id	sid	eid	entity	type
ma-125	1	1	2023	CARDINAL
ma-125	2	1	j. math	PERSON
ma-125	4	1	3 (	CARDINAL
ma-125	4	2	2023	CARDINAL
ma-125	4	3	11doi	CARDINAL
ma-125	4	4	10.28924	CARDINAL
ma-125	4	5	hilbert c∗−modules fakhr-dine	ORG
ma-125	4	6	nhari1	PERSON
ma-125	4	7	mohamed rossafi2,∗ 1laboratory	PERSON
ma-125	4	8	133	CARDINAL
ma-125	4	9	morocco	GPE
ma-125	5	1	2lasma	CARDINAL
ma-125	5	2	el mahraz	ORG
ma-125	5	3	sidi mohamed ben abdellah	PERSON
ma-125	5	4	1796	DATE
ma-125	5	5	atlas	PERSON
ma-125	5	6	morocco	GPE
ma-125	9	1	k − g−fusion	ORG
ma-125	10	1	linear bounded	ORG
ma-125	11	1	k −	PERSON
ma-125	12	1	1	CARDINAL
ma-125	13	1	schaefer	PERSON
ma-125	13	2	3	CARDINAL
ma-125	13	3	1952	DATE
ma-125	13	4	gabor	ORG
ma-125	14	1	5	CARDINAL
ma-125	15	1	2000	DATE
ma-125	15	2	frank-larson	PERSON
ma-125	15	3	4	CARDINAL
ma-125	16	1	6].many	CARDINAL
ma-125	16	2	hilbert c∗-modules	PERSON
ma-125	16	3	hilbert	PERSON
ma-125	17	1	hilbert	ORG
ma-125	19	1	31	CARDINAL
ma-125	19	2	2022.2010	CARDINAL
ma-125	20	1	41a58	CARDINAL
ma-125	20	2	42c15	CARDINAL
ma-125	22	1	k − g−fusion	ORG
ma-125	22	2	c∗-algebra	ORG
ma-125	22	3	hilbert c∗-modules	PERSON
ma-125	23	1	1	CARDINAL
ma-125	24	1	j. math	PERSON
ma-125	26	1	10.28924	CARDINAL
ma-125	27	1	∈ hj	PERSON
ma-125	27	2	fj〉‖	DATE
ma-125	27	3	〉	CARDINAL
ma-125	27	4	〉	CARDINAL
ma-125	27	5	1.1	CARDINAL
ma-125	28	1	8	CARDINAL
ma-125	28	2	c∗-algebra	ORG
ma-125	30	1	〉	CARDINAL
ma-125	33	1	〉	CARDINAL
ma-125	33	2	0	CARDINAL
ma-125	33	3	〉	CARDINAL
ma-125	33	4	0	CARDINAL
ma-125	34	1	0.(ii	CARDINAL
ma-125	34	2	〉	CARDINAL
ma-125	34	3	∈	ORG
ma-125	34	4	〉	CARDINAL
ma-125	35	1	∈	ORG
ma-125	37	1	a∗a	ORG
ma-125	37	2	1 2	CARDINAL
ma-125	39	1	〉 1 2	MONEY
ma-125	39	2	1.2	CARDINAL
ma-125	40	1	10	CARDINAL
ma-125	40	2	∈	ORG
ma-125	41	1	∗ptwj	ORG
ma-125	42	1	lemma 1.3.	ORG
ma-125	43	1	2	CARDINAL
ma-125	44	1	two	CARDINAL
ma-125	44	2	∈	ORG
ma-125	47	1	0	CARDINAL
ma-125	47	2	0	CARDINAL
ma-125	47	3	〉	CARDINAL
ma-125	47	4	m′〈x	GPE
ma-125	47	5	〉	CARDINAL
ma-125	47	6	k. lemma	PERSON
ma-125	47	7	1.4	CARDINAL
ma-125	48	1	1	CARDINAL
ma-125	49	1	u and h	ORG
