id	sid	tid	token	lemma	pos
ejpam-201	1	1	5_201_gordji.dvi	5_201_gordji.dvi	NUM
ejpam-201	1	2	european	european	ADJ
ejpam-201	1	3	journal	journal	NOUN
ejpam-201	1	4	of	of	ADP
ejpam-201	1	5	pure	pure	ADJ
ejpam-201	1	6	and	and	CCONJ
ejpam-201	1	7	applied	apply	VERB
ejpam-201	1	8	mathematics	mathematic	NOUN
ejpam-201	1	9	vol	vol	NOUN
ejpam-201	1	10	.	.	PROPN
ejpam-201	1	11	2	2	NUM
ejpam-201	1	12	,	,	PUNCT
ejpam-201	1	13	no	no	INTJ
ejpam-201	1	14	.	.	NOUN
ejpam-201	1	15	3	3	NUM
ejpam-201	1	16	,	,	PUNCT
ejpam-201	1	17	2009	2009	NUM
ejpam-201	1	18	,	,	PUNCT
ejpam-201	1	19	(	(	PUNCT
ejpam-201	1	20	361	361	NUM
ejpam-201	1	21	-	-	SYM
ejpam-201	1	22	371	371	NUM
ejpam-201	1	23	)	)	PUNCT
ejpam-201	1	24	issn	issn	PROPN
ejpam-201	1	25	1307	1307	NUM
ejpam-201	1	26	-	-	SYM
ejpam-201	1	27	5543	5543	NUM
ejpam-201	1	28	–	–	PUNCT
ejpam-201	1	29	www.ejpam.com	www.ejpam.com	X
ejpam-201	1	30	module	module	NOUN
ejpam-201	1	31	extension	extension	NOUN
ejpam-201	1	32	banach	banach	NOUN
ejpam-201	1	33	algebras	algebra	VERB
ejpam-201	1	34	and	and	CCONJ
ejpam-201	1	35	(	(	PUNCT
ejpam-201	1	36	σ	σ	PROPN
ejpam-201	1	37	,	,	PUNCT
ejpam-201	1	38	τ)-amenability	τ)-amenability	PUNCT
ejpam-201	1	39	m.	m.	PROPN
ejpam-201	1	40	eshaghi	eshaghi	PROPN
ejpam-201	1	41	gordji1∗	gordji1∗	PROPN
ejpam-201	1	42	and	and	CCONJ
ejpam-201	1	43	a.	a.	NOUN
ejpam-201	1	44	niyazi	niyazi	PROPN
ejpam-201	1	45	motlagh2	motlagh2	NOUN
ejpam-201	2	1	1	1	NUM
ejpam-201	2	2	department	department	NOUN
ejpam-201	2	3	of	of	ADP
ejpam-201	2	4	mathematics	mathematic	NOUN
ejpam-201	2	5	,	,	PUNCT
ejpam-201	2	6	semnan	semnan	PROPN
ejpam-201	2	7	university	university	NOUN
ejpam-201	2	8	,	,	PUNCT
ejpam-201	2	9	p.	p.	PROPN
ejpam-201	2	10	o.	o.	PROPN
ejpam-201	2	11	box	box	PROPN
ejpam-201	2	12	35195	35195	NUM
ejpam-201	2	13	-	-	SYM
ejpam-201	2	14	363	363	NUM
ejpam-201	2	15	,	,	PUNCT
ejpam-201	2	16	semnan	semnan	NOUN
ejpam-201	2	17	,	,	PUNCT
ejpam-201	2	18	iran	iran	PROPN
ejpam-201	2	19	.	.	PUNCT
ejpam-201	3	1	2	2	NUM
ejpam-201	3	2	department	department	NOUN
ejpam-201	3	3	of	of	ADP
ejpam-201	3	4	mathematics	mathematic	NOUN
ejpam-201	3	5	,	,	PUNCT
ejpam-201	3	6	ferdowsi	ferdowsi	NOUN
ejpam-201	3	7	university	university	NOUN
ejpam-201	3	8	,	,	PUNCT
ejpam-201	3	9	p.	p.	PROPN
ejpam-201	3	10	o.	o.	PROPN
ejpam-201	3	11	box	box	PROPN
ejpam-201	3	12	1159	1159	NUM
ejpam-201	3	13	,	,	PUNCT
ejpam-201	3	14	mashhad	mashhad	PROPN
ejpam-201	3	15	91775	91775	NUM
ejpam-201	3	16	,	,	PUNCT
ejpam-201	3	17	iran	iran	PROPN
ejpam-201	3	18	abstract	abstract	NOUN
ejpam-201	3	19	.	.	PUNCT
ejpam-201	4	1	in	in	ADP
ejpam-201	4	2	this	this	DET
ejpam-201	4	3	paper	paper	NOUN
ejpam-201	4	4	among	among	ADP
ejpam-201	4	5	other	other	ADJ
ejpam-201	4	6	things	thing	NOUN
ejpam-201	4	7	we	we	PRON
ejpam-201	4	8	find	find	VERB
ejpam-201	4	9	some	some	DET
ejpam-201	4	10	necessary	necessary	ADJ
ejpam-201	4	11	and	and	CCONJ
ejpam-201	4	12	sufficient	sufficient	ADJ
ejpam-201	4	13	conditions	condition	NOUN
ejpam-201	4	14	for	for	ADP
ejpam-201	4	15	a	a	DET
ejpam-201	4	16	banach	banach	NOUN
ejpam-201	4	17	algebra	algebra	NOUN
ejpam-201	4	18	a	a	PRON
ejpam-201	4	19	,	,	PUNCT
ejpam-201	4	20	to	to	PART
ejpam-201	4	21	be	be	AUX
ejpam-201	4	22	(	(	PUNCT
ejpam-201	4	23	σ	σ	NOUN
ejpam-201	4	24	,	,	PUNCT
ejpam-201	4	25	τ)-amenable	τ)-amenable	ADJ
ejpam-201	4	26	,	,	PUNCT
ejpam-201	4	27	where	where	SCONJ
ejpam-201	4	28	σ	σ	PROPN
ejpam-201	4	29	and	and	CCONJ
ejpam-201	4	30	τ	τ	PROPN
ejpam-201	4	31	are	be	AUX
ejpam-201	4	32	continuous	continuous	ADJ
ejpam-201	4	33	homomorphisms	homomorphisms	PROPN
ejpam-201	4	34	ona	ona	PROPN
ejpam-201	4	35	.	.	PUNCT
ejpam-201	4	36	2000	2000	NUM
ejpam-201	4	37	mathematics	mathematic	NOUN
ejpam-201	4	38	subject	subject	NOUN
ejpam-201	4	39	classifications	classification	NOUN
ejpam-201	4	40	:	:	PUNCT
ejpam-201	4	41	primary	primary	ADJ
ejpam-201	4	42	46h25	46h25	NUM
ejpam-201	4	43	;	;	PUNCT
ejpam-201	4	44	secondary	secondary	ADJ
ejpam-201	4	45	47b47	47b47	NUM
ejpam-201	4	46	key	key	ADJ
ejpam-201	4	47	words	word	NOUN
ejpam-201	4	48	and	and	CCONJ
ejpam-201	4	49	phrases	phrase	NOUN
ejpam-201	4	50	:	:	PUNCT
ejpam-201	4	51	(	(	PUNCT
ejpam-201	4	52	σ	σ	PROPN
ejpam-201	4	53	,	,	PUNCT
ejpam-201	4	54	τ)−derivation	τ)−derivation	PROPN
ejpam-201	4	55	;	;	PUNCT
ejpam-201	4	56	arens	aren	NOUN
ejpam-201	4	57	product	product	NOUN
ejpam-201	4	58	;	;	PUNCT
ejpam-201	4	59	approximate	approximate	ADJ
ejpam-201	4	60	identity	identity	NOUN
ejpam-201	4	61	1	1	NUM
ejpam-201	4	62	.	.	PUNCT
ejpam-201	4	63	introduction	introduction	NOUN
ejpam-201	4	64	.	.	PUNCT
ejpam-201	5	1	let	let	VERB
ejpam-201	5	2	a	a	PRON
ejpam-201	5	3	be	be	AUX
ejpam-201	5	4	a	a	DET
ejpam-201	5	5	banach	banach	NOUN
ejpam-201	5	6	algebra	algebra	NOUN
ejpam-201	5	7	and	and	CCONJ
ejpam-201	5	8	x	x	ADJ
ejpam-201	5	9	be	be	AUX
ejpam-201	5	10	a	a	DET
ejpam-201	5	11	banach	banach	NOUN
ejpam-201	5	12	a	a	DET
ejpam-201	5	13	-bimodule	-bimodule	NOUN
ejpam-201	5	14	,	,	PUNCT
ejpam-201	5	15	that	that	PRON
ejpam-201	5	16	x	x	PRON
ejpam-201	5	17	is	be	AUX
ejpam-201	5	18	both	both	CCONJ
ejpam-201	5	19	a	a	DET
ejpam-201	5	20	banach	banach	NOUN
ejpam-201	5	21	space	space	NOUN
ejpam-201	5	22	and	and	CCONJ
ejpam-201	5	23	an	an	DET
ejpam-201	5	24	algebraica	algebraica	NOUN
ejpam-201	5	25	-bimodule	-bimodule	NOUN
ejpam-201	5	26	,	,	PUNCT
ejpam-201	5	27	and	and	CCONJ
ejpam-201	5	28	the	the	DET
ejpam-201	5	29	module	module	NOUN
ejpam-201	5	30	operations	operation	NOUN
ejpam-201	5	31	(	(	PUNCT
ejpam-201	5	32	a	a	PRON
ejpam-201	5	33	,	,	PUNCT
ejpam-201	5	34	x	x	NOUN
ejpam-201	5	35	)	)	PUNCT
ejpam-201	5	36	7→	7→	NUM
ejpam-201	5	37	ax	ax	NOUN
ejpam-201	5	38	and	and	CCONJ
ejpam-201	5	39	(	(	PUNCT
ejpam-201	5	40	a	a	PRON
ejpam-201	5	41	,	,	PUNCT
ejpam-201	5	42	x	x	NOUN
ejpam-201	5	43	)	)	PUNCT
ejpam-201	5	44	7→	7→	NUM
ejpam-201	5	45	xa	xa	NOUN
ejpam-201	5	46	from	from	ADP
ejpam-201	5	47	a	a	DET
ejpam-201	5	48	×x	×x	NOUN
ejpam-201	5	49	into	into	ADP
ejpam-201	5	50	x	x	SYM
ejpam-201	5	51	are	be	AUX
ejpam-201	5	52	(	(	PUNCT
ejpam-201	5	53	jointly	jointly	ADV
ejpam-201	5	54	)	)	PUNCT
ejpam-201	5	55	continuous	continuous	ADJ
ejpam-201	5	56	.	.	PUNCT
ejpam-201	6	1	then	then	ADV
ejpam-201	6	2	x	x	X
ejpam-201	6	3	∗	∗	NOUN
ejpam-201	6	4	is	be	AUX
ejpam-201	6	5	also	also	ADV
ejpam-201	6	6	a	a	DET
ejpam-201	6	7	banacha	banacha	NOUN
ejpam-201	6	8	-bimodule	-bimodule	NOUN
ejpam-201	6	9	under	under	ADP
ejpam-201	6	10	the	the	DET
ejpam-201	6	11	following	follow	VERB
ejpam-201	6	12	module	module	NOUN
ejpam-201	6	13	actions	action	NOUN
ejpam-201	6	14	:	:	PUNCT
ejpam-201	6	15	(	(	PUNCT
ejpam-201	6	16	a	a	DET
ejpam-201	6	17	·	·	PUNCT
ejpam-201	6	18	f	f	X
ejpam-201	6	19	)	)	PUNCT
ejpam-201	6	20	(	(	PUNCT
ejpam-201	6	21	x	x	X
ejpam-201	6	22	)	)	PUNCT
ejpam-201	6	23	=	=	SYM
ejpam-201	6	24	f	f	PROPN
ejpam-201	6	25	(	(	PUNCT
ejpam-201	6	26	xa	xa	PROPN
ejpam-201	6	27	)	)	PUNCT
ejpam-201	6	28	,	,	PUNCT
ejpam-201	6	29	∗corresponding	∗corresponde	VERB
ejpam-201	6	30	author	author	NOUN
ejpam-201	6	31	.	.	PUNCT
ejpam-201	7	1	email	email	NOUN
ejpam-201	7	2	addresses	address	NOUN
ejpam-201	7	3	:	:	PUNCT
ejpam-201	7	4	madjid.eshaghi	madjid.eshaghi	X
ejpam-201	7	5	�	�	NOUN
ejpam-201	7	6	gmail	gmail	NOUN
ejpam-201	7	7	.	.	PUNCT
ejpam-201	8	1	om	om	PROPN
ejpam-201	8	2	(	(	PUNCT
ejpam-201	8	3	m.	m.	NOUN
ejpam-201	8	4	gordji	gordji	PROPN
ejpam-201	8	5	)	)	PUNCT
ejpam-201	8	6	,	,	PUNCT
ejpam-201	8	7	ab	ab	PROPN
ejpam-201	8	8	−	−	PROPN
ejpam-201	8	9	ni40	ni40	PROPN
ejpam-201	8	10	�	�	PROPN
ejpam-201	8	11	stu	stu	PROPN
ejpam-201	8	12	-	-	PUNCT
ejpam-201	8	13	mail.um.a	mail.um.a	PROPN
ejpam-201	8	14	.ir	.ir	PUNCT
ejpam-201	8	15	andniazimotlagh	andniazimotlagh	PROPN
ejpam-201	8	16	�	�	PROPN
ejpam-201	8	17	gmail	gmail	NOUN
ejpam-201	8	18	.	.	PUNCT
ejpam-201	9	1	om	om	PROPN
ejpam-201	9	2	(	(	PUNCT
ejpam-201	9	3	a.	a.	NOUN
ejpam-201	9	4	motlagh	motlagh	PROPN
ejpam-201	9	5	)	)	PUNCT
ejpam-201	9	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-201	10	1	361	361	NUM
ejpam-201	10	2	c	c	X
ejpam-201	10	3	©	©	PROPN
ejpam-201	10	4	2009	2009	NUM
ejpam-201	10	5	ejpam	ejpam	NOUN
ejpam-201	10	6	all	all	DET
ejpam-201	10	7	rights	right	NOUN
ejpam-201	10	8	reserved	reserve	VERB
ejpam-201	10	9	.	.	PUNCT
ejpam-201	11	1	m.	m.	NOUN
ejpam-201	11	2	gordji	gordji	PROPN
ejpam-201	11	3	and	and	CCONJ
ejpam-201	11	4	a.	a.	NOUN
ejpam-201	11	5	motlagh	motlagh	PROPN
ejpam-201	11	6	/	/	SYM
ejpam-201	11	7	eur	eur	PROPN
ejpam-201	11	8	.	.	PUNCT
ejpam-201	12	1	j.	j.	PROPN
ejpam-201	12	2	pure	pure	PROPN
ejpam-201	12	3	appl	appl	PROPN
ejpam-201	12	4	.	.	PROPN
ejpam-201	12	5	math	math	PROPN
ejpam-201	12	6	,	,	PUNCT
ejpam-201	12	7	2	2	NUM
ejpam-201	12	8	(	(	PUNCT
ejpam-201	12	9	2009	2009	NUM
ejpam-201	12	10	)	)	PUNCT
ejpam-201	12	11	,	,	PUNCT
ejpam-201	12	12	(	(	PUNCT
ejpam-201	12	13	361	361	NUM
ejpam-201	12	14	-	-	SYM
ejpam-201	12	15	371	371	NUM
ejpam-201	12	16	)	)	PUNCT
ejpam-201	12	17	362	362	NUM
ejpam-201	12	18	(	(	PUNCT
ejpam-201	12	19	f	f	X
ejpam-201	12	20	·	·	PUNCT
ejpam-201	12	21	a)(x	a)(x	PROPN
ejpam-201	12	22	)	)	PUNCT
ejpam-201	13	1	=	=	SYM
ejpam-201	13	2	f	f	PROPN
ejpam-201	13	3	(	(	PUNCT
ejpam-201	13	4	ax	ax	NOUN
ejpam-201	13	5	)	)	PUNCT
ejpam-201	13	6	,	,	PUNCT
ejpam-201	13	7	a	a	DET
ejpam-201	13	8	∈a	∈a	ADJ
ejpam-201	13	9	,	,	PUNCT
ejpam-201	13	10	x	x	PUNCT
ejpam-201	13	11	∈	∈	NOUN
ejpam-201	13	12	x	x	X
ejpam-201	13	13	,	,	PUNCT
ejpam-201	13	14	f	f	PROPN
ejpam-201	13	15	∈x	∈x	NOUN
ejpam-201	13	16	∗.	∗.	VERB
ejpam-201	13	17	let	let	VERB
ejpam-201	13	18	a	a	PRON
ejpam-201	13	19	be	be	AUX
ejpam-201	13	20	a	a	DET
ejpam-201	13	21	banach	banach	NOUN
ejpam-201	13	22	algebra	algebra	NOUN
ejpam-201	13	23	.	.	PUNCT
ejpam-201	14	1	given	give	VERB
ejpam-201	14	2	f	f	PROPN
ejpam-201	14	3	∈	∈	PROPN
ejpam-201	14	4	a	a	DET
ejpam-201	14	5	∗	∗	NOUN
ejpam-201	14	6	and	and	CCONJ
ejpam-201	14	7	f	f	PROPN
ejpam-201	14	8	∈	∈	PROPN
ejpam-201	14	9	a	a	DET
ejpam-201	14	10	∗∗	∗∗	PROPN
ejpam-201	14	11	,	,	PUNCT
ejpam-201	14	12	then	then	ADV
ejpam-201	14	13	f	f	PROPN
ejpam-201	14	14	f	f	PROPN
ejpam-201	14	15	and	and	CCONJ
ejpam-201	14	16	f	f	PROPN
ejpam-201	14	17	f	f	PROPN
ejpam-201	14	18	are	be	AUX
ejpam-201	14	19	defined	define	VERB
ejpam-201	14	20	ina	ina	PROPN
ejpam-201	14	21	∗	∗	NOUN
ejpam-201	14	22	by	by	ADP
ejpam-201	14	23	the	the	DET
ejpam-201	14	24	following	follow	VERB
ejpam-201	14	25	formulae	formulae	NOUN
ejpam-201	14	26	f	f	PROPN
ejpam-201	14	27	f	f	PROPN
ejpam-201	14	28	(	(	PUNCT
ejpam-201	14	29	a	a	PROPN
ejpam-201	14	30	)	)	PUNCT
ejpam-201	15	1	=	=	SYM
ejpam-201	16	1	f	f	X
ejpam-201	16	2	(	(	PUNCT
ejpam-201	16	3	f	f	X
ejpam-201	16	4	·	·	PUNCT
ejpam-201	16	5	a	a	X
ejpam-201	16	6	)	)	PUNCT
ejpam-201	16	7	,	,	PUNCT
ejpam-201	16	8	f	f	PROPN
ejpam-201	16	9	f(a	f(a	PROPN
ejpam-201	16	10	)	)	PUNCT
ejpam-201	16	11	=	=	SYM
ejpam-201	16	12	f(a	f(a	X
ejpam-201	16	13	·	·	PUNCT
ejpam-201	16	14	f	f	X
ejpam-201	16	15	)	)	PUNCT
ejpam-201	16	16	(	(	PUNCT
ejpam-201	16	17	a	a	DET
ejpam-201	16	18	∈a	∈a	ADJ
ejpam-201	16	19	)	)	PUNCT
ejpam-201	16	20	.	.	PUNCT
ejpam-201	17	1	next	next	ADV
ejpam-201	17	2	,	,	PUNCT
ejpam-201	17	3	for	for	ADP
ejpam-201	17	4	f	f	PROPN
ejpam-201	17	5	,	,	PUNCT
ejpam-201	17	6	g	g	PROPN
ejpam-201	17	7	∈a	∈a	VERB
ejpam-201	17	8	∗∗	∗∗	PROPN
ejpam-201	17	9	,	,	PUNCT
ejpam-201	17	10	fg	fg	PROPN
ejpam-201	17	11	is	be	AUX
ejpam-201	17	12	defined	define	VERB
ejpam-201	17	13	ina	ina	PROPN
ejpam-201	17	14	∗∗	∗∗	X
ejpam-201	17	15	by	by	ADP
ejpam-201	17	16	the	the	DET
ejpam-201	17	17	formulae	formulae	NOUN
ejpam-201	17	18	(	(	PUNCT
ejpam-201	17	19	fg	fg	PROPN
ejpam-201	17	20	)	)	PUNCT
ejpam-201	17	21	(	(	PUNCT
ejpam-201	17	22	f	f	X
ejpam-201	17	23	)	)	PUNCT
ejpam-201	18	1	=	=	PUNCT
ejpam-201	18	2	f(g	f(g	PROPN
ejpam-201	18	3	f	f	PROPN
ejpam-201	18	4	)	)	PUNCT
ejpam-201	18	5	,	,	PUNCT
ejpam-201	18	6	this	this	DET
ejpam-201	18	7	product	product	NOUN
ejpam-201	18	8	is	be	AUX
ejpam-201	18	9	called	call	VERB
ejpam-201	18	10	first	first	ADJ
ejpam-201	18	11	arens	arens	PROPN
ejpam-201	18	12	product	product	NOUN
ejpam-201	18	13	ona	ona	PROPN
ejpam-201	18	14	∗∗	∗∗	PROPN
ejpam-201	18	15	anda	anda	PROPN
ejpam-201	18	16	∗∗	∗∗	PROPN
ejpam-201	18	17	with	with	ADP
ejpam-201	18	18	the	the	DET
ejpam-201	18	19	first	first	ADJ
ejpam-201	18	20	arens	aren	NOUN
ejpam-201	18	21	product	product	NOUN
ejpam-201	18	22	is	be	AUX
ejpam-201	18	23	a	a	DET
ejpam-201	18	24	banach	banach	NOUN
ejpam-201	18	25	algebra	algebra	NOUN
ejpam-201	18	26	.	.	PUNCT
ejpam-201	19	1	let	let	VERB
ejpam-201	19	2	a	a	PRON
ejpam-201	19	3	be	be	AUX
ejpam-201	19	4	a	a	DET
ejpam-201	19	5	banach	banach	NOUN
ejpam-201	19	6	algebra	algebra	NOUN
ejpam-201	19	7	and	and	CCONJ
ejpam-201	19	8	x	x	ADJ
ejpam-201	19	9	be	be	AUX
ejpam-201	19	10	a	a	DET
ejpam-201	19	11	banach	banach	NOUN
ejpam-201	19	12	a	a	DET
ejpam-201	19	13	-bimodule	-bimodule	NOUN
ejpam-201	19	14	.	.	PUNCT
ejpam-201	20	1	the	the	DET
ejpam-201	20	2	banach	banach	NOUN
ejpam-201	20	3	space	space	NOUN
ejpam-201	20	4	x	x	PUNCT
ejpam-201	20	5	∗∗	∗∗	NOUN
ejpam-201	20	6	is	be	AUX
ejpam-201	20	7	a	a	DET
ejpam-201	20	8	banacha	banacha	NOUN
ejpam-201	20	9	∗∗-bimodule	∗∗-bimodule	NOUN
ejpam-201	20	10	under	under	ADP
ejpam-201	20	11	following	follow	VERB
ejpam-201	20	12	actions	action	NOUN
ejpam-201	20	13	f	f	X
ejpam-201	20	14	·	·	PUNCT
ejpam-201	20	15	g	g	PROPN
ejpam-201	20	16	=	=	PROPN
ejpam-201	20	17	w∗	w∗	PROPN
ejpam-201	20	18	−	−	PROPN
ejpam-201	20	19	lim	lim	PROPN
ejpam-201	21	1	i	i	PRON
ejpam-201	21	2	lim	lim	PROPN
ejpam-201	21	3	j	j	PROPN
ejpam-201	21	4	ai	ai	VERB
ejpam-201	21	5	x	x	PROPN
ejpam-201	21	6	j	j	PROPN
ejpam-201	21	7	,	,	PUNCT
ejpam-201	21	8	g	g	PROPN
ejpam-201	21	9	·	·	PUNCT
ejpam-201	21	10	f	f	X
ejpam-201	22	1	=	=	PUNCT
ejpam-201	22	2	w∗	w∗	PROPN
ejpam-201	23	1	−	−	PROPN
ejpam-201	24	1	lim	lim	PROPN
ejpam-201	24	2	j	j	PROPN
ejpam-201	24	3	lim	lim	PROPN
ejpam-201	24	4	i	i	PRON
ejpam-201	24	5	x	x	PROPN
ejpam-201	24	6	jai	jai	VERB
ejpam-201	24	7	where	where	SCONJ
ejpam-201	24	8	f	f	PROPN
ejpam-201	24	9	=	=	SYM
ejpam-201	24	10	w∗	w∗	PROPN
ejpam-201	24	11	−	−	PROPN
ejpam-201	24	12	limi	limi	PROPN
ejpam-201	24	13	ai	ai	VERB
ejpam-201	24	14	,	,	PUNCT
ejpam-201	24	15	g	g	PROPN
ejpam-201	24	16	=	=	PROPN
ejpam-201	24	17	w∗	w∗	PROPN
ejpam-201	24	18	−	−	PROPN
ejpam-201	24	19	lim	lim	PROPN
ejpam-201	24	20	j	j	PROPN
ejpam-201	24	21	x	x	SYM
ejpam-201	24	22	j	j	PROPN
ejpam-201	24	23	,	,	PUNCT
ejpam-201	24	24	(	(	PUNCT
ejpam-201	24	25	ai	ai	VERB
ejpam-201	24	26	)	)	PUNCT
ejpam-201	24	27	is	be	AUX
ejpam-201	24	28	a	a	DET
ejpam-201	24	29	net	net	ADJ
ejpam-201	24	30	ina	ina	NOUN
ejpam-201	24	31	,	,	PUNCT
