id	sid	eid	entity	type
ap-1410	1	1	acta polytechnica vol	PERSON
ap-1410	2	1	51	CARDINAL
ap-1410	3	1	4/2011	CARDINAL
ap-1410	3	2	z. riečanová	PERSON
ap-1410	3	3	m. zajac	PERSON
ap-1410	6	1	hilbert space	ORG
ap-1410	6	2	linear operators	ORG
ap-1410	7	1	1	CARDINAL
ap-1410	7	2	linear operators	ORG
ap-1410	7	3	hilbert space h.	ORG
ap-1410	7	4	m. k. bennet	PERSON
ap-1410	7	5	1994	DATE
ap-1410	8	1	2	CARDINAL
ap-1410	9	1	hilbert space h.	ORG
ap-1410	10	1	p(h	PERSON
ap-1410	12	1	1	CARDINAL
ap-1410	13	1	2	CARDINAL
ap-1410	13	2	0	CARDINAL
ap-1410	13	3	1	CARDINAL
ap-1410	13	4	0,1	CARDINAL
ap-1410	13	5	two	CARDINAL
ap-1410	13	6	⊕	GPE
ap-1410	15	1	⊕	PERSON
ap-1410	15	2	⊕	PERSON
ap-1410	15	3	⊕	PERSON
ap-1410	16	1	⊕	PERSON
ap-1410	16	2	y ⊕ z	PERSON
ap-1410	16	3	⊕	PERSON
ap-1410	16	4	1	CARDINAL
ap-1410	16	5	x′	DATE
ap-1410	16	6	1 ⊕	FAC
ap-1410	17	1	1994	DATE
ap-1410	17	2	1	CARDINAL
ap-1410	18	1	2	CARDINAL
ap-1410	18	2	riečanová	PERSON
ap-1410	19	1	4	CARDINAL
ap-1410	20	1	3	CARDINAL
ap-1410	20	2	kôpka	ORG
ap-1410	21	1	5	CARDINAL
ap-1410	22	1	2	CARDINAL
ap-1410	22	2	⊕	GPE
ap-1410	23	1	x⊕	PERSON
ap-1410	23	2	x⊕	PERSON
ap-1410	24	1	⊕	PERSON
ap-1410	24	2	⊕	PERSON
ap-1410	25	1	⊕	PERSON
ap-1410	26	1	0	CARDINAL
ap-1410	31	1	∈	ORG
ap-1410	31	2	∈	ORG
ap-1410	33	1	hilbertian	NORP
ap-1410	33	2	1	CARDINAL
ap-1410	33	3	44	CARDINAL
ap-1410	34	1	1	CARDINAL
ap-1410	35	1	d(a	GPE
ap-1410	36	1	linear operators on h	ORG
ap-1410	36	2	l(h	PRODUCT
ap-1410	37	1	73	CARDINAL
ap-1410	37	2	acta polytechnica vol	PERSON
ap-1410	38	1	51	CARDINAL
ap-1410	39	1	4/2011	CARDINAL
ap-1410	39	2	0	CARDINAL
ap-1410	42	1	one	CARDINAL
ap-1410	42	2	∈	PRODUCT
ap-1410	42	3	tx	ORG
ap-1410	45	1	y ∈	PERSON
ap-1410	46	1	y∗ ∈	ORG
ap-1410	46	2	tx	ORG
ap-1410	48	1	tx	ORG
ap-1410	49	1	1	CARDINAL
ap-1410	49	2	98	CARDINAL
ap-1410	50	1	zero	CARDINAL
ap-1410	50	2	0	CARDINAL
ap-1410	51	1	1	CARDINAL
ap-1410	52	1	68	CARDINAL
ap-1410	52	2	94	CARDINAL
ap-1410	53	1	two	CARDINAL
ap-1410	54	1	⊂	GPE
ap-1410	55	1	algebras	ORG
ap-1410	55	2	two	CARDINAL
ap-1410	55	3	one	CARDINAL
ap-1410	56	1	2	CARDINAL
ap-1410	56	2	1	CARDINAL
ap-1410	56	3	chapter 4	LAW
ap-1410	57	1	3	CARDINAL
ap-1410	58	1	∈	ORG
