DET
ma-222	40	2	unit	unit	NOUN
ma-222	40	3	sphere	sphere	NOUN
ma-222	40	4	is	be	AUX
ma-222	40	5	denoted	denote	VERB
ma-222	40	6	as	as	ADP
ma-222	40	7	sx	sx	NOUN
ma-222	40	8	=	=	PUNCT
ma-222	40	9	{	{	PUNCT
ma-222	40	10	x	x	PUNCT
ma-222	40	11	∈	∈	NOUN
ma-222	40	12	x	x	X
ma-222	40	13	:	:	PUNCT
ma-222	40	14	‖x‖	‖x‖	X
ma-222	40	15	=	=	SYM
ma-222	40	16	1	1	NUM
ma-222	40	17	}	}	PUNCT
ma-222	40	18	.	.	PUNCT
ma-222	41	1	let	let	VERB
ma-222	41	2	’s	’s	PRON
ma-222	41	3	assume	assume	VERB
ma-222	41	4	that	that	SCONJ
ma-222	41	5	dimx	dimx	NOUN
ma-222	41	6	is	be	AUX
ma-222	41	7	greaterthan	greaterthan	ADV
ma-222	41	8	or	or	CCONJ
ma-222	41	9	equal	equal	ADJ
ma-222	41	10	to	to	ADP
ma-222	41	11	2	2	NUM
ma-222	41	12	.	.	NOUN
ma-222	42	1	2	2	NUM
ma-222	42	2	.	.	X
ma-222	43	1	the	the	DET
ma-222	43	2	constant	constant	ADJ
ma-222	43	3	lα	lα	NOUN
ma-222	43	4	,	,	PUNCT
ma-222	43	5	β(x	β(x	NOUN
ma-222	43	6	)	)	PUNCT
ma-222	43	7	combining	combine	VERB
ma-222	43	8	the	the	DET
ma-222	43	9	extended	extended	ADJ
ma-222	43	10	isosceles	isoscele	NOUN
ma-222	43	11	and	and	CCONJ
ma-222	43	12	pythagorean	pythagorean	PROPN
ma-222	43	13	orthogonalities	orthogonality	NOUN
ma-222	43	14	,	,	PUNCT
ma-222	43	15	we	we	PRON
ma-222	43	16	define	define	VERB
ma-222	43	17	a	a	DET
ma-222	43	18	new	new	ADJ
ma-222	43	19	constantto	constantto	NOUN
ma-222	43	20	describe	describe	VERB
ma-222	43	21	the	the	DET
ma-222	43	22	difference	difference	NOUN
ma-222	43	23	between	between	ADP
ma-222	43	24	these	these	DET
ma-222	43	25	two	two	NUM
ma-222	43	26	orthogonalities	orthogonality	NOUN
ma-222	43	27	.	.	PUNCT
ma-222	44	1	definition	definition	NOUN
ma-222	44	2	2.1	2.1	NUM
ma-222	44	3	.	.	PUNCT
ma-222	45	1	let	let	VERB
ma-222	45	2	x	x	PRON
ma-222	45	3	be	be	AUX
ma-222	45	4	a	a	DET
ma-222	45	5	banach	banach	NOUN
ma-222	45	6	space	space	NOUN
ma-222	45	7	,	,	PUNCT
ma-222	45	8	the	the	DET
ma-222	45	9	geometric	geometric	ADJ
ma-222	45	10	constant	constant	NOUN
ma-222	45	11	of	of	ADP
ma-222	45	12	the	the	DET
ma-222	45	13	isosceles	isoscele	NOUN
ma-222	45	14	orthogonality	orthogonality	NOUN
ma-222	45	15	type	type	NOUN
ma-222	45	16	is	be	AUX
ma-222	45	17	defined	define	VERB
ma-222	45	18	as	as	ADP
ma-222	45	19	lα	lα	ADJ
ma-222	45	20	,	,	PUNCT
ma-222	45	21	β(x	β(x	NOUN
ma-222	45	22	)	)	PUNCT
ma-222	45	23	=	=	SYM
ma-222	45	24	sup	sup	NOUN
ma-222	45	25	{	{	PUNCT
ma-222	45	26	‖x	‖x	NOUN
ma-222	45	27	−	−	PROPN
ma-222	46	1	βy‖2	βy‖2	PROPN
ma-222	46	2	+	+	CCONJ
ma-222	46	3	‖αx	‖αx	NUM
ma-222	46	4	−	−	PROPN
ma-222	46	5	y‖2	y‖2	X
ma-222	46	6	‖x	‖x	NOUN
ma-222	46	7	−	−	PROPN
ma-222	46	8	y‖2	y‖2	PROPN
ma-222	46	9	+	+	CCONJ
ma-222	46	10	‖αx	‖αx	PROPN
ma-222	46	11	−	−	NOUN
ma-222	46	12	βy‖2	βy‖2	NOUN
ma-222	46	13	:	:	PUNCT
ma-222	46	14	x	x	PROPN
ma-222	46	15	⊥i	⊥i	PROPN
ma-222	46	16	y	y	PROPN
ma-222	46	17	,	,	PUNCT
ma-222	46	18	(	(	PUNCT
ma-222	46	19	x	x	X
ma-222	46	20	,	,	PUNCT
ma-222	46	21	y	y	PROPN
ma-222	46	22	)	)	PUNCT
ma-222	46	23	6=	6=	ADP
ma-222	46	24	(	(	PUNCT
ma-222	46	25	0	0	NUM
ma-222	46	26	,	,	PUNCT
ma-222	46	27	0	0	NUM
ma-222	46	28	)	)	PUNCT
ma-222	46	29	}	}	PUNCT
ma-222	46	30	,	,	PUNCT
ma-222	46	31	where	where	SCONJ
ma-222	46	32	α	α	X
ma-222	46	33	,	,	PUNCT
ma-222	46	34	β	β	X
ma-222	46	35	≥	≥	NOUN
ma-222	46	36	0	0	NUM
ma-222	46	37	,	,	PUNCT
ma-222	46	38	α	α	PROPN
ma-222	46	39	6=	6=	ADP
ma-222	46	40	1	1	NUM
ma-222	46	41	,	,	PUNCT
ma-222	46	42	β	β	X
ma-222	46	43	6=	6=	ADP
ma-222	46	44	1	1	NUM
ma-222	46	45	.	.	PUNCT
ma-222	46	46	in	in	ADP
ma-222	46	47	this	this	DET
ma-222	46	48	section	section	NOUN
ma-222	46	49	,	,	PUNCT
ma-222	46	50	we	we	PRON
ma-222	46	51	first	first	ADV
ma-222	46	52	give	give	VERB
ma-222	46	53	bounds	bound	NOUN
ma-222	46	54	on	on	ADP
ma-222	46	55	the	the	DET
ma-222	46	56	constant	constant	ADJ
ma-222	46	57	lα	lα	NOUN
ma-222	46	58	,	,	PUNCT
ma-222	46	59	β(x	β(x	NOUN
ma-222	46	60	)	)	PUNCT
ma-222	46	61	and	and	CCONJ
ma-222	46	62	its	its	PRON
ma-222	46	63	value	value	NOUN
ma-222	46	64	in	in	ADP
ma-222	46	65	some	some	DET
ma-222	46	66	particularspaces	particularspace	NOUN
ma-222	46	67	is	be	AUX
ma-222	46	68	obtained	obtain	VERB
ma-222	46	69	.	.	PUNCT
ma-222	47	1	we	we	PRON
ma-222	47	2	find	find	VERB
ma-222	47	3	that	that	SCONJ
ma-222	47	4	x	x	PRON
ma-222	47	5	is	be	AUX
ma-222	47	6	a	a	DET
ma-222	47	7	hilbert	hilbert	NOUN
ma-222	47	8	space	space	NOUN
ma-222	47	9	if	if	SCONJ
ma-222	47	10	and	and	CCONJ
ma-222	47	11	only	only	ADV
ma-222	47	12	if	if	SCONJ
ma-222	47	13	the	the	DET
ma-222	47	14	constant	constant	ADJ
ma-222	47	15	lα	lα	NOUN
ma-222	47	16	,	,	PUNCT
ma-222	47	17	β(x	β(x	NOUN
ma-222	47	18	)	)	PUNCT
ma-222	47	19	value	value	NOUN
ma-222	47	20	is1	is1	NOUN
ma-222	47	21	.	.	PUNCT
ma-222	48	1	moreover	moreover	ADV
ma-222	48	2	,	,	PUNCT
ma-222	48	3	the	the	DET
ma-222	48	4	relationship	relationship	NOUN
ma-222	48	5	between	between	ADP
ma-222	48	6	lα	lα	NOUN
ma-222	48	7	,	,	PUNCT
ma-222	48	8	β(x	β(x	NOUN
ma-222	48	9	)	)	PUNCT
ma-222	48	10	and	and	CCONJ
ma-222	48	11	uniformly	uniformly	ADV
ma-222	48	12	non	non	ADJ
ma-222	48	13	-	-	ADJ
ma-222	48	14	square	square	ADJ
ma-222	48	15	is	be	AUX
ma-222	48	16	given	give	VERB
ma-222	48	17	.	.	PUNCT
ma-222	49	1	now	now	ADV
ma-222	49	2	,	,	PUNCT
ma-222	49	3	we	we	PRON
ma-222	49	4	recallthe	recallthe	VERB
ma-222	49	5	notion	notion	NOUN
ma-222	49	6	of	of	ADP
ma-222	49	7	the	the	DET
ma-222	49	8	uniformly	uniformly	ADJ
ma-222	49	9	non	non	ADJ
ma-222	49	10	-	-	ADJ
ma-222	49	11	square	square	ADJ
ma-222	49	12	.	.	PUNCT
ma-222	50	1	definition	definition	NOUN
ma-222	50	2	2.2	2.2	NUM
ma-222	50	3	.	.	PUNCT
ma-222	51	1	(	(	PUNCT
ma-222	51	2	[	[	X
ma-222	51	3	10	10	NUM
ma-222	51	4	]	]	SYM
ma-222	51	5	)	)	PUNCT
ma-222	51	6	a	a	DET
ma-222	51	7	banach	banach	NOUN
ma-222	51	8	space	space	NOUN
ma-222	51	9	x	x	PUNCT
ma-222	51	10	is	be	AUX
ma-222	51	11	called	call	VERB
ma-222	51	12	uniformly	uniformly	ADV
ma-222	51	13	non	non	ADJ
ma-222	51	14	-	-	ADJ
ma-222	51	15	square	square	ADJ
ma-222	51	16	if	if	SCONJ
ma-222	51	17	there	there	PRON
ma-222	51	18	exists	exist	VERB
ma-222	51	19	δ	δ	PROPN
ma-222	51	20	∈	∈	PROPN
ma-222	51	21	(	(	PUNCT
ma-222	51	22	0	0	NUM
ma-222	51	23	,	,	PUNCT
ma-222	51	24	1	1	NUM
ma-222	51	25	)	)	PUNCT
ma-222	51	26	such	such	ADJ
ma-222	51	27	that	that	PRON
ma-222	51	28	for	for	ADP
ma-222	51	29	any	any	DET
ma-222	51	30	x	x	NOUN
ma-222	51	31	,	,	PUNCT
ma-222	51	32	y	y	PROPN
ma-222	51	33	∈	∈	PROPN
ma-222	51	34	sx	sx	PROPN
ma-222	51	35	,	,	PUNCT
ma-222	51	36	then	then	ADV
ma-222	51	37	‖x	‖x	PUNCT
ma-222	52	1	+	+	CCONJ
ma-222	52	2	y‖	y‖	PROPN
ma-222	52	3	2	2	NUM
ma-222	52	4	≤	≤	NOUN
ma-222	52	5	1−	1−	NUM
ma-222	52	6	δ	δ	NOUN
ma-222	52	7	or	or	CCONJ
ma-222	52	8	‖x	‖x	NOUN
ma-222	52	9	−	−	PROPN
ma-222	53	1	y‖	y‖	NOUN
ma-222	53	2	2	2	NUM
ma-222	53	3	≤	≤	NOUN
ma-222	53	4	1−	1−	NUM
ma-222	53	5	δ	δ	PROPN
ma-222	53	6	.	.	PUNCT
ma-222	54	1	https://doi.org/10.28924/ada/ma.4.6	https://doi.org/10.28924/ada/ma.4.6	PROPN
ma-222	54	2	eur	eur	PROPN
ma-222	54	3	.	.	PUNCT
ma-222	55	1	j.	j.	PROPN
ma-222	55	2	math	math	PROPN
ma-222	55	3	.	.	PUNCT
ma-222	56	1	anal	anal	PROPN
ma-222	56	2	.	.	PUNCT
ma-222	57	1	10.28924	10.28924	NUM
ma-222	57	2	/	/	SYM
ma-222	57	3	ada	ada	PROPN
ma-222	57	4	/	/	SYM
ma-222	57	5	ma.4.6	ma.4.6	NOUN
ma-222	57	6	3	3	NUM
ma-222	57	7	proposition	proposition	NOUN
ma-222	57	8	2.1	2.1	NUM
ma-222	57	9	.	.	PUNCT
ma-222	58	1	let	let	VERB
ma-222	58	2	x	x	PRON
ma-222	58	3	be	be	AUX
ma-222	58	4	a	a	DET
ma-222	58	5	banach	banach	NOUN
ma-222	58	6	space	space	NOUN
ma-222	58	7	,	,	PUNCT
ma-222	58	8	then	then	ADV
ma-222	58	9	1	1	NUM
ma-222	58	10	≤	≤	NUM
ma-222	58	11	lα	lα	NOUN
ma-222	58	12	,	,	PUNCT
ma-222	58	13	β(x	β(x	NOUN
ma-222	58	14	)	)	PUNCT
ma-222	58	15	≤	≤	NUM
ma-222	58	16			NUM
ma-222	58	17	2	2	NUM
ma-222	58	18	1+β2	1+β2	NOUN
ma-222	58	19	,	,	PUNCT
ma-222	58	20	0	0	NUM
ma-222	58	21	≤	≤	NUM
ma-222	59	1	β	β	NOUN
ma-222	59	2	≤	≤	NUM
ma-222	59	3	α	α	PRON
ma-222	59	4	<	<	X
ma-222	59	5	1	1	NUM
ma-222	59	6	;	;	PUNCT
ma-222	59	7	2	2	NUM
ma-222	59	8	1+α2	1+α2	NUM
ma-222	59	9	,	,	PUNCT
ma-222	59	10	0	0	NUM
ma-222	59	11	≤	≤	NUM
ma-222	59	12	α	α	NOUN
ma-222	59	13	≤	≤	NOUN
ma-222	59	14	β	β	X
ma-222	59	15	<	<	X
ma-222	59	16	1	1	NUM
ma-222	59	17	;	;	PUNCT
ma-222	59	18	α2+β2	α2+β2	PROPN
ma-222	59	19	1+β2	1+β2	NUM
ma-222	59	20	,	,	PUNCT
ma-222	59	21	1	1	NUM
ma-222	59	22	<	<	X
ma-222	59	23	β	β	X
ma-222	59	24	≤	≤	NUM
ma-222	59	25	α	α	NOUN
ma-222	59	26	;	;	PUNCT
ma-222	59	27	α2+β2	α2+β2	NUM
ma-222	59	28	1+α2	1+α2	NUM
ma-222	59	29	,	,	PUNCT
ma-222	59	30	1	1	NUM
ma-222	59	31	<	<	X
ma-222	59	32	α	α	PRON
ma-222	59	33	≤	≤	PUNCT
ma-222	59	34	β	β	X
ma-222	59	35	.	.	PUNCT
ma-222	60	1	proof	proof	NOUN
ma-222	60	2	.	.	PUNCT
ma-222	61	1	let	let	VERB
ma-222	61	2	x0	x0	PROPN
ma-222	61	3	=	=	PUNCT
ma-222	61	4	0	0	NUM
ma-222	61	5	,	,	PUNCT
ma-222	61	6	y0	y0	PROPN
ma-222	61	7	6=	6=	ADP
ma-222	61	8	0	0	NUM
ma-222	61	9	,	,	PUNCT
ma-222	61	10	satisfy	satisfy	VERB
ma-222	61	11	x0	x0	PROPN
ma-222	61	12	⊥i	⊥i	PROPN
ma-222	61	13	y0	y0	NOUN
ma-222	61	14	,	,	PUNCT
ma-222	61	15	hence	hence	ADV
ma-222	61	16	lα	lα	ADJ
ma-222	61	17	,	,	PUNCT
ma-222	61	18	β(x	β(x	NOUN
ma-222	61	19	)	)	PUNCT
ma-222	61	20	≥	≥	NOUN
ma-222	61	21	‖x0	‖x0	NOUN
ma-222	62	1	−	−	PROPN
ma-222	62	2	βy0‖2	βy0‖2	NOUN
ma-222	62	3	+	+	CCONJ
ma-222	62	4	‖αx0	‖αx0	PROPN
ma-222	62	5	−	−	PROPN
ma-222	62	6	y0‖2	y0‖2	NUM
ma-222	62	7	‖x0	‖x0	NOUN
ma-222	62	8	−	−	PROPN
ma-222	62	9	y0‖2	y0‖2	X
ma-222	63	1	+	+	CCONJ
ma-222	63	2	‖αx0	‖αx0	PROPN
ma-222	63	3	−	−	PROPN
ma-222	63	4	βy0‖2	βy0‖2	NOUN
ma-222	63	5	=	=	SYM
ma-222	64	1	1	1	X
ma-222	64	2	.	.	PUNCT
ma-222	64	3	on	on	ADP
ma-222	64	4	the	the	DET
ma-222	64	5	other	other	ADJ
ma-222	64	6	hand	hand	NOUN
ma-222	64	7	,	,	PUNCT
ma-222	64	8	using	use	VERB
ma-222	64	9	the	the	DET
ma-222	64	10	triangle	triangle	NOUN
ma-222	64	11	inequality	inequality	NOUN
ma-222	64	12	,	,	PUNCT
ma-222	64	13	we	we	PRON
ma-222	64	14	get	get	VERB
ma-222	64	15	:	:	PUNCT
ma-222	64	16	‖x	‖x	NOUN