ejpam-201	24	32	(	(	PUNCT
ejpam-201	24	33	x	x	X
ejpam-201	24	34	j	j	NOUN
ejpam-201	24	35	)	)	PUNCT
ejpam-201	24	36	and	and	CCONJ
ejpam-201	24	37	is	be	AUX
ejpam-201	24	38	a	a	DET
ejpam-201	24	39	net	net	NOUN
ejpam-201	24	40	in	in	ADP
ejpam-201	24	41	x	x	X
ejpam-201	24	42	.	.	PUNCT
ejpam-201	25	1	suppose	suppose	VERB
ejpam-201	25	2	that	that	SCONJ
ejpam-201	25	3	ϕ	ϕ	NOUN
ejpam-201	25	4	:	:	PUNCT
ejpam-201	25	5	a	a	DET
ejpam-201	25	6	→	→	SYM
ejpam-201	25	7	b	b	PROPN
ejpam-201	25	8	is	be	AUX
ejpam-201	25	9	a	a	DET
ejpam-201	25	10	banach	banach	NOUN
ejpam-201	25	11	algebra	algebra	NOUN
ejpam-201	25	12	homomorphism	homomorphism	NOUN
ejpam-201	25	13	.	.	PUNCT
ejpam-201	26	1	the	the	DET
ejpam-201	26	2	banach	banach	NOUN
ejpam-201	26	3	algebrab	algebrab	NOUN
ejpam-201	26	4	is	be	AUX
ejpam-201	26	5	considered	consider	VERB
ejpam-201	26	6	as	as	ADP
ejpam-201	26	7	a	a	DET
ejpam-201	26	8	banacha	banacha	NOUN
ejpam-201	26	9	bimodule	bimodule	NOUN
ejpam-201	26	10	by	by	ADP
ejpam-201	26	11	the	the	DET
ejpam-201	26	12	following	follow	VERB
ejpam-201	26	13	module	module	NOUN
ejpam-201	26	14	actions	action	NOUN
ejpam-201	26	15	a	a	DET
ejpam-201	26	16	·	·	SYM
ejpam-201	26	17	b	b	X
ejpam-201	26	18	=	=	SYM
ejpam-201	26	19	ϕ(a)b	ϕ(a)b	PROPN
ejpam-201	26	20	,	,	PUNCT
ejpam-201	26	21	b	b	X
ejpam-201	26	22	·	·	PUNCT
ejpam-201	26	23	a	a	DET
ejpam-201	26	24	=	=	NOUN
ejpam-201	26	25	bϕ(a	bϕ(a	NOUN
ejpam-201	26	26	)	)	PUNCT
ejpam-201	26	27	(	(	PUNCT
ejpam-201	26	28	a	a	DET
ejpam-201	26	29	∈a	∈a	ADJ
ejpam-201	26	30	,	,	PUNCT
ejpam-201	26	31	b	b	PROPN
ejpam-201	26	32	∈b	∈b	PROPN
ejpam-201	26	33	)	)	PUNCT
ejpam-201	27	1	we	we	PRON
ejpam-201	27	2	denotebϕ	denotebϕ	VERB
ejpam-201	27	3	the	the	DET
ejpam-201	27	4	abovea	abovea	PROPN
ejpam-201	27	5	-bimodule	-bimodule	PROPN
ejpam-201	27	6	.	.	PUNCT
ejpam-201	28	1	let	let	VERB
ejpam-201	28	2	a	a	PRON
ejpam-201	28	3	be	be	AUX
ejpam-201	28	4	a	a	DET
ejpam-201	28	5	banach	banach	NOUN
ejpam-201	28	6	algebra	algebra	NOUN
ejpam-201	28	7	and	and	CCONJ
ejpam-201	28	8	σ	σ	PROPN
ejpam-201	28	9	,	,	PUNCT
ejpam-201	28	10	τ	τ	PROPN
ejpam-201	28	11	be	be	VERB
ejpam-201	28	12	continuous	continuous	ADJ
ejpam-201	28	13	homomorphisms	homomorphism	NOUN
ejpam-201	28	14	on	on	ADP
ejpam-201	28	15	a	a	PRON
ejpam-201	28	16	.	.	PUNCT
ejpam-201	29	1	suppose	suppose	VERB
ejpam-201	29	2	that	that	SCONJ
ejpam-201	29	3	x	x	PRON
ejpam-201	29	4	is	be	AUX
ejpam-201	29	5	a	a	DET
ejpam-201	29	6	banach	banach	NOUN
ejpam-201	29	7	a	a	DET
ejpam-201	29	8	-bimodule	-bimodule	NOUN
ejpam-201	29	9	.	.	PUNCT
ejpam-201	30	1	a	a	DET
ejpam-201	30	2	linear	linear	ADJ
ejpam-201	30	3	mapping	mapping	NOUN
ejpam-201	30	4	d	d	NOUN
ejpam-201	30	5	:	:	PUNCT
ejpam-201	30	6	a	a	PRON
ejpam-201	30	7	→	→	X
ejpam-201	30	8	x	x	SYM
ejpam-201	30	9	is	be	AUX
ejpam-201	30	10	called	call	VERB
ejpam-201	30	11	a	a	DET
ejpam-201	30	12	(	(	PUNCT
ejpam-201	30	13	σ	σ	NOUN
ejpam-201	30	14	,	,	PUNCT
ejpam-201	30	15	τ)-derivation	τ)-derivation	NOUN
ejpam-201	30	16	if	if	SCONJ
ejpam-201	30	17	d(ab	d(ab	NOUN
ejpam-201	30	18	)	)	PUNCT
ejpam-201	30	19	=	=	SYM
ejpam-201	30	20	d(a)σ(b	d(a)σ(b	PROPN
ejpam-201	30	21	)	)	PUNCT
ejpam-201	30	22	+	+	NOUN
ejpam-201	30	23	τ(a)d(b	τ(a)d(b	X
ejpam-201	30	24	)	)	PUNCT
ejpam-201	30	25	(	(	PUNCT
ejpam-201	30	26	a	a	X
ejpam-201	30	27	,	,	PUNCT
ejpam-201	30	28	b	b	PROPN
ejpam-201	30	29	∈	∈	PROPN
ejpam-201	30	30	a	a	PRON
ejpam-201	30	31	)	)	PUNCT
ejpam-201	30	32	.	.	PUNCT
ejpam-201	31	1	for	for	ADP
ejpam-201	31	2	example	example	NOUN
ejpam-201	31	3	every	every	DET
ejpam-201	31	4	ordinary	ordinary	ADJ
ejpam-201	31	5	derivation	derivation	NOUN
ejpam-201	31	6	of	of	ADP
ejpam-201	31	7	an	an	DET
ejpam-201	31	8	algebraa	algebraa	NOUN
ejpam-201	31	9	into	into	ADP
ejpam-201	31	10	an	an	DET
ejpam-201	31	11	a	a	DET
ejpam-201	31	12	-bimodule	-bimodule	NOUN
ejpam-201	31	13	x	x	NUM
ejpam-201	31	14	is	be	AUX
ejpam-201	31	15	an	an	DET
ejpam-201	31	16	(	(	PUNCT
ejpam-201	31	17	ida	ida	PROPN
ejpam-201	31	18	,	,	PUNCT
ejpam-201	31	19	ida	ida	PROPN
ejpam-201	31	20	)	)	PUNCT
ejpam-201	31	21	-derivation	-derivation	PROPN
ejpam-201	31	22	,	,	PUNCT
ejpam-201	31	23	where	where	SCONJ
ejpam-201	31	24	ida	ida	PROPN
ejpam-201	31	25	is	be	AUX
ejpam-201	31	26	the	the	DET
ejpam-201	31	27	identity	identity	NOUN
ejpam-201	31	28	mapping	mapping	NOUN
ejpam-201	31	29	on	on	ADP
ejpam-201	31	30	the	the	DET
ejpam-201	31	31	algebraa	algebraa	NOUN
ejpam-201	31	32	.	.	PUNCT
ejpam-201	32	1	m.	m.	NOUN
ejpam-201	32	2	gordji	gordji	PROPN
ejpam-201	32	3	and	and	CCONJ
ejpam-201	32	4	a.	a.	NOUN
ejpam-201	32	5	motlagh	motlagh	PROPN
ejpam-201	32	6	/	/	SYM
ejpam-201	32	7	eur	eur	PROPN
ejpam-201	32	8	.	.	PUNCT
ejpam-201	33	1	j.	j.	PROPN
ejpam-201	33	2	pure	pure	PROPN
ejpam-201	33	3	appl	appl	PROPN
ejpam-201	33	4	.	.	PROPN
ejpam-201	33	5	math	math	PROPN
ejpam-201	33	6	,	,	PUNCT
ejpam-201	33	7	2	2	NUM
ejpam-201	33	8	(	(	PUNCT
ejpam-201	33	9	2009	2009	NUM
ejpam-201	33	10	)	)	PUNCT
ejpam-201	33	11	,	,	PUNCT
ejpam-201	33	12	(	(	PUNCT
ejpam-201	33	13	361	361	NUM
ejpam-201	33	14	-	-	SYM
ejpam-201	33	15	371	371	NUM
ejpam-201	33	16	)	)	PUNCT
ejpam-201	33	17	363	363	NUM
ejpam-201	33	18	a	a	DET
ejpam-201	33	19	linear	linear	ADJ
ejpam-201	33	20	mapping	mapping	NOUN
ejpam-201	34	1	d	d	NOUN
ejpam-201	34	2	:	:	PUNCT
ejpam-201	34	3	a	a	DET
ejpam-201	34	4	−→	−→	NOUN
ejpam-201	34	5	x	x	PUNCT
ejpam-201	34	6	is	be	AUX
ejpam-201	34	7	called	call	VERB
ejpam-201	34	8	(	(	PUNCT
ejpam-201	34	9	σ	σ	PROPN
ejpam-201	34	10	,	,	PUNCT
ejpam-201	34	11	τ)-inner	τ)-inner	PUNCT
ejpam-201	34	12	derivation	derivation	NOUN
ejpam-201	34	13	if	if	SCONJ
ejpam-201	34	14	there	there	PRON
ejpam-201	34	15	exists	exist	VERB
ejpam-201	34	16	x	x	X
ejpam-201	34	17	∈	∈	PROPN
ejpam-201	34	18	x	x	X
ejpam-201	34	19	such	such	ADJ
ejpam-201	34	20	that	that	SCONJ
ejpam-201	34	21	d(a	d(a	PROPN
ejpam-201	34	22	)	)	PUNCT
ejpam-201	34	23	=	=	PUNCT
ejpam-201	34	24	τ(a)x	τ(a)x	PROPN
ejpam-201	34	25	−	−	PROPN
ejpam-201	34	26	xσ(a	xσ(a	PUNCT
ejpam-201	34	27	)	)	PUNCT
ejpam-201	34	28	(	(	PUNCT
ejpam-201	34	29	a	a	DET
ejpam-201	34	30	∈a	∈a	ADJ
ejpam-201	34	31	)	)	PUNCT
ejpam-201	34	32	.	.	PUNCT
ejpam-201	35	1	see	see	VERB
ejpam-201	35	2	also	also	ADV
ejpam-201	35	3	[	[	X
ejpam-201	35	4	3–6	3–6	NUM
ejpam-201	35	5	]	]	X
ejpam-201	35	6	.	.	PUNCT
ejpam-201	36	1	we	we	PRON
ejpam-201	36	2	denote	denote	VERB
ejpam-201	36	3	the	the	DET
ejpam-201	36	4	set	set	NOUN
ejpam-201	36	5	of	of	ADP
ejpam-201	36	6	continuous	continuous	ADJ
ejpam-201	36	7	(	(	PUNCT
ejpam-201	36	8	σ	σ	NOUN
ejpam-201	36	9	,	,	PUNCT
ejpam-201	36	10	τ)-derivations	τ)-derivations	PUNCT
ejpam-201	36	11	froma	froma	ADJ
ejpam-201	36	12	intox	intox	NOUN
ejpam-201	36	13	by	by	ADP
ejpam-201	36	14	z1	z1	PROPN
ejpam-201	36	15	(	(	PUNCT
ejpam-201	36	16	σ	σ	PROPN
ejpam-201	36	17	,	,	PUNCT
ejpam-201	36	18	τ	τ	X
ejpam-201	36	19	)	)	PUNCT
ejpam-201	36	20	(	(	PUNCT
ejpam-201	36	21	a	a	PRON
ejpam-201	36	22	,	,	PUNCT
ejpam-201	36	23	x	x	SYM
ejpam-201	36	24	)	)	PUNCT
ejpam-201	36	25	and	and	CCONJ
ejpam-201	36	26	the	the	DET
ejpam-201	36	27	set	set	NOUN
ejpam-201	36	28	of	of	ADP
ejpam-201	36	29	inner	inner	ADJ
ejpam-201	36	30	(	(	PUNCT
ejpam-201	36	31	σ	σ	NOUN
ejpam-201	36	32	,	,	PUNCT
ejpam-201	36	33	τ)-derivations	τ)-derivations	PUNCT
ejpam-201	36	34	by	by	ADP
ejpam-201	36	35	b1	b1	NOUN
ejpam-201	36	36	(	(	PUNCT
ejpam-201	36	37	σ	σ	PROPN
ejpam-201	36	38	,	,	PUNCT
ejpam-201	36	39	τ	τ	X
ejpam-201	36	40	)	)	PUNCT
ejpam-201	36	41	(	(	PUNCT
ejpam-201	36	42	a	a	DET
ejpam-201	36	43	,	,	PUNCT
ejpam-201	36	44	x	x	NOUN
ejpam-201	36	45	)	)	PUNCT
ejpam-201	36	46	.	.	PUNCT
ejpam-201	37	1	we	we	PRON
ejpam-201	37	2	define	define	VERB
ejpam-201	37	3	the	the	DET
ejpam-201	37	4	space	space	NOUN
ejpam-201	37	5	h1	h1	NOUN
ejpam-201	37	6	(	(	PUNCT
ejpam-201	37	7	σ	σ	PROPN
ejpam-201	37	8	,	,	PUNCT
ejpam-201	37	9	τ	τ	X
ejpam-201	37	10	)	)	PUNCT
ejpam-201	37	11	(	(	PUNCT
ejpam-201	37	12	a	a	PRON
ejpam-201	37	13	,	,	PUNCT
ejpam-201	37	14	x	x	SYM
ejpam-201	37	15	)	)	PUNCT
ejpam-201	37	16	as	as	ADP
ejpam-201	37	17	the	the	DET
ejpam-201	37	18	quotient	quotient	NOUN
ejpam-201	37	19	space	space	NOUN
ejpam-201	37	20	z1	z1	PROPN
ejpam-201	37	21	(	(	PUNCT
ejpam-201	37	22	σ	σ	PROPN
ejpam-201	37	23	,	,	PUNCT
ejpam-201	37	24	τ	τ	X
ejpam-201	37	25	)	)	PUNCT
ejpam-201	37	26	(	(	PUNCT
ejpam-201	37	27	a	a	PRON
ejpam-201	37	28	,	,	PUNCT
ejpam-201	37	29	x	x	NOUN
ejpam-201	37	30	)	)	PUNCT
ejpam-201	37	31	/b1	/b1	NOUN
ejpam-201	37	32	(	(	PUNCT
ejpam-201	37	33	σ	σ	PROPN
ejpam-201	37	34	,	,	PUNCT
ejpam-201	37	35	τ	τ	X
ejpam-201	37	36	)	)	PUNCT
ejpam-201	37	37	(	(	PUNCT
ejpam-201	37	38	a	a	DET
ejpam-201	37	39	,	,	PUNCT
ejpam-201	37	40	x	x	NOUN
ejpam-201	37	41	)	)	PUNCT
ejpam-201	37	42	.	.	PUNCT
ejpam-201	38	1	the	the	DET
ejpam-201	38	2	space	space	NOUN
ejpam-201	38	3	h1	h1	NOUN
ejpam-201	38	4	(	(	PUNCT
ejpam-201	38	5	σ	σ	PROPN
ejpam-201	38	6	,	,	PUNCT
ejpam-201	38	7	τ	τ	X
ejpam-201	38	8	)	)	PUNCT
ejpam-201	38	9	(	(	PUNCT
ejpam-201	38	10	a	a	DET
ejpam-201	38	11	,	,	PUNCT
ejpam-201	38	12	x	x	X
ejpam-201	38	13	)	)	PUNCT
ejpam-201	38	14	is	be	AUX
ejpam-201	38	15	called	call	VERB
ejpam-201	38	16	the	the	DET
ejpam-201	38	17	first	first	ADJ
ejpam-201	38	18	(	(	PUNCT
ejpam-201	38	19	σ	σ	NOUN
ejpam-201	38	20	,	,	PUNCT
ejpam-201	38	21	τ)-cohomology	τ)-cohomology	PUNCT
ejpam-201	38	22	group	group	NOUN
ejpam-201	38	23	ofa	ofa	PROPN
ejpam-201	38	24	with	with	ADP
ejpam-201	38	25	coefficients	coefficient	NOUN
ejpam-201	38	26	inx	inx	VERB
ejpam-201	38	27	.	.	PUNCT
ejpam-201	39	1	a	a	PRON
ejpam-201	39	2	is	be	AUX
ejpam-201	39	3	called	call	VERB
ejpam-201	39	4	(	(	PUNCT
ejpam-201	39	5	σ	σ	PROPN
ejpam-201	39	6	,	,	PUNCT
ejpam-201	39	7	τ)-amenable	τ)-amenable	PUNCT
ejpam-201	39	8	if	if	SCONJ
ejpam-201	39	9	h1	h1	PROPN
ejpam-201	39	10	(	(	PUNCT
ejpam-201	39	11	σ	σ	PROPN
ejpam-201	39	12	,	,	PUNCT
ejpam-201	39	13	τ	τ	X
ejpam-201	39	14	)	)	PUNCT
ejpam-201	39	15	(	(	PUNCT
ejpam-201	39	16	a	a	DET
ejpam-201	39	17	,	,	PUNCT
ejpam-201	39	18	x	x	NOUN
ejpam-201	39	19	∗	∗	NOUN
ejpam-201	39	20	)	)	PUNCT
ejpam-201	39	21	=	=	PRON
ejpam-201	39	22	{	{	PUNCT
ejpam-201	39	23	0	0	NUM
ejpam-201	39	24	}	}	PUNCT
ejpam-201	39	25	,	,	PUNCT
ejpam-201	39	26	for	for	ADP
ejpam-201	39	27	each	each	DET
ejpam-201	39	28	banach	banach	NOUN
ejpam-201	39	29	a	a	DET
ejpam-201	39	30	-bimodule	-bimodule	NOUN
ejpam-201	39	31	x	x	X
ejpam-201	39	32	.	.	PUNCT
ejpam-201	40	1	let	let	VERB
ejpam-201	40	2	a	a	PRON
ejpam-201	40	3	be	be	AUX
ejpam-201	40	4	a	a	DET
ejpam-201	40	5	banach	banach	NOUN
ejpam-201	40	6	algebra	algebra	NOUN
ejpam-201	40	7	and	and	CCONJ
ejpam-201	40	8	let	let	VERB
ejpam-201	40	9	x	x	PRON
ejpam-201	40	10	be	be	AUX
ejpam-201	40	11	a	a	DET
ejpam-201	40	12	banach	banach	NOUN
ejpam-201	40	13	a	a	DET
ejpam-201	40	14	-bimodule	-bimodule	NOUN
ejpam-201	40	15	.	.	PUNCT
ejpam-201	41	1	define	define	VERB
ejpam-201	41	2	a	a	DET
ejpam-201	41	3	⊕1x	⊕1x	NOUN
ejpam-201	41	4	by	by	ADP
ejpam-201	41	5	actions	action	NOUN
ejpam-201	41	6	:	:	PUNCT
ejpam-201	41	7	(	(	PUNCT
ejpam-201	41	8	a	a	PRON
ejpam-201	41	9	,	,	PUNCT
ejpam-201	41	10	x	x	NOUN
ejpam-201	41	11	)	)	PUNCT
ejpam-201	42	1	+	+	CCONJ
ejpam-201	42	2	(	(	PUNCT
ejpam-201	42	3	b	b	X
ejpam-201	42	4	,	,	PUNCT
ejpam-201	42	5	y	y	NOUN
ejpam-201	42	6	)	)	PUNCT
ejpam-201	42	7	=	=	SYM
ejpam-201	43	1	(	(	PUNCT
ejpam-201	43	2	a+	a+	X
ejpam-201	43	3	b	b	NOUN
ejpam-201	43	4	,	,	PUNCT
ejpam-201	43	5	x	x	PROPN
ejpam-201	44	1	+	+	NUM
ejpam-201	44	2	y	y	X
ejpam-201	44	3	)	)	PUNCT
ejpam-201	44	4	a(b	a(b	NOUN
ejpam-201	44	5	,	,	PUNCT
ejpam-201	44	6	x	x	NOUN
ejpam-201	44	7	)	)	PUNCT
ejpam-201	44	8	=	=	SYM
ejpam-201	44	9	(	(	PUNCT
ejpam-201	44	10	ab	ab	NOUN
ejpam-201	44	11	,	,	PUNCT
ejpam-201	44	12	ax	ax	NOUN
ejpam-201	44	13	)	)	PUNCT
ejpam-201	44	14	,	,	PUNCT
ejpam-201	44	15	(	(	PUNCT
ejpam-201	44	16	b	b	NOUN
ejpam-201	44	17	,	,	PUNCT
ejpam-201	44	18	x)a	x)a	PUNCT
ejpam-201	45	1	=	=	PRON
ejpam-201	45	2	(	(	PUNCT
ejpam-201	45	3	ba	ba	PROPN
ejpam-201	45	4	,	,	PUNCT
ejpam-201	45	5	xa	xa	PROPN
ejpam-201	45	6	)	)	PUNCT
ejpam-201	45	7	(	(	PUNCT
ejpam-201	45	8	a	a	PRON
ejpam-201	45	9	,	,	PUNCT
ejpam-201	45	10	x)(b	x)(b	ADJ
ejpam-201	45	11	,	,	PUNCT
ejpam-201	45	12	y	y	NOUN
ejpam-201	45	13	)	)	PUNCT
ejpam-201	45	14	=	=	SYM
ejpam-201	45	15	(	(	PUNCT
ejpam-201	45	16	ab	ab	PROPN
ejpam-201	45	17	,	,	PUNCT
ejpam-201	45	18	a	a	DET
ejpam-201	45	19	y	y	PROPN
ejpam-201	45	20	+	+	PROPN
ejpam-201	45	21	x	x	PROPN
ejpam-201	45	22	b	b	X
ejpam-201	45	23	)	)	PUNCT
ejpam-201	45	24	,	,	PUNCT
ejpam-201	45	25	for	for	ADP
ejpam-201	45	26	every	every	DET
ejpam-201	45	27	a	a	PROPN
ejpam-201	45	28	,	,	PUNCT
ejpam-201	45	29	b	b	PROPN
ejpam-201	45	30	∈a	∈a	ADJ
ejpam-201	45	31	and	and	CCONJ
ejpam-201	45	32	x	x	NOUN
ejpam-201	45	33	,	,	PUNCT
ejpam-201	45	34	y	y	PROPN
ejpam-201	45	35	∈	∈	PROPN
ejpam-201	45	36	x	x	X
ejpam-201	45	37	.	.	PUNCT
ejpam-201	46	1	it	it	PRON
ejpam-201	46	2	is	be	AUX
ejpam-201	46	3	cleara	cleara	NOUN
ejpam-201	46	4	⊕1x	⊕1x	PRON
ejpam-201	46	5	is	be	AUX
ejpam-201	46	6	a	a	DET
ejpam-201	46	7	banach	banach	NOUN
ejpam-201	46	8	algebra	algebra	NOUN
ejpam-201	46	9	with	with	ADP
ejpam-201	46	10	the	the	DET
ejpam-201	46	11	following	follow	VERB
ejpam-201	46	12	norm	norm	NOUN
ejpam-201	46	13	:	:	PUNCT
ejpam-201	46	14	‖(a	‖(a	NOUN
ejpam-201	46	15	,	,	PUNCT
ejpam-201	46	16	x)‖	x)‖	NOUN
ejpam-201	47	1	=	=	SYM
ejpam-201	47	2	‖a‖+	‖a‖+	PROPN
ejpam-201	47	3	‖x‖.	‖x‖.	VERB
ejpam-201	47	4	this	this	DET
ejpam-201	47	5	banach	banach	NOUN
ejpam-201	47	6	algebra	algebra	NOUN
ejpam-201	47	7	is	be	AUX
ejpam-201	47	8	called	call	VERB
ejpam-201	47	9	module	module	NOUN
ejpam-201	47	10	extension	extension	NOUN
ejpam-201	47	11	banach	banach	NOUN
ejpam-201	47	12	algebra	algebra	NOUN
ejpam-201	47	13	.	.	PUNCT
ejpam-201	48	1	we	we	PRON
ejpam-201	48	2	use	use	VERB
ejpam-201	48	3	some	some	DET
ejpam-201	48	4	ideas	idea	NOUN
ejpam-201	48	5	and	and	CCONJ
ejpam-201	48	6	terminology	terminology	NOUN
ejpam-201	48	7	of	of	ADP
ejpam-201	48	8	[	[	X
ejpam-201	48	9	2	2	NUM
ejpam-201	48	10	]	]	PUNCT
ejpam-201	48	11	to	to	PART
ejpam-201	48	12	investigate	investigate	VERB
ejpam-201	48	13	(	(	PUNCT
ejpam-201	48	14	σ	σ	NOUN
ejpam-201	48	15	,	,	PUNCT
ejpam-201	48	16	τ)-amenability	τ)-amenability	NOUN
ejpam-201	48	17	of	of	ADP
ejpam-201	48	18	banach	banach	NOUN
ejpam-201	48	19	algebras	algebra	NOUN
ejpam-201	48	20	.	.	PUNCT
ejpam-201	49	1	2	2	X
ejpam-201	49	2	.	.	X
ejpam-201	49	3	(	(	PUNCT
ejpam-201	49	4	σ	σ	NOUN
ejpam-201	49	5	,	,	PUNCT
ejpam-201	49	6	τ)-amenability	τ)-amenability	NOUN
ejpam-201	49	7	of	of	ADP
ejpam-201	49	8	banach	banach	NOUN
