id	sid	tid	token	lemma	pos
ap-1817	1	1	acta	acta	PROPN
ap-1817	1	2	polytechnica	polytechnica	PROPN
ap-1817	1	3	acta	acta	PROPN
ap-1817	1	4	polytechnica	polytechnica	PROPN
ap-1817	1	5	53(3):314–316	53(3):314–316	PROPN
ap-1817	1	6	,	,	PUNCT
ap-1817	1	7	2013	2013	NUM
ap-1817	1	8	©	©	PROPN
ap-1817	1	9	czech	czech	PROPN
ap-1817	1	10	technical	technical	PROPN
ap-1817	1	11	university	university	PROPN
ap-1817	1	12	in	in	ADP
ap-1817	1	13	prague	prague	PROPN
ap-1817	1	14	,	,	PUNCT
ap-1817	1	15	2013	2013	NUM
ap-1817	1	16	available	available	ADJ
ap-1817	1	17	online	online	ADV
ap-1817	1	18	at	at	ADP
ap-1817	1	19	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	ADJ
ap-1817	1	20	intervals	interval	NOUN
ap-1817	1	21	in	in	ADP
ap-1817	1	22	generalized	generalized	ADJ
ap-1817	1	23	effect	effect	NOUN
ap-1817	1	24	algebras	algebra	NOUN
ap-1817	1	25	and	and	CCONJ
ap-1817	1	26	their	their	PRON
ap-1817	1	27	sub	sub	ADJ
ap-1817	1	28	-	-	ADJ
ap-1817	1	29	generalized	generalized	ADJ
ap-1817	1	30	effect	effect	NOUN
ap-1817	1	31	algebras	algebras	PROPN
ap-1817	1	32	zdenka	zdenka	PROPN
ap-1817	1	33	riečanová∗	riečanová∗	PROPN
ap-1817	1	34	,	,	PUNCT
ap-1817	1	35	michal	michal	PROPN
ap-1817	1	36	zajac	zajac	PROPN
ap-1817	1	37	department	department	PROPN
ap-1817	1	38	of	of	ADP
ap-1817	1	39	mathematics	mathematic	NOUN
ap-1817	1	40	,	,	PUNCT
ap-1817	1	41	faculty	faculty	NOUN
ap-1817	1	42	of	of	ADP
ap-1817	1	43	electrical	electrical	ADJ
ap-1817	1	44	engineering	engineering	NOUN
ap-1817	1	45	and	and	CCONJ
ap-1817	1	46	information	information	NOUN
ap-1817	1	47	technology	technology	PROPN
ap-1817	1	48	stu	stu	PROPN
ap-1817	1	49	,	,	PUNCT
ap-1817	1	50	ilkovičova	ilkovičova	VERB
ap-1817	1	51	3	3	NUM
ap-1817	1	52	,	,	PUNCT
ap-1817	1	53	sk-81219	sk-81219	ADJ
ap-1817	1	54	bratislava	bratislava	PROPN
ap-1817	1	55	∗	∗	NOUN
ap-1817	1	56	corresponding	correspond	VERB
ap-1817	1	57	author	author	NOUN
ap-1817	1	58	:	:	PUNCT
ap-1817	1	59	zdenka.riecanova@stuba.sk	zdenka.riecanova@stuba.sk	PROPN
ap-1817	1	60	abstract	abstract	NOUN
ap-1817	1	61	.	.	PUNCT
ap-1817	2	1	we	we	PRON
ap-1817	2	2	consider	consider	VERB
ap-1817	2	3	subsets	subset	NOUN
ap-1817	2	4	g	g	ADP
ap-1817	2	5	of	of	ADP
ap-1817	2	6	a	a	DET
ap-1817	2	7	generalized	generalized	ADJ
ap-1817	2	8	effect	effect	NOUN
ap-1817	2	9	algebra	algebra	NOUN
ap-1817	2	10	e	e	NOUN
ap-1817	2	11	with	with	ADP
ap-1817	2	12	0	0	NUM
ap-1817	2	13	∈	∈	PROPN
ap-1817	2	14	g	g	NOUN
ap-1817	2	15	and	and	CCONJ
ap-1817	2	16	such	such	ADJ
ap-1817	2	17	that	that	SCONJ
ap-1817	2	18	every	every	DET
ap-1817	2	19	interval	interval	NOUN
ap-1817	2	20	[	[	X
ap-1817	2	21	0	0	NUM
ap-1817	2	22	,	,	PUNCT
ap-1817	2	23	q]g	q]g	ADV
ap-1817	2	24	=	=	PUNCT
ap-1817	3	1	[	[	X
ap-1817	3	2	0	0	NUM
ap-1817	3	3	,	,	PUNCT
ap-1817	3	4	q]e	q]e	ADJ
ap-1817	3	5	∩g	∩g	NOUN
ap-1817	3	6	of	of	ADP
ap-1817	3	7	g	g	PROPN
ap-1817	3	8	(	(	PUNCT
ap-1817	3	9	q	q	NOUN
ap-1817	3	10	∈	∈	PROPN
ap-1817	3	11	g	g	NOUN
ap-1817	3	12	,	,	PUNCT
ap-1817	3	13	q	q	X
ap-1817	3	14	6=	6=	NUM
ap-1817	3	15	0	0	NUM
ap-1817	3	16	)	)	PUNCT
ap-1817	3	17	is	be	AUX
ap-1817	3	18	a	a	DET
ap-1817	3	19	sub	sub	ADJ
ap-1817	3	20	-	-	ADJ
ap-1817	3	21	effect	effect	ADJ
ap-1817	3	22	algebra	algebra	NOUN
ap-1817	3	23	of	of	ADP
ap-1817	3	24	the	the	DET
ap-1817	3	25	effect	effect	NOUN
ap-1817	3	26	algebra	algebra	NOUN
ap-1817	3	27	[	[	X
ap-1817	3	28	0	0	NUM
ap-1817	3	29	,	,	PUNCT
ap-1817	3	30	q]e	q]e	ADV
ap-1817	3	31	.	.	PUNCT
ap-1817	4	1	we	we	PRON
ap-1817	4	2	give	give	VERB
ap-1817	4	3	a	a	DET
ap-1817	4	4	condition	condition	NOUN
ap-1817	4	5	on	on	ADP
ap-1817	4	6	e	e	NOUN
ap-1817	4	7	and	and	CCONJ
ap-1817	4	8	g	g	PROPN
ap-1817	4	9	under	under	ADP
ap-1817	4	10	which	which	PRON
ap-1817	4	11	every	every	DET
ap-1817	4	12	such	such	ADJ
ap-1817	4	13	g	g	PROPN
ap-1817	4	14	is	be	AUX
ap-1817	4	15	a	a	DET
ap-1817	4	16	sub	sub	ADJ
ap-1817	4	17	-	-	ADJ
ap-1817	4	18	generalized	generalized	ADJ
ap-1817	4	19	effect	effect	NOUN
ap-1817	4	20	algebra	algebra	NOUN
ap-1817	4	21	of	of	ADP
ap-1817	4	22	e.	e.	PROPN
ap-1817	4	23	keywords	keywords	PROPN
ap-1817	4	24	:	:	PUNCT
ap-1817	4	25	generalized	generalized	ADJ
ap-1817	4	26	effect	effect	NOUN
ap-1817	4	27	algebra	algebra	NOUN
ap-1817	4	28	,	,	PUNCT
ap-1817	4	29	effect	effect	NOUN
ap-1817	4	30	algebra	algebra	NOUN
ap-1817	4	31	,	,	PUNCT
ap-1817	4	32	hilbert	hilbert	NOUN
ap-1817	4	33	space	space	NOUN
ap-1817	4	34	,	,	PUNCT
ap-1817	4	35	densely	densely	ADV
ap-1817	4	36	defined	define	VERB
ap-1817	4	37	linear	linear	PROPN
ap-1817	4	38	operators	operator	NOUN
ap-1817	4	39	,	,	PUNCT
ap-1817	4	40	embedding	embed	VERB
ap-1817	4	41	,	,	PUNCT
ap-1817	4	42	positive	positive	ADJ
ap-1817	4	43	operators	operator	NOUN
ap-1817	4	44	valued	value	VERB
ap-1817	4	45	state	state	NOUN
ap-1817	4	46	.	.	PUNCT
ap-1817	5	1	1	1	X
ap-1817	5	2	.	.	X
ap-1817	5	3	introduction	introduction	NOUN
ap-1817	5	4	and	and	CCONJ
ap-1817	5	5	some	some	DET
ap-1817	5	6	basic	basic	ADJ
ap-1817	5	7	definitions	definition	NOUN
ap-1817	5	8	and	and	CCONJ
ap-1817	5	9	facts	fact	VERB
ap-1817	5	10	the	the	DET
ap-1817	5	11	hilbert	hilbert	NOUN
ap-1817	5	12	space	space	NOUN
ap-1817	5	13	effect	effect	NOUN
ap-1817	5	14	algebra	algebra	VERB
ap-1817	5	15	e(h	e(h	PROPN
ap-1817	5	16	)	)	PUNCT
ap-1817	5	17	on	on	ADP
ap-1817	5	18	a	a	DET
ap-1817	5	19	hilbert	hilbert	NOUN
ap-1817	5	20	space	space	NOUN
ap-1817	5	21	h	h	NOUN
ap-1817	5	22	is	be	AUX
ap-1817	5	23	the	the	DET
ap-1817	5	24	set	set	NOUN
ap-1817	5	25	of	of	ADP
ap-1817	5	26	positive	positive	ADJ
ap-1817	5	27	operators	operator	NOUN
ap-1817	5	28	dominated	dominate	VERB
ap-1817	5	29	by	by	ADP
ap-1817	5	30	the	the	DET
ap-1817	5	31	identity	identity	NOUN
ap-1817	5	32	operator	operator	NOUN
ap-1817	5	33	i.	i.	NOUN
ap-1817	5	34	in	in	ADP
ap-1817	5	35	the	the	DET
ap-1817	5	36	quantum	quantum	ADJ
ap-1817	5	37	mechanical	mechanical	ADJ
ap-1817	5	38	framework	framework	NOUN
ap-1817	5	39	the	the	DET
ap-1817	5	40	elements	element	NOUN
ap-1817	5	41	of	of	ADP
ap-1817	5	42	an	an	DET
ap-1817	5	43	effect	effect	NOUN
ap-1817	5	44	algebra	algebra	NOUN
ap-1817	5	45	represent	represent	VERB
ap-1817	5	46	quantum	quantum	ADJ
ap-1817	5	47	effects	effect	NOUN
ap-1817	5	48	and	and	CCONJ
ap-1817	5	49	these	these	PRON
ap-1817	5	50	are	be	AUX
ap-1817	5	51	important	important	ADJ
ap-1817	5	52	for	for	ADP
ap-1817	5	53	quantum	quantum	ADJ
ap-1817	5	54	statistics	statistic	NOUN
ap-1817	5	55	and	and	CCONJ
ap-1817	5	56	for	for	ADP
ap-1817	5	57	quantum	quantum	ADJ
ap-1817	5	58	mechanical	mechanical	ADJ
ap-1817	5	59	theory	theory	NOUN
ap-1817	5	60	(	(	PUNCT
ap-1817	5	61	see	see	VERB
ap-1817	5	62	[	[	X
ap-1817	5	63	2	2	NUM
ap-1817	5	64	,	,	PUNCT
ap-1817	5	65	3	3	NUM
ap-1817	5	66	]	]	NUM
ap-1817	5	67	)	)	PUNCT
ap-1817	5	68	.	.	PUNCT
ap-1817	6	1	one	one	PRON
ap-1817	6	2	may	may	AUX
ap-1817	6	3	think	think	VERB
ap-1817	6	4	of	of	ADP
ap-1817	6	5	quantum	quantum	NOUN
ap-1817	6	6	effects	effect	NOUN
ap-1817	6	7	as	as	ADP
ap-1817	6	8	elementary	elementary	ADJ
ap-1817	6	9	yesno	yesno	ADJ
ap-1817	6	10	measurements	measurement	NOUN
ap-1817	6	11	that	that	PRON
ap-1817	6	12	may	may	AUX
ap-1817	6	13	be	be	AUX
ap-1817	6	14	unsharp	unsharp	ADJ
ap-1817	6	15	or	or	CCONJ
ap-1817	6	16	imprecise	imprecise	ADV
ap-1817	6	17	.	.	PUNCT
ap-1817	7	1	effect	effect	NOUN
ap-1817	7	2	algebras	algebra	NOUN
ap-1817	7	3	were	be	AUX
ap-1817	7	4	introduced	introduce	VERB
ap-1817	7	5	by	by	ADP
ap-1817	7	6	d.	d.	PROPN
ap-1817	7	7	foulis	foulis	PROPN
ap-1817	7	8	and	and	CCONJ
ap-1817	7	9	m.k	m.k	PROPN
ap-1817	7	10	.	.	PUNCT
ap-1817	7	11	bennet	bennet	PROPN
ap-1817	7	12	in	in	ADP
ap-1817	7	13	1994	1994	NUM
ap-1817	7	14	[	[	X
ap-1817	7	15	1	1	NUM
ap-1817	7	16	]	]	PUNCT
ap-1817	7	17	.	.	PUNCT
ap-1817	8	1	the	the	DET
ap-1817	8	2	prototype	prototype	NOUN
ap-1817	8	3	for	for	ADP
ap-1817	8	4	the	the	DET
ap-1817	8	5	abstract	abstract	ADJ
ap-1817	8	6	definition	definition	NOUN
ap-1817	8	7	of	of	ADP
ap-1817	8	8	an	an	DET
ap-1817	8	9	effect	effect	NOUN
ap-1817	8	10	algebra	algebra	NOUN
ap-1817	8	11	was	be	AUX
ap-1817	8	12	the	the	DET
ap-1817	8	13	set	set	NOUN
ap-1817	8	14	e(h	e(h	PROPN
ap-1817	8	15	)	)	PUNCT
ap-1817	8	16	(	(	PUNCT
ap-1817	8	17	hilbert	hilbert	NOUN
ap-1817	8	18	space	space	NOUN
ap-1817	8	19	effects	effect	NOUN
ap-1817	8	20	)	)	PUNCT
ap-1817	8	21	of	of	ADP
ap-1817	8	22	all	all	DET
ap-1817	8	23	selfadjoint	selfadjoint	NOUN
ap-1817	8	24	operators	operator	NOUN
ap-1817	8	25	between	between	ADP
ap-1817	8	26	null	null	ADJ
ap-1817	8	27	and	and	CCONJ
ap-1817	8	28	identity	identity	NOUN
ap-1817	8	29	operators	operator	NOUN
ap-1817	8	30	in	in	ADP
ap-1817	8	31	a	a	DET
ap-1817	8	32	complex	complex	ADJ
ap-1817	8	33	hilbert	hilbert	NOUN
ap-1817	8	34	space	space	NOUN
ap-1817	8	35	h.	h.	PROPN
ap-1817	8	36	if	if	SCONJ
ap-1817	8	37	a	a	DET
ap-1817	8	38	quantum	quantum	ADJ
ap-1817	8	39	mechanical	mechanical	ADJ
ap-1817	8	40	system	system	NOUN
ap-1817	8	41	is	be	AUX
ap-1817	8	42	represented	represent	VERB
ap-1817	8	43	in	in	ADP
ap-1817	8	44	the	the	DET
ap-1817	8	45	usual	usual	ADJ
ap-1817	8	46	way	way	NOUN
ap-1817	8	47	by	by	ADP
ap-1817	8	48	a	a	DET
ap-1817	8	49	complex	complex	ADJ
ap-1817	8	50	hilbert	hilbert	NOUN
ap-1817	8	51	space	space	NOUN
ap-1817	8	52	h	h	NOUN
ap-1817	8	53	then	then	ADV
ap-1817	8	54	self	self	NOUN
ap-1817	8	55	-	-	PUNCT
ap-1817	8	56	adjoint	adjoint	NOUN
ap-1817	8	57	operators	operator	NOUN
ap-1817	8	58	from	from	ADP
ap-1817	8	59	e(h	e(h	PROPN
ap-1817	8	60	)	)	PUNCT
ap-1817	8	61	represent	represent	VERB
ap-1817	8	62	yes	yes	NOUN
ap-1817	8	63	-	-	PUNCT
ap-1817	8	64	no	no	PRON
ap-1817	8	65	measurements	measurement	NOUN
ap-1817	8	66	that	that	PRON
ap-1817	8	67	may	may	AUX
ap-1817	8	68	be	be	AUX
ap-1817	8	69	unsharp	unsharp	ADJ
ap-1817	8	70	.	.	PUNCT
ap-1817	9	1	recently	recently	ADV
ap-1817	9	2	several	several	ADJ
ap-1817	9	3	examples	example	NOUN
ap-1817	9	4	and	and	CCONJ
ap-1817	9	5	properties	property	NOUN
ap-1817	9	6	of	of	ADP
ap-1817	9	7	operator	operator	NOUN
ap-1817	9	8	(	(	PUNCT
ap-1817	9	9	generalized	generalized	ADJ
ap-1817	9	10	)	)	PUNCT
ap-1817	9	11	effect	effect	NOUN
ap-1817	9	12	algebras	algebra	NOUN
ap-1817	9	13	were	be	AUX
ap-1817	9	14	studied	study	VERB
ap-1817	9	15	in	in	ADP
ap-1817	9	16	papers	paper	NOUN
ap-1817	9	17	polakovič	polakovič	VERB
