id	sid	eid	entity	type
ma-58	1	1	2022	CARDINAL
ma-58	2	1	j. math	PERSON
ma-58	3	1	2 (	CARDINAL
ma-58	3	2	2022	CARDINAL
ma-58	3	3	10.28924	CARDINAL
ma-58	3	4	mohamed rossafi1,∗	PERSON
ma-58	3	5	roumaissae el jazzar2	PERSON
ma-58	3	6	ali kacha2 1lasma	PERSON
ma-58	3	7	el mahraz	ORG
ma-58	3	8	sidi mohamed ben abdellah	PERSON
ma-58	4	1	b. p.	PERSON
ma-58	4	2	1796	DATE
ma-58	5	1	atlas	GPE
ma-58	5	2	morocco	GPE
ma-58	5	3	ibn tofail	PERSON
ma-58	5	4	kenitra	GPE
ma-58	5	5	morocco roumaissae.eljazzar@uit.ac.ma	GPE
ma-58	6	1	pro-c∗-modules	PERSON
ma-58	9	1	schaeffer	PERSON
ma-58	9	2	1952	DATE
ma-58	10	1	3].in 1986	DATE
ma-58	10	2	schaeffer	PERSON
ma-58	10	3	grossman andmeyer	PERSON
ma-58	12	1	proc∗-algebras	ORG
ma-58	12	2	hilbert modules	ORG
ma-58	13	1	hilbert c∗-modules	PERSON
ma-58	13	2	9].operator	CARDINAL
ma-58	13	3	li	PERSON
ma-58	13	4	cio	GPE
ma-58	13	5	11	CARDINAL
ma-58	13	6	16	CARDINAL
ma-58	14	1	three	CARDINAL
ma-58	15	1	section 2	LAW
ma-58	16	1	section 3	LAW
ma-58	17	1	hilbert pro-c∗-modules	PERSON
ma-58	17	2	weshow	GPE
ma-58	17	3	hilbert pro-c∗-modules	PERSON
ma-58	18	1	18 nov 2021	CARDINAL
ma-58	20	1	hilbert pro-c∗-modules	PERSON
ma-58	21	1	1	CARDINAL
ma-58	22	1	j. math	PERSON
ma-58	24	1	10.28924	CARDINAL
ma-58	24	2	ma.2.4 22	DATE
ma-58	26	1	4–6,8	CARDINAL
ma-58	26	2	12,14,15	CARDINAL
ma-58	27	1	hilbert pro-c∗-modules	PERSON
ma-58	27	2	hilbert	PERSON
ma-58	27	3	complexnumbers.pro-c∗-algebra	ORG
ma-58	27	4	0if	ORG
ma-58	27	5	0	CARDINAL
ma-58	27	6	c∗-seminorm	ORG
ma-58	28	1	∈	ORG
ma-58	28	2	pro-c∗-algebra	ORG
ma-58	29	1	pro-c∗-algebra	PERSON
ma-58	29	2	s(a	PERSON
ma-58	30	1	2.1	CARDINAL
ma-58	31	1	c∗-algebra	ORG
ma-58	31	2	2.2	CARDINAL
ma-58	32	1	8	CARDINAL
ma-58	32	2	1a	CARDINAL
ma-58	33	1	p(a	NORP
ma-58	33	2	1a	CARDINAL
ma-58	33	3	1(3	CARDINAL
ma-58	33	4	∈	ORG
ma-58	33	5	p(a	GPE
ma-58	33	6	1a ≤	MONEY
ma-58	33	7	∈	ORG
ma-58	33	8	0 ≤	MONEY
ma-58	33	9	0 ≤	MONEY
ma-58	33	10	∈	ORG
ma-58	33	11	∈	ORG
ma-58	33	12	0 ≤	MONEY
ma-58	33	13	2.3	CARDINAL
ma-58	34	1	15	CARDINAL
ma-58	34	2	pro-c∗-algebra	ORG
ma-58	35	1	〉	CARDINAL
ma-58	35	2	first	ORDINAL