ejpam-201	49	9	algebras	algebras	X
ejpam-201	49	10	.	.	PUNCT
ejpam-201	50	1	let	let	VERB
ejpam-201	50	2	a	a	PRON
ejpam-201	50	3	be	be	AUX
ejpam-201	50	4	a	a	DET
ejpam-201	50	5	banach	banach	NOUN
ejpam-201	50	6	algebra	algebra	NOUN
ejpam-201	50	7	and	and	CCONJ
ejpam-201	50	8	let	let	VERB
ejpam-201	50	9	σ	σ	NOUN
ejpam-201	50	10	,	,	PUNCT
ejpam-201	50	11	τ	τ	PROPN
ejpam-201	50	12	be	be	VERB
ejpam-201	50	13	continuous	continuous	ADJ
ejpam-201	50	14	homomorphisms	homomorphism	NOUN
ejpam-201	50	15	on	on	ADP
ejpam-201	50	16	a	a	PRON
ejpam-201	50	17	.	.	PUNCT
ejpam-201	51	1	suppose	suppose	VERB
ejpam-201	51	2	that	that	SCONJ
ejpam-201	51	3	x	x	PRON
ejpam-201	51	4	is	be	AUX
ejpam-201	51	5	a	a	DET
ejpam-201	51	6	banach	banach	NOUN
ejpam-201	51	7	a	a	DET
ejpam-201	51	8	-bimodule	-bimodule	NOUN
ejpam-201	51	9	.	.	PUNCT
ejpam-201	52	1	then	then	ADV
ejpam-201	52	2	x	x	PRON
ejpam-201	52	3	is	be	AUX
ejpam-201	52	4	a	a	DET
ejpam-201	52	5	banach	banach	NOUN
ejpam-201	52	6	a	a	DET
ejpam-201	52	7	-bimodule	-bimodule	NOUN
ejpam-201	52	8	by	by	ADP
ejpam-201	52	9	the	the	DET
ejpam-201	52	10	following	follow	VERB
ejpam-201	52	11	module	module	NOUN
ejpam-201	52	12	actions	action	NOUN
ejpam-201	52	13	:	:	PUNCT
ejpam-201	52	14	a	a	PRON
ejpam-201	52	15	·	·	PUNCT
ejpam-201	52	16	x	x	SYM
ejpam-201	52	17	=	=	SYM
ejpam-201	52	18	τ(a)b	τ(a)b	PROPN
ejpam-201	52	19	,	,	PUNCT
ejpam-201	52	20	x	x	X
ejpam-201	52	21	·	·	PUNCT
ejpam-201	52	22	a	a	X
ejpam-201	52	23	=	=	X
ejpam-201	52	24	bσ(a	bσ(a	NUM
ejpam-201	52	25	)	)	PUNCT
ejpam-201	52	26	(	(	PUNCT
ejpam-201	52	27	a	a	DET
ejpam-201	52	28	∈a	∈a	ADJ
ejpam-201	52	29	,	,	PUNCT
ejpam-201	52	30	x	x	PUNCT
ejpam-201	52	31	∈	∈	NOUN
ejpam-201	52	32	x	x	X
ejpam-201	52	33	)	)	PUNCT
ejpam-201	52	34	.	.	PUNCT
ejpam-201	53	1	m.	m.	NOUN
ejpam-201	53	2	gordji	gordji	PROPN
ejpam-201	53	3	and	and	CCONJ
ejpam-201	53	4	a.	a.	NOUN
ejpam-201	53	5	motlagh	motlagh	PROPN
ejpam-201	53	6	/	/	SYM
ejpam-201	53	7	eur	eur	PROPN
ejpam-201	53	8	.	.	PUNCT
ejpam-201	54	1	j.	j.	PROPN
ejpam-201	54	2	pure	pure	PROPN
ejpam-201	54	3	appl	appl	PROPN
ejpam-201	54	4	.	.	PROPN
ejpam-201	54	5	math	math	PROPN
ejpam-201	54	6	,	,	PUNCT
ejpam-201	54	7	2	2	NUM
ejpam-201	54	8	(	(	PUNCT
ejpam-201	54	9	2009	2009	NUM
ejpam-201	54	10	)	)	PUNCT
ejpam-201	54	11	,	,	PUNCT
ejpam-201	54	12	(	(	PUNCT
ejpam-201	54	13	361	361	NUM
ejpam-201	54	14	-	-	SYM
ejpam-201	54	15	371	371	NUM
ejpam-201	54	16	)	)	PUNCT
ejpam-201	54	17	364	364	NUM
ejpam-201	54	18	we	we	PRON
ejpam-201	54	19	denote	denote	VERB
ejpam-201	54	20	x(σ	x(σ	PROPN
ejpam-201	54	21	,	,	PUNCT
ejpam-201	54	22	τ	τ	X
ejpam-201	54	23	)	)	PUNCT
ejpam-201	54	24	for	for	ADP
ejpam-201	54	25	this	this	PRON
ejpam-201	54	26	a	a	DET
ejpam-201	54	27	-bimodule	-bimodule	NOUN
ejpam-201	54	28	.	.	PUNCT
ejpam-201	55	1	it	it	PRON
ejpam-201	55	2	is	be	AUX
ejpam-201	55	3	easy	easy	ADJ
ejpam-201	55	4	to	to	PART
ejpam-201	55	5	check	check	VERB
ejpam-201	55	6	that	that	DET
ejpam-201	55	7	(	(	PUNCT
ejpam-201	55	8	x(σ	x(σ	PROPN
ejpam-201	55	9	,	,	PUNCT
ejpam-201	55	10	τ	τ	X
ejpam-201	55	11	)	)	PUNCT
ejpam-201	55	12	)	)	PUNCT
ejpam-201	55	13	∗	∗	NOUN
ejpam-201	55	14	=	=	PUNCT
ejpam-201	55	15	x	x	SYM
ejpam-201	55	16	∗	∗	NOUN
ejpam-201	55	17	(	(	PUNCT
ejpam-201	55	18	τ	τ	PROPN
ejpam-201	55	19	,	,	PUNCT
ejpam-201	55	20	σ	σ	PROPN
ejpam-201	55	21	)	)	PUNCT
ejpam-201	55	22	,	,	PUNCT
ejpam-201	55	23	and	and	CCONJ
ejpam-201	55	24	that	that	SCONJ
ejpam-201	55	25	every	every	DET
ejpam-201	55	26	(	(	PUNCT
ejpam-201	55	27	σ	σ	NOUN
ejpam-201	55	28	,	,	PUNCT
ejpam-201	55	29	τ)-derivation	τ)-derivation	NOUN
ejpam-201	55	30	from	from	ADP
ejpam-201	55	31	a	a	DET
ejpam-201	55	32	into	into	NOUN
ejpam-201	55	33	x	x	SYM
ejpam-201	55	34	is	be	AUX
ejpam-201	55	35	a	a	DET
ejpam-201	55	36	derivation	derivation	NOUN
ejpam-201	55	37	from	from	ADP
ejpam-201	55	38	a	a	PRON
ejpam-201	55	39	into	into	ADP
ejpam-201	55	40	x(σ	x(σ	PROPN
ejpam-201	55	41	,	,	PUNCT
ejpam-201	55	42	τ	τ	PROPN
ejpam-201	55	43	)	)	PUNCT
ejpam-201	55	44	.	.	PUNCT
ejpam-201	56	1	thus	thus	ADV
ejpam-201	56	2	we	we	PRON
ejpam-201	56	3	can	can	AUX
ejpam-201	56	4	show	show	VERB
ejpam-201	56	5	that	that	SCONJ
ejpam-201	56	6	a	a	PRON
ejpam-201	56	7	is	be	AUX
ejpam-201	56	8	amenable	amenable	ADJ
ejpam-201	56	9	,	,	PUNCT
ejpam-201	56	10	if	if	SCONJ
ejpam-201	56	11	and	and	CCONJ
ejpam-201	56	12	only	only	ADV
ejpam-201	56	13	if	if	SCONJ
ejpam-201	56	14	a	a	PRON
ejpam-201	56	15	is	be	AUX
ejpam-201	56	16	(	(	PUNCT
ejpam-201	56	17	σ	σ	NOUN
ejpam-201	56	18	,	,	PUNCT
ejpam-201	56	19	τ)-amenable	τ)-amenable	ADJ
ejpam-201	56	20	,	,	PUNCT
ejpam-201	56	21	for	for	ADP
ejpam-201	56	22	each	each	DET
ejpam-201	56	23	σ	σ	PROPN
ejpam-201	56	24	,	,	PUNCT
ejpam-201	56	25	τ	τ	PROPN
ejpam-201	56	26	∈	∈	PROPN
ejpam-201	56	27	hom(a	hom(a	PROPN
ejpam-201	56	28	)	)	PUNCT
ejpam-201	56	29	.	.	PUNCT
ejpam-201	57	1	first	first	ADV
ejpam-201	57	2	we	we	PRON
ejpam-201	57	3	give	give	VERB
ejpam-201	57	4	the	the	DET
ejpam-201	57	5	following	follow	VERB
ejpam-201	57	6	examples	example	NOUN
ejpam-201	57	7	for	for	ADP
ejpam-201	57	8	(	(	PUNCT
ejpam-201	57	9	σ	σ	NOUN
ejpam-201	57	10	,	,	PUNCT
ejpam-201	57	11	τ)-amenability	τ)-amenability	NOUN
ejpam-201	57	12	of	of	ADP
ejpam-201	57	13	banach	banach	NOUN
ejpam-201	57	14	algebras	algebra	NOUN
ejpam-201	57	15	.	.	PUNCT
ejpam-201	57	16	example	example	NOUN
ejpam-201	57	17	2.1	2.1	NUM
ejpam-201	57	18	.	.	PUNCT
ejpam-201	58	1	it	it	PRON
ejpam-201	58	2	is	be	AUX
ejpam-201	58	3	easy	easy	ADJ
ejpam-201	58	4	to	to	PART
ejpam-201	58	5	see	see	VERB
ejpam-201	58	6	that	that	SCONJ
ejpam-201	58	7	ℓ1	ℓ1	NOUN
ejpam-201	58	8	is	be	AUX
ejpam-201	58	9	a	a	DET
ejpam-201	58	10	banach	banach	NOUN
ejpam-201	58	11	algebra	algebra	NOUN
ejpam-201	58	12	equipped	equip	VERB
ejpam-201	58	13	with	with	ADP
ejpam-201	58	14	the	the	DET
ejpam-201	58	15	following	follow	VERB
ejpam-201	58	16	product	product	NOUN
ejpam-201	58	17	[	[	X
ejpam-201	58	18	7	7	X
ejpam-201	58	19	]	]	X
ejpam-201	58	20	a	a	DET
ejpam-201	58	21	·	·	PUNCT
ejpam-201	58	22	b	b	X
ejpam-201	58	23	=	=	SYM
ejpam-201	58	24	a(1)b	a(1)b	PROPN
ejpam-201	58	25	(	(	PUNCT
ejpam-201	58	26	a	a	PRON
ejpam-201	58	27	,	,	PUNCT
ejpam-201	58	28	b	b	PROPN
ejpam-201	58	29	∈	∈	NOUN
ejpam-201	58	30	ℓ1	ℓ1	NOUN
ejpam-201	58	31	)	)	PUNCT
ejpam-201	58	32	,	,	PUNCT
ejpam-201	58	33	and	and	CCONJ
ejpam-201	58	34	ℓ1	ℓ1	NOUN
ejpam-201	58	35	has	have	VERB
ejpam-201	58	36	a	a	DET
ejpam-201	58	37	left	left	ADJ
ejpam-201	58	38	identity	identity	NOUN
ejpam-201	58	39	e	e	NOUN
ejpam-201	58	40	defined	define	VERB
ejpam-201	58	41	by	by	ADP
ejpam-201	58	42	e(n	e(n	PROPN
ejpam-201	58	43	)	)	PUNCT
ejpam-201	58	44	=	=	PUNCT
ejpam-201	59	1			PROPN
ejpam-201	59	2			X
ejpam-201	59	3			NOUN
ejpam-201	59	4	1	1	NUM
ejpam-201	60	1	i	i	NOUN
ejpam-201	60	2	f	f	PROPN
ejpam-201	60	3	n	n	NOUN
ejpam-201	60	4	=	=	SYM
ejpam-201	60	5	1	1	NUM
ejpam-201	60	6	0	0	NUM
ejpam-201	61	1	i	i	PRON
ejpam-201	61	2	f	f	PROPN
ejpam-201	61	3	n	n	PROPN
ejpam-201	61	4	6=	6=	PROPN
ejpam-201	61	5	1	1	NUM
ejpam-201	61	6	.	.	PUNCT
ejpam-201	62	1	the	the	DET
ejpam-201	62	2	dual	dual	ADJ
ejpam-201	62	3	space	space	NOUN
ejpam-201	62	4	(	(	PUNCT
ejpam-201	62	5	ℓ1)∗	ℓ1)∗	PROPN
ejpam-201	62	6	=	=	SYM
ejpam-201	62	7	ℓ∞	ℓ∞	PROPN
ejpam-201	62	8	is	be	AUX
ejpam-201	62	9	a	a	DET
ejpam-201	62	10	ℓ1	ℓ1	NOUN
ejpam-201	62	11	-	-	PUNCT
ejpam-201	62	12	bimodule	bimodule	NOUN
ejpam-201	62	13	via	via	ADP
ejpam-201	62	14	the	the	DET
ejpam-201	62	15	ordinary	ordinary	ADJ
ejpam-201	62	16	actions	action	NOUN
ejpam-201	62	17	as	as	SCONJ
ejpam-201	62	18	follows	follow	VERB
ejpam-201	62	19	a	a	DET
ejpam-201	62	20	·	·	PUNCT
ejpam-201	62	21	f	f	X
ejpam-201	62	22	=	=	SYM
ejpam-201	62	23	f	f	PROPN
ejpam-201	62	24	(	(	PUNCT
ejpam-201	62	25	a)e	a)e	PROPN
ejpam-201	62	26	,	,	PUNCT
ejpam-201	62	27	f	f	PROPN
ejpam-201	62	28	·	·	PUNCT
ejpam-201	62	29	a	a	X
ejpam-201	62	30	=	=	PUNCT
ejpam-201	62	31	a(1	a(1	PROPN
ejpam-201	62	32	)	)	PUNCT
ejpam-201	62	33	f	f	NOUN
ejpam-201	62	34	(	(	PUNCT
ejpam-201	62	35	a	a	DET
ejpam-201	62	36	∈	∈	NOUN
ejpam-201	62	37	ℓ1	ℓ1	NOUN
ejpam-201	62	38	,	,	PUNCT
ejpam-201	62	39	f	f	PROPN
ejpam-201	62	40	∈	∈	PROPN
ejpam-201	62	41	ℓ∞	ℓ∞	PROPN
ejpam-201	62	42	)	)	PUNCT
ejpam-201	62	43	,	,	PUNCT
ejpam-201	62	44	where	where	SCONJ
ejpam-201	62	45	e	e	NOUN
ejpam-201	62	46	is	be	AUX
ejpam-201	62	47	regarded	regard	VERB
ejpam-201	62	48	as	as	ADP
ejpam-201	62	49	an	an	DET
ejpam-201	62	50	element	element	NOUN
ejpam-201	62	51	of	of	ADP
ejpam-201	62	52	ℓ∞.	ℓ∞.	PROPN
ejpam-201	62	53	next	next	ADJ
ejpam-201	62	54	let	let	VERB
ejpam-201	62	55	σ	σ	NOUN
ejpam-201	62	56	:	:	PUNCT
ejpam-201	62	57	ℓ1	ℓ1	VERB
ejpam-201	62	58	−→	−→	NOUN
ejpam-201	62	59	ℓ1	ℓ1	NOUN
ejpam-201	62	60	be	be	VERB
ejpam-201	62	61	a	a	DET
ejpam-201	62	62	bounded	bounded	ADJ
ejpam-201	62	63	homomorphism	homomorphism	NOUN
ejpam-201	62	64	.	.	PUNCT
ejpam-201	63	1	we	we	PRON
ejpam-201	63	2	have	have	VERB
ejpam-201	63	3	a(1)σ(b	a(1)σ(b	NUM
ejpam-201	63	4	)	)	PUNCT
ejpam-201	64	1	=	=	PUNCT
ejpam-201	65	1	σ(a	σ(a	PROPN
ejpam-201	65	2	·	·	PUNCT
ejpam-201	65	3	b	b	X
ejpam-201	65	4	)	)	PUNCT
ejpam-201	65	5	=	=	SYM
ejpam-201	65	6	σ(a	σ(a	PROPN
ejpam-201	65	7	)	)	PUNCT
ejpam-201	65	8	·	·	PUNCT
ejpam-201	65	9	σ(b	σ(b	PROPN
ejpam-201	65	10	)	)	PUNCT
ejpam-201	65	11	=	=	SYM
ejpam-201	65	12	σ(a)(1)σ(b	σ(a)(1)σ(b	X
ejpam-201	65	13	)	)	PUNCT
ejpam-201	65	14	and	and	CCONJ
ejpam-201	65	15	so	so	ADV
ejpam-201	65	16	σ(b)(a(1	σ(b)(a(1	NOUN
ejpam-201	65	17	)	)	PUNCT
ejpam-201	65	18	−σ(a)(1	−σ(a)(1	NOUN
ejpam-201	65	19	)	)	PUNCT
ejpam-201	65	20	)	)	PUNCT
ejpam-201	66	1	=	=	SYM
ejpam-201	66	2	0	0	NUM
ejpam-201	67	1	for	for	ADP
ejpam-201	67	2	all	all	DET
ejpam-201	67	3	a	a	DET
ejpam-201	67	4	,	,	PUNCT
ejpam-201	67	5	b	b	X
ejpam-201	67	6	∈	∈	PROPN
ejpam-201	67	7	n.	n.	NOUN
ejpam-201	67	8	since	since	SCONJ
ejpam-201	67	9	σ	σ	PROPN
ejpam-201	67	10	6=	6=	PROPN
ejpam-201	67	11	0	0	NUM
ejpam-201	67	12	,	,	PUNCT
ejpam-201	67	13	we	we	PRON
ejpam-201	67	14	have	have	VERB
ejpam-201	67	15	�	�	PROPN
ejpam-201	67	16	σ(a	σ(a	PROPN
ejpam-201	67	17	)	)	PUNCT
ejpam-201	67	18	�	�	PROPN
ejpam-201	67	19	(	(	PUNCT
ejpam-201	67	20	1	1	NUM
ejpam-201	67	21	)	)	PUNCT
ejpam-201	67	22	=	=	PUNCT
ejpam-201	68	1	a(1	a(1	PROPN
ejpam-201	68	2	)	)	PUNCT
ejpam-201	68	3	(	(	PUNCT
ejpam-201	68	4	a	a	DET
ejpam-201	68	5	∈	∈	NOUN
ejpam-201	68	6	ℓ1	ℓ1	NOUN
ejpam-201	68	7	)	)	PUNCT
ejpam-201	68	8	(	(	PUNCT
ejpam-201	68	9	2.1	2.1	NUM
ejpam-201	68	10	)	)	PUNCT
ejpam-201	68	11	in	in	ADP
ejpam-201	68	12	[	[	X
ejpam-201	68	13	5	5	NUM
ejpam-201	68	14	]	]	PUNCT
ejpam-201	68	15	has	have	AUX
ejpam-201	68	16	been	be	AUX
ejpam-201	68	17	shown	show	VERB
ejpam-201	68	18	that	that	SCONJ
ejpam-201	68	19	ℓ1	ℓ1	NOUN
ejpam-201	68	20	is	be	AUX
ejpam-201	68	21	(	(	PUNCT
ejpam-201	68	22	σ	σ	NOUN
ejpam-201	68	23	,	,	PUNCT
ejpam-201	68	24	τ)-weakly	τ)-weakly	PUNCT
ejpam-201	68	25	amenable	amenable	ADJ
ejpam-201	68	26	for	for	ADP
ejpam-201	68	27	all	all	DET
ejpam-201	68	28	homomorphisms	homomorphisms	PROPN
ejpam-201	68	29	σ	σ	PROPN
ejpam-201	68	30	,	,	PUNCT
ejpam-201	68	31	τ	τ	PROPN
ejpam-201	68	32	but	but	CCONJ
ejpam-201	68	33	for	for	ADP
ejpam-201	68	34	some	some	DET
ejpam-201	68	35	homomorphisms	homomorphism	NOUN
ejpam-201	68	36	σ	σ	NOUN
ejpam-201	68	37	and	and	CCONJ
ejpam-201	68	38	τ	τ	PRON
ejpam-201	68	39	it	it	PRON
ejpam-201	68	40	is	be	AUX
ejpam-201	68	41	not	not	PART
ejpam-201	68	42	(	(	PUNCT
ejpam-201	68	43	σ	σ	NOUN
ejpam-201	68	44	,	,	PUNCT
ejpam-201	68	45	τ)-amenable	τ)-amenable	ADJ
ejpam-201	68	46	.	.	PUNCT
ejpam-201	69	1	in	in	ADP
ejpam-201	69	2	the	the	DET
ejpam-201	69	3	following	following	NOUN
ejpam-201	69	4	we	we	PRON
ejpam-201	69	5	prove	prove	VERB
ejpam-201	69	6	if	if	SCONJ
ejpam-201	69	7	the	the	DET
ejpam-201	69	8	banach	banach	NOUN
ejpam-201	69	9	algebra	algebra	NOUN
ejpam-201	69	10	ℓ1	ℓ1	NOUN
ejpam-201	69	11	is	be	AUX
ejpam-201	69	12	(	(	PUNCT
ejpam-201	69	13	σ	σ	NOUN
ejpam-201	69	14	,	,	PUNCT
ejpam-201	69	15	τ)-amenable	τ)-amenable	ADJ
ejpam-201	69	16	,	,	PUNCT
ejpam-201	69	17	then	then	ADV
ejpam-201	69	18	τ(a	τ(a	NOUN
ejpam-201	69	19	)	)	PUNCT
ejpam-201	70	1	=	=	SYM
ejpam-201	70	2	a(1)c	a(1)c	NOUN
ejpam-201	70	3	where	where	SCONJ
ejpam-201	70	4	c(1	c(1	NOUN
ejpam-201	70	5	)	)	PUNCT
ejpam-201	70	6	=	=	SYM
ejpam-201	70	7	1	1	X
ejpam-201	70	8	.	.	X
ejpam-201	70	9	m.	m.	NOUN
ejpam-201	70	10	gordji	gordji	PROPN
ejpam-201	70	11	and	and	CCONJ
ejpam-201	70	12	a.	a.	NOUN
ejpam-201	70	13	motlagh	motlagh	PROPN
ejpam-201	70	14	/	/	SYM
ejpam-201	70	15	eur	eur	PROPN
ejpam-201	70	16	.	.	PUNCT
ejpam-201	71	1	j.	j.	PROPN
ejpam-201	71	2	pure	pure	PROPN
ejpam-201	71	3	appl	appl	PROPN
ejpam-201	71	4	.	.	PROPN
ejpam-201	71	5	math	math	PROPN
ejpam-201	71	6	,	,	PUNCT
ejpam-201	71	7	2	2	NUM
ejpam-201	71	8	(	(	PUNCT
ejpam-201	71	9	2009	2009	NUM
ejpam-201	71	10	)	)	PUNCT
ejpam-201	71	11	,	,	PUNCT
ejpam-201	71	12	(	(	PUNCT
ejpam-201	71	13	361	361	NUM
ejpam-201	71	14	-	-	SYM
ejpam-201	71	15	371	371	NUM
ejpam-201	71	16	)	)	PUNCT
ejpam-201	71	17	365	365	NUM
ejpam-201	71	18	let	let	VERB
ejpam-201	71	19	b	b	NOUN
ejpam-201	71	20	=	=	SYM
ejpam-201	71	21	ℓ1	ℓ1	VERB
ejpam-201	71	22	by	by	ADP
ejpam-201	71	23	product	product	NOUN
ejpam-201	71	24	a	a	DET
ejpam-201	71	25	•	•	NOUN
ejpam-201	71	26	b	b	NOUN
ejpam-201	71	27	=	=	SYM
ejpam-201	71	28	a(2)b	a(2)b	PROPN
ejpam-201	71	29	.	.	PUNCT
ejpam-201	72	1	then	then	ADV
ejpam-201	72	2	b	b	PROPN
ejpam-201	72	3	is	be	AUX
ejpam-201	72	4	a	a	DET
ejpam-201	72	5	banach	banach	NOUN
ejpam-201	72	6	algebra	algebra	NOUN
ejpam-201	72	7	and	and	CCONJ
ejpam-201	72	8	for	for	ADP
ejpam-201	72	9	each	each	DET
ejpam-201	72	10	bounded	bound	VERB
ejpam-201	72	11	homomorphism	homomorphism	PROPN
ejpam-201	72	12	ψ	ψ	X
ejpam-201	72	13	:	:	PUNCT
ejpam-201	72	14	b	b	X
ejpam-201	72	15	−→	−→	NOUN
ejpam-201	72	16	b	b	NOUN
ejpam-201	72	17	we	we	PRON
ejpam-201	72	18	have	have	VERB
ejpam-201	72	19	�	�	PROPN
ejpam-201	72	20	ψ(a	ψ(a	PROPN
ejpam-201	72	21	)	)	PUNCT
ejpam-201	72	22	�	�	PROPN
ejpam-201	72	23	(	(	PUNCT
ejpam-201	72	24	2	2	NUM
ejpam-201	72	25	)	)	PUNCT
ejpam-201	72	26	=	=	PUNCT
ejpam-201	73	1	a(2	a(2	PROPN
ejpam-201	73	2	)	)	PUNCT
ejpam-201	73	3	.	.	PUNCT
ejpam-201	74	1	let	let	VERB
ejpam-201	74	2	a	a	DET
ejpam-201	74	3	∈	∈	NOUN
ejpam-201	74	4	ℓ1	ℓ1	NOUN
ejpam-201	74	5	define	define	VERB
ejpam-201	74	6	a′	a′	NOUN
ejpam-201	74	7	∈	∈	NOUN
ejpam-201	74	8	ℓ1	ℓ1	NOUN
ejpam-201	74	9	by	by	ADP
ejpam-201	74	10	a′	a′	PROPN
ejpam-201	74	11	=	=	SYM
ejpam-201	74	12	�	�	PROPN
ejpam-201	74	13	a(2	a(2	PROPN
ejpam-201	74	14	)	)	PUNCT
ejpam-201	74	15	,	,	PUNCT
ejpam-201	74	16	a(1	a(1	PROPN