ap-1817	9	18	,	,	PUNCT
ap-1817	9	19	riečanová	riečanová	PROPN
ap-1817	10	1	[	[	X
ap-1817	10	2	9	9	NUM
ap-1817	10	3	]	]	PUNCT
ap-1817	10	4	,	,	PUNCT
ap-1817	10	5	polakovič	polakovič	VERB
ap-1817	10	6	[	[	PUNCT
ap-1817	10	7	10	10	NUM
ap-1817	10	8	]	]	PUNCT
ap-1817	10	9	,	,	PUNCT
ap-1817	10	10	paseka	paseka	ADP
ap-1817	10	11	,	,	PUNCT
ap-1817	10	12	riečanová	riečanová	PROPN
ap-1817	11	1	[	[	X
ap-1817	11	2	8	8	NUM
ap-1817	11	3	]	]	PUNCT
ap-1817	11	4	,	,	PUNCT
ap-1817	11	5	riečanová	riečanová	PROPN
ap-1817	11	6	,	,	PUNCT
ap-1817	11	7	zajac	zajac	PROPN
ap-1817	11	8	,	,	PUNCT
ap-1817	11	9	pulmannová	pulmannová	PROPN
ap-1817	12	1	[	[	X
ap-1817	12	2	12	12	NUM
ap-1817	12	3	]	]	PUNCT
ap-1817	12	4	,	,	PUNCT
ap-1817	12	5	pulmannová	pulmannová	PROPN
ap-1817	12	6	,	,	PUNCT
ap-1817	12	7	riečanová	riečanová	PROPN
ap-1817	12	8	,	,	PUNCT
ap-1817	12	9	zajac	zajac	PROPN
ap-1817	13	1	[	[	X
ap-1817	13	2	11	11	NUM
ap-1817	13	3	]	]	PUNCT
ap-1817	13	4	,	,	PUNCT
ap-1817	13	5	riečanová	riečanová	PROPN
ap-1817	13	6	,	,	PUNCT
ap-1817	13	7	zajac	zajac	PROPN
ap-1817	14	1	[	[	X
ap-1817	14	2	13	13	NUM
ap-1817	14	3	]	]	PUNCT
ap-1817	14	4	and	and	CCONJ
ap-1817	14	5	riečanová	riečanová	PROPN
ap-1817	15	1	[	[	X
ap-1817	15	2	14	14	NUM
ap-1817	15	3	]	]	PUNCT
ap-1817	15	4	the	the	DET
ap-1817	15	5	abstract	abstract	ADJ
ap-1817	15	6	definition	definition	NOUN
ap-1817	15	7	of	of	ADP
ap-1817	15	8	an	an	DET
ap-1817	15	9	effect	effect	NOUN
ap-1817	15	10	algebra	algebra	NOUN
ap-1817	15	11	follows	follow	VERB
ap-1817	15	12	the	the	DET
ap-1817	15	13	properties	property	NOUN
ap-1817	15	14	of	of	ADP
ap-1817	15	15	the	the	DET
ap-1817	15	16	usual	usual	ADJ
ap-1817	15	17	sum	sum	NOUN
ap-1817	15	18	of	of	ADP
ap-1817	15	19	operators	operator	NOUN
ap-1817	15	20	in	in	ADP
ap-1817	15	21	the	the	DET
ap-1817	15	22	interval	interval	NOUN
ap-1817	15	23	[	[	X
ap-1817	15	24	0	0	NUM
ap-1817	15	25	,	,	PUNCT
ap-1817	15	26	i	i	PRON
ap-1817	15	27	]	]	X
ap-1817	15	28	(	(	PUNCT
ap-1817	15	29	i.e.	i.e.	X
ap-1817	15	30	between	between	ADP
ap-1817	15	31	null	null	ADJ
ap-1817	15	32	and	and	CCONJ
ap-1817	15	33	identity	identity	NOUN
ap-1817	15	34	operators	operator	NOUN
ap-1817	15	35	in	in	ADP
ap-1817	15	36	h	h	NOUN
ap-1817	15	37	)	)	PUNCT
ap-1817	15	38	and	and	CCONJ
ap-1817	15	39	it	it	PRON
ap-1817	15	40	is	be	AUX
ap-1817	15	41	the	the	DET
ap-1817	15	42	following	following	NOUN
ap-1817	15	43	.	.	PUNCT
ap-1817	16	1	definition	definition	NOUN
ap-1817	16	2	1.1	1.1	NUM
ap-1817	16	3	(	(	PUNCT
ap-1817	16	4	foulis	foulis	PROPN
ap-1817	16	5	,	,	PUNCT
ap-1817	16	6	bennet	bennet	PROPN
ap-1817	17	1	[	[	X
ap-1817	17	2	1	1	NUM
ap-1817	17	3	]	]	NUM
ap-1817	17	4	)	)	PUNCT
ap-1817	17	5	.	.	PUNCT
ap-1817	18	1	a	a	DET
ap-1817	18	2	partial	partial	ADJ
ap-1817	18	3	algebra	algebra	NOUN
ap-1817	18	4	(	(	PUNCT
ap-1817	18	5	e;⊕	e;⊕	ADJ
ap-1817	18	6	,	,	PUNCT
ap-1817	18	7	0	0	NUM
ap-1817	18	8	,	,	PUNCT
ap-1817	18	9	1	1	NUM
ap-1817	18	10	)	)	PUNCT
ap-1817	18	11	is	be	AUX
ap-1817	18	12	called	call	VERB
ap-1817	18	13	an	an	DET
ap-1817	18	14	effect	effect	NOUN
ap-1817	18	15	algebra	algebra	NOUN
ap-1817	18	16	if	if	SCONJ
ap-1817	18	17	0,1	0,1	NUM
ap-1817	18	18	are	be	AUX
ap-1817	18	19	two	two	NUM
ap-1817	18	20	distinguished	distinguished	ADJ
ap-1817	18	21	elements	element	NOUN
ap-1817	18	22	and	and	CCONJ
ap-1817	18	23	⊕	⊕	PROPN
ap-1817	18	24	is	be	AUX
ap-1817	18	25	a	a	DET
ap-1817	18	26	partially	partially	ADV
ap-1817	18	27	defined	define	VERB
ap-1817	18	28	binary	binary	ADJ
ap-1817	18	29	operation	operation	NOUN
ap-1817	18	30	on	on	ADP
ap-1817	18	31	e	e	PROPN
ap-1817	18	32	which	which	PRON
ap-1817	18	33	satisfy	satisfy	VERB
ap-1817	18	34	the	the	DET
ap-1817	18	35	following	follow	VERB
ap-1817	18	36	conditions	condition	NOUN
ap-1817	18	37	for	for	ADP
ap-1817	18	38	any	any	DET
ap-1817	18	39	x	x	NOUN
ap-1817	18	40	,	,	PUNCT
ap-1817	18	41	y	y	PROPN
ap-1817	18	42	,	,	PUNCT
ap-1817	18	43	z	z	NOUN
ap-1817	18	44	∈	∈	PROPN
ap-1817	19	1	e	e	NOUN
ap-1817	19	2	:	:	PUNCT
ap-1817	19	3	(	(	PUNCT
ap-1817	19	4	e1	e1	NOUN
ap-1817	19	5	)	)	PUNCT
ap-1817	19	6	x⊕	x⊕	PROPN
ap-1817	19	7	y	y	PROPN
ap-1817	19	8	=	=	SYM
ap-1817	19	9	y	y	PROPN
ap-1817	19	10	⊕	⊕	PROPN
ap-1817	19	11	x	x	PUNCT
ap-1817	20	1	if	if	SCONJ
ap-1817	20	2	x⊕	x⊕	PROPN
ap-1817	20	3	y	y	PROPN
ap-1817	20	4	is	be	AUX
ap-1817	20	5	defined	define	VERB
ap-1817	20	6	,	,	PUNCT
ap-1817	20	7	(	(	PUNCT
ap-1817	20	8	e2	e2	PROPN
ap-1817	20	9	)	)	PUNCT
ap-1817	20	10	(	(	PUNCT
ap-1817	20	11	x⊕	x⊕	PROPN
ap-1817	20	12	y)⊕	y)⊕	NOUN
ap-1817	20	13	z	z	NOUN
ap-1817	20	14	=	=	SYM
ap-1817	20	15	x⊕	x⊕	PROPN
ap-1817	20	16	(	(	PUNCT
ap-1817	20	17	y⊕	y⊕	PROPN
ap-1817	20	18	z	z	PROPN
ap-1817	20	19	)	)	PUNCT
ap-1817	20	20	if	if	SCONJ
ap-1817	20	21	one	one	NUM
ap-1817	20	22	side	side	NOUN
ap-1817	20	23	is	be	AUX
ap-1817	20	24	defined	define	VERB
ap-1817	20	25	,	,	PUNCT
ap-1817	20	26	(	(	PUNCT
ap-1817	20	27	e3	e3	NOUN
ap-1817	20	28	)	)	PUNCT
ap-1817	20	29	for	for	ADP
ap-1817	20	30	every	every	DET
ap-1817	20	31	x	x	SYM
ap-1817	20	32	∈	∈	PROPN
ap-1817	20	33	e	e	NOUN
ap-1817	20	34	there	there	PRON
ap-1817	20	35	exists	exist	VERB
ap-1817	20	36	a	a	DET
ap-1817	20	37	unique	unique	ADJ
ap-1817	20	38	y	y	PROPN
ap-1817	20	39	∈	∈	PROPN
ap-1817	20	40	e	e	NOUN
ap-1817	20	41	such	such	ADJ
ap-1817	20	42	that	that	SCONJ
ap-1817	20	43	x⊕	x⊕	PROPN
ap-1817	20	44	y	y	PROPN
ap-1817	20	45	=	=	SYM
ap-1817	20	46	1	1	NUM
ap-1817	20	47	(	(	PUNCT
ap-1817	20	48	we	we	PRON
ap-1817	20	49	put	put	VERB
ap-1817	20	50	x′	x′	PROPN
ap-1817	21	1	=	=	SYM
ap-1817	21	2	y	y	PROPN
ap-1817	21	3	)	)	PUNCT
ap-1817	21	4	,	,	PUNCT
ap-1817	21	5	(	(	PUNCT
ap-1817	21	6	e4	e4	PROPN
ap-1817	21	7	)	)	PUNCT
ap-1817	21	8	if	if	SCONJ
ap-1817	21	9	1⊕	1⊕	NUM
ap-1817	21	10	x	x	SYM
ap-1817	21	11	is	be	AUX
ap-1817	21	12	defined	define	VERB
ap-1817	21	13	then	then	ADV
ap-1817	21	14	x	x	X
ap-1817	21	15	=	=	SYM
ap-1817	21	16	0	0	X
ap-1817	21	17	.	.	PUNCT
ap-1817	22	1	immediately	immediately	ADV
ap-1817	22	2	in	in	ADP
ap-1817	22	3	1994	1994	NUM
ap-1817	22	4	the	the	DET
ap-1817	22	5	study	study	NOUN
ap-1817	22	6	of	of	ADP
ap-1817	22	7	generalizations	generalization	NOUN
ap-1817	22	8	of	of	ADP
ap-1817	22	9	effect	effect	NOUN
ap-1817	22	10	algebras	algebra	NOUN
ap-1817	22	11	(	(	PUNCT
ap-1817	22	12	without	without	ADP
ap-1817	22	13	the	the	DET
ap-1817	22	14	top	top	ADJ
ap-1817	22	15	element	element	NOUN
ap-1817	22	16	1	1	NUM
ap-1817	22	17	)	)	PUNCT
ap-1817	22	18	was	be	AUX
ap-1817	22	19	started	start	VERB
ap-1817	22	20	by	by	ADP
ap-1817	22	21	several	several	ADJ
ap-1817	22	22	authors	author	NOUN
ap-1817	22	23	(	(	PUNCT
ap-1817	22	24	foulis	foulis	PROPN
ap-1817	22	25	and	and	CCONJ
ap-1817	22	26	bennet	bennet	NOUN
ap-1817	23	1	[	[	X
ap-1817	23	2	1	1	NUM
ap-1817	23	3	]	]	PUNCT
ap-1817	23	4	,	,	PUNCT
ap-1817	23	5	kalmbach	kalmbach	PROPN
ap-1817	23	6	and	and	CCONJ
ap-1817	23	7	riečanová	riečanová	ADJ
ap-1817	24	1	[	[	X
ap-1817	24	2	4	4	NUM
ap-1817	24	3	]	]	PUNCT
ap-1817	24	4	,	,	PUNCT
ap-1817	24	5	hedlíková	hedlíková	NOUN
ap-1817	24	6	and	and	CCONJ
ap-1817	24	7	pulmannová	pulmannová	X
ap-1817	24	8	[	[	X
ap-1817	24	9	5	5	NUM
ap-1817	24	10	]	]	PUNCT
ap-1817	24	11	,	,	PUNCT
ap-1817	24	12	kôpka	kôpka	NOUN
ap-1817	24	13	and	and	CCONJ
ap-1817	24	14	chovanec	chovanec	NOUN
ap-1817	25	1	[	[	X
ap-1817	25	2	6	6	NUM
ap-1817	25	3	]	]	PUNCT
ap-1817	25	4	)	)	PUNCT
ap-1817	25	5	.	.	PUNCT
ap-1817	26	1	it	it	PRON
ap-1817	26	2	was	be	AUX
ap-1817	26	3	found	find	VERB
ap-1817	26	4	out	out	ADP
ap-1817	26	5	that	that	SCONJ
ap-1817	26	6	all	all	DET
ap-1817	26	7	these	these	DET
ap-1817	26	8	generalizations	generalization	NOUN
ap-1817	26	9	coincide	coincide	VERB
ap-1817	26	10	and	and	CCONJ
ap-1817	26	11	their	their	PRON
ap-1817	26	12	common	common	ADJ
ap-1817	26	13	definition	definition	NOUN
ap-1817	26	14	is	be	AUX
ap-1817	26	15	the	the	DET
ap-1817	26	16	following	following	NOUN
ap-1817	26	17	:	:	PUNCT
ap-1817	26	18	definition	definition	NOUN
ap-1817	26	19	1.2	1.2	NUM
ap-1817	26	20	.	.	PUNCT
ap-1817	27	1	a	a	DET
ap-1817	27	2	generalized	generalized	ADJ
ap-1817	27	3	effect	effect	NOUN
ap-1817	27	4	algebra	algebra	NOUN
ap-1817	27	5	(	(	PUNCT
ap-1817	27	6	e;⊕	e;⊕	ADJ
ap-1817	27	7	,	,	PUNCT
ap-1817	27	8	0	0	NUM
ap-1817	27	9	)	)	PUNCT
ap-1817	27	10	is	be	AUX
ap-1817	27	11	a	a	DET
ap-1817	27	12	set	set	NOUN
ap-1817	27	13	e	e	NOUN
ap-1817	27	14	with	with	ADP
ap-1817	27	15	element	element	NOUN
ap-1817	27	16	0	0	NUM
ap-1817	27	17	∈	∈	PROPN
ap-1817	27	18	e	e	NOUN
ap-1817	27	19	and	and	CCONJ
ap-1817	27	20	partial	partial	ADJ
ap-1817	27	21	binary	binary	ADJ
ap-1817	27	22	operation	operation	NOUN
ap-1817	27	23	⊕	⊕	PROPN
ap-1817	27	24	satisfying	satisfy	VERB
ap-1817	27	25	for	for	ADP
ap-1817	27	26	any	any	DET
ap-1817	27	27	x	x	NOUN
ap-1817	27	28	,	,	PUNCT
ap-1817	27	29	y	y	PROPN
ap-1817	27	30	,	,	PUNCT
ap-1817	27	31	z	z	NOUN
ap-1817	27	32	∈	∈	PROPN
ap-1817	27	33	e	e	NOUN
ap-1817	27	34	conditions	condition	NOUN
ap-1817	27	35	(	(	PUNCT
ap-1817	27	36	ge1	ge1	NOUN
ap-1817	27	37	)	)	PUNCT
ap-1817	27	38	x⊕	x⊕	PROPN
ap-1817	27	39	y	y	PROPN
ap-1817	27	40	=	=	SYM
ap-1817	27	41	y	y	PROPN
ap-1817	27	42	⊕	⊕	PROPN
ap-1817	27	43	x	x	PUNCT
ap-1817	28	1	if	if	SCONJ
ap-1817	28	2	one	one	NUM
ap-1817	28	3	side	side	NOUN
ap-1817	28	4	is	be	AUX
ap-1817	28	5	defined	define	VERB
ap-1817	28	6	,	,	PUNCT
ap-1817	28	7	(	(	PUNCT
ap-1817	28	8	ge2	ge2	PROPN
ap-1817	28	9	)	)	PUNCT
ap-1817	28	10	(	(	PUNCT
ap-1817	28	11	x⊕y)⊕z	x⊕y)⊕z	X
ap-1817	28	12	=	=	SYM
ap-1817	28	13	x⊕(y⊕z	x⊕(y⊕z	NOUN
ap-1817	28	14	)	)	PUNCT
ap-1817	28	15	if	if	SCONJ
ap-1817	28	16	one	one	NUM
ap-1817	28	17	side	side	NOUN
ap-1817	28	18	is	be	AUX
ap-1817	28	19	defined	define	VERB
ap-1817	28	20	,	,	PUNCT
ap-1817	28	21	(	(	PUNCT
ap-1817	28	22	ge3	ge3	NOUN
ap-1817	28	23	)	)	PUNCT
ap-1817	29	1	if	if	SCONJ
ap-1817	29	2	x⊕	x⊕	PROPN
ap-1817	29	3	y	y	PROPN
ap-1817	29	4	=	=	SYM
ap-1817	29	5	x⊕	x⊕	PROPN
ap-1817	29	6	z	z	PROPN
ap-1817	29	7	then	then	ADV
ap-1817	29	8	y	y	PROPN
ap-1817	29	9	=	=	SYM
ap-1817	29	10	z	z	PROPN
ap-1817	29	11	,	,	PUNCT
ap-1817	29	12	(	(	PUNCT
ap-1817	29	13	ge4	ge4	PROPN
ap-1817	29	14	)	)	PUNCT
ap-1817	29	15	if	if	SCONJ
ap-1817	29	16	x⊕	x⊕	PROPN
ap-1817	29	17	y	y	PROPN
ap-1817	29	18	=	=	PUNCT
ap-1817	29	19	0	0	PUNCT
ap-1817	29	20	then	then	ADV
ap-1817	29	21	x	x	X
