id	sid	eid	entity	type
ma-222	1	1	2024	CARDINAL
ma-222	2	1	j. math	PERSON
ma-222	4	1	4 (2024	CARDINAL
ma-222	4	2	6doi	CARDINAL
ma-222	4	3	10.28924	CARDINAL
ma-222	4	4	qichuan ni	PERSON
ma-222	4	5	yin zhou	PERSON
ma-222	4	6	qin qian	PERSON
ma-222	4	7	246133	DATE
ma-222	4	8	china	GPE
ma-222	4	9	liuq67@aqnu.edu.cn	ORG
ma-222	4	10	15212956918@163.com	CARDINAL
ma-222	4	11	liuq67@aqnu.edu.cn	ORG
ma-222	5	1	α−β	CARDINAL
ma-222	5	2	first	ORDINAL
ma-222	9	1	1	CARDINAL
ma-222	9	2	hilbert spaces	ORG
ma-222	10	1	three	CARDINAL
ma-222	11	1	1945,james	CARDINAL
ma-222	11	2	8	CARDINAL
ma-222	11	3	‖x	PERSON
ma-222	11	4	− y‖. balestro	PERSON
ma-222	11	5	4	CARDINAL
ma-222	11	6	‖x	PERSON
ma-222	12	1	+ ‖y‖2	DATE
ma-222	12	2	birkhoff	ORG
ma-222	12	3	5	CARDINAL
ma-222	12	4	‖x	PERSON
ma-222	12	5	∈	ORG
ma-222	12	6	r.	NORP
ma-222	12	7	three	CARDINAL
ma-222	12	8	2	CARDINAL
ma-222	13	1	9	CARDINAL
ma-222	13	2	the years	DATE
ma-222	14	1	familyof	CARDINAL
ma-222	14	2	carlson	PERSON
ma-222	15	1	6	CARDINAL
ma-222	15	2	1961	DATE
ma-222	15	3	pythagorean orthogo-nalities	PERSON
ma-222	16	1	0	CARDINAL
ma-222	16	2	22	CARDINAL
ma-222	16	3	jan 2024	DATE
ma-222	18	1	hilbert spaces.1 https://adac.ee	ORG
ma-222	19	1	j. math	PERSON
ma-222	21	1	10.28924	CARDINAL
ma-222	21	2	2a	CARDINAL
ma-222	21	3	carlson orthogonality	ORG
ma-222	22	1	7	CARDINAL
ma-222	22	2	1983	DATE
ma-222	23	1	6= 1	DATE
ma-222	23	2	two years later	DATE
ma-222	23	3	3	CARDINAL
ma-222	24	1	‖x	PERSON
ma-222	26	1	βy‖2	CARDINAL
ma-222	27	1	βy‖2	CARDINAL
ma-222	31	1	two	CARDINAL
ma-222	32	1	11	CARDINAL
ma-222	32	2	12	CARDINAL
ma-222	33	1	‖x	PERSON
ma-222	34	1	− y‖ ‖x‖ :	PERSON
ma-222	37	1	1	CARDINAL
ma-222	38	1	13-15	CARDINAL
ma-222	39	1	‖x‖ ≤ 1}and	FAC
ma-222	40	1	1	CARDINAL
ma-222	41	1	dimx	PERSON
ma-222	41	2	2	CARDINAL
ma-222	42	1	2	CARDINAL
ma-222	43	1	two	CARDINAL
ma-222	44	1	2.1	CARDINAL
ma-222	45	1	β(x	PERSON
ma-222	46	1	βy‖2	CARDINAL
ma-222	46	2	0	CARDINAL
ma-222	46	3	0	DATE
ma-222	46	4	0	CARDINAL
ma-222	46	5	1	CARDINAL
ma-222	46	6	1	CARDINAL
ma-222	46	7	first	ORDINAL
ma-222	46	8	β(x	PERSON
ma-222	47	1	is1	ORG
ma-222	48	1	β(x	PERSON
ma-222	50	1	2.2	CARDINAL
ma-222	51	1	10	CARDINAL
ma-222	51	2	0	CARDINAL
ma-222	51	3	1	CARDINAL