ejpam-201	74	17	)	)	PUNCT
ejpam-201	74	18	,	,	PUNCT
ejpam-201	74	19	a(3	a(3	PROPN
ejpam-201	74	20	)	)	PUNCT
ejpam-201	74	21	,	,	PUNCT
ejpam-201	74	22	·	·	PUNCT
ejpam-201	74	23	·	·	PUNCT
ejpam-201	74	24	·	·	PUNCT
ejpam-201	74	25	�	�	PROPN
ejpam-201	74	26	.	.	PUNCT
ejpam-201	75	1	let	let	VERB
ejpam-201	75	2	ϕ	ϕ	NOUN
ejpam-201	75	3	:	:	PUNCT
ejpam-201	75	4	ℓ1	ℓ1	VERB
ejpam-201	75	5	−→	−→	NOUN
ejpam-201	75	6	b	b	NOUN
ejpam-201	75	7	defined	define	VERB
ejpam-201	75	8	by	by	ADP
ejpam-201	75	9	ϕ(a	ϕ(a	NOUN
ejpam-201	75	10	)	)	PUNCT
ejpam-201	76	1	=	=	PUNCT
ejpam-201	76	2	a′.	a′.	NOUN
ejpam-201	76	3	it	it	PRON
ejpam-201	76	4	is	be	AUX
ejpam-201	76	5	clear	clear	ADJ
ejpam-201	76	6	that	that	SCONJ
ejpam-201	76	7	ϕ	ϕ	NOUN
ejpam-201	76	8	is	be	AUX
ejpam-201	76	9	a	a	DET
ejpam-201	76	10	homomorphism	homomorphism	NOUN
ejpam-201	76	11	.	.	PUNCT
ejpam-201	77	1	consider	consider	VERB
ejpam-201	77	2	the	the	DET
ejpam-201	77	3	banach	banach	NOUN
ejpam-201	77	4	ℓ1	ℓ1	NOUN
ejpam-201	77	5	-	-	PUNCT
ejpam-201	77	6	bimodule	bimodule	NOUN
ejpam-201	77	7	bϕ	bϕ	ADP
ejpam-201	77	8	under	under	ADP
ejpam-201	77	9	actions	action	NOUN
ejpam-201	77	10	a	a	DET
ejpam-201	77	11	◦	◦	NOUN
ejpam-201	77	12	b	b	NOUN
ejpam-201	77	13	=	=	SYM
ejpam-201	77	14	ϕ(a	ϕ(a	NOUN
ejpam-201	77	15	)	)	PUNCT
ejpam-201	77	16	•	•	NUM
ejpam-201	77	17	b	b	X
ejpam-201	77	18	=	=	PUNCT
ejpam-201	77	19	a′	a′	PROPN
ejpam-201	77	20	•	•	PROPN
ejpam-201	77	21	b	b	X
ejpam-201	77	22	=	=	NOUN
ejpam-201	77	23	a′(2)b	a′(2)b	NOUN
ejpam-201	77	24	=	=	PUNCT
ejpam-201	77	25	a(1)b	a(1)b	PROPN
ejpam-201	77	26	and	and	CCONJ
ejpam-201	77	27	b	b	X
ejpam-201	77	28	◦	◦	NOUN
ejpam-201	77	29	a	a	PRON
ejpam-201	77	30	=	=	X
ejpam-201	77	31	b	b	NOUN
ejpam-201	77	32	•ϕ(a	•ϕ(a	PROPN
ejpam-201	77	33	)	)	PUNCT
ejpam-201	77	34	=	=	SYM
ejpam-201	77	35	b	b	NOUN
ejpam-201	77	36	•	•	NOUN
ejpam-201	77	37	a′	a′	NOUN
ejpam-201	77	38	=	=	SYM
ejpam-201	77	39	b(2)a′	b(2)a′	NOUN
ejpam-201	77	40	for	for	ADP
ejpam-201	77	41	each	each	DET
ejpam-201	77	42	a	a	DET
ejpam-201	77	43	∈	∈	NOUN
ejpam-201	77	44	ℓ1	ℓ1	NOUN
ejpam-201	77	45	,	,	PUNCT
ejpam-201	77	46	b	b	X
ejpam-201	77	47	∈bϕ.	∈bϕ.	ADV
ejpam-201	77	48	let	let	VERB
ejpam-201	77	49	d	d	NOUN
ejpam-201	77	50	:	:	PUNCT
ejpam-201	77	51	ℓ1	ℓ1	VERB
ejpam-201	77	52	−→b∗	−→b∗	ADJ
ejpam-201	77	53	ϕ	ϕ	NOUN
ejpam-201	77	54	be	be	AUX
ejpam-201	77	55	a	a	DET
ejpam-201	77	56	bounded	bounded	ADJ
ejpam-201	77	57	(	(	PUNCT
ejpam-201	77	58	σ	σ	NOUN
ejpam-201	77	59	,	,	PUNCT
ejpam-201	77	60	τ)-derivation	τ)-derivation	NOUN
ejpam-201	77	61	.	.	PUNCT
ejpam-201	78	1	we	we	PRON
ejpam-201	78	2	have	have	VERB
ejpam-201	78	3	�	�	PROPN
ejpam-201	78	4	d(a	d(a	PROPN
ejpam-201	78	5	·	·	PUNCT
ejpam-201	78	6	b	b	X
ejpam-201	78	7	)	)	PUNCT
ejpam-201	78	8	�	�	PROPN
ejpam-201	78	9	(	(	PUNCT
ejpam-201	78	10	c	c	NOUN
ejpam-201	78	11	)	)	PUNCT
ejpam-201	78	12	=	=	SYM
ejpam-201	79	1	d(a)σ(b)(c	d(a)σ(b)(c	X
ejpam-201	79	2	)	)	PUNCT
ejpam-201	79	3	+	+	ADJ
ejpam-201	79	4	τ(a)d(b)(c	τ(a)d(b)(c	X
ejpam-201	79	5	)	)	PUNCT
ejpam-201	79	6	a(1)d(b)(c	a(1)d(b)(c	PROPN
ejpam-201	79	7	)	)	PUNCT
ejpam-201	79	8	=	=	SYM
ejpam-201	79	9	d(a)(σ(b	d(a)(σ(b	PROPN
ejpam-201	79	10	)	)	PUNCT
ejpam-201	79	11	◦	◦	NOUN
ejpam-201	79	12	c	c	X
ejpam-201	79	13	)	)	PUNCT
ejpam-201	80	1	+	+	CCONJ
ejpam-201	80	2	d(b)(c	d(b)(c	PUNCT
ejpam-201	80	3	◦	◦	NOUN
ejpam-201	80	4	τ(a	τ(a	NOUN
ejpam-201	80	5	)	)	PUNCT
ejpam-201	80	6	)	)	PUNCT
ejpam-201	81	1	a(1)d(b)(c	a(1)d(b)(c	PROPN
ejpam-201	81	2	)	)	PUNCT
ejpam-201	81	3	=	=	SYM
ejpam-201	81	4	b(1)d(a)(c	b(1)d(a)(c	X
ejpam-201	81	5	)	)	PUNCT
ejpam-201	82	1	+	+	CCONJ
ejpam-201	82	2	c(2)d(b)(τ(a	c(2)d(b)(τ(a	NOUN
ejpam-201	82	3	)	)	PUNCT
ejpam-201	82	4	)	)	PUNCT
ejpam-201	82	5	for	for	ADP
ejpam-201	82	6	all	all	DET
ejpam-201	82	7	a	a	DET
ejpam-201	82	8	,	,	PUNCT
ejpam-201	82	9	b	b	X
ejpam-201	82	10	∈	∈	NOUN
ejpam-201	82	11	ℓ1	ℓ1	NOUN
ejpam-201	82	12	and	and	CCONJ
ejpam-201	82	13	c	c	NOUN
ejpam-201	82	14	∈	∈	NOUN
ejpam-201	82	15	bϕ	bϕ	ADP
ejpam-201	82	16	.	.	PUNCT
ejpam-201	83	1	by	by	ADP
ejpam-201	83	2	taking	take	VERB
ejpam-201	83	3	a	a	DET
ejpam-201	83	4	=	=	SYM
ejpam-201	83	5	b	b	NOUN
ejpam-201	83	6	we	we	PRON
ejpam-201	83	7	obtain	obtain	VERB
ejpam-201	83	8	d(a)(τ(a	d(a)(τ(a	NOUN
ejpam-201	83	9	)	)	PUNCT
ejpam-201	83	10	)	)	PUNCT
ejpam-201	83	11	=	=	PUNCT
ejpam-201	84	1	0	0	X
ejpam-201	84	2	.	.	PUNCT
ejpam-201	84	3	also	also	ADV
ejpam-201	84	4	by	by	ADP
ejpam-201	84	5	taking	take	VERB
ejpam-201	84	6	c	c	NOUN
ejpam-201	84	7	∈	∈	NOUN
ejpam-201	84	8	bϕ	bϕ	ADP
ejpam-201	84	9	such	such	ADJ
ejpam-201	84	10	that	that	DET
ejpam-201	84	11	c(2	c(2	PROPN
ejpam-201	84	12	)	)	PUNCT
ejpam-201	84	13	=	=	SYM
ejpam-201	84	14	0	0	NUM
ejpam-201	85	1	we	we	PRON
ejpam-201	85	2	can	can	AUX
ejpam-201	85	3	conclude	conclude	VERB
ejpam-201	85	4	a(1)d(b	a(1)d(b	PRON
ejpam-201	85	5	)	)	PUNCT
ejpam-201	85	6	=	=	SYM
ejpam-201	85	7	b(1)d(a	b(1)d(a	PROPN
ejpam-201	85	8	)	)	PUNCT
ejpam-201	85	9	.	.	PUNCT
ejpam-201	86	1	if	if	SCONJ
ejpam-201	86	2	ℓ1	ℓ1	NOUN
ejpam-201	86	3	is	be	AUX
ejpam-201	86	4	(	(	PUNCT
ejpam-201	86	5	σ	σ	NOUN
ejpam-201	86	6	,	,	PUNCT
ejpam-201	86	7	τ)-amenable	τ)-amenable	ADJ
ejpam-201	86	8	,	,	PUNCT
ejpam-201	86	9	then	then	ADV
ejpam-201	86	10	there	there	PRON
ejpam-201	86	11	exists	exist	VERB
ejpam-201	86	12	f	f	PROPN
ejpam-201	86	13	∈	∈	PROPN
ejpam-201	86	14	b∗	b∗	PROPN
ejpam-201	86	15	ϕ	ϕ	NOUN
ejpam-201	86	16	such	such	ADJ
ejpam-201	87	1	that	that	PRON
ejpam-201	87	2	d	d	NOUN
ejpam-201	88	1	=	=	SYM
ejpam-201	88	2	d	d	X
ejpam-201	88	3	f	f	PROPN
ejpam-201	88	4	is	be	AUX
ejpam-201	88	5	a	a	DET
ejpam-201	88	6	(	(	PUNCT
ejpam-201	88	7	σ	σ	NOUN
ejpam-201	88	8	,	,	PUNCT
ejpam-201	88	9	τ)-inner	τ)-inner	PUNCT
ejpam-201	88	10	derivation	derivation	NOUN
ejpam-201	88	11	.	.	PUNCT
ejpam-201	89	1	so	so	ADV
ejpam-201	89	2	we	we	PRON
ejpam-201	89	3	have	have	VERB
ejpam-201	89	4	a(1)d	a(1)d	PROPN
ejpam-201	89	5	f	f	PROPN
ejpam-201	89	6	(	(	PUNCT
ejpam-201	89	7	b	b	NOUN
ejpam-201	89	8	)	)	PUNCT
ejpam-201	89	9	=	=	PUNCT
ejpam-201	90	1	b(1)d	b(1)d	PROPN
ejpam-201	90	2	f	f	X
ejpam-201	90	3	(	(	PUNCT
ejpam-201	90	4	a	a	NOUN
ejpam-201	90	5	)	)	PUNCT
ejpam-201	90	6	a(1	a(1	ADJ
ejpam-201	90	7	)	)	PUNCT
ejpam-201	90	8	f	f	NOUN
ejpam-201	90	9	(	(	PUNCT
ejpam-201	90	10	b(1)c	b(1)c	NOUN
ejpam-201	90	11	−	−	PROPN
ejpam-201	90	12	c(2)τ(b	c(2)τ(b	NOUN
ejpam-201	90	13	)	)	PUNCT
ejpam-201	90	14	)	)	PUNCT
ejpam-201	91	1	=	=	SYM
ejpam-201	91	2	b(1	b(1	PROPN
ejpam-201	91	3	)	)	PUNCT
ejpam-201	91	4	f	f	NOUN
ejpam-201	91	5	(	(	PUNCT
ejpam-201	91	6	a(1)c	a(1)c	NOUN
ejpam-201	91	7	−	−	PROPN
ejpam-201	91	8	c(2)τ(a	c(2)τ(a	NOUN
ejpam-201	91	9	)	)	PUNCT
ejpam-201	91	10	)	)	PUNCT
ejpam-201	91	11	for	for	ADP
ejpam-201	91	12	all	all	DET
ejpam-201	91	13	a	a	DET
ejpam-201	91	14	,	,	PUNCT
ejpam-201	91	15	b	b	X
ejpam-201	91	16	∈	∈	NOUN
ejpam-201	91	17	ℓ1	ℓ1	NOUN
ejpam-201	91	18	and	and	CCONJ
ejpam-201	91	19	c	c	NOUN
ejpam-201	91	20	∈	∈	NOUN
ejpam-201	91	21	bϕ	bϕ	ADP
ejpam-201	91	22	.	.	PUNCT
ejpam-201	92	1	then	then	ADV
ejpam-201	92	2	f	f	PROPN
ejpam-201	92	3	(	(	PUNCT
ejpam-201	92	4	b(1)c(2)τ(a)−	b(1)c(2)τ(a)−	NOUN
ejpam-201	92	5	a(1)c(2)τ(b	a(1)c(2)τ(b	PROPN
ejpam-201	92	6	)	)	PUNCT
ejpam-201	92	7	)	)	PUNCT
ejpam-201	93	1	=	=	PUNCT
ejpam-201	93	2	0	0	X
ejpam-201	93	3	.	.	PUNCT
ejpam-201	94	1	since	since	SCONJ
ejpam-201	94	2	f	f	PROPN
ejpam-201	94	3	∈	∈	PROPN
ejpam-201	94	4	b∗	b∗	PROPN
ejpam-201	94	5	ϕ	ϕ	PROPN
ejpam-201	94	6	is	be	AUX
ejpam-201	94	7	arbitrary	arbitrary	ADJ
ejpam-201	94	8	,	,	PUNCT
ejpam-201	94	9	immediately	immediately	ADV
ejpam-201	94	10	is	be	AUX
ejpam-201	94	11	conclude	conclude	VERB
ejpam-201	94	12	a(1)τ(b	a(1)τ(b	NOUN
ejpam-201	94	13	)	)	PUNCT
ejpam-201	94	14	=	=	PUNCT
ejpam-201	94	15	b(1)τ(a	b(1)τ(a	NOUN
ejpam-201	94	16	)	)	PUNCT
ejpam-201	94	17	.	.	PUNCT
ejpam-201	95	1	by	by	ADP
ejpam-201	95	2	taking	take	VERB
ejpam-201	95	3	b	b	NOUN
ejpam-201	95	4	=	=	SYM
ejpam-201	95	5	e	e	X
ejpam-201	95	6	we	we	PRON
ejpam-201	95	7	have	have	VERB
ejpam-201	95	8	τ(a	τ(a	NOUN
ejpam-201	95	9	)	)	PUNCT
ejpam-201	95	10	=	=	SYM
ejpam-201	95	11	a(1)τ(e	a(1)τ(e	PROPN
ejpam-201	95	12	)	)	PUNCT
ejpam-201	95	13	,	,	PUNCT
ejpam-201	95	14	where	where	SCONJ
ejpam-201	95	15	τ(e)(1	τ(e)(1	NOUN
ejpam-201	95	16	)	)	PUNCT
ejpam-201	95	17	=	=	SYM
ejpam-201	96	1	1	1	X
ejpam-201	96	2	.	.	PUNCT
ejpam-201	97	1	so	so	ADV
ejpam-201	97	2	we	we	PRON
ejpam-201	97	3	have	have	VERB
ejpam-201	97	4	the	the	DET
ejpam-201	97	5	following	follow	VERB
ejpam-201	97	6	result	result	NOUN
ejpam-201	97	7	.	.	PUNCT
ejpam-201	98	1	corollary	corollary	ADJ
ejpam-201	98	2	2.1	2.1	NUM
ejpam-201	98	3	.	.	PUNCT
ejpam-201	99	1	let	let	VERB
ejpam-201	99	2	σ	σ	PROPN
ejpam-201	99	3	,	,	PUNCT
ejpam-201	99	4	τ	τ	X
ejpam-201	99	5	be	be	VERB
ejpam-201	99	6	two	two	NUM
ejpam-201	99	7	continuous	continuous	ADJ
ejpam-201	99	8	homomorphisms	homomorphism	NOUN
ejpam-201	99	9	on	on	ADP
ejpam-201	99	10	ℓ1	ℓ1	NOUN
ejpam-201	99	11	(	(	PUNCT
ejpam-201	99	12	by	by	ADP
ejpam-201	99	13	above	above	ADP
ejpam-201	99	14	product	product	NOUN
ejpam-201	99	15	)	)	PUNCT
ejpam-201	99	16	.	.	PUNCT
ejpam-201	100	1	if	if	SCONJ
ejpam-201	100	2	ℓ1	ℓ1	NOUN
ejpam-201	100	3	is	be	AUX
ejpam-201	100	4	(	(	PUNCT
ejpam-201	100	5	σ	σ	PROPN
ejpam-201	100	6	,	,	PUNCT
ejpam-201	100	7	τ)-amenable	τ)-amenable	PUNCT
ejpam-201	100	8	then	then	ADV
ejpam-201	100	9	there	there	PRON
ejpam-201	100	10	is	be	VERB
ejpam-201	100	11	c	c	NOUN
ejpam-201	100	12	∈	∈	NOUN
ejpam-201	100	13	ℓ1	ℓ1	NOUN
ejpam-201	100	14	such	such	ADJ
ejpam-201	100	15	that	that	SCONJ
ejpam-201	100	16	τ(a	τ(a	NOUN
ejpam-201	100	17	)	)	PUNCT
ejpam-201	100	18	=	=	SYM
ejpam-201	100	19	a(1)c	a(1)c	PROPN
ejpam-201	100	20	,	,	PUNCT
ejpam-201	100	21	and	and	CCONJ
ejpam-201	100	22	c(1	c(1	PROPN
ejpam-201	100	23	)	)	PUNCT
ejpam-201	100	24	=	=	SYM
ejpam-201	100	25	1	1	X
ejpam-201	100	26	.	.	X
ejpam-201	100	27	m.	m.	NOUN
ejpam-201	100	28	gordji	gordji	PROPN
ejpam-201	100	29	and	and	CCONJ
ejpam-201	100	30	a.	a.	NOUN
ejpam-201	100	31	motlagh	motlagh	PROPN
ejpam-201	100	32	/	/	SYM
ejpam-201	100	33	eur	eur	PROPN
ejpam-201	100	34	.	.	PUNCT
ejpam-201	101	1	j.	j.	PROPN
ejpam-201	101	2	pure	pure	PROPN
ejpam-201	101	3	appl	appl	PROPN
ejpam-201	101	4	.	.	PROPN
ejpam-201	101	5	math	math	PROPN
ejpam-201	101	6	,	,	PUNCT
ejpam-201	101	7	2	2	NUM
ejpam-201	101	8	(	(	PUNCT
ejpam-201	101	9	2009	2009	NUM
ejpam-201	101	10	)	)	PUNCT
ejpam-201	101	11	,	,	PUNCT
ejpam-201	101	12	(	(	PUNCT
ejpam-201	101	13	361	361	NUM
ejpam-201	101	14	-	-	SYM
ejpam-201	101	15	371	371	NUM
ejpam-201	101	16	)	)	PUNCT
ejpam-201	101	17	366	366	NUM
ejpam-201	101	18	example	example	NOUN
ejpam-201	101	19	2.2	2.2	NUM
ejpam-201	101	20	.	.	PUNCT
ejpam-201	102	1	leta	leta	PROPN
ejpam-201	102	2	be	be	AUX
ejpam-201	102	3	a	a	DET
ejpam-201	102	4	banach	banach	NOUN
ejpam-201	102	5	algebra	algebra	NOUN
ejpam-201	102	6	.	.	PUNCT
ejpam-201	103	1	thena	thena	PROPN
ejpam-201	103	2	has	have	VERB
ejpam-201	103	3	a	a	DET
ejpam-201	103	4	bounded	bound	VERB
ejpam-201	103	5	approximate	approximate	ADJ
ejpam-201	103	6	identity	identity	NOUN
ejpam-201	103	7	if	if	SCONJ
ejpam-201	103	8	and	and	CCONJ
ejpam-201	103	9	only	only	ADV
ejpam-201	103	10	ifa	ifa	PROPN
ejpam-201	103	11	is	be	AUX
ejpam-201	103	12	(	(	PUNCT
ejpam-201	103	13	i	i	PROPN
ejpam-201	103	14	d	d	PROPN
ejpam-201	103	15	,	,	PUNCT
ejpam-201	103	16	0	0	NUM
ejpam-201	103	17	)	)	PUNCT
ejpam-201	103	18	and	and	CCONJ
ejpam-201	103	19	(	(	PUNCT
ejpam-201	103	20	0	0	NUM
ejpam-201	103	21	,	,	PUNCT
ejpam-201	103	22	id)-amenable	id)-amenable	ADJ
ejpam-201	103	23	.	.	PUNCT
ejpam-201	104	1	corollary	corollary	ADJ
ejpam-201	104	2	2.2	2.2	NUM
ejpam-201	104	3	.	.	PUNCT
ejpam-201	105	1	leta	leta	PROPN
ejpam-201	105	2	be	be	AUX
ejpam-201	105	3	a	a	DET
ejpam-201	105	4	c∗−algebra	c∗−algebra	PROPN
ejpam-201	105	5	ora	ora	PROPN
ejpam-201	105	6	=	=	SYM
ejpam-201	105	7	l1(g	l1(g	PROPN
ejpam-201	105	8	)	)	PUNCT
ejpam-201	105	9	for	for	ADP
ejpam-201	105	10	a	a	DET
ejpam-201	105	11	locally	locally	ADV
ejpam-201	105	12	compact	compact	ADJ
ejpam-201	105	13	topological	topological	ADJ
ejpam-201	105	14	group	group	NOUN
ejpam-201	105	15	g.	g.	PROPN
ejpam-201	105	16	thena	thena	PROPN
ejpam-201	105	17	is	be	AUX
ejpam-201	105	18	(	(	PUNCT
ejpam-201	105	19	i	i	PROPN
ejpam-201	105	20	d	d	PROPN
ejpam-201	105	21	,	,	PUNCT
ejpam-201	105	22	0	0	NUM
ejpam-201	105	23	)	)	PUNCT
ejpam-201	105	24	and	and	CCONJ
ejpam-201	105	25	(	(	PUNCT
ejpam-201	105	26	0	0	NUM
ejpam-201	105	27	,	,	PUNCT
ejpam-201	105	28	id)-amenable	id)-amenable	ADJ
ejpam-201	105	29	.	.	PUNCT
ejpam-201	106	1	let	let	VERB
ejpam-201	106	2	t	t	NOUN
ejpam-201	106	3	:	:	PUNCT
ejpam-201	106	4	a	a	DET
ejpam-201	106	5	→	→	SYM
ejpam-201	106	6	b	b	X
ejpam-201	106	7	be	be	AUX
ejpam-201	106	8	a	a	DET
ejpam-201	106	9	continuous	continuous	ADJ
ejpam-201	106	10	linear	linear	NOUN
ejpam-201	106	11	map	map	NOUN
ejpam-201	106	12	between	between	ADP
ejpam-201	106	13	banach	banach	NOUN
ejpam-201	106	14	algebras	algebra	NOUN
ejpam-201	106	15	.	.	PUNCT
ejpam-201	107	1	two	two	NUM
ejpam-201	107	2	continuous	continuous	ADJ
ejpam-201	107	3	linear	linear	PROPN
ejpam-201	107	4	maps	map	NOUN
ejpam-201	107	5	t	t	NOUN
ejpam-201	107	6	′	′	NUM
ejpam-201	107	7	:	:	PUNCT
ejpam-201	107	8	b∗	b∗	ADJ
ejpam-201	107	9	→	→	SYM
ejpam-201	107	10	a	a	DET
ejpam-201	107	11	∗	∗	NOUN
ejpam-201	107	12	and	and	CCONJ
ejpam-201	107	13	t	t	NOUN
ejpam-201	108	1	′′	′′	PROPN
ejpam-201	108	2	:	:	PUNCT
ejpam-201	108	3	a	a	DET
ejpam-201	108	4	∗∗	∗∗	PROPN
ejpam-201	108	5	→	→	SYM
ejpam-201	108	6	b∗∗	b∗∗	NOUN
ejpam-201	108	7	are	be	AUX
ejpam-201	108	8	known	know	VERB
ejpam-201	108	9	,	,	PUNCT
ejpam-201	108	10	that	that	PRON
ejpam-201	108	11	are	be	AUX
ejpam-201	108	12	defined	define	VERB
ejpam-201	108	13	by	by	ADP
ejpam-201	108	14	the	the	DET
ejpam-201	108	15	following	follow	VERB
ejpam-201	108	16	formula	formula	NOUN
ejpam-201	108	17	�	�	PROPN
ejpam-201	108	18	t	t	PROPN
ejpam-201	108	19	′	′	PROPN
ejpam-201	108	20	(	(	PUNCT
ejpam-201	108	21	f	f	PROPN
ejpam-201	108	22	)	)	PUNCT
ejpam-201	108	23	�	�	PROPN
ejpam-201	108	24	(	(	PUNCT
ejpam-201	108	25	a	a	NOUN
ejpam-201	108	26	)	)	PUNCT
ejpam-201	108	27	=	=	SYM
ejpam-201	108	28	f	f	PROPN
ejpam-201	108	29	�	�	PROPN
ejpam-201	108	30	t	t	PROPN
ejpam-201	108	31	(	(	PUNCT
ejpam-201	108	32	a	a	PRON
ejpam-201	108	33	)	)	PUNCT
ejpam-201	108	34	�	�	PROPN
ejpam-201	108	35	,	,	PUNCT
ejpam-201	108	36	�	�	PROPN
ejpam-201	108	37	t	t	PROPN
ejpam-201	108	38	′′(g	′′(g	PROPN
ejpam-201	108	39	)	)	PUNCT
ejpam-201	108	40	�	�	PROPN
ejpam-201	108	41	(	(	PUNCT
ejpam-201	108	42	f	f	PROPN
ejpam-201	108	43	)	)	PUNCT