ma-125	49	2	two	CARDINAL
ma-125	51	1	−1‖−1 ≤ t ∗t	MONEY
ma-125	52	1	tt ∗	PERSON
ma-125	52	2	‖(tt	ORG
ma-125	53	1	1.5	CARDINAL
ma-125	54	1	10	CARDINAL
ma-125	55	1	j. math	PERSON
ma-125	57	1	10.28924	CARDINAL
ma-125	57	2	∈	ORG
ma-125	59	1	wi	ORG
ma-125	60	1	two	CARDINAL
ma-125	60	2	0	CARDINAL
ma-125	60	3	a〈x	GPE
ma-125	60	4	〉 ≤	MONEY
ma-125	61	1	λipwi	PERSON
ma-125	61	2	〉 ≤	MONEY
ma-125	61	3	〉	CARDINAL
ma-125	61	4	∀x	ORG
ma-125	61	5	∈	PRODUCT
ma-125	61	6	1.1	CARDINAL
ma-125	62	1	1	CARDINAL
ma-125	63	1	inequality∑	NORP
ma-125	63	2	λipwi	PERSON
ma-125	63	3	〉 ≤	MONEY
ma-125	63	4	〉	CARDINAL
ma-125	63	5	∀x ∈ h.	ORG
ma-125	63	6	1.6	CARDINAL
ma-125	64	1	10]let	CARDINAL
ma-125	64	2	{wj	PERSON
ma-125	64	3	λ∗j fj	PERSON
ma-125	64	4	∈	ORG
ma-125	68	1	∈	ORG
ma-125	68	2	sλf = tλuλf = ∑ j∈j v2 j	PERSON
ma-125	68	3	λ∗j	PERSON
ma-125	69	1	〉	CARDINAL
ma-125	70	1	j∈j v2 j 〈λjpwj	PERSON
ma-125	70	2	〉	CARDINAL
ma-125	70	3	∈	ORG
ma-125	70	4	1.2	CARDINAL
ma-125	70	5	a〈f	GPE
ma-125	70	6	〉 ≤	MONEY
ma-125	71	1	〉 ≤	MONEY
ma-125	72	1	〉	CARDINAL
ma-125	72	2	∈	ORG
ma-125	73	1	||uλ(f	PERSON
ma-125	75	1	j∈j v2 j 〈λjpwj	PERSON
ma-125	75	2	〉	CARDINAL
ma-125	78	1	√ a||f ||	PERSON
ma-125	82	1	j. math	PERSON
ma-125	84	1	10.28924	CARDINAL
ma-125	85	1	1.3	CARDINAL
ma-125	85	2	lemma 1.4	ORG
ma-125	86	1	aih ≤ sλ ≤ bih	ORG
ma-125	87	1	2	CARDINAL
ma-125	89	1	1	CARDINAL
ma-125	89	2	2	DATE
ma-125	89	3	1	CARDINAL
ma-125	89	4	k ∈	ORG
ma-125	89	5	hilbert a−modules	PERSON
ma-125	90	1	2.1	CARDINAL
ma-125	91	1	j , vi j}j∈j	PERSON
ma-125	91	2	k−	NORP
ma-125	91	3	0	CARDINAL
ma-125	93	1	2.2	CARDINAL
ma-125	94	1	{wj	PERSON
ma-125	94	2	two	CARDINAL
ma-125	94	3	∈	ORG
ma-125	94	4	∈	ORG
ma-125	94	5	j ∈ j	PERSON
ma-125	94	6	{wj	PERSON
ma-125	94	7	0	CARDINAL
ma-125	94	8	σ ⊂ j	ORG
ma-125	94	9	lσ2	ORG
ma-125	94	10	λ∗j xj + ∑	PERSON
ma-125	94	11	j∈σc	DATE
ma-125	94	12	θ ∗ j xj	ORG
ma-125	94	13	lσ2	ORG
ma-125	94	14	∈ hj	PERSON
ma-125	94	15	xj	ORG
ma-125	94	16	xj〉‖	DATE
ma-125	96	1	1	CARDINAL
ma-125	96	2	2	CARDINAL
ma-125	96	3	{wj	PERSON
ma-125	97	1	{wj	PERSON
ma-125	97	2	{vj	PERSON