ma-58	35	3	〉	CARDINAL
ma-58	35	4	η ∈ e2	ORG
ma-58	35	5	〉	CARDINAL
ma-58	36	1	j. math	PERSON
ma-58	38	1	10.28924	CARDINAL
ma-58	38	2	ma.2.4 33	DATE
ma-58	38	3	〉	CARDINAL
ma-58	38	4	0	CARDINAL
ma-58	39	1	η ∈	PERSON
ma-58	39	2	hilbert pro-c∗-module	PERSON
ma-58	40	1	√ p(〈ξ	PERSON
ma-58	40	2	∈	PRODUCT
ma-58	41	1	homa(x	PERSON
ma-58	42	1	2.4	CARDINAL
ma-58	43	1	1	CARDINAL
ma-58	44	1	∈	ORG
ma-58	44	2	η ∈	PERSON
ma-58	44	3	0	CARDINAL
ma-58	44	4	∈	ORG
ma-58	45	1	2.5	CARDINAL
ma-58	46	1	1	CARDINAL
ma-58	46	2	two	CARDINAL
ma-58	47	1	0	CARDINAL
ma-58	47	2	6	CARDINAL
ma-58	47	3	∈	ORG
ma-58	47	4	0	CARDINAL
ma-58	47	5	∈	ORG
ma-58	47	6	‖t‖∞	GPE
ma-58	49	1	∈	ORG
ma-58	49	2	6 1}it	CARDINAL
ma-58	49	3	6	CARDINAL
ma-58	50	1	2.6	CARDINAL
ma-58	51	1	2	CARDINAL
ma-58	52	1	pro-c∗-algebra	ORG
ma-58	53	1	∈	ORG
ma-58	53	2	〉 ≤	MONEY
ma-58	53	3	〉 ≤	MONEY
ma-58	53	4	〉	CARDINAL
ma-58	54	1	3	CARDINAL
ma-58	56	1	3.1	CARDINAL
ma-58	57	1	pro-c∗-algebra	ORG
ma-58	57	2	k ∈	PERSON
ma-58	58	1	two	CARDINAL
ma-58	58	2	0	CARDINAL
ma-58	58	3	k∗ξ	ORG
ma-58	58	4	〉 ≤	MONEY
ma-58	58	5	∈	ORG
ma-58	59	1	3.1	CARDINAL
ma-58	60	1	j. math	PERSON
ma-58	62	1	10.28924	CARDINAL
ma-58	63	1	k∗ξ	ORG
ma-58	63	2	〉	CARDINAL
ma-58	65	1	1	CARDINAL
ma-58	65	2	k-operator	ORG
ma-58	67	1	3.2	CARDINAL
ma-58	68	1	pro-c∗-algebra	PERSON
ma-58	68	2	k ∈	PERSON
ma-58	69	1	two	CARDINAL
ma-58	69	2	〉 ≤	MONEY
ma-58	69	3	ξ〉b∗,∀ξ ∈	PERSON
ma-58	70	1	3.2	CARDINAL
ma-58	71	1	〉	CARDINAL
ma-58	72	1	1	CARDINAL
ma-58	73	1	3.3	CARDINAL
ma-58	77	1	c∗-algebra	ORG
ma-58	80	1	〉	CARDINAL
ma-58	82	1	1 2	CARDINAL
ma-58	88	1	1 2 + 1	CARDINAL
ma-58	88	2	〉	CARDINAL
ma-58	88	3	1 2 + 1	CARDINAL
ma-58	89	1	12 + 1	DATE
ma-58	89	2	i∈n∗-tight	ORDINAL
ma-58	89	3	k : h → h	ORG
ma-58	89	4	k∗ξ	ORG
ma-58	89	5	k∗ξ	ORG
ma-58	89	6	1 2 + 1	CARDINAL
ma-58	89	7	〉	CARDINAL
ma-58	89	8	1 2 + 1	CARDINAL
ma-58	91	1	j. math	PERSON
ma-58	93	1	10.28924	CARDINAL
ma-58	93	2	ma.2.4 5this	DATE
ma-58	93	3	1	CARDINAL
ma-58	93	4	12 + 1	CARDINAL
ma-58	94	1	3.4	CARDINAL
ma-58	95	1	1	CARDINAL
ma-58	95	2	k ∈	PERSON
ma-58	95	3	k ∈	PERSON
ma-58	96	1	3.5	CARDINAL
ma-58	99	1	k ∈	PERSON