ejpam-201	108	44	=	=	SYM
ejpam-201	108	45	g	g	PROPN
ejpam-201	108	46	�	�	PROPN
ejpam-201	108	47	t	t	PROPN
ejpam-201	108	48	′	′	PROPN
ejpam-201	108	49	(	(	PUNCT
ejpam-201	108	50	f	f	PROPN
ejpam-201	108	51	)	)	PUNCT
ejpam-201	108	52	�	�	PROPN
ejpam-201	108	53	where	where	SCONJ
ejpam-201	108	54	a	a	DET
ejpam-201	108	55	∈a	∈a	ADJ
ejpam-201	108	56	,	,	PUNCT
ejpam-201	108	57	f	f	PROPN
ejpam-201	108	58	∈b∗	∈b∗	NOUN
ejpam-201	108	59	and	and	CCONJ
ejpam-201	108	60	g	g	PROPN
ejpam-201	108	61	∈a	∈a	ADJ
ejpam-201	108	62	∗∗.	∗∗.	PROPN
ejpam-201	108	63	lemma	lemma	PROPN
ejpam-201	108	64	2.1	2.1	NUM
ejpam-201	108	65	.	.	PUNCT
ejpam-201	109	1	let	let	VERB
ejpam-201	109	2	a	a	PRON
ejpam-201	109	3	be	be	AUX
ejpam-201	109	4	a	a	DET
ejpam-201	109	5	banach	banach	NOUN
ejpam-201	109	6	algebra	algebra	NOUN
ejpam-201	109	7	,	,	PUNCT
ejpam-201	109	8	x	x	PRON
ejpam-201	109	9	be	be	AUX
ejpam-201	109	10	a	a	DET
ejpam-201	109	11	banach	banach	NOUN
ejpam-201	109	12	a	a	DET
ejpam-201	109	13	-bimodule	-bimodule	NOUN
ejpam-201	109	14	,	,	PUNCT
ejpam-201	109	15	and	and	CCONJ
ejpam-201	109	16	let	let	VERB
ejpam-201	109	17	σ	σ	PROPN
ejpam-201	109	18	and	and	CCONJ
ejpam-201	109	19	τ	τ	PROPN
ejpam-201	109	20	be	be	AUX
ejpam-201	109	21	two	two	NUM
ejpam-201	109	22	continuous	continuous	ADJ
ejpam-201	109	23	homomorphisms	homomorphism	NOUN
ejpam-201	109	24	on	on	ADP
ejpam-201	109	25	a	a	PRON
ejpam-201	109	26	.	.	PUNCT
ejpam-201	110	1	suppose	suppose	VERB
ejpam-201	110	2	that	that	SCONJ
ejpam-201	110	3	d	d	X
ejpam-201	110	4	:	:	PUNCT
ejpam-201	110	5	a	a	DET
ejpam-201	110	6	−→	−→	NOUN
ejpam-201	110	7	x	x	SYM
ejpam-201	110	8	is	be	AUX
ejpam-201	110	9	(	(	PUNCT
ejpam-201	110	10	σ	σ	PROPN
ejpam-201	110	11	,	,	PUNCT
ejpam-201	110	12	τ)derivation	τ)derivation	PROPN
ejpam-201	110	13	.	.	PUNCT
ejpam-201	111	1	then	then	ADV
ejpam-201	111	2	d′′	d′′	NOUN
ejpam-201	111	3	:	:	PUNCT
ejpam-201	111	4	a	a	DET
ejpam-201	111	5	∗∗	∗∗	NOUN
ejpam-201	111	6	−→x	−→x	SYM
ejpam-201	111	7	∗∗	∗∗	NOUN
ejpam-201	111	8	is	be	AUX
ejpam-201	111	9	a	a	DET
ejpam-201	111	10	(	(	PUNCT
ejpam-201	111	11	σ′′,τ′′)-derivation	σ′′,τ′′)-derivation	NOUN
ejpam-201	111	12	.	.	PUNCT
ejpam-201	112	1	proof	proof	NOUN
ejpam-201	112	2	.	.	PUNCT
ejpam-201	113	1	let	let	VERB
ejpam-201	113	2	f	f	X
ejpam-201	113	3	,	,	PUNCT
ejpam-201	113	4	g	g	PROPN
ejpam-201	113	5	∈	∈	PROPN
ejpam-201	113	6	a	a	DET
ejpam-201	113	7	∗∗	∗∗	NOUN
ejpam-201	113	8	and	and	CCONJ
ejpam-201	113	9	let	let	VERB
ejpam-201	113	10	f	f	PROPN
ejpam-201	113	11	=	=	PUNCT
ejpam-201	113	12	w∗	w∗	PROPN
ejpam-201	113	13	−	−	PROPN
ejpam-201	113	14	limα	limα	PROPN
ejpam-201	113	15	aα	aα	PROPN
ejpam-201	113	16	,	,	PUNCT
ejpam-201	113	17	g	g	PROPN
ejpam-201	113	18	=	=	PROPN
ejpam-201	113	19	w∗	w∗	PROPN
ejpam-201	113	20	−	−	PROPN
ejpam-201	113	21	limβ	limβ	ADJ
ejpam-201	113	22	bβ	bβ	NOUN
ejpam-201	113	23	in	in	ADP
ejpam-201	113	24	a	a	DET
ejpam-201	113	25	∗∗	∗∗	PROPN
ejpam-201	113	26	,	,	PUNCT
ejpam-201	113	27	where	where	SCONJ
ejpam-201	113	28	(	(	PUNCT
ejpam-201	113	29	aα	aα	NOUN
ejpam-201	113	30	)	)	PUNCT
ejpam-201	113	31	,	,	PUNCT
ejpam-201	113	32	(	(	PUNCT
ejpam-201	113	33	bβ	bβ	NOUN
ejpam-201	113	34	)	)	PUNCT
ejpam-201	113	35	are	be	AUX
ejpam-201	113	36	nets	net	NOUN
ejpam-201	113	37	ina	ina	PROPN
ejpam-201	113	38	with	with	ADP
ejpam-201	113	39	||aα||	||aα||	PROPN
ejpam-201	113	40	≤	≤	NUM
ejpam-201	113	41	||f	||f	PROPN
ejpam-201	113	42	||	||	NOUN
ejpam-201	113	43	,	,	PUNCT
ejpam-201	113	44	||bβ	||bβ	X
ejpam-201	113	45	||	||	NOUN
ejpam-201	113	46	≤	≤	NUM
ejpam-201	113	47	||g||	||g||	NOUN
ejpam-201	113	48	.	.	PUNCT
ejpam-201	114	1	then	then	ADV
ejpam-201	114	2	d′′(fg	d′′(fg	NOUN
ejpam-201	114	3	)	)	PUNCT
ejpam-201	115	1	=	=	SYM
ejpam-201	115	2	d′′	d′′	PROPN
ejpam-201	115	3	�	�	PROPN
ejpam-201	115	4	w∗	w∗	PROPN
ejpam-201	115	5	−	−	PROPN
ejpam-201	115	6	lim	lim	PROPN
ejpam-201	115	7	α	α	PROPN
ejpam-201	115	8	w∗	w∗	PROPN
ejpam-201	116	1	−	−	PROPN
ejpam-201	117	1	lim	lim	PROPN
ejpam-201	117	2	β	β	PROPN
ejpam-201	117	3	aαbβ	aαbβ	PROPN
ejpam-201	117	4	�	�	PROPN
ejpam-201	117	5	=	=	SYM
ejpam-201	117	6	w∗	w∗	PROPN
ejpam-201	117	7	−	−	PROPN
ejpam-201	117	8	lim	lim	PROPN
ejpam-201	117	9	α	α	PROPN
ejpam-201	117	10	w∗	w∗	PROPN
ejpam-201	118	1	−	−	PROPN
ejpam-201	118	2	lim	lim	PROPN
ejpam-201	118	3	β	β	PROPN
ejpam-201	118	4	d′′(aαbβ	d′′(aαbβ	PROPN
ejpam-201	118	5	)	)	PUNCT
ejpam-201	119	1	=	=	X
ejpam-201	119	2	w∗	w∗	NOUN
ejpam-201	119	3	−	−	PROPN
ejpam-201	119	4	lim	lim	PROPN
ejpam-201	119	5	α	α	PROPN
ejpam-201	119	6	w∗	w∗	PROPN
ejpam-201	120	1	−	−	PROPN
ejpam-201	120	2	lim	lim	PROPN
ejpam-201	120	3	β	β	PROPN
ejpam-201	120	4	�	�	PROPN
ejpam-201	120	5	τ(aα)d(bβ	τ(aα)d(bβ	PUNCT
ejpam-201	120	6	)	)	PUNCT
ejpam-201	120	7	+	+	CCONJ
ejpam-201	120	8	d(aα)σ(bβ	d(aα)σ(bβ	PUNCT
ejpam-201	120	9	)	)	PUNCT
ejpam-201	120	10	�	�	PROPN
ejpam-201	120	11	=	=	PUNCT
ejpam-201	120	12	τ′′(f)d′′(g	τ′′(f)d′′(g	PUNCT
ejpam-201	120	13	)	)	PUNCT
ejpam-201	120	14	+	+	NUM
ejpam-201	120	15	d′′(f)σ′′(g	d′′(f)σ′′(g	NOUN
ejpam-201	120	16	)	)	PUNCT
ejpam-201	121	1	and	and	CCONJ
ejpam-201	121	2	so	so	ADV
ejpam-201	121	3	d′′	d′′	PROPN
ejpam-201	121	4	is	be	AUX
ejpam-201	121	5	a	a	DET
ejpam-201	121	6	(	(	PUNCT
ejpam-201	121	7	σ′′,τ′′)-derivation	σ′′,τ′′)-derivation	NOUN
ejpam-201	121	8	.	.	PUNCT
ejpam-201	122	1	now	now	ADV
ejpam-201	122	2	we	we	PRON
ejpam-201	122	3	are	be	AUX
ejpam-201	122	4	ready	ready	ADJ
ejpam-201	122	5	to	to	PART
ejpam-201	122	6	state	state	VERB
ejpam-201	122	7	some	some	DET
ejpam-201	122	8	equivalent	equivalent	ADJ
ejpam-201	122	9	conditions	condition	NOUN
ejpam-201	122	10	by	by	ADP
ejpam-201	122	11	(	(	PUNCT
ejpam-201	122	12	σ	σ	NOUN
ejpam-201	122	13	,	,	PUNCT
ejpam-201	122	14	τ)-amenability	τ)-amenability	NOUN
ejpam-201	122	15	of	of	ADP
ejpam-201	122	16	banach	banach	NOUN
ejpam-201	122	17	algebras	algebra	NOUN
ejpam-201	122	18	.	.	PUNCT
ejpam-201	123	1	m.	m.	NOUN
ejpam-201	123	2	gordji	gordji	PROPN
ejpam-201	123	3	and	and	CCONJ
ejpam-201	123	4	a.	a.	NOUN
ejpam-201	123	5	motlagh	motlagh	PROPN
ejpam-201	123	6	/	/	SYM
ejpam-201	123	7	eur	eur	PROPN
ejpam-201	123	8	.	.	PUNCT
ejpam-201	124	1	j.	j.	PROPN
ejpam-201	124	2	pure	pure	PROPN
ejpam-201	124	3	appl	appl	PROPN
ejpam-201	124	4	.	.	PROPN
ejpam-201	124	5	math	math	PROPN
ejpam-201	124	6	,	,	PUNCT
ejpam-201	124	7	2	2	NUM
ejpam-201	124	8	(	(	PUNCT
ejpam-201	124	9	2009	2009	NUM
ejpam-201	124	10	)	)	PUNCT
ejpam-201	124	11	,	,	PUNCT
ejpam-201	124	12	(	(	PUNCT
ejpam-201	124	13	361	361	NUM
ejpam-201	124	14	-	-	SYM
ejpam-201	124	15	371	371	NUM
ejpam-201	124	16	)	)	PUNCT
ejpam-201	124	17	367	367	NUM
ejpam-201	124	18	theorem	theorem	VERB
ejpam-201	124	19	2.1	2.1	NUM
ejpam-201	124	20	.	.	PUNCT
ejpam-201	125	1	let	let	VERB
ejpam-201	125	2	σ	σ	NOUN
ejpam-201	125	3	and	and	CCONJ
ejpam-201	125	4	τ	τ	PROPN
ejpam-201	125	5	be	be	AUX
ejpam-201	125	6	two	two	NUM
ejpam-201	125	7	continuous	continuous	ADJ
ejpam-201	125	8	homomorphisms	homomorphism	NOUN
ejpam-201	125	9	on	on	ADP
ejpam-201	125	10	banach	banach	NOUN
ejpam-201	125	11	algebra	algebra	NOUN
ejpam-201	126	1	a	a	PRON
ejpam-201	126	2	.	.	PUNCT
ejpam-201	127	1	the	the	DET
ejpam-201	127	2	following	follow	VERB
ejpam-201	127	3	statements	statement	NOUN
ejpam-201	127	4	are	be	AUX
ejpam-201	127	5	equivalent	equivalent	ADJ
ejpam-201	127	6	:	:	PUNCT
ejpam-201	127	7	1	1	X
ejpam-201	127	8	.	.	X
ejpam-201	127	9	a	a	PRON
ejpam-201	127	10	is	be	AUX
ejpam-201	127	11	(	(	PUNCT
ejpam-201	127	12	σ	σ	NOUN
ejpam-201	127	13	,	,	PUNCT
ejpam-201	127	14	τ)-amenable	τ)-amenable	ADJ
ejpam-201	127	15	.	.	PUNCT
ejpam-201	128	1	2	2	X
ejpam-201	128	2	.	.	X
ejpam-201	128	3	for	for	ADP
ejpam-201	128	4	each	each	DET
ejpam-201	128	5	banach	banach	NOUN
ejpam-201	128	6	algebrab	algebrab	NOUN
ejpam-201	128	7	and	and	CCONJ
ejpam-201	128	8	every	every	DET
ejpam-201	128	9	homomorphism	homomorphism	NOUN
ejpam-201	128	10	ϕ	ϕ	X
ejpam-201	128	11	:	:	PUNCT
ejpam-201	128	12	a	a	DET
ejpam-201	128	13	−→b	−→b	NOUN
ejpam-201	128	14	,	,	PUNCT
ejpam-201	128	15	h1	h1	PROPN
ejpam-201	128	16	(	(	PUNCT
ejpam-201	128	17	σ	σ	PROPN
ejpam-201	128	18	,	,	PUNCT
ejpam-201	128	19	τ	τ	X
ejpam-201	128	20	)	)	PUNCT
ejpam-201	128	21	(	(	PUNCT
ejpam-201	128	22	a	a	DET
ejpam-201	128	23	,	,	PUNCT
ejpam-201	128	24	b∗	b∗	ADJ
ejpam-201	128	25	ϕ	ϕ	NOUN
ejpam-201	128	26	)	)	PUNCT
ejpam-201	128	27	=	=	PUNCT
ejpam-201	128	28	0	0	X
ejpam-201	128	29	.	.	NOUN
ejpam-201	129	1	3	3	X
ejpam-201	129	2	.	.	X
ejpam-201	129	3	for	for	ADP
ejpam-201	129	4	each	each	DET
ejpam-201	129	5	banach	banach	NOUN
ejpam-201	129	6	algebra	algebra	NOUN
ejpam-201	129	7	b	b	NOUN
ejpam-201	129	8	and	and	CCONJ
ejpam-201	129	9	every	every	DET
ejpam-201	129	10	injective	injective	ADJ
ejpam-201	129	11	homomorphism	homomorphism	PROPN
ejpam-201	129	12	ϕ	ϕ	NOUN
ejpam-201	129	13	:	:	PUNCT
ejpam-201	129	14	a	a	DET
ejpam-201	129	15	−→	−→	NOUN
ejpam-201	129	16	b	b	NOUN
ejpam-201	129	17	,	,	PUNCT
ejpam-201	129	18	h1	h1	PROPN
ejpam-201	129	19	(	(	PUNCT
ejpam-201	129	20	σ	σ	PROPN
ejpam-201	129	21	,	,	PUNCT
ejpam-201	129	22	τ	τ	X
ejpam-201	129	23	)	)	PUNCT
ejpam-201	129	24	(	(	PUNCT
ejpam-201	129	25	a	a	DET
ejpam-201	129	26	,	,	PUNCT
ejpam-201	129	27	b∗	b∗	ADJ
ejpam-201	129	28	ϕ	ϕ	NOUN
ejpam-201	129	29	)	)	PUNCT
ejpam-201	129	30	=	=	PUNCT
ejpam-201	130	1	0	0	NUM
ejpam-201	130	2	.	.	NOUN
ejpam-201	131	1	4	4	NUM
ejpam-201	131	2	.	.	X
ejpam-201	131	3	for	for	ADP
ejpam-201	131	4	each	each	DET
ejpam-201	131	5	banach	banach	NOUN
ejpam-201	131	6	algebra	algebra	NOUN
ejpam-201	131	7	b	b	NOUN
ejpam-201	131	8	and	and	CCONJ
ejpam-201	131	9	every	every	DET
ejpam-201	131	10	injective	injective	ADJ
ejpam-201	131	11	homomorphism	homomorphism	PROPN
ejpam-201	131	12	ϕ	ϕ	NOUN
ejpam-201	131	13	:	:	PUNCT
ejpam-201	131	14	a	a	DET
ejpam-201	131	15	−→	−→	NOUN
ejpam-201	131	16	b	b	NOUN
ejpam-201	131	17	,	,	PUNCT
ejpam-201	131	18	if	if	SCONJ
ejpam-201	131	19	d	d	X
ejpam-201	131	20	:	:	PUNCT
ejpam-201	131	21	a	a	DET
ejpam-201	131	22	−→bϕ	−→bϕ	NOUN
ejpam-201	131	23	∗	∗	NOUN
ejpam-201	131	24	is	be	AUX
ejpam-201	131	25	a	a	DET
ejpam-201	131	26	(	(	PUNCT
ejpam-201	131	27	σ	σ	NOUN
ejpam-201	131	28	,	,	PUNCT
ejpam-201	131	29	τ)-derivation	τ)-derivation	NOUN
ejpam-201	131	30	satisfies	satisfie	NOUN
ejpam-201	131	31	(	(	PUNCT
ejpam-201	131	32	d(a))(ϕ(b	d(a))(ϕ(b	NOUN
ejpam-201	131	33	)	)	PUNCT
ejpam-201	131	34	)	)	PUNCT
ejpam-201	132	1	+	+	CCONJ
ejpam-201	132	2	(	(	PUNCT
ejpam-201	132	3	d(b))(ϕ(a	d(b))(ϕ(a	NOUN
ejpam-201	132	4	)	)	PUNCT
ejpam-201	132	5	)	)	PUNCT
ejpam-201	133	1	=	=	SYM
ejpam-201	133	2	0	0	PUNCT
ejpam-201	133	3	(	(	PUNCT
ejpam-201	133	4	a	a	PRON
ejpam-201	133	5	,	,	PUNCT
ejpam-201	133	6	b	b	PROPN
ejpam-201	133	7	∈a	∈a	NUM
ejpam-201	133	8	)	)	PUNCT
ejpam-201	133	9	,	,	PUNCT
ejpam-201	133	10	then	then	ADV
ejpam-201	133	11	d	d	X
ejpam-201	133	12	is	be	AUX
ejpam-201	133	13	(	(	PUNCT
ejpam-201	133	14	σ	σ	NOUN
ejpam-201	133	15	,	,	PUNCT
ejpam-201	133	16	τ)-inner	τ)-inner	PUNCT
ejpam-201	133	17	derivation	derivation	NOUN
ejpam-201	133	18	.	.	PUNCT
ejpam-201	134	1	proof	proof	NOUN
ejpam-201	134	2	.	.	PUNCT
ejpam-201	135	1	clearly	clearly	ADV
ejpam-201	135	2	(	(	PUNCT
ejpam-201	135	3	1)⇒	1)⇒	NUM
ejpam-201	135	4	(	(	PUNCT
ejpam-201	135	5	2)⇒	2)⇒	NUM
ejpam-201	135	6	(	(	PUNCT
ejpam-201	135	7	3)⇒	3)⇒	NUM
ejpam-201	135	8	(	(	PUNCT
ejpam-201	135	9	4	4	NUM
ejpam-201	135	10	)	)	PUNCT
ejpam-201	135	11	.	.	PUNCT
ejpam-201	136	1	it	it	PRON
ejpam-201	136	2	is	be	AUX
ejpam-201	136	3	sufficient	sufficient	ADJ
ejpam-201	136	4	to	to	PART
ejpam-201	136	5	show	show	VERB
ejpam-201	136	6	that	that	SCONJ
ejpam-201	136	7	(	(	PUNCT
ejpam-201	136	8	4)⇒	4)⇒	X
ejpam-201	136	9	(	(	PUNCT
ejpam-201	136	10	1	1	NUM
ejpam-201	136	11	)	)	PUNCT
ejpam-201	136	12	.	.	PUNCT
ejpam-201	137	1	letx	letx	PROPN
ejpam-201	137	2	be	be	AUX
ejpam-201	137	3	a	a	DET
ejpam-201	137	4	banacha	banacha	NOUN
ejpam-201	137	5	-bimodule	-bimodule	NOUN
ejpam-201	137	6	and	and	CCONJ
ejpam-201	137	7	d	d	NOUN
ejpam-201	137	8	:	:	PUNCT
ejpam-201	137	9	a	a	DET
ejpam-201	137	10	−→x	−→x	NOUN
ejpam-201	137	11	∗	∗	NOUN
ejpam-201	137	12	be	be	VERB
ejpam-201	137	13	a	a	DET
ejpam-201	137	14	(	(	PUNCT
ejpam-201	137	15	σ	σ	NOUN
ejpam-201	137	16	,	,	PUNCT
ejpam-201	137	17	τ)-derivation	τ)-derivation	NOUN
ejpam-201	137	18	.	.	PUNCT
ejpam-201	138	1	setb	setb	NOUN
ejpam-201	139	1	=	=	PRON
ejpam-201	139	2	a⊕1x	a⊕1x	PRON
ejpam-201	139	3	and	and	CCONJ
ejpam-201	139	4	define	define	VERB
ejpam-201	139	5	injective	injective	ADJ
ejpam-201	139	6	homomorphism	homomorphism	PROPN
ejpam-201	139	7	ϕ	ϕ	NOUN
ejpam-201	139	8	:	:	PUNCT
ejpam-201	139	9	a	a	DET
ejpam-201	139	10	−→	−→	NOUN
ejpam-201	139	11	b	b	NOUN
ejpam-201	139	12	by	by	ADP
ejpam-201	139	13	ϕ(a	ϕ(a	NOUN
ejpam-201	139	14	)	)	PUNCT
ejpam-201	140	1	=	=	SYM
ejpam-201	140	2	(	(	PUNCT
ejpam-201	140	3	a	a	PRON
ejpam-201	140	4	,	,	PUNCT
ejpam-201	140	5	0	0	NUM
ejpam-201	140	6	)	)	PUNCT
ejpam-201	141	1	and	and	CCONJ
ejpam-201	141	2	so	so	ADV
ejpam-201	141	3	we	we	PRON
ejpam-201	141	4	can	can	AUX
ejpam-201	141	5	assume	assume	VERB
ejpam-201	141	6	that	that	SCONJ
ejpam-201	141	7	a	a	PRON
ejpam-201	141	8	is	be	AUX
ejpam-201	141	9	a	a	DET
ejpam-201	141	10	subalgebra	subalgebra	NOUN
ejpam-201	141	11	of	of	ADP
ejpam-201	141	12	b	b	PROPN
ejpam-201	141	13	.	.	PUNCT
ejpam-201	142	1	define	define	VERB
ejpam-201	143	1	d	d	X
ejpam-201	143	2	:	:	PUNCT
ejpam-201	143	3	a	a	DET
ejpam-201	143	4	−→b∗	−→b∗	PROPN
ejpam-201	143	5	ϕ	ϕ	NOUN
ejpam-201	143	6	by	by	ADP
ejpam-201	143	7	d(a	d(a	PROPN
ejpam-201	143	8	)	)	PUNCT
ejpam-201	143	9	=	=	SYM
ejpam-201	143	10	(	(	PUNCT
ejpam-201	143	11	0	0	NUM
ejpam-201	143	12	,	,	PUNCT
ejpam-201	143	13	d(a	d(a	PROPN
ejpam-201	143	14	)	)	PUNCT
ejpam-201	143	15	)	)	PUNCT
ejpam-201	143	16	.	.	PUNCT
ejpam-201	144	1	the	the	DET
ejpam-201	144	2	map	map	NOUN
ejpam-201	144	3	d	d	X
ejpam-201	144	4	is	be	AUX
ejpam-201	144	5	(	(	PUNCT
ejpam-201	144	6	σ	σ	NOUN
ejpam-201	144	7	,	,	PUNCT
ejpam-201	144	8	τ)-derivation	τ)-derivation	NOUN
ejpam-201	144	9	,	,	PUNCT
ejpam-201	144	10	since	since	SCONJ
ejpam-201	144	11	d(ab	d(ab	NOUN
ejpam-201	144	12	)	)	PUNCT
ejpam-201	144	13	=	=	SYM
ejpam-201	144	14	(	(	PUNCT
ejpam-201	144	15	0	0	NUM
ejpam-201	144	16	,	,	PUNCT
ejpam-201	144	17	d(ab	d(ab	NOUN
ejpam-201	144	18	)	)	PUNCT
ejpam-201	144	19	)	)	PUNCT
ejpam-201	145	1	=	=	SYM
ejpam-201	145	2	(	(	PUNCT
ejpam-201	145	3	0	0	NUM
ejpam-201	145	4	,	,	PUNCT
ejpam-201	145	5	d(a)σ(b	d(a)σ(b	PROPN
ejpam-201	145	6	)	)	PUNCT
ejpam-201	145	7	+	+	NOUN
ejpam-201	145	8	τ(a)d(b	τ(a)d(b	X
ejpam-201	145	9	)	)	PUNCT
ejpam-201	145	10	)	)	PUNCT
ejpam-201	146	1	=	=	SYM
ejpam-201	146	2	(	(	PUNCT
ejpam-201	146	3	0	0	NUM