ma-125	98	1	λ∗j xj + ∑	PERSON
ma-125	98	2	j∈σc	DATE
ma-125	98	3	θ ∗ j xj	ORG
ma-125	99	1	〉	CARDINAL
ma-125	100	1	2	CARDINAL
ma-125	100	2	1	CARDINAL
ma-125	100	3	σ ⊂ j	ORG
ma-125	100	4	j∈σc	DATE
ma-125	102	1	j. math	PERSON
ma-125	104	1	10.28924	CARDINAL
ma-125	105	1	〉	CARDINAL
ma-125	105	2	〉 ≤	MONEY
ma-125	106	1	〉	CARDINAL
ma-125	106	2	〉	CARDINAL
ma-125	107	1	j∈σc	DATE
ma-125	107	2	〉	CARDINAL
ma-125	108	1	{wj	PERSON
ma-125	110	1	2.3	CARDINAL
ma-125	111	1	j , vi j}j∈j	PERSON
ma-125	111	2	∈	ORG
ma-125	112	1	ku =	PERSON
ma-125	112	2	uk	GPE
ma-125	114	1	uwi j	ORG
ma-125	114	2	j ∈ j	PERSON
ma-125	117	1	〉	CARDINAL
ma-125	117	2	a〈(u+)∗u∗k∗f	ORG
ma-125	121	1	jpwi j u∗puwi j f	PERSON
ma-125	121	2	jpwi j u∗puwi j	PERSON
ma-125	123	1	2.4	DATE
ma-125	124	1	j , vi j}j∈j	PERSON
ma-125	124	2	k−	NORP
ma-125	124	3	∈	ORG
ma-125	124	4	r(k	ORG
ma-125	127	1	0	CARDINAL
ma-125	128	1	〉	CARDINAL
ma-125	131	1	jpwi j u∗puwi j f	PERSON
ma-125	131	2	jpwi j u∗puwi j	PERSON
ma-125	131	3	〉	CARDINAL
ma-125	135	1	j. math	PERSON
ma-125	137	1	10.28924	CARDINAL
ma-125	138	1	〉	CARDINAL
ma-125	139	1	k+)∗k∗u∗f	GPE
ma-125	139	2	k+)∗k∗u∗f	NORP
ma-125	140	1	〉	CARDINAL
ma-125	145	1	jpwi j u∗puwi j f	PERSON
ma-125	145	2	jpwi j u∗puwi j	PERSON
ma-125	145	3	〉 ≤ b‖u‖2〈f	MONEY
ma-125	145	4	〉	CARDINAL
ma-125	147	1	2.5	CARDINAL
ma-125	148	1	j , vi j}j∈j	PERSON
ma-125	148	2	0 ≤	MONEY
ma-125	149	1	2 ≤	QUANTITY
ma-125	151	1	j ∈ j	PERSON
ma-125	151	2	w	PERSON
ma-125	152	1	ac	ORG
ma-125	153	1	〉	CARDINAL
ma-125	154	1	2a〈k∗f	DATE
ma-125	154	2	∑ j∈σi v2	PERSON
ma-125	156	1	jpwi	PERSON
ma-125	156	2	j f	PERSON
ma-125	156	3	w	PERSON
ma-125	156	4	jpwi	PERSON
ma-125	157	1	〉 ≤	MONEY
ma-125	157	2	max	PERSON
ma-125	158	1	〉	CARDINAL
ma-125	159	1	2.6	CARDINAL
ma-125	161	1	vi j}j∈i	PERSON
ma-125	161	2	j , vi j}j∈j	PERSON
ma-125	163	1	⊂	GPE
ma-125	163	2	∩	PERSON
ma-125	163	3	vi j}j∈σi∩i	PERSON
ma-125	164	1	j∈σi∩i v2	PERSON
ma-125	166	1	j f	PERSON
ma-125	166	2	jpwi	PERSON
ma-125	166	3	∑ j∈σi v2	PERSON
ma-125	168	1	j f	PERSON
ma-125	168	2	jpwi	PERSON
ma-125	170	1	one	CARDINAL