ap-1817	29	22	=	=	SYM
ap-1817	29	23	y	y	PROPN
ap-1817	29	24	=	=	SYM
ap-1817	29	25	0	0	PROPN
ap-1817	29	26	,	,	PUNCT
ap-1817	29	27	(	(	PUNCT
ap-1817	29	28	ge5	ge5	PROPN
ap-1817	29	29	)	)	PUNCT
ap-1817	29	30	x⊕	x⊕	PROPN
ap-1817	29	31	0	0	PUNCT
ap-1817	30	1	=	=	PUNCT
ap-1817	30	2	x	x	PROPN
ap-1817	30	3	for	for	ADP
ap-1817	30	4	all	all	DET
ap-1817	30	5	x	x	SYM
ap-1817	30	6	∈	∈	PROPN
ap-1817	30	7	e.	e.	PROPN
ap-1817	30	8	in	in	ADP
ap-1817	30	9	every	every	DET
ap-1817	30	10	(	(	PUNCT
ap-1817	30	11	generalized	generalized	ADJ
ap-1817	30	12	)	)	PUNCT
ap-1817	30	13	effect	effect	NOUN
ap-1817	30	14	algebra	algebra	NOUN
ap-1817	30	15	e	e	PRON
ap-1817	30	16	a	a	DET
ap-1817	30	17	partial	partial	ADJ
ap-1817	30	18	order	order	NOUN
ap-1817	30	19	≤	≤	NOUN
ap-1817	30	20	and	and	CCONJ
ap-1817	30	21	a	a	DET
ap-1817	30	22	binary	binary	ADJ
ap-1817	30	23	operation	operation	NOUN
ap-1817	30	24	can	can	AUX
ap-1817	30	25	be	be	AUX
ap-1817	30	26	introduced	introduce	VERB
ap-1817	30	27	as	as	SCONJ
ap-1817	30	28	follows	follow	VERB
ap-1817	30	29	:	:	PUNCT
ap-1817	30	30	for	for	ADP
ap-1817	30	31	any	any	PRON
ap-1817	30	32	a	a	NOUN
ap-1817	30	33	,	,	PUNCT
ap-1817	30	34	b	b	X
ap-1817	30	35	∈	∈	PROPN
ap-1817	30	36	e	e	NOUN
ap-1817	30	37	,	,	PUNCT
ap-1817	30	38	a	a	DET
ap-1817	30	39	≤	≤	PROPN
ap-1817	30	40	b	b	NOUN
ap-1817	30	41	and	and	CCONJ
ap-1817	30	42	b	b	NOUN
ap-1817	30	43	a	a	DET
ap-1817	30	44	=	=	SYM
ap-1817	30	45	c	c	PROPN
ap-1817	30	46	iff	iff	PROPN
ap-1817	30	47	a⊕	a⊕	PROPN
ap-1817	30	48	c	c	PROPN
ap-1817	30	49	is	be	AUX
ap-1817	30	50	defined	define	VERB
ap-1817	30	51	and	and	CCONJ
ap-1817	30	52	a⊕	a⊕	PRON
ap-1817	30	53	c	c	PROPN
ap-1817	30	54	=	=	PROPN
ap-1817	30	55	b.	b.	PROPN
ap-1817	31	1	throughout	throughout	ADP
ap-1817	31	2	the	the	DET
ap-1817	31	3	paper	paper	NOUN
ap-1817	31	4	we	we	PRON
ap-1817	31	5	assume	assume	VERB
ap-1817	31	6	that	that	SCONJ
ap-1817	31	7	h	h	NOUN
ap-1817	31	8	is	be	AUX
ap-1817	31	9	an	an	DET
ap-1817	31	10	infinite	infinite	ADJ
ap-1817	31	11	-	-	PUNCT
ap-1817	31	12	dimensional	dimensional	ADJ
ap-1817	31	13	complex	complex	ADJ
ap-1817	31	14	hilbert	hilbert	NOUN
ap-1817	31	15	space	space	NOUN
ap-1817	31	16	.	.	PUNCT
ap-1817	32	1	for	for	ADP
ap-1817	32	2	notions	notion	NOUN
ap-1817	32	3	and	and	CCONJ
ap-1817	32	4	results	result	NOUN
ap-1817	32	5	on	on	ADP
ap-1817	32	6	hilbert	hilbert	NOUN
ap-1817	32	7	space	space	NOUN
ap-1817	32	8	operators	operator	NOUN
ap-1817	32	9	we	we	PRON
ap-1817	32	10	refer	refer	VERB
ap-1817	32	11	the	the	DET
ap-1817	32	12	reader	reader	NOUN
ap-1817	32	13	to	to	ADP
ap-1817	32	14	[	[	X
ap-1817	32	15	7	7	NUM
ap-1817	32	16	]	]	PUNCT
ap-1817	32	17	.	.	PUNCT
ap-1817	33	1	we	we	PRON
ap-1817	33	2	will	will	AUX
ap-1817	33	3	assume	assume	VERB
ap-1817	33	4	that	that	SCONJ
ap-1817	33	5	the	the	DET
ap-1817	33	6	domains	domain	NOUN
ap-1817	33	7	d(a	d(a	PROPN
ap-1817	33	8	)	)	PUNCT
ap-1817	33	9	of	of	ADP
ap-1817	33	10	all	all	PRON
ap-1817	33	11	considered	consider	VERB
ap-1817	33	12	linear	linear	PROPN
ap-1817	33	13	operators	operator	NOUN
ap-1817	33	14	a	a	PRON
ap-1817	33	15	are	be	AUX
ap-1817	33	16	dense	dense	ADJ
ap-1817	33	17	linear	linear	ADJ
ap-1817	33	18	subspaces	subspace	NOUN
ap-1817	33	19	of	of	ADP
ap-1817	33	20	h	h	NOUN
ap-1817	33	21	(	(	PUNCT
ap-1817	33	22	in	in	ADP
ap-1817	33	23	the	the	DET
ap-1817	33	24	metric	metric	ADJ
ap-1817	33	25	topology	topology	NOUN
ap-1817	33	26	induced	induce	VERB
ap-1817	33	27	by	by	ADP
ap-1817	33	28	the	the	DET
ap-1817	33	29	inner	inner	ADJ
ap-1817	33	30	product	product	NOUN
ap-1817	33	31	)	)	PUNCT
ap-1817	33	32	.	.	PUNCT
ap-1817	34	1	we	we	PRON
ap-1817	34	2	say	say	VERB
ap-1817	34	3	that	that	SCONJ
ap-1817	34	4	operators	operator	NOUN
ap-1817	34	5	a	a	PRON
ap-1817	34	6	are	be	AUX
ap-1817	34	7	densely	densely	ADV
ap-1817	34	8	defined	define	VERB
ap-1817	34	9	in	in	ADP
ap-1817	34	10	h.	h.	PROPN
ap-1817	34	11	the	the	DET
ap-1817	34	12	set	set	NOUN
ap-1817	34	13	of	of	ADP
ap-1817	34	14	all	all	DET
ap-1817	34	15	densely	densely	ADV
ap-1817	34	16	defined	define	VERB
ap-1817	34	17	linear	linear	NOUN
ap-1817	34	18	operators	operator	NOUN
ap-1817	34	19	on	on	ADP
ap-1817	34	20	h	h	NOUN
ap-1817	34	21	will	will	AUX
ap-1817	34	22	be	be	AUX
ap-1817	34	23	denoted	denote	VERB
ap-1817	34	24	by	by	ADP
ap-1817	34	25	l(h	l(h	PROPN
ap-1817	34	26	)	)	PUNCT
ap-1817	34	27	.	.	PUNCT
ap-1817	35	1	recall	recall	VERB
ap-1817	35	2	that	that	PRON
ap-1817	35	3	a	a	PRON
ap-1817	35	4	:	:	PUNCT
ap-1817	35	5	d(a)→	d(a)→	PUNCT
ap-1817	35	6	h	h	NOUN
ap-1817	35	7	is	be	AUX
ap-1817	35	8	a	a	DET
ap-1817	35	9	bounded	bounded	ADJ
ap-1817	35	10	operator	operator	NOUN
ap-1817	35	11	if	if	SCONJ
ap-1817	35	12	there	there	PRON
ap-1817	35	13	exists	exist	VERB
ap-1817	35	14	a	a	DET
ap-1817	35	15	real	real	ADJ
ap-1817	35	16	constant	constant	ADJ
ap-1817	35	17	c	c	NOUN
ap-1817	35	18	>	>	X
ap-1817	35	19	0	0	NUM
ap-1817	35	20	such	such	ADJ
ap-1817	35	21	that	that	SCONJ
ap-1817	35	22	‖ax‖	‖ax‖	ADJ
ap-1817	35	23	≤	≤	NOUN
ap-1817	35	24	c‖x‖	c‖x‖	NOUN
ap-1817	35	25	for	for	ADP
ap-1817	35	26	all	all	DET
ap-1817	35	27	x	x	SYM
ap-1817	35	28	∈	∈	PROPN
ap-1817	35	29	d(a	d(a	PROPN
ap-1817	35	30	)	)	PUNCT
ap-1817	35	31	.	.	PUNCT
ap-1817	36	1	if	if	SCONJ
ap-1817	36	2	a	a	PRON
ap-1817	36	3	is	be	AUX
ap-1817	36	4	not	not	PART
ap-1817	36	5	bounded	bound	VERB
ap-1817	36	6	then	then	ADV
ap-1817	36	7	it	it	PRON
ap-1817	36	8	is	be	AUX
ap-1817	36	9	called	call	VERB
ap-1817	36	10	unbounded	unbounded	ADJ
ap-1817	36	11	.	.	PUNCT
ap-1817	37	1	recall	recall	VERB
ap-1817	37	2	that	that	SCONJ
ap-1817	37	3	if	if	SCONJ
ap-1817	37	4	(	(	PUNCT
ap-1817	37	5	e;⊕	e;⊕	ADJ
ap-1817	37	6	,	,	PUNCT
ap-1817	37	7	0	0	NUM
ap-1817	37	8	,	,	PUNCT
ap-1817	37	9	1	1	NUM
ap-1817	37	10	)	)	PUNCT
ap-1817	37	11	is	be	AUX
ap-1817	37	12	an	an	DET
ap-1817	37	13	effect	effect	NOUN
ap-1817	37	14	algebra	algebra	NOUN
ap-1817	37	15	(	(	PUNCT
ap-1817	37	16	(	(	PUNCT
ap-1817	37	17	e;⊕	e;⊕	ADJ
ap-1817	37	18	,	,	PUNCT
ap-1817	37	19	0	0	NUM
ap-1817	37	20	)	)	PUNCT
ap-1817	37	21	is	be	AUX
ap-1817	37	22	a	a	DET
ap-1817	37	23	generalized	generalized	ADJ
ap-1817	37	24	effect	effect	NOUN
ap-1817	37	25	algebra	algebra	NOUN
ap-1817	37	26	)	)	PUNCT
ap-1817	37	27	then	then	ADV
ap-1817	37	28	a	a	DET
ap-1817	37	29	subset	subset	NOUN
ap-1817	37	30	g	g	NOUN
ap-1817	37	31	6=	6=	NOUN
ap-1817	37	32	∅	∅	NOUN
ap-1817	37	33	such	such	ADJ
ap-1817	37	34	that	that	SCONJ
ap-1817	37	35	1	1	NUM
ap-1817	37	36	∈	∈	PROPN
ap-1817	37	37	g	g	NOUN
ap-1817	37	38	(	(	PUNCT
ap-1817	37	39	0	0	NUM
ap-1817	37	40	∈	∈	PROPN
ap-1817	37	41	g	g	NOUN
ap-1817	37	42	respectively	respectively	ADV
ap-1817	37	43	)	)	PUNCT
ap-1817	37	44	is	be	AUX
ap-1817	37	45	a	a	DET
ap-1817	37	46	sub	sub	ADJ
ap-1817	37	47	-	-	ADJ
ap-1817	37	48	effect	effect	ADJ
ap-1817	37	49	algebra	algebra	NOUN
ap-1817	37	50	(	(	PUNCT
ap-1817	37	51	sub	sub	ADJ
ap-1817	37	52	-	-	ADJ
ap-1817	37	53	generalized	generalized	ADJ
ap-1817	37	54	effect	effect	NOUN
ap-1817	37	55	algebra	algebra	NOUN
ap-1817	37	56	)	)	PUNCT
ap-1817	37	57	of	of	ADP
ap-1817	37	58	e	e	PROPN
ap-1817	37	59	iff	iff	VERB
ap-1817	37	60	314	314	NUM
ap-1817	37	61	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-1817	37	62	vol	vol	NOUN
ap-1817	37	63	.	.	PUNCT
ap-1817	38	1	53	53	NUM
ap-1817	38	2	no	no	NOUN
ap-1817	38	3	.	.	PUNCT
ap-1817	39	1	3/2013	3/2013	PROPN
ap-1817	39	2	intervals	interval	NOUN
ap-1817	39	3	in	in	ADP
ap-1817	39	4	generalized	generalized	ADJ
ap-1817	39	5	effect	effect	NOUN
ap-1817	39	6	algebras	algebra	NOUN
ap-1817	39	7	and	and	CCONJ
ap-1817	39	8	their	their	PRON
ap-1817	39	9	sub	sub	ADJ
ap-1817	39	10	-	-	ADJ
ap-1817	39	11	generalized	generalized	ADJ
ap-1817	39	12	effect	effect	NOUN
ap-1817	39	13	algebras	algebra	NOUN
ap-1817	39	14	(	(	PUNCT
ap-1817	39	15	s	s	NOUN
ap-1817	39	16	)	)	PUNCT
ap-1817	39	17	for	for	ADP
ap-1817	39	18	any	any	DET
ap-1817	39	19	a	a	DET
ap-1817	39	20	,	,	PUNCT
ap-1817	39	21	b	b	NOUN
ap-1817	39	22	,	,	PUNCT
ap-1817	39	23	c	c	PROPN
ap-1817	39	24	∈	∈	PROPN
ap-1817	39	25	e	e	NOUN
ap-1817	39	26	with	with	ADP
ap-1817	39	27	a⊕	a⊕	PROPN
ap-1817	39	28	b	b	PROPN
ap-1817	39	29	=	=	SYM
ap-1817	39	30	c	c	PROPN
ap-1817	39	31	in	in	ADP
ap-1817	39	32	e	e	NOUN
ap-1817	39	33	the	the	DET
ap-1817	39	34	fact	fact	NOUN
ap-1817	39	35	that	that	SCONJ
ap-1817	39	36	two	two	NUM
ap-1817	39	37	out	out	ADP
ap-1817	39	38	of	of	ADP
ap-1817	39	39	elements	element	NOUN
ap-1817	39	40	a	a	DET
ap-1817	39	41	,	,	PUNCT
ap-1817	39	42	b	b	NOUN
ap-1817	39	43	,	,	PUNCT
ap-1817	39	44	c	c	PROPN
ap-1817	39	45	are	be	AUX
ap-1817	39	46	in	in	ADP
ap-1817	39	47	g	g	PROPN
ap-1817	39	48	implies	imply	VERB
ap-1817	39	49	that	that	SCONJ
ap-1817	39	50	all	all	DET
ap-1817	39	51	a	a	DET
ap-1817	39	52	,	,	PUNCT
ap-1817	39	53	b	b	NOUN
ap-1817	39	54	,	,	PUNCT
ap-1817	39	55	c	c	PROPN
ap-1817	39	56	∈	∈	PROPN
ap-1817	39	57	g.	g.	PROPN
ap-1817	39	58	moreover	moreover	ADV
ap-1817	39	59	,	,	PUNCT
ap-1817	39	60	as	as	SCONJ
ap-1817	39	61	we	we	PRON
ap-1817	39	62	can	can	AUX
ap-1817	39	63	easily	easily	ADV
ap-1817	39	64	check	check	VERB
ap-1817	39	65	,	,	PUNCT
ap-1817	39	66	every	every	DET
ap-1817	39	67	subgeneralized	subgeneralize	VERB
ap-1817	39	68	effect	effect	NOUN
ap-1817	39	69	algebra	algebra	NOUN
ap-1817	39	70	is	be	AUX
ap-1817	39	71	a	a	DET
ap-1817	39	72	generalized	generalized	ADJ
ap-1817	39	73	effect	effect	NOUN
ap-1817	39	74	algebra	algebra	NOUN
ap-1817	39	75	in	in	ADP
ap-1817	39	76	its	its	PRON
ap-1817	39	77	own	own	ADJ
ap-1817	39	78	right	right	NOUN
ap-1817	39	79	.	.	PUNCT
ap-1817	40	1	2	2	X
ap-1817	40	2	.	.	X
ap-1817	40	3	sub	sub	ADJ
ap-1817	40	4	-	-	ADJ
ap-1817	40	5	generalized	generalized	ADJ
ap-1817	40	6	effect	effect	NOUN
ap-1817	40	7	algebras	algebra	NOUN
ap-1817	40	8	of	of	ADP
ap-1817	40	9	generalized	generalized	ADJ
ap-1817	40	10	effect	effect	NOUN
ap-1817	40	11	algebras	algebra	VERB
ap-1817	40	12	a	a	DET
ap-1817	40	13	significant	significant	ADJ
ap-1817	40	14	property	property	NOUN
ap-1817	40	15	of	of	ADP
ap-1817	40	16	a	a	DET
ap-1817	40	17	generalized	generalized	ADJ
ap-1817	40	18	effect	effect	NOUN
ap-1817	40	19	algebra	algebra	NOUN
ap-1817	40	20	(	(	PUNCT
ap-1817	40	21	e;⊕	e;⊕	ADJ
ap-1817	40	22	,	,	PUNCT
ap-1817	40	23	0	0	NUM
ap-1817	40	24	)	)	PUNCT
ap-1817	40	25	is	be	AUX
