id	sid	tid	token	lemma	pos
ejpam-441	1	1	9_441_gordji.dvi	9_441_gordji.dvi	NUM
ejpam-441	1	2	european	european	ADJ
ejpam-441	1	3	journal	journal	NOUN
ejpam-441	1	4	of	of	ADP
ejpam-441	1	5	pure	pure	ADJ
ejpam-441	1	6	and	and	CCONJ
ejpam-441	1	7	applied	apply	VERB
ejpam-441	1	8	mathematics	mathematic	NOUN
ejpam-441	1	9	vol	vol	NOUN
ejpam-441	1	10	.	.	PROPN
ejpam-441	2	1	2	2	NUM
ejpam-441	2	2	,	,	PUNCT
ejpam-441	2	3	no	no	INTJ
ejpam-441	2	4	.	.	NOUN
ejpam-441	2	5	4	4	NUM
ejpam-441	2	6	,	,	PUNCT
ejpam-441	2	7	2009	2009	NUM
ejpam-441	2	8	,	,	PUNCT
ejpam-441	2	9	(	(	PUNCT
ejpam-441	2	10	574	574	NUM
ejpam-441	2	11	-	-	SYM
ejpam-441	2	12	577	577	NUM
ejpam-441	2	13	)	)	PUNCT
ejpam-441	2	14	issn	issn	PROPN
ejpam-441	2	15	1307	1307	NUM
ejpam-441	2	16	-	-	SYM
ejpam-441	2	17	5543	5543	NUM
ejpam-441	2	18	–	–	PUNCT
ejpam-441	2	19	www.ejpam.com	www.ejpam.com	X
ejpam-441	2	20	second	second	ADJ
ejpam-441	2	21	duals	dual	NOUN
ejpam-441	2	22	of	of	ADP
ejpam-441	2	23	measure	measure	NOUN
ejpam-441	2	24	algebras	algebras	PROPN
ejpam-441	2	25	m.	m.	PROPN
ejpam-441	2	26	eshaghi	eshaghi	PROPN
ejpam-441	2	27	gordji1∗	gordji1∗	PROPN
ejpam-441	2	28	,	,	PUNCT
ejpam-441	2	29	and	and	CCONJ
ejpam-441	2	30	a.	a.	NOUN
ejpam-441	2	31	ebadian2	ebadian2	PROPN
ejpam-441	2	32	1	1	NUM
ejpam-441	2	33	department	department	NOUN
ejpam-441	2	34	of	of	ADP
ejpam-441	2	35	mathematics	mathematic	NOUN
ejpam-441	2	36	,	,	PUNCT
ejpam-441	2	37	semnan	semnan	PROPN
ejpam-441	2	38	university	university	PROPN
ejpam-441	2	39	,	,	PUNCT
ejpam-441	2	40	semnan	semnan	PROPN
ejpam-441	2	41	,	,	PUNCT
ejpam-441	2	42	iran	iran	PROPN
ejpam-441	2	43	2	2	NUM
ejpam-441	2	44	department	department	NOUN
ejpam-441	2	45	of	of	ADP
ejpam-441	2	46	mathematics	mathematics	PROPN
ejpam-441	2	47	,	,	PUNCT
ejpam-441	2	48	urmia	urmia	PROPN
ejpam-441	2	49	university	university	PROPN
ejpam-441	2	50	,	,	PUNCT
ejpam-441	2	51	urmia	urmia	PROPN
ejpam-441	2	52	,	,	PUNCT
ejpam-441	2	53	iran	iran	PROPN
ejpam-441	2	54	abstract	abstract	NOUN
ejpam-441	2	55	.	.	PUNCT
ejpam-441	3	1	in	in	ADP
ejpam-441	3	2	this	this	DET
ejpam-441	3	3	paper	paper	NOUN
ejpam-441	3	4	we	we	PRON
ejpam-441	3	5	show	show	VERB
ejpam-441	3	6	that	that	SCONJ
ejpam-441	3	7	m(g)∗∗	m(g)∗∗	NOUN
ejpam-441	3	8	determines	determine	VERB
ejpam-441	3	9	g	g	NOUN
ejpam-441	3	10	when	when	SCONJ
ejpam-441	3	11	g	g	PROPN
ejpam-441	3	12	is	be	AUX
ejpam-441	3	13	a	a	DET
ejpam-441	3	14	compact	compact	ADJ
ejpam-441	3	15	topological	topological	ADJ
ejpam-441	3	16	group	group	NOUN
ejpam-441	3	17	.	.	PUNCT
ejpam-441	4	1	it	it	PRON
ejpam-441	4	2	is	be	AUX
ejpam-441	4	3	a	a	DET
ejpam-441	4	4	new	new	ADJ
ejpam-441	4	5	proof	proof	NOUN
ejpam-441	4	6	for	for	ADP
ejpam-441	4	7	theorem	theorem	NOUN
ejpam-441	4	8	of	of	ADP
ejpam-441	4	9	gharamani	gharamani	NOUN
ejpam-441	4	10	and	and	CCONJ
ejpam-441	4	11	mcclure	mcclure	PROPN
ejpam-441	4	12	.	.	PROPN
ejpam-441	5	1	2000	2000	NUM
ejpam-441	5	2	mathematics	mathematics	PROPN
ejpam-441	5	3	subject	subject	NOUN
ejpam-441	5	4	classifications	classification	NOUN
ejpam-441	5	5	:	:	PUNCT
ejpam-441	5	6	46hxx	46hxx	ADJ
ejpam-441	5	7	key	key	ADJ
ejpam-441	5	8	words	word	NOUN
ejpam-441	5	9	and	and	CCONJ
ejpam-441	5	10	phrases	phrase	NOUN
ejpam-441	5	11	:	:	PUNCT
ejpam-441	5	12	topological	topological	ADJ
ejpam-441	5	13	group	group	NOUN
ejpam-441	5	14	,	,	PUNCT
ejpam-441	5	15	arens	arens	PROPN
ejpam-441	5	16	product	product	NOUN
ejpam-441	5	17	,	,	PUNCT
ejpam-441	5	18	isomorphism	isomorphism	VERB
ejpam-441	5	19	the	the	DET
ejpam-441	5	20	second	second	ADJ
ejpam-441	5	21	dual	dual	ADJ
ejpam-441	5	22	space	space	NOUN
ejpam-441	5	23	a	a	DET
ejpam-441	5	24	∗∗	∗∗	NOUN
ejpam-441	5	25	of	of	ADP
ejpam-441	5	26	a	a	DET
ejpam-441	5	27	banach	banach	NOUN
ejpam-441	5	28	algebra	algebra	NOUN
ejpam-441	5	29	a	a	DET
ejpam-441	5	30	admits	admit	VERB
ejpam-441	5	31	the	the	DET