ma-125	172	1	j. math	PERSON
ma-125	174	1	10.28924	CARDINAL
ma-125	174	2	7	CARDINAL
ma-125	174	3	2.7	CARDINAL
ma-125	175	1	{wi j	PERSON
ma-125	175	2	j , vi j}j∈j	PERSON
ma-125	176	1	∑ j∈i v2	PERSON
ma-125	177	1	jpwi	GPE
ma-125	177	2	r(k	ORG
ma-125	181	1	f ∈ r(k	PRODUCT
ma-125	181	2	∑ j∈σi v2	PERSON
ma-125	183	1	j f	PERSON
ma-125	183	2	jpwi	PERSON
ma-125	184	1	〉	CARDINAL
ma-125	184	2	∑ j∈σi∪i v2	PERSON
ma-125	186	1	j f	PERSON
ma-125	186	2	jpwi	PERSON
ma-125	186	3	∑ j∈i v2	PERSON
ma-125	188	1	j f	PERSON
ma-125	188	2	jpwi	PERSON
ma-125	188	3	〉	CARDINAL
ma-125	188	4	〉	CARDINAL
ma-125	188	5	∑ j∈i v2	PERSON
ma-125	189	1	a−	ORG
ma-125	189	2	〉	CARDINAL
ma-125	190	1	2.8	CARDINAL
ma-125	191	1	j , vi j}j∈j	PERSON
ma-125	192	1	j(wi j	PERSON
ma-125	193	1	ci j	PERSON
ma-125	195	1	j f	PERSON
ma-125	196	1	j ∈ j	PERSON
ma-125	196	2	j , vi j}j∈j	PERSON
ma-125	196	3	mini∈[m],j∈j ci j)a	PERSON
ma-125	197	1	j , vi j}j∈j	PERSON
ma-125	198	1	∑ j∈σi v2	PERSON
ma-125	200	1	jpw̃i j	PERSON
ma-125	200	2	〉	CARDINAL
ma-125	200	3	∑ j∈σi v2	PERSON
ma-125	205	1	∑ j∈σi v2	PERSON
ma-125	209	1	∑ j∈σi v2	PERSON
ma-125	210	1	j f	PERSON
ma-125	210	2	jpwi	PERSON
ma-125	212	1	∑ j∈σi v2	PERSON
ma-125	214	1	j f	PERSON
ma-125	214	2	jpwi	PERSON
ma-125	215	1	i∈[m],j∈j	DATE
ma-125	215	2	ci j)a〈k∗f	PERSON
ma-125	215	3	〉	CARDINAL
ma-125	215	4	2.9	CARDINAL
ma-125	216	1	j , vi	PERSON
ma-125	220	1	j −	PERSON
ma-125	220	2	vi j}j∈(σi∪δi	PERSON
ma-125	221	1	j , vi j}j∈j	PERSON
ma-125	223	1	j. math	PERSON
ma-125	225	1	10.28924	CARDINAL
ma-125	226	1	j = ∪j∈njj	PERSON
ma-125	228	1	1	CARDINAL
ma-125	229	1	less than 1	CARDINAL
ma-125	230	1	that∑	NORP
ma-125	230	2	∑ j∈(σi1∪δi1	PERSON
ma-125	232	1	jpwi j	ORG
ma-125	232	2	〉	CARDINAL
ma-125	235	1	jpwi j	ORG
ma-125	235	2	that∑	NORP
ma-125	237	1	jpwi j	ORG
ma-125	237	2	〉	CARDINAL
ma-125	237	3	+1jj	DATE
ma-125	239	1	σni}i∈[m	PERSON
ma-125	239	2	j −	PERSON
ma-125	240	1	∈	ORG
ma-125	240	2	kn ∈	PERSON
ma-125	240	3	kn > kn−1	ORG
ma-125	240	4	∑ j∈kn v2	PERSON
ma-125	243	1	〉	CARDINAL
ma-125	243	2	kn =	PERSON
ma-125	245	1	the archimedean property	ORG