ap-1817	40	26	the	the	DET
ap-1817	40	27	fact	fact	NOUN
ap-1817	40	28	that	that	SCONJ
ap-1817	40	29	for	for	ADP
ap-1817	40	30	any	any	DET
ap-1817	40	31	q	q	NOUN
ap-1817	40	32	∈	∈	PROPN
ap-1817	40	33	e	e	NOUN
ap-1817	40	34	,	,	PUNCT
ap-1817	40	35	q	q	X
ap-1817	40	36	6=	6=	NUM
ap-1817	40	37	0	0	NUM
ap-1817	40	38	,	,	PUNCT
ap-1817	40	39	the	the	DET
ap-1817	40	40	interval	interval	NOUN
ap-1817	40	41	[	[	X
ap-1817	40	42	0	0	NUM
ap-1817	40	43	,	,	PUNCT
ap-1817	40	44	q]e	q]e	ADJ
ap-1817	40	45	=	=	SYM
ap-1817	40	46	{	{	PUNCT
ap-1817	40	47	c	c	NOUN
ap-1817	40	48	∈	∈	PROPN
ap-1817	40	49	e	e	NOUN
ap-1817	40	50	|	|	ADV
ap-1817	40	51	there	there	PRON
ap-1817	40	52	exists	exist	VERB
ap-1817	40	53	d	d	X
ap-1817	40	54	∈	∈	PROPN
ap-1817	40	55	e	e	NOUN
ap-1817	40	56	such	such	ADJ
ap-1817	40	57	that	that	SCONJ
ap-1817	40	58	c⊕	c⊕	PROPN
ap-1817	40	59	d	d	X
ap-1817	40	60	=	=	SYM
ap-1817	40	61	q	q	X
ap-1817	40	62	}	}	PUNCT
ap-1817	40	63	is	be	AUX
ap-1817	40	64	an	an	DET
ap-1817	40	65	effect	effect	NOUN
ap-1817	40	66	algebra	algebra	NOUN
ap-1817	40	67	with	with	ADP
ap-1817	40	68	top	top	ADJ
ap-1817	40	69	element	element	NOUN
ap-1817	40	70	q	q	PROPN
ap-1817	40	71	and	and	CCONJ
ap-1817	40	72	the	the	DET
ap-1817	40	73	partial	partial	ADJ
ap-1817	40	74	binary	binary	PROPN
ap-1817	40	75	operation	operation	NOUN
ap-1817	40	76	⊕q	⊕q	PROPN
ap-1817	40	77	defined	define	VERB
ap-1817	40	78	for	for	ADP
ap-1817	40	79	a	a	DET
ap-1817	40	80	,	,	PUNCT
ap-1817	40	81	b	b	PROPN
ap-1817	40	82	∈	∈	PROPN
ap-1817	41	1	[	[	X
ap-1817	41	2	0	0	NUM
ap-1817	41	3	,	,	PUNCT
ap-1817	41	4	q]e	q]e	ADP
ap-1817	41	5	iff	iff	PROPN
ap-1817	41	6	a⊕	a⊕	PROPN
ap-1817	41	7	b	b	PROPN
ap-1817	41	8	≤	≤	PROPN
ap-1817	41	9	q.	q.	NOUN
ap-1817	41	10	then	then	ADV
ap-1817	41	11	we	we	PRON
ap-1817	41	12	set	set	VERB
ap-1817	41	13	a⊕q	a⊕q	PROPN
ap-1817	41	14	b	b	PROPN
ap-1817	41	15	=	=	SYM
ap-1817	41	16	a⊕	a⊕	PROPN
ap-1817	41	17	b	b	NOUN
ap-1817	41	18	(	(	PUNCT
ap-1817	41	19	we	we	PRON
ap-1817	41	20	write	write	VERB
ap-1817	41	21	⊕q	⊕q	NOUN
ap-1817	41	22	=	=	PUNCT
ap-1817	41	23	⊕|[0,q]e	⊕|[0,q]e	X
ap-1817	41	24	)	)	PUNCT
ap-1817	41	25	.	.	PUNCT
ap-1817	42	1	thus	thus	ADV
ap-1817	42	2	if	if	SCONJ
ap-1817	42	3	a	a	DET
ap-1817	42	4	set	set	NOUN
ap-1817	42	5	g	g	NOUN
ap-1817	42	6	⊆	⊆	NUM
ap-1817	42	7	e	e	NOUN
ap-1817	42	8	with	with	ADP
ap-1817	42	9	0	0	NUM
ap-1817	42	10	∈	∈	PROPN
ap-1817	42	11	g	g	NOUN
ap-1817	42	12	is	be	AUX
ap-1817	42	13	a	a	DET
ap-1817	42	14	sub	sub	ADJ
ap-1817	42	15	-	-	ADJ
ap-1817	42	16	generalized	generalized	ADJ
ap-1817	42	17	effect	effect	NOUN
ap-1817	42	18	algebra	algebra	NOUN
ap-1817	42	19	of	of	ADP
ap-1817	42	20	e	e	NOUN
ap-1817	42	21	,	,	PUNCT
ap-1817	42	22	then	then	ADV
ap-1817	42	23	the	the	DET
ap-1817	42	24	same	same	ADJ
ap-1817	42	25	is	be	AUX
ap-1817	42	26	true	true	ADJ
ap-1817	42	27	for	for	ADP
ap-1817	42	28	all	all	PRON
ap-1817	42	29	[	[	X
ap-1817	42	30	0	0	NUM
ap-1817	42	31	,	,	PUNCT
ap-1817	42	32	q]e	q]e	ADJ
ap-1817	42	33	∩g	∩g	ADJ
ap-1817	42	34	and	and	CCONJ
ap-1817	42	35	[	[	X
ap-1817	42	36	0	0	NUM
ap-1817	42	37	,	,	PUNCT
ap-1817	42	38	q]e	q]e	ADJ
ap-1817	42	39	,	,	PUNCT
ap-1817	42	40	q	q	PROPN
ap-1817	42	41	∈	∈	PROPN
ap-1817	42	42	e.	e.	PROPN
ap-1817	42	43	more	more	ADV
ap-1817	42	44	precisely	precisely	ADV
ap-1817	42	45	,	,	PUNCT
ap-1817	42	46	theorem	theorem	VERB
ap-1817	42	47	2.1	2.1	NUM
ap-1817	42	48	.	.	PUNCT
ap-1817	43	1	let	let	VERB
ap-1817	43	2	e	e	PRON
ap-1817	43	3	be	be	AUX
ap-1817	43	4	a	a	DET
ap-1817	43	5	generalized	generalized	ADJ
ap-1817	43	6	effect	effect	NOUN
ap-1817	43	7	algebra	algebra	NOUN
ap-1817	43	8	and	and	CCONJ
ap-1817	43	9	0	0	NUM
ap-1817	43	10	∈	∈	NOUN
ap-1817	43	11	g	g	PROPN
ap-1817	43	12	⊆	⊆	NUM
ap-1817	43	13	e.	e.	PROPN
ap-1817	43	14	then	then	ADV
ap-1817	43	15	the	the	DET
ap-1817	43	16	following	follow	VERB
ap-1817	43	17	assertions	assertion	NOUN
ap-1817	43	18	are	be	AUX
ap-1817	43	19	equivalent	equivalent	ADJ
ap-1817	43	20	:	:	PUNCT
ap-1817	43	21	(	(	PUNCT
ap-1817	43	22	1	1	NUM
ap-1817	43	23	.	.	PUNCT
ap-1817	43	24	)	)	PUNCT
ap-1817	44	1	g	g	NOUN
ap-1817	44	2	is	be	AUX
ap-1817	44	3	a	a	DET
ap-1817	44	4	sub	sub	ADJ
ap-1817	44	5	-	-	ADJ
ap-1817	44	6	generalized	generalized	ADJ
ap-1817	44	7	effect	effect	NOUN
ap-1817	44	8	algebra	algebra	NOUN
ap-1817	44	9	of	of	ADP
ap-1817	44	10	e.	e.	PROPN
ap-1817	44	11	(	(	PUNCT
ap-1817	44	12	2	2	NUM
ap-1817	44	13	.	.	PUNCT
ap-1817	44	14	)	)	PUNCT
ap-1817	44	15	for	for	ADP
ap-1817	44	16	all	all	DET
ap-1817	44	17	nonzero	nonzero	NOUN
ap-1817	44	18	q	q	X
ap-1817	44	19	∈	∈	PROPN
ap-1817	44	20	e	e	X
ap-1817	44	21	the	the	DET
ap-1817	44	22	set	set	NOUN
ap-1817	44	23	g	g	PROPN
ap-1817	44	24	∩	∩	NOUN
ap-1817	44	25	[	[	X
ap-1817	44	26	0	0	NUM
ap-1817	44	27	,	,	PUNCT
ap-1817	44	28	q]e	q]e	ADJ
ap-1817	44	29	is	be	AUX
ap-1817	44	30	a	a	DET
ap-1817	44	31	sub	sub	ADJ
ap-1817	44	32	-	-	ADJ
ap-1817	44	33	generalized	generalized	ADJ
ap-1817	44	34	effect	effect	NOUN
ap-1817	44	35	algebra	algebra	NOUN
ap-1817	44	36	of	of	ADP
ap-1817	44	37	[	[	X
ap-1817	44	38	0	0	NUM
ap-1817	44	39	,	,	PUNCT
ap-1817	44	40	q]e	q]e	ADP
ap-1817	44	41	considered	consider	VERB
ap-1817	44	42	as	as	ADP
ap-1817	44	43	a	a	DET
ap-1817	44	44	generalized	generalized	ADJ
ap-1817	44	45	effect	effect	NOUN
ap-1817	44	46	algebra	algebra	NOUN
ap-1817	44	47	.	.	PUNCT
ap-1817	45	1	proof	proof	NOUN
ap-1817	45	2	.	.	PUNCT
ap-1817	46	1	(	(	PUNCT
ap-1817	46	2	1.)⇒	1.)⇒	NUM
ap-1817	46	3	(	(	PUNCT
ap-1817	46	4	2	2	NUM
ap-1817	46	5	.	.	PUNCT
ap-1817	46	6	)	)	PUNCT
ap-1817	47	1	this	this	DET
ap-1817	47	2	implication	implication	NOUN
ap-1817	47	3	is	be	AUX
ap-1817	47	4	obvious	obvious	ADJ
ap-1817	47	5	.	.	PUNCT
ap-1817	48	1	(	(	PUNCT
ap-1817	48	2	2	2	NUM
ap-1817	48	3	.	.	NUM
ap-1817	48	4	)	)	PUNCT
ap-1817	48	5	⇒	⇒	NOUN
ap-1817	48	6	(	(	PUNCT
ap-1817	48	7	1	1	NUM
ap-1817	48	8	.	.	PUNCT
ap-1817	48	9	)	)	PUNCT
ap-1817	48	10	let	let	VERB
ap-1817	48	11	a	a	DET
ap-1817	48	12	,	,	PUNCT
ap-1817	48	13	b	b	NOUN
ap-1817	48	14	,	,	PUNCT
ap-1817	48	15	c	c	PROPN
ap-1817	48	16	∈	∈	PROPN
ap-1817	48	17	e	e	NOUN
ap-1817	48	18	,	,	PUNCT
ap-1817	48	19	a	a	DET
ap-1817	48	20	⊕	⊕	PROPN
ap-1817	48	21	b	b	PROPN
ap-1817	48	22	=	=	PROPN
ap-1817	48	23	c.	c.	PROPN
ap-1817	48	24	substituting	substitute	VERB
ap-1817	48	25	c	c	PROPN
ap-1817	48	26	=	=	PUNCT
ap-1817	48	27	q	q	X
ap-1817	48	28	into	into	ADP
ap-1817	48	29	(	(	PUNCT
ap-1817	48	30	2	2	X
ap-1817	48	31	)	)	PUNCT
ap-1817	48	32	we	we	PRON
ap-1817	48	33	obtain	obtain	VERB
ap-1817	48	34	that	that	SCONJ
ap-1817	48	35	g	g	NOUN
ap-1817	48	36	∩	∩	NOUN
ap-1817	48	37	[	[	X
ap-1817	48	38	0	0	NUM
ap-1817	48	39	,	,	PUNCT
ap-1817	48	40	c]e	c]e	PROPN
ap-1817	48	41	is	be	AUX
ap-1817	48	42	a	a	DET
ap-1817	48	43	subgeneralized	subgeneralize	VERB
ap-1817	48	44	effect	effect	NOUN
ap-1817	48	45	algebra	algebra	NOUN
ap-1817	48	46	of	of	ADP
ap-1817	48	47	[	[	X
ap-1817	48	48	0	0	NUM
ap-1817	48	49	,	,	PUNCT
ap-1817	48	50	c]e	c]e	PROPN
ap-1817	48	51	.	.	PUNCT
ap-1817	49	1	hence	hence	ADV
ap-1817	49	2	a	a	DET
ap-1817	49	3	,	,	PUNCT
ap-1817	49	4	b	b	NOUN
ap-1817	49	5	,	,	PUNCT
ap-1817	49	6	c	c	PROPN
ap-1817	49	7	∈	∈	PROPN
ap-1817	50	1	[	[	X
ap-1817	50	2	0	0	NUM
ap-1817	50	3	,	,	PUNCT
ap-1817	50	4	c]e	c]e	PROPN
ap-1817	50	5	satisfy	satisfy	VERB
ap-1817	50	6	the	the	DET
ap-1817	50	7	property	property	NOUN
ap-1817	50	8	(	(	PUNCT
ap-1817	50	9	s	s	NOUN
ap-1817	50	10	)	)	PUNCT
ap-1817	50	11	,	,	PUNCT
ap-1817	50	12	i.e.	i.e.	X
ap-1817	50	13	,	,	PUNCT
ap-1817	50	14	g	g	PROPN
ap-1817	50	15	is	be	AUX
ap-1817	50	16	a	a	DET
ap-1817	50	17	subgeneralized	subgeneralize	VERB
ap-1817	50	18	effect	effect	NOUN
ap-1817	50	19	algebra	algebra	NOUN
ap-1817	50	20	of	of	ADP
ap-1817	50	21	e.	e.	PROPN
ap-1817	50	22	the	the	DET
ap-1817	50	23	following	follow	VERB
ap-1817	50	24	example	example	NOUN
ap-1817	50	25	shows	show	VERB
ap-1817	50	26	that	that	SCONJ
ap-1817	50	27	the	the	DET
ap-1817	50	28	condition	condition	NOUN
ap-1817	50	29	(	(	PUNCT
ap-1817	50	30	2	2	NUM
ap-1817	50	31	.	.	PUNCT
ap-1817	50	32	)	)	PUNCT
ap-1817	50	33	in	in	ADP
ap-1817	50	34	theorem	theorem	ADJ
ap-1817	50	35	2.1	2.1	NUM
ap-1817	50	36	can	can	AUX
ap-1817	50	37	not	not	PART
ap-1817	50	38	be	be	AUX
ap-1817	50	39	replaced	replace	VERB
ap-1817	50	40	by	by	ADP
ap-1817	50	41	a	a	DET
ap-1817	50	42	stronger	strong	ADJ
ap-1817	50	43	one	one	NOUN
ap-1817	50	44	:	:	PUNCT
ap-1817	50	45	(	(	PUNCT
ap-1817	50	46	2	2	NUM
ap-1817	50	47	’	'	PUNCT
ap-1817	50	48	.	.	PUNCT
ap-1817	50	49	)	)	PUNCT
ap-1817	51	1	for	for	ADP
ap-1817	51	2	all	all	DET
ap-1817	51	3	nonzero	nonzero	NOUN
ap-1817	51	4	q	q	X
ap-1817	51	5	∈	∈	PROPN
ap-1817	51	6	e	e	X
ap-1817	51	7	the	the	DET
ap-1817	51	8	set	set	NOUN
ap-1817	51	9	g	g	PROPN
ap-1817	51	10	∩	∩	NOUN
ap-1817	51	11	[	[	X
ap-1817	51	12	0	0	NUM
ap-1817	51	13	,	,	PUNCT
ap-1817	51	14	q]e	q]e	ADJ
ap-1817	51	15	is	be	AUX
ap-1817	51	16	a	a	DET
ap-1817	51	17	sub	sub	ADJ
ap-1817	51	18	-	-	ADJ
ap-1817	51	19	effect	effect	ADJ
ap-1817	51	20	algebra	algebra	NOUN
ap-1817	51	21	of	of	ADP
ap-1817	51	22	the	the	DET
ap-1817	51	23	effect	effect	NOUN
ap-1817	51	24	algebra	algebra	NOUN
ap-1817	51	25	[	[	X
ap-1817	51	26	0	0	NUM
ap-1817	51	27	,	,	PUNCT
ap-1817	51	28	q]e	q]e	ADJ
ap-1817	51	29	.	.	PUNCT
ap-1817	51	30	example	example	NOUN
ap-1817	51	31	2.2	2.2	NUM
ap-1817	51	32	.	.	PUNCT
ap-1817	52	1	let	let	VERB
ap-1817	52	2	e	e	NOUN
ap-1817	52	3	=	=	PRON
ap-1817	52	4	r+	r+	NOUN
ap-1817	52	5	and	and	CCONJ
ap-1817	52	6	g	g	NOUN
ap-1817	52	7	=	=	PUNCT
ap-1817	52	8	q+	q+	ADP
ap-1817	52	9	be	be	AUX
ap-1817	52	10	the	the	DET
ap-1817	52	11	sets	set	NOUN
ap-1817	52	12	of	of	ADP
ap-1817	52	13	all	all	DET
ap-1817	52	14	non	non	ADJ
ap-1817	52	15	-	-	ADJ
ap-1817	52	16	negative	negative	ADJ
ap-1817	52	17	real	real	ADJ
ap-1817	52	18	and	and	CCONJ
ap-1817	52	19	rational	rational	ADJ
ap-1817	52	20	numbers	number	NOUN
ap-1817	52	21	,	,	PUNCT
ap-1817	52	22	respectively	respectively	ADV
ap-1817	52	23	and	and	CCONJ
ap-1817	52	24	let	let	VERB
ap-1817	52	25	+	+	CCONJ
ap-1817	52	26	denote	denote	VERB
ap-1817	52	27	the	the	DET
ap-1817	52	28	usual	usual	ADJ
ap-1817	52	29	sum	sum	NOUN
ap-1817	52	30	of	of	ADP
ap-1817	52	31	real	real	ADJ
ap-1817	52	32	numbers	number	NOUN
ap-1817	52	33	.	.	PUNCT
ap-1817	53	1	then	then	ADV
ap-1817	53	2	(	(	PUNCT
ap-1817	53	3	2	2	X