ma-222	64	17	−	−	PROPN
ma-222	65	1	βy‖2	βy‖2	PROPN
ma-222	65	2	+	+	CCONJ
ma-222	65	3	‖αx	‖αx	NUM
ma-222	65	4	−	−	PROPN
ma-222	65	5	y‖2	y‖2	X
ma-222	65	6	‖x	‖x	NOUN
ma-222	65	7	−	−	PROPN
ma-222	65	8	y‖2	y‖2	PROPN
ma-222	65	9	+	+	CCONJ
ma-222	66	1	‖αx	‖αx	NUM
ma-222	66	2	−	−	NOUN
ma-222	66	3	βy‖2	βy‖2	NOUN
ma-222	66	4	≤	≤	PROPN
ma-222	67	1	(	(	PUNCT
ma-222	67	2	∣∣∣1−β2	∣∣∣1−β2	NOUN
ma-222	67	3	∣∣∣	∣∣∣	NOUN
ma-222	67	4	‖x	‖x	PUNCT
ma-222	68	1	+	+	CCONJ
ma-222	68	2	y‖+	y‖+	PROPN
ma-222	68	3	∣∣∣1+β2	∣∣∣1+β2	NOUN
ma-222	68	4	∣∣∣	∣∣∣	PROPN
ma-222	69	1	‖x	‖x	PROPN
ma-222	70	1	−	−	PROPN
ma-222	71	1	y‖)2	y‖)2	PROPN
ma-222	71	2	+	+	CCONJ
ma-222	71	3	(	(	PUNCT
ma-222	71	4	∣∣α−12	∣∣α−12	X
ma-222	71	5	∣∣	∣∣	NUM
ma-222	71	6	‖x	‖x	PUNCT
ma-222	72	1	+	+	CCONJ
ma-222	72	2	y‖+	y‖+	ADJ
ma-222	72	3	∣∣α+12	∣∣α+12	NOUN
ma-222	72	4	∣∣	∣∣	NUM
ma-222	72	5	‖x	‖x	PUNCT
ma-222	73	1	−	−	PROPN
ma-222	73	2	y‖)2	y‖)2	PROPN
ma-222	73	3	‖x	‖x	NOUN
ma-222	74	1	−	−	PROPN
ma-222	75	1	y‖2	y‖2	X
ma-222	75	2	+	+	CCONJ
ma-222	75	3	(	(	PUNCT
ma-222	75	4	∣∣∣α−β2	∣∣∣α−β2	ADJ
ma-222	75	5	∣∣∣	∣∣∣	NOUN
ma-222	75	6	‖x	‖x	NOUN
ma-222	75	7	+	+	CCONJ
ma-222	75	8	y‖	y‖	PROPN
ma-222	76	1	−	−	PROPN
ma-222	76	2	∣∣∣α+β2	∣∣∣α+β2	PROPN
ma-222	76	3	∣∣∣	∣∣∣	NOUN
ma-222	77	1	‖x	‖x	PROPN
ma-222	78	1	−	−	PROPN
ma-222	79	1	y‖)2	y‖)2	PROPN
ma-222	79	2	.	.	PUNCT
ma-222	80	1	if	if	SCONJ
ma-222	80	2	we	we	PRON
ma-222	80	3	take	take	VERB
ma-222	80	4	the	the	DET
ma-222	80	5	categorical	categorical	ADJ
ma-222	80	6	approach	approach	NOUN
ma-222	80	7	,	,	PUNCT
ma-222	80	8	there	there	PRON
ma-222	80	9	will	will	AUX
ma-222	80	10	be	be	AUX
ma-222	80	11	the	the	DET
ma-222	80	12	following	follow	VERB
ma-222	80	13	four	four	NUM
ma-222	80	14	approaches	approach	NOUN
ma-222	80	15	.	.	PUNCT
ma-222	81	1	case	case	NOUN
ma-222	81	2	1	1	NUM
ma-222	81	3	when	when	SCONJ
ma-222	81	4	0	0	NUM
ma-222	81	5	≤	≤	NUM
ma-222	81	6	β	β	NOUN
ma-222	81	7	≤	≤	NUM
ma-222	81	8	α	α	PRON
ma-222	81	9	<	<	X
ma-222	81	10	1	1	NUM
ma-222	81	11	,	,	PUNCT
ma-222	81	12	we	we	PRON
ma-222	81	13	have	have	VERB
ma-222	81	14	‖x	‖x	NOUN
ma-222	81	15	−	−	PUNCT
ma-222	82	1	βy‖2	βy‖2	PROPN
ma-222	82	2	+	+	CCONJ
ma-222	82	3	‖αx	‖αx	NUM
ma-222	82	4	−	−	PROPN
ma-222	82	5	y‖2	y‖2	X
ma-222	82	6	‖x	‖x	NOUN
ma-222	82	7	−	−	PROPN
ma-222	82	8	y‖2	y‖2	PROPN
ma-222	82	9	+	+	CCONJ
ma-222	82	10	‖αx	‖αx	PROPN
ma-222	82	11	−	−	NOUN
ma-222	82	12	βy‖2	βy‖2	NOUN
ma-222	82	13	≤	≤	NOUN
ma-222	82	14	2	2	NUM
ma-222	82	15	1	1	NUM
ma-222	82	16	+	+	CCONJ
ma-222	82	17	β2	β2	NOUN
ma-222	82	18	.	.	PUNCT
ma-222	83	1	case	case	NOUN
ma-222	83	2	2	2	NUM
ma-222	83	3	when	when	SCONJ
ma-222	83	4	0	0	NUM
ma-222	83	5	≤	≤	NUM
ma-222	83	6	α	α	NOUN
ma-222	83	7	≤	≤	NOUN
ma-222	83	8	β	β	X
ma-222	83	9	<	<	X
ma-222	83	10	1	1	NUM
ma-222	83	11	,	,	PUNCT
ma-222	83	12	we	we	PRON
ma-222	83	13	have	have	VERB
ma-222	83	14	‖x	‖x	NOUN
ma-222	83	15	−	−	PUNCT
ma-222	84	1	βy‖2	βy‖2	PROPN
ma-222	84	2	+	+	CCONJ
ma-222	84	3	‖αx	‖αx	NUM
ma-222	84	4	−	−	PROPN
ma-222	84	5	y‖2	y‖2	X
ma-222	84	6	‖x	‖x	NOUN
ma-222	84	7	−	−	PROPN
ma-222	84	8	y‖2	y‖2	PROPN
ma-222	84	9	+	+	CCONJ
ma-222	84	10	‖αx	‖αx	PROPN
ma-222	84	11	−	−	NOUN
ma-222	84	12	βy‖2	βy‖2	NOUN
ma-222	84	13	≤	≤	NOUN
ma-222	84	14	2	2	NUM
ma-222	84	15	1	1	NUM
ma-222	84	16	+	+	CCONJ
ma-222	84	17	α2	α2	ADJ
ma-222	84	18	.	.	PUNCT
ma-222	85	1	case	case	NOUN
ma-222	85	2	3	3	NUM
ma-222	86	1	when	when	SCONJ
ma-222	86	2	1	1	NUM
ma-222	86	3	<	<	X
ma-222	86	4	β	β	X
ma-222	86	5	≤	≤	NUM
ma-222	86	6	α	α	X
ma-222	86	7	,	,	PUNCT
ma-222	86	8	we	we	PRON
ma-222	86	9	have	have	VERB
ma-222	86	10	‖x	‖x	NOUN
ma-222	86	11	−	−	PUNCT
ma-222	87	1	βy‖2	βy‖2	PROPN
ma-222	87	2	+	+	CCONJ
ma-222	87	3	‖αx	‖αx	NUM
ma-222	87	4	−	−	PROPN
ma-222	87	5	y‖2	y‖2	X
ma-222	87	6	‖x	‖x	NOUN
ma-222	87	7	−	−	PROPN
ma-222	87	8	y‖2	y‖2	PROPN
ma-222	87	9	+	+	CCONJ
ma-222	87	10	‖αx	‖αx	PROPN
ma-222	87	11	−	−	NOUN
ma-222	87	12	βy‖2	βy‖2	NOUN
ma-222	87	13	≤	≤	ADV
ma-222	87	14	α2	α2	ADJ
ma-222	88	1	+	+	CCONJ
ma-222	88	2	β2	β2	VERB
ma-222	88	3	1	1	NUM
ma-222	88	4	+	+	CCONJ
ma-222	88	5	β2	β2	NOUN
ma-222	88	6	.	.	PUNCT
ma-222	89	1	case	case	NOUN
ma-222	89	2	4	4	NUM
ma-222	89	3	when	when	SCONJ
ma-222	89	4	1	1	NUM
ma-222	89	5	<	<	X
ma-222	89	6	α	α	X
ma-222	89	7	≤	≤	NOUN
ma-222	90	1	β	β	X
ma-222	90	2	,	,	PUNCT
ma-222	90	3	we	we	PRON
ma-222	90	4	have	have	VERB
ma-222	90	5	‖x	‖x	NOUN
ma-222	90	6	−	−	PUNCT
ma-222	91	1	βy‖2	βy‖2	PROPN
ma-222	91	2	+	+	CCONJ
ma-222	91	3	‖αx	‖αx	NUM
ma-222	91	4	−	−	PROPN
ma-222	91	5	y‖2	y‖2	X
ma-222	91	6	‖x	‖x	NOUN
ma-222	91	7	−	−	PROPN
ma-222	91	8	y‖2	y‖2	PROPN
ma-222	91	9	+	+	CCONJ
ma-222	91	10	‖αx	‖αx	PROPN
ma-222	91	11	−	−	NOUN
ma-222	91	12	βy‖2	βy‖2	NOUN
ma-222	91	13	≤	≤	ADV
ma-222	91	14	α2	α2	ADJ
ma-222	92	1	+	+	CCONJ
ma-222	92	2	β2	β2	VERB
ma-222	92	3	1	1	NUM
ma-222	92	4	+	+	CCONJ
ma-222	92	5	α2	α2	ADJ
ma-222	92	6	.	.	PUNCT
ma-222	93	1	�	�	PROPN
ma-222	93	2	next	next	ADV
ma-222	93	3	,	,	PUNCT
ma-222	93	4	we	we	PRON
ma-222	93	5	will	will	AUX
ma-222	93	6	show	show	VERB
ma-222	93	7	that	that	SCONJ
ma-222	93	8	there	there	PRON
ma-222	93	9	are	be	VERB
ma-222	93	10	points	point	NOUN
ma-222	93	11	in	in	ADP
ma-222	93	12	some	some	DET
ma-222	93	13	particular	particular	ADJ
ma-222	93	14	spaces	space	NOUN
ma-222	93	15	where	where	SCONJ
ma-222	93	16	the	the	DET
ma-222	93	17	value	value	NOUN
ma-222	93	18	of	of	ADP
ma-222	93	19	the	the	DET
ma-222	93	20	constant	constant	ADJ
ma-222	93	21	lα	lα	NOUN
ma-222	93	22	,	,	PUNCT
ma-222	93	23	β(x	β(x	NOUN
ma-222	93	24	)	)	PUNCT
ma-222	93	25	is	be	AUX
ma-222	93	26	an	an	DET
ma-222	93	27	upper	upper	ADJ
ma-222	93	28	bound	bind	VERB
ma-222	93	29	.	.	PUNCT
ma-222	94	1	example	example	NOUN
ma-222	94	2	2.1	2.1	NUM
ma-222	94	3	.	.	PUNCT
ma-222	95	1	let	let	VERB
ma-222	95	2	0	0	NUM
ma-222	95	3	≤	≤	NOUN
ma-222	95	4	β	β	X
ma-222	95	5	<	<	X
ma-222	95	6	1	1	NUM
ma-222	95	7	,	,	PUNCT
ma-222	95	8	α	α	NOUN
ma-222	95	9	=	=	PUNCT
ma-222	95	10	β	β	X
ma-222	95	11	and	and	CCONJ
ma-222	95	12	x	x	ADJ
ma-222	95	13	be	be	AUX
ma-222	95	14	the	the	DET
ma-222	95	15	space	space	NOUN
ma-222	95	16	r2	r2	NOUN
ma-222	95	17	with	with	ADP
ma-222	95	18	l1	l1	PROPN
ma-222	95	19	norm	norm	NOUN
ma-222	95	20	defined	define	VERB
ma-222	95	21	by	by	ADP
ma-222	95	22	‖(x1	‖(x1	PROPN
ma-222	95	23	,	,	PUNCT
ma-222	95	24	x2)‖	x2)‖	PROPN
ma-222	95	25	=	=	SYM
ma-222	95	26	|x1|+	|x1|+	NOUN
ma-222	95	27	|x2|	|x2|	PROPN
ma-222	95	28	,	,	PUNCT
ma-222	95	29	then	then	ADV
ma-222	95	30	lα	lα	ADJ
ma-222	95	31	,	,	PUNCT
ma-222	95	32	β(x	β(x	NOUN
ma-222	95	33	)	)	PUNCT
ma-222	95	34	=	=	SYM
ma-222	95	35	2	2	NUM
ma-222	95	36	1+β2	1+β2	NOUN
ma-222	95	37	.	.	PUNCT
ma-222	96	1	https://doi.org/10.28924/ada/ma.4.6	https://doi.org/10.28924/ada/ma.4.6	PROPN
ma-222	96	2	eur	eur	PROPN
ma-222	96	3	.	.	PUNCT
ma-222	97	1	j.	j.	PROPN
ma-222	97	2	math	math	PROPN
ma-222	97	3	.	.	PUNCT
ma-222	98	1	anal	anal	PROPN
ma-222	98	2	.	.	PUNCT
ma-222	99	1	10.28924	10.28924	NUM
ma-222	99	2	/	/	SYM
ma-222	99	3	ada	ada	PROPN
ma-222	99	4	/	/	SYM
ma-222	99	5	ma.4.6	ma.4.6	NOUN
ma-222	99	6	4	4	NUM
ma-222	99	7	let	let	VERB
ma-222	99	8	x	x	PUNCT
ma-222	99	9	=	=	SYM
ma-222	99	10	(	(	PUNCT
ma-222	99	11	1	1	NUM
ma-222	99	12	,	,	PUNCT
ma-222	99	13	1	1	NUM
ma-222	99	14	)	)	PUNCT
ma-222	99	15	,	,	PUNCT
ma-222	99	16	y	y	PROPN
ma-222	99	17	=	=	SYM
ma-222	99	18	(	(	PUNCT
ma-222	99	19	1,−1	1,−1	NUM
ma-222	99	20	)	)	PUNCT
ma-222	99	21	,	,	PUNCT
ma-222	99	22	satisfy	satisfy	NOUN
ma-222	99	23	x	x	PUNCT
ma-222	99	24	⊥i	⊥i	PROPN
ma-222	99	25	y	y	PROPN
ma-222	99	26	.	.	PUNCT
ma-222	100	1	we	we	PRON
ma-222	100	2	get	get	VERB
ma-222	100	3	‖αx	‖αx	NUM
ma-222	100	4	−	−	PROPN
ma-222	100	5	βy‖	βy‖	PROPN
ma-222	100	6	=	=	SYM
ma-222	100	7	2β	2β	NOUN
ma-222	100	8	,	,	PUNCT
ma-222	100	9	‖x	‖x	NOUN
ma-222	100	10	−	−	NOUN
ma-222	101	1	y‖	y‖	NOUN
ma-222	101	2	=	=	PUNCT
ma-222	101	3	‖x	‖x	NOUN
ma-222	102	1	−	−	PROPN
ma-222	102	2	βy‖	βy‖	PROPN
ma-222	102	3	=	=	SYM
ma-222	102	4	‖αx	‖αx	PROPN
ma-222	102	5	−	−	PROPN
ma-222	102	6	y‖	y‖	NOUN
ma-222	102	7	=	=	SYM
ma-222	102	8	2	2	X
ma-222	102	9	.	.	PUNCT
ma-222	102	10	thus	thus	ADV
ma-222	102	11	,	,	PUNCT
ma-222	102	12	lα	lα	ADJ
ma-222	102	13	,	,	PUNCT
ma-222	102	14	β(x	β(x	NOUN
ma-222	102	15	)	)	PUNCT
ma-222	102	16	=	=	SYM
ma-222	102	17	2	2	NUM
ma-222	102	18	1+β2	1+β2	NUM
ma-222	102	19	.	.	PUNCT
ma-222	102	20	example	example	NOUN
ma-222	102	21	2.2	2.2	NUM
ma-222	102	22	.	.	PUNCT
ma-222	103	1	let	let	VERB
ma-222	103	2	0	0	NUM
ma-222	103	3	≤	≤	NOUN
ma-222	103	4	β	β	X
ma-222	103	5	<	<	X
ma-222	103	6	1	1	NUM
ma-222	103	7	,	,	PUNCT
ma-222	103	8	α	α	NOUN
ma-222	103	9	=	=	PUNCT
ma-222	103	10	β	β	X
ma-222	103	11	and	and	CCONJ
ma-222	103	12	x	x	ADJ
ma-222	103	13	be	be	AUX
ma-222	103	14	the	the	DET
ma-222	103	15	space	space	NOUN
ma-222	103	16	r2	r2	NOUN
ma-222	103	17	with	with	ADP
ma-222	103	18	l∞	l∞	NOUN
ma-222	103	19	norm	norm	NOUN
ma-222	103	20	defined	define	VERB
ma-222	103	21	by	by	ADP
ma-222	103	22	‖(x1	‖(x1	PROPN
ma-222	103	23	,	,	PUNCT
ma-222	103	24	x2)‖	x2)‖	PROPN
ma-222	103	25	=	=	SYM
ma-222	103	26	max{|x1|	max{|x1|	PROPN
ma-222	103	27	,	,	PUNCT
ma-222	103	28	|x2|	|x2|	PROPN
ma-222	103	29	}	}	PUNCT
ma-222	103	30	,	,	PUNCT
ma-222	103	31	then	then	ADV
ma-222	103	32	lα	lα	ADJ
ma-222	103	33	,	,	PUNCT
ma-222	103	34	β(x	β(x	NOUN
ma-222	103	35	)	)	PUNCT
ma-222	103	36	=	=	SYM
ma-222	103	37	2	2	NUM
ma-222	103	38	1+β2	1+β2	NUM
ma-222	103	39	.	.	PUNCT
ma-222	104	1	let	let	VERB
ma-222	104	2	x	x	PUNCT
ma-222	104	3	=	=	SYM
ma-222	104	4	(	(	PUNCT
ma-222	104	5	1	1	NUM
ma-222	104	6	,	,	PUNCT
ma-222	104	7	0	0	NUM
ma-222	104	8	)	)	PUNCT
ma-222	104	9	,	,	PUNCT
ma-222	104	10	y	y	PROPN
ma-222	104	11	=	=	PRON
ma-222	104	12	(	(	PUNCT
ma-222	104	13	0,−1	0,−1	PROPN
ma-222	104	14	)	)	PUNCT
ma-222	104	15	,	,	PUNCT
ma-222	104	16	satisfy	satisfy	NOUN
ma-222	104	17	x	x	PUNCT
ma-222	104	18	⊥i	⊥i	PROPN
ma-222	104	19	y	y	PROPN
ma-222	104	20	.	.	PUNCT
ma-222	105	1	we	we	PRON
ma-222	105	2	get	get	VERB
ma-222	105	3	‖αx	‖αx	NUM