ejpam-201	146	4	,	,	PUNCT
ejpam-201	146	5	d(a))(0,σ(b	d(a))(0,σ(b	PROPN
ejpam-201	146	6	)	)	PUNCT
ejpam-201	146	7	)	)	PUNCT
ejpam-201	147	1	+	+	CCONJ
ejpam-201	147	2	(	(	PUNCT
ejpam-201	147	3	0,τ(a))(0	0,τ(a))(0	NUM
ejpam-201	147	4	,	,	PUNCT
ejpam-201	147	5	d(b	d(b	NOUN
ejpam-201	147	6	)	)	PUNCT
ejpam-201	147	7	)	)	PUNCT
ejpam-201	147	8	=	=	SYM
ejpam-201	147	9	d(a)ϕ(σ(b	d(a)ϕ(σ(b	NUM
ejpam-201	147	10	)	)	PUNCT
ejpam-201	147	11	)	)	PUNCT
ejpam-201	148	1	+	+	VERB
ejpam-201	148	2	ϕ(τ(a))d(b	ϕ(τ(a))d(b	X
ejpam-201	148	3	)	)	PUNCT
ejpam-201	148	4	=	=	SYM
ejpam-201	148	5	d(a	d(a	PROPN
ejpam-201	148	6	)	)	PUNCT
ejpam-201	148	7	·	·	PUNCT
ejpam-201	148	8	σ(b	σ(b	PROPN
ejpam-201	148	9	)	)	PUNCT
ejpam-201	149	1	+	+	NOUN
ejpam-201	149	2	τ(a	τ(a	NOUN
ejpam-201	149	3	)	)	PUNCT
ejpam-201	149	4	·	·	PUNCT
ejpam-201	149	5	d(b	d(b	X
ejpam-201	149	6	)	)	PUNCT
ejpam-201	149	7	(	(	PUNCT
ejpam-201	149	8	a	a	PRON
ejpam-201	149	9	,	,	PUNCT
ejpam-201	149	10	b	b	PROPN
ejpam-201	149	11	∈a	∈a	NUM
ejpam-201	149	12	)	)	PUNCT
ejpam-201	149	13	.	.	PUNCT
ejpam-201	150	1	since	since	SCONJ
ejpam-201	150	2	(	(	PUNCT
ejpam-201	150	3	d(a))(ϕ(b	d(a))(ϕ(b	PROPN
ejpam-201	150	4	)	)	PUNCT
ejpam-201	150	5	)	)	PUNCT
ejpam-201	151	1	+	+	CCONJ
ejpam-201	151	2	(	(	PUNCT
ejpam-201	151	3	d(b))(ϕ(a	d(b))(ϕ(a	NOUN
ejpam-201	151	4	)	)	PUNCT
ejpam-201	151	5	)	)	PUNCT
ejpam-201	152	1	=	=	PUNCT
ejpam-201	152	2	(	(	PUNCT
ejpam-201	152	3	0	0	NUM
ejpam-201	152	4	,	,	PUNCT
ejpam-201	152	5	d(a))((b	d(a))((b	NOUN
ejpam-201	152	6	,	,	PUNCT
ejpam-201	152	7	0	0	NUM
ejpam-201	152	8	)	)	PUNCT
ejpam-201	152	9	)	)	PUNCT
ejpam-201	153	1	+	+	CCONJ
ejpam-201	153	2	(	(	PUNCT
ejpam-201	153	3	0	0	NUM
ejpam-201	153	4	,	,	PUNCT
ejpam-201	153	5	d(b))((a	d(b))((a	NOUN
ejpam-201	153	6	,	,	PUNCT
ejpam-201	153	7	0	0	NUM
ejpam-201	153	8	)	)	PUNCT
ejpam-201	153	9	)	)	PUNCT
ejpam-201	154	1	=	=	SYM
ejpam-201	154	2	0	0	NUM
ejpam-201	154	3	,	,	PUNCT
ejpam-201	154	4	we	we	PRON
ejpam-201	154	5	have	have	VERB
ejpam-201	154	6	(	(	PUNCT
ejpam-201	154	7	d(a))(ϕ(b	d(a))(ϕ(b	NUM
ejpam-201	154	8	)	)	PUNCT
ejpam-201	154	9	)	)	PUNCT
ejpam-201	155	1	+	+	CCONJ
ejpam-201	155	2	(	(	PUNCT
ejpam-201	155	3	d(b))(ϕ(a	d(b))(ϕ(a	NOUN
ejpam-201	155	4	)	)	PUNCT
ejpam-201	155	5	)	)	PUNCT
ejpam-201	156	1	=	=	SYM
ejpam-201	156	2	0	0	X
ejpam-201	156	3	.	.	PUNCT
ejpam-201	156	4	m.	m.	NOUN
ejpam-201	156	5	gordji	gordji	PROPN
ejpam-201	156	6	and	and	CCONJ
ejpam-201	156	7	a.	a.	NOUN
ejpam-201	156	8	motlagh	motlagh	PROPN
ejpam-201	156	9	/	/	SYM
ejpam-201	156	10	eur	eur	PROPN
ejpam-201	156	11	.	.	PUNCT
ejpam-201	157	1	j.	j.	PROPN
ejpam-201	157	2	pure	pure	PROPN
ejpam-201	157	3	appl	appl	PROPN
ejpam-201	157	4	.	.	PROPN
ejpam-201	157	5	math	math	PROPN
ejpam-201	157	6	,	,	PUNCT
ejpam-201	157	7	2	2	NUM
ejpam-201	157	8	(	(	PUNCT
ejpam-201	157	9	2009	2009	NUM
ejpam-201	157	10	)	)	PUNCT
ejpam-201	157	11	,	,	PUNCT
ejpam-201	157	12	(	(	PUNCT
ejpam-201	157	13	361	361	NUM
ejpam-201	157	14	-	-	SYM
ejpam-201	157	15	371	371	NUM
ejpam-201	157	16	)	)	PUNCT
ejpam-201	157	17	368	368	NUM
ejpam-201	157	18	it	it	PRON
ejpam-201	157	19	follows	follow	VERB
ejpam-201	157	20	from	from	ADP
ejpam-201	157	21	our	our	PRON
ejpam-201	157	22	assumption	assumption	NOUN
ejpam-201	157	23	that	that	SCONJ
ejpam-201	157	24	d	d	NOUN
ejpam-201	157	25	is	be	AUX
ejpam-201	157	26	a	a	DET
ejpam-201	157	27	(	(	PUNCT
ejpam-201	157	28	σ	σ	NOUN
ejpam-201	157	29	,	,	PUNCT
ejpam-201	157	30	τ)-inner	τ)-inner	PUNCT
ejpam-201	157	31	derivation	derivation	NOUN
ejpam-201	157	32	.	.	PUNCT
ejpam-201	158	1	hence	hence	ADV
ejpam-201	158	2	there	there	PRON
ejpam-201	158	3	are	be	VERB
ejpam-201	158	4	f	f	PROPN
ejpam-201	158	5	∈a	∈a	ADJ
ejpam-201	158	6	∗	∗	NOUN
ejpam-201	158	7	and	and	CCONJ
ejpam-201	158	8	g	g	PROPN
ejpam-201	158	9	∈	∈	PROPN
ejpam-201	158	10	x	x	PUNCT
ejpam-201	158	11	∗	∗	VERB
ejpam-201	158	12	such	such	ADJ
ejpam-201	158	13	that	that	SCONJ
ejpam-201	158	14	(	(	PUNCT
ejpam-201	158	15	0	0	NUM
ejpam-201	158	16	,	,	PUNCT
ejpam-201	158	17	d(a	d(a	PROPN
ejpam-201	158	18	)	)	PUNCT
ejpam-201	158	19	)	)	PUNCT
ejpam-201	159	1	=	=	SYM
ejpam-201	159	2	d(a	d(a	PROPN
ejpam-201	159	3	)	)	PUNCT
ejpam-201	159	4	=	=	PRON
ejpam-201	159	5	(	(	PUNCT
ejpam-201	159	6	σ(a	σ(a	PROPN
ejpam-201	159	7	)	)	PUNCT
ejpam-201	159	8	,	,	PUNCT
ejpam-201	159	9	0	0	NUM
ejpam-201	159	10	)	)	PUNCT
ejpam-201	159	11	(	(	PUNCT
ejpam-201	159	12	f	f	X
ejpam-201	159	13	,	,	PUNCT
ejpam-201	159	14	g)−	g)−	PROPN
ejpam-201	159	15	(	(	PUNCT
ejpam-201	159	16	f	f	PROPN
ejpam-201	159	17	,	,	PUNCT
ejpam-201	159	18	g)(τ(a	g)(τ(a	PROPN
ejpam-201	159	19	)	)	PUNCT
ejpam-201	159	20	,	,	PUNCT
ejpam-201	159	21	0	0	NUM
ejpam-201	159	22	)	)	PUNCT
ejpam-201	159	23	=	=	SYM
ejpam-201	159	24	(	(	PUNCT
ejpam-201	159	25	σ(a	σ(a	PROPN
ejpam-201	159	26	)	)	PUNCT
ejpam-201	159	27	f	f	NOUN
ejpam-201	160	1	−	−	PROPN
ejpam-201	160	2	f	f	X
ejpam-201	160	3	τ(a),σ(a)g	τ(a),σ(a)g	PUNCT
ejpam-201	160	4	−	−	NOUN
ejpam-201	160	5	gτ(a	gτ(a	NOUN
ejpam-201	160	6	)	)	PUNCT
ejpam-201	160	7	)	)	PUNCT
ejpam-201	160	8	.	.	PUNCT
ejpam-201	161	1	thus	thus	ADV
ejpam-201	161	2	d(a	d(a	X
ejpam-201	161	3	)	)	PUNCT
ejpam-201	161	4	=	=	SYM
ejpam-201	161	5	σ(a)g	σ(a)g	PROPN
ejpam-201	161	6	−	−	NOUN
ejpam-201	161	7	gτ(a	gτ(a	NOUN
ejpam-201	161	8	)	)	PUNCT
ejpam-201	161	9	,	,	PUNCT
ejpam-201	161	10	hence	hence	ADV
ejpam-201	161	11	d	d	X
ejpam-201	161	12	is	be	AUX
ejpam-201	161	13	(	(	PUNCT
ejpam-201	161	14	σ	σ	NOUN
ejpam-201	161	15	,	,	PUNCT
ejpam-201	161	16	τ)-inner	τ)-inner	PUNCT
ejpam-201	161	17	derivation	derivation	NOUN
ejpam-201	161	18	.	.	PUNCT
ejpam-201	162	1	definition	definition	NOUN
ejpam-201	162	2	2.1	2.1	NUM
ejpam-201	162	3	.	.	PUNCT
ejpam-201	163	1	leta	leta	PROPN
ejpam-201	163	2	be	be	AUX
ejpam-201	163	3	a	a	DET
ejpam-201	163	4	banach	banach	NOUN
ejpam-201	163	5	algebra	algebra	NOUN
ejpam-201	163	6	and	and	CCONJ
ejpam-201	163	7	σ	σ	PROPN
ejpam-201	163	8	be	be	AUX
ejpam-201	163	9	a	a	DET
ejpam-201	163	10	continuous	continuous	ADJ
ejpam-201	163	11	homomorphisms	homomorphism	NOUN
ejpam-201	163	12	on	on	ADP
ejpam-201	163	13	a	a	PRON
ejpam-201	163	14	.	.	PUNCT
ejpam-201	164	1	the	the	DET
ejpam-201	164	2	banach	banach	NOUN
ejpam-201	164	3	algebra	algebra	NOUN
ejpam-201	164	4	a	a	PRON
ejpam-201	164	5	is	be	AUX
ejpam-201	164	6	called	call	VERB
ejpam-201	164	7	approximately	approximately	ADV
ejpam-201	164	8	σ	σ	NOUN
ejpam-201	164	9	-	-	ADJ
ejpam-201	164	10	contractible	contractible	ADJ
ejpam-201	164	11	,	,	PUNCT
ejpam-201	164	12	if	if	SCONJ
ejpam-201	164	13	for	for	ADP
ejpam-201	164	14	each	each	DET
ejpam-201	164	15	banach	banach	NOUN
ejpam-201	164	16	a	a	DET
ejpam-201	164	17	-bimodule	-bimodule	NOUN
ejpam-201	164	18	x	x	NOUN
ejpam-201	164	19	and	and	CCONJ
ejpam-201	164	20	σ	σ	NOUN
ejpam-201	164	21	-	-	PUNCT
ejpam-201	164	22	derivation	derivation	NOUN
ejpam-201	164	23	d	d	NOUN
ejpam-201	164	24	:	:	PUNCT
ejpam-201	164	25	a	a	DET
ejpam-201	164	26	−→	−→	NOUN
ejpam-201	164	27	x	x	X
ejpam-201	164	28	,	,	PUNCT
ejpam-201	164	29	there	there	PRON
ejpam-201	164	30	exists	exist	VERB
ejpam-201	164	31	a	a	DET
ejpam-201	164	32	bounded	bounded	ADJ
ejpam-201	164	33	net	net	NOUN
ejpam-201	164	34	(	(	PUNCT
ejpam-201	164	35	xα	xα	ADJ
ejpam-201	164	36	)	)	PUNCT
ejpam-201	165	1	⊆	⊆	NUM
ejpam-201	165	2	x	x	X
ejpam-201	165	3	such	such	ADJ
ejpam-201	165	4	that	that	SCONJ
ejpam-201	165	5	d(a	d(a	PROPN
ejpam-201	165	6	)	)	PUNCT
ejpam-201	165	7	=	=	PROPN
ejpam-201	165	8	lim	lim	PROPN
ejpam-201	165	9	α	α	PROPN
ejpam-201	165	10	�	�	PROPN
ejpam-201	165	11	σ(a)xα	σ(a)xα	PART
ejpam-201	165	12	−	−	PROPN
ejpam-201	165	13	xασ(a	xασ(a	PROPN
ejpam-201	165	14	)	)	PUNCT
ejpam-201	165	15	�	�	PROPN
ejpam-201	165	16	(	(	PUNCT
ejpam-201	165	17	a	a	DET
ejpam-201	165	18	∈a	∈a	ADJ
ejpam-201	165	19	)	)	PUNCT
ejpam-201	165	20	.	.	PUNCT
ejpam-201	166	1	in	in	ADP
ejpam-201	166	2	the	the	DET
ejpam-201	166	3	following	follow	VERB
ejpam-201	166	4	theorem	theorem	NOUN
ejpam-201	166	5	we	we	PRON
ejpam-201	166	6	follow	follow	VERB
ejpam-201	166	7	the	the	DET
ejpam-201	166	8	structure	structure	NOUN
ejpam-201	166	9	of	of	ADP
ejpam-201	166	10	proposition	proposition	NOUN
ejpam-201	166	11	2.8.59	2.8.59	NUM
ejpam-201	166	12	[	[	X
ejpam-201	166	13	1	1	NUM
ejpam-201	166	14	]	]	PUNCT
ejpam-201	166	15	.	.	PUNCT
ejpam-201	167	1	theorem	theorem	VERB
ejpam-201	167	2	2.2	2.2	NUM
ejpam-201	167	3	.	.	PUNCT
ejpam-201	168	1	leta	leta	PROPN
ejpam-201	168	2	be	be	AUX
ejpam-201	168	3	a	a	DET
ejpam-201	168	4	banach	banach	NOUN
ejpam-201	168	5	algebra	algebra	NOUN
ejpam-201	168	6	and	and	CCONJ
ejpam-201	168	7	σ	σ	PROPN
ejpam-201	168	8	be	be	VERB
ejpam-201	168	9	a	a	DET
ejpam-201	168	10	bounded	bounded	ADJ
ejpam-201	168	11	homomorphism	homomorphism	NOUN
ejpam-201	168	12	on	on	ADP
ejpam-201	168	13	a	a	PRON
ejpam-201	168	14	.	.	PUNCT
ejpam-201	169	1	then	then	ADV
ejpam-201	169	2	the	the	DET
ejpam-201	169	3	following	follow	VERB
ejpam-201	169	4	assertion	assertion	NOUN
ejpam-201	169	5	are	be	AUX
ejpam-201	169	6	equivalent	equivalent	ADJ
ejpam-201	169	7	:	:	PUNCT
ejpam-201	169	8	1	1	X
ejpam-201	169	9	.	.	X
ejpam-201	169	10	a	a	PRON
ejpam-201	169	11	is	be	AUX
ejpam-201	169	12	σ	σ	NOUN
ejpam-201	169	13	-	-	NOUN
ejpam-201	169	14	amenable	amenable	ADJ
ejpam-201	169	15	.	.	PUNCT
ejpam-201	170	1	2	2	X
ejpam-201	170	2	.	.	X
ejpam-201	170	3	for	for	ADP
ejpam-201	170	4	everya	everya	ADJ
ejpam-201	170	5	-bimodule	-bimodule	PROPN
ejpam-201	170	6	x	x	SYM
ejpam-201	170	7	,	,	PUNCT
ejpam-201	170	8	h1	h1	PROPN
ejpam-201	170	9	(	(	PUNCT
ejpam-201	170	10	σ	σ	PROPN
ejpam-201	170	11	,	,	PUNCT
ejpam-201	170	12	σ	σ	PROPN
ejpam-201	170	13	)	)	PUNCT
ejpam-201	170	14	(	(	PUNCT
ejpam-201	170	15	a	a	PRON
ejpam-201	170	16	,	,	PUNCT
ejpam-201	170	17	x	x	NOUN
ejpam-201	170	18	∗∗	∗∗	NOUN
ejpam-201	170	19	)	)	PUNCT
ejpam-201	170	20	=	=	SYM
ejpam-201	170	21	0	0	NUM
ejpam-201	170	22	3	3	X
ejpam-201	170	23	.	.	PUNCT
ejpam-201	171	1	a	a	PRON
ejpam-201	171	2	is	be	AUX
ejpam-201	171	3	approximately	approximately	ADV
ejpam-201	171	4	σ	σ	NOUN
ejpam-201	171	5	-	-	PUNCT
ejpam-201	171	6	contractible	contractible	ADJ
ejpam-201	171	7	.	.	PUNCT
ejpam-201	172	1	proof	proof	NOUN
ejpam-201	172	2	.	.	PUNCT
ejpam-201	173	1	(	(	PUNCT
ejpam-201	173	2	1)⇒	1)⇒	NUM
ejpam-201	173	3	(	(	PUNCT
ejpam-201	173	4	2	2	NUM
ejpam-201	173	5	)	)	PUNCT
ejpam-201	173	6	is	be	AUX
ejpam-201	173	7	trivially	trivially	ADV
ejpam-201	173	8	.	.	PUNCT
ejpam-201	174	1	(	(	PUNCT
ejpam-201	174	2	2)⇒	2)⇒	NUM
ejpam-201	174	3	(	(	PUNCT
ejpam-201	174	4	3	3	NUM
ejpam-201	174	5	):	):	PUNCT
ejpam-201	174	6	let	let	VERB
ejpam-201	174	7	d	d	NOUN
ejpam-201	174	8	:	:	PUNCT
ejpam-201	174	9	a	a	DET
ejpam-201	174	10	−→	−→	NOUN
ejpam-201	174	11	x	x	PUNCT
ejpam-201	174	12	be	be	AUX
ejpam-201	174	13	a	a	DET
ejpam-201	174	14	σ	σ	NOUN
ejpam-201	174	15	-	-	PUNCT
ejpam-201	174	16	derivation	derivation	NOUN
ejpam-201	174	17	from	from	ADP
ejpam-201	174	18	a	a	PRON
ejpam-201	174	19	into	into	ADP
ejpam-201	174	20	a	a	DET
ejpam-201	174	21	-bimodule	-bimodule	NOUN
ejpam-201	174	22	x	x	NOUN
ejpam-201	174	23	and	and	CCONJ
ejpam-201	174	24	let	let	VERB
ejpam-201	174	25	jx	jx	NOUN
ejpam-201	174	26	:	:	PUNCT
ejpam-201	174	27	x	x	PUNCT
ejpam-201	174	28	−→	−→	NOUN
ejpam-201	174	29	x	x	INTJ
ejpam-201	174	30	∗∗	∗∗	NOUN
ejpam-201	174	31	be	be	VERB
ejpam-201	174	32	the	the	DET
ejpam-201	174	33	canonical	canonical	ADJ
ejpam-201	174	34	embedding	embed	VERB
ejpam-201	174	35	,	,	PUNCT
ejpam-201	174	36	then	then	ADV
ejpam-201	174	37	for	for	SCONJ
ejpam-201	174	38	each	each	DET
ejpam-201	174	39	a	a	PROPN
ejpam-201	174	40	,	,	PUNCT
ejpam-201	174	41	b	b	X
ejpam-201	174	42	∈a	∈a	ADJ
ejpam-201	174	43	we	we	PRON
ejpam-201	174	44	have	have	AUX
ejpam-201	174	45	ed(ab	ed(ab	NOUN
ejpam-201	174	46	)	)	PUNCT
ejpam-201	175	1	=	=	PRON
ejpam-201	176	1	(	(	PUNCT
ejpam-201	176	2	jx	jx	PROPN
ejpam-201	176	3	◦	◦	NOUN
ejpam-201	176	4	d)(ab	d)(ab	NUM
ejpam-201	176	5	)	)	PUNCT
ejpam-201	176	6	=	=	SYM
ejpam-201	176	7	jx	jx	PROPN
ejpam-201	176	8	�	�	PROPN
ejpam-201	176	9	σ(a)d(b	σ(a)d(b	PROPN
ejpam-201	176	10	)	)	PUNCT
ejpam-201	176	11	+	+	NUM
ejpam-201	176	12	d(a)σ(b	d(a)σ(b	PROPN
ejpam-201	176	13	)	)	PUNCT
ejpam-201	176	14	�	�	PROPN
ejpam-201	176	15	m.	m.	NOUN
ejpam-201	176	16	gordji	gordji	PROPN
ejpam-201	176	17	and	and	CCONJ
ejpam-201	176	18	a.	a.	NOUN
ejpam-201	176	19	motlagh	motlagh	PROPN
ejpam-201	176	20	/	/	SYM
ejpam-201	176	21	eur	eur	PROPN
ejpam-201	176	22	.	.	PUNCT
ejpam-201	177	1	j.	j.	PROPN
ejpam-201	177	2	pure	pure	PROPN
ejpam-201	177	3	appl	appl	PROPN
ejpam-201	177	4	.	.	PROPN
ejpam-201	177	5	math	math	PROPN
ejpam-201	177	6	,	,	PUNCT
ejpam-201	177	7	2	2	NUM
ejpam-201	177	8	(	(	PUNCT
ejpam-201	177	9	2009	2009	NUM
ejpam-201	177	10	)	)	PUNCT
ejpam-201	177	11	,	,	PUNCT
ejpam-201	177	12	(	(	PUNCT
ejpam-201	177	13	361	361	NUM
ejpam-201	177	14	-	-	SYM
ejpam-201	177	15	371	371	NUM
ejpam-201	177	16	)	)	PUNCT
ejpam-201	177	17	369	369	NUM
ejpam-201	177	18	=	=	SYM
ejpam-201	177	19	σ(a)ed(b	σ(a)ed(b	X
ejpam-201	177	20	)	)	PUNCT
ejpam-201	177	21	+	+	SYM
ejpam-201	177	22	ed(a)σ(b	ed(a)σ(b	NOUN
ejpam-201	177	23	)	)	PUNCT
ejpam-201	177	24	.	.	PUNCT
ejpam-201	178	1	thus	thus	ADV
ejpam-201	178	2	ed	ed	NOUN
ejpam-201	178	3	is	be	AUX
ejpam-201	178	4	a	a	DET
ejpam-201	178	5	σ	σ	NOUN
ejpam-201	178	6	-	-	PUNCT
ejpam-201	178	7	derivation	derivation	NOUN
ejpam-201	178	8	.	.	PUNCT
ejpam-201	179	1	then	then	ADV
ejpam-201	179	2	by	by	ADP
ejpam-201	179	3	(	(	PUNCT
ejpam-201	179	4	2	2	X
ejpam-201	179	5	)	)	PUNCT
ejpam-201	179	6	there	there	PRON
ejpam-201	179	7	exists	exist	VERB
ejpam-201	179	8	λ	λ	X
ejpam-201	179	9	∈	∈	PROPN
ejpam-201	179	10	x	x	X
ejpam-201	180	1	∗∗	∗∗	X
ejpam-201	180	2	such	such	ADJ
ejpam-201	180	3	that	that	PRON
ejpam-201	180	4	ed(a	ed(a	NOUN
ejpam-201	180	5	)	)	PUNCT
ejpam-201	180	6	=	=	SYM
ejpam-201	180	7	σ(a)λ	σ(a)λ	PROPN
ejpam-201	180	8	−	−	PROPN
ejpam-201	180	9	λσ(a	λσ(a	NUM
ejpam-201	180	10	)	)	PUNCT
ejpam-201	180	11	(	(	PUNCT
ejpam-201	180	12	a	a	DET
ejpam-201	180	13	∈	∈	PROPN
ejpam-201	180	14	a	a	PRON
ejpam-201	180	15	)	)	PUNCT
ejpam-201	180	16	.	.	PUNCT
ejpam-201	181	1	set	set	VERB
ejpam-201	181	2	m	m	NOUN
ejpam-201	181	3	=	=	SYM
ejpam-201	181	4	||λ||,u	||λ||,u	X
ejpam-201	181	5	=	=	SYM
ejpam-201	181	6	x[m	x[m	PROPN
ejpam-201	181	7	]	]	PUNCT
ejpam-201	181	8	.	.	PUNCT
ejpam-201	182	1	then	then	ADV
ejpam-201	182	2	λ	λ	PROPN
ejpam-201	182	3	∈	∈	PROPN
ejpam-201	182	4	jx	jx	PROPN
ejpam-201	182	5	(	(	PUNCT
ejpam-201	182	6	u	u	NOUN
ejpam-201	182	7	)	)	PUNCT
ejpam-201	182	8	w∗	w∗	NOUN
ejpam-201	182	9	.	.	PUNCT
ejpam-201	183	1	let	let	VERB
ejpam-201	183	2	a1	a1	NOUN
ejpam-201	183	3	,	,	PUNCT