ap-1817	53	4	)	)	PUNCT
ap-1817	53	5	obviously	obviously	ADV
ap-1817	53	6	holds	hold	VERB
ap-1817	53	7	but	but	CCONJ
ap-1817	53	8	for	for	ADP
ap-1817	53	9	nonrational	nonrational	ADJ
ap-1817	53	10	q	q	X
ap-1817	53	11	>	>	X
ap-1817	53	12	0	0	NUM
ap-1817	53	13	,	,	PUNCT
ap-1817	53	14	e.g.	e.g.	ADV
ap-1817	53	15	for	for	ADP
ap-1817	53	16	q	q	NOUN
ap-1817	53	17	=	=	NOUN
ap-1817	53	18	√	√	NUM
ap-1817	53	19	2	2	NUM
ap-1817	53	20	,	,	PUNCT
ap-1817	53	21	we	we	PRON
ap-1817	53	22	have	have	VERB
ap-1817	53	23	g	g	NOUN
ap-1817	53	24	∩	∩	NOUN
ap-1817	53	25	[	[	X
ap-1817	53	26	0	0	NUM
ap-1817	53	27	,	,	PUNCT
ap-1817	53	28	q]e	q]e	ADJ
ap-1817	53	29	is	be	AUX
ap-1817	53	30	not	not	PART
ap-1817	53	31	a	a	DET
ap-1817	53	32	sub	sub	ADJ
ap-1817	53	33	-	-	ADJ
ap-1817	53	34	effect	effect	ADJ
ap-1817	53	35	algebra	algebra	NOUN
ap-1817	53	36	of	of	ADP
ap-1817	53	37	[	[	X
ap-1817	53	38	0	0	NUM
ap-1817	53	39	,	,	PUNCT
ap-1817	53	40	q]e	q]e	ADV
ap-1817	53	41	.	.	PUNCT
ap-1817	54	1	it	it	PRON
ap-1817	54	2	is	be	AUX
ap-1817	54	3	easy	easy	ADJ
ap-1817	54	4	to	to	PART
ap-1817	54	5	see	see	VERB
ap-1817	54	6	that	that	SCONJ
ap-1817	54	7	if	if	SCONJ
ap-1817	54	8	g	g	PROPN
ap-1817	54	9	is	be	AUX
ap-1817	54	10	a	a	DET
ap-1817	54	11	sub	sub	ADJ
ap-1817	54	12	-	-	ADJ
ap-1817	54	13	generalized	generalized	ADJ
ap-1817	54	14	effect	effect	NOUN
ap-1817	54	15	algebra	algebra	NOUN
ap-1817	54	16	of	of	ADP
ap-1817	54	17	a	a	DET
ap-1817	54	18	generalized	generalized	ADJ
ap-1817	54	19	effect	effect	NOUN
ap-1817	54	20	algebra	algebra	NOUN
ap-1817	54	21	e	e	NOUN
ap-1817	54	22	,	,	PUNCT
ap-1817	54	23	then	then	ADV
ap-1817	54	24	for	for	ADP
ap-1817	54	25	all	all	DET
ap-1817	54	26	q	q	PROPN
ap-1817	54	27	∈	∈	PROPN
ap-1817	54	28	g	g	NOUN
ap-1817	54	29	,	,	PUNCT
ap-1817	54	30	q	q	X
ap-1817	54	31	6=	6=	NUM
ap-1817	54	32	0	0	NUM
ap-1817	54	33	,	,	PUNCT
ap-1817	54	34	the	the	DET
ap-1817	54	35	intersection	intersection	NOUN
ap-1817	54	36	[	[	X
ap-1817	54	37	0	0	NUM
ap-1817	54	38	,	,	PUNCT
ap-1817	54	39	q]g	q]g	ADV
ap-1817	54	40	=	=	PUNCT
ap-1817	55	1	[	[	X
ap-1817	55	2	0	0	NUM
ap-1817	55	3	,	,	PUNCT
ap-1817	55	4	q]e	q]e	ADJ
ap-1817	55	5	∩g	∩g	NOUN
ap-1817	55	6	is	be	AUX
ap-1817	55	7	a	a	DET
ap-1817	55	8	sub	sub	ADJ
ap-1817	55	9	-	-	ADJ
ap-1817	55	10	generalized	generalized	ADJ
ap-1817	55	11	effect	effect	NOUN
ap-1817	55	12	algebra	algebra	NOUN
ap-1817	55	13	of	of	ADP
ap-1817	55	14	[	[	X
ap-1817	55	15	0	0	NUM
ap-1817	55	16	,	,	PUNCT
ap-1817	55	17	q]e	q]e	ADP
ap-1817	55	18	considered	consider	VERB
ap-1817	55	19	as	as	ADP
ap-1817	55	20	a	a	DET
ap-1817	55	21	generalized	generalized	ADJ
ap-1817	55	22	effect	effect	NOUN
ap-1817	55	23	algebra	algebra	NOUN
ap-1817	55	24	.	.	PUNCT
ap-1817	56	1	our	our	PRON
ap-1817	56	2	goal	goal	NOUN
ap-1817	56	3	,	,	PUNCT
ap-1817	56	4	roughly	roughly	ADV
ap-1817	56	5	speaking	speak	VERB
ap-1817	56	6	,	,	PUNCT
ap-1817	56	7	is	be	AUX
ap-1817	56	8	to	to	PART
ap-1817	56	9	investigate	investigate	VERB
ap-1817	56	10	under	under	ADP
ap-1817	56	11	what	what	DET
ap-1817	56	12	conditions	condition	NOUN
ap-1817	56	13	the	the	DET
ap-1817	56	14	converse	converse	NOUN
ap-1817	56	15	holds	hold	VERB
ap-1817	56	16	.	.	PUNCT
ap-1817	57	1	theorem	theorem	VERB
ap-1817	57	2	2.3	2.3	NUM
ap-1817	57	3	.	.	PUNCT
ap-1817	58	1	let	let	VERB
ap-1817	58	2	g	g	PRON
ap-1817	58	3	be	be	AUX
ap-1817	58	4	a	a	DET
ap-1817	58	5	subset	subset	NOUN
ap-1817	58	6	of	of	ADP
ap-1817	58	7	a	a	DET
ap-1817	58	8	generalized	generalized	ADJ
ap-1817	58	9	effect	effect	NOUN
ap-1817	58	10	algebra	algebra	NOUN
ap-1817	58	11	(	(	PUNCT
ap-1817	58	12	e;⊕	e;⊕	ADJ
ap-1817	58	13	,	,	PUNCT
ap-1817	58	14	0	0	NUM
ap-1817	58	15	)	)	PUNCT
ap-1817	58	16	such	such	ADJ
ap-1817	58	17	that	that	DET
ap-1817	58	18	0	0	NUM
ap-1817	58	19	∈	∈	PROPN
ap-1817	58	20	e	e	NOUN
ap-1817	58	21	and	and	CCONJ
ap-1817	58	22	for	for	ADP
ap-1817	58	23	every	every	DET
ap-1817	58	24	c	c	NOUN
ap-1817	58	25	∈	∈	PROPN
ap-1817	58	26	e	e	NOUN
ap-1817	58	27	there	there	PRON
ap-1817	58	28	exists	exist	VERB
ap-1817	58	29	g	g	PROPN
ap-1817	58	30	∈	∈	PROPN
ap-1817	58	31	g	g	PROPN
ap-1817	58	32	with	with	ADP
ap-1817	58	33	c	c	PROPN
ap-1817	58	34	≤	≤	PROPN
ap-1817	58	35	g.	g.	PROPN
ap-1817	59	1	then	then	ADV
ap-1817	59	2	the	the	DET
ap-1817	59	3	following	follow	VERB
ap-1817	59	4	conditions	condition	NOUN
ap-1817	59	5	are	be	AUX
ap-1817	59	6	equivalent	equivalent	ADJ
ap-1817	59	7	:	:	PUNCT
ap-1817	59	8	(	(	PUNCT
ap-1817	59	9	1	1	NUM
ap-1817	59	10	.	.	PUNCT
ap-1817	59	11	)	)	PUNCT
ap-1817	60	1	g	g	NOUN
ap-1817	60	2	is	be	AUX
ap-1817	60	3	a	a	DET
ap-1817	60	4	sub	sub	ADJ
ap-1817	60	5	-	-	ADJ
ap-1817	60	6	generalized	generalized	ADJ
ap-1817	60	7	effect	effect	NOUN
ap-1817	60	8	algebra	algebra	NOUN
ap-1817	60	9	of	of	ADP
ap-1817	60	10	(	(	PUNCT
ap-1817	60	11	e;⊕	e;⊕	ADJ
ap-1817	60	12	,	,	PUNCT
ap-1817	60	13	0	0	NUM
ap-1817	60	14	)	)	PUNCT
ap-1817	60	15	.	.	PUNCT
ap-1817	61	1	(	(	PUNCT
ap-1817	61	2	2	2	NUM
ap-1817	61	3	.	.	PUNCT
ap-1817	61	4	)	)	PUNCT
ap-1817	62	1	for	for	ADP
ap-1817	62	2	any	any	DET
ap-1817	62	3	q	q	PROPN
ap-1817	62	4	∈	∈	PROPN
ap-1817	62	5	g	g	NOUN
ap-1817	62	6	,	,	PUNCT
ap-1817	62	7	q	q	X
ap-1817	62	8	6=	6=	NUM
ap-1817	62	9	0	0	NUM
ap-1817	63	1	the	the	DET
ap-1817	63	2	interval	interval	NOUN
ap-1817	63	3	[	[	X
ap-1817	63	4	0	0	NUM
ap-1817	63	5	,	,	PUNCT
ap-1817	63	6	q]g	q]g	ADV
ap-1817	63	7	=	=	PUNCT
ap-1817	64	1	[	[	X
ap-1817	64	2	0	0	NUM
ap-1817	64	3	,	,	PUNCT
ap-1817	64	4	q]e	q]e	ADJ
ap-1817	64	5	∩g	∩g	NOUN
ap-1817	64	6	in	in	ADP
ap-1817	64	7	g	g	PROPN
ap-1817	64	8	is	be	AUX
ap-1817	64	9	a	a	DET
ap-1817	64	10	sub	sub	ADJ
ap-1817	64	11	-	-	ADJ
ap-1817	64	12	effect	effect	ADJ
ap-1817	64	13	algebra	algebra	NOUN
ap-1817	64	14	of	of	ADP
ap-1817	64	15	the	the	DET
ap-1817	64	16	effect	effect	NOUN
ap-1817	64	17	algebra	algebra	NOUN
ap-1817	64	18	[	[	X
ap-1817	64	19	0	0	NUM
ap-1817	64	20	,	,	PUNCT
ap-1817	64	21	q]e	q]e	ADJ
ap-1817	64	22	.	.	PUNCT
ap-1817	65	1	proof	proof	NOUN
ap-1817	65	2	.	.	PUNCT
ap-1817	66	1	(	(	PUNCT
ap-1817	66	2	1	1	NUM
ap-1817	66	3	.	.	PUNCT
ap-1817	66	4	)	)	PUNCT
ap-1817	66	5	⇒	⇒	NOUN
ap-1817	66	6	(	(	PUNCT
ap-1817	66	7	2	2	NUM
ap-1817	66	8	.	.	PUNCT
ap-1817	66	9	)	)	PUNCT
ap-1817	67	1	this	this	PRON
ap-1817	67	2	is	be	AUX
ap-1817	67	3	obvious	obvious	ADJ
ap-1817	67	4	since	since	SCONJ
ap-1817	67	5	(	(	PUNCT
ap-1817	67	6	1	1	NUM
ap-1817	67	7	.	.	PUNCT
ap-1817	67	8	)	)	PUNCT
ap-1817	68	1	implies	imply	VERB
ap-1817	68	2	that	that	SCONJ
ap-1817	68	3	g	g	PROPN
ap-1817	68	4	satisfies	satisfy	VERB
ap-1817	68	5	the	the	DET
ap-1817	68	6	condition	condition	NOUN
ap-1817	68	7	(	(	PUNCT
ap-1817	68	8	s	s	NOUN
ap-1817	68	9	)	)	PUNCT
ap-1817	68	10	,	,	PUNCT
ap-1817	68	11	hence	hence	ADV
ap-1817	68	12	[	[	X
ap-1817	68	13	0	0	NUM
ap-1817	68	14	,	,	PUNCT
ap-1817	68	15	q]e	q]e	ADJ
ap-1817	68	16	is	be	AUX
ap-1817	68	17	an	an	DET
ap-1817	68	18	effect	effect	NOUN
ap-1817	68	19	algebra	algebra	NOUN
ap-1817	68	20	for	for	ADP
ap-1817	68	21	every	every	DET
ap-1817	68	22	nonzero	nonzero	NOUN
ap-1817	68	23	q	q	X
ap-1817	68	24	∈	∈	PROPN
ap-1817	68	25	g.	g.	NOUN
ap-1817	68	26	thus	thus	ADV
ap-1817	68	27	the	the	DET
ap-1817	68	28	intersection	intersection	NOUN
ap-1817	68	29	of	of	ADP
ap-1817	68	30	two	two	NUM
ap-1817	68	31	generalized	generalized	ADJ
ap-1817	68	32	effect	effect	NOUN
ap-1817	68	33	algebras	algebra	VERB
ap-1817	69	1	[	[	X
ap-1817	69	2	0	0	NUM
ap-1817	69	3	,	,	PUNCT
ap-1817	69	4	q]e	q]e	ADJ
ap-1817	69	5	∩g	∩g	ADJ
ap-1817	69	6	=	=	PUNCT
ap-1817	70	1	[	[	X
ap-1817	70	2	0	0	NUM
ap-1817	70	3	,	,	PUNCT
ap-1817	70	4	q]g	q]g	ADV
ap-1817	70	5	is	be	AUX
ap-1817	70	6	an	an	DET
ap-1817	70	7	effect	effect	NOUN
ap-1817	70	8	algebra	algebra	NOUN
ap-1817	70	9	,	,	PUNCT
ap-1817	70	10	as	as	ADP
ap-1817	70	11	q	q	PROPN
ap-1817	70	12	∈	∈	PROPN
ap-1817	70	13	g.	g.	NOUN
ap-1817	70	14	(	(	PUNCT
ap-1817	70	15	2	2	NUM
ap-1817	70	16	.	.	PUNCT
ap-1817	70	17	)	)	PUNCT
ap-1817	70	18	⇒	⇒	NOUN
ap-1817	70	19	(	(	PUNCT
ap-1817	70	20	1	1	NUM
ap-1817	70	21	.	.	PUNCT
ap-1817	70	22	)	)	PUNCT
ap-1817	71	1	let	let	VERB
ap-1817	71	2	a	a	DET
ap-1817	71	3	,	,	PUNCT
ap-1817	71	4	b	b	PROPN
ap-1817	71	5	∈	∈	PROPN
ap-1817	71	6	g	g	NOUN
ap-1817	71	7	with	with	ADP
ap-1817	71	8	a	a	DET
ap-1817	71	9	⊕	⊕	PROPN
ap-1817	71	10	b	b	PROPN
ap-1817	71	11	=	=	SYM
ap-1817	71	12	c	c	PROPN
ap-1817	71	13	∈	∈	PROPN
ap-1817	71	14	e.	e.	PROPN
ap-1817	71	15	there	there	PRON
ap-1817	71	16	exists	exist	VERB
ap-1817	71	17	g	g	PROPN
ap-1817	71	18	∈	∈	PROPN
ap-1817	71	19	g	g	PROPN
ap-1817	71	20	with	with	ADP
ap-1817	71	21	c	c	NOUN
ap-1817	71	22	≤	≤	NUM
ap-1817	71	23	g	g	NOUN
ap-1817	71	24	and	and	CCONJ
ap-1817	71	25	hence	hence	ADV
ap-1817	71	26	a	a	DET
ap-1817	71	27	⊕	⊕	PROPN
ap-1817	71	28	b	b	PROPN
ap-1817	71	29	∈	∈	PROPN
ap-1817	72	1	[	[	X
ap-1817	72	2	0	0	NUM
ap-1817	72	3	,	,	PUNCT
ap-1817	72	4	g]e	g]e	ADV
ap-1817	72	5	∩g	∩g	NOUN
ap-1817	72	6	=	=	PUNCT
ap-1817	73	1	[	[	X
ap-1817	73	2	0	0	NUM
ap-1817	73	3	,	,	PUNCT
ap-1817	73	4	g]g	g]g	VERB
ap-1817	73	5	which	which	PRON
ap-1817	73	6	,	,	PUNCT
ap-1817	73	7	by	by	ADP
ap-1817	73	8	(	(	PUNCT
ap-1817	73	9	2	2	NUM
ap-1817	73	10	.	.	NUM
ap-1817	73	11	)	)	PUNCT
ap-1817	73	12	,	,	PUNCT
ap-1817	73	13	gives	give	VERB
ap-1817	73	14	a⊕	a⊕	PROPN
ap-1817	73	15	b	b	PROPN
ap-1817	73	16	∈	∈	PROPN
ap-1817	73	17	g.	g.	NOUN
ap-1817	74	1	if	if	SCONJ
ap-1817	74	2	a	a	PRON
ap-1817	74	3	,	,	PUNCT
ap-1817	74	4	c	c	PROPN
ap-1817	74	5	∈	∈	PROPN
ap-1817	74	6	g	g	PROPN
ap-1817	74	7	,	,	PUNCT
ap-1817	74	8	b	b	X
ap-1817	74	9	∈	∈	PROPN
ap-1817	74	10	e	e	NOUN
ap-1817	74	11	and	and	CCONJ
ap-1817	74	12	a	a	DET
ap-1817	74	13	⊕	⊕	PROPN
ap-1817	74	14	b	b	PROPN
ap-1817	74	15	=	=	SYM
ap-1817	74	16	c	c	PROPN
ap-1817	74	17	,	,	PUNCT
ap-1817	74	18	then	then	ADV
ap-1817	74	19	by	by	ADP
ap-1817	74	20	(	(	PUNCT
ap-1817	74	21	2	2	NUM
ap-1817	74	22	.	.	PUNCT
ap-1817	74	23	)	)	PUNCT
ap-1817	75	1	we	we	PRON
ap-1817	75	2	have	have	VERB
ap-1817	75	3	b	b	PROPN
ap-1817	75	4	∈	∈	PROPN
ap-1817	75	5	g.	g.	NOUN
ap-1817	75	6	this	this	PRON
ap-1817	75	7	proves	prove	VERB
ap-1817	75	8	that	that	SCONJ
ap-1817	75	9	g	g	PROPN
ap-1817	75	10	is	be	AUX
ap-1817	75	11	a	a	DET
ap-1817	75	12	sub	sub	ADJ
ap-1817	75	13	-	-	ADJ
ap-1817	75	14	generalized	generalized	ADJ
ap-1817	75	15	effect	effect	NOUN
ap-1817	75	16	algebra	algebra	NOUN