ma-222	51	4	‖x	PERSON
ma-222	52	1	2 ≤ 1−	QUANTITY
ma-222	53	1	2 ≤ 1−	QUANTITY
ma-222	55	1	j. math	PERSON
ma-222	57	1	10.28924	CARDINAL
ma-222	57	2	3	CARDINAL
ma-222	57	3	2.1	CARDINAL
ma-222	58	1	1 ≤	QUANTITY
ma-222	58	2	β(x	PERSON
ma-222	58	3	0 ≤	QUANTITY
ma-222	59	1	1	CARDINAL
ma-222	59	2	2 1+α2	DATE
ma-222	59	3	0 ≤	MONEY
ma-222	59	4	1	CARDINAL
ma-222	59	5	α2+β2 1+β2	PRODUCT
ma-222	59	6	1	CARDINAL
ma-222	59	7	α2+β2 1+α2	ORG
ma-222	59	8	1	CARDINAL
ma-222	61	1	0	CARDINAL
ma-222	61	2	x0 ⊥i y0	PERSON
ma-222	64	1	1	CARDINAL
ma-222	64	2	‖x	PERSON
ma-222	71	1	‖x	PERSON
ma-222	72	1	‖x	PERSON
ma-222	80	1	four	CARDINAL
ma-222	81	1	1	CARDINAL
ma-222	81	2	0 ≤	QUANTITY
ma-222	81	3	‖x	PERSON
ma-222	83	1	2	CARDINAL
ma-222	83	2	0 ≤ α	QUANTITY
ma-222	83	3	1	CARDINAL
ma-222	83	4	‖x	PERSON
ma-222	85	1	3	CARDINAL
ma-222	86	1	‖x	PERSON
ma-222	89	1	4	CARDINAL
ma-222	89	2	1	CARDINAL
ma-222	90	1	‖x	PERSON
ma-222	93	1	β(x	PERSON
ma-222	94	1	2.1	CARDINAL
ma-222	95	1	0 ≤	QUANTITY
ma-222	95	2	1	CARDINAL
ma-222	95	3	‖(x1	DATE
ma-222	95	4	2 1+β2	DATE
ma-222	97	1	j. math	PERSON
ma-222	99	1	10.28924	CARDINAL
ma-222	99	2	1	CARDINAL
ma-222	99	3	1	CARDINAL
ma-222	99	4	1,−1	CARDINAL
ma-222	100	1	βy‖	CARDINAL
ma-222	100	2	2β	CARDINAL
ma-222	102	1	βy‖	CARDINAL
ma-222	102	2	− y‖	PERSON
ma-222	102	3	2	CARDINAL
ma-222	102	4	β(x	PERSON
ma-222	102	5	2 1+β2	DATE
ma-222	102	6	2.2	CARDINAL
ma-222	103	1	0 ≤	QUANTITY
ma-222	103	2	1	CARDINAL
ma-222	103	3	‖(x1	DATE
ma-222	103	4	2 1+β2	DATE
ma-222	104	1	1	CARDINAL
ma-222	104	2	0	DATE
ma-222	104	3	0,−1	CARDINAL
ma-222	105	1	βy‖	CARDINAL
ma-222	107	1	βy‖	CARDINAL
ma-222	107	2	− y‖	PERSON
ma-222	107	3	1	CARDINAL
ma-222	107	4	β(x	PERSON
ma-222	107	5	2 1+β2	DATE
ma-222	108	1	2.2	CARDINAL
ma-222	109	1	0 ≤	MONEY
ma-222	110	1	β(x	PERSON
ma-222	110	2	1	CARDINAL
ma-222	112	1	3	CARDINAL
ma-222	112	2	β(x	PERSON
ma-222	113	1	1	CARDINAL
ma-222	113	2	β(x	PERSON
ma-222	113	3	1	CARDINAL
ma-222	113	4	‖x	PERSON
ma-222	117	1	βy‖2	CARDINAL
ma-222	118	1	βy‖2	CARDINAL
ma-222	119	1	0 ≤ α <	QUANTITY
ma-222	119	2	1	CARDINAL
ma-222	119	3	n →∞	ORG
ma-222	119	4	‖x	PERSON
ma-222	121	1	βy‖2	CARDINAL
ma-222	122	1	0 ≤	QUANTITY
ma-222	122	2	1	CARDINAL
ma-222	122	3	second	ORDINAL