ap-1410	61	1	0	CARDINAL
ap-1410	61	2	∃e	CARDINAL
ap-1410	61	3	ae	ORG
ap-1410	62	1	∈	ORG
ap-1410	62	2	1	CARDINAL
ap-1410	64	1	1	CARDINAL
ap-1410	64	2	0	CARDINAL
ap-1410	64	3	ae	ORG
ap-1410	64	4	ae	ORG
ap-1410	65	1	1	CARDINAL
ap-1410	65	2	∀λ ∈	PERSON
ap-1410	66	1	second	ORDINAL
ap-1410	66	2	first	ORDINAL
ap-1410	66	3	∈	ORG
ap-1410	66	4	ae	ORG
ap-1410	66	5	0	CARDINAL
ap-1410	67	1	4	CARDINAL
ap-1410	70	1	a.	PERSON
ap-1410	71	1	3	CARDINAL
ap-1410	73	1	5	CARDINAL
ap-1410	73	2	0	CARDINAL
ap-1410	74	1	∀x	GPE
ap-1410	74	2	x)| ≤ k‖x‖2	QUANTITY
ap-1410	76	1	0	CARDINAL
ap-1410	76	2	∀x	GPE
ap-1410	76	3	x)| ≤ k‖x‖2	QUANTITY
ap-1410	76	4	1 4	CARDINAL
ap-1410	80	1	‖x‖ =	PERSON
ap-1410	81	1	1	CARDINAL
ap-1410	81	2	|(ax	PRODUCT
ap-1410	83	1	2	CARDINAL
ap-1410	83	2	4	CARDINAL
ap-1410	85	1	k 4	PERSON
ap-1410	90	1	k 4	PERSON
ap-1410	90	2	2‖x‖2	CARDINAL
ap-1410	92	1	k(‖x‖2 + ‖y‖2	ORG
ap-1410	93	1	2k	CARDINAL
ap-1410	94	1	∀x	GPE
ap-1410	95	1	3	CARDINAL
ap-1410	95	2	ϕ(y	ORG
ap-1410	96	1	d(a	GPE
ap-1410	99	1	‖ϕ‖	ORG
ap-1410	100	1	3	CARDINAL
ap-1410	102	1	74	CARDINAL
ap-1410	102	2	acta polytechnica vol	PERSON
ap-1410	103	1	51	CARDINAL
ap-1410	104	1	4/2011	CARDINAL
ap-1410	104	2	6	CARDINAL
ap-1410	106	1	0 ≤	MONEY
ap-1410	107	1	5	CARDINAL
ap-1410	108	1	3	CARDINAL
ap-1410	108	2	two	CARDINAL
ap-1410	108	3	0	CARDINAL
ap-1410	108	4	1	CARDINAL
ap-1410	108	5	more than one	CARDINAL
ap-1410	109	1	7	CARDINAL
ap-1410	109	2	0	CARDINAL
ap-1410	109	3	1	CARDINAL
ap-1410	109	4	⊕2	ORG
ap-1410	110	1	1	CARDINAL
ap-1410	114	1	⊕2	ORG
ap-1410	114	2	⊕2	ORG
ap-1410	114	3	⊕2	ORG
ap-1410	114	4	1	CARDINAL
ap-1410	114	5	⊕2	ORG
ap-1410	114	6	⊕2	ORG
ap-1410	114	7	0	DATE
ap-1410	114	8	1	CARDINAL
ap-1410	114	9	e;⊕2	ORG
ap-1410	114	10	0	CARDINAL
ap-1410	114	11	1	CARDINAL
ap-1410	115	1	0	DATE
ap-1410	115	2	1	CARDINAL
ap-1410	115	3	e;⊕2	ORG
ap-1410	115	4	0	CARDINAL
ap-1410	115	5	1	CARDINAL
ap-1410	115	6	two	CARDINAL
ap-1410	115	7	0	CARDINAL
ap-1410	115	8	⊕2	ORG
ap-1410	115	9	1	CARDINAL
ap-1410	115	10	0	CARDINAL
ap-1410	115	11	b⊕2	ORG
ap-1410	115	12	1	CARDINAL
ap-1410	116	1	two	CARDINAL
ap-1410	116	2	⊕2	ORG
ap-1410	116	3	⊕2	ORG
ap-1410	116	4	8	CARDINAL