ap-1817	75	17	of	of	ADP
ap-1817	75	18	e.	e.	PROPN
ap-1817	75	19	example	example	PROPN
ap-1817	76	1	2.4	2.4	NUM
ap-1817	76	2	.	.	PUNCT
ap-1817	77	1	assume	assume	VERB
ap-1817	77	2	that	that	SCONJ
ap-1817	77	3	h	h	NOUN
ap-1817	77	4	is	be	AUX
ap-1817	77	5	an	an	DET
ap-1817	77	6	infinitedimensional	infinitedimensional	ADJ
ap-1817	77	7	complex	complex	ADJ
ap-1817	77	8	hilbert	hilbert	NOUN
ap-1817	77	9	space	space	NOUN
ap-1817	77	10	.	.	PUNCT
ap-1817	78	1	further	far	ADV
ap-1817	78	2	,	,	PUNCT
ap-1817	78	3	let	let	VERB
ap-1817	78	4	b+(h	b+(h	NUM
ap-1817	78	5	)	)	PUNCT
ap-1817	78	6	be	be	AUX
ap-1817	78	7	the	the	DET
ap-1817	78	8	set	set	NOUN
ap-1817	78	9	of	of	ADP
ap-1817	78	10	all	all	DET
ap-1817	78	11	bonded	bond	VERB
ap-1817	78	12	positive	positive	ADJ
ap-1817	78	13	linear	linear	PROPN
ap-1817	78	14	operators	operator	NOUN
ap-1817	78	15	with	with	ADP
ap-1817	78	16	domain	domain	NOUN
ap-1817	78	17	h.	h.	NOUN
ap-1817	78	18	in	in	ADP
ap-1817	78	19	[	[	X
ap-1817	78	20	12	12	NUM
ap-1817	78	21	]	]	X
ap-1817	78	22	it	it	PRON
ap-1817	78	23	was	be	AUX
ap-1817	78	24	proved	prove	VERB
ap-1817	78	25	that	that	SCONJ
ap-1817	78	26	for	for	ADP
ap-1817	78	27	any	any	DET
ap-1817	78	28	dense	dense	ADJ
ap-1817	78	29	linear	linear	NOUN
ap-1817	78	30	subspace	subspace	NOUN
ap-1817	78	31	d	d	PROPN
ap-1817	78	32	⊆	⊆	NUM
ap-1817	78	33	h	h	NOUN
ap-1817	78	34	the	the	DET
ap-1817	78	35	set	set	NOUN
ap-1817	78	36	gd(h	gd(h	NOUN
ap-1817	78	37	)	)	PUNCT
ap-1817	78	38	=	=	SYM
ap-1817	78	39	b+(h	b+(h	PROPN
ap-1817	78	40	)	)	PUNCT
ap-1817	78	41	∪	∪	NOUN
ap-1817	78	42	{	{	PUNCT
ap-1817	78	43	a	a	DET
ap-1817	78	44	:	:	PUNCT
ap-1817	78	45	d	d	NOUN
ap-1817	78	46	→	→	SYM
ap-1817	78	47	h	h	NOUN
ap-1817	78	48	|	|	ADV
ap-1817	78	49	a	a	DET
ap-1817	78	50	≥	≥	NOUN
ap-1817	78	51	0	0	NUM
ap-1817	78	52	,	,	PUNCT
ap-1817	78	53	unbounded	unbounded	ADJ
ap-1817	78	54	linear	linear	NOUN
ap-1817	78	55	operator	operator	NOUN
ap-1817	78	56	with	with	ADP
ap-1817	78	57	d(a	d(a	PROPN
ap-1817	78	58	)	)	PUNCT
ap-1817	78	59	=	=	SYM
ap-1817	79	1	d	d	X
ap-1817	79	2	}	}	PUNCT
ap-1817	79	3	is	be	AUX
ap-1817	79	4	a	a	DET
ap-1817	79	5	generalized	generalized	ADJ
ap-1817	79	6	effect	effect	NOUN
ap-1817	79	7	algebra	algebra	NOUN
ap-1817	79	8	with	with	ADP
ap-1817	79	9	the	the	DET
ap-1817	79	10	operation	operation	NOUN
ap-1817	79	11	⊕d	⊕d	NOUN
ap-1817	79	12	which	which	PRON
ap-1817	79	13	for	for	ADP
ap-1817	79	14	any	any	DET
ap-1817	79	15	a	a	PRON
ap-1817	79	16	,	,	PUNCT
ap-1817	79	17	b	b	PROPN
ap-1817	79	18	∈	∈	PROPN
ap-1817	79	19	gd(h	gd(h	NOUN
ap-1817	79	20	)	)	PUNCT
ap-1817	79	21	coincides	coincide	VERB
ap-1817	79	22	with	with	ADP
ap-1817	79	23	the	the	DET
ap-1817	79	24	usual	usual	ADJ
ap-1817	79	25	sum	sum	NOUN
ap-1817	79	26	of	of	ADP
ap-1817	79	27	linear	linear	PROPN
ap-1817	79	28	operators	operator	NOUN
ap-1817	79	29	,	,	PUNCT
ap-1817	79	30	i.e.	i.e.	X
ap-1817	79	31	a⊕d	a⊕d	PROPN
ap-1817	79	32	b	b	X
ap-1817	79	33	=	=	SYM
ap-1817	79	34	a	a	PROPN
ap-1817	79	35	+	+	PROPN
ap-1817	79	36	b.	b.	NOUN
ap-1817	80	1	it	it	PRON
ap-1817	80	2	is	be	AUX
ap-1817	80	3	easy	easy	ADJ
ap-1817	80	4	to	to	PART
ap-1817	80	5	show	show	VERB
ap-1817	80	6	that	that	SCONJ
ap-1817	80	7	b+(h	b+(h	PROPN
ap-1817	80	8	)	)	PUNCT
ap-1817	80	9	is	be	AUX
ap-1817	80	10	a	a	DET
ap-1817	80	11	sub	sub	ADJ
ap-1817	80	12	-	-	ADJ
ap-1817	80	13	generalized	generalized	ADJ
ap-1817	80	14	effect	effect	NOUN
ap-1817	80	15	algebra	algebra	NOUN
ap-1817	80	16	of	of	ADP
ap-1817	80	17	gd(h	gd(h	NOUN
ap-1817	80	18	)	)	PUNCT
ap-1817	80	19	.	.	PUNCT
ap-1817	81	1	for	for	ADP
ap-1817	81	2	every	every	DET
ap-1817	81	3	q	q	PROPN
ap-1817	81	4	∈	∈	PROPN
ap-1817	81	5	b+(h	b+(h	PROPN
ap-1817	81	6	)	)	PUNCT
ap-1817	81	7	,	,	PUNCT
ap-1817	81	8	q	q	X
ap-1817	81	9	6=	6=	NUM
ap-1817	81	10	0	0	NUM
ap-1817	81	11	,	,	PUNCT
ap-1817	81	12	the	the	DET
ap-1817	81	13	intervals	interval	NOUN
ap-1817	81	14	under	under	ADP
ap-1817	81	15	q	q	NOUN
ap-1817	81	16	in	in	ADP
ap-1817	81	17	b+(h	b+(h	PROPN
ap-1817	81	18	)	)	PUNCT
ap-1817	81	19	and	and	CCONJ
ap-1817	81	20	gd(h	gd(h	NOUN
ap-1817	81	21	)	)	PUNCT
ap-1817	81	22	coincide	coincide	NOUN
ap-1817	81	23	,	,	PUNCT
ap-1817	81	24	i.e.	i.e.	X
ap-1817	81	25	[	[	X
ap-1817	81	26	0	0	NUM
ap-1817	81	27	,	,	PUNCT
ap-1817	81	28	q]b+(h	q]b+(h	X
ap-1817	81	29	)	)	PUNCT
ap-1817	81	30	=	=	PUNCT
ap-1817	82	1	[	[	X
ap-1817	82	2	0	0	NUM
ap-1817	82	3	,	,	PUNCT
ap-1817	82	4	q]gd(h	q]gd(h	NUM
ap-1817	82	5	)	)	PUNCT
ap-1817	82	6	∩	∩	NOUN
ap-1817	82	7	b+(h	b+(h	PROPN
ap-1817	82	8	)	)	PUNCT
ap-1817	82	9	=	=	PUNCT
ap-1817	83	1	[	[	X
ap-1817	83	2	0	0	NUM
ap-1817	83	3	,	,	PUNCT
ap-1817	83	4	q]gd(h	q]gd(h	NUM
ap-1817	83	5	)	)	PUNCT
ap-1817	83	6	and	and	CCONJ
ap-1817	83	7	they	they	PRON
ap-1817	83	8	also	also	ADV
ap-1817	83	9	coincide	coincide	VERB
ap-1817	83	10	as	as	SCONJ
ap-1817	83	11	effect	effect	NOUN
ap-1817	83	12	algebras	algebra	NOUN
ap-1817	83	13	.	.	PUNCT
ap-1817	84	1	this	this	PRON
ap-1817	84	2	shows	show	VERB
ap-1817	84	3	that	that	SCONJ
ap-1817	84	4	conditions	condition	NOUN
ap-1817	84	5	(	(	PUNCT
ap-1817	84	6	1	1	NUM
ap-1817	84	7	.	.	PUNCT
ap-1817	84	8	)	)	PUNCT
ap-1817	84	9	and	and	CCONJ
ap-1817	84	10	(	(	PUNCT
ap-1817	84	11	2	2	NUM
ap-1817	84	12	.	.	PUNCT
ap-1817	84	13	)	)	PUNCT
ap-1817	84	14	from	from	ADP
ap-1817	84	15	theorem	theorem	ADJ
ap-1817	84	16	2.3	2.3	NUM
ap-1817	84	17	hold	hold	NOUN
ap-1817	84	18	.	.	PUNCT
ap-1817	85	1	open	open	ADJ
ap-1817	85	2	problem	problem	NOUN
ap-1817	85	3	2.5	2.5	NUM
ap-1817	85	4	.	.	PUNCT
ap-1817	86	1	example	example	NOUN
ap-1817	86	2	2.4	2.4	NUM
ap-1817	86	3	shows	show	VERB
ap-1817	86	4	that	that	SCONJ
ap-1817	86	5	,	,	PUNCT
ap-1817	86	6	in	in	ADP
ap-1817	86	7	theorem	theorem	NOUN
ap-1817	86	8	2.3	2.3	NUM
ap-1817	86	9	,	,	PUNCT
ap-1817	86	10	the	the	DET
ap-1817	86	11	condition	condition	NOUN
ap-1817	86	12	“	"	PUNCT
ap-1817	86	13	to	to	ADP
ap-1817	86	14	every	every	DET
ap-1817	86	15	q	q	NOUN
ap-1817	86	16	∈	∈	PROPN
ap-1817	86	17	e	e	NOUN
ap-1817	86	18	there	there	PRON
ap-1817	86	19	exists	exist	VERB
ap-1817	86	20	c	c	PROPN
ap-1817	86	21	∈	∈	PROPN
ap-1817	86	22	g	g	PROPN
ap-1817	86	23	with	with	ADP
ap-1817	86	24	q	q	PROPN
ap-1817	86	25	≤	≤	PROPN
ap-1817	86	26	c	c	X
ap-1817	86	27	”	"	PUNCT
ap-1817	86	28	is	be	AUX
ap-1817	86	29	only	only	ADV
ap-1817	86	30	sufficient	sufficient	ADJ
ap-1817	86	31	but	but	CCONJ
ap-1817	86	32	not	not	PART
ap-1817	86	33	necessary	necessary	ADJ
ap-1817	86	34	for	for	ADP
ap-1817	86	35	the	the	DET
ap-1817	86	36	equivalence	equivalence	NOUN
ap-1817	86	37	of	of	ADP
ap-1817	86	38	conditions	condition	NOUN
ap-1817	86	39	(	(	PUNCT
ap-1817	86	40	1	1	NUM
ap-1817	86	41	.	.	PUNCT
ap-1817	86	42	)	)	PUNCT
ap-1817	87	1	and	and	CCONJ
ap-1817	87	2	(	(	PUNCT
ap-1817	87	3	2	2	NUM
ap-1817	87	4	.	.	NUM
ap-1817	87	5	)	)	PUNCT
ap-1817	87	6	.	.	PUNCT
ap-1817	88	1	thus	thus	ADV
ap-1817	88	2	the	the	DET
ap-1817	88	3	open	open	ADJ
ap-1817	88	4	problem	problem	NOUN
ap-1817	88	5	remains	remain	VERB
ap-1817	88	6	to	to	PART
ap-1817	88	7	find	find	VERB
ap-1817	88	8	a	a	DET
ap-1817	88	9	necessary	necessary	ADJ
ap-1817	88	10	and	and	CCONJ
ap-1817	88	11	sufficient	sufficient	ADJ
ap-1817	88	12	condition	condition	NOUN
ap-1817	88	13	for	for	ADP
ap-1817	88	14	the	the	DET
ap-1817	88	15	equivalence	equivalence	NOUN
ap-1817	88	16	of	of	ADP
ap-1817	88	17	(	(	PUNCT
ap-1817	88	18	1	1	NUM
ap-1817	88	19	.	.	PUNCT
ap-1817	88	20	)	)	PUNCT
ap-1817	89	1	and	and	CCONJ
ap-1817	89	2	(	(	PUNCT
ap-1817	89	3	2	2	NUM
ap-1817	89	4	.	.	PUNCT
ap-1817	89	5	)	)	PUNCT
ap-1817	89	6	in	in	ADP
ap-1817	89	7	theorem	theorem	NOUN
ap-1817	89	8	2.3	2.3	NUM
ap-1817	89	9	.	.	PUNCT
ap-1817	90	1	in	in	ADP
ap-1817	90	2	fact	fact	NOUN
ap-1817	90	3	,	,	PUNCT
ap-1817	90	4	for	for	ADP
ap-1817	90	5	every	every	DET
ap-1817	90	6	dense	dense	ADJ
ap-1817	90	7	subspace	subspace	NOUN
ap-1817	90	8	d	d	PROPN
ap-1817	90	9	of	of	ADP
ap-1817	90	10	h	h	NOUN
ap-1817	90	11	,	,	PUNCT
ap-1817	90	12	the	the	DET
ap-1817	90	13	generalized	generalized	ADJ
ap-1817	90	14	effect	effect	NOUN
ap-1817	90	15	algebra	algebra	NOUN
ap-1817	90	16	gd(h	gd(h	NOUN
ap-1817	90	17	)	)	PUNCT
ap-1817	90	18	=	=	SYM
ap-1817	90	19	b+(h	b+(h	PROPN
ap-1817	90	20	)	)	PUNCT
ap-1817	90	21	∪	∪	VERB
ap-1817	90	22	u+	u+	NUM
ap-1817	90	23	d(h	d(h	PROPN
ap-1817	90	24	)	)	PUNCT
ap-1817	90	25	,	,	PUNCT
ap-1817	90	26	where	where	SCONJ
ap-1817	90	27	u+	u+	ADP
ap-1817	90	28	d(h	d(h	PROPN
ap-1817	90	29	)	)	PUNCT
ap-1817	90	30	is	be	AUX
ap-1817	90	31	the	the	DET
ap-1817	90	32	set	set	NOUN
ap-1817	90	33	of	of	ADP
ap-1817	90	34	all	all	DET
ap-1817	90	35	unbounded	unbounded	ADJ
ap-1817	90	36	positive	positive	ADJ
ap-1817	90	37	linear	linear	PROPN
ap-1817	90	38	operators	operator	NOUN
ap-1817	90	39	with	with	ADP
ap-1817	90	40	domain	domain	NOUN
ap-1817	90	41	d	d	NOUN
ap-1817	90	42	and	and	CCONJ
ap-1817	90	43	the	the	DET
ap-1817	90	44	null	null	ADJ
ap-1817	90	45	operator	operator	NOUN
ap-1817	90	46	0	0	NUM
ap-1817	90	47	.	.	PUNCT
ap-1817	91	1	clearly	clearly	ADV
ap-1817	91	2	,	,	PUNCT
ap-1817	91	3	b+(h	b+(h	PROPN
ap-1817	91	4	)	)	PUNCT
ap-1817	91	5	∩	∩	NOUN
ap-1817	91	6	u+	u+	X
ap-1817	91	7	d(h	d(h	PROPN
ap-1817	91	8	)	)	PUNCT
ap-1817	92	1	=	=	PRON
ap-1817	92	2	{	{	PUNCT
ap-1817	92	3	0	0	NUM
ap-1817	92	4	}	}	PUNCT
ap-1817	92	5	.	.	PUNCT
ap-1817	93	1	on	on	ADP
ap-1817	93	2	the	the	DET
ap-1817	93	3	other	other	ADJ
ap-1817	93	4	hand	hand	NOUN
ap-1817	93	5	,	,	PUNCT
ap-1817	93	6	while	while	SCONJ
ap-1817	93	7	b+(h	b+(h	PROPN
ap-1817	93	8	)	)	PUNCT
ap-1817	93	9	is	be	AUX
ap-1817	93	10	a	a	DET
ap-1817	93	11	sub	sub	ADJ
ap-1817	93	12	-	-	ADJ
ap-1817	93	13	generalized	generalized	ADJ
ap-1817	93	14	effect	effect	NOUN
ap-1817	93	15	algebra	algebra	NOUN
ap-1817	93	16	of	of	ADP
ap-1817	93	17	gd(h	gd(h	PROPN
ap-1817	93	18	)	)	PUNCT
ap-1817	93	19	,	,	PUNCT
ap-1817	93	20	the	the	DET
ap-1817	93	21	same	same	ADJ
ap-1817	93	22	is	be	AUX
ap-1817	93	23	not	not	PART
ap-1817	93	24	true	true	ADJ
ap-1817	93	25	for	for	ADP
ap-1817	93	26	u+	u+	NOUN
ap-1817	93	27	d(h	d(h	PROPN
ap-1817	93	28	)	)	PUNCT
ap-1817	93	29	.	.	PUNCT
ap-1817	94	1	this	this	PRON
ap-1817	94	2	shows	show	VERB
ap-1817	94	3	that	that	SCONJ
ap-1817	94	4	the	the	DET
ap-1817	94	5	union	union	NOUN
ap-1817	94	6	of	of	ADP
ap-1817	94	7	{	{	PUNCT
ap-1817	94	8	0	0	NUM