ma-58	99	2	k 6= 0	ORG
ma-58	101	1	a〈ξ	ORG
ma-58	101	2	〉 ≤	MONEY
ma-58	101	3	ξ〉b∗,∀ξ ∈	PERSON
ma-58	102	1	k∗ξ	ORG
ma-58	102	2	k∗ξ	ORG
ma-58	102	3	∈	ORG
ma-58	102	4	k∗ξ〉(‖k‖−1∞ a)∗	FAC
ma-58	102	5	〉 ≤	MONEY
ma-58	102	6	ξ〉b∗,∀ξ ∈	PERSON
ma-58	107	1	r∗	PERSON
ma-58	108	1	∑	PERSON
ma-58	109	1	∈	ORG
ma-58	110	1	r∗	PERSON
ma-58	111	1	r∗	PERSON
ma-58	111	2	∑	PERSON
ma-58	113	1	3.6	CARDINAL
ma-58	116	1	∑	PERSON
ma-58	117	1	∈	ORG
ma-58	120	1	∀ξ	PERSON
ma-58	120	2	η ∈	PERSON
ma-58	120	3	η	ORG
ma-58	120	4	〉	CARDINAL
ma-58	121	1	j. math	PERSON
ma-58	123	1	10.28924	CARDINAL
ma-58	123	2	ma.2.4 6	DATE
ma-58	123	3	∑	ORG
ma-58	123	4	〉	CARDINAL
ma-58	124	1	2	CARDINAL
ma-58	124	2	3.4	CARDINAL
ma-58	125	1	ξ〉a∗1 ≤ ∑	QUANTITY
ma-58	125	2	〉 ≤	MONEY
ma-58	125	3	ξ〉b∗.	ORG
ma-58	126	1	∈	ORG
ma-58	127	1	3.3	CARDINAL
ma-58	129	1	wewill	PERSON
ma-58	130	1	∈	ORG
ma-58	131	1	− ξm〉a∗	EVENT
ma-58	132	1	− ξm	PERSON
ma-58	132	2	− ξm	PERSON
ma-58	134	1	0	CARDINAL
ma-58	134	2	∈	ORG
ma-58	136	1	ξm	ORDINAL
ma-58	136	2	− ξm〉a∗(a∗)−1	PERSON
ma-58	137	1	− ξm〉a∗	EVENT
ma-58	138	1	∈	ORG
ma-58	138	2	3.3	CARDINAL
ma-58	138	3	b)2p(〈ξn − ξ	ORG
ma-58	142	1	∈	ORG
ma-58	142	2	0	CARDINAL
ma-58	143	1	a〈ξ	ORG
ma-58	143	2	〉	CARDINAL
ma-58	143	3	〉	CARDINAL
ma-58	144	1	0	CARDINAL
ma-58	144	2	∈	ORG
ma-58	144	3	〉	CARDINAL
ma-58	144	4	〉	CARDINAL
ma-58	144	5	〉	CARDINAL
ma-58	145	1	∑	ORG
ma-58	147	1	∑	PERSON
ma-58	149	1	r∗	PERSON
ma-58	149	2	r∗r	ORG
ma-58	150	1	j. math	PERSON
ma-58	152	1	10.28924	CARDINAL
ma-58	152	2	k ∈	PERSON
ma-58	153	1	3.7	CARDINAL
ma-58	154	1	k ∈	PERSON
ma-58	158	1	a〈ξ	ORG
ma-58	158	2	〉 ≤	MONEY
ma-58	158	3	ξ〉b∗,∀ξ ∈	PERSON
ma-58	159	1	∈	PRODUCT
ma-58	159	2	a〈kξ	PERSON
ma-58	159	3	kξ〉a∗ ≤ ∑	FAC
ma-58	159	4	〉 ≤	MONEY
ma-58	159	5	kξ〉b∗ ≤ ‖k‖∞b〈ξ	ORG
ma-58	159	6	ξ〉(‖k‖∞b)∗.	CARDINAL
ma-58	159	7	‖k‖∞b.by	GPE
ma-58	159	8	∑	PERSON
ma-58	160	1	∑	PERSON
ma-58	161	1	k∗t ∗i tikξ	PERSON
ma-58	162	1	3.8	CARDINAL
ma-58	163	1	k ∈	PERSON
ma-58	166	1	3.7	CARDINAL
ma-58	167	1	4	CARDINAL
ma-58	167	2	a⊗b	GPE
ma-58	167	3	a⊗alg	GPE
ma-58	169	1	∈	ORG
ma-58	169	2	η ∈	PERSON
ma-58	169	3	∈	ORG