ap-1410	116	5	0	DATE
ap-1410	116	6	e;⊕2	ORG
ap-1410	116	7	0	CARDINAL
ap-1410	117	1	⊕2	ORG
ap-1410	117	2	⊕1 ⊂ ⊕2	ORG
ap-1410	117	3	⊕2	ORG
ap-1410	117	4	⊕2	ORG
ap-1410	117	5	9	CARDINAL
ap-1410	117	6	e;⊕1	PERSON
ap-1410	117	7	0	DATE
ap-1410	117	8	e;⊕2	ORG
ap-1410	117	9	0	CARDINAL
ap-1410	117	10	algebras	ORG
ap-1410	117	11	⊕1 ⊂ ⊕2	ORG
ap-1410	118	1	⊆	CARDINAL
ap-1410	119	1	≤1	PERSON
ap-1410	119	2	⊕2	ORG
ap-1410	119	3	≤1	ORG
ap-1410	120	1	0	CARDINAL
ap-1410	120	2	⊆	CARDINAL
ap-1410	120	3	0	CARDINAL
ap-1410	120	4	∈	ORG
ap-1410	121	1	⊕2	ORG
ap-1410	121	2	at least two	CARDINAL
ap-1410	121	3	⊕2	ORG
ap-1410	121	4	⊕2	ORG
ap-1410	123	1	10	CARDINAL
ap-1410	123	2	0	CARDINAL
ap-1410	123	3	1	DATE
ap-1410	123	4	2	CARDINAL
ap-1410	125	1	0	CARDINAL
ap-1410	125	2	1	DATE
ap-1410	125	3	2	DATE
ap-1410	125	4	4	DATE
ap-1410	125	5	6	DATE
ap-1410	126	1	⊕2	ORG
ap-1410	126	2	0	CARDINAL
ap-1410	126	3	4	CARDINAL
ap-1410	127	1	⊕2	ORG
ap-1410	128	1	5	CARDINAL
ap-1410	128	2	≤1	PERSON
ap-1410	129	1	⊕1 ⊂ ⊕2	ORG
ap-1410	129	2	0	DATE
ap-1410	129	3	0	CARDINAL
ap-1410	129	4	algebras	ORG
ap-1410	130	1	g	PERSON
ap-1410	132	1	0	CARDINAL
ap-1410	132	2	⊆	CARDINAL
ap-1410	132	3	0	CARDINAL
ap-1410	135	1	b)⊕1	ORG
ap-1410	136	1	first	ORDINAL
ap-1410	136	2	0	CARDINAL
ap-1410	139	1	0	CARDINAL
ap-1410	140	1	0	CARDINAL
ap-1410	146	1	0	CARDINAL
ap-1410	147	1	two	CARDINAL
ap-1410	147	2	three	CARDINAL
ap-1410	148	1	1	CARDINAL
ap-1410	148	2	2	CARDINAL
ap-1410	148	3	3	CARDINAL
ap-1410	149	1	0	CARDINAL
ap-1410	149	2	0	CARDINAL
ap-1410	150	1	0	CARDINAL
ap-1410	150	2	3]e2	CARDINAL
ap-1410	150	3	0	CARDINAL
ap-1410	150	4	1	DATE
ap-1410	150	5	2	DATE
ap-1410	150	6	3	CARDINAL
ap-1410	150	7	⊆	CARDINAL
ap-1410	150	8	0	CARDINAL
ap-1410	150	9	3]e1	CARDINAL
ap-1410	152	1	4	CARDINAL
ap-1410	154	1	75	CARDINAL
ap-1410	154	2	acta polytechnica vol	PERSON
ap-1410	155	1	51	CARDINAL
ap-1410	156	1	4/2011	CARDINAL
ap-1410	157	1	11	CARDINAL
ap-1410	159	1	d(a	GPE
ap-1410	163	1	d(a	GPE
ap-1410	164	1	∈	ORG
ap-1410	164	2	⊕	GPE
ap-1410	164	3	a⊕b	DATE
ap-1410	165	1	at least one	CARDINAL
ap-1410	166	1	0	DATE
ap-1410	168	1	a+b	PERSON
ap-1410	168	2	at least one	CARDINAL
ap-1410	168	3	d(a	GPE