ma-222	105	4	−	−	PROPN
ma-222	105	5	βy‖	βy‖	PROPN
ma-222	105	6	=	=	SYM
ma-222	105	7	β	β	NOUN
ma-222	105	8	,	,	PUNCT
ma-222	105	9	‖x	‖x	NOUN
ma-222	105	10	−	−	PROPN
ma-222	106	1	y‖	y‖	NOUN
ma-222	106	2	=	=	PUNCT
ma-222	106	3	‖x	‖x	NOUN
ma-222	107	1	−	−	PROPN
ma-222	107	2	βy‖	βy‖	PROPN
ma-222	107	3	=	=	SYM
ma-222	107	4	‖αx	‖αx	PROPN
ma-222	107	5	−	−	PROPN
ma-222	107	6	y‖	y‖	NOUN
ma-222	107	7	=	=	PUNCT
ma-222	107	8	1	1	X
ma-222	107	9	.	.	PUNCT
ma-222	107	10	thus	thus	ADV
ma-222	107	11	,	,	PUNCT
ma-222	107	12	lα	lα	ADJ
ma-222	107	13	,	,	PUNCT
ma-222	107	14	β(x	β(x	NOUN
ma-222	107	15	)	)	PUNCT
ma-222	107	16	=	=	SYM
ma-222	107	17	2	2	NUM
ma-222	107	18	1+β2	1+β2	NUM
ma-222	107	19	.	.	PUNCT
ma-222	108	1	proposition	proposition	NOUN
ma-222	108	2	2.2	2.2	NUM
ma-222	108	3	.	.	PUNCT
ma-222	109	1	let	let	VERB
ma-222	109	2	x	x	PRON
ma-222	109	3	be	be	AUX
ma-222	109	4	a	a	DET
ma-222	109	5	banach	banach	NOUN
ma-222	109	6	space	space	NOUN
ma-222	109	7	,	,	PUNCT
ma-222	109	8	0	0	NUM
ma-222	109	9	≤	≤	NUM
ma-222	110	1	β	β	NOUN
ma-222	110	2	≤	≤	NUM
ma-222	110	3	α	α	PRON
ma-222	110	4	<	<	X
ma-222	110	5	1	1	NUM
ma-222	110	6	,	,	PUNCT
ma-222	110	7	then	then	ADV
ma-222	110	8	lα	lα	ADJ
ma-222	110	9	,	,	PUNCT
ma-222	110	10	β(x	β(x	NOUN
ma-222	110	11	)	)	PUNCT
ma-222	110	12	=	=	SYM
ma-222	110	13	1	1	NUM
ma-222	110	14	if	if	SCONJ
ma-222	110	15	and	and	CCONJ
ma-222	110	16	only	only	ADV
ma-222	110	17	if	if	SCONJ
ma-222	110	18	x	x	PRON
ma-222	110	19	is	be	AUX
ma-222	110	20	a	a	DET
ma-222	110	21	hilbert	hilbert	NOUN
ma-222	110	22	space	space	NOUN
ma-222	110	23	.	.	PUNCT
ma-222	111	1	proof	proof	NOUN
ma-222	111	2	.	.	PUNCT
ma-222	112	1	since	since	SCONJ
ma-222	112	2	x	x	PRON
ma-222	112	3	is	be	AUX
ma-222	112	4	a	a	DET
ma-222	112	5	hilbert	hilbert	NOUN
ma-222	112	6	space	space	NOUN
ma-222	112	7	,	,	PUNCT
ma-222	112	8	combined	combine	VERB
ma-222	112	9	with	with	ADP
ma-222	112	10	reference	reference	NOUN
ma-222	112	11	[	[	X
ma-222	112	12	3	3	NUM
ma-222	112	13	]	]	PUNCT
ma-222	112	14	,	,	PUNCT
ma-222	112	15	we	we	PRON
ma-222	112	16	have	have	VERB
ma-222	112	17	lα	lα	NOUN
ma-222	112	18	,	,	PUNCT
ma-222	112	19	β(x	β(x	NOUN
ma-222	112	20	)	)	PUNCT
ma-222	112	21	=	=	SYM
ma-222	113	1	1	1	X
ma-222	113	2	.	.	PUNCT
ma-222	113	3	conversely	conversely	ADV
ma-222	113	4	,	,	PUNCT
ma-222	113	5	assuming	assume	VERB
ma-222	113	6	that	that	SCONJ
ma-222	113	7	lα	lα	NOUN
ma-222	113	8	,	,	PUNCT
ma-222	113	9	β(x	β(x	NOUN
ma-222	113	10	)	)	PUNCT
ma-222	113	11	=	=	SYM
ma-222	113	12	1	1	NUM
ma-222	113	13	and	and	CCONJ
ma-222	113	14	useing	use	VERB
ma-222	113	15	the	the	DET
ma-222	113	16	homogeneity	homogeneity	NOUN
ma-222	113	17	of	of	ADP
ma-222	113	18	x	x	PROPN
ma-222	113	19	⊥	⊥	PROPN
ma-222	113	20	y	y	PROPN
ma-222	113	21	,	,	PUNCT
ma-222	113	22	we	we	PRON
ma-222	113	23	can	can	AUX
ma-222	113	24	prove	prove	VERB
ma-222	113	25	by	by	ADP
ma-222	113	26	induction	induction	NOUN
ma-222	113	27	that	that	SCONJ
ma-222	113	28	‖x	‖x	NOUN
ma-222	114	1	−	−	PROPN
ma-222	114	2	y‖2	y‖2	X
ma-222	114	3	+	+	CCONJ
ma-222	115	1	‖αnx	‖αnx	PROPN
ma-222	116	1	−	−	PROPN
ma-222	117	1	βy‖2	βy‖2	NOUN
ma-222	117	2	≥	≥	NOUN
ma-222	117	3	‖αnx	‖αnx	ADJ
ma-222	117	4	−	−	X
ma-222	117	5	y‖2	y‖2	PROPN
ma-222	117	6	+	+	CCONJ
ma-222	117	7	‖x	‖x	NOUN
ma-222	117	8	−	−	PROPN
ma-222	118	1	βy‖2	βy‖2	NOUN
ma-222	118	2	.	.	PUNCT
ma-222	119	1	since	since	SCONJ
ma-222	119	2	0	0	NUM
ma-222	119	3	≤	≤	NUM
ma-222	119	4	α	α	NOUN
ma-222	119	5	<	<	X
ma-222	119	6	1	1	NUM
ma-222	119	7	,	,	PUNCT
ma-222	119	8	taking	take	VERB
ma-222	119	9	the	the	DET
ma-222	119	10	limit	limit	NOUN
ma-222	119	11	n	n	PRON
ma-222	119	12	→∞	→∞	NOUN
ma-222	119	13	,	,	PUNCT
ma-222	119	14	we	we	PRON
ma-222	119	15	get	get	VERB
ma-222	119	16	‖x	‖x	NOUN
ma-222	119	17	−	−	PROPN
ma-222	119	18	y‖2	y‖2	X
ma-222	119	19	≥	≥	PROPN
ma-222	119	20	(	(	PUNCT
ma-222	119	21	1−	1−	NUM
ma-222	119	22	β2	β2	NOUN
ma-222	119	23	)	)	PUNCT
ma-222	119	24	‖y‖2	‖y‖2	PROPN
ma-222	120	1	+	+	CCONJ
ma-222	120	2	‖x	‖x	NOUN
ma-222	120	3	−	−	PROPN
ma-222	121	1	βy‖2	βy‖2	NOUN
ma-222	121	2	.	.	PUNCT
ma-222	122	1	if	if	SCONJ
ma-222	122	2	0	0	NUM
ma-222	122	3	≤	≤	NUM
ma-222	122	4	β	β	X
ma-222	122	5	<	<	X
ma-222	122	6	1	1	NUM
ma-222	122	7	,	,	PUNCT
ma-222	122	8	a	a	DET
ma-222	122	9	second	second	ADJ
ma-222	122	10	induction	induction	NOUN
ma-222	122	11	shows	show	VERB
ma-222	122	12	that	that	SCONJ
ma-222	122	13	‖x	‖x	NOUN
ma-222	122	14	−	−	PROPN
ma-222	122	15	y‖2	y‖2	X
ma-222	122	16	=	=	SYM
ma-222	122	17	(	(	PUNCT
ma-222	122	18	1−	1−	NUM
ma-222	122	19	β2n	β2n	NOUN
ma-222	122	20	)	)	PUNCT
ma-222	122	21	‖y‖2	‖y‖2	PROPN
ma-222	123	1	+	+	NUM
ma-222	123	2	‖x	‖x	NOUN
ma-222	123	3	−	−	NOUN
ma-222	123	4	βny‖2	βny‖2	NOUN
ma-222	123	5	.	.	PUNCT
ma-222	124	1	also	also	ADV
ma-222	124	2	takingthe	takingthe	DET
ma-222	124	3	limit	limit	NOUN
ma-222	124	4	n	n	ADP
ma-222	124	5	→∞	→∞	NOUN
ma-222	124	6	,	,	PUNCT
ma-222	124	7	therefore	therefore	ADV
ma-222	124	8	,	,	PUNCT
ma-222	124	9	in	in	ADP
ma-222	124	10	this	this	DET
ma-222	124	11	case	case	NOUN
ma-222	124	12	we	we	PRON
ma-222	124	13	get	get	VERB
ma-222	124	14	‖x	‖x	NOUN
ma-222	124	15	−	−	PROPN
ma-222	124	16	y‖2	y‖2	PRON
ma-222	124	17	≥	≥	PROPN
ma-222	124	18	‖x‖2	‖x‖2	VERB
ma-222	125	1	+	+	CCONJ
ma-222	125	2	‖y‖2	‖y‖2	PROPN
ma-222	125	3	.	.	PUNCT
ma-222	126	1	then	then	ADV
ma-222	126	2	,	,	PUNCT
ma-222	126	3	x	x	PROPN
ma-222	126	4	⊥i	⊥i	PROPN
ma-222	126	5	y	y	PROPN
ma-222	126	6	implies	imply	VERB
ma-222	126	7	‖x	‖x	NOUN
ma-222	127	1	+	+	PUNCT
ma-222	127	2	y‖2	y‖2	X
ma-222	127	3	+	+	CCONJ
ma-222	127	4	‖x	‖x	NOUN
ma-222	127	5	−	−	PROPN
ma-222	127	6	y‖2	y‖2	X
ma-222	127	7	≥	≥	NOUN
ma-222	127	8	2‖x‖2	2‖x‖2	NUM
ma-222	128	1	+	+	CCONJ
ma-222	128	2	2‖y‖2	2‖y‖2	NOUN
ma-222	128	3	for	for	ADP
ma-222	128	4	all	all	DET
ma-222	128	5	x	x	NOUN
ma-222	128	6	,	,	PUNCT
ma-222	128	7	y	y	PROPN
ma-222	128	8	∈	∈	PROPN
ma-222	128	9	x	x	INTJ
ma-222	128	10	,	,	PUNCT
ma-222	128	11	hence	hence	ADV
ma-222	128	12	we	we	PRON
ma-222	128	13	can	can	AUX
ma-222	128	14	assert	assert	VERB
ma-222	128	15	that	that	SCONJ
ma-222	128	16	x	x	PRON
ma-222	128	17	is	be	AUX
ma-222	128	18	a	a	DET
ma-222	128	19	hilbert	hilbert	NOUN
ma-222	128	20	space	space	NOUN
ma-222	128	21	.	.	PUNCT
ma-222	129	1	�	�	PROPN
ma-222	129	2	among	among	ADP
ma-222	129	3	the	the	DET
ma-222	129	4	many	many	ADJ
ma-222	129	5	properties	property	NOUN
ma-222	129	6	of	of	ADP
ma-222	129	7	banach	banach	NOUN
ma-222	129	8	spaces	space	NOUN
ma-222	129	9	,	,	PUNCT
ma-222	129	10	we	we	PRON
ma-222	129	11	give	give	VERB
ma-222	129	12	below	below	ADP
ma-222	129	13	a	a	DET
ma-222	129	14	sufficient	sufficient	ADJ
ma-222	129	15	condition	condition	NOUN
ma-222	129	16	that	that	SCONJ
ma-222	129	17	x	x	PRON
ma-222	129	18	is	be	AUX
ma-222	129	19	nota	nota	PROPN
ma-222	129	20	uniform	uniform	ADJ
ma-222	129	21	non	non	ADJ
ma-222	129	22	-	-	ADJ
ma-222	129	23	square	square	ADJ
ma-222	129	24	space	space	NOUN
ma-222	129	25	.	.	PUNCT
ma-222	130	1	in	in	ADP
ma-222	130	2	the	the	DET
ma-222	130	3	process	process	NOUN
ma-222	130	4	of	of	ADP
ma-222	130	5	proving	proving	NOUN
ma-222	130	6	,	,	PUNCT
ma-222	130	7	we	we	PRON
ma-222	130	8	apply	apply	VERB
ma-222	130	9	the	the	DET
ma-222	130	10	lemma	lemma	PROPN
ma-222	130	11	given	give	VERB
ma-222	130	12	by	by	ADP
ma-222	130	13	james	james	PROPN
ma-222	130	14	.	.	PUNCT
ma-222	131	1	lemma	lemma	PROPN
ma-222	131	2	2.1	2.1	NUM
ma-222	131	3	.	.	PUNCT
ma-222	132	1	[	[	X
ma-222	132	2	8	8	NUM
ma-222	132	3	,	,	PUNCT
ma-222	132	4	lemma	lemma	PROPN
ma-222	132	5	4.1	4.1	NUM
ma-222	132	6	]	]	PUNCT
ma-222	132	7	let	let	VERB
ma-222	132	8	x	x	PRON
ma-222	132	9	be	be	AUX
ma-222	132	10	a	a	DET
ma-222	132	11	banach	banach	NOUN
ma-222	132	12	space	space	NOUN
ma-222	132	13	and	and	CCONJ
ma-222	132	14	x	x	NOUN
ma-222	132	15	,	,	PUNCT
ma-222	132	16	y	y	PROPN
ma-222	132	17	∈	∈	PROPN
ma-222	132	18	x	x	INTJ
ma-222	132	19	.	.	PUNCT
ma-222	133	1	if	if	SCONJ
ma-222	133	2	x	x	SYM
ma-222	133	3	⊥i	⊥i	PROPN
ma-222	133	4	y	y	PROPN
ma-222	133	5	,	,	PUNCT
ma-222	133	6	then	then	ADV
ma-222	133	7	the	the	DET
ma-222	133	8	following	follow	VERB
ma-222	133	9	inequality	inequality	NOUN
ma-222	133	10	holds	hold	VERB
ma-222	133	11	.	.	PUNCT
ma-222	134	1	(	(	PUNCT
ma-222	134	2	i	i	NOUN
ma-222	134	3	)	)	PUNCT
ma-222	134	4	‖x	‖x	PUNCT
ma-222	135	1	+	+	CCONJ
ma-222	136	1	ky‖	ky‖	VERB
ma-222	136	2	≤	≤	ADJ
ma-222	136	3	|k	|k	NOUN
ma-222	136	4	|‖x	|‖x	PROPN
ma-222	136	5	±	±	NUM
ma-222	136	6	y‖	y‖	PROPN
ma-222	136	7	and	and	CCONJ
ma-222	136	8	‖x	‖x	NOUN
ma-222	136	9	±	±	NUM
ma-222	136	10	y‖	y‖	PROPN
ma-222	136	11	≤	≤	NUM
ma-222	136	12	‖x	‖x	PUNCT
ma-222	137	1	+	+	CCONJ
ma-222	137	2	ky‖	ky‖	PROPN
ma-222	137	3	,	,	PUNCT
ma-222	137	4	when	when	SCONJ
ma-222	137	5	|k	|k	NOUN
ma-222	137	6	|	|	ADV
ma-222	137	7	≥	≥	NOUN
ma-222	137	8	1	1	NUM
ma-222	137	9	.	.	PUNCT
ma-222	137	10	(	(	PUNCT
ma-222	137	11	ii	ii	NOUN
ma-222	137	12	)	)	PUNCT
ma-222	137	13	‖x	‖x	PUNCT
ma-222	138	1	+	+	CCONJ
ma-222	139	1	ky‖	ky‖	VERB
ma-222	139	2	≤	≤	NUM
ma-222	139	3	‖x	‖x	NOUN
ma-222	139	4	±	±	NUM
ma-222	139	5	y‖	y‖	PROPN
ma-222	139	6	and	and	CCONJ
ma-222	139	7	|k	|k	NOUN
ma-222	139	8	|‖x	|‖x	PROPN
ma-222	139	9	±	±	NUM
ma-222	139	10	y‖	y‖	PROPN
ma-222	139	11	≤	≤	NUM
ma-222	139	12	‖x	‖x	PUNCT
ma-222	140	1	+	+	CCONJ
ma-222	140	2	ky‖	ky‖	PROPN
ma-222	140	3	,	,	PUNCT
ma-222	140	4	when	when	SCONJ
ma-222	140	5	|k	|k	NOUN
ma-222	140	6	|	|	ADV
ma-222	140	7	≤	≤	NUM
ma-222	140	8	1	1	NUM
ma-222	140	9	.	.	PUNCT
ma-222	141	1	proposition	proposition	NOUN
ma-222	141	2	2.3	2.3	NUM
ma-222	141	3	.	.	PUNCT
ma-222	142	1	let	let	VERB
ma-222	142	2	x	x	PRON
ma-222	142	3	be	be	AUX
ma-222	142	4	a	a	DET
ma-222	142	5	finite	finite	ADJ
ma-222	142	6	dimensional	dimensional	ADJ
ma-222	142	7	banach	banach	NOUN
ma-222	142	8	space	space	NOUN
ma-222	142	9	,	,	PUNCT
ma-222	142	10	if	if	SCONJ
ma-222	142	11	lα	lα	ADJ
ma-222	142	12	,	,	PUNCT
ma-222	142	13	β(x	β(x	NOUN
ma-222	142	14	)	)	PUNCT
ma-222	142	15	=	=	SYM