ma-58	169	4	〉	CARDINAL
ma-58	169	5	⊗alg	NORP
ma-58	169	6	a⊗alg b.	PERSON
ma-58	170	1	⊗	ORG
ma-58	170	2	〉	CARDINAL
ma-58	171	1	∑n i=1	PERSON
ma-58	171	2	x⊗algy	GPE
ma-58	172	1	ξj〉a⊗〈ηi	ORG
ma-58	172	2	0	CARDINAL
ma-58	174	1	j. math	PERSON
ma-58	176	1	10.28924	CARDINAL
ma-58	181	1	∈	ORG
ma-58	181	2	∈	ORG
ma-58	181	3	a⊗b	GPE
ma-58	181	4	a⊗alg	GPE
ma-58	183	1	∈	ORG
ma-58	183	2	η ∈	PERSON
ma-58	183	3	∈	ORG
ma-58	183	4	〉	CARDINAL
ma-58	183	5	⊗alg	NORP
ma-58	183	6	a⊗alg b.	PERSON
ma-58	184	1	⊗	ORG
ma-58	184	2	〉	CARDINAL
ma-58	184	3	〉	CARDINAL
ma-58	185	1	∑n i=1	PERSON
ma-58	185	2	x⊗algy	GPE
ma-58	186	1	ξj〉a⊗〈ηi	ORG
ma-58	192	1	∈	ORG
ma-58	192	2	∈	ORG
ma-58	192	3	9])let	CARDINAL
ma-58	193	1	4.1	CARDINAL
ma-58	194	1	two	CARDINAL
ma-58	195	1	⊂	GPE
ma-58	195	2	⊂	GPE
ma-58	196	1	st ⊗	PERSON
ma-58	198	1	k∗ξ〉aa∗ ≤ ∑	PERSON
ma-58	198	2	ξ〉ab∗,∀ξ ∈	PERSON
ma-58	199	1	η〉bd∗,∀η ∈	NORP
ma-58	200	1	j. math	PERSON
ma-58	202	1	10.28924	CARDINAL
ma-58	202	2	a〈k∗ξ	ORG
ma-58	202	3	d〈η	ORG
ma-58	202	4	∀η	PRODUCT
ma-58	202	5	l∗η	DATE
ma-58	202	6	l∗η〉b)(a∗ ⊗ c∗	PERSON
ma-58	202	7	ξ〉a ⊗ 〈η	ORG
ma-58	202	8	∀η	ORG
ma-58	202	9	⊗ l∗η	PERSON
ma-58	202	10	k∗ξ ⊗	ORG
ma-58	202	11	⊗ pjη〉a⊗b ≤	MONEY
ma-58	202	12	⊗ η	PERSON
ma-58	202	13	⊗ η〉a⊗b(b	PERSON
ma-58	202	14	∈	ORG
ma-58	202	15	∀η	PRODUCT
ma-58	202	16	⊗ η	PERSON
ma-58	202	17	c)〈(k	ORG
ma-58	202	18	⊗ η	PERSON
ma-58	202	19	k ⊗	PERSON
ma-58	202	20	⊗	CARDINAL
ma-58	202	21	⊗ η	PERSON
ma-58	202	22	⊗ η〉a⊗b(b	PERSON
ma-58	203	1	hilbert a⊗b	PERSON
ma-58	203	2	b ⊗d	PERSON
ma-58	203	3	∑	PERSON
ma-58	203	4	∈	ORG
ma-58	204	1	spη = ∑ j∈j p	PERSON
ma-58	204	2	∀η	PERSON
ma-58	204	3	∈	PRODUCT
ma-58	204	4	st ⊗	PERSON
ma-58	204	5	⊗ η	PERSON
ma-58	205	1	∑	PERSON
ma-58	205	2	∑	PERSON
ma-58	205	3	∑	PERSON
ma-58	205	4	⊗	ORG
ma-58	206	1	j. math	PERSON
ma-58	208	1	10.28924	CARDINAL
ma-58	208	2	ma.2.4 10	DATE
ma-58	209	1	∑	PERSON
ma-58	209	2	⊗ pj)(ξ ⊗ η	PERSON
ma-58	211	1	st ⊗sp	GPE
ma-58	215	1	st ⊗	PERSON
ma-58	216	1	st⊗p	DATE
ma-58	216	2	st ⊗	PERSON
ma-58	217	1	1	CARDINAL
ma-58	217	2	n. haddadzadeh	PERSON
ma-58	218	1	j. ind	PERSON
ma-58	220	1	9(4	CARDINAL