ma-222	122	4	‖x	PERSON
ma-222	122	5	1−	TIME
ma-222	124	1	n →∞	ORG
ma-222	124	2	‖x	PERSON
ma-222	125	1	+ ‖y‖2	GPE
ma-222	126	1	‖x	PERSON
ma-222	127	1	2‖x‖2	CARDINAL
ma-222	130	1	james	PERSON
ma-222	131	1	2.1	CARDINAL
ma-222	132	1	8	CARDINAL
ma-222	132	2	4.1	CARDINAL
ma-222	134	1	‖x	PERSON
ma-222	136	1	‖x	PERSON
ma-222	137	1	1	CARDINAL
ma-222	139	1	± y‖ ≤	MONEY
ma-222	139	2	‖x	PERSON
ma-222	141	1	2.3	CARDINAL
ma-222	142	1	β(x	PERSON
ma-222	142	2	2 1+β2	DATE
ma-222	143	1	1	CARDINAL
ma-222	145	1	2 1+β2	DATE
ma-222	145	2	∈	PRODUCT
ma-222	145	3	⊥i yn and	PERSON
ma-222	145	4	lim	PERSON
ma-222	147	1	− yn‖2 +	PERSON
ma-222	147	2	2 1 +	DATE
ma-222	149	1	j. math	PERSON
ma-222	151	1	10.28924	CARDINAL
ma-222	151	2	x0	ORG
ma-222	151	3	x0	CARDINAL
ma-222	151	4	lim k→∞	PERSON
ma-222	151	5	lim k→∞	PERSON
ma-222	152	1	2.1	CARDINAL
ma-222	154	1	1 +	DATE
ma-222	158	1	‖α0x0 −	FAC
ma-222	160	1	− β0y0‖ ≤	ORG
ma-222	160	2	1−	TIME
ma-222	164	1	max	PERSON
ma-222	164	2	‖x0 + y0‖	DATE
ma-222	167	1	‖x0‖	PRODUCT
ma-222	167	2	0	CARDINAL
ma-222	167	3	1	CARDINAL
ma-222	168	1	3	CARDINAL
ma-222	169	1	3.1	CARDINAL
ma-222	170	1	l′α	NORP
ma-222	171	1	βy‖2	CARDINAL
ma-222	171	2	0	CARDINAL
ma-222	171	3	1	CARDINAL
ma-222	171	4	1	CARDINAL
ma-222	172	1	∞− `1	PRODUCT
ma-222	172	2	1 2	CARDINAL
ma-222	172	3	3.1	CARDINAL
ma-222	173	1	α2+β2 1+α2	PRODUCT
ma-222	173	2	α2+β2 1+β2 2	ORG
ma-222	173	3	2 1+β2 ≤	QUANTITY
ma-222	173	4	β(x	PERSON
ma-222	173	5	0 ≤	QUANTITY
ma-222	174	1	1	CARDINAL
ma-222	174	2	2 1+α2	DATE
ma-222	174	3	0 ≤	MONEY
ma-222	174	4	1	CARDINAL
ma-222	174	5	α2+β2 1+β2	PRODUCT
ma-222	174	6	1	CARDINAL
ma-222	174	7	α2+β2 1+α2	ORG
ma-222	174	8	1	CARDINAL
ma-222	176	1	j. math	PERSON
ma-222	178	1	10.28924	CARDINAL
ma-222	178	2	6	CARDINAL
ma-222	179	1	2.1	CARDINAL
ma-222	179	2	‖x	PERSON
ma-222	180	1	βy‖2	CARDINAL
ma-222	183	1	‖x	PERSON
ma-222	188	1	y‖)2	GPE
ma-222	189	1	1	CARDINAL
ma-222	190	1	0 ≤	QUANTITY
ma-222	190	2	‖x	PERSON
ma-222	191	1	βy‖2	CARDINAL
ma-222	192	1	2	CARDINAL
ma-222	192	2	0 ≤ α	QUANTITY
ma-222	192	3	1	CARDINAL
ma-222	192	4	‖x	PERSON
ma-222	193	1	βy‖2	CARDINAL
ma-222	195	1	3	CARDINAL
ma-222	196	1	‖x	PERSON
ma-222	197	1	βy‖2	CARDINAL
ma-222	198	1	4	CARDINAL