ma-222	142	16	2	2	NUM
ma-222	142	17	1+β2	1+β2	NUM
ma-222	142	18	for	for	ADP
ma-222	142	19	some	some	DET
ma-222	142	20	0	0	NUM
ma-222	142	21	≤	≤	NOUN
ma-222	142	22	β0	β0	ADJ
ma-222	142	23	≤	≤	PUNCT
ma-222	143	1	α0	α0	ADJ
ma-222	143	2	<	<	X
ma-222	143	3	1	1	NUM
ma-222	143	4	,	,	PUNCT
ma-222	143	5	then	then	ADV
ma-222	143	6	x	x	PUNCT
ma-222	143	7	is	be	AUX
ma-222	143	8	not	not	PART
ma-222	143	9	uniformly	uniformly	ADV
ma-222	143	10	non	non	ADJ
ma-222	143	11	-	-	ADJ
ma-222	143	12	square	square	ADJ
ma-222	143	13	.	.	PUNCT
ma-222	144	1	proof	proof	NOUN
ma-222	144	2	.	.	PUNCT
ma-222	145	1	since	since	SCONJ
ma-222	145	2	lα	lα	NOUN
ma-222	145	3	,	,	PUNCT
ma-222	145	4	β(x	β(x	NOUN
ma-222	145	5	)	)	PUNCT
ma-222	145	6	=	=	SYM
ma-222	145	7	2	2	NUM
ma-222	145	8	1+β2	1+β2	NOUN
ma-222	145	9	,	,	PUNCT
ma-222	145	10	there	there	PRON
ma-222	145	11	exist	exist	VERB
ma-222	145	12	xn	xn	PROPN
ma-222	145	13	∈	∈	PROPN
ma-222	145	14	sx	sx	PROPN
ma-222	145	15	,	,	PUNCT
ma-222	145	16	yn	yn	PROPN
ma-222	145	17	∈	∈	PROPN
ma-222	145	18	bx	bx	NOUN
ma-222	145	19	that	that	PRON
ma-222	145	20	satisfy	satisfy	VERB
ma-222	145	21	xn	xn	PROPN
ma-222	145	22	⊥i	⊥i	PROPN
ma-222	145	23	yn	yn	PROPN
ma-222	145	24	and	and	CCONJ
ma-222	145	25	lim	lim	PROPN
ma-222	145	26	n→∞	n→∞	X
ma-222	146	1	‖xn	‖xn	PROPN
ma-222	146	2	−	−	PROPN
ma-222	146	3	βyn‖2	βyn‖2	PUNCT
ma-222	147	1	+	+	CCONJ
ma-222	147	2	‖αxn	‖αxn	ADP
ma-222	147	3	−	−	PROPN
ma-222	147	4	yn‖2	yn‖2	PROPN
ma-222	147	5	‖xn	‖xn	PROPN
ma-222	147	6	−	−	PUNCT
ma-222	147	7	yn‖2	yn‖2	PROPN
ma-222	147	8	+	+	SYM
ma-222	147	9	‖αxn	‖αxn	PROPN
ma-222	147	10	−	−	PROPN
ma-222	147	11	βyn‖2	βyn‖2	PUNCT
ma-222	147	12	=	=	SYM
ma-222	147	13	2	2	NUM
ma-222	147	14	1	1	NUM
ma-222	147	15	+	+	CCONJ
ma-222	147	16	β2	β2	NOUN
ma-222	147	17	.	.	PUNCT
ma-222	148	1	https://doi.org/10.28924/ada/ma.4.6	https://doi.org/10.28924/ada/ma.4.6	PROPN
ma-222	148	2	eur	eur	PROPN
ma-222	148	3	.	.	PUNCT
ma-222	149	1	j.	j.	PROPN
ma-222	149	2	math	math	PROPN
ma-222	149	3	.	.	PUNCT
ma-222	150	1	anal	anal	PROPN
ma-222	150	2	.	.	PUNCT
ma-222	151	1	10.28924	10.28924	NUM
ma-222	151	2	/	/	SYM
ma-222	151	3	ada	ada	PROPN
ma-222	151	4	/	/	SYM
ma-222	151	5	ma.4.6	ma.4.6	NOUN
ma-222	151	6	5at	5at	NOUN
ma-222	151	7	the	the	DET
ma-222	151	8	same	same	ADJ
ma-222	151	9	time	time	NOUN
ma-222	151	10	,	,	PUNCT
ma-222	151	11	a	a	DET
ma-222	151	12	banach	banach	NOUN
ma-222	151	13	space	space	NOUN
ma-222	151	14	x	x	VERB
ma-222	151	15	is	be	AUX
ma-222	151	16	finite	finite	ADJ
ma-222	151	17	dimensional	dimensional	ADJ
ma-222	151	18	,	,	PUNCT
ma-222	151	19	then	then	ADV
ma-222	151	20	there	there	PRON
ma-222	151	21	exist	exist	VERB
ma-222	151	22	x0	x0	PROPN
ma-222	151	23	,	,	PUNCT
ma-222	151	24	y0	y0	PROPN
ma-222	151	25	∈	∈	NOUN
ma-222	151	26	bx	bx	NOUN
ma-222	151	27	that	that	PRON
ma-222	151	28	satisfy	satisfy	VERB
ma-222	151	29	x0	x0	PROPN
ma-222	151	30	⊥i	⊥i	PROPN
ma-222	151	31	y0	y0	PROPN
ma-222	151	32	and	and	CCONJ
ma-222	151	33	lim	lim	PROPN
ma-222	151	34	k→∞	k→∞	NOUN
ma-222	151	35	∥∥xnk∥∥	∥∥xnk∥∥	NOUN
ma-222	151	36	=	=	SYM
ma-222	151	37	‖x0‖	‖x0‖	PROPN
ma-222	151	38	,	,	PUNCT
ma-222	151	39	lim	lim	PROPN
ma-222	151	40	k→∞	k→∞	PROPN
ma-222	151	41	∥∥ynk∥∥	∥∥ynk∥∥	NOUN
ma-222	151	42	=	=	SYM
ma-222	151	43	‖y0‖	‖y0‖	PROPN
ma-222	151	44	.	.	PUNCT
ma-222	152	1	combine	combine	VERB
ma-222	152	2	lemma	lemma	PROPN
ma-222	152	3	2.1	2.1	NUM
ma-222	152	4	,	,	PUNCT
ma-222	152	5	we	we	PRON
ma-222	152	6	have	have	VERB
ma-222	152	7	‖xn	‖xn	PROPN
ma-222	152	8	−	−	PROPN
ma-222	152	9	β0yn‖	β0yn‖	NOUN
ma-222	152	10	≤	≤	PUNCT
ma-222	152	11	‖xn	‖xn	PUNCT
ma-222	152	12	+	+	CCONJ
ma-222	152	13	yn‖	yn‖	NOUN
ma-222	152	14	and	and	CCONJ
ma-222	152	15	‖α0xn	‖α0xn	PROPN
ma-222	153	1	−	−	PROPN
ma-222	154	1	yn‖	yn‖	NOUN
ma-222	154	2	≤	≤	PROPN
ma-222	154	3	‖xn	‖xn	PROPN
ma-222	154	4	+	+	NUM
ma-222	154	5	yn‖.thus	yn‖.thus	NOUN
ma-222	154	6	,	,	PUNCT
ma-222	154	7	‖xn	‖xn	PROPN
ma-222	154	8	+	+	CCONJ
ma-222	154	9	yn‖2	yn‖2	PROPN
ma-222	154	10	+	+	SYM
ma-222	154	11	‖xn	‖xn	PROPN
ma-222	154	12	+	+	CCONJ
ma-222	154	13	yn‖2	yn‖2	PROPN
ma-222	154	14	‖xn	‖xn	PROPN
ma-222	154	15	+	+	CCONJ
ma-222	154	16	yn‖2	yn‖2	PROPN
ma-222	154	17	+	+	CCONJ
ma-222	154	18	(	(	PUNCT
ma-222	154	19	∣∣∣α−β2	∣∣∣α−β2	ADJ
ma-222	154	20	∣∣∣−	∣∣∣−	PROPN
ma-222	154	21	∣∣∣α+β2	∣∣∣α+β2	PROPN
ma-222	154	22	∣∣∣)2‖xn	∣∣∣)2‖xn	PROPN
ma-222	154	23	+	+	CCONJ
ma-222	154	24	yn‖2	yn‖2	PROPN
ma-222	154	25	≤	≤	ADJ
ma-222	154	26	2	2	NUM
ma-222	154	27	1	1	NUM
ma-222	154	28	+	+	CCONJ
ma-222	154	29	β2	β2	NOUN
ma-222	154	30	,	,	PUNCT
ma-222	154	31	‖xn	‖xn	PROPN
ma-222	154	32	+	+	CCONJ
ma-222	154	33	yn‖2	yn‖2	PROPN
ma-222	154	34	+	+	SYM
ma-222	154	35	‖xn	‖xn	PROPN
ma-222	154	36	+	+	CCONJ
ma-222	154	37	yn‖2	yn‖2	PROPN
ma-222	154	38	(	(	PUNCT
ma-222	154	39	1	1	NUM
ma-222	154	40	+	+	CCONJ
ma-222	154	41	β2	β2	NOUN
ma-222	154	42	)	)	PUNCT
ma-222	155	1	‖xn	‖xn	PROPN
ma-222	155	2	+	+	PUNCT
ma-222	155	3	yn‖2	yn‖2	PROPN
ma-222	155	4	≤	≤	ADJ
ma-222	155	5	2	2	NUM
ma-222	155	6	1	1	NUM
ma-222	155	7	+	+	CCONJ
ma-222	155	8	β2	β2	NOUN
ma-222	155	9	.	.	PUNCT
ma-222	156	1	we	we	PRON
ma-222	156	2	can	can	AUX
ma-222	156	3	obtain	obtain	VERB
ma-222	156	4	‖x0	‖x0	ADJ
ma-222	156	5	−	−	NOUN
ma-222	156	6	β0y0‖	β0y0‖	PUNCT
ma-222	156	7	=	=	PUNCT
ma-222	157	1	‖x0	‖x0	PROPN
ma-222	158	1	+	+	NUM
ma-222	158	2	y0‖	y0‖	PROPN
ma-222	158	3	and	and	CCONJ
ma-222	158	4	‖α0x0	‖α0x0	NOUN
ma-222	158	5	−	−	PROPN
ma-222	159	1	y0‖	y0‖	NOUN
ma-222	159	2	=	=	SYM
ma-222	159	3	‖x0	‖x0	PROPN
ma-222	160	1	+	+	X
ma-222	160	2	y0‖.	y0‖.	NOUN
ma-222	160	3	since	since	SCONJ
ma-222	160	4	‖x0	‖x0	ADJ
ma-222	160	5	−	−	PROPN
ma-222	160	6	β0y0‖	β0y0‖	SYM
ma-222	160	7	≤	≤	NUM
ma-222	160	8	(	(	PUNCT
ma-222	160	9	1−	1−	NUM
ma-222	160	10	β0	β0	NOUN
ma-222	160	11	)	)	PUNCT
ma-222	161	1	‖x0‖+β0	‖x0‖+β0	PROPN
ma-222	161	2	‖x0	‖x0	PROPN
ma-222	162	1	+	+	CCONJ
ma-222	162	2	y0‖	y0‖	PROPN
ma-222	162	3	,	,	PUNCT
ma-222	162	4	then	then	ADV
ma-222	162	5	‖x0	‖x0	PROPN
ma-222	163	1	+	+	NUM
ma-222	163	2	y0‖	y0‖	PROPN
ma-222	163	3	≤	≤	NOUN
ma-222	163	4	‖x0‖.	‖x0‖.	ADV
ma-222	163	5	moreover	moreover	ADV
ma-222	163	6	,	,	PUNCT
ma-222	163	7	we	we	PRON
ma-222	163	8	can	can	AUX
ma-222	163	9	prove	prove	VERB
ma-222	163	10	that	that	SCONJ
ma-222	163	11	‖x0	‖x0	PROPN
ma-222	164	1	+	+	NUM
ma-222	164	2	y0‖	y0‖	PROPN
ma-222	164	3	≤	≤	NUM
ma-222	164	4	‖y0‖,then	‖y0‖,then	SCONJ
ma-222	164	5	max	max	PROPN
ma-222	164	6	{	{	PUNCT
ma-222	164	7	‖x0	‖x0	PROPN
ma-222	164	8	+	+	X
ma-222	164	9	y0‖	y0‖	PROPN
ma-222	164	10	,	,	PUNCT
ma-222	164	11	‖x0	‖x0	PROPN
ma-222	164	12	−	−	PROPN
ma-222	165	1	y0‖	y0‖	PROPN
ma-222	165	2	}	}	PUNCT
ma-222	165	3	=	=	PUNCT
ma-222	166	1	‖x0	‖x0	PROPN
ma-222	167	1	+	+	NUM
ma-222	167	2	y0‖	y0‖	PROPN
ma-222	167	3	≤	≤	NUM
ma-222	167	4	min	min	NOUN
ma-222	167	5	{	{	PUNCT
ma-222	167	6	‖x0‖	‖x0‖	PROPN
ma-222	167	7	,	,	PUNCT
ma-222	167	8	‖y0‖	‖y0‖	NOUN
ma-222	167	9	}	}	PUNCT
ma-222	167	10	≤	≤	NOUN
ma-222	167	11	1	1	NUM
ma-222	167	12	<	<	SYM
ma-222	167	13	1	1	NUM
ma-222	167	14	+	+	CCONJ
ma-222	167	15	δ	δ	PROPN
ma-222	167	16	for	for	ADP
ma-222	167	17	any	any	DET
ma-222	167	18	δ	δ	PROPN
ma-222	167	19	∈	∈	PROPN
ma-222	167	20	(	(	PUNCT
ma-222	167	21	0	0	NUM
ma-222	167	22	,	,	PUNCT
ma-222	167	23	1	1	NUM
ma-222	167	24	)	)	PUNCT
ma-222	167	25	,	,	PUNCT
ma-222	167	26	this	this	PRON
ma-222	167	27	means	mean	VERB
ma-222	167	28	that	that	SCONJ
ma-222	167	29	x	x	PRON
ma-222	167	30	is	be	AUX
ma-222	167	31	not	not	PART
ma-222	167	32	uniformly	uniformly	ADV
ma-222	167	33	non	non	ADJ
ma-222	167	34	-	-	ADJ
ma-222	167	35	square	square	ADJ
ma-222	167	36	.	.	PUNCT
ma-222	168	1	�	�	PROPN
ma-222	168	2	3	3	NUM
ma-222	168	3	.	.	PUNCT
ma-222	169	1	the	the	DET
ma-222	169	2	constant	constant	ADJ
ma-222	169	3	l′α	l′α	NOUN
ma-222	169	4	,	,	PUNCT
ma-222	169	5	β(x)in	β(x)in	INTJ
ma-222	169	6	this	this	DET
ma-222	169	7	section	section	NOUN
ma-222	169	8	,	,	PUNCT
ma-222	169	9	if	if	SCONJ
ma-222	169	10	x	x	PRON
ma-222	169	11	and	and	CCONJ
ma-222	169	12	y	y	PROPN
ma-222	169	13	satisfy	satisfy	VERB
ma-222	169	14	the	the	DET
ma-222	169	15	isosceles	isoscele	NOUN
ma-222	169	16	orthogonality	orthogonality	NOUN
ma-222	169	17	condition	condition	NOUN
ma-222	169	18	and	and	CCONJ
ma-222	169	19	restrict	restrict	VERB
ma-222	169	20	x	x	PUNCT
ma-222	169	21	,	,	PUNCT
ma-222	169	22	y	y	PROPN
ma-222	169	23	∈	∈	PROPN
ma-222	169	24	sx	sx	PROPN
ma-222	169	25	,	,	PUNCT
ma-222	169	26	then	then	ADV
ma-222	169	27	we	we	PRON
ma-222	169	28	define	define	VERB
ma-222	169	29	the	the	DET
ma-222	169	30	new	new	ADJ
ma-222	169	31	constant	constant	ADJ
ma-222	169	32	:	:	PUNCT
ma-222	169	33	definition	definition	NOUN
ma-222	169	34	3.1	3.1	NUM
ma-222	169	35	.	.	PUNCT
ma-222	170	1	let	let	VERB
ma-222	170	2	x	x	PRON
ma-222	170	3	be	be	AUX
ma-222	170	4	a	a	DET
ma-222	170	5	banach	banach	NOUN
ma-222	170	6	space	space	NOUN
ma-222	170	7	,	,	PUNCT
ma-222	170	8	another	another	DET
ma-222	170	9	geometric	geometric	ADJ
ma-222	170	10	constant	constant	NOUN
ma-222	170	11	of	of	ADP
ma-222	170	12	the	the	DET
ma-222	170	13	isosceles	isoscele	NOUN
ma-222	170	14	orthogonal	orthogonal	ADJ
ma-222	170	15	type	type	NOUN
ma-222	170	16	is	be	AUX
ma-222	170	17	defined	define	VERB
ma-222	170	18	as	as	ADP
ma-222	170	19	l′α	l′α	ADJ
ma-222	170	20	,	,	PUNCT
ma-222	170	21	β(x	β(x	NOUN
ma-222	170	22	)	)	PUNCT
ma-222	170	23	=	=	SYM
ma-222	170	24	sup	sup	NOUN
ma-222	170	25	{	{	PUNCT
ma-222	170	26	‖x	‖x	NOUN
ma-222	170	27	−	−	PROPN
ma-222	171	1	βy‖2	βy‖2	PROPN
ma-222	171	2	+	+	CCONJ
ma-222	171	3	‖αx	‖αx	NUM
ma-222	171	4	−	−	PROPN
ma-222	171	5	y‖2	y‖2	X
ma-222	171	6	‖x	‖x	NOUN
ma-222	171	7	−	−	PROPN
ma-222	171	8	y‖2	y‖2	PROPN
ma-222	171	9	+	+	CCONJ
ma-222	171	10	‖αx	‖αx	NUM
ma-222	171	11	−	−	NOUN
ma-222	171	12	βy‖2	βy‖2	NOUN
ma-222	171	13	:	:	PUNCT
ma-222	171	14	x	x	X
ma-222	171	15	,	,	PUNCT
ma-222	171	16	y	y	PROPN
ma-222	171	17	∈	∈	PROPN
ma-222	171	18	sx	sx	PROPN
ma-222	171	19	,	,	PUNCT
ma-222	171	20	x	x	PROPN