ejpam-201	183	4	a2	a2	PROPN
ejpam-201	183	5	,	,	PUNCT
ejpam-201	183	6	a3	a3	NOUN
ejpam-201	183	7	,	,	PUNCT
ejpam-201	183	8	.	.	PUNCT
ejpam-201	183	9	.	.	PUNCT
ejpam-201	184	1	.	.	PUNCT
ejpam-201	185	1	,	,	PUNCT
ejpam-201	185	2	an	an	DET
ejpam-201	185	3	∈a	∈a	ADJ
ejpam-201	185	4	,	,	PUNCT
ejpam-201	185	5	then	then	ADV
ejpam-201	185	6	v	v	NOUN
ejpam-201	185	7	=	=	SYM
ejpam-201	185	8	πn	πn	PUNCT
ejpam-201	186	1	j=1	j=1	PROPN
ejpam-201	186	2	�	�	PROPN
ejpam-201	186	3	σ(a	σ(a	PROPN
ejpam-201	186	4	j)u	j)u	PROPN
ejpam-201	187	1	−uσ(a	−uσ(a	PROPN
ejpam-201	187	2	j	j	PROPN
ejpam-201	187	3	)	)	PUNCT
ejpam-201	187	4	�	�	PROPN
ejpam-201	187	5	is	be	AUX
ejpam-201	187	6	a	a	DET
ejpam-201	187	7	convex	convex	NOUN
ejpam-201	187	8	subset	subset	NOUN
ejpam-201	187	9	of	of	ADP
ejpam-201	187	10	x	x	X
ejpam-201	187	11	(	(	PUNCT
ejpam-201	187	12	n	n	CCONJ
ejpam-201	187	13	)	)	PUNCT
ejpam-201	187	14	and	and	CCONJ
ejpam-201	187	15	(	(	PUNCT
ejpam-201	187	16	d(a1	d(a1	NOUN
ejpam-201	187	17	)	)	PUNCT
ejpam-201	187	18	,	,	PUNCT
ejpam-201	187	19	d(a2	d(a2	NOUN
ejpam-201	187	20	)	)	PUNCT
ejpam-201	187	21	,	,	PUNCT
ejpam-201	187	22	.	.	PUNCT
ejpam-201	187	23	.	.	PUNCT
ejpam-201	188	1	.	.	PUNCT
ejpam-201	189	1	,	,	PUNCT
ejpam-201	189	2	d(an	d(an	NOUN
ejpam-201	189	3	)	)	PUNCT
ejpam-201	189	4	)	)	PUNCT
ejpam-201	189	5	∈	∈	PROPN
ejpam-201	189	6	v	v	ADP
ejpam-201	189	7	weak	weak	ADJ
ejpam-201	189	8	.	.	PUNCT
ejpam-201	190	1	thus	thus	ADV
ejpam-201	190	2	for	for	ADP
ejpam-201	190	3	each	each	DET
ejpam-201	190	4	finite	finite	PROPN
ejpam-201	190	5	subset	subset	VERB
ejpam-201	190	6	f	f	PROPN
ejpam-201	190	7	ofa	ofa	PROPN
ejpam-201	190	8	,	,	PUNCT
ejpam-201	190	9	and	and	CCONJ
ejpam-201	190	10	ǫ	ǫ	X
ejpam-201	190	11	>	>	X
ejpam-201	190	12	0	0	NUM
ejpam-201	190	13	,	,	PUNCT
ejpam-201	190	14	there	there	PRON
ejpam-201	190	15	exists	exist	VERB
ejpam-201	190	16	x(f	x(f	PROPN
ejpam-201	190	17	,	,	PUNCT
ejpam-201	190	18	ǫ	ǫ	NOUN
ejpam-201	190	19	)	)	PUNCT
ejpam-201	190	20	∈u	∈u	VERB
ejpam-201	190	21	such	such	ADJ
ejpam-201	190	22	that	that	SCONJ
ejpam-201	190	23	||d(a)−	||d(a)−	PROPN
ejpam-201	190	24	(	(	PUNCT
ejpam-201	190	25	σ(a)x(f	σ(a)x(f	NOUN
ejpam-201	190	26	,	,	PUNCT
ejpam-201	190	27	ǫ	ǫ	NOUN
ejpam-201	190	28	)	)	PUNCT
ejpam-201	190	29	−	−	ADP
ejpam-201	190	30	x(f	x(f	NOUN
ejpam-201	190	31	,	,	PUNCT
ejpam-201	190	32	ǫ)σ(a))||	ǫ)σ(a))||	NUM
ejpam-201	190	33	<	<	X
ejpam-201	190	34	ǫ	ǫ	X
ejpam-201	190	35	(	(	PUNCT
ejpam-201	190	36	a	a	DET
ejpam-201	190	37	∈	∈	ADJ
ejpam-201	190	38	f	f	X
ejpam-201	190	39	)	)	PUNCT
ejpam-201	190	40	.	.	PUNCT
ejpam-201	191	1	the	the	DET
ejpam-201	191	2	family	family	NOUN
ejpam-201	191	3	of	of	ADP
ejpam-201	191	4	such	such	ADJ
ejpam-201	191	5	pairs	pair	NOUN
ejpam-201	191	6	(	(	PUNCT
ejpam-201	191	7	f	f	X
ejpam-201	191	8	,	,	PUNCT
ejpam-201	191	9	ǫ	ǫ	NOUN
ejpam-201	191	10	)	)	PUNCT
ejpam-201	191	11	is	be	AUX
ejpam-201	191	12	a	a	DET
ejpam-201	191	13	directed	direct	VERB
ejpam-201	191	14	if	if	SCONJ
ejpam-201	191	15	order	order	NOUN
ejpam-201	191	16	≤	≤	NOUN
ejpam-201	191	17	given	give	VERB
ejpam-201	191	18	by	by	ADP
ejpam-201	191	19	(	(	PUNCT
ejpam-201	191	20	f1,ǫ1)≤	f1,ǫ1)≤	PROPN
ejpam-201	191	21	(	(	PUNCT
ejpam-201	191	22	f2,ǫ2)⇔	f2,ǫ2)⇔	PROPN
ejpam-201	191	23	f1	f1	PROPN
ejpam-201	191	24	⊆	⊆	NUM
ejpam-201	191	25	f2,ǫ1	f2,ǫ1	PROPN
ejpam-201	191	26	≤	≤	PROPN
ejpam-201	191	27	ǫ2	ǫ2	NOUN
ejpam-201	191	28	.	.	PUNCT
ejpam-201	192	1	also	also	ADV
ejpam-201	192	2	we	we	PRON
ejpam-201	192	3	have	have	VERB
ejpam-201	192	4	d(a	d(a	PROPN
ejpam-201	192	5	)	)	PUNCT
ejpam-201	193	1	=	=	SYM
ejpam-201	193	2	lim	lim	PROPN
ejpam-201	193	3	(	(	PUNCT
ejpam-201	193	4	f	f	PROPN
ejpam-201	193	5	,	,	PUNCT
ejpam-201	193	6	ǫ	ǫ	NOUN
ejpam-201	193	7	)	)	PUNCT
ejpam-201	193	8	�	�	PROPN
ejpam-201	193	9	σ(a)x(f	σ(a)x(f	NOUN
ejpam-201	193	10	,	,	PUNCT
ejpam-201	193	11	ǫ	ǫ	NOUN
ejpam-201	193	12	)	)	PUNCT
ejpam-201	193	13	−	−	ADP
ejpam-201	193	14	x(f	x(f	NOUN
ejpam-201	193	15	,	,	PUNCT
ejpam-201	193	16	ǫ)σ(a	ǫ)σ(a	NOUN
ejpam-201	193	17	)	)	PUNCT
ejpam-201	193	18	�	�	PROPN
ejpam-201	193	19	.	.	PUNCT
ejpam-201	194	1	(	(	PUNCT
ejpam-201	194	2	3)⇒	3)⇒	NUM
ejpam-201	194	3	(	(	PUNCT
ejpam-201	194	4	1	1	NUM
ejpam-201	194	5	):	):	PUNCT
ejpam-201	194	6	let	let	VERB
ejpam-201	194	7	d	d	NOUN
ejpam-201	194	8	:	:	PUNCT
ejpam-201	194	9	a	a	DET
ejpam-201	194	10	−→	−→	NOUN
ejpam-201	194	11	x	x	SYM
ejpam-201	194	12	∗	∗	NOUN
ejpam-201	194	13	be	be	VERB
ejpam-201	194	14	a	a	DET
ejpam-201	194	15	σ	σ	NOUN
ejpam-201	194	16	-	-	PUNCT
ejpam-201	194	17	derivation	derivation	NOUN
ejpam-201	194	18	.	.	PUNCT
ejpam-201	195	1	then	then	ADV
ejpam-201	195	2	there	there	PRON
ejpam-201	195	3	exists	exist	VERB
ejpam-201	195	4	a	a	DET
ejpam-201	195	5	net	net	NOUN
ejpam-201	195	6	(	(	PUNCT
ejpam-201	195	7	x	x	NOUN
ejpam-201	195	8	′	′	NUM
ejpam-201	195	9	α	α	NOUN
ejpam-201	195	10	)	)	PUNCT
ejpam-201	196	1	⊆	⊆	NUM
ejpam-201	196	2	x	x	SYM
ejpam-201	196	3	∗	∗	NOUN
ejpam-201	196	4	such	such	ADJ
ejpam-201	196	5	that	that	SCONJ
ejpam-201	196	6	d(a	d(a	PROPN
ejpam-201	196	7	)	)	PUNCT
ejpam-201	196	8	=	=	SYM
ejpam-201	196	9	limα	limα	PROPN
ejpam-201	196	10	�	�	PROPN
ejpam-201	196	11	σ(a)x	σ(a)x	PROPN
ejpam-201	196	12	′	′	NUM
ejpam-201	196	13	α	α	NOUN
ejpam-201	196	14	−	−	NOUN
ejpam-201	196	15	x	x	PUNCT
ejpam-201	196	16	′	′	NUM
ejpam-201	196	17	α	α	PROPN
ejpam-201	196	18	σ(a	σ(a	PROPN
ejpam-201	196	19	)	)	PUNCT
ejpam-201	196	20	�	�	PROPN
ejpam-201	196	21	(	(	PUNCT
ejpam-201	196	22	a	a	DET
ejpam-201	196	23	∈	∈	PROPN
ejpam-201	196	24	a	a	PRON
ejpam-201	196	25	)	)	PUNCT
ejpam-201	196	26	.	.	PUNCT
ejpam-201	197	1	by	by	ADP
ejpam-201	197	2	passing	pass	VERB
ejpam-201	197	3	to	to	ADP
ejpam-201	197	4	a	a	DET
ejpam-201	197	5	subnet	subnet	NOUN
ejpam-201	197	6	we	we	PRON
ejpam-201	197	7	may	may	AUX
ejpam-201	197	8	assume	assume	VERB
ejpam-201	197	9	that	that	SCONJ
ejpam-201	197	10	w∗	w∗	NOUN
ejpam-201	197	11	−	−	PROPN
ejpam-201	197	12	lim	lim	NOUN
ejpam-201	197	13	x	x	PROPN
ejpam-201	198	1	′	′	NUM
ejpam-201	198	2	α	α	NOUN
ejpam-201	198	3	=	=	PUNCT
ejpam-201	198	4	x	x	SYM
ejpam-201	198	5	′	′	NOUN
ejpam-201	198	6	in	in	ADP
ejpam-201	198	7	x	x	PROPN
ejpam-201	198	8	∗	∗	NOUN
ejpam-201	198	9	and	and	CCONJ
ejpam-201	198	10	then	then	ADV
ejpam-201	198	11	d(a	d(a	PROPN
ejpam-201	198	12	)	)	PUNCT
ejpam-201	198	13	=	=	PUNCT
ejpam-201	199	1	σ(a)x	σ(a)x	PROPN
ejpam-201	199	2	′	′	NOUN
ejpam-201	200	1	−	−	PUNCT
ejpam-201	200	2	x	x	SYM
ejpam-201	200	3	′σ(a	′σ(a	NUM
ejpam-201	200	4	)	)	PUNCT
ejpam-201	200	5	.	.	PUNCT
ejpam-201	201	1	thus	thus	ADV
ejpam-201	201	2	a	a	PRON
ejpam-201	201	3	is	be	AUX
ejpam-201	201	4	σ	σ	NOUN
ejpam-201	201	5	-	-	NOUN
ejpam-201	201	6	amenable	amenable	ADJ
ejpam-201	201	7	.	.	PUNCT
ejpam-201	202	1	theorem	theorem	VERB
ejpam-201	202	2	2.3	2.3	NUM
ejpam-201	202	3	.	.	PUNCT
ejpam-201	203	1	let	let	VERB
ejpam-201	203	2	a	a	PRON
ejpam-201	203	3	be	be	AUX
ejpam-201	203	4	a	a	DET
ejpam-201	203	5	banach	banach	NOUN
ejpam-201	203	6	algebra	algebra	NOUN
ejpam-201	203	7	and	and	CCONJ
ejpam-201	203	8	σ	σ	PROPN
ejpam-201	203	9	be	be	AUX
ejpam-201	203	10	a	a	DET
ejpam-201	203	11	continuous	continuous	ADJ
ejpam-201	203	12	homomorphism	homomorphism	NOUN
ejpam-201	203	13	on	on	ADP
ejpam-201	203	14	a	a	PRON
ejpam-201	203	15	.	.	PUNCT
ejpam-201	204	1	ifa	ifa	PROPN
ejpam-201	204	2	∗∗	∗∗	PROPN
ejpam-201	204	3	is	be	AUX
ejpam-201	204	4	σ′′-amenable	σ′′-amenable	ADJ
ejpam-201	204	5	,	,	PUNCT
ejpam-201	204	6	thena	thena	ADJ
ejpam-201	204	7	is	be	AUX
ejpam-201	204	8	σ	σ	NOUN
ejpam-201	204	9	-	-	NOUN
ejpam-201	204	10	amenable	amenable	ADJ
ejpam-201	204	11	.	.	PUNCT
ejpam-201	205	1	proof	proof	NOUN
ejpam-201	205	2	.	.	PUNCT
ejpam-201	206	1	let	let	VERB
ejpam-201	206	2	x	x	PRON
ejpam-201	206	3	be	be	AUX
ejpam-201	206	4	a	a	DET
ejpam-201	206	5	banach	banach	NOUN
ejpam-201	206	6	a	a	DET
ejpam-201	206	7	-bimodule	-bimodule	NOUN
ejpam-201	206	8	,	,	PUNCT
ejpam-201	206	9	and	and	CCONJ
ejpam-201	206	10	d	d	NOUN
ejpam-201	206	11	:	:	PUNCT
ejpam-201	206	12	a	a	DET
ejpam-201	206	13	−→	−→	NOUN
ejpam-201	206	14	x	x	X
ejpam-201	206	15	∗∗	∗∗	NOUN
ejpam-201	206	16	be	be	AUX
ejpam-201	206	17	a	a	DET
ejpam-201	206	18	σ	σ	NOUN
ejpam-201	206	19	-	-	PUNCT
ejpam-201	206	20	derivation	derivation	NOUN
ejpam-201	206	21	.	.	PUNCT
ejpam-201	207	1	then	then	ADV
ejpam-201	207	2	by	by	ADP
ejpam-201	207	3	lemma	lemma	PROPN
ejpam-201	207	4	2.1	2.1	NUM
ejpam-201	207	5	,	,	PUNCT
ejpam-201	207	6	d′′	d′′	NOUN
ejpam-201	207	7	:	:	PUNCT
ejpam-201	207	8	a	a	DET
ejpam-201	207	9	∗∗	∗∗	NOUN
ejpam-201	207	10	−→	−→	NOUN
ejpam-201	207	11	x	x	SYM
ejpam-201	207	12	∗∗∗∗	∗∗∗∗	PRON
ejpam-201	207	13	is	be	AUX
ejpam-201	207	14	a	a	DET
ejpam-201	207	15	σ′′-derivation	σ′′-derivation	NOUN
ejpam-201	207	16	.	.	PUNCT
ejpam-201	208	1	since	since	SCONJ
ejpam-201	208	2	a	a	DET
ejpam-201	208	3	∗∗	∗∗	PROPN
ejpam-201	208	4	is	be	AUX
ejpam-201	208	5	σ′′amenable	σ′′amenable	ADJ
ejpam-201	208	6	,	,	PUNCT
ejpam-201	208	7	then	then	ADV
ejpam-201	208	8	there	there	PRON
ejpam-201	208	9	exists	exist	VERB
ejpam-201	208	10	x	x	PUNCT
ejpam-201	208	11	(	(	PUNCT
ejpam-201	208	12	4	4	X
ejpam-201	208	13	)	)	PUNCT
ejpam-201	208	14	∈	∈	PROPN
ejpam-201	208	15	x	x	PUNCT
ejpam-201	208	16	∗∗∗∗	∗∗∗∗	NOUN
ejpam-201	208	17	such	such	ADJ
ejpam-201	208	18	that	that	DET
ejpam-201	208	19	d′′(a′′	d′′(a′′	NOUN
ejpam-201	208	20	)	)	PUNCT
ejpam-201	208	21	=	=	SYM
ejpam-201	209	1	σ′′(a′′)x	σ′′(a′′)x	PROPN
ejpam-201	209	2	(	(	PUNCT
ejpam-201	209	3	4)−	4)−	NOUN
ejpam-201	209	4	x	x	X
ejpam-201	209	5	(	(	PUNCT
ejpam-201	209	6	4)σ′′(a′′	4)σ′′(a′′	NOUN
ejpam-201	209	7	)	)	PUNCT
ejpam-201	209	8	,	,	PUNCT
ejpam-201	209	9	(	(	PUNCT
ejpam-201	209	10	a′′	a′′	NOUN
ejpam-201	209	11	∈a	∈a	ADJ
ejpam-201	209	12	∗∗	∗∗	PROPN
ejpam-201	209	13	)	)	PUNCT
ejpam-201	209	14	.	.	PUNCT
ejpam-201	210	1	we	we	PRON
ejpam-201	210	2	havex	havex	VERB
ejpam-201	210	3	∗∗∗∗	∗∗∗∗	NOUN
ejpam-201	210	4	=	=	NOUN
ejpam-201	210	5	x	x	NOUN
ejpam-201	210	6	∗∗⊕(x	∗∗⊕(x	NOUN
ejpam-201	210	7	∗)⊥	∗)⊥	PROPN
ejpam-201	210	8	(	(	PUNCT
ejpam-201	210	9	asa	asa	PROPN
ejpam-201	210	10	∗∗-bimodules	∗∗-bimodules	PROPN
ejpam-201	210	11	)	)	PUNCT
ejpam-201	210	12	.	.	PUNCT
ejpam-201	211	1	let	let	VERB
ejpam-201	211	2	p	p	NOUN
ejpam-201	211	3	:x	:x	PROPN
ejpam-201	211	4	∗∗∗∗	∗∗∗∗	NOUN
ejpam-201	211	5	−→x	−→x	X
ejpam-201	211	6	∗∗	∗∗	X
ejpam-201	211	7	be	be	VERB
ejpam-201	211	8	the	the	DET
ejpam-201	211	9	natural	natural	ADJ
ejpam-201	211	10	projection	projection	NOUN
ejpam-201	211	11	.	.	PUNCT
ejpam-201	212	1	then	then	ADV
ejpam-201	212	2	for	for	ADP
ejpam-201	212	3	each	each	PRON
ejpam-201	212	4	a	a	DET
ejpam-201	212	5	∈	∈	PROPN
ejpam-201	212	6	a	a	PRON
ejpam-201	212	7	,	,	PUNCT
ejpam-201	212	8	we	we	PRON
ejpam-201	212	9	have	have	VERB
ejpam-201	212	10	d(a	d(a	PROPN
ejpam-201	212	11	)	)	PUNCT
ejpam-201	213	1	=	=	NOUN
ejpam-201	213	2	σ(a)p(x	σ(a)p(x	NOUN
ejpam-201	213	3	(	(	PUNCT
ejpam-201	213	4	4	4	NUM
ejpam-201	213	5	)	)	PUNCT
ejpam-201	213	6	)	)	PUNCT
ejpam-201	214	1	−	−	PROPN
ejpam-201	214	2	p(x	p(x	NOUN
ejpam-201	214	3	(	(	PUNCT
ejpam-201	214	4	4))σ(a	4))σ(a	NOUN
ejpam-201	214	5	)	)	PUNCT
ejpam-201	214	6	,	,	PUNCT
ejpam-201	214	7	and	and	CCONJ
ejpam-201	214	8	so	so	ADV
ejpam-201	214	9	d	d	ADP
ejpam-201	214	10	∈	∈	PROPN
ejpam-201	214	11	n	n	PRON
ejpam-201	214	12	1	1	NUM
ejpam-201	214	13	(	(	PUNCT
ejpam-201	214	14	σ	σ	PROPN
ejpam-201	214	15	,	,	PUNCT
ejpam-201	214	16	σ	σ	PROPN
ejpam-201	214	17	)	)	PUNCT
ejpam-201	214	18	(	(	PUNCT
ejpam-201	214	19	a	a	DET
ejpam-201	214	20	,	,	PUNCT
ejpam-201	214	21	x	x	NOUN
ejpam-201	214	22	∗∗	∗∗	NOUN
ejpam-201	214	23	)	)	PUNCT
ejpam-201	214	24	.	.	PUNCT
ejpam-201	215	1	thus	thus	ADV
ejpam-201	215	2	by	by	ADP
ejpam-201	215	3	above	above	ADP
ejpam-201	215	4	theorem	theorem	PROPN
ejpam-201	215	5	,	,	PUNCT
ejpam-201	215	6	a	a	PRON
ejpam-201	215	7	is	be	AUX
ejpam-201	215	8	σ	σ	NOUN
ejpam-201	215	9	-	-	NOUN
ejpam-201	215	10	amenable	amenable	ADJ
ejpam-201	215	11	.	.	PUNCT
ejpam-201	216	1	references	reference	NOUN
ejpam-201	216	2	370	370	NUM
ejpam-201	216	3	in	in	ADP
ejpam-201	216	4	the	the	DET
ejpam-201	216	5	following	following	NOUN
ejpam-201	216	6	we	we	PRON
ejpam-201	216	7	fined	fine	VERB
ejpam-201	216	8	an	an	DET
ejpam-201	216	9	easy	easy	ADJ
ejpam-201	216	10	equivalent	equivalent	ADJ
ejpam-201	216	11	condition	condition	NOUN
ejpam-201	216	12	for	for	ADP
ejpam-201	216	13	σ	σ	PROPN
ejpam-201	216	14	-	-	PUNCT
ejpam-201	216	15	amenability	amenability	NOUN
ejpam-201	216	16	of	of	ADP
ejpam-201	216	17	a	a	DET
ejpam-201	216	18	banach	banach	NOUN
ejpam-201	216	19	algebra	algebra	NOUN
ejpam-201	216	20	.	.	PUNCT
ejpam-201	217	1	proposition	proposition	NOUN
ejpam-201	217	2	2.1	2.1	NUM
ejpam-201	217	3	.	.	PUNCT
ejpam-201	218	1	leta	leta	PROPN
ejpam-201	218	2	be	be	AUX
ejpam-201	218	3	a	a	DET
ejpam-201	218	4	banach	banach	NOUN
ejpam-201	218	5	algebra	algebra	NOUN
ejpam-201	218	6	and	and	CCONJ
ejpam-201	218	7	let	let	VERB
ejpam-201	218	8	σ	σ	NOUN
ejpam-201	218	9	be	be	AUX
ejpam-201	218	10	a	a	DET
ejpam-201	218	11	continuous	continuous	ADJ
ejpam-201	218	12	homomorphism	homomorphism	NOUN
ejpam-201	218	13	on	on	ADP
ejpam-201	218	14	a	a	PRON
ejpam-201	218	15	.	.	PUNCT
ejpam-201	219	1	then	then	ADV
ejpam-201	219	2	a	a	PRON
ejpam-201	219	3	is	be	AUX
ejpam-201	219	4	a	a	DET
ejpam-201	219	5	σ	σ	NOUN
ejpam-201	219	6	-	-	NOUN
ejpam-201	219	7	amenable	amenable	ADJ
ejpam-201	219	8	if	if	SCONJ
ejpam-201	219	9	and	and	CCONJ
ejpam-201	219	10	only	only	ADV
ejpam-201	219	11	if	if	SCONJ
ejpam-201	219	12	for	for	ADP
ejpam-201	219	13	every	every	DET
ejpam-201	219	14	banach	banach	NOUN
ejpam-201	219	15	algebra	algebra	NOUN
ejpam-201	219	16	b	b	NOUN
ejpam-201	219	17	and	and	CCONJ
ejpam-201	219	18	every	every	DET
ejpam-201	219	19	injective	injective	ADJ
ejpam-201	219	20	homomorphism	homomorphism	PROPN
ejpam-201	219	21	ϕ	ϕ	NOUN
ejpam-201	219	22	:	:	PUNCT
ejpam-201	219	23	a	a	DET
ejpam-201	219	24	−→b	−→b	NOUN
ejpam-201	219	25	,	,	PUNCT
ejpam-201	219	26	h1	h1	PROPN
ejpam-201	219	27	(	(	PUNCT
ejpam-201	219	28	σ	σ	PROPN
ejpam-201	219	29	,	,	PUNCT
ejpam-201	219	30	σ	σ	PROPN
ejpam-201	219	31	)	)	PUNCT
ejpam-201	219	32	(	(	PUNCT
ejpam-201	219	33	a	a	PRON
ejpam-201	219	34	,	,	PUNCT
ejpam-201	219	35	b∗∗	b∗∗	NOUN
ejpam-201	219	36	ϕ	ϕ	NOUN
ejpam-201	219	37	)	)	PUNCT
ejpam-201	220	1	=	=	SYM
ejpam-201	220	2	0	0	X
ejpam-201	220	3	.	.	PUNCT
ejpam-201	220	4	proof	proof	NOUN
ejpam-201	220	5	.	.	PUNCT
ejpam-201	221	1	one	one	NUM
ejpam-201	221	2	side	side	NOUN
ejpam-201	221	3	is	be	AUX
ejpam-201	221	4	clear	clear	ADJ
ejpam-201	221	5	,	,	PUNCT
ejpam-201	221	6	so	so	ADV
ejpam-201	221	7	we	we	PRON