ap-1817	94	9	}	}	PUNCT
ap-1817	94	10	with	with	ADP
ap-1817	94	11	the	the	DET
ap-1817	94	12	difference	difference	NOUN
ap-1817	94	13	of	of	ADP
ap-1817	94	14	two	two	NUM
ap-1817	94	15	sub	sub	ADJ
ap-1817	94	16	-	-	ADJ
ap-1817	94	17	generalized	generalized	ADJ
ap-1817	94	18	effect	effect	NOUN
ap-1817	94	19	algebras	algebra	NOUN
ap-1817	94	20	of	of	ADP
ap-1817	94	21	the	the	DET
ap-1817	94	22	generalized	generalized	ADJ
ap-1817	94	23	effect	effect	NOUN
ap-1817	94	24	algebra	algebra	NOUN
ap-1817	94	25	e	e	PRON
ap-1817	94	26	need	need	AUX
ap-1817	94	27	not	not	PART
ap-1817	94	28	be	be	AUX
ap-1817	94	29	again	again	ADV
ap-1817	94	30	a	a	DET
ap-1817	94	31	sub	sub	ADJ
ap-1817	94	32	-	-	ADJ
ap-1817	94	33	generalized	generalized	ADJ
ap-1817	94	34	effect	effect	NOUN
ap-1817	94	35	algebra	algebra	NOUN
ap-1817	94	36	of	of	ADP
ap-1817	94	37	e.	e.	PROPN
ap-1817	94	38	example	example	PROPN
ap-1817	94	39	2.6	2.6	NUM
ap-1817	94	40	.	.	PUNCT
ap-1817	95	1	let	let	VERB
ap-1817	95	2	u+	u+	PROPN
ap-1817	95	3	d(h	d(h	PROPN
ap-1817	95	4	)	)	PUNCT
ap-1817	96	1	=	=	PRON
ap-1817	96	2	(	(	PUNCT
ap-1817	96	3	gd(h)\b+(h	gd(h)\b+(h	PROPN
ap-1817	96	4	)	)	PUNCT
ap-1817	96	5	)	)	PUNCT
ap-1817	96	6	∪{0	∪{0	PROPN
ap-1817	96	7	}	}	PUNCT
ap-1817	96	8	be	be	VERB
ap-1817	96	9	the	the	DET
ap-1817	96	10	set	set	NOUN
ap-1817	96	11	of	of	ADP
ap-1817	96	12	all	all	DET
ap-1817	96	13	positive	positive	ADJ
ap-1817	96	14	unbounded	unbounded	ADJ
ap-1817	96	15	operators	operator	NOUN
ap-1817	96	16	in	in	ADP
ap-1817	96	17	h	h	NOUN
ap-1817	96	18	with	with	ADP
ap-1817	96	19	domain	domain	NOUN
ap-1817	96	20	d	d	NOUN
ap-1817	96	21	and	and	CCONJ
ap-1817	96	22	the	the	DET
ap-1817	96	23	null	null	ADJ
ap-1817	96	24	operator	operator	NOUN
ap-1817	96	25	0	0	NUM
ap-1817	96	26	.	.	PUNCT
ap-1817	97	1	315	315	NUM
ap-1817	97	2	z.	z.	PROPN
ap-1817	97	3	riečanová	riečanová	PROPN
ap-1817	97	4	,	,	PUNCT
ap-1817	97	5	m.	m.	NOUN
ap-1817	97	6	zajac	zajac	PROPN
ap-1817	97	7	acta	acta	PROPN
ap-1817	97	8	polytechnica	polytechnica	PROPN
ap-1817	97	9	then	then	ADV
ap-1817	97	10	u+	u+	X
ap-1817	97	11	d(h	d(h	PROPN
ap-1817	97	12	)	)	PUNCT
ap-1817	98	1	is	be	AUX
ap-1817	98	2	not	not	PART
ap-1817	98	3	a	a	DET
ap-1817	98	4	sub	sub	ADJ
ap-1817	98	5	-	-	ADJ
ap-1817	98	6	generalized	generalized	ADJ
ap-1817	98	7	effect	effect	NOUN
ap-1817	98	8	algebra	algebra	NOUN
ap-1817	98	9	of	of	ADP
ap-1817	98	10	gd(h	gd(h	PROPN
ap-1817	98	11	)	)	PUNCT
ap-1817	98	12	because	because	SCONJ
ap-1817	98	13	for	for	ADP
ap-1817	98	14	a	a	DET
ap-1817	98	15	∈	∈	PROPN
ap-1817	98	16	b+(h	b+(h	PROPN
ap-1817	98	17	)	)	PUNCT
ap-1817	98	18	and	and	CCONJ
ap-1817	98	19	u	u	NOUN
ap-1817	98	20	,	,	PUNCT
ap-1817	98	21	v	v	PROPN
ap-1817	98	22	∈	∈	PROPN
ap-1817	98	23	u+	u+	X
ap-1817	98	24	d(h	d(h	PROPN
ap-1817	98	25	)	)	PUNCT
ap-1817	98	26	such	such	ADJ
ap-1817	98	27	that	that	DET
ap-1817	98	28	v	v	NOUN
ap-1817	98	29	=	=	SYM
ap-1817	98	30	u	u	NOUN
ap-1817	98	31	+	+	NOUN
ap-1817	98	32	a	a	PRON
ap-1817	98	33	we	we	PRON
ap-1817	98	34	have	have	VERB
ap-1817	98	35	a	a	DET
ap-1817	98	36	/∈	/∈	PUNCT
ap-1817	98	37	u+	u+	NOUN
ap-1817	98	38	d(h	d(h	PROPN
ap-1817	98	39	)	)	PUNCT
ap-1817	98	40	.	.	PUNCT
ap-1817	99	1	it	it	PRON
ap-1817	99	2	follows	follow	VERB
ap-1817	99	3	that	that	SCONJ
ap-1817	99	4	there	there	PRON
ap-1817	99	5	are	be	VERB
ap-1817	99	6	q	q	PROPN
ap-1817	99	7	∈	∈	PROPN
ap-1817	99	8	u+	u+	X
ap-1817	99	9	d(h	d(h	PROPN
ap-1817	99	10	)	)	PUNCT
ap-1817	99	11	,	,	PUNCT
ap-1817	99	12	q	q	X
ap-1817	100	1	6=	6=	NUM
ap-1817	100	2	0	0	NUM
ap-1817	100	3	,	,	PUNCT
ap-1817	100	4	such	such	ADJ
ap-1817	100	5	that	that	SCONJ
ap-1817	101	1	[	[	X
ap-1817	101	2	0	0	NUM
ap-1817	101	3	,	,	PUNCT
ap-1817	101	4	q]u+	q]u+	PROPN
ap-1817	101	5	d	d	PROPN
ap-1817	101	6	(	(	PUNCT
ap-1817	101	7	h	h	NOUN
ap-1817	101	8	)	)	PUNCT
ap-1817	101	9	=	=	PUNCT
ap-1817	102	1	[	[	X
ap-1817	102	2	0	0	NUM
ap-1817	102	3	,	,	PUNCT
ap-1817	102	4	q]gd(h	q]gd(h	NUM
ap-1817	102	5	)	)	PUNCT
ap-1817	102	6	∩	∩	NOUN
ap-1817	102	7	u+	u+	X
ap-1817	102	8	d(h	d(h	PROPN
ap-1817	102	9	)	)	PUNCT
ap-1817	102	10	is	be	AUX
ap-1817	102	11	not	not	PART
ap-1817	102	12	a	a	DET
ap-1817	102	13	sub	sub	ADJ
ap-1817	102	14	-	-	ADJ
ap-1817	102	15	effect	effect	ADJ
ap-1817	102	16	algebra	algebra	NOUN
ap-1817	102	17	in	in	ADP
ap-1817	102	18	[	[	X
ap-1817	102	19	0	0	NUM
ap-1817	102	20	,	,	PUNCT
ap-1817	102	21	q]gd(h	q]gd(h	NUM
ap-1817	102	22	)	)	PUNCT
ap-1817	102	23	.	.	PUNCT
ap-1817	103	1	acknowledgements	acknowledgement	NOUN
ap-1817	103	2	this	this	DET
ap-1817	103	3	work	work	NOUN
ap-1817	103	4	was	be	AUX
ap-1817	103	5	supported	support	VERB
ap-1817	103	6	by	by	ADP
ap-1817	103	7	grants	grant	NOUN
ap-1817	103	8	vega	vega	PROPN
ap-1817	103	9	1/0297/11	1/0297/11	PROPN
ap-1817	103	10	and	and	CCONJ
ap-1817	103	11	vega	vega	PROPN
ap-1817	103	12	1/0426/12	1/0426/12	NUM
ap-1817	103	13	of	of	ADP
ap-1817	103	14	the	the	DET
ap-1817	103	15	ministry	ministry	PROPN
ap-1817	103	16	of	of	ADP
ap-1817	103	17	education	education	NOUN
ap-1817	103	18	of	of	ADP
ap-1817	103	19	the	the	DET
ap-1817	103	20	slovak	slovak	ADJ
ap-1817	103	21	republic	republic	NOUN
ap-1817	103	22	and	and	CCONJ
ap-1817	103	23	by	by	ADP
ap-1817	103	24	grant	grant	NOUN
ap-1817	103	25	apvv-0178	apvv-0178	ADV
ap-1817	103	26	-	-	PUNCT
ap-1817	103	27	11	11	NUM
ap-1817	103	28	of	of	ADP
ap-1817	103	29	the	the	DET
ap-1817	103	30	slovak	slovak	ADJ
ap-1817	103	31	research	research	NOUN
ap-1817	103	32	and	and	CCONJ
ap-1817	103	33	development	development	NOUN
ap-1817	103	34	agency	agency	NOUN
ap-1817	103	35	.	.	PUNCT
ap-1817	104	1	references	reference	NOUN
ap-1817	104	2	[	[	X
ap-1817	104	3	1	1	NUM
ap-1817	104	4	]	]	X
ap-1817	104	5	foulis	foulis	PROPN
ap-1817	104	6	,	,	PUNCT
ap-1817	104	7	d.	d.	PROPN
ap-1817	104	8	j.	j.	PROPN
ap-1817	104	9	,	,	PUNCT
ap-1817	104	10	bennet	bennet	PROPN
ap-1817	104	11	,	,	PUNCT
ap-1817	104	12	m.	m.	PROPN
ap-1817	104	13	k.	k.	PROPN
ap-1817	104	14	:	:	PUNCT
ap-1817	104	15	effect	effect	NOUN
ap-1817	104	16	algebras	algebra	NOUN
ap-1817	104	17	and	and	CCONJ
ap-1817	104	18	unsharp	unsharp	ADJ
ap-1817	104	19	quantum	quantum	ADJ
ap-1817	104	20	logics	logic	NOUN
ap-1817	104	21	,	,	PUNCT
ap-1817	104	22	found	find	VERB
ap-1817	104	23	.	.	PUNCT
ap-1817	105	1	phys	phy	NOUN
ap-1817	105	2	.	.	PUNCT
ap-1817	106	1	24	24	NUM
ap-1817	106	2	,	,	PUNCT
ap-1817	106	3	(	(	PUNCT
ap-1817	106	4	1994	1994	NUM
ap-1817	106	5	)	)	PUNCT
ap-1817	106	6	1331–1352	1331–1352	NUM
ap-1817	106	7	.	.	PUNCT
ap-1817	107	1	[	[	X
ap-1817	107	2	2	2	NUM
ap-1817	107	3	]	]	PUNCT
ap-1817	107	4	foulis	foulis	PROPN
ap-1817	107	5	,	,	PUNCT
ap-1817	107	6	d.	d.	PROPN
ap-1817	107	7	j.	j.	PROPN
ap-1817	107	8	:	:	PUNCT
ap-1817	107	9	observables	observable	NOUN
ap-1817	107	10	,	,	PUNCT
ap-1817	107	11	states	state	NOUN
ap-1817	107	12	and	and	CCONJ
ap-1817	107	13	symmetries	symmetry	NOUN
ap-1817	107	14	in	in	ADP
ap-1817	107	15	the	the	DET
ap-1817	107	16	context	context	NOUN
ap-1817	107	17	of	of	ADP
ap-1817	107	18	cb	cb	NOUN
ap-1817	107	19	-	-	PUNCT
ap-1817	107	20	effect	effect	NOUN
ap-1817	107	21	algebras	algebra	NOUN
ap-1817	107	22	,	,	PUNCT
ap-1817	107	23	reports	report	NOUN
ap-1817	107	24	on	on	ADP
ap-1817	107	25	mathematical	mathematical	ADJ
ap-1817	107	26	physics	physics	NOUN
ap-1817	107	27	,	,	PUNCT
ap-1817	107	28	60	60	NUM
ap-1817	107	29	(	(	PUNCT
ap-1817	107	30	2007	2007	NUM
ap-1817	107	31	)	)	PUNCT
ap-1817	107	32	,	,	PUNCT
ap-1817	107	33	329–346	329–346	NUM
ap-1817	107	34	.	.	PUNCT
ap-1817	108	1	[	[	X
ap-1817	108	2	3	3	NUM
ap-1817	108	3	]	]	X
ap-1817	108	4	foulis	foulis	PROPN
ap-1817	108	5	,	,	PUNCT
ap-1817	108	6	d.	d.	PROPN
ap-1817	108	7	j.	j.	PROPN
ap-1817	108	8	:	:	PUNCT
ap-1817	108	9	effects	effect	NOUN
ap-1817	108	10	,	,	PUNCT
ap-1817	108	11	observables	observable	NOUN
ap-1817	108	12	and	and	CCONJ
ap-1817	108	13	symmetries	symmetry	NOUN
ap-1817	108	14	in	in	ADP
ap-1817	108	15	physics	physics	PROPN
ap-1817	108	16	,	,	PUNCT
ap-1817	108	17	found	find	VERB
ap-1817	108	18	.	.	PUNCT
ap-1817	109	1	phys	phy	NOUN
ap-1817	109	2	.	.	PUNCT
ap-1817	110	1	37	37	NUM
ap-1817	110	2	(	(	PUNCT
ap-1817	110	3	2007	2007	NUM
ap-1817	110	4	)	)	PUNCT
ap-1817	110	5	,	,	PUNCT
ap-1817	110	6	1421–1446	1421–1446	NUM
ap-1817	110	7	.	.	PUNCT
ap-1817	111	1	[	[	X
ap-1817	111	2	4	4	X
ap-1817	111	3	]	]	X
ap-1817	111	4	kalmbach	kalmbach	PROPN
ap-1817	111	5	,	,	PUNCT
ap-1817	111	6	g.	g.	PROPN
ap-1817	111	7	,	,	PUNCT
ap-1817	111	8	riečanová	riečanová	PROPN
ap-1817	111	9	,	,	PUNCT
ap-1817	111	10	z.	z.	PROPN
ap-1817	111	11	:	:	PUNCT
ap-1817	111	12	an	an	DET
ap-1817	111	13	axiomatization	axiomatization	NOUN
ap-1817	111	14	for	for	ADP
ap-1817	111	15	abelian	abelian	PROPN
ap-1817	111	16	relative	relative	PROPN
ap-1817	111	17	inverses	inverses	PROPN
ap-1817	111	18	,	,	PUNCT
ap-1817	111	19	demonstratio	demonstratio	PROPN
ap-1817	111	20	math	math	PROPN
ap-1817	111	21	.	.	PUNCT
ap-1817	112	1	27	27	NUM
ap-1817	112	2	(	(	PUNCT
ap-1817	112	3	1994	1994	NUM
ap-1817	112	4	)	)	PUNCT
ap-1817	112	5	,	,	PUNCT
ap-1817	112	6	769–780	769–780	NUM
ap-1817	112	7	.	.	PUNCT
ap-1817	113	1	[	[	X
ap-1817	113	2	5	5	NUM
ap-1817	113	3	]	]	X
ap-1817	113	4	hedlíková	hedlíková	NOUN
ap-1817	113	5	,	,	PUNCT
ap-1817	113	6	j.	j.	PROPN
ap-1817	113	7	,	,	PUNCT
ap-1817	113	8	pulmannová	pulmannová	PROPN
ap-1817	113	9	,	,	PUNCT
ap-1817	113	10	s.	s.	PROPN
ap-1817	113	11	:	:	PUNCT
ap-1817	113	12	generalized	generalized	ADJ
ap-1817	113	13	difference	difference	NOUN
ap-1817	113	14	posets	poset	NOUN
ap-1817	113	15	and	and	CCONJ
ap-1817	113	16	orthoalgebras	orthoalgebra	NOUN
ap-1817	113	17	,	,	PUNCT
ap-1817	113	18	acta	acta	PROPN
ap-1817	113	19	math	math	PROPN
ap-1817	113	20	.	.	PUNCT
ap-1817	114	1	univ	univ	PROPN
ap-1817	114	2	.	.	PROPN
ap-1817	114	3	comenianae	comenianae	PROPN
ap-1817	114	4	45	45	NUM
ap-1817	114	5	(	(	PUNCT
ap-1817	114	6	1996	1996	NUM
ap-1817	114	7	)	)	PUNCT
ap-1817	114	8	,	,	PUNCT
ap-1817	114	9	247–279	247–279	NUM
ap-1817	114	10	.	.	PUNCT
ap-1817	115	1	[	[	X
ap-1817	115	2	6	6	NUM
ap-1817	115	3	]	]	X
ap-1817	115	4	kôpka	kôpka	NOUN
ap-1817	115	5	,	,	PUNCT
ap-1817	115	6	f.	f.	PROPN
ap-1817	115	7	,	,	PUNCT
ap-1817	115	8	chovanec	chovanec	PROPN
ap-1817	115	9	,	,	PUNCT
ap-1817	115	10	f.	f.	PROPN
ap-1817	115	11	:	:	PUNCT
ap-1817	115	12	d	d	X
ap-1817	115	13	-	-	PUNCT