ma-222	198	2	1	CARDINAL
ma-222	199	1	‖x	PERSON
ma-222	200	1	βy‖2	CARDINAL
ma-222	200	2	2 1 +	DATE
ma-222	201	1	β(x	PERSON
ma-222	202	1	3.1	CARDINAL
ma-222	203	1	1 2	CARDINAL
ma-222	203	2	1	CARDINAL
ma-222	203	3	0	CARDINAL
ma-222	204	1	2	CARDINAL
ma-222	204	2	1 2	CARDINAL
ma-222	204	3	0.91	CARDINAL
ma-222	206	1	1+y2	CARDINAL
ma-222	206	2	−1 ≤ y1 ≤ y2	MONEY
ma-222	206	3	0 ≤ y1 ≤	QUANTITY
ma-222	208	1	two	CARDINAL
ma-222	208	2	2	CARDINAL
ma-222	209	1	two	CARDINAL
ma-222	210	1	1	CARDINAL
ma-222	210	2	1	CARDINAL
ma-222	211	1	1	CARDINAL
ma-222	211	2	0 ≤	MONEY
ma-222	213	1	1 + y2	QUANTITY
ma-222	213	2	1− x1	TIME
ma-222	214	1	1− y2	QUANTITY
ma-222	215	1	j. math	PERSON
ma-222	217	1	10.28924	CARDINAL
ma-222	217	2	1	CARDINAL
ma-222	218	1	13	CARDINAL
ma-222	218	2	12	CARDINAL
ma-222	219	1	1	CARDINAL
ma-222	219	2	1 2 + 3 2y2	DATE
ma-222	220	1	βy‖	CARDINAL
ma-222	220	2	1 2 + 1	CARDINAL
ma-222	222	1	1 + y2.in	DATE
ma-222	222	2	2	CARDINAL
ma-222	222	3	1 2	CARDINAL
ma-222	222	4	1 3	TIME
ma-222	222	5	12	CARDINAL
ma-222	224	1	2	CARDINAL
ma-222	224	2	1 2	CARDINAL
ma-222	224	3	0.91	CARDINAL
ma-222	224	4	1	CARDINAL
ma-222	224	5	12	CARDINAL
ma-222	225	1	2	CARDINAL
ma-222	225	2	1	CARDINAL
ma-222	225	3	1 + y1	QUANTITY
ma-222	225	4	−1 ≤ y1	MONEY
ma-222	226	1	‖(x1 + y1	GPE
ma-222	226	2	2 +	DATE
ma-222	226	3	2 + y1	QUANTITY
ma-222	231	1	2	CARDINAL
ma-222	233	1	1	CARDINAL
ma-222	234	1	2 + 32y1	DATE
ma-222	234	2	1 + 12y1	CARDINAL
ma-222	234	3	2 + y1.in	DATE
ma-222	234	4	2	CARDINAL
ma-222	234	5	1 2	CARDINAL
ma-222	235	1	2 3	CARDINAL
ma-222	237	1	2	CARDINAL
ma-222	237	2	1 2	CARDINAL
ma-222	237	3	0.91	CARDINAL
ma-222	237	4	1,−12).similarly	CARDINAL
ma-222	237	5	2	CARDINAL
ma-222	237	6	2	CARDINAL
ma-222	237	7	1 2	CARDINAL
ma-222	237	8	0.91	CARDINAL
ma-222	238	1	4	CARDINAL
ma-222	238	2	anhui	GPE
ma-222	238	3	2023ah050487	CARDINAL
ma-222	239	1	1	CARDINAL
ma-222	239	2	j. alonso	PERSON
ma-222	239	3	normed linear spaces	ORG
ma-222	239	4	ii	ORG
ma-222	240	1	4 (1989	CARDINAL
ma-222	241	1	121–131.[2	CARDINAL
ma-222	241	2	j. alonso	PERSON
ma-222	241	3	h. martin	PERSON
ma-222	241	4	s. wu	PERSON
ma-222	241	5	normed linear spaces	ORG
ma-222	241	6	83	DATE
ma-222	241	7	2012	DATE
ma-222	241	8	153	CARDINAL