ejpam-201	221	8	prove	prove	VERB
ejpam-201	221	9	the	the	DET
ejpam-201	221	10	other	other	ADJ
ejpam-201	221	11	side	side	NOUN
ejpam-201	221	12	.	.	PUNCT
ejpam-201	222	1	let	let	VERB
ejpam-201	222	2	x	x	PRON
ejpam-201	222	3	be	be	AUX
ejpam-201	222	4	a	a	DET
ejpam-201	222	5	banach	banach	NOUN
ejpam-201	222	6	a	a	DET
ejpam-201	222	7	bimodule	bimodule	NOUN
ejpam-201	222	8	and	and	CCONJ
ejpam-201	222	9	d	d	NOUN
ejpam-201	222	10	:	:	PUNCT
ejpam-201	222	11	a	a	DET
ejpam-201	222	12	−→x	−→x	ADJ
ejpam-201	222	13	∗∗	∗∗	NOUN
ejpam-201	222	14	be	be	AUX
ejpam-201	222	15	a	a	DET
ejpam-201	222	16	σ	σ	NOUN
ejpam-201	222	17	-	-	NOUN
ejpam-201	222	18	derivation	derivation	NOUN
ejpam-201	222	19	.	.	PUNCT
ejpam-201	223	1	if	if	SCONJ
ejpam-201	223	2	φ	φ	PROPN
ejpam-201	223	3	:	:	PUNCT
ejpam-201	223	4	a	a	DET
ejpam-201	223	5	−→a	−→a	PROPN
ejpam-201	223	6	⊕1x	⊕1x	PRON
ejpam-201	223	7	is	be	AUX
ejpam-201	223	8	defined	define	VERB
ejpam-201	223	9	by	by	ADP
ejpam-201	223	10	ϕ(a	ϕ(a	NOUN
ejpam-201	223	11	)	)	PUNCT
ejpam-201	223	12	=	=	SYM
ejpam-201	223	13	(	(	PUNCT
ejpam-201	223	14	a	a	PRON
ejpam-201	223	15	,	,	PUNCT
ejpam-201	223	16	0	0	NUM
ejpam-201	223	17	)	)	PUNCT
ejpam-201	223	18	.	.	PUNCT
ejpam-201	224	1	then	then	ADV
ejpam-201	224	2	ϕ	ϕ	PROPN
ejpam-201	224	3	is	be	AUX
ejpam-201	224	4	injective	injective	ADJ
ejpam-201	224	5	and	and	CCONJ
ejpam-201	224	6	ϕ∗∗	ϕ∗∗	NOUN
ejpam-201	224	7	:	:	PUNCT
ejpam-201	224	8	a	a	DET
ejpam-201	224	9	∗∗	∗∗	PROPN
ejpam-201	224	10	−→	−→	NOUN
ejpam-201	224	11	(	(	PUNCT
ejpam-201	224	12	a⊕1x	a⊕1x	PROPN
ejpam-201	224	13	)	)	PUNCT
ejpam-201	225	1	∗∗	∗∗	PROPN
ejpam-201	225	2	the	the	DET
ejpam-201	225	3	second	second	ADJ
ejpam-201	225	4	transpose	transpose	NOUN
ejpam-201	225	5	of	of	ADP
ejpam-201	225	6	ϕ	ϕ	PROPN
ejpam-201	225	7	is	be	AUX
ejpam-201	225	8	a	a	DET
ejpam-201	225	9	banach	banach	NOUN
ejpam-201	225	10	algebra	algebra	NOUN
ejpam-201	225	11	homomorphism	homomorphism	NOUN
ejpam-201	225	12	and	and	CCONJ
ejpam-201	226	1	(	(	PUNCT
ejpam-201	226	2	(	(	PUNCT
ejpam-201	226	3	a	a	PRON
ejpam-201	226	4	⊕1	⊕1	PROPN
ejpam-201	226	5	x	x	SYM
ejpam-201	226	6	)	)	PUNCT
ejpam-201	226	7	ϕ	ϕ	X
ejpam-201	226	8	)	)	PUNCT
ejpam-201	226	9	∗∗	∗∗	NOUN
ejpam-201	226	10	≃	≃	NOUN
ejpam-201	226	11	(	(	PUNCT
ejpam-201	226	12	a	a	DET
ejpam-201	226	13	∗∗	∗∗	PROPN
ejpam-201	226	14	⊕1	⊕1	PROPN
ejpam-201	226	15	x	x	SYM
ejpam-201	226	16	∗∗)ϕ∗∗	∗∗)ϕ∗∗	PROPN
ejpam-201	226	17	as	as	ADP
ejpam-201	226	18	a	a	DET
ejpam-201	226	19	∗∗-bimodules	∗∗-bimodule	NOUN
ejpam-201	226	20	.	.	PUNCT
ejpam-201	227	1	then	then	ADV
ejpam-201	227	2	h1	h1	PROPN
ejpam-201	227	3	(	(	PUNCT
ejpam-201	227	4	σ	σ	PROPN
ejpam-201	227	5	,	,	PUNCT
ejpam-201	227	6	σ	σ	PROPN
ejpam-201	227	7	)	)	PUNCT
ejpam-201	227	8	(	(	PUNCT
ejpam-201	227	9	a	a	DET
ejpam-201	227	10	,	,	PUNCT
ejpam-201	227	11	(	(	PUNCT
ejpam-201	227	12	a	a	DET
ejpam-201	227	13	∗∗⊕1x	∗∗⊕1x	PROPN
ejpam-201	227	14	∗∗)ϕ∗∗	∗∗)ϕ∗∗	PROPN
ejpam-201	227	15	)	)	PUNCT
ejpam-201	227	16	=	=	PRON
ejpam-201	227	17	h1	h1	NOUN
ejpam-201	227	18	(	(	PUNCT
ejpam-201	227	19	σ	σ	PROPN
ejpam-201	227	20	,	,	PUNCT
ejpam-201	227	21	σ	σ	PROPN
ejpam-201	227	22	)	)	PUNCT
ejpam-201	227	23	(	(	PUNCT
ejpam-201	227	24	a	a	DET
ejpam-201	227	25	,	,	PUNCT
ejpam-201	227	26	(	(	PUNCT
ejpam-201	227	27	(	(	PUNCT
ejpam-201	227	28	a	a	DET
ejpam-201	227	29	⊕1x	⊕1x	PROPN
ejpam-201	227	30	)	)	PUNCT
ejpam-201	227	31	ϕ	ϕ	NOUN
ejpam-201	227	32	)	)	PUNCT
ejpam-201	227	33	∗∗	∗∗	NOUN
ejpam-201	227	34	)	)	PUNCT
ejpam-201	227	35	=	=	PRON
ejpam-201	227	36	{	{	PUNCT
ejpam-201	227	37	0	0	NUM
ejpam-201	227	38	}	}	PUNCT
ejpam-201	227	39	.	.	PUNCT
ejpam-201	228	1	(	(	PUNCT
ejpam-201	228	2	2.2	2.2	NUM
ejpam-201	228	3	)	)	PUNCT
ejpam-201	228	4	now	now	ADV
ejpam-201	228	5	we	we	PRON
ejpam-201	228	6	define	define	VERB
ejpam-201	228	7	d1	d1	PROPN
ejpam-201	228	8	:	:	PUNCT
ejpam-201	228	9	a	a	DET
ejpam-201	228	10	−→	−→	NOUN
ejpam-201	228	11	a	a	DET
ejpam-201	228	12	∗∗	∗∗	NOUN
ejpam-201	228	13	⊕1	⊕1	PROPN
ejpam-201	228	14	x	x	SYM
ejpam-201	229	1	∗∗	∗∗	X
ejpam-201	229	2	by	by	ADP
ejpam-201	229	3	d1(a	d1(a	PROPN
ejpam-201	229	4	)	)	PUNCT
ejpam-201	229	5	=	=	SYM
ejpam-201	229	6	(	(	PUNCT
ejpam-201	229	7	0	0	NUM
ejpam-201	229	8	,	,	PUNCT
ejpam-201	229	9	d(a	d(a	PROPN
ejpam-201	229	10	)	)	PUNCT
ejpam-201	229	11	)	)	PUNCT
ejpam-201	229	12	.	.	PUNCT
ejpam-201	230	1	for	for	ADP
ejpam-201	230	2	a	a	DET
ejpam-201	230	3	,	,	PUNCT
ejpam-201	230	4	b	b	X
ejpam-201	230	5	∈	∈	PROPN
ejpam-201	230	6	a	a	DET
ejpam-201	230	7	we	we	PRON
ejpam-201	230	8	have	have	VERB
ejpam-201	230	9	d1(ab	d1(ab	NOUN
ejpam-201	230	10	)	)	PUNCT
ejpam-201	230	11	=	=	SYM
ejpam-201	230	12	d1(a)ϕ	d1(a)ϕ	ADJ
ejpam-201	230	13	∗∗(bb	∗∗(bb	NOUN
ejpam-201	230	14	)	)	PUNCT
ejpam-201	230	15	+	+	NUM
ejpam-201	230	16	ϕ∗∗(ba)d1(b	ϕ∗∗(ba)d1(b	NOUN
ejpam-201	230	17	)	)	PUNCT
ejpam-201	230	18	.	.	PUNCT
ejpam-201	231	1	thus	thus	ADV
ejpam-201	231	2	d1	d1	PROPN
ejpam-201	231	3	is	be	AUX
ejpam-201	231	4	a	a	DET
ejpam-201	231	5	σ	σ	NOUN
ejpam-201	231	6	-	-	PUNCT
ejpam-201	231	7	derivation	derivation	NOUN
ejpam-201	231	8	from	from	ADP
ejpam-201	231	9	a	a	DET
ejpam-201	231	10	into	into	ADP
ejpam-201	231	11	(	(	PUNCT
ejpam-201	231	12	a	a	DET
ejpam-201	231	13	∗∗	∗∗	PROPN
ejpam-201	231	14	⊕1x	⊕1x	PROPN
ejpam-201	231	15	∗∗)ϕ∗∗	∗∗)ϕ∗∗	PROPN
ejpam-201	231	16	.	.	PUNCT
ejpam-201	232	1	by	by	ADP
ejpam-201	232	2	(	(	PUNCT
ejpam-201	232	3	2.2	2.2	NUM
ejpam-201	232	4	)	)	PUNCT
ejpam-201	232	5	,	,	PUNCT
ejpam-201	232	6	d1	d1	PROPN
ejpam-201	232	7	is	be	AUX
ejpam-201	232	8	σ	σ	NOUN
ejpam-201	232	9	-	-	PUNCT
ejpam-201	232	10	inner	inner	NOUN
ejpam-201	232	11	.	.	PUNCT
ejpam-201	233	1	therefore	therefore	ADV
ejpam-201	233	2	there	there	PRON
ejpam-201	233	3	exist	exist	VERB
ejpam-201	233	4	a′′	a′′	NOUN
ejpam-201	233	5	∈	∈	PROPN
ejpam-201	233	6	a	a	DET
ejpam-201	233	7	∗∗	∗∗	PROPN
ejpam-201	233	8	,	,	PUNCT
ejpam-201	233	9	x	x	PUNCT
ejpam-201	233	10	′′	′′	NOUN
ejpam-201	233	11	∈	∈	PROPN
ejpam-201	233	12	x	x	PUNCT
ejpam-201	234	1	∗∗	∗∗	X
ejpam-201	234	2	such	such	ADJ
ejpam-201	234	3	that	that	PRON
ejpam-201	234	4	(	(	PUNCT
ejpam-201	234	5	0	0	NUM
ejpam-201	234	6	,	,	PUNCT
ejpam-201	234	7	d(a	d(a	PROPN
ejpam-201	234	8	)	)	PUNCT
ejpam-201	234	9	)	)	PUNCT
ejpam-201	234	10	=	=	PUNCT
ejpam-201	234	11	d1(a	d1(a	PROPN
ejpam-201	234	12	)	)	PUNCT
ejpam-201	234	13	=	=	SYM
ejpam-201	234	14	(	(	PUNCT
ejpam-201	234	15	a	a	DET
ejpam-201	234	16	′′	′′	PROPN
ejpam-201	234	17	,	,	PUNCT
ejpam-201	234	18	x	x	PROPN
ejpam-201	234	19	′′)(0,σ(a))−	′′)(0,σ(a))−	PROPN
ejpam-201	234	20	(	(	PUNCT
ejpam-201	234	21	0,σ(a))(a′′	0,σ(a))(a′′	PROPN
ejpam-201	234	22	,	,	PUNCT
ejpam-201	234	23	x	x	PUNCT
ejpam-201	234	24	′′	′′	PROPN
ejpam-201	234	25	)	)	PUNCT
ejpam-201	234	26	,	,	PUNCT
ejpam-201	234	27	thus	thus	ADV
ejpam-201	234	28	d	d	X
ejpam-201	234	29	is	be	AUX
ejpam-201	234	30	σ	σ	NOUN
ejpam-201	234	31	-	-	PUNCT
ejpam-201	234	32	inner	inner	NOUN
ejpam-201	234	33	.	.	PUNCT
ejpam-201	235	1	therefore	therefore	ADV
ejpam-201	235	2	h1	h1	PROPN
ejpam-201	235	3	(	(	PUNCT
ejpam-201	235	4	σ	σ	PROPN
ejpam-201	235	5	,	,	PUNCT
ejpam-201	235	6	σ	σ	PROPN
ejpam-201	235	7	)	)	PUNCT
ejpam-201	235	8	(	(	PUNCT
ejpam-201	235	9	a	a	DET
ejpam-201	235	10	,	,	PUNCT
ejpam-201	235	11	x	x	NOUN
ejpam-201	235	12	∗∗	∗∗	NOUN
ejpam-201	235	13	)	)	PUNCT
ejpam-201	235	14	=	=	SYM
ejpam-201	235	15	0	0	NUM
ejpam-201	235	16	,	,	PUNCT
ejpam-201	235	17	and	and	CCONJ
ejpam-201	235	18	by	by	ADP
ejpam-201	235	19	theorem	theorem	NOUN
ejpam-201	235	20	2.2	2.2	NUM
ejpam-201	235	21	,	,	PUNCT
ejpam-201	235	22	a	a	PRON
ejpam-201	235	23	is	be	AUX
ejpam-201	235	24	σamenable	σamenable	ADJ
ejpam-201	235	25	.	.	PUNCT
ejpam-201	236	1	acknowledgements	acknowledgement	NOUN
ejpam-201	236	2	the	the	DET
ejpam-201	236	3	authors	author	NOUN
ejpam-201	236	4	would	would	AUX
ejpam-201	236	5	like	like	VERB
ejpam-201	236	6	to	to	PART
ejpam-201	236	7	thank	thank	VERB
ejpam-201	236	8	professor	professor	PROPN
ejpam-201	236	9	m.	m.	PROPN
ejpam-201	236	10	s.	s.	PROPN
ejpam-201	236	11	moslehian	moslehian	PROPN
ejpam-201	236	12	for	for	ADP
ejpam-201	236	13	his	his	PRON
ejpam-201	236	14	useful	useful	ADJ
ejpam-201	236	15	comments	comment	NOUN
ejpam-201	236	16	.	.	PUNCT
ejpam-201	237	1	references	reference	NOUN
ejpam-201	237	2	[	[	X
ejpam-201	237	3	1	1	NUM
ejpam-201	237	4	]	]	PUNCT
ejpam-201	237	5	h.	h.	PROPN
ejpam-201	237	6	g.	g.	PROPN
ejpam-201	237	7	dales	dales	PROPN
ejpam-201	237	8	,	,	PUNCT
ejpam-201	237	9	banach	banach	NOUN
ejpam-201	237	10	algebra	algebra	NOUN
ejpam-201	237	11	and	and	CCONJ
ejpam-201	237	12	automatic	automatic	ADJ
ejpam-201	237	13	continuity	continuity	NOUN
ejpam-201	237	14	,	,	PUNCT
ejpam-201	237	15	oxford	oxford	PROPN
ejpam-201	237	16	university	university	PROPN
ejpam-201	237	17	press	press	NOUN
ejpam-201	237	18	,	,	PUNCT
ejpam-201	237	19	2001	2001	NUM
ejpam-201	237	20	.	.	PUNCT
ejpam-201	238	1	references	reference	NOUN
ejpam-201	238	2	371	371	NUM
ejpam-201	238	3	[	[	X
ejpam-201	238	4	2	2	NUM
ejpam-201	238	5	]	]	PUNCT
ejpam-201	238	6	m.	m.	NOUN
ejpam-201	238	7	eshaghi	eshaghi	PROPN
ejpam-201	238	8	gordji	gordji	PROPN
ejpam-201	238	9	,	,	PUNCT
ejpam-201	238	10	homomorphisms	homomorphism	NOUN
ejpam-201	238	11	,	,	PUNCT
ejpam-201	238	12	amenability	amenability	NOUN
ejpam-201	238	13	and	and	CCONJ
ejpam-201	238	14	weak	weak	ADJ
ejpam-201	238	15	amenability	amenability	NOUN
ejpam-201	238	16	of	of	ADP
ejpam-201	238	17	banach	banach	NOUN
ejpam-201	238	18	algebras	algebra	NOUN
ejpam-201	238	19	,	,	PUNCT
ejpam-201	238	20	vietnam	vietnam	PROPN
ejpam-201	238	21	j.	j.	PROPN
ejpam-201	238	22	math	math	PROPN
ejpam-201	238	23	.	.	PUNCT
ejpam-201	239	1	36	36	NUM
ejpam-201	239	2	(	(	PUNCT
ejpam-201	239	3	2008	2008	NUM
ejpam-201	239	4	)	)	PUNCT
ejpam-201	239	5	,	,	PUNCT
ejpam-201	239	6	no	no	INTJ
ejpam-201	239	7	.	.	NOUN
ejpam-201	239	8	3	3	NUM
ejpam-201	239	9	,	,	PUNCT
ejpam-201	239	10	253–260	253–260	NUM
ejpam-201	239	11	.	.	PUNCT
ejpam-201	240	1	[	[	X
ejpam-201	240	2	3	3	X
ejpam-201	240	3	]	]	X
ejpam-201	240	4	m.	m.	NOUN
ejpam-201	240	5	mirzavaziri	mirzavaziri	PROPN
ejpam-201	240	6	,	,	PUNCT
ejpam-201	240	7	m.	m.	PROPN
ejpam-201	240	8	s.	s.	PROPN
ejpam-201	240	9	moslehian	moslehian	PROPN
ejpam-201	240	10	,	,	PUNCT
ejpam-201	240	11	σ	σ	NOUN
ejpam-201	240	12	-	-	PUNCT
ejpam-201	240	13	derivations	derivation	NOUN
ejpam-201	240	14	in	in	ADP
ejpam-201	240	15	banach	banach	NOUN
ejpam-201	240	16	algebras	algebra	NOUN
ejpam-201	240	17	,	,	PUNCT
ejpam-201	240	18	bull	bull	NOUN
ejpam-201	240	19	.	.	PUNCT
ejpam-201	241	1	iranian	iranian	ADJ
ejpam-201	241	2	math	math	PROPN
ejpam-201	241	3	.	.	PUNCT
ejpam-201	242	1	soc	soc	PROPN
ejpam-201	242	2	.	.	PUNCT
ejpam-201	243	1	32	32	NUM
ejpam-201	243	2	(	(	PUNCT
ejpam-201	243	3	2006	2006	NUM
ejpam-201	243	4	)	)	PUNCT
ejpam-201	243	5	,	,	PUNCT
ejpam-201	243	6	no	no	INTJ
ejpam-201	243	7	.	.	NOUN
ejpam-201	243	8	1	1	NUM
ejpam-201	243	9	,	,	PUNCT
ejpam-201	243	10	65–78	65–78	NUM
ejpam-201	243	11	[	[	X
ejpam-201	243	12	4	4	NUM
ejpam-201	243	13	]	]	PUNCT
ejpam-201	243	14	m.	m.	NOUN
ejpam-201	243	15	s.	s.	PROPN
ejpam-201	243	16	moslehian	moslehian	PROPN
ejpam-201	243	17	,	,	PUNCT
ejpam-201	243	18	approximate	approximate	ADJ
ejpam-201	243	19	(	(	PUNCT
ejpam-201	243	20	σ−	σ−	NOUN
ejpam-201	243	21	τ)-contractibility	τ)-contractibility	NOUN
ejpam-201	243	22	,	,	PUNCT
ejpam-201	243	23	nonlinear	nonlinear	ADJ
ejpam-201	243	24	funct	funct	NOUN
ejpam-201	243	25	.	.	PUNCT
ejpam-201	244	1	anal	anal	PROPN
ejpam-201	244	2	.	.	PUNCT
ejpam-201	244	3	appl	appl	PROPN
ejpam-201	244	4	.	.	PROPN
ejpam-201	245	1	,	,	PUNCT
ejpam-201	245	2	11	11	NUM
ejpam-201	245	3	(	(	PUNCT
ejpam-201	245	4	2006	2006	NUM
ejpam-201	245	5	)	)	PUNCT
ejpam-201	245	6	,	,	PUNCT
ejpam-201	245	7	no	no	INTJ
ejpam-201	245	8	.	.	NOUN
ejpam-201	245	9	5	5	NUM
ejpam-201	245	10	,	,	PUNCT
ejpam-201	245	11	805–813	805–813	NUM
ejpam-201	245	12	.	.	PUNCT
ejpam-201	246	1	[	[	X
ejpam-201	246	2	5	5	NUM
ejpam-201	246	3	]	]	PUNCT
ejpam-201	246	4	m.	m.	NOUN
ejpam-201	246	5	s.	s.	PROPN
ejpam-201	246	6	moslehian	moslehian	PROPN
ejpam-201	246	7	and	and	CCONJ
ejpam-201	246	8	a.	a.	PROPN
ejpam-201	246	9	n.	n.	PROPN
ejpam-201	246	10	motlagh	motlagh	PROPN
ejpam-201	246	11	,	,	PUNCT
ejpam-201	246	12	(	(	PUNCT
ejpam-201	246	13	σ	σ	NOUN
ejpam-201	246	14	,	,	PUNCT
ejpam-201	246	15	τ)-amenability	τ)-amenability	NOUN
ejpam-201	246	16	of	of	ADP
ejpam-201	246	17	banach	banach	NOUN
ejpam-201	246	18	algebras	algebra	NOUN
ejpam-201	246	19	,	,	PUNCT
ejpam-201	246	20	preprint	preprint	NOUN
ejpam-201	246	21	.	.	PUNCT
ejpam-201	247	1	[	[	X
ejpam-201	247	2	6	6	NUM
ejpam-201	247	3	]	]	PUNCT
ejpam-201	247	4	m.	m.	NOUN
ejpam-201	247	5	mirzavaziri	mirzavaziri	PROPN
ejpam-201	247	6	and	and	CCONJ
ejpam-201	247	7	m.	m.	PROPN
ejpam-201	247	8	s.	s.	PROPN
ejpam-201	247	9	moslehian	moslehian	PROPN
ejpam-201	247	10	,	,	PUNCT
ejpam-201	247	11	automatic	automatic	ADJ
ejpam-201	247	12	continuity	continuity	NOUN
ejpam-201	247	13	of	of	ADP
ejpam-201	247	14	σ	σ	NOUN
ejpam-201	247	15	-	-	PUNCT
ejpam-201	247	16	derivations	derivation	NOUN
ejpam-201	247	17	in	in	ADP
ejpam-201	247	18	c∗algebras	c∗algebra	NOUN
ejpam-201	247	19	,	,	PUNCT
ejpam-201	247	20	proc	proc	NOUN
ejpam-201	247	21	.	.	PUNCT
ejpam-201	248	1	amer	amer	PROPN
ejpam-201	248	2	.	.	PUNCT
ejpam-201	248	3	math	math	PROPN
ejpam-201	248	4	.	.	PUNCT
ejpam-201	249	1	soc	soc	PROPN
ejpam-201	249	2	.	.	PUNCT
ejpam-201	250	1	,	,	PUNCT
ejpam-201	250	2	11	11	NUM
ejpam-201	250	3	(	(	PUNCT
ejpam-201	250	4	2006	2006	NUM
ejpam-201	250	5	)	)	PUNCT
ejpam-201	250	6	,	,	PUNCT
ejpam-201	250	7	no	no	INTJ
ejpam-201	250	8	.	.	NOUN
ejpam-201	250	9	5	5	NUM
ejpam-201	250	10	,	,	PUNCT
ejpam-201	250	11	805–813	805–813	NUM
ejpam-201	250	12	.	.	PUNCT
ejpam-201	251	1	[	[	X
ejpam-201	251	2	7	7	X
ejpam-201	251	3	]	]	X
ejpam-201	251	4	yong	yong	PROPN
ejpam-201	251	5	zhang	zhang	PROPN
ejpam-201	251	6	,	,	PUNCT
ejpam-201	251	7	weak	weak	ADJ
ejpam-201	251	8	amenability	amenability	NOUN
ejpam-201	251	9	of	of	ADP
ejpam-201	251	10	a	a	DET
ejpam-201	251	11	class	class	NOUN
ejpam-201	251	12	of	of	ADP
ejpam-201	251	13	banach	banach	NOUN
ejpam-201	251	14	algebras	algebra	NOUN
ejpam-201	251	15	,	,	PUNCT
ejpam-201	251	16	canada	canada	PROPN
ejpam-201	251	17	.	.	PUNCT
ejpam-201	251	18	math	math	PROPN
ejpam-201	251	19	.	.	PUNCT
ejpam-201	252	1	bull	bull	NOUN
ejpam-201	252	2	.	.	PUNCT
ejpam-201	253	1	vol	vol	NOUN
ejpam-201	253	2	.	.	PUNCT
ejpam-201	254	1	44(4	44(4	NOUN
ejpam-201	254	2	)	)	PUNCT
ejpam-201	254	3	,	,	PUNCT
ejpam-201	254	4	2001	2001	NUM
ejpam-201	254	5	pp.504	pp.504	NOUN
ejpam-201	254	6	-	-	PUNCT
ejpam-201	254	7	508	508	NUM