ejpam-441	5	32	banach	banach	NOUN
ejpam-441	5	33	algebra	algebra	NOUN
ejpam-441	5	34	product	product	NOUN
ejpam-441	5	35	known	know	VERB
ejpam-441	5	36	as	as	ADP
ejpam-441	5	37	first	first	ADV
ejpam-441	5	38	(	(	PUNCT
ejpam-441	5	39	left	left	ADJ
ejpam-441	5	40	)	)	PUNCT
ejpam-441	5	41	arens	aren	NOUN
ejpam-441	5	42	product	product	NOUN
ejpam-441	5	43	.	.	PUNCT
ejpam-441	6	1	this	this	DET
ejpam-441	6	2	product	product	NOUN
ejpam-441	6	3	extends	extend	VERB
ejpam-441	6	4	the	the	DET
ejpam-441	6	5	product	product	NOUN
ejpam-441	6	6	of	of	ADP
ejpam-441	6	7	a	a	PRON
ejpam-441	6	8	as	as	ADV
ejpam-441	6	9	canonically	canonically	ADV
ejpam-441	6	10	embedded	embed	VERB
ejpam-441	6	11	in	in	ADP
ejpam-441	6	12	a	a	DET
ejpam-441	6	13	∗∗.	∗∗.	NOUN
ejpam-441	6	14	we	we	PRON
ejpam-441	6	15	briefly	briefly	ADV
ejpam-441	6	16	recall	recall	VERB
ejpam-441	6	17	the	the	DET
ejpam-441	6	18	definition	definition	NOUN
ejpam-441	6	19	of	of	ADP
ejpam-441	6	20	this	this	DET
ejpam-441	6	21	product	product	NOUN
ejpam-441	6	22	.	.	PUNCT
ejpam-441	7	1	for	for	ADP
ejpam-441	7	2	m	m	PROPN
ejpam-441	7	3	,	,	PUNCT
ejpam-441	7	4	n	n	PRON
ejpam-441	7	5	∈a	∈a	ADJ
ejpam-441	7	6	∗∗	∗∗	PROPN
ejpam-441	7	7	,	,	PUNCT
ejpam-441	7	8	their	their	PRON
ejpam-441	7	9	first	first	ADJ
ejpam-441	7	10	(	(	PUNCT
ejpam-441	7	11	left	left	ADJ
ejpam-441	7	12	)	)	PUNCT
ejpam-441	7	13	arens	aren	NOUN
ejpam-441	7	14	product	product	NOUN
ejpam-441	7	15	indicated	indicate	VERB
ejpam-441	7	16	by	by	ADP
ejpam-441	7	17	mn	mn	PROPN
ejpam-441	7	18	is	be	AUX
ejpam-441	7	19	given	give	VERB
ejpam-441	7	20	by	by	ADP
ejpam-441	7	21	〈	〈	PROPN
ejpam-441	7	22	mn	mn	PROPN
ejpam-441	7	23	,	,	PUNCT
ejpam-441	7	24	f	f	PROPN
ejpam-441	7	25	〉	〉	NOUN
ejpam-441	7	26	=	=	PUNCT
ejpam-441	7	27	〈	〈	PROPN
ejpam-441	7	28	m	m	PROPN
ejpam-441	7	29	,	,	PUNCT
ejpam-441	7	30	nf	nf	ADJ
ejpam-441	7	31	〉	〉	NOUN
ejpam-441	7	32	(	(	PUNCT
ejpam-441	7	33	f	f	PROPN
ejpam-441	7	34	∈a	∈a	ADJ
ejpam-441	7	35	∗	∗	NOUN
ejpam-441	7	36	)	)	PUNCT
ejpam-441	7	37	,	,	PUNCT
ejpam-441	7	38	where	where	SCONJ
ejpam-441	7	39	nf	nf	ADJ
ejpam-441	7	40	∈a	∈a	ADJ
ejpam-441	7	41	∗	∗	NOUN
ejpam-441	7	42	is	be	AUX
ejpam-441	7	43	defined	define	VERB
ejpam-441	7	44	by	by	ADP
ejpam-441	7	45	〈	〈	NOUN
ejpam-441	7	46	nf	nf	NOUN
ejpam-441	7	47	,	,	PUNCT
ejpam-441	7	48	a	a	DET
ejpam-441	7	49	〉	〉	NOUN
ejpam-441	7	50	=	=	SYM
ejpam-441	7	51	〈	〈	PROPN
ejpam-441	7	52	n	n	CCONJ
ejpam-441	7	53	,	,	PUNCT
ejpam-441	7	54	f	f	PROPN
ejpam-441	7	55	a	a	DET
ejpam-441	7	56	〉	〉	NOUN
ejpam-441	7	57	(	(	PUNCT
ejpam-441	7	58	a	a	DET
ejpam-441	7	59	∈a	∈a	ADJ
ejpam-441	7	60	)	)	PUNCT
ejpam-441	7	61	.	.	PUNCT
ejpam-441	8	1	∗corresponding	∗corresponde	VERB
ejpam-441	8	2	author	author	NOUN
ejpam-441	8	3	.	.	PUNCT
ejpam-441	9	1	email	email	NOUN
ejpam-441	9	2	addresses	address	NOUN
ejpam-441	9	3	:	:	PUNCT
ejpam-441	9	4	madjid.eshaghi	madjid.eshaghi	X
ejpam-441	9	5	�	�	NOUN
ejpam-441	9	6	gmail	gmail	NOUN
ejpam-441	9	7	.	.	PUNCT
ejpam-441	10	1	om	om	PROPN
ejpam-441	10	2	&	&	CCONJ
ejpam-441	10	3	madjideg	madjideg	PROPN
ejpam-441	10	4	�	�	PROPN
ejpam-441	10	5	walla	walla	PROPN
ejpam-441	10	6	.	.	PUNCT
ejpam-441	11	1	om	om	PROPN
ejpam-441	11	2	(	(	PUNCT
ejpam-441	11	3	m.	m.	PROPN
ejpam-441	11	4	gordji),ebadian.ali	gordji),ebadian.ali	PROPN
ejpam-441	11	5	�	�	PROPN
ejpam-441	11	6	gmail	gmail	NOUN
ejpam-441	11	7	.	.	PUNCT
ejpam-441	12	1	om	om	PROPN
ejpam-441	12	2	(	(	PUNCT
ejpam-441	12	3	a.	a.	PROPN
ejpam-441	12	4	ebadian	ebadian	PROPN
ejpam-441	12	5	)	)	PUNCT
ejpam-441	12	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-441	13	1	574	574	NUM
ejpam-441	13	2	c	c	X
ejpam-441	13	3	©	©	PROPN
ejpam-441	13	4	2009	2009	NUM
ejpam-441	13	5	ejpam	ejpam	NOUN
ejpam-441	13	6	all	all	DET
ejpam-441	13	7	rights	right	NOUN
ejpam-441	13	8	reserved	reserve	VERB
ejpam-441	13	9	.	.	PUNCT
ejpam-441	14	1	m.	m.	NOUN
ejpam-441	14	2	gordji	gordji	PROPN