ma-222	241	9	e. z. andalafte	PERSON
ma-222	241	10	c. r. diminnie	PERSON
ma-222	241	11	r. w. freese	PERSON
ma-222	242	1	japon	GPE
ma-222	243	1	30	CARDINAL
ma-222	243	2	1985	DATE
ma-222	243	3	341–349.[4	CARDINAL
ma-222	243	4	normed spaces	ORG
ma-222	245	1	91	CARDINAL
ma-222	245	2	2017	CARDINAL
ma-222	246	1	201–236	CARDINAL
ma-222	247	1	g. birkhoff	PERSON
ma-222	248	1	j. 1 (1935	PERSON
ma-222	248	2	169	CARDINAL
ma-222	249	1	7094	CARDINAL
ma-222	249	2	s. o. carlsson	PERSON
ma-222	249	3	normed linear spaces	ORG
ma-222	250	1	ark.	GPE
ma-222	250	2	4 (1961	DATE
ma-222	250	3	297–318	DATE
ma-222	251	1	c. r. diminnie	PERSON
ma-222	251	2	r. w. freese	PERSON
ma-222	251	3	e. z. andalafte	PERSON
ma-222	251	4	pythagorean	ORG
ma-222	251	5	j. approx	PERSON
ma-222	253	1	39	CARDINAL
ma-222	253	2	1983	DATE
ma-222	254	1	295–298	CARDINAL
ma-222	255	1	90073	CARDINAL
ma-222	257	1	j. math	PERSON
ma-222	259	1	10.28924	CARDINAL
ma-222	259	2	8	CARDINAL
ma-222	259	3	8	CARDINAL
ma-222	259	4	r. c. james	PERSON
ma-222	259	5	normed linear spaces	ORG
ma-222	260	1	j. 12 (	PERSON
ma-222	260	2	291	CARDINAL
ma-222	262	1	7094	CARDINAL
ma-222	262	2	r. c. james	PERSON
ma-222	262	3	normed linear spaces	ORG
ma-222	263	1	amer	PERSON
ma-222	265	1	61	CARDINAL
ma-222	265	2	1947)265-292	CARDINAL
ma-222	266	1	r. c. james	PERSON
ma-222	266	2	ann.	PERSON
ma-222	267	1	80 (1964	DATE
ma-222	268	1	542–550	CARDINAL
ma-222	269	1	https://doi.org/10.2307/ 1970663.[11	ORG
ma-222	269	2	s. wu	PERSON
ma-222	271	1	323	CARDINAL
ma-222	271	2	2006	DATE
ma-222	271	3	1–7	CARDINAL
ma-222	272	1	h. mizuguchi	PERSON
ma-222	273	1	30(2015	CARDINAL
ma-222	273	2	2761–2770	CARDINAL
ma-222	274	1	p. l. papini	PERSON
ma-222	274	2	s. wu	PERSON
ma-222	277	1	397	CARDINAL
ma-222	277	2	2013)285–291	CARDINAL
ma-222	277	3	q. liu	PERSON
ma-222	277	4	z. yang	PERSON
ma-222	277	5	y. li	PERSON
ma-222	277	6	2022	CARDINAL
ma-222	278	1	2111.08392.[15	GPE
ma-222	278	2	z. yang	PERSON
ma-222	278	3	y. li	PERSON
ma-222	279	1	j. 62	PERSON
ma-222	279	2	2022	CARDINAL
ma-222	279	3	271–287	CARDINAL
ma-222	281	1	https://doi.org/10.2298/fil1610761	NORP
ma-222	281	2	1	CARDINAL
ma-222	281	3	2	CARDINAL
ma-222	282	1	3	CARDINAL
ma-222	283	1	4	CARDINAL