ap-1817	115	14	posets	poset	NOUN
ap-1817	115	15	,	,	PUNCT
ap-1817	115	16	math	math	NOUN
ap-1817	115	17	.	.	PUNCT
ap-1817	116	1	slovaca	slovaca	NOUN
ap-1817	116	2	44	44	NUM
ap-1817	116	3	(	(	PUNCT
ap-1817	116	4	1994	1994	NUM
ap-1817	116	5	)	)	PUNCT
ap-1817	116	6	,	,	PUNCT
ap-1817	116	7	21–34	21–34	NUM
ap-1817	116	8	.	.	PUNCT
ap-1817	117	1	[	[	X
ap-1817	117	2	7	7	NUM
ap-1817	117	3	]	]	X
ap-1817	117	4	blank	blank	NOUN
ap-1817	117	5	,	,	PUNCT
ap-1817	117	6	j.	j.	PROPN
ap-1817	117	7	,	,	PUNCT
ap-1817	117	8	exner	exner	PROPN
ap-1817	117	9	,	,	PUNCT
ap-1817	117	10	p.	p.	PROPN
ap-1817	117	11	,	,	PUNCT
ap-1817	117	12	havlíček	havlíček	PROPN
ap-1817	117	13	,	,	PUNCT
ap-1817	117	14	m.	m.	NOUN
ap-1817	117	15	:	:	PUNCT
ap-1817	117	16	hilbert	hilbert	NOUN
ap-1817	117	17	space	space	NOUN
ap-1817	117	18	operators	operator	NOUN
ap-1817	117	19	in	in	ADP
ap-1817	117	20	quantum	quantum	ADJ
ap-1817	117	21	physics	physics	NOUN
ap-1817	117	22	(	(	PUNCT
ap-1817	117	23	second	second	ADJ
ap-1817	117	24	edition	edition	NOUN
ap-1817	117	25	)	)	PUNCT
ap-1817	117	26	,	,	PUNCT
ap-1817	117	27	springer	springer	NOUN
ap-1817	117	28	2008	2008	NUM
ap-1817	117	29	.	.	PUNCT
ap-1817	118	1	[	[	X
ap-1817	118	2	8	8	X
ap-1817	118	3	]	]	X
ap-1817	118	4	j.	j.	PROPN
ap-1817	118	5	paseka	paseka	PROPN
ap-1817	118	6	,	,	PUNCT
ap-1817	118	7	z.	z.	PROPN
ap-1817	118	8	riečanová	riečanová	PROPN
ap-1817	118	9	:	:	PUNCT
ap-1817	118	10	considerable	considerable	ADJ
ap-1817	118	11	sets	set	NOUN
ap-1817	118	12	of	of	ADP
ap-1817	118	13	linear	linear	PROPN
ap-1817	118	14	operators	operator	NOUN
ap-1817	118	15	in	in	ADP
ap-1817	118	16	hilbert	hilbert	PROPN
ap-1817	118	17	spaces	space	NOUN
ap-1817	118	18	as	as	ADP
ap-1817	118	19	operator	operator	NOUN
ap-1817	118	20	generalized	generalized	ADJ
ap-1817	118	21	effect	effect	NOUN
ap-1817	118	22	algebras	algebra	NOUN
ap-1817	118	23	,	,	PUNCT
ap-1817	118	24	found	find	VERB
ap-1817	118	25	.	.	PUNCT
ap-1817	119	1	phys	phy	NOUN
ap-1817	119	2	.	.	PUNCT
ap-1817	120	1	41	41	NUM
ap-1817	120	2	(	(	PUNCT
ap-1817	120	3	2011	2011	NUM
ap-1817	120	4	)	)	PUNCT
ap-1817	120	5	,	,	PUNCT
ap-1817	120	6	1634–1647	1634–1647	NUM
ap-1817	120	7	.	.	PUNCT
ap-1817	121	1	[	[	X
ap-1817	121	2	9	9	NUM
ap-1817	121	3	]	]	X
ap-1817	121	4	polakovič	polakovič	X
ap-1817	121	5	,	,	PUNCT
ap-1817	121	6	m.	m.	NOUN
ap-1817	121	7	,	,	PUNCT
ap-1817	121	8	riečanová	riečanová	PROPN
ap-1817	121	9	,	,	PUNCT
ap-1817	121	10	z.	z.	PROPN
ap-1817	121	11	:	:	PUNCT
ap-1817	121	12	generalized	generalized	ADJ
ap-1817	121	13	effect	effect	NOUN
ap-1817	121	14	algebras	algebra	NOUN
ap-1817	121	15	of	of	ADP
ap-1817	121	16	positive	positive	ADJ
ap-1817	121	17	operators	operator	NOUN
ap-1817	121	18	densely	densely	ADV
ap-1817	121	19	defined	define	VERB
ap-1817	121	20	in	in	ADP
ap-1817	121	21	hilbert	hilbert	NOUN
ap-1817	121	22	spaces	space	NOUN
ap-1817	121	23	,	,	PUNCT
ap-1817	121	24	internat	internat	PROPN
ap-1817	121	25	.	.	PUNCT
ap-1817	122	1	j.	j.	PROPN
ap-1817	122	2	theor	theor	PROPN
ap-1817	122	3	.	.	PUNCT
ap-1817	123	1	phys	phy	NOUN
ap-1817	123	2	.	.	PUNCT
ap-1817	124	1	50	50	NUM
ap-1817	124	2	(	(	PUNCT
ap-1817	124	3	2011	2011	NUM
ap-1817	124	4	)	)	PUNCT
ap-1817	124	5	,	,	PUNCT
ap-1817	124	6	1167–1174	1167–1174	NUM
ap-1817	124	7	.	.	PUNCT
ap-1817	125	1	[	[	X
ap-1817	125	2	10	10	NUM
ap-1817	125	3	]	]	X
ap-1817	125	4	polakovič	polakovič	X
ap-1817	125	5	,	,	PUNCT
ap-1817	125	6	m.	m.	NOUN
ap-1817	125	7	:	:	PUNCT
ap-1817	125	8	generalized	generalized	ADJ
ap-1817	125	9	effect	effect	NOUN
ap-1817	125	10	algebras	algebra	NOUN
ap-1817	125	11	of	of	ADP
ap-1817	125	12	bounded	bound	VERB
ap-1817	125	13	positive	positive	ADJ
ap-1817	125	14	operators	operator	NOUN
ap-1817	125	15	defined	define	VERB
ap-1817	125	16	on	on	ADP
ap-1817	125	17	hilbert	hilbert	PROPN
ap-1817	125	18	spaces	space	NOUN
ap-1817	125	19	,	,	PUNCT
ap-1817	125	20	reports	report	NOUN
ap-1817	125	21	on	on	ADP
ap-1817	125	22	mathematical	mathematical	ADJ
ap-1817	125	23	physics	physics	NOUN
ap-1817	125	24	,	,	PUNCT
ap-1817	125	25	68	68	NUM
ap-1817	125	26	(	(	PUNCT
ap-1817	125	27	2011	2011	NUM
ap-1817	125	28	)	)	PUNCT
ap-1817	125	29	,	,	PUNCT
ap-1817	125	30	241–250	241–250	NUM
ap-1817	125	31	.	.	PUNCT
ap-1817	126	1	[	[	X
ap-1817	126	2	11	11	NUM
ap-1817	126	3	]	]	X
ap-1817	126	4	pulmannová	pulmannová	PROPN
ap-1817	126	5	,	,	PUNCT
ap-1817	126	6	s.	s.	PROPN
ap-1817	126	7	,	,	PUNCT
ap-1817	126	8	riečanová	riečanová	PROPN
ap-1817	126	9	,	,	PUNCT
ap-1817	126	10	z.	z.	PROPN
ap-1817	126	11	,	,	PUNCT
ap-1817	126	12	zajac	zajac	PROPN
ap-1817	126	13	,	,	PUNCT
ap-1817	126	14	m.	m.	NOUN
ap-1817	126	15	:	:	PUNCT
ap-1817	126	16	topological	topological	ADJ
ap-1817	126	17	properties	property	NOUN
ap-1817	126	18	of	of	ADP
ap-1817	126	19	operator	operator	NOUN
ap-1817	126	20	generalized	generalized	ADJ
ap-1817	126	21	effect	effect	NOUN
ap-1817	126	22	algebras	algebra	NOUN
ap-1817	126	23	,	,	PUNCT
ap-1817	126	24	reports	report	NOUN
ap-1817	126	25	of	of	ADP
ap-1817	126	26	mathematical	mathematical	ADJ
ap-1817	126	27	physics	physics	NOUN
ap-1817	126	28	,	,	PUNCT
ap-1817	126	29	69	69	NUM
ap-1817	126	30	(	(	PUNCT
ap-1817	126	31	2012	2012	NUM
ap-1817	126	32	)	)	PUNCT
ap-1817	126	33	,	,	PUNCT
ap-1817	126	34	no	no	INTJ
ap-1817	126	35	.	.	NOUN
ap-1817	126	36	2	2	NUM
ap-1817	126	37	,	,	PUNCT
ap-1817	126	38	311–320	311–320	NUM
ap-1817	126	39	.	.	PUNCT
ap-1817	127	1	[	[	X
ap-1817	127	2	12	12	NUM
ap-1817	127	3	]	]	PUNCT
ap-1817	127	4	riečanová	riečanová	PROPN
ap-1817	127	5	,	,	PUNCT
ap-1817	127	6	z.	z.	PROPN
ap-1817	127	7	,	,	PUNCT
ap-1817	127	8	zajac	zajac	PROPN
ap-1817	127	9	,	,	PUNCT
ap-1817	127	10	m.	m.	NOUN
ap-1817	127	11	,	,	PUNCT
ap-1817	127	12	pulmannová	pulmannová	PROPN
ap-1817	127	13	,	,	PUNCT
ap-1817	127	14	s.	s.	PROPN
ap-1817	127	15	:	:	PUNCT
ap-1817	127	16	effect	effect	NOUN
ap-1817	127	17	algebras	algebra	NOUN
ap-1817	127	18	of	of	ADP
ap-1817	127	19	positive	positive	ADJ
ap-1817	127	20	linear	linear	PROPN
ap-1817	127	21	operators	operator	NOUN
ap-1817	127	22	densely	densely	ADV
ap-1817	127	23	defined	define	VERB
ap-1817	127	24	on	on	ADP
ap-1817	127	25	hilbert	hilbert	PROPN
ap-1817	127	26	spaces	space	NOUN
ap-1817	127	27	,	,	PUNCT
ap-1817	127	28	reports	report	NOUN
ap-1817	127	29	of	of	ADP
ap-1817	127	30	mathematical	mathematical	ADJ
ap-1817	127	31	physics	physics	NOUN
ap-1817	127	32	68	68	NUM
ap-1817	127	33	(	(	PUNCT
ap-1817	127	34	2011	2011	NUM
ap-1817	127	35	)	)	PUNCT
ap-1817	127	36	,	,	PUNCT
ap-1817	127	37	no	no	INTJ
ap-1817	127	38	.	.	NOUN
ap-1817	127	39	3	3	NUM
ap-1817	127	40	,	,	PUNCT
ap-1817	127	41	261–270	261–270	NUM
ap-1817	127	42	.	.	PUNCT
ap-1817	128	1	[	[	X
ap-1817	128	2	13	13	NUM
ap-1817	128	3	]	]	SYM
ap-1817	128	4	riečanová	riečanová	PROPN
ap-1817	128	5	,	,	PUNCT
ap-1817	128	6	z.	z.	PROPN
ap-1817	128	7	,	,	PUNCT
ap-1817	128	8	zajac	zajac	PROPN
ap-1817	128	9	,	,	PUNCT
ap-1817	128	10	m.	m.	NOUN
ap-1817	128	11	:	:	PUNCT
ap-1817	128	12	extension	extension	NOUN
ap-1817	128	13	of	of	ADP
ap-1817	128	14	effect	effect	NOUN
ap-1817	128	15	algebra	algebra	NOUN
ap-1817	128	16	operations	operation	NOUN
ap-1817	128	17	,	,	PUNCT
ap-1817	128	18	acta	acta	PROPN
ap-1817	128	19	polytechnica	polytechnica	PROPN
ap-1817	128	20	51	51	NUM
ap-1817	128	21	(	(	PUNCT
ap-1817	128	22	2011	2011	NUM
ap-1817	128	23	)	)	PUNCT
ap-1817	129	1	no	no	INTJ
ap-1817	129	2	.	.	NOUN
ap-1817	130	1	4	4	NUM
ap-1817	130	2	,	,	PUNCT
ap-1817	130	3	73–77	73–77	NUM
ap-1817	130	4	.	.	PUNCT
ap-1817	131	1	[	[	X
ap-1817	131	2	14	14	NUM
ap-1817	131	3	]	]	SYM
ap-1817	131	4	riečanová	riečanová	PROPN
ap-1817	131	5	,	,	PUNCT
ap-1817	131	6	z.	z.	PROPN
ap-1817	131	7	:	:	PUNCT
ap-1817	131	8	effect	effect	NOUN
ap-1817	131	9	algebra	algebra	NOUN
ap-1817	131	10	of	of	ADP
ap-1817	131	11	positive	positive	ADJ
ap-1817	131	12	self	self	NOUN
ap-1817	131	13	-	-	PUNCT
ap-1817	131	14	adjoint	adjoint	NOUN
ap-1817	131	15	operators	operator	NOUN
ap-1817	131	16	densely	densely	ADV
ap-1817	131	17	defined	define	VERB
ap-1817	131	18	on	on	ADP
ap-1817	131	19	hilbert	hilbert	PROPN
ap-1817	131	20	spaces	space	NOUN
ap-1817	131	21	,	,	PUNCT
ap-1817	131	22	acta	acta	PROPN
ap-1817	131	23	polytechnica	polytechnica	PROPN
ap-1817	131	24	51	51	NUM
ap-1817	131	25	(	(	PUNCT
ap-1817	131	26	2011	2011	NUM
ap-1817	131	27	)	)	PUNCT
ap-1817	132	1	no	no	INTJ
ap-1817	132	2	.	.	NOUN
ap-1817	133	1	4	4	NUM
ap-1817	133	2	,	,	PUNCT
ap-1817	133	3	78–82	78–82	NUM
ap-1817	133	4	.	.	PUNCT
ap-1817	134	1	[	[	X
ap-1817	134	2	15	15	NUM
ap-1817	134	3	]	]	X
ap-1817	134	4	riečanová	riečanová	PROPN
ap-1817	134	5	,	,	PUNCT
ap-1817	134	6	z.	z.	PROPN
ap-1817	134	7	:	:	PUNCT
ap-1817	135	1	subalgebras	subalgebras	PROPN
ap-1817	135	2	,	,	PUNCT
ap-1817	135	3	intervals	interval	NOUN
ap-1817	135	4	and	and	CCONJ
ap-1817	135	5	central	central	ADJ
ap-1817	135	6	elements	element	NOUN
ap-1817	135	7	of	of	ADP
ap-1817	135	8	generalized	generalized	ADJ
ap-1817	135	9	effect	effect	NOUN
ap-1817	135	10	algebras	algebra	NOUN
ap-1817	135	11	.	.	PUNCT
ap-1817	136	1	international	international	ADJ
ap-1817	136	2	journal	journal	PROPN
ap-1817	136	3	of	of	ADP
ap-1817	136	4	theoretic	theoretic	ADJ
ap-1817	136	5	physics	physics	NOUN
ap-1817	136	6	38	38	NUM
ap-1817	136	7	,	,	PUNCT
ap-1817	136	8	(	(	PUNCT
ap-1817	136	9	1999	1999	NUM
ap-1817	136	10	)	)	PUNCT
ap-1817	136	11	3209–3220	3209–3220	NUM
ap-1817	136	12	.	.	PUNCT
ap-1817	137	1	316	316	NUM
ap-1817	137	2	acta	acta	PROPN
ap-1817	137	3	polytechnica	polytechnica	PROPN
ap-1817	137	4	53(3):314–316	53(3):314–316	PROPN
ap-1817	137	5	,	,	PUNCT
ap-1817	137	6	2013	2013	NUM
ap-1817	137	7	1	1	NUM
ap-1817	137	8	introduction	introduction	NOUN
ap-1817	137	9	and	and	CCONJ
ap-1817	137	10	some	some	DET
ap-1817	137	11	basic	basic	ADJ
ap-1817	137	12	definitions	definition	NOUN
ap-1817	137	13	and	and	CCONJ
ap-1817	137	14	facts	fact	NOUN
ap-1817	137	15	2	2	NUM
ap-1817	137	16	sub	sub	ADJ
ap-1817	137	17	-	-	ADJ
ap-1817	137	18	generalized	generalized	ADJ
ap-1817	137	19	effect	effect	NOUN
ap-1817	137	20	algebras	algebra	NOUN
ap-1817	137	21	of	of	ADP
ap-1817	137	22	generalized	generalized	ADJ
ap-1817	137	23	effect	effect	NOUN
ap-1817	137	24	algebras	algebra	VERB
ap-1817	137	25	acknowledgements	acknowledgement	NOUN
ap-1817	137	26	references	reference	NOUN