ma-222	171	21	⊥i	⊥i	PROPN
ma-222	171	22	y	y	PROPN
ma-222	171	23	}	}	PUNCT
ma-222	171	24	,	,	PUNCT
ma-222	171	25	where	where	SCONJ
ma-222	171	26	α	α	X
ma-222	171	27	,	,	PUNCT
ma-222	171	28	β	β	X
ma-222	171	29	≥	≥	NOUN
ma-222	171	30	0	0	NUM
ma-222	171	31	,	,	PUNCT
ma-222	171	32	α	α	PROPN
ma-222	171	33	6=	6=	ADP
ma-222	171	34	1	1	NUM
ma-222	171	35	,	,	PUNCT
ma-222	171	36	β	β	X
ma-222	171	37	6=	6=	ADP
ma-222	171	38	1	1	X
ma-222	171	39	.	.	PUNCT
ma-222	172	1	we	we	PRON
ma-222	172	2	give	give	VERB
ma-222	172	3	bounds	bound	NOUN
ma-222	172	4	on	on	ADP
ma-222	172	5	the	the	DET
ma-222	172	6	constant	constant	ADJ
ma-222	172	7	l′α	l′α	NOUN
ma-222	172	8	,	,	PUNCT
ma-222	172	9	β(x	β(x	NOUN
ma-222	172	10	)	)	PUNCT
ma-222	172	11	and	and	CCONJ
ma-222	172	12	calculate	calculate	VERB
ma-222	172	13	its	its	PRON
ma-222	172	14	value	value	NOUN
ma-222	172	15	in	in	ADP
ma-222	172	16	`	`	PUNCT
ma-222	172	17	∞−	∞−	X
ma-222	172	18	`	`	PUNCT
ma-222	172	19	1	1	NUM
ma-222	172	20	normed	norme	VERB
ma-222	172	21	linear	linear	PROPN
ma-222	172	22	spacewhen	spacewhen	PROPN
ma-222	172	23	α	α	X
ma-222	172	24	=	=	PUNCT
ma-222	172	25	β	β	X
ma-222	172	26	=	=	SYM
ma-222	172	27	1	1	NUM
ma-222	172	28	2	2	NUM
ma-222	172	29	.	.	PUNCT
ma-222	172	30	proposition	proposition	NOUN
ma-222	172	31	3.1	3.1	NUM
ma-222	172	32	.	.	PUNCT
ma-222	173	1	let	let	VERB
ma-222	173	2	x	x	PRON
ma-222	173	3	be	be	AUX
ma-222	173	4	a	a	DET
ma-222	173	5	banach	banach	NOUN
ma-222	173	6	space	space	NOUN
ma-222	173	7	,	,	PUNCT
ma-222	173	8	then	then	PROPN
ma-222	173	9	α2+β2	α2+β2	PROPN
ma-222	173	10	1+α2	1+α2	NUM
ma-222	173	11	α2+β2	α2+β2	PROPN
ma-222	173	12	1+β2	1+β2	NUM
ma-222	173	13	2	2	NUM
ma-222	173	14	1+α2	1+α2	NUM
ma-222	173	15	2	2	NUM
ma-222	173	16	1+β2	1+β2	NUM
ma-222	173	17	≤	≤	NOUN
ma-222	173	18	l′α	l′α	ADP
ma-222	173	19	,	,	PUNCT
ma-222	173	20	β(x	β(x	NOUN
ma-222	173	21	)	)	PUNCT
ma-222	173	22	≤	≤	NUM
ma-222	173	23			NUM
ma-222	173	24	2	2	NUM
ma-222	173	25	1+β2	1+β2	NOUN
ma-222	173	26	,	,	PUNCT
ma-222	173	27	0	0	NUM
ma-222	173	28	≤	≤	NUM
ma-222	174	1	β	β	NOUN
ma-222	174	2	≤	≤	NUM
ma-222	174	3	α	α	PRON
ma-222	174	4	<	<	X
ma-222	174	5	1	1	NUM
ma-222	174	6	;	;	PUNCT
ma-222	174	7	2	2	NUM
ma-222	174	8	1+α2	1+α2	NUM
ma-222	174	9	,	,	PUNCT
ma-222	174	10	0	0	NUM
ma-222	174	11	≤	≤	NUM
ma-222	174	12	α	α	NOUN
ma-222	174	13	≤	≤	NOUN
ma-222	174	14	β	β	X
ma-222	174	15	<	<	X
ma-222	174	16	1	1	NUM
ma-222	174	17	;	;	PUNCT
ma-222	174	18	α2+β2	α2+β2	PROPN
ma-222	174	19	1+β2	1+β2	NUM
ma-222	174	20	,	,	PUNCT
ma-222	174	21	1	1	NUM
ma-222	174	22	<	<	X
ma-222	174	23	β	β	X
ma-222	174	24	≤	≤	NUM
ma-222	174	25	α	α	NOUN
ma-222	174	26	;	;	PUNCT
ma-222	174	27	α2+β2	α2+β2	NUM
ma-222	174	28	1+α2	1+α2	NUM
ma-222	174	29	,	,	PUNCT
ma-222	174	30	1	1	NUM
ma-222	174	31	<	<	X
ma-222	174	32	α	α	X
ma-222	174	33	≤	≤	PUNCT
ma-222	174	34	β	β	X
ma-222	174	35	.	.	PUNCT
ma-222	175	1	https://doi.org/10.28924/ada/ma.4.6	https://doi.org/10.28924/ada/ma.4.6	PROPN
ma-222	175	2	eur	eur	PROPN
ma-222	175	3	.	.	PUNCT
ma-222	176	1	j.	j.	PROPN
ma-222	176	2	math	math	PROPN
ma-222	176	3	.	.	PUNCT
ma-222	177	1	anal	anal	PROPN
ma-222	177	2	.	.	PUNCT
ma-222	178	1	10.28924	10.28924	NUM
ma-222	178	2	/	/	SYM
ma-222	178	3	ada	ada	PROPN
ma-222	178	4	/	/	SYM
ma-222	178	5	ma.4.6	ma.4.6	NOUN
ma-222	178	6	6	6	NUM
ma-222	178	7	proof	proof	NOUN
ma-222	178	8	.	.	PUNCT
ma-222	179	1	combined	combine	VERB
ma-222	179	2	with	with	ADP
ma-222	179	3	the	the	DET
ma-222	179	4	idea	idea	NOUN
ma-222	179	5	of	of	ADP
ma-222	179	6	proposition	proposition	NOUN
ma-222	179	7	2.1	2.1	NUM
ma-222	179	8	,	,	PUNCT
ma-222	179	9	we	we	PRON
ma-222	179	10	have	have	VERB
ma-222	179	11	‖x	‖x	NOUN
ma-222	179	12	−	−	PUNCT
ma-222	180	1	βy‖2	βy‖2	PROPN
ma-222	180	2	+	+	CCONJ
ma-222	180	3	‖αx	‖αx	NUM
ma-222	180	4	−	−	PROPN
ma-222	180	5	y‖2	y‖2	X
ma-222	180	6	‖x	‖x	NOUN
ma-222	180	7	−	−	PROPN
ma-222	180	8	y‖2	y‖2	PROPN
ma-222	180	9	+	+	CCONJ
ma-222	180	10	‖αx	‖αx	PROPN
ma-222	180	11	−	−	PROPN
ma-222	180	12	βy‖2	βy‖2	NOUN
ma-222	180	13	≥	≥	NOUN
ma-222	180	14	(	(	PUNCT
ma-222	180	15	∣∣∣1−β2	∣∣∣1−β2	PROPN
ma-222	180	16	∣∣∣	∣∣∣	NOUN
ma-222	180	17	‖x	‖x	PROPN
ma-222	181	1	+	+	CCONJ
ma-222	181	2	y‖	y‖	PROPN
ma-222	181	3	−	−	PROPN
ma-222	181	4	∣∣∣1+β2	∣∣∣1+β2	PROPN
ma-222	181	5	∣∣∣	∣∣∣	PROPN
ma-222	181	6	‖x	‖x	PROPN
ma-222	182	1	−	−	PROPN
ma-222	182	2	y‖)2	y‖)2	PROPN
ma-222	182	3	+	+	CCONJ
ma-222	182	4	(	(	PUNCT
ma-222	182	5	∣∣α−12	∣∣α−12	X
ma-222	182	6	∣∣	∣∣	NUM
ma-222	182	7	‖x	‖x	X
ma-222	183	1	+	+	CCONJ
ma-222	183	2	y‖	y‖	PROPN
ma-222	183	3	−	−	ADP
ma-222	183	4	∣∣α+12	∣∣α+12	NOUN
ma-222	183	5	∣∣	∣∣	NUM
ma-222	183	6	‖x	‖x	PUNCT
ma-222	184	1	−	−	PROPN
ma-222	184	2	y‖)2	y‖)2	PROPN
ma-222	184	3	‖x	‖x	NOUN
ma-222	185	1	−	−	PROPN
ma-222	186	1	y‖2	y‖2	X
ma-222	186	2	+	+	CCONJ
ma-222	186	3	(	(	PUNCT
ma-222	186	4	∣∣∣α−β2	∣∣∣α−β2	ADJ
ma-222	186	5	∣∣∣	∣∣∣	NOUN
ma-222	186	6	‖x	‖x	NOUN
ma-222	187	1	+	+	CCONJ
ma-222	187	2	y‖+	y‖+	PROPN
ma-222	187	3	∣∣∣α+β2	∣∣∣α+β2	PROPN
ma-222	187	4	∣∣∣	∣∣∣	PROPN
ma-222	187	5	‖x	‖x	PROPN
ma-222	188	1	−	−	PROPN
ma-222	188	2	y‖)2	y‖)2	PROPN
ma-222	188	3	.	.	PUNCT
ma-222	189	1	case	case	NOUN
ma-222	189	2	1	1	NUM
ma-222	190	1	when	when	SCONJ
ma-222	190	2	0	0	NUM
ma-222	190	3	≤	≤	NUM
ma-222	190	4	β	β	NOUN
ma-222	190	5	≤	≤	NUM
ma-222	190	6	α	α	PRON
ma-222	190	7	<	<	X
ma-222	190	8	1	1	NUM
ma-222	190	9	,	,	PUNCT
ma-222	190	10	we	we	PRON
ma-222	190	11	have	have	VERB
ma-222	190	12	‖x	‖x	NOUN
ma-222	190	13	−	−	PUNCT
ma-222	191	1	βy‖2	βy‖2	PROPN
ma-222	191	2	+	+	CCONJ
ma-222	191	3	‖αx	‖αx	NUM
ma-222	191	4	−	−	PROPN
ma-222	191	5	y‖2	y‖2	X
ma-222	191	6	‖x	‖x	NOUN
ma-222	191	7	−	−	PROPN
ma-222	191	8	y‖2	y‖2	PROPN
ma-222	191	9	+	+	CCONJ
ma-222	191	10	‖αx	‖αx	PROPN
ma-222	191	11	−	−	PROPN
ma-222	191	12	βy‖2	βy‖2	NOUN
ma-222	191	13	≥	≥	NOUN
ma-222	191	14	α2	α2	ADJ
ma-222	191	15	+	+	CCONJ
ma-222	191	16	β2	β2	VERB
ma-222	191	17	1	1	NUM
ma-222	191	18	+	+	CCONJ
ma-222	191	19	α2	α2	ADJ
ma-222	191	20	.	.	PUNCT
ma-222	192	1	case	case	NOUN
ma-222	192	2	2	2	NUM
ma-222	192	3	when	when	SCONJ
ma-222	192	4	0	0	NUM
ma-222	192	5	≤	≤	NUM
ma-222	192	6	α	α	NOUN
ma-222	192	7	≤	≤	NOUN
ma-222	192	8	β	β	X
ma-222	192	9	<	<	X
ma-222	192	10	1	1	NUM
ma-222	192	11	,	,	PUNCT
ma-222	192	12	we	we	PRON
ma-222	192	13	have	have	VERB
ma-222	192	14	‖x	‖x	NOUN
ma-222	192	15	−	−	PUNCT
ma-222	193	1	βy‖2	βy‖2	PROPN
ma-222	193	2	+	+	CCONJ
ma-222	193	3	‖αx	‖αx	NUM
ma-222	193	4	−	−	PROPN
ma-222	193	5	y‖2	y‖2	X
ma-222	193	6	‖x	‖x	NOUN
ma-222	193	7	−	−	PROPN
ma-222	193	8	y‖2	y‖2	PROPN
ma-222	193	9	+	+	CCONJ
ma-222	193	10	‖αx	‖αx	PROPN
ma-222	193	11	−	−	PROPN
ma-222	193	12	βy‖2	βy‖2	NOUN
ma-222	193	13	≥	≥	NOUN
ma-222	193	14	α2	α2	ADJ
ma-222	194	1	+	+	CCONJ
ma-222	194	2	β2	β2	VERB
ma-222	194	3	1	1	NUM
ma-222	194	4	+	+	CCONJ
ma-222	194	5	β2	β2	NOUN
ma-222	194	6	.	.	PUNCT
ma-222	195	1	case	case	NOUN
ma-222	195	2	3	3	NUM
ma-222	196	1	when	when	SCONJ
ma-222	196	2	1	1	NUM
ma-222	196	3	<	<	X
ma-222	196	4	β	β	X
ma-222	196	5	≤	≤	NUM
ma-222	196	6	α	α	X
ma-222	196	7	,	,	PUNCT
ma-222	196	8	we	we	PRON
ma-222	196	9	have	have	VERB
ma-222	196	10	‖x	‖x	NOUN
ma-222	196	11	−	−	PUNCT
ma-222	197	1	βy‖2	βy‖2	PROPN
ma-222	197	2	+	+	CCONJ
ma-222	197	3	‖αx	‖αx	NUM
ma-222	197	4	−	−	PROPN
ma-222	197	5	y‖2	y‖2	X
ma-222	197	6	‖x	‖x	NOUN
ma-222	197	7	−	−	PROPN
ma-222	197	8	y‖2	y‖2	PROPN
ma-222	197	9	+	+	CCONJ
ma-222	197	10	‖αx	‖αx	PROPN
ma-222	197	11	−	−	NOUN
ma-222	197	12	βy‖2	βy‖2	NOUN
ma-222	197	13	≥	≥	NOUN
ma-222	197	14	2	2	NUM
ma-222	197	15	1	1	NUM
ma-222	197	16	+	+	CCONJ
ma-222	197	17	α2	α2	ADJ
ma-222	197	18	.	.	PUNCT
ma-222	198	1	case	case	NOUN
ma-222	198	2	4	4	NUM
ma-222	198	3	when	when	SCONJ
ma-222	198	4	1	1	NUM
ma-222	198	5	<	<	X
ma-222	198	6	α	α	X
ma-222	198	7	≤	≤	NOUN
ma-222	199	1	β	β	X
ma-222	199	2	,	,	PUNCT
ma-222	199	3	we	we	PRON
ma-222	199	4	have	have	VERB
ma-222	199	5	‖x	‖x	NOUN
ma-222	199	6	−	−	PUNCT
ma-222	200	1	βy‖2	βy‖2	PROPN
ma-222	200	2	+	+	CCONJ
ma-222	200	3	‖αx	‖αx	NUM
ma-222	200	4	−	−	PROPN
ma-222	200	5	y‖2	y‖2	X
ma-222	200	6	‖x	‖x	NOUN
ma-222	200	7	−	−	PROPN
ma-222	200	8	y‖2	y‖2	PROPN
ma-222	200	9	+	+	CCONJ
ma-222	200	10	‖αx	‖αx	PROPN
ma-222	200	11	−	−	NOUN
ma-222	200	12	βy‖2	βy‖2	NOUN
ma-222	200	13	≥	≥	NOUN
ma-222	200	14	2	2	NUM
ma-222	200	15	1	1	NUM
ma-222	200	16	+	+	CCONJ
ma-222	200	17	β2	β2	NOUN
ma-222	200	18	.	.	PUNCT
ma-222	201	1	on	on	ADP
ma-222	201	2	the	the	DET
ma-222	201	3	other	other	ADJ
ma-222	201	4	hand	hand	NOUN
ma-222	201	5	,	,	PUNCT
ma-222	201	6	the	the	DET
ma-222	201	7	upper	upper	ADJ
ma-222	201	8	bound	bind	VERB
ma-222	201	9	on	on	ADP
ma-222	201	10	the	the	DET
ma-222	201	11	constant	constant	ADJ
ma-222	201	12	l′α	l′α	NOUN
ma-222	201	13	,	,	PUNCT
ma-222	201	14	β(x	β(x	NOUN
ma-222	201	15	)	)	PUNCT
ma-222	201	16	is	be	AUX
ma-222	201	17	the	the	DET
ma-222	201	18	same	same	ADJ
ma-222	201	19	as	as	ADP
ma-222	201	20	the	the	DET
ma-222	201	21	upper	upper	ADJ
ma-222	201	22	bound	bound	ADJ
ma-222	201	23	onthe	onthe	NOUN
ma-222	201	24	constant	constant	ADJ
ma-222	201	25	lα	lα	NOUN
ma-222	201	26	,	,	PUNCT
ma-222	201	27	β(x	β(x	NOUN
ma-222	201	28	)	)	PUNCT
ma-222	201	29	.	.	PUNCT
ma-222	202	1	�	�	PROPN
ma-222	202	2	example	example	NOUN
ma-222	202	3	3.1	3.1	NUM
ma-222	202	4	.	.	PUNCT
ma-222	203	1	let	let	VERB
ma-222	203	2	α	α	NOUN
ma-222	203	3	=	=	PUNCT
ma-222	203	4	β	β	X
ma-222	203	5	=	=	SYM
ma-222	203	6	1	1	NUM
ma-222	203	7	2	2	NUM
ma-222	203	8	and	and	CCONJ
ma-222	203	9	x	x	AUX
ma-222	203	10	be	be	AUX
ma-222	203	11	the	the	DET
ma-222	203	12	space	space	NOUN
ma-222	203	13	r2	r2	NOUN
ma-222	203	14	with	with	ADP
ma-222	203	15	`	`	PUNCT
ma-222	203	16	∞	∞	NUM
ma-222	203	17	−	−	PROPN
ma-222	203	18	`	`	PUNCT
ma-222	203	19	1	1	NUM
ma-222	203	20	norm	norm	NOUN
ma-222	203	21	defined	define	VERB
ma-222	203	22	by	by	ADP
ma-222	203	23	‖x‖	‖x‖	PROPN
ma-222	203	24	=	=	SYM
ma-222	203	25	{	{	PUNCT
ma-222	203	26	‖x‖1	‖x‖1	NOUN
ma-222	203	27	,	,	PUNCT
ma-222	203	28	x1x2	x1x2	PUNCT
ma-222	203	29	≤	≤	ADV