ma-125	245	2	∈	ORG
ma-125	246	1	2	CARDINAL
ma-125	246	2	∈	ORG
ma-125	246	3	that∑	NORP
ma-125	246	4	∑ j∈αi v2 i	PERSON
ma-125	248	1	jpwi j fr	PERSON
ma-125	250	1	〉	CARDINAL
ma-125	253	1	jpwi j fr	PERSON
ma-125	253	2	jpwi j fr 〉 + ∑	PERSON
ma-125	253	3	∑ j∈αi∩j−(j1∪	PERSON
ma-125	256	1	jpwi j fr	PERSON
ma-125	256	2	jpwi j fr 〉	PERSON
ma-125	256	3	j∈(σr	PERSON
ma-125	260	1	jpwi j fr	PERSON
ma-125	260	2	jpwi j fr 〉 + ∑	PERSON
ma-125	262	1	jpwi j fr	PERSON
ma-125	262	2	jpwi j fr 〉	PERSON
ma-125	262	3	1	CARDINAL
ma-125	262	4	a. � https://doi.org/10.28924/ada/ma.3.11 eur	PERSON
ma-125	263	1	j. math	PERSON
ma-125	265	1	10.28924	CARDINAL
ma-125	265	2	2.10	CARDINAL
ma-125	266	1	j , vi j}j∈j	PERSON
ma-125	266	2	j − ∪i∈[m]δi	PERSON
ma-125	266	3	vi j}j∈(σi∪δi	PERSON
ma-125	266	4	a. theorem	PERSON
ma-125	266	5	2.11	CARDINAL
ma-125	271	1	6=	CARDINAL
ma-125	273	1	j∈i	NORP
ma-125	274	1	− vkjλkjpwkj	PERSON
ma-125	274	2	vi jλi jpwi	PERSON
ma-125	275	1	− vkjλkjpwkj	PERSON
ma-125	276	1	〉 ≤	MONEY
ma-125	276	2	j∈i v2	PERSON
ma-125	278	1	j f	PERSON
ma-125	278	2	jpwi	PERSON
ma-125	278	3	j∈i v2 kj〈λkjpwkj	PERSON
ma-125	279	1	j , vi j}j∈j	PERSON
ma-125	279	2	1)(n + 1	DATE
ma-125	280	1	∑ i∈[m]bi	PERSON
ma-125	282	1	∈	ORG
ma-125	285	1	j f	PERSON
ma-125	285	2	jpwi	PERSON
ma-125	286	1	〉	CARDINAL
ma-125	286	2	∑ j∈σk v2	PERSON
ma-125	288	1	j f	PERSON
ma-125	288	2	jpwi	PERSON
ma-125	290	1	j f	PERSON
ma-125	290	2	jpwi	PERSON
ma-125	290	3	v2 kj〈λkjpwkj f	PERSON
ma-125	292	1	− vkjλkjpwkj	PERSON
ma-125	292	2	vi jλi jpwi	PERSON
ma-125	293	1	− vkjλkjpwkj	PERSON
ma-125	295	1	j f	PERSON
ma-125	295	2	jpwi	PERSON
ma-125	297	1	1)(n + 1	DATE
ma-125	299	1	j f	PERSON
ma-125	299	2	jpwi	PERSON
ma-125	300	1	1)(n + 1	DATE
ma-125	303	1	j f	PERSON
ma-125	303	2	jpwi	PERSON
ma-125	306	1	j. math	PERSON
ma-125	308	1	10.28924	CARDINAL
ma-125	308	2	2.12	CARDINAL
ma-125	309	1	{wj	PERSON
ma-125	309	2	two	CARDINAL
ma-125	310	1	0 ≤	QUANTITY
ma-125	311	1	1 2	CARDINAL
ma-125	311	2	1 2	CARDINAL
ma-125	312	1	〉 ≤	MONEY
ma-125	312	2	〉	CARDINAL
ma-125	313	1	{wj	PERSON
ma-125	313	2	1 2	CARDINAL