ma-58	220	2	2017	CARDINAL
ma-58	220	3	259	CARDINAL
ma-58	220	4	n. haddadzadeh	PERSON
ma-58	221	1	j. ind	PERSON
ma-58	223	1	5(2)(2013	CARDINAL
ma-58	223	2	r. j. duffin	PERSON
ma-58	223	3	a. c. schaeffer	PERSON
ma-58	224	1	amer	PERSON
ma-58	226	1	72	DATE
ma-58	226	2	1952	DATE
ma-58	226	3	341	CARDINAL
ma-58	226	4	∗-algebras	PRODUCT
ma-58	226	5	48	DATE
ma-58	226	6	1988	DATE
ma-58	226	7	1-81.[5	CARDINAL
ma-58	226	8	c∗-algebras	ORG
ma-58	226	9	univ	NORP
ma-58	227	1	münster	PERSON
ma-58	227	2	1997	DATE
ma-58	227	3	1	CARDINAL
ma-58	227	4	north holland	GPE
ma-58	227	5	amsterdam	GPE
ma-58	227	6	2005.[7	CARDINAL
ma-58	227	7	a. grossman	PERSON
ma-58	227	8	y. meyer	PERSON
ma-58	227	9	j. math	ORG
ma-58	229	1	27	CARDINAL
ma-58	229	2	1271-1283.[8	DATE
ma-58	229	3	a. inoue	PERSON
ma-58	229	4	c∗-algebra	ORG
ma-58	229	5	fac	ORG
ma-58	230	1	sci	ORG
ma-58	230	2	kyushu univ	PERSON
ma-58	233	1	25(2	CARDINAL
ma-58	233	2	1972	DATE
ma-58	233	3	197-235.[9	QUANTITY
ma-58	233	4	m. joita	PERSON
ma-58	233	5	topol	PERSON
ma-58	235	1	156	CARDINAL
ma-58	235	2	2008	DATE
ma-58	235	3	83	CARDINAL
ma-58	235	4	e. c. lance	PERSON
ma-58	235	5	hilbert c∗-modules	PERSON
ma-58	235	6	london	GPE
ma-58	237	1	210.cambridge univ.	ORG
ma-58	238	1	cambridge	GPE
ma-58	238	2	c. y. li	PERSON
ma-58	238	3	h. x.	PERSON
ma-58	239	1	birkhäuser basel	PERSON
ma-58	239	2	2006.67-82.[12	CARDINAL
ma-58	239	3	north holland	GPE
ma-58	239	4	amsterdam	GPE
ma-58	239	5	1986.[13	CARDINAL
ma-58	239	6	m. naroei and	PERSON
ma-58	239	7	a. nazari	PERSON
ma-58	241	1	16 (2019	CARDINAL
ma-58	241	2	105–117.[14	CARDINAL
ma-58	241	3	n. c. phillips	PERSON
ma-58	241	4	j. oper.	PERSON
ma-58	242	1	19 (1988	DATE
ma-58	242	2	159	CARDINAL
ma-58	242	3	n. c. phillips	PERSON
ma-58	242	4	representable k-	PERSON
ma-58	242	5	σ -c∗-algebras	PERSON
ma-58	242	6	3	CARDINAL
ma-58	242	7	441	CARDINAL
ma-58	242	8	m. rossafi	PERSON
ma-58	242	9	s. kabbaj	PERSON
ma-58	242	10	j. linear topol	PERSON
ma-58	244	1	8 (2019	CARDINAL
ma-58	244	2	85	CARDINAL
ma-58	245	1	1	CARDINAL
ma-58	245	2	2	CARDINAL
ma-58	245	3	3	CARDINAL
ma-58	246	1	4	CARDINAL