ma-222	203	30	0	0	NUM
ma-222	203	31	,	,	PUNCT
ma-222	203	32	‖x‖∞	‖x‖∞	PROPN
ma-222	203	33	,	,	PUNCT
ma-222	203	34	x1x2	x1x2	X
ma-222	203	35	≥	≥	PROPN
ma-222	203	36	0	0	NUM
ma-222	203	37	.	.	PUNCT
ma-222	204	1	then	then	ADV
ma-222	204	2	l′1	l′1	VERB
ma-222	204	3	2	2	NUM
ma-222	204	4	,	,	PUNCT
ma-222	204	5	1	1	NUM
ma-222	204	6	2	2	NUM
ma-222	204	7	(	(	PUNCT
ma-222	204	8	x	x	NOUN
ma-222	204	9	)	)	PUNCT
ma-222	204	10	=	=	SYM
ma-222	204	11	0.91	0.91	NUM
ma-222	204	12	.	.	PUNCT
ma-222	205	1	proof	proof	NOUN
ma-222	205	2	.	.	PUNCT
ma-222	206	1	if	if	SCONJ
ma-222	206	2	x	x	PRON
ma-222	206	3	=	=	SYM
ma-222	206	4	(	(	PUNCT
ma-222	206	5	y1	y1	PROPN
ma-222	206	6	,	,	PUNCT
ma-222	206	7	1+y1	1+y1	NUM
ma-222	206	8	)	)	PUNCT
ma-222	206	9	,	,	PUNCT
ma-222	206	10	y	y	PROPN
ma-222	206	11	=	=	PUNCT
ma-222	206	12	(	(	PUNCT
ma-222	206	13	y2	y2	PROPN
ma-222	206	14	,	,	PUNCT
ma-222	206	15	1+y2	1+y2	NUM
ma-222	206	16	)	)	PUNCT
ma-222	206	17	,	,	PUNCT
ma-222	206	18	where	where	SCONJ
ma-222	206	19	−1	−1	NOUN
ma-222	206	20	≤	≤	NUM
ma-222	206	21	y1	y1	NOUN
ma-222	206	22	≤	≤	NUM
ma-222	206	23	y2	y2	NOUN
ma-222	206	24	≤	≤	ADJ
ma-222	206	25	0	0	NUM
ma-222	206	26	;	;	PUNCT
ma-222	206	27	x	x	SYM
ma-222	206	28	=	=	SYM
ma-222	206	29	(	(	PUNCT
ma-222	206	30	y1	y1	INTJ
ma-222	206	31	,	,	PUNCT
ma-222	206	32	y1−1	y1−1	PROPN
ma-222	206	33	)	)	PUNCT
ma-222	206	34	,	,	PUNCT
ma-222	206	35	y	y	PROPN
ma-222	206	36	=	=	PUNCT
ma-222	206	37	(	(	PUNCT
ma-222	206	38	y2	y2	PROPN
ma-222	206	39	,	,	PUNCT
ma-222	206	40	y2−1),where	y2−1),where	ADV
ma-222	206	41	0	0	NUM
ma-222	206	42	≤	≤	NUM
ma-222	206	43	y1	y1	NOUN
ma-222	206	44	≤	≤	NUM
ma-222	207	1	y2	y2	NOUN
ma-222	207	2	≤	≤	ADV
ma-222	207	3	1	1	NUM
ma-222	207	4	.	.	PUNCT
ma-222	208	1	the	the	DET
ma-222	208	2	two	two	NUM
ma-222	208	3	cases	case	NOUN
ma-222	208	4	above	above	ADP
ma-222	208	5	,	,	PUNCT
ma-222	208	6	which	which	PRON
ma-222	208	7	are	be	AUX
ma-222	208	8	determined	determine	VERB
ma-222	208	9	by	by	ADP
ma-222	208	10	x	x	PROPN
ma-222	208	11	⊥i	⊥i	PROPN
ma-222	208	12	y	y	PROPN
ma-222	208	13	,	,	PUNCT
ma-222	208	14	we	we	PRON
ma-222	208	15	have	have	AUX
ma-222	208	16	|y1	|y1	VERB
ma-222	208	17	−	−	PROPN
ma-222	208	18	y2|	y2|	NOUN
ma-222	208	19	=	=	SYM
ma-222	208	20	2	2	NUM
ma-222	208	21	,	,	PUNCT
ma-222	208	22	are	be	AUX
ma-222	208	23	contradictory	contradictory	ADJ
ma-222	208	24	.	.	PUNCT
ma-222	209	1	to	to	PART
ma-222	209	2	estimate	estimate	VERB
ma-222	209	3	this	this	DET
ma-222	209	4	constant	constant	ADJ
ma-222	209	5	value	value	NOUN
ma-222	209	6	,	,	PUNCT
ma-222	209	7	it	it	PRON
ma-222	209	8	is	be	AUX
ma-222	209	9	only	only	ADV
ma-222	209	10	necessary	necessary	ADJ
ma-222	209	11	to	to	ADP
ma-222	209	12	considerthe	considerthe	NOUN
ma-222	209	13	following	follow	VERB
ma-222	209	14	two	two	NUM
ma-222	209	15	cases	case	NOUN
ma-222	209	16	.	.	PUNCT
ma-222	210	1	case	case	NOUN
ma-222	210	2	1	1	NUM
ma-222	210	3	:	:	PUNCT
ma-222	210	4	assuming	assume	VERB
ma-222	210	5	that	that	SCONJ
ma-222	210	6	x	x	X
ma-222	210	7	=	=	SYM
ma-222	210	8	(	(	PUNCT
ma-222	210	9	x1	x1	PROPN
ma-222	210	10	,	,	PUNCT
ma-222	210	11	1	1	NUM
ma-222	210	12	)	)	PUNCT
ma-222	210	13	,	,	PUNCT
ma-222	211	1	y	y	PROPN
ma-222	211	2	=	=	PUNCT
ma-222	211	3	(	(	PUNCT
ma-222	211	4	1	1	NUM
ma-222	211	5	,	,	PUNCT
ma-222	211	6	y2	y2	PROPN
ma-222	211	7	)	)	PUNCT
ma-222	211	8	,	,	PUNCT
ma-222	211	9	0	0	NUM
ma-222	211	10	≤	≤	NUM
ma-222	211	11	x1	x1	NUM
ma-222	211	12	≤	≤	NUM
ma-222	212	1	y2	y2	NOUN
ma-222	212	2	≤	≤	ADJ
ma-222	212	3	1	1	NUM
ma-222	212	4	.	.	PUNCT
ma-222	213	1	since	since	SCONJ
ma-222	213	2	x	x	PROPN
ma-222	213	3	⊥i	⊥i	PROPN
ma-222	213	4	y	y	PROPN
ma-222	213	5	,	,	PUNCT
ma-222	213	6	we	we	PRON
ma-222	213	7	have	have	VERB
ma-222	213	8	1	1	NUM
ma-222	213	9	+	+	NUM
ma-222	213	10	y2	y2	NOUN
ma-222	213	11	=	=	SYM
ma-222	213	12	(	(	PUNCT
ma-222	213	13	1−	1−	NUM
ma-222	213	14	x1	x1	NUM
ma-222	213	15	)	)	PUNCT
ma-222	214	1	+	+	CCONJ
ma-222	214	2	(	(	PUNCT
ma-222	214	3	1−	1−	NUM
ma-222	214	4	y2	y2	NOUN
ma-222	214	5	)	)	PUNCT
ma-222	214	6	,	,	PUNCT
ma-222	214	7	https://doi.org/10.28924/ada/ma.4.6	https://doi.org/10.28924/ada/ma.4.6	PROPN
ma-222	214	8	eur	eur	NOUN
ma-222	214	9	.	.	PUNCT
ma-222	215	1	j.	j.	PROPN
ma-222	215	2	math	math	PROPN
ma-222	215	3	.	.	PUNCT
ma-222	216	1	anal	anal	PROPN
ma-222	216	2	.	.	PUNCT
ma-222	217	1	10.28924	10.28924	NUM
ma-222	217	2	/	/	SYM
ma-222	217	3	ada	ada	PROPN
ma-222	217	4	/	/	SYM
ma-222	217	5	ma.4.6	ma.4.6	NOUN
ma-222	217	6	7hence	7hence	NUM
ma-222	217	7	x1	x1	NOUN
ma-222	217	8	+	+	CCONJ
ma-222	217	9	2y2	2y2	NUM
ma-222	217	10	=	=	SYM
ma-222	217	11	1	1	NUM
ma-222	217	12	,	,	PUNCT
ma-222	217	13	y2	y2	NOUN
ma-222	217	14	∈	∈	PROPN
ma-222	218	1	[	[	X
ma-222	218	2	13	13	NUM
ma-222	218	3	,	,	PUNCT
ma-222	218	4	12	12	NUM
ma-222	218	5	]	]	PUNCT
ma-222	218	6	.	.	PUNCT
ma-222	219	1	then	then	ADV
ma-222	219	2	‖αx	‖αx	NUM
ma-222	219	3	−	−	PROPN
ma-222	219	4	y‖	y‖	NOUN
ma-222	219	5	=	=	SYM
ma-222	219	6	1	1	NUM
ma-222	219	7	,	,	PUNCT
ma-222	219	8	‖x	‖x	NOUN
ma-222	219	9	−	−	PROPN
ma-222	219	10	βy‖	βy‖	PROPN
ma-222	219	11	=	=	PUNCT
ma-222	219	12	1	1	NUM
ma-222	219	13	2	2	NUM
ma-222	219	14	+	+	CCONJ
ma-222	219	15	3	3	NUM
ma-222	219	16	2y2	2y2	NUM
ma-222	219	17	,	,	PUNCT
ma-222	219	18	‖αx	‖αx	PROPN
ma-222	219	19	−	−	PROPN
ma-222	220	1	βy‖	βy‖	PROPN
ma-222	220	2	=	=	PUNCT
ma-222	220	3	1	1	NUM
ma-222	220	4	2	2	NUM
ma-222	220	5	+	+	NUM
ma-222	220	6	1	1	NUM
ma-222	220	7	2y2and	2y2and	NUM
ma-222	220	8	‖x	‖x	NUM
ma-222	221	1	−	−	NOUN
ma-222	221	2	y‖	y‖	NOUN
ma-222	221	3	=	=	PUNCT
ma-222	222	1	1	1	NUM
ma-222	222	2	+	+	NOUN
ma-222	222	3	y2.in	y2.in	PRON
ma-222	222	4	fact	fact	NOUN
ma-222	222	5	,	,	PUNCT
ma-222	222	6	l′1	l′1	ADJ
ma-222	222	7	2	2	NUM
ma-222	222	8	,	,	PUNCT
ma-222	222	9	1	1	NUM
ma-222	222	10	2	2	NUM
ma-222	222	11	(	(	PUNCT
ma-222	222	12	x	x	NOUN
ma-222	222	13	)	)	PUNCT
ma-222	222	14	=	=	SYM
ma-222	222	15	max	max	PROPN
ma-222	222	16	1	1	NUM
ma-222	222	17	3	3	NUM
ma-222	222	18	≤y2≤	≤y2≤	NOUN
ma-222	222	19	12	12	NUM
ma-222	222	20	9y22	9y22	NUM
ma-222	223	1	+	+	CCONJ
ma-222	223	2	6y2	6y2	NUM
ma-222	223	3	+	+	CCONJ
ma-222	223	4	5	5	NUM
ma-222	223	5	5y22	5y22	NUM
ma-222	223	6	+	+	CCONJ
ma-222	223	7	10y2	10y2	NUM
ma-222	223	8	+	+	NUM
ma-222	223	9	5	5	NUM
ma-222	223	10	.	.	PUNCT
ma-222	224	1	by	by	ADP
ma-222	224	2	simple	simple	ADJ
ma-222	224	3	calculation	calculation	NOUN
ma-222	224	4	,	,	PUNCT
ma-222	224	5	we	we	PRON
ma-222	224	6	find	find	VERB
ma-222	224	7	that	that	SCONJ
ma-222	224	8	l′1	l′1	ADJ
ma-222	224	9	2	2	NUM
ma-222	224	10	,	,	PUNCT
ma-222	224	11	1	1	NUM
ma-222	224	12	2	2	NUM
ma-222	224	13	(	(	PUNCT
ma-222	224	14	x	x	NOUN
ma-222	224	15	)	)	PUNCT
ma-222	224	16	=	=	SYM
ma-222	224	17	0.91	0.91	NUM
ma-222	224	18	is	be	AUX
ma-222	224	19	obtained	obtain	VERB
ma-222	224	20	at	at	ADP
ma-222	224	21	the	the	DET
ma-222	224	22	point	point	NOUN
ma-222	224	23	(	(	PUNCT
ma-222	224	24	1	1	NUM
ma-222	224	25	,	,	PUNCT
ma-222	224	26	12	12	NUM
ma-222	224	27	)	)	PUNCT
ma-222	224	28	.	.	PUNCT
ma-222	225	1	case	case	NOUN
ma-222	225	2	2	2	NUM
ma-222	225	3	:	:	PUNCT
ma-222	225	4	assuming	assume	VERB
ma-222	225	5	that	that	SCONJ
ma-222	225	6	x	x	X
ma-222	225	7	=	=	SYM
ma-222	225	8	(	(	PUNCT
ma-222	225	9	x1	x1	PROPN
ma-222	225	10	,	,	PUNCT
ma-222	225	11	1	1	NUM
ma-222	225	12	)	)	PUNCT
ma-222	225	13	,	,	PUNCT
ma-222	225	14	y	y	PROPN
ma-222	225	15	=	=	SYM
ma-222	225	16	(	(	PUNCT
ma-222	225	17	y1	y1	INTJ
ma-222	225	18	,	,	PUNCT
ma-222	225	19	1	1	NUM
ma-222	225	20	+	+	CCONJ
ma-222	225	21	y1	y1	NOUN
ma-222	225	22	)	)	PUNCT
ma-222	225	23	satisfy	satisfy	VERB
ma-222	225	24	−1	−1	NOUN
ma-222	225	25	≤	≤	NUM
ma-222	225	26	y1	y1	NOUN
ma-222	225	27	≤	≤	NOUN
ma-222	225	28	0	0	NUM
ma-222	225	29	≤	≤	NUM
ma-222	225	30	x1	x1	PROPN
ma-222	225	31	≤	≤	NUM
ma-222	225	32	1	1	NUM
ma-222	225	33	.	.	PUNCT
ma-222	226	1	since	since	SCONJ
ma-222	226	2	x	x	PROPN
ma-222	226	3	⊥i	⊥i	PROPN
ma-222	226	4	y	y	PROPN
ma-222	226	5	,	,	PUNCT
ma-222	226	6	we	we	PRON
ma-222	226	7	have	have	VERB
ma-222	226	8	‖(x1	‖(x1	PROPN
ma-222	226	9	+	+	CCONJ
ma-222	226	10	y1	y1	NOUN
ma-222	226	11	,	,	PUNCT
ma-222	226	12	2	2	NUM
ma-222	226	13	+	+	CCONJ
ma-222	226	14	y1)‖	y1)‖	NOUN
ma-222	226	15	=	=	SYM
ma-222	226	16	‖(x1	‖(x1	PROPN
ma-222	226	17	−	−	PROPN
ma-222	226	18	y1,−y1)‖.if	y1,−y1)‖.if	PROPN
ma-222	226	19	−x1	−x1	PROPN
ma-222	226	20	≤	≤	PROPN
ma-222	226	21	y1	y1	PROPN
ma-222	226	22	,	,	PUNCT
ma-222	226	23	then	then	ADV
ma-222	226	24	2	2	NUM
ma-222	226	25	+	+	NUM
ma-222	226	26	y1	y1	NOUN
ma-222	226	27	=	=	SYM
ma-222	227	1	x1	x1	NUM
ma-222	228	1	−	−	PROPN
ma-222	228	2	y1	y1	NOUN
ma-222	228	3	is	be	AUX
ma-222	228	4	true	true	ADJ
ma-222	228	5	,	,	PUNCT
ma-222	228	6	hence	hence	ADV
ma-222	228	7	x1	x1	PROPN
ma-222	229	1	−	−	NOUN
ma-222	230	1	2y1	2y1	NUM
ma-222	231	1	=	=	SYM
ma-222	231	2	2	2	NUM
ma-222	231	3	,	,	PUNCT
ma-222	231	4	y1	y1	PROPN
ma-222	231	5	∈	∈	PROPN
ma-222	232	1	[	[	X
ma-222	232	2	−23	−23	X
ma-222	232	3	,	,	PUNCT
ma-222	232	4	−12	−12	X
ma-222	232	5	]	]	PUNCT
ma-222	232	6	.	.	PUNCT
ma-222	233	1	we	we	PRON
ma-222	233	2	have	have	VERB
ma-222	233	3	‖αx	‖αx	NUM
ma-222	233	4	−	−	PROPN
ma-222	233	5	y‖	y‖	NOUN
ma-222	233	6	=	=	SYM
ma-222	233	7	1	1	NUM
ma-222	233	8	,	,	PUNCT
ma-222	233	9	‖x	‖x	NOUN
ma-222	233	10	−	−	PROPN
ma-222	234	1	βy‖	βy‖	PROPN
ma-222	234	2	=	=	SYM
ma-222	234	3	2	2	NUM
ma-222	234	4	+	+	SYM
ma-222	234	5	32y1	32y1	NUM
ma-222	234	6	,	,	PUNCT
ma-222	234	7	‖αx	‖αx	PROPN
ma-222	234	8	−	−	PROPN
ma-222	234	9	βy‖	βy‖	PROPN
ma-222	234	10	=	=	PUNCT
ma-222	234	11	1	1	NUM
ma-222	234	12	+	+	CCONJ
ma-222	234	13	12y1	12y1	NUM
ma-222	234	14	and	and	CCONJ
ma-222	234	15	‖x	‖x	NOUN
ma-222	234	16	−	−	PROPN
ma-222	234	17	y‖	y‖	NOUN
ma-222	234	18	=	=	SYM
ma-222	234	19	2	2	NUM
ma-222	234	20	+	+	CCONJ
ma-222	234	21	y1.in	y1.in	PRON
ma-222	234	22	the	the	DET
ma-222	234	23	same	same	ADJ
ma-222	234	24	way	way	NOUN
ma-222	234	25	,	,	PUNCT
ma-222	234	26	l′1	l′1	ADJ
ma-222	234	27	2	2	NUM