ap-1410	173	1	⋃	DATE
ap-1410	174	1	∩ gd1(h	PERSON
ap-1410	176	1	⊕	PERSON
ap-1410	177	1	6	CARDINAL
ap-1410	178	1	12	CARDINAL
ap-1410	179	1	6	CARDINAL
ap-1410	179	2	11	CARDINAL
ap-1410	179	3	0	DATE
ap-1410	180	1	∈	ORG
ap-1410	180	2	⊕	GPE
ap-1410	180	3	⊕	GPE
ap-1410	182	1	13	CARDINAL
ap-1410	183	1	8	CARDINAL
ap-1410	183	2	11	CARDINAL
ap-1410	187	1	d(h)b	PERSON
ap-1410	188	1	d(h)b	PERSON
ap-1410	190	1	⊕	GPE
ap-1410	190	2	⊂	GPE
ap-1410	191	1	two	CARDINAL
ap-1410	192	1	theorems 12 and	ORG
ap-1410	192	2	13	CARDINAL
ap-1410	192	3	14	CARDINAL
ap-1410	193	1	d(a	GPE
ap-1410	194	1	d(a	GPE
ap-1410	196	1	d(h)b	PERSON
ap-1410	196	2	⊕	GPE
ap-1410	197	1	sp(h);⊕	ORG
ap-1410	198	1	algebras gd	NORP
ap-1410	199	1	algebras sp	ORG
ap-1410	200	1	15	CARDINAL
ap-1410	201	1	algebras gd	NORP
ap-1410	201	2	1	CARDINAL
ap-1410	202	1	2	CARDINAL
ap-1410	203	1	⋃	DATE
ap-1410	205	1	algebras sp	ORG
ap-1410	206	1	∈	ORG
ap-1410	206	2	1) spd1(h	DATE
ap-1410	206	3	∩ spd2	ORG
ap-1410	207	1	2	CARDINAL
ap-1410	208	1	⋃	DATE
ap-1410	210	1	16	CARDINAL
ap-1410	212	1	⊕	GPE
ap-1410	213	1	5	CARDINAL
ap-1410	214	1	∈	ORG
ap-1410	215	1	⊕|[0,q]e	DATE
ap-1410	215	2	76	CARDINAL
ap-1410	216	1	51	CARDINAL
ap-1410	217	1	4/2011	CARDINAL
ap-1410	218	1	0	CARDINAL
ap-1410	218	2	0	CARDINAL
ap-1410	219	1	0	CARDINAL
ap-1410	219	2	⊕|[0,q]e	DATE
ap-1410	220	1	7	CARDINAL
ap-1410	221	1	algebras	ORG
ap-1410	221	2	0	CARDINAL
ap-1410	221	3	0	DATE
ap-1410	221	4	0	CARDINAL
ap-1410	221	5	q]vd(h	GPE
ap-1410	221	6	⊕d|[0,q]vd(h	ORG
ap-1410	221	7	0	DATE
ap-1410	221	8	8	CARDINAL
ap-1410	222	1	⊕	GPE
ap-1410	222	2	section 2	LAW
ap-1410	223	1	0	CARDINAL
ap-1410	223	2	⊂	GPE
ap-1410	225	1	0	CARDINAL
ap-1410	225	2	q]vd(h	GPE
ap-1410	225	3	⊂	GPE
ap-1410	226	1	∈	ORG
ap-1410	228	1	0	CARDINAL
ap-1410	228	2	0	CARDINAL
ap-1410	228	3	0	DATE
ap-1410	230	1	d(q	PERSON
ap-1410	231	1	18	CARDINAL
ap-1410	231	2	7	CARDINAL
ap-1410	231	3	8	CARDINAL
ap-1410	232	1	17	CARDINAL
ap-1410	233	1	0	CARDINAL
ap-1410	233	2	1	CARDINAL
ap-1410	233	3	1	CARDINAL
ap-1410	234	1	1	CARDINAL
ap-1410	234	2	2	CARDINAL
ap-1410	234	3	⊕	GPE
ap-1410	234	4	e. 3	DATE
ap-1410	235	1	ω	ORG
ap-1410	235	2	ω(a	ORG
ap-1410	235	3	0	CARDINAL