ma-125	316	1	σ ⊂ j	ORG
ma-125	316	2	∈	ORG
ma-125	317	1	j∈σc v2 j	PERSON
ma-125	317	2	〉	CARDINAL
ma-125	321	1	+ 1 2 ∑	QUANTITY
ma-125	321	2	j∈σc	DATE
ma-125	321	3	〉	CARDINAL
ma-125	322	1	〉	CARDINAL
ma-125	322	2	1 2 ∑	QUANTITY
ma-125	322	3	+ 1 2 ∑	QUANTITY
ma-125	322	4	〉	CARDINAL
ma-125	323	1	〉	CARDINAL
ma-125	323	2	〉	CARDINAL
ma-125	324	1	〉	CARDINAL
ma-125	324	2	〉	CARDINAL
ma-125	325	1	〉	CARDINAL
ma-125	325	2	〉	CARDINAL
ma-125	325	3	〉	CARDINAL
ma-125	329	1	j. math	PERSON
ma-125	331	1	10.28924	CARDINAL
ma-125	332	1	intereston	PERSON
ma-125	335	1	1	CARDINAL
ma-125	335	2	a. alijani	PERSON
ma-125	335	3	m. dehghan	PERSON
ma-125	335	4	hilbert	GPE
ma-125	336	1	sci	ORG
ma-125	336	2	bull.	PERSON
ma-125	337	1	73	CARDINAL
ma-125	337	2	2011	DATE
ma-125	337	3	89	CARDINAL
ma-125	338	1	hilbert c∗-modules	PERSON
ma-125	339	1	amer	PERSON
ma-125	341	1	135	CARDINAL
ma-125	341	2	2007	DATE
ma-125	341	3	469	CARDINAL
ma-125	342	1	a.c. schaeffer	PERSON
ma-125	343	1	amer	PERSON
ma-125	345	1	72	DATE
ma-125	345	2	1952	DATE
ma-125	346	1	341–366	CARDINAL
ma-125	347	1	m. frank	PERSON
ma-125	347	2	d.r. larson	PERSON
ma-125	347	3	hilbert c∗-modules	PERSON
ma-125	350	1	math.247	ORG
ma-125	350	2	2000	DATE
ma-125	350	3	207	CARDINAL
ma-125	350	4	d. gabor	PERSON
ma-125	351	1	1	CARDINAL
ma-125	351	2	j. inst	PERSON
ma-125	352	1	eng	PERSON
ma-125	353	1	93 (1946	DATE
ma-125	354	1	429–441	CARDINAL
ma-125	354	2	lance	ORG
ma-125	354	3	hilbert c∗−modules	PERSON
ma-125	354	4	london	GPE
ma-125	357	1	cambridge	GPE
ma-125	357	2	1995.[7	DATE
ma-125	357	3	s. kabbaj	PERSON
ma-125	357	4	m. rossafi	PERSON
ma-125	358	1	5	CARDINAL
ma-125	358	2	2018	DATE
ma-125	358	3	1-13.[8	CARDINAL
ma-125	358	4	i. kaplansky	PERSON
ma-125	358	5	amer	PERSON
ma-125	359	1	j. math	PERSON
ma-125	360	1	75	CARDINAL
ma-125	360	2	1953	DATE
ma-125	360	3	839	CARDINAL
ma-125	361	1	2372552.[9	CARDINAL
ma-125	361	2	a. khorsavi	PERSON
ma-125	361	3	b. khorsavi	PERSON
ma-125	361	4	hilbert c∗-modules	PERSON
ma-125	362	1	j. wavel	PERSON
ma-125	365	1	433	CARDINAL
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