ma-222	234	28	,	,	PUNCT
ma-222	234	29	1	1	NUM
ma-222	234	30	2	2	NUM
ma-222	234	31	(	(	PUNCT
ma-222	234	32	x	x	NOUN
ma-222	234	33	)	)	PUNCT
ma-222	234	34	=	=	SYM
ma-222	234	35	max	max	PROPN
ma-222	235	1	−	−	PROPN
ma-222	235	2	2	2	NUM
ma-222	235	3	3	3	NUM
ma-222	235	4	≤y1≤−	≤y1≤−	NOUN
ma-222	235	5	12	12	NUM
ma-222	235	6	9y21	9y21	NUM
ma-222	236	1	+	+	CCONJ
ma-222	236	2	24y1	24y1	NUM
ma-222	236	3	+	+	NUM
ma-222	236	4	20	20	NUM
ma-222	236	5	5y21	5y21	NUM
ma-222	236	6	+	+	CCONJ
ma-222	236	7	20y1	20y1	NUM
ma-222	236	8	+	+	NUM
ma-222	236	9	20	20	NUM
ma-222	236	10	.	.	PUNCT
ma-222	237	1	by	by	ADP
ma-222	237	2	simple	simple	ADJ
ma-222	237	3	calculation	calculation	NOUN
ma-222	237	4	,	,	PUNCT
ma-222	237	5	we	we	PRON
ma-222	237	6	find	find	VERB
ma-222	237	7	that	that	SCONJ
ma-222	237	8	l′1	l′1	ADJ
ma-222	237	9	2	2	NUM
ma-222	237	10	,	,	PUNCT
ma-222	237	11	1	1	NUM
ma-222	237	12	2	2	NUM
ma-222	237	13	(	(	PUNCT
ma-222	237	14	x	x	NOUN
ma-222	237	15	)	)	PUNCT
ma-222	237	16	=	=	SYM
ma-222	237	17	0.91	0.91	NUM
ma-222	237	18	is	be	AUX
ma-222	237	19	obtained	obtain	VERB
ma-222	237	20	at	at	ADP
ma-222	237	21	the	the	DET
ma-222	237	22	point	point	NOUN
ma-222	237	23	(	(	PUNCT
ma-222	237	24	1,−12).similarly	1,−12).similarly	NUM
ma-222	237	25	,	,	PUNCT
ma-222	237	26	if	if	SCONJ
ma-222	237	27	y1	y1	ADJ
ma-222	237	28	≤	≤	NUM
ma-222	237	29	−x1	−x1	NOUN
ma-222	237	30	,	,	PUNCT
ma-222	237	31	such	such	ADJ
ma-222	237	32	as	as	ADP
ma-222	237	33	case	case	NOUN
ma-222	237	34	2	2	NUM
ma-222	237	35	,	,	PUNCT
ma-222	237	36	prove	prove	VERB
ma-222	237	37	omission.combined	omission.combine	VERB
ma-222	237	38	with	with	ADP
ma-222	237	39	all	all	PRON
ma-222	237	40	of	of	ADP
ma-222	237	41	the	the	DET
ma-222	237	42	above	above	NOUN
ma-222	237	43	,	,	PUNCT
ma-222	237	44	we	we	PRON
ma-222	237	45	get	get	VERB
ma-222	237	46	l′1	l′1	ADJ
ma-222	237	47	2	2	NUM
ma-222	237	48	,	,	PUNCT
ma-222	237	49	1	1	NUM
ma-222	237	50	2	2	NUM
ma-222	237	51	(	(	PUNCT
ma-222	237	52	x	x	NOUN
ma-222	237	53	)	)	PUNCT
ma-222	237	54	=	=	SYM
ma-222	237	55	0.91	0.91	NUM
ma-222	237	56	.	.	PUNCT
ma-222	238	1	�	�	PROPN
ma-222	238	2	4	4	NUM
ma-222	238	3	.	.	X
ma-222	238	4	funding	funding	NOUN
ma-222	238	5	statement	statement	NOUN
ma-222	238	6	this	this	DET
ma-222	238	7	research	research	NOUN
ma-222	238	8	work	work	NOUN
ma-222	238	9	was	be	AUX
ma-222	238	10	funded	fund	VERB
ma-222	238	11	by	by	ADP
ma-222	238	12	anhui	anhui	PROPN
ma-222	238	13	province	province	PROPN
ma-222	238	14	higher	high	ADJ
ma-222	238	15	education	education	PROPN
ma-222	238	16	science	science	NOUN
ma-222	238	17	research	research	NOUN
ma-222	238	18	project(natural	project(natural	ADJ
ma-222	238	19	science	science	NOUN
ma-222	238	20	)	)	PUNCT
ma-222	238	21	,	,	PUNCT
ma-222	238	22	2023ah050487	2023ah050487	NUM
ma-222	238	23	.	.	PUNCT
ma-222	239	1	references	reference	NOUN
ma-222	239	2	[	[	X
ma-222	239	3	1	1	X
ma-222	239	4	]	]	PUNCT
ma-222	239	5	j.	j.	PROPN
ma-222	239	6	alonso	alonso	PROPN
ma-222	239	7	,	,	PUNCT
ma-222	239	8	c.	c.	PROPN
ma-222	239	9	benítez	benítez	NOUN
ma-222	239	10	,	,	PUNCT
ma-222	239	11	orthogonality	orthogonality	NOUN
ma-222	239	12	in	in	ADP
ma-222	239	13	normed	normed	ADJ
ma-222	239	14	linear	linear	PROPN
ma-222	239	15	spaces	space	NOUN
ma-222	239	16	,	,	PUNCT
ma-222	239	17	a	a	DET
ma-222	239	18	survey	survey	NOUN
ma-222	239	19	,	,	PUNCT
ma-222	239	20	ii	ii	PROPN
ma-222	239	21	,	,	PUNCT
ma-222	239	22	relations	relation	NOUN
ma-222	239	23	between	between	ADP
ma-222	239	24	main	main	ADJ
ma-222	239	25	orthogonalities	orthogonality	NOUN
ma-222	239	26	,	,	PUNCT
ma-222	239	27	extracta	extracta	PROPN
ma-222	239	28	math	math	PROPN
ma-222	239	29	.	.	PUNCT
ma-222	240	1	4	4	NUM
ma-222	240	2	(	(	PUNCT
ma-222	240	3	1989	1989	NUM
ma-222	240	4	)	)	PUNCT
ma-222	241	1	121–131.[2	121–131.[2	NUM
ma-222	241	2	]	]	PUNCT
ma-222	241	3	j.	j.	PROPN
ma-222	241	4	alonso	alonso	PROPN
ma-222	241	5	,	,	PUNCT
ma-222	241	6	h.	h.	PROPN
ma-222	241	7	martin	martin	PROPN
ma-222	241	8	,	,	PUNCT
ma-222	241	9	s.	s.	PROPN
ma-222	241	10	wu	wu	PROPN
ma-222	241	11	,	,	PUNCT
ma-222	241	12	on	on	ADP
ma-222	241	13	birkhoff	birkhoff	NOUN
ma-222	241	14	orthogonality	orthogonality	NOUN
ma-222	241	15	and	and	CCONJ
ma-222	241	16	isosceles	isoscele	NOUN
ma-222	241	17	orthogonality	orthogonality	NOUN
ma-222	241	18	in	in	ADP
ma-222	241	19	normed	normed	ADJ
ma-222	241	20	linear	linear	PROPN
ma-222	241	21	spaces	space	NOUN
ma-222	241	22	,	,	PUNCT
ma-222	241	23	aequat.math	aequat.math	PROPN
ma-222	241	24	.	.	PROPN
ma-222	241	25	83	83	NUM
ma-222	241	26	(	(	PUNCT
ma-222	241	27	2012	2012	NUM
ma-222	241	28	)	)	PUNCT
ma-222	241	29	153	153	NUM
ma-222	241	30	-	-	SYM
ma-222	241	31	189	189	NUM
ma-222	241	32	.	.	PUNCT
ma-222	241	33	https://doi.org/10.1007/s00010-011-0092-z.[3	https://doi.org/10.1007/s00010-011-0092-z.[3	PROPN
ma-222	241	34	]	]	X
ma-222	241	35	e.	e.	PROPN
ma-222	241	36	z.	z.	PROPN
ma-222	241	37	andalafte	andalafte	PROPN
ma-222	241	38	,	,	PUNCT
ma-222	241	39	c.	c.	PROPN
ma-222	241	40	r.	r.	PROPN
ma-222	241	41	diminnie	diminnie	PROPN
ma-222	241	42	,	,	PUNCT
ma-222	241	43	r.	r.	PROPN
ma-222	241	44	w.	w.	PROPN
ma-222	241	45	freese	freese	PROPN
ma-222	241	46	,	,	PUNCT
ma-222	241	47	(	(	PUNCT
ma-222	241	48	α	α	NOUN
ma-222	241	49	,	,	PUNCT
ma-222	241	50	β)−orthogonality	β)−orthogonality	NOUN
ma-222	241	51	and	and	CCONJ
ma-222	241	52	a	a	DET
ma-222	241	53	characterization	characterization	NOUN
ma-222	241	54	of	of	ADP
ma-222	241	55	inner	inner	ADJ
ma-222	241	56	product	product	NOUN
ma-222	241	57	spaces	space	NOUN
ma-222	241	58	,	,	PUNCT
ma-222	241	59	math	math	NOUN
ma-222	241	60	.	.	PUNCT
ma-222	242	1	japon	japon	PROPN
ma-222	242	2	.	.	PUNCT
ma-222	243	1	30	30	NUM
ma-222	243	2	(	(	PUNCT
ma-222	243	3	1985	1985	NUM
ma-222	243	4	)	)	PUNCT
ma-222	243	5	341–349.[4	341–349.[4	NUM
ma-222	243	6	]	]	X
ma-222	243	7	v.	v.	CCONJ
ma-222	243	8	balestro	balestro	PROPN
ma-222	243	9	,	,	PUNCT
ma-222	243	10	angles	angle	NOUN
ma-222	243	11	in	in	ADP
ma-222	243	12	normed	normed	ADJ
ma-222	243	13	spaces	space	NOUN
ma-222	243	14	,	,	PUNCT
ma-222	243	15	aequat	aequat	PROPN
ma-222	243	16	.	.	PUNCT
ma-222	244	1	math	math	NOUN
ma-222	244	2	.	.	PUNCT
ma-222	245	1	91	91	NUM
ma-222	245	2	(	(	PUNCT
ma-222	245	3	2017	2017	NUM
ma-222	245	4	)	)	PUNCT
ma-222	246	1	201–236	201–236	NUM
ma-222	246	2	.	.	PUNCT
ma-222	247	1	https://doi.org/10.1007/	https://doi.org/10.1007/	PROPN
ma-222	247	2	s00010	s00010	PROPN
ma-222	247	3	-	-	PUNCT
ma-222	247	4	016	016	NUM
ma-222	247	5	-	-	PUNCT
ma-222	247	6	0445	0445	NUM
ma-222	247	7	-	-	PUNCT
ma-222	247	8	8.[5	8.[5	NUM
ma-222	247	9	]	]	X
ma-222	247	10	g.	g.	NOUN
ma-222	247	11	birkhoff	birkhoff	PROPN
ma-222	247	12	,	,	PUNCT
ma-222	247	13	orthogonality	orthogonality	NOUN
ma-222	247	14	in	in	ADP
ma-222	247	15	linear	linear	ADJ
ma-222	247	16	metric	metric	ADJ
ma-222	247	17	spaces	space	NOUN
ma-222	247	18	,	,	PUNCT
ma-222	247	19	duke	duke	PROPN
ma-222	247	20	.	.	PUNCT
ma-222	247	21	math	math	PROPN
ma-222	247	22	.	.	PUNCT
ma-222	248	1	j.	j.	PROPN
ma-222	248	2	1	1	NUM
ma-222	248	3	(	(	PUNCT
ma-222	248	4	1935	1935	NUM
ma-222	248	5	)	)	PUNCT
ma-222	248	6	169	169	NUM
ma-222	248	7	-	-	SYM
ma-222	248	8	172	172	NUM
ma-222	248	9	.	.	PUNCT
ma-222	249	1	https://doi.org/10.1215/	https://doi.org/10.1215/	PROPN
ma-222	249	2	s0012	s0012	PROPN
ma-222	249	3	-	-	PUNCT
ma-222	249	4	7094	7094	NUM
ma-222	249	5	-	-	SYM
ma-222	249	6	35	35	NUM
ma-222	249	7	-	-	PUNCT
ma-222	249	8	00115	00115	NUM
ma-222	249	9	-	-	PUNCT
ma-222	249	10	6.[6	6.[6	PROPN
ma-222	249	11	]	]	PUNCT
ma-222	249	12	s.	s.	PROPN
ma-222	249	13	o.	o.	PROPN
ma-222	249	14	carlsson	carlsson	PROPN
ma-222	249	15	,	,	PUNCT
ma-222	249	16	orthogonality	orthogonality	NOUN
ma-222	249	17	in	in	ADP
ma-222	249	18	normed	normed	ADJ
ma-222	249	19	linear	linear	PROPN
ma-222	249	20	spaces	space	NOUN
ma-222	249	21	,	,	PUNCT
ma-222	250	1	ark	ark	PROPN
ma-222	250	2	.	.	PROPN
ma-222	250	3	mat	mat	PROPN
ma-222	250	4	.	.	NOUN
ma-222	250	5	4	4	NUM
ma-222	250	6	(	(	PUNCT
ma-222	250	7	1961	1961	NUM
ma-222	250	8	)	)	PUNCT
ma-222	250	9	297–318	297–318	NUM
ma-222	250	10	.	.	PUNCT
ma-222	251	1	https://doi.org/10.1007/	https://doi.org/10.1007/	PROPN
ma-222	251	2	bf02591506.[7	bf02591506.[7	PROPN
ma-222	251	3	]	]	X
ma-222	251	4	c.	c.	PROPN
ma-222	251	5	r.	r.	PROPN
ma-222	251	6	diminnie	diminnie	PROPN
ma-222	251	7	,	,	PUNCT
ma-222	251	8	r.	r.	PROPN
ma-222	251	9	w.	w.	PROPN
ma-222	251	10	freese	freese	PROPN
ma-222	251	11	,	,	PUNCT
ma-222	251	12	e.	e.	PROPN
ma-222	251	13	z.	z.	PROPN
ma-222	251	14	andalafte	andalafte	PROPN
ma-222	251	15	,	,	PUNCT
ma-222	251	16	an	an	DET
ma-222	251	17	extension	extension	NOUN
ma-222	251	18	of	of	ADP
ma-222	251	19	pythagorean	pythagorean	PROPN
ma-222	251	20	and	and	CCONJ
ma-222	251	21	isosceles	isoscele	NOUN
ma-222	251	22	orthogonality	orthogonality	NOUN
ma-222	251	23	and	and	CCONJ
ma-222	251	24	character	character	NOUN
ma-222	251	25	-	-	PUNCT
ma-222	251	26	ization	ization	NOUN
ma-222	251	27	of	of	ADP
ma-222	251	28	inner	inner	ADJ
ma-222	251	29	product	product	NOUN
ma-222	251	30	spaces	space	NOUN
ma-222	251	31	,	,	PUNCT
ma-222	251	32	j.	j.	PROPN
ma-222	251	33	approx	approx	PROPN
ma-222	251	34	.	.	PUNCT
ma-222	252	1	theory	theory	NOUN
ma-222	252	2	.	.	PUNCT
ma-222	253	1	39	39	NUM
ma-222	253	2	(	(	PUNCT
ma-222	253	3	1983	1983	NUM
ma-222	253	4	)	)	PUNCT
ma-222	254	1	295–298	295–298	NUM
ma-222	254	2	.	.	PUNCT
ma-222	255	1	https://doi.org/10.1016/0021-9045(83	https://doi.org/10.1016/0021-9045(83	NOUN
ma-222	255	2	)	)	PUNCT
ma-222	255	3	90073	90073	NUM
ma-222	255	4	-	-	SYM
ma-222	255	5	4	4	NUM
ma-222	255	6	.	.	PUNCT
ma-222	256	1	https://doi.org/10.28924/ada/ma.4.6	https://doi.org/10.28924/ada/ma.4.6	PROPN
ma-222	256	2	https://doi.org/10.1007/s00010-011-0092-z	https://doi.org/10.1007/s00010-011-0092-z	NOUN
ma-222	256	3	https://doi.org/10.1007/s00010-016-0445-8	https://doi.org/10.1007/s00010-016-0445-8	NUM