ap-1410	235	4	0	CARDINAL
ap-1410	235	5	4	CARDINAL
ap-1410	236	1	e. theorem 18	PERSON
ap-1410	237	1	x̃ ∈ d(q	ORG
ap-1410	237	2	x̃	ORG
ap-1410	238	1	0	CARDINAL
ap-1410	238	2	0	CARDINAL
ap-1410	239	1	0	CARDINAL
ap-1410	239	2	1	CARDINAL
ap-1410	239	3	1	CARDINAL
ap-1410	239	4	x̃	ORG
ap-1410	239	5	0	CARDINAL
ap-1410	241	1	0	CARDINAL
ap-1410	242	1	state	ORG
ap-1410	243	1	0	CARDINAL
ap-1410	244	1	0	CARDINAL
ap-1410	244	2	1	CARDINAL
ap-1410	245	1	1/0297/11	CARDINAL
ap-1410	245	2	vega 1/0021/10	ORG
ap-1410	245	3	the ministry of education	ORG
ap-1410	245	4	the slovak republic	GPE
ap-1410	246	1	1	CARDINAL
ap-1410	246	2	j.	PERSON
ap-1410	246	3	havĺıček	ORG
ap-1410	246	4	m.: hilbert	PERSON
ap-1410	246	5	second	ORDINAL
ap-1410	247	1	2008	DATE
ap-1410	248	1	2	CARDINAL
ap-1410	248	2	d. j., bennet	PERSON
ap-1410	248	3	m. k.:	PERSON
ap-1410	248	4	algebras	ORG
ap-1410	248	5	quantum	ORG
ap-1410	250	1	24	CARDINAL
ap-1410	250	2	1	CARDINAL
ap-1410	250	3	352	CARDINAL
ap-1410	251	1	3	CARDINAL
ap-1410	251	2	j.	PERSON
ap-1410	251	3	pulmannová	NORP
ap-1410	251	4	s.	PERSON
ap-1410	252	1	univ.	ORG
ap-1410	252	2	45 (1996	DATE
ap-1410	252	3	247–279	CARDINAL
ap-1410	253	1	4	CARDINAL
ap-1410	253	2	g.	PERSON
ap-1410	253	3	riečanová	PERSON
ap-1410	253	4	z.	PERSON
ap-1410	253	5	abelian	NORP
ap-1410	253	6	demonstratio	ORG
ap-1410	254	1	27 (1996	DATE
ap-1410	254	2	769–780	CARDINAL
ap-1410	255	1	5	CARDINAL
ap-1410	255	2	chovanec	PERSON
ap-1410	256	1	44 (1994	DATE
ap-1410	256	2	21–34	CARDINAL
ap-1410	257	1	6	CARDINAL
ap-1410	257	2	z.	PERSON
ap-1410	257	3	hilbert spaces	ORG
ap-1410	258	1	7	CARDINAL
ap-1410	258	2	z.	PERSON
ap-1410	259	1	algebras	ORG
ap-1410	260	1	international journal of theoretic physics	ORG
ap-1410	260	2	38 (1999	DATE
ap-1410	260	3	3	CARDINAL
ap-1410	260	4	220	CARDINAL
ap-1410	261	1	8	CARDINAL
ap-1410	261	2	z.	PERSON
ap-1410	261	3	zajac	GPE
ap-1410	261	4	pulmannová	NORP
ap-1410	261	5	s.	PERSON
ap-1410	261	6	algebras of positive linear	ORG
ap-1410	261	7	hilbert spaces	ORG
ap-1410	262	1	riečanová e-mail	PERSON
ap-1410	262	2	m. zajac e-mail	PERSON
ap-1410	262	3	zajacm@stuba.sk	PERSON
ap-1410	262	4	stu	PERSON
ap-1410	262	5	3	CARDINAL