ejpam-441	14	3	and	and	CCONJ
ejpam-441	14	4	a.	a.	NOUN
ejpam-441	14	5	ebadian	ebadian	PROPN
ejpam-441	14	6	/	/	SYM
ejpam-441	14	7	eur	eur	PROPN
ejpam-441	14	8	.	.	PUNCT
ejpam-441	15	1	j.	j.	PROPN
ejpam-441	15	2	pure	pure	PROPN
ejpam-441	15	3	appl	appl	PROPN
ejpam-441	15	4	.	.	PROPN
ejpam-441	15	5	math	math	PROPN
ejpam-441	15	6	,	,	PUNCT
ejpam-441	15	7	2	2	NUM
ejpam-441	15	8	(	(	PUNCT
ejpam-441	15	9	2009	2009	NUM
ejpam-441	15	10	)	)	PUNCT
ejpam-441	15	11	,	,	PUNCT
ejpam-441	15	12	(	(	PUNCT
ejpam-441	15	13	574	574	NUM
ejpam-441	15	14	-	-	SYM
ejpam-441	15	15	577	577	NUM
ejpam-441	15	16	)	)	PUNCT
ejpam-441	15	17	575	575	NUM
ejpam-441	15	18	(	(	PUNCT
ejpam-441	15	19	see	see	VERB
ejpam-441	15	20	[	[	X
ejpam-441	15	21	1	1	X
ejpam-441	15	22	]	]	PUNCT
ejpam-441	15	23	and	and	CCONJ
ejpam-441	15	24	[	[	X
ejpam-441	15	25	2	2	NUM
ejpam-441	15	26	]	]	NUM
ejpam-441	15	27	)	)	PUNCT
ejpam-441	15	28	.	.	PUNCT
ejpam-441	16	1	wendel	wendel	PROPN
ejpam-441	16	2	in	in	ADP
ejpam-441	16	3	[	[	X
ejpam-441	16	4	6	6	NUM
ejpam-441	16	5	]	]	PUNCT
ejpam-441	16	6	proved	prove	VERB
ejpam-441	16	7	that	that	SCONJ
ejpam-441	16	8	for	for	ADP
ejpam-441	16	9	locally	locally	ADV
ejpam-441	16	10	compact	compact	ADJ
ejpam-441	16	11	groups	group	NOUN
ejpam-441	16	12	g1	g1	PROPN
ejpam-441	16	13	and	and	CCONJ
ejpam-441	16	14	g2	g2	PROPN
ejpam-441	16	15	,	,	PUNCT
ejpam-441	16	16	the	the	DET
ejpam-441	16	17	group	group	NOUN
ejpam-441	16	18	algebras	algebra	VERB
ejpam-441	16	19	l1(g1	l1(g1	PROPN
ejpam-441	16	20	)	)	PUNCT
ejpam-441	16	21	and	and	CCONJ
ejpam-441	16	22	l1(g2	l1(g2	PROPN
ejpam-441	16	23	)	)	PUNCT
ejpam-441	16	24	are	be	AUX
ejpam-441	16	25	isometrically	isometrically	PROPN
ejpam-441	16	26	isomorphic	isomorphic	ADJ
ejpam-441	16	27	if	if	SCONJ
ejpam-441	16	28	and	and	CCONJ
ejpam-441	16	29	only	only	ADV
ejpam-441	16	30	if	if	SCONJ
ejpam-441	16	31	g1	g1	PROPN
ejpam-441	16	32	and	and	CCONJ
ejpam-441	16	33	g2	g2	PROPN
ejpam-441	16	34	are	be	AUX
ejpam-441	16	35	isomorphic	isomorphic	ADJ
ejpam-441	16	36	in	in	ADP
ejpam-441	16	37	the	the	DET
ejpam-441	16	38	category	category	NOUN
ejpam-441	16	39	of	of	ADP
ejpam-441	16	40	topological	topological	ADJ
ejpam-441	16	41	groups	group	NOUN
ejpam-441	16	42	.	.	PUNCT
ejpam-441	17	1	johnson	johnson	PROPN
ejpam-441	17	2	in	in	ADP
ejpam-441	17	3	[	[	X
ejpam-441	17	4	5	5	NUM
ejpam-441	17	5	]	]	PUNCT
ejpam-441	17	6	proved	prove	VERB
ejpam-441	17	7	that	that	SCONJ
ejpam-441	17	8	the	the	DET
ejpam-441	17	9	algebra	algebra	PROPN
ejpam-441	17	10	m(g	m(g	PROPN
ejpam-441	17	11	)	)	PUNCT
ejpam-441	17	12	determines	determine	VERB
ejpam-441	17	13	g	g	NOUN
ejpam-441	17	14	when	when	SCONJ
ejpam-441	17	15	g	g	PROPN
ejpam-441	17	16	is	be	AUX
ejpam-441	17	17	a	a	DET
ejpam-441	17	18	locally	locally	ADV
ejpam-441	17	19	compact	compact	ADJ
ejpam-441	17	20	group	group	NOUN
ejpam-441	17	21	.	.	PUNCT
ejpam-441	18	1	in	in	ADP
ejpam-441	18	2	[	[	X
ejpam-441	18	3	3	3	NUM
ejpam-441	18	4	]	]	X
ejpam-441	18	5	ghahramani	ghahramani	PROPN
ejpam-441	18	6	and	and	CCONJ
ejpam-441	18	7	lau	lau	PROPN
ejpam-441	18	8	have	have	AUX
ejpam-441	18	9	proved	prove	VERB
ejpam-441	18	10	that	that	SCONJ
ejpam-441	18	11	l1(g	l1(g	PROPN
ejpam-441	18	12	)	)	PUNCT
ejpam-441	18	13	∗∗	∗∗	PROPN
ejpam-441	18	14	determines	determine	VERB
ejpam-441	18	15	g	g	NOUN
ejpam-441	18	16	when	when	SCONJ
ejpam-441	18	17	g	g	PROPN
ejpam-441	18	18	is	be	AUX
ejpam-441	18	19	a	a	DET
ejpam-441	18	20	locally	locally	ADV
ejpam-441	18	21	compact	compact	ADJ
ejpam-441	18	22	group	group	NOUN
ejpam-441	18	23	.	.	PUNCT
ejpam-441	19	1	ghahramani	ghahramani	PROPN
ejpam-441	19	2	and	and	CCONJ
ejpam-441	19	3	mcclure	mcclure	PROPN
ejpam-441	19	4	in	in	ADP
ejpam-441	19	5	[	[	X
ejpam-441	19	6	4	4	NUM
ejpam-441	19	7	]	]	PUNCT
ejpam-441	19	8	proved	prove	VERB
ejpam-441	19	9	that	that	SCONJ
ejpam-441	19	10	the	the	DET
ejpam-441	19	11	algebra	algebra	NOUN
ejpam-441	19	12	(	(	PUNCT
ejpam-441	19	13	m(g	m(g	PROPN
ejpam-441	19	14	)	)	PUNCT
ejpam-441	19	15	)	)	PUNCT
ejpam-441	20	1	∗∗	∗∗	NOUN
ejpam-441	20	2	determines	determine	VERB
ejpam-441	20	3	g	g	NOUN
ejpam-441	20	4	when	when	SCONJ
ejpam-441	20	5	g	g	PROPN
ejpam-441	20	6	is	be	AUX
ejpam-441	20	7	a	a	DET
ejpam-441	20	8	compact	compact	ADJ
ejpam-441	20	9	topological	topological	ADJ
ejpam-441	20	10	group	group	NOUN
ejpam-441	20	11	.	.	PUNCT
ejpam-441	21	1	in	in	ADP
ejpam-441	21	2	this	this	DET
ejpam-441	21	3	paper	paper	NOUN
ejpam-441	21	4	we	we	PRON
ejpam-441	21	5	define	define	VERB
ejpam-441	21	6	some	some	DET
ejpam-441	21	7	new	new	ADJ
ejpam-441	21	8	ideals	ideal	NOUN
ejpam-441	21	9	in	in	ADP
ejpam-441	21	10	banach	banach	NOUN
ejpam-441	21	11	algebras	algebra	NOUN
ejpam-441	21	12	and	and	CCONJ
ejpam-441	21	13	we	we	PRON
ejpam-441	21	14	apply	apply	VERB
ejpam-441	21	15	this	this	DET
ejpam-441	21	16	ideals	ideal	NOUN
ejpam-441	21	17	to	to	PART
ejpam-441	21	18	consider	consider	VERB
ejpam-441	21	19	a	a	DET
ejpam-441	21	20	new	new	ADJ
ejpam-441	21	21	proof	proof	NOUN
ejpam-441	21	22	to	to	PART
ejpam-441	21	23	show	show	VERB
ejpam-441	21	24	that	that	SCONJ
ejpam-441	21	25	(	(	PUNCT
ejpam-441	21	26	m(g))∗∗	m(g))∗∗	NOUN
ejpam-441	21	27	determines	determine	VERB
ejpam-441	21	28	g	g	NOUN
ejpam-441	21	29	when	when	SCONJ
ejpam-441	21	30	g	g	PROPN
ejpam-441	21	31	is	be	AUX
ejpam-441	21	32	compact	compact	ADJ
ejpam-441	21	33	.	.	PUNCT
ejpam-441	22	1	let	let	VERB
ejpam-441	22	2	a	a	PRON
ejpam-441	22	3	be	be	AUX
ejpam-441	22	4	a	a	DET
ejpam-441	22	5	banach	banach	NOUN
ejpam-441	22	6	algebra	algebra	NOUN
ejpam-441	22	7	.	.	PUNCT
ejpam-441	23	1	we	we	PRON
ejpam-441	23	2	consider	consider	VERB
ejpam-441	23	3	zl(a	zl(a	NUM
ejpam-441	23	4	)	)	PUNCT
ejpam-441	23	5	:	:	PUNCT
ejpam-441	24	1	=	=	X
ejpam-441	24	2	{	{	PUNCT
ejpam-441	24	3	a	a	DET
ejpam-441	24	4	∈a	∈a	NOUN
ejpam-441	24	5	:	:	PUNCT
ejpam-441	24	6	a	a	DET
ejpam-441	24	7	∗∗	∗∗	PROPN
ejpam-441	24	8	·	·	PUNCT
ejpam-441	24	9	b⊣	b⊣	NOUN
ejpam-441	24	10	⊆	⊆	NUM
ejpam-441	24	11	ca	ca	NOUN
ejpam-441	24	12	}	}	PUNCT
ejpam-441	24	13	.	.	PUNCT
ejpam-441	25	1	it	it	PRON
ejpam-441	25	2	is	be	AUX
ejpam-441	25	3	easy	easy	ADJ
ejpam-441	25	4	to	to	PART
ejpam-441	25	5	show	show	VERB
ejpam-441	25	6	that	that	SCONJ
ejpam-441	25	7	zl(a	zl(a	NUM
ejpam-441	25	8	)	)	PUNCT
ejpam-441	25	9	is	be	AUX
ejpam-441	25	10	a	a	DET
ejpam-441	25	11	two	two	NUM
ejpam-441	25	12	sided	sided	ADJ
ejpam-441	25	13	ideal	ideal	ADJ
ejpam-441	25	14	ofa	ofa	PROPN
ejpam-441	26	1	so	so	ADV
ejpam-441	26	2	it	it	PRON
ejpam-441	26	3	is	be	AUX
ejpam-441	26	4	a	a	DET
ejpam-441	26	5	left	left	ADJ
ejpam-441	26	6	ideal	ideal	NOUN
ejpam-441	26	7	ofa	ofa	PROPN
ejpam-441	26	8	∗∗.	∗∗.	PROPN
ejpam-441	26	9	also	also	ADV
ejpam-441	26	10	zl(a	zl(a	NUM
ejpam-441	26	11	)	)	PUNCT
ejpam-441	26	12	is	be	AUX
ejpam-441	26	13	the	the	DET
ejpam-441	26	14	union	union	NOUN
ejpam-441	26	15	of	of	ADP
ejpam-441	26	16	all	all	DET
ejpam-441	26	17	two	two	NUM
ejpam-441	26	18	sided	sided	ADJ
ejpam-441	26	19	ideals	ideal	NOUN
ejpam-441	26	20	ofa	ofa	PROPN
ejpam-441	26	21	which	which	PRON
ejpam-441	26	22	are	be	AUX
ejpam-441	26	23	left	leave	VERB
ejpam-441	26	24	ideals	ideal	NOUN
ejpam-441	26	25	ofa	ofa	PROPN
ejpam-441	26	26	∗∗.	∗∗.	PROPN
ejpam-441	26	27	first	first	ADV
ejpam-441	26	28	we	we	PRON
ejpam-441	26	29	prove	prove	VERB
ejpam-441	26	30	the	the	DET
ejpam-441	26	31	following	follow	VERB
ejpam-441	26	32	lemma	lemma	PROPN
ejpam-441	26	33	.	.	PUNCT
ejpam-441	27	1	lemma	lemma	PROPN
ejpam-441	27	2	1	1	X
ejpam-441	27	3	.	.	PUNCT
ejpam-441	28	1	let	let	VERB
ejpam-441	28	2	θ	θ	NOUN
ejpam-441	28	3	:	:	PUNCT
ejpam-441	28	4	a	a	DET
ejpam-441	28	5	→b	→b	PUNCT
ejpam-441	28	6	be	be	AUX
ejpam-441	28	7	an	an	DET
ejpam-441	28	8	isometrically	isometrically	PROPN
ejpam-441	28	9	isomorphism	isomorphism	NOUN
ejpam-441	28	10	between	between	ADP
ejpam-441	28	11	banach	banach	NOUN
ejpam-441	28	12	algebras	algebra	NOUN
ejpam-441	28	13	.	.	PUNCT
ejpam-441	29	1	then	then	ADV
ejpam-441	29	2	θ	θ	PROPN
ejpam-441	29	3	(	(	PUNCT
ejpam-441	29	4	zl(a	zl(a	NUM
ejpam-441	29	5	)	)	PUNCT
ejpam-441	29	6	)	)	PUNCT
ejpam-441	30	1	=	=	SYM
ejpam-441	30	2	zl(b	zl(b	NOUN
ejpam-441	30	3	)	)	PUNCT
ejpam-441	30	4	.	.	PUNCT
ejpam-441	31	1	proof	proof	NOUN
ejpam-441	31	2	.	.	PUNCT
ejpam-441	32	1	let	let	VERB
ejpam-441	32	2	θ	θ	NOUN
ejpam-441	32	3	:	:	PUNCT
ejpam-441	32	4	a	a	DET
ejpam-441	32	5	→b	→b	PUNCT
ejpam-441	32	6	be	be	AUX
ejpam-441	32	7	an	an	DET
ejpam-441	32	8	isometrically	isometrically	PROPN
ejpam-441	32	9	isomorphism	isomorphism	NOUN
ejpam-441	32	10	between	between	ADP
ejpam-441	32	11	banach	banach	NOUN
ejpam-441	32	12	algebras	algebra	NOUN
ejpam-441	32	13	.	.	PUNCT
ejpam-441	33	1	then	then	ADV
ejpam-441	33	2	θ	θ	PROPN
ejpam-441	34	1	′′	′′	PROPN
ejpam-441	34	2	is	be	AUX
ejpam-441	34	3	a	a	DET
ejpam-441	34	4	isometrically	isometrically	PROPN
ejpam-441	34	5	isomorphism	isomorphism	NOUN
ejpam-441	34	6	between	between	ADP
ejpam-441	34	7	banach	banach	NOUN
ejpam-441	34	8	algebras	algebra	VERB
ejpam-441	34	9	a	a	DET
ejpam-441	34	10	∗∗	∗∗	PROPN
ejpam-441	34	11	and	and	CCONJ
ejpam-441	34	12	b∗∗.	b∗∗.	NOUN
ejpam-441	34	13	let	let	VERB
ejpam-441	34	14	a	a	DET
ejpam-441	34	15	∈	∈	PROPN
ejpam-441	34	16	zl(a	zl(a	NUM
ejpam-441	34	17	)	)	PUNCT
ejpam-441	34	18	and	and	CCONJ
ejpam-441	34	19	b′′	b′′	VERB
ejpam-441	34	20	∈b∗∗.	∈b∗∗.	PROPN
ejpam-441	34	21	then	then	ADV
ejpam-441	34	22	there	there	PRON
ejpam-441	34	23	exists	exist	VERB
ejpam-441	34	24	a′′	a′′	PROPN
ejpam-441	34	25	∈a	∈a	ADJ
ejpam-441	34	26	∗∗	∗∗	PROPN
ejpam-441	34	27	such	such	ADJ
ejpam-441	34	28	that	that	DET
ejpam-441	34	29	b′′	b′′	PROPN
ejpam-441	34	30	=	=	PROPN
ejpam-441	34	31	θ	θ	PROPN
ejpam-441	34	32	′′(a′′	′′(a′′	NOUN
ejpam-441	34	33	)	)	PUNCT
ejpam-441	34	34	.	.	PUNCT
ejpam-441	35	1	thus	thus	ADV
ejpam-441	35	2	b′′õθ	b′′õθ	PRON
ejpam-441	35	3	(	(	PUNCT
ejpam-441	35	4	a	a	X
ejpam-441	35	5	)	)	PUNCT
ejpam-441	35	6	=	=	SYM
ejpam-441	35	7	θ	θ	X
ejpam-441	35	8	′′(a′′)õθ	′′(a′′)õθ	NOUN
ejpam-441	35	9	(	(	PUNCT
ejpam-441	35	10	a	a	NOUN
ejpam-441	35	11	)	)	PUNCT
ejpam-441	35	12	=	=	SYM
ejpam-441	35	13	θ	θ	NOUN
ejpam-441	35	14	′′(a′′ba	′′(a′′ba	NOUN
ejpam-441	35	15	)	)	PUNCT
ejpam-441	36	1	=	=	X
ejpam-441	36	2	úθ	úθ	X
ejpam-441	36	3	(	(	PUNCT
ejpam-441	36	4	a′′b)a	a′′b)a	PROPN
ejpam-441	36	5	∈øθ	∈øθ	PRON
ejpam-441	36	6	(	(	PUNCT
ejpam-441	36	7	a	a	X
ejpam-441	36	8	)	)	PUNCT
ejpam-441	36	9	=	=	SYM
ejpam-441	36	10	cb	cb	PROPN
ejpam-441	36	11	.	.	PUNCT
ejpam-441	37	1	then	then	ADV
ejpam-441	37	2	θ	θ	PROPN
ejpam-441	37	3	(	(	PUNCT
ejpam-441	37	4	zl(a	zl(a	NUM
ejpam-441	37	5	)	)	PUNCT
ejpam-441	37	6	)	)	PUNCT
ejpam-441	37	7	⊂	⊂	PROPN
ejpam-441	37	8	zl(b	zl(b	NOUN
ejpam-441	37	9	)	)	PUNCT
ejpam-441	37	10	.	.	PUNCT
ejpam-441	38	1	�	�	PROPN
ejpam-441	38	2	theorem	theorem	VERB
ejpam-441	38	3	1	1	NUM
ejpam-441	38	4	.	.	PUNCT
ejpam-441	39	1	let	let	VERB
ejpam-441	39	2	g	g	PRON
ejpam-441	39	3	be	be	AUX
ejpam-441	39	4	a	a	DET
ejpam-441	39	5	compact	compact	ADJ
ejpam-441	39	6	group	group	NOUN
ejpam-441	39	7	.	.	PUNCT
ejpam-441	40	1	then	then	ADV
ejpam-441	40	2	zl((m(g	zl((m(g	NUM
ejpam-441	40	3	)	)	PUNCT
ejpam-441	40	4	)	)	PUNCT
ejpam-441	41	1	∗∗	∗∗	NOUN
ejpam-441	41	2	)	)	PUNCT
ejpam-441	42	1	=	=	PUNCT
ejpam-441	42	2	π	π	X
ejpam-441	42	3	′′	′′	PROPN
ejpam-441	42	4	(	(	PUNCT
ejpam-441	42	5	ł1(g))∗∗.	ł1(g))∗∗.	PROPN
ejpam-441	42	6	proof	proof	NOUN
ejpam-441	42	7	.	.	PUNCT
ejpam-441	43	1	let	let	VERB
ejpam-441	43	2	(	(	PUNCT
ejpam-441	43	3	eα	eα	X
ejpam-441	43	4	)	)	PUNCT
ejpam-441	43	5	be	be	VERB
ejpam-441	43	6	a	a	DET
ejpam-441	43	7	bounded	bounded	ADJ
ejpam-441	43	8	approximate	approximate	ADJ
ejpam-441	43	9	identity	identity	NOUN
ejpam-441	43	10	of	of	ADP
ejpam-441	43	11	l1(g	l1(g	PROPN
ejpam-441	43	12	)	)	PUNCT
ejpam-441	43	13	with	with	ADP
ejpam-441	43	14	bound	bound	ADJ
ejpam-441	43	15	1	1	NUM
ejpam-441	43	16	,	,	PUNCT
ejpam-441	43	17	and	and	CCONJ
ejpam-441	43	18	with	with	ADP
ejpam-441	43	19	cluster	cluster	NOUN
ejpam-441	43	20	point	point	NOUN
ejpam-441	43	21	e	e	PROPN
ejpam-441	43	22	∈	∈	PROPN
ejpam-441	43	23	l1(g	l1(g	PROPN
ejpam-441	43	24	)	)	PUNCT
ejpam-441	43	25	∗∗	∗∗	PROPN
ejpam-441	43	26	.	.	PUNCT
ejpam-441	44	1	we	we	PRON
ejpam-441	44	2	denote	denote	VERB
ejpam-441	44	3	π	π	X
ejpam-441	44	4	:	:	PUNCT
ejpam-441	44	5	l1(g	l1(g	X
ejpam-441	44	6	)	)	PUNCT
ejpam-441	44	7	−→	−→	PROPN
ejpam-441	44	8	m(g	m(g	PROPN
ejpam-441	44	9	)	)	PUNCT
ejpam-441	44	10	the	the	DET
ejpam-441	44	11	inclusion	inclusion	NOUN
ejpam-441	44	12	map	map	NOUN
ejpam-441	44	13	,	,	PUNCT
ejpam-441	44	14	m.	m.	NOUN
ejpam-441	44	15	gordji	gordji	PROPN
ejpam-441	44	16	and	and	CCONJ
ejpam-441	44	17	a.	a.	NOUN
ejpam-441	44	18	ebadian	ebadian	PROPN
ejpam-441	44	19	/	/	SYM
ejpam-441	44	20	eur	eur	PROPN
ejpam-441	44	21	.	.	PUNCT
ejpam-441	45	1	j.	j.	PROPN
ejpam-441	45	2	pure	pure	PROPN
ejpam-441	45	3	appl	appl	PROPN
ejpam-441	45	4	.	.	PROPN
ejpam-441	45	5	math	math	PROPN
ejpam-441	45	6	,	,	PUNCT
ejpam-441	45	7	2	2	NUM
ejpam-441	45	8	(	(	PUNCT
ejpam-441	45	9	2009	2009	NUM
ejpam-441	45	10	)	)	PUNCT
ejpam-441	45	11	,	,	PUNCT
ejpam-441	45	12	(	(	PUNCT
ejpam-441	45	13	574	574	NUM
ejpam-441	45	14	-	-	SYM
ejpam-441	45	15	577	577	NUM
ejpam-441	45	16	)	)	PUNCT
ejpam-441	45	17	576	576	NUM
ejpam-441	45	18	then	then	ADV
ejpam-441	45	19	the	the	DET
ejpam-441	45	20	map	map	NOUN
ejpam-441	45	21	m	m	VERB
ejpam-441	45	22	7−→	7−→	NOUN
ejpam-441	45	23	(	(	PUNCT
ejpam-441	45	24	π	π	PROPN
ejpam-441	45	25	′′	′′	PROPN
ejpam-441	45	26	(	(	PUNCT
ejpam-441	45	27	e))bm	e))bm	NOUN
ejpam-441	45	28	:	:	PUNCT
ejpam-441	45	29	m(g)−→	m(g)−→	PROPN
ejpam-441	45	30	π	π	X
ejpam-441	45	31	′′	′′	PROPN
ejpam-441	45	32	(	(	PUNCT
ejpam-441	45	33	l1(g)∗∗	l1(g)∗∗	PROPN
ejpam-441	45	34	)	)	PUNCT
ejpam-441	45	35	is	be	AUX
ejpam-441	45	36	isometric	isometric	ADJ
ejpam-441	45	37	embedding	embedding	NOUN
ejpam-441	45	38	.	.	PUNCT
ejpam-441	46	1	we	we	PRON
ejpam-441	46	2	denote	denote	VERB
ejpam-441	46	3	this	this	DET
ejpam-441	46	4	map	map	NOUN
ejpam-441	46	5	with	with	ADP
ejpam-441	46	6	γe	γe	INTJ
ejpam-441	46	7	.	.	PUNCT
ejpam-441	47	1	since	since	SCONJ
ejpam-441	47	2	the	the	DET
ejpam-441	47	3	restriction	restriction	NOUN
ejpam-441	47	4	of	of	ADP
ejpam-441	47	5	γe	γe	PUNCT
ejpam-441	47	6	to	to	ADP
ejpam-441	47	7	l1(g	l1(g	PROPN
ejpam-441	47	8	)	)	PUNCT
ejpam-441	47	9	is	be	AUX
ejpam-441	47	10	identity	identity	NOUN
ejpam-441	47	11	map	map	NOUN
ejpam-441	47	12	,	,	PUNCT
ejpam-441	47	13	then	then	ADV
ejpam-441	47	14	γe(m	γe(m	NUM
ejpam-441	47	15	)	)	PUNCT
ejpam-441	47	16	∈ûπ(l1(g	∈ûπ(l1(g	NUM
ejpam-441	47	17	)	)	PUNCT
ejpam-441	47	18	)	)	PUNCT
ejpam-441	48	1	if	if	SCONJ
ejpam-441	48	2	and	and	CCONJ
ejpam-441	48	3	only	only	ADV
ejpam-441	48	4	if	if	SCONJ
ejpam-441	48	5	m	m	PROPN
ejpam-441	48	6	∈	∈	PROPN
ejpam-441	48	7	l1(g	l1(g	PROPN
ejpam-441	48	8	)	)	PUNCT
ejpam-441	48	9	.	.	PUNCT
ejpam-441	49	1	it	it	PRON
ejpam-441	49	2	is	be	AUX
ejpam-441	49	3	easy	easy	ADJ
ejpam-441	49	4	to	to	PART
ejpam-441	49	5	show	show	VERB
ejpam-441	49	6	that	that	SCONJ
ejpam-441	49	7	γe	γe	X
ejpam-441	49	8	′′	′′	PROPN
ejpam-441	49	9	is	be	AUX
ejpam-441	49	10	isometrically	isometrically	PROPN
ejpam-441	49	11	embedding	embed	VERB
ejpam-441	49	12	from	from	ADP
ejpam-441	49	13	(	(	PUNCT
ejpam-441	49	14	m(g)∗∗	m(g)∗∗	NOUN
ejpam-441	49	15	)	)	PUNCT
ejpam-441	49	16	into	into	ADP
ejpam-441	49	17	π	π	PROPN
ejpam-441	49	18	′′′′	′′′′	PROPN
ejpam-441	49	19	(	(	PUNCT
ejpam-441	49	20	(	(	PUNCT
ejpam-441	49	21	l1(g))∗∗∗∗	l1(g))∗∗∗∗	PROPN
ejpam-441	49	22	)	)	PUNCT
ejpam-441	49	23	.	.	PUNCT
ejpam-441	50	1	the	the	DET
ejpam-441	50	2	restriction	restriction	NOUN
ejpam-441	50	3	of	of	ADP
ejpam-441	50	4	γe	γe	CCONJ
ejpam-441	50	5	′′	′′	PROPN
ejpam-441	50	6	to	to	ADP
ejpam-441	50	7	π	π	PROPN
ejpam-441	50	8	′′	′′	PROPN
ejpam-441	50	9	(	(	PUNCT
ejpam-441	50	10	l1(g)∗∗	l1(g)∗∗	PROPN
ejpam-441	50	11	)	)	PUNCT
ejpam-441	50	12	is	be	AUX
ejpam-441	50	13	identity	identity	NOUN
ejpam-441	50	14	map	map	NOUN
ejpam-441	50	15	,	,	PUNCT
ejpam-441	50	16	then	then	ADV
ejpam-441	50	17	for	for	ADP
ejpam-441	50	18	every	every	DET
ejpam-441	50	19	m′′	m′′	PROPN
ejpam-441	50	20	∈	∈	PROPN
ejpam-441	50	21	(	(	PUNCT
ejpam-441	50	22	m(g)∗∗	m(g)∗∗	NOUN
ejpam-441	50	23	)	)	PUNCT
ejpam-441	50	24	,	,	PUNCT
ejpam-441	50	25	γe	γe	CCONJ
ejpam-441	51	1	′′	′′	PROPN
ejpam-441	51	2	(	(	PUNCT
ejpam-441	51	3	m	m	PROPN
ejpam-441	51	4	′′	′′	PROPN
ejpam-441	51	5	)	)	PUNCT
ejpam-441	51	6	∈	∈	PROPN
ejpam-441	51	7	ûπ′′(l1(g)∗∗	ûπ′′(l1(g)∗∗	PROPN
ejpam-441	51	8	)	)	PUNCT
ejpam-441	51	9	if	if	SCONJ
ejpam-441	51	10	and	and	CCONJ
ejpam-441	51	11	only	only	ADV
ejpam-441	51	12	if	if	SCONJ
ejpam-441	51	13	m	m	VERB
ejpam-441	51	14	′′	′′	PROPN
ejpam-441	51	15	∈	∈	PROPN
ejpam-441	51	16	ûπ′′(l1(g)∗∗	ûπ′′(l1(g)∗∗	PROPN
ejpam-441	51	17	)	)	PUNCT
ejpam-441	51	18	.	.	PUNCT
ejpam-441	52	1	let	let	VERB
ejpam-441	52	2	now	now	ADV
ejpam-441	52	3	m′′	m′′	VERB
ejpam-441	52	4	∈	∈	PROPN
ejpam-441	52	5	zl((m(g	zl((m(g	PROPN
ejpam-441	52	6	)	)	PUNCT
ejpam-441	52	7	∗∗	∗∗	NOUN
ejpam-441	52	8	)	)	PUNCT
ejpam-441	52	9	)	)	PUNCT
ejpam-441	52	10	,	,	PUNCT
ejpam-441	52	11	then	then	ADV
ejpam-441	52	12	(	(	PUNCT
ejpam-441	52	13	m(g))∗∗∗∗óm′′	m(g))∗∗∗∗óm′′	PROPN
ejpam-441	52	14	⊆û(m(g)∗∗	⊆û(m(g)∗∗	NOUN
ejpam-441	52	15	)	)	PUNCT
ejpam-441	52	16	.	.	PUNCT
ejpam-441	53	1	thus	thus	ADV
ejpam-441	53	2	π	π	PROPN
ejpam-441	53	3	′′′′	′′′′	PROPN
ejpam-441	53	4	(	(	PUNCT
ejpam-441	53	5	l1(g))∗∗∗∗óm′′	l1(g))∗∗∗∗óm′′	NOUN
ejpam-441	53	6	⊆û(m(g)∗∗	⊆û(m(g)∗∗	NOUN
ejpam-441	53	7	)	)	PUNCT
ejpam-441	53	8	.	.	PUNCT
ejpam-441	54	1	(	(	PUNCT
ejpam-441	54	2	1	1	X
ejpam-441	54	3	)	)	PUNCT
ejpam-441	54	4	on	on	ADP
ejpam-441	54	5	the	the	DET
ejpam-441	54	6	other	other	ADJ
ejpam-441	54	7	hand	hand	NOUN
ejpam-441	54	8	,	,	PUNCT
ejpam-441	54	9	we	we	PRON
ejpam-441	54	10	have	have	VERB
ejpam-441	54	11	direct	direct	ADJ
ejpam-441	54	12	sum	sum	NOUN
ejpam-441	54	13	decompositions	decomposition	NOUN
ejpam-441	54	14	(	(	PUNCT
ejpam-441	54	15	l1(g))∗∗∗∗	l1(g))∗∗∗∗	NOUN
ejpam-441	54	16	=	=	PROPN
ejpam-441	54	17	ûl1(g)∗∗⊕û(l1(g)∗	ûl1(g)∗∗⊕û(l1(g)∗	PROPN
ejpam-441	54	18	)	)	PUNCT
ejpam-441	55	1	⊥	⊥	PROPN
ejpam-441	55	2	(	(	PUNCT
ejpam-441	55	3	2	2	NUM
ejpam-441	55	4	)	)	PUNCT
ejpam-441	55	5	and	and	CCONJ
ejpam-441	55	6	(	(	PUNCT
ejpam-441	55	7	m(g))∗∗∗∗	m(g))∗∗∗∗	NOUN
ejpam-441	55	8	=	=	NOUN
ejpam-441	55	9	úm(g)∗∗⊕û(m(g)∗	úm(g)∗∗⊕û(m(g)∗	NOUN
ejpam-441	55	10	)	)	PUNCT
ejpam-441	55	11	⊥	⊥	NOUN
ejpam-441	55	12	.	.	PUNCT
ejpam-441	56	1	(	(	PUNCT
ejpam-441	56	2	3	3	X
ejpam-441	56	3	)	)	PUNCT
ejpam-441	56	4	so	so	SCONJ
ejpam-441	56	5	we	we	PRON
ejpam-441	56	6	have	have	VERB
ejpam-441	56	7	π	π	PROPN
ejpam-441	56	8	′′′′	′′′′	PROPN
ejpam-441	56	9	(	(	PUNCT
ejpam-441	56	10	û(l1(g)∗	û(l1(g)∗	NOUN
ejpam-441	56	11	)	)	PUNCT
ejpam-441	57	1	⊥	⊥	NOUN
ejpam-441	57	2	)	)	PUNCT
ejpam-441	57	3	⊆û(m(g)∗	⊆û(m(g)∗	NOUN
ejpam-441	57	4	)	)	PUNCT
ejpam-441	57	5	⊥	⊥	NOUN
ejpam-441	57	6	.	.	PUNCT
ejpam-441	58	1	(	(	PUNCT
ejpam-441	58	2	4	4	NUM
ejpam-441	58	3	)	)	PUNCT
ejpam-441	58	4	since	since	SCONJ
ejpam-441	58	5	π	π	PROPN
ejpam-441	58	6	′′′′	′′′′	PROPN
ejpam-441	58	7	(	(	PUNCT
ejpam-441	58	8	l1(g)∗∗∗∗	l1(g)∗∗∗∗	PROPN
ejpam-441	58	9	)	)	PUNCT
ejpam-441	58	10	is	be	AUX
ejpam-441	58	11	an	an	DET
ejpam-441	58	12	ideal	ideal	NOUN
ejpam-441	58	13	of	of	ADP
ejpam-441	58	14	m(g)∗∗∗∗	m(g)∗∗∗∗	NOUN
ejpam-441	58	15	,	,	PUNCT
ejpam-441	58	16	then	then	ADV
ejpam-441	58	17	by	by	ADP
ejpam-441	58	18	(	(	PUNCT
ejpam-441	58	19	2	2	NUM
ejpam-441	58	20	)	)	PUNCT
ejpam-441	58	21	and	and	CCONJ
ejpam-441	58	22	(	(	PUNCT
ejpam-441	58	23	4	4	NUM
ejpam-441	58	24	)	)	PUNCT
ejpam-441	58	25	,	,	PUNCT
ejpam-441	58	26	we	we	PRON
ejpam-441	58	27	have	have	VERB
ejpam-441	58	28	π	π	PROPN
ejpam-441	58	29	′′′′	′′′′	PROPN
ejpam-441	58	30	(	(	PUNCT
ejpam-441	58	31	l1(g))∗∗∗∗óm′′	l1(g))∗∗∗∗óm′′	NOUN
ejpam-441	58	32	⊆	⊆	NUM
ejpam-441	59	1	[	[	X
ejpam-441	59	2	(	(	PUNCT
ejpam-441	59	3	û(m(g)∗∗))∩π	û(m(g)∗∗))∩π	ADV
ejpam-441	59	4	′′′′	′′′′	PROPN
ejpam-441	59	5	(	(	PUNCT
ejpam-441	59	6	l1(g))∗∗∗∗	l1(g))∗∗∗∗	PROPN
ejpam-441	59	7	]	]	X
ejpam-441	59	8	=	=	SYM
ejpam-441	59	9	ûπ	ûπ	PROPN
ejpam-441	59	10	′′	′′	PROPN
ejpam-441	59	11	(	(	PUNCT
ejpam-441	59	12	l1(g)∗∗	l1(g)∗∗	PROPN
ejpam-441	59	13	)	)	PUNCT
ejpam-441	59	14	.	.	PUNCT
ejpam-441	60	1	therefore	therefore	ADV
ejpam-441	60	2	γe	γe	PRON
ejpam-441	60	3	′′(m′′	′′(m′′	VERB
ejpam-441	60	4	)	)	PUNCT
ejpam-441	60	5	∈	∈	PROPN
ejpam-441	60	6	û	û	NOUN
ejpam-441	60	7	π	π	X
ejpam-441	60	8	′′	′′	PROPN
ejpam-441	60	9	(	(	PUNCT
ejpam-441	60	10	l1(g)∗∗	l1(g)∗∗	PROPN
ejpam-441	60	11	)	)	PUNCT
ejpam-441	60	12	and	and	CCONJ
ejpam-441	60	13	m′′	m′′	PROPN
ejpam-441	60	14	∈	∈	PROPN
ejpam-441	60	15	π′′(l1(g)∗∗	π′′(l1(g)∗∗	PROPN
ejpam-441	60	16	)	)	PUNCT
ejpam-441	60	17	,	,	PUNCT
ejpam-441	60	18	hence	hence	ADV
ejpam-441	60	19	,	,	PUNCT
ejpam-441	60	20	zl(m(g	zl(m(g	NOUN
ejpam-441	60	21	)	)	PUNCT
ejpam-441	60	22	∗∗	∗∗	NOUN
ejpam-441	60	23	)	)	PUNCT
ejpam-441	60	24	⊆	⊆	NUM
ejpam-441	60	25	π′′(l1(g)∗∗	π′′(l1(g)∗∗	NOUN
ejpam-441	60	26	)	)	PUNCT
ejpam-441	60	27	.	.	PUNCT
ejpam-441	61	1	on	on	ADP
ejpam-441	61	2	the	the	DET
ejpam-441	61	3	other	other	ADJ
ejpam-441	61	4	hand	hand	NOUN
ejpam-441	61	5	since	since	SCONJ
ejpam-441	61	6	g	g	PROPN
ejpam-441	61	7	is	be	AUX
ejpam-441	61	8	compact	compact	ADJ
ejpam-441	61	9	then	then	ADV
ejpam-441	61	10	π′′(l1(g	π′′(l1(g	PROPN
ejpam-441	61	11	)	)	PUNCT
ejpam-441	61	12	∗∗	∗∗	PROPN
ejpam-441	61	13	)	)	PUNCT
ejpam-441	61	14	is	be	AUX
ejpam-441	61	15	a	a	DET
ejpam-441	61	16	two	two	NUM
ejpam-441	61	17	sided	sided	ADJ
ejpam-441	61	18	ideal	ideal	NOUN
ejpam-441	61	19	of	of	ADP
ejpam-441	61	20	π′′′′(l1(g)∗∗∗∗	π′′′′(l1(g)∗∗∗∗	PROPN
ejpam-441	61	21	)	)	PUNCT
ejpam-441	61	22	,	,	PUNCT
ejpam-441	61	23	so	so	SCONJ
ejpam-441	61	24	zl(π	zl(π	PUNCT
ejpam-441	61	25	′′(l1(g)∗∗	′′(l1(g)∗∗	NOUN
ejpam-441	61	26	)	)	PUNCT
ejpam-441	61	27	)	)	PUNCT
ejpam-441	62	1	=	=	SYM
ejpam-441	62	2	π′′(l1(g)∗∗	π′′(l1(g)∗∗	PROPN
ejpam-441	62	3	)	)	PUNCT
ejpam-441	62	4	and	and	CCONJ
ejpam-441	62	5	zl(π	zl(π	NUM
ejpam-441	62	6	′′(l1(g)∗∗	′′(l1(g)∗∗	NOUN
ejpam-441	62	7	)	)	PUNCT
ejpam-441	62	8	)	)	PUNCT
ejpam-441	62	9	is	be	AUX
ejpam-441	62	10	a	a	DET
ejpam-441	62	11	two	two	NUM
ejpam-441	62	12	sided	sided	ADJ
ejpam-441	62	13	ideal	ideal	NOUN
ejpam-441	62	14	of	of	ADP
ejpam-441	62	15	m(g)∗∗∗∗.	m(g)∗∗∗∗.	PROPN
ejpam-441	62	16	hence	hence	ADV
ejpam-441	62	17	,	,	PUNCT
ejpam-441	62	18	π′′(l1(g)∗∗)⊆	π′′(l1(g)∗∗)⊆	NOUN
ejpam-441	62	19	zl(m(g	zl(m(g	NUM
ejpam-441	62	20	)	)	PUNCT
ejpam-441	62	21	∗∗	∗∗	NOUN
ejpam-441	62	22	)	)	PUNCT
ejpam-441	62	23	.	.	PUNCT
ejpam-441	63	1	�	�	PROPN
ejpam-441	63	2	we	we	PRON
ejpam-441	63	3	now	now	ADV
ejpam-441	63	4	apply	apply	VERB
ejpam-441	63	5	above	above	ADP
ejpam-441	63	6	theorem	theorem	NOUN
ejpam-441	63	7	to	to	PART
ejpam-441	63	8	show	show	VERB
ejpam-441	63	9	that	that	SCONJ
ejpam-441	63	10	m(g)∗∗	m(g)∗∗	NOUN
ejpam-441	63	11	determines	determine	VERB
ejpam-441	63	12	g	g	NOUN
ejpam-441	63	13	when	when	SCONJ
ejpam-441	63	14	g	g	PROPN
ejpam-441	63	15	is	be	AUX
ejpam-441	63	16	a	a	DET
ejpam-441	63	17	compact	compact	ADJ
ejpam-441	63	18	topological	topological	ADJ
ejpam-441	63	19	group	group	NOUN
ejpam-441	63	20	.	.	PUNCT
ejpam-441	64	1	it	it	PRON
ejpam-441	64	2	is	be	AUX
ejpam-441	64	3	a	a	DET
ejpam-441	64	4	new	new	ADJ
ejpam-441	64	5	proof	proof	NOUN
ejpam-441	64	6	for	for	ADP
ejpam-441	64	