ma-222	256	4	https://doi.org/10.1007/s00010-016-0445-8	https://doi.org/10.1007/s00010-016-0445-8	NUM
ma-222	256	5	https://doi.org/10.1215/s0012-7094-35-00115-6	https://doi.org/10.1215/s0012-7094-35-00115-6	ADV
ma-222	256	6	https://doi.org/10.1215/s0012-7094-35-00115-6	https://doi.org/10.1215/s0012-7094-35-00115-6	ADV
ma-222	256	7	https://doi.org/10.1007/bf02591506	https://doi.org/10.1007/bf02591506	VERB
ma-222	256	8	https://doi.org/10.1007/bf02591506	https://doi.org/10.1007/bf02591506	NOUN
ma-222	256	9	https://doi.org/10.1016/0021-9045(83)90073-4	https://doi.org/10.1016/0021-9045(83)90073-4	PROPN
ma-222	256	10	https://doi.org/10.1016/0021-9045(83)90073-4	https://doi.org/10.1016/0021-9045(83)90073-4	PROPN
ma-222	256	11	eur	eur	PROPN
ma-222	256	12	.	.	PUNCT
ma-222	257	1	j.	j.	PROPN
ma-222	257	2	math	math	PROPN
ma-222	257	3	.	.	PUNCT
ma-222	258	1	anal	anal	PROPN
ma-222	258	2	.	.	PUNCT
ma-222	259	1	10.28924	10.28924	NUM
ma-222	259	2	/	/	SYM
ma-222	259	3	ada	ada	PROPN
ma-222	259	4	/	/	SYM
ma-222	259	5	ma.4.6	ma.4.6	NOUN
ma-222	259	6	8	8	NUM
ma-222	259	7	[	[	NOUN
ma-222	259	8	8	8	NUM
ma-222	259	9	]	]	X
ma-222	259	10	r.	r.	PROPN
ma-222	259	11	c.	c.	PROPN
ma-222	259	12	james	james	PROPN
ma-222	259	13	,	,	PUNCT
ma-222	259	14	orthogonality	orthogonality	NOUN
ma-222	259	15	in	in	ADP
ma-222	259	16	normed	normed	ADJ
ma-222	259	17	linear	linear	PROPN
ma-222	259	18	spaces	space	NOUN
ma-222	259	19	,	,	PUNCT
ma-222	259	20	duke	duke	PROPN
ma-222	259	21	.	.	PUNCT
ma-222	259	22	math	math	PROPN
ma-222	259	23	.	.	PUNCT
ma-222	260	1	j.	j.	PROPN
ma-222	260	2	12	12	NUM
ma-222	260	3	(	(	PUNCT
ma-222	260	4	1945	1945	NUM
ma-222	260	5	)	)	PUNCT
ma-222	260	6	291	291	NUM
ma-222	260	7	-	-	SYM
ma-222	260	8	301	301	NUM
ma-222	260	9	.	.	PUNCT
ma-222	261	1	https://doi.org/10	https://doi.org/10	PROPN
ma-222	261	2	.	.	PUNCT
ma-222	262	1	1215	1215	NUM
ma-222	262	2	/	/	SYM
ma-222	262	3	s0012	s0012	NOUN
ma-222	262	4	-	-	PUNCT
ma-222	262	5	7094	7094	NUM
ma-222	262	6	-	-	PUNCT
ma-222	262	7	45	45	NUM
ma-222	262	8	-	-	PUNCT
ma-222	262	9	01223	01223	NUM
ma-222	262	10	-	-	PUNCT
ma-222	262	11	3.[9	3.[9	NUM
ma-222	262	12	]	]	PUNCT
ma-222	262	13	r.	r.	PROPN
ma-222	262	14	c.	c.	PROPN
ma-222	262	15	james	james	PROPN
ma-222	262	16	,	,	PUNCT
ma-222	262	17	orthogonality	orthogonality	NOUN
ma-222	262	18	and	and	CCONJ
ma-222	262	19	linear	linear	ADJ
ma-222	262	20	functionals	functional	NOUN
ma-222	262	21	in	in	ADP
ma-222	262	22	normed	normed	ADJ
ma-222	262	23	linear	linear	PROPN
ma-222	262	24	spaces	space	NOUN
ma-222	262	25	,	,	PUNCT
ma-222	262	26	trans	trans	PROPN
ma-222	262	27	.	.	PROPN
ma-222	263	1	amer	amer	PROPN
ma-222	263	2	.	.	PUNCT
ma-222	263	3	math	math	PROPN
ma-222	263	4	.	.	PUNCT
ma-222	264	1	soc	soc	PROPN
ma-222	264	2	.	.	PUNCT
ma-222	265	1	61	61	NUM
ma-222	265	2	(	(	PUNCT
ma-222	265	3	1947)265	1947)265	NUM
ma-222	265	4	-	-	SYM
ma-222	265	5	292	292	NUM
ma-222	265	6	.	.	PUNCT
ma-222	266	1	https://doi.org/10.2307/1990220.[10	https://doi.org/10.2307/1990220.[10	PROPN
ma-222	266	2	]	]	PUNCT
ma-222	266	3	r.	r.	PROPN
ma-222	266	4	c.	c.	PROPN
ma-222	266	5	james	james	PROPN
ma-222	266	6	,	,	PUNCT
ma-222	266	7	uniformly	uniformly	ADV
ma-222	266	8	non	non	ADJ
ma-222	266	9	-	-	ADJ
ma-222	266	10	square	square	ADJ
ma-222	266	11	banach	banach	NOUN
ma-222	266	12	spaces	space	NOUN
ma-222	266	13	,	,	PUNCT
ma-222	266	14	ann	ann	PROPN
ma-222	266	15	.	.	PROPN
ma-222	266	16	of	of	ADP
ma-222	266	17	math	math	NOUN
ma-222	266	18	.	.	PUNCT
ma-222	267	1	80	80	NUM
ma-222	267	2	(	(	PUNCT
ma-222	267	3	1964	1964	NUM
ma-222	267	4	)	)	PUNCT
ma-222	268	1	542–550	542–550	NUM
ma-222	268	2	.	.	PUNCT
ma-222	269	1	https://doi.org/10.2307/	https://doi.org/10.2307/	PROPN
ma-222	269	2	1970663.[11	1970663.[11	NUM
ma-222	269	3	]	]	X
ma-222	269	4	d.	d.	PROPN
ma-222	269	5	ji	ji	PROPN
ma-222	269	6	,	,	PUNCT
ma-222	269	7	s.	s.	PROPN
ma-222	269	8	wu	wu	PROPN
ma-222	269	9	,	,	PUNCT
ma-222	269	10	quantitative	quantitative	ADJ
ma-222	269	11	characterization	characterization	NOUN
ma-222	269	12	of	of	ADP
ma-222	269	13	the	the	DET
ma-222	269	14	difference	difference	NOUN
ma-222	269	15	between	between	ADP
ma-222	269	16	birkhoff	birkhoff	NOUN
ma-222	269	17	orthogonality	orthogonality	NOUN
ma-222	269	18	and	and	CCONJ
ma-222	269	19	isosceles	isoscele	NOUN
ma-222	269	20	orthogo	orthogo	VERB
ma-222	269	21	-	-	PUNCT
ma-222	269	22	nality	nality	NOUN
ma-222	269	23	,	,	PUNCT
ma-222	269	24	j.	j.	PROPN
ma-222	269	25	math	math	PROPN
ma-222	269	26	.	.	PUNCT
ma-222	270	1	anal	anal	PROPN
ma-222	270	2	.	.	PUNCT
ma-222	270	3	appl	appl	PROPN
ma-222	270	4	.	.	PROPN
ma-222	271	1	323	323	NUM
ma-222	271	2	(	(	PUNCT
ma-222	271	3	2006	2006	NUM
ma-222	271	4	)	)	PUNCT
ma-222	271	5	1–7	1–7	X
ma-222	271	6	.	.	PUNCT
ma-222	272	1	https://doi.org/10.1016/j.jmaa.2005.10.004.[12	https://doi.org/10.1016/j.jmaa.2005.10.004.[12	PROPN
ma-222	272	2	]	]	X
ma-222	272	3	h.	h.	PROPN
ma-222	272	4	mizuguchi	mizuguchi	PROPN
ma-222	272	5	,	,	PUNCT
ma-222	272	6	the	the	DET
ma-222	272	7	constants	constant	NOUN
ma-222	272	8	to	to	PART
ma-222	272	9	measure	measure	VERB
ma-222	272	10	the	the	DET
ma-222	272	11	differences	difference	NOUN
ma-222	272	12	between	between	ADP
ma-222	272	13	birkhoff	birkhoff	NOUN
ma-222	272	14	and	and	CCONJ
ma-222	272	15	isosceles	isoscele	NOUN
ma-222	272	16	orthogonalities	orthogonality	NOUN
ma-222	272	17	,	,	PUNCT
ma-222	272	18	filomat	filomat	NOUN
ma-222	272	19	.	.	PUNCT
ma-222	273	1	30(2015	30(2015	NUM
ma-222	273	2	)	)	PUNCT
ma-222	273	3	2761–2770	2761–2770	NUM
ma-222	273	4	.	.	PUNCT
ma-222	274	1	https://doi.org/10.2298/fil1610761m.[13	https://doi.org/10.2298/fil1610761m.[13	NOUN
ma-222	274	2	]	]	X
ma-222	274	3	p.	p.	PROPN
ma-222	274	4	l.	l.	PROPN
ma-222	274	5	papini	papini	PROPN
ma-222	274	6	,	,	PUNCT
ma-222	274	7	s.	s.	PROPN
ma-222	274	8	wu	wu	PROPN
ma-222	274	9	,	,	PUNCT
ma-222	274	10	measurements	measurement	NOUN
ma-222	274	11	of	of	ADP
ma-222	274	12	differences	difference	NOUN
ma-222	274	13	between	between	ADP
ma-222	274	14	orthogonality	orthogonality	NOUN
ma-222	274	15	types	type	NOUN
ma-222	274	16	,	,	PUNCT
ma-222	274	17	j.	j.	PROPN
ma-222	274	18	math	math	PROPN
ma-222	274	19	.	.	PUNCT
ma-222	275	1	anal	anal	PROPN
ma-222	275	2	.	.	PUNCT
ma-222	276	1	appl	appl	PROPN
ma-222	276	2	.	.	PROPN
ma-222	277	1	397	397	NUM
ma-222	277	2	(	(	PUNCT
ma-222	277	3	2013)285–291	2013)285–291	NUM
ma-222	277	4	.	.	PUNCT
ma-222	277	5	https://doi.org/10.1016/j.jmaa.2012.07.059.[14	https://doi.org/10.1016/j.jmaa.2012.07.059.[14	PROPN
ma-222	277	6	]	]	X
ma-222	277	7	q.	q.	PROPN
ma-222	277	8	liu	liu	PROPN
ma-222	277	9	,	,	PUNCT
ma-222	277	10	z.	z.	PROPN
ma-222	277	11	yang	yang	PROPN
ma-222	277	12	,	,	PUNCT
ma-222	277	13	y.	y.	PROPN
ma-222	277	14	li	li	PROPN
ma-222	277	15	,	,	PUNCT
ma-222	277	16	new	new	ADJ
ma-222	277	17	geometric	geometric	ADJ
ma-222	277	18	constants	constant	NOUN
ma-222	277	19	of	of	ADP
ma-222	277	20	isosceles	isoscele	NOUN
ma-222	277	21	orthogonal	orthogonal	ADJ
ma-222	277	22	type	type	NOUN
ma-222	277	23	,	,	PUNCT
ma-222	277	24	(	(	PUNCT
ma-222	277	25	2022	2022	NUM
ma-222	277	26	)	)	PUNCT
ma-222	277	27	.	.	PUNCT
ma-222	278	1	http://arxiv.org/abs/	http://arxiv.org/abs/	NOUN
ma-222	278	2	2111.08392.[15	2111.08392.[15	NUM
ma-222	278	3	]	]	PUNCT
ma-222	278	4	z.	z.	PROPN
ma-222	278	5	yang	yang	PROPN
ma-222	278	6	,	,	PUNCT
ma-222	278	7	y.	y.	PROPN
ma-222	278	8	li	li	PROPN
ma-222	278	9	,	,	PUNCT
ma-222	278	10	a	a	DET
ma-222	278	11	new	new	ADJ
ma-222	278	12	geometric	geometric	ADJ
ma-222	278	13	constant	constant	NOUN
ma-222	278	14	in	in	ADP
ma-222	278	15	banach	banach	NOUN
ma-222	278	16	spaces	space	NOUN
ma-222	278	17	related	relate	VERB
ma-222	278	18	to	to	ADP
ma-222	278	19	the	the	DET
ma-222	278	20	isosceles	isoscele	NOUN
ma-222	278	21	orthogonality	orthogonality	NOUN
ma-222	278	22	,	,	PUNCT
ma-222	278	23	kyungpookmath	kyungpookmath	PROPN
ma-222	278	24	.	.	PUNCT
ma-222	279	1	j.	j.	PROPN
ma-222	279	2	62	62	NUM
ma-222	279	3	(	(	PUNCT
ma-222	279	4	2022	2022	NUM
ma-222	279	5	)	)	PUNCT
ma-222	279	6	271–287	271–287	NUM
ma-222	279	7	.	.	PUNCT
ma-222	280	1	https://doi.org/10.5666/kmj.2022.62.2.271	https://doi.org/10.5666/kmj.2022.62.2.271	PROPN
ma-222	280	2	.	.	PUNCT
ma-222	281	1	https://doi.org/10.28924/ada/ma.4.6	https://doi.org/10.28924/ada/ma.4.6	NUM
ma-222	281	2	https://doi.org/10.1215/s0012-7094-45-01223-3	https://doi.org/10.1215/s0012-7094-45-01223-3	PRON
ma-222	281	3	https://doi.org/10.1215/s0012-7094-45-01223-3	https://doi.org/10.1215/s0012-7094-45-01223-3	PRON
ma-222	281	4	https://doi.org/10.2307/1990220	https://doi.org/10.2307/1990220	NUM
ma-222	281	5	https://doi.org/10.2307/1970663	https://doi.org/10.2307/1970663	X
ma-222	281	6	https://doi.org/10.2307/1970663	https://doi.org/10.2307/1970663	X
ma-222	281	7	https://doi.org/10.1016/j.jmaa.2005.10.004	https://doi.org/10.1016/j.jmaa.2005.10.004	PROPN
ma-222	281	8	https://doi.org/10.2298/fil1610761	https://doi.org/10.2298/fil1610761	VERB
ma-222	281	9	m	m	PROPN
ma-222	281	10	https://doi.org/10.1016/j.jmaa.2012.07.059	https://doi.org/10.1016/j.jmaa.2012.07.059	ADJ
ma-222	281	11	http://arxiv.org/abs/2111.08392	http://arxiv.org/abs/2111.08392	NOUN
ma-222	281	12	http://arxiv.org/abs/2111.08392	http://arxiv.org/abs/2111.08392	NOUN
ma-222	281	13	https://doi.org/10.5666/kmj.2022.62.2.271	https://doi.org/10.5666/kmj.2022.62.2.271	PROPN
ma-222	281	14	1	1	NUM
ma-222	281	15	.	.	PUNCT
ma-222	281	16	introduction	introduction	NOUN
ma-222	281	17	2	2	NUM
ma-222	281	18	.	.	PUNCT
ma-222	282	1	the	the	DET
ma-222	282	2	constant	constant	ADJ
ma-222	282	3	l,(x	l,(x	NOUN
ma-222	282	4	)	)	PUNCT
ma-222	282	5	3	3	NUM
ma-222	282	6	.	.	PUNCT
ma-222	283	1	the	the	DET
ma-222	283	2	constant	constant	ADJ
ma-222	283	3	l,(x	l,(x	NOUN
ma-222	283	4	)	)	PUNCT
ma-222	283	5	4	4	NUM
ma-222	283	6	.	.	X
ma-222	283	7	funding	funding	NOUN
ma-222	283	8	statement	statement	NOUN
ma-222	283	9	references	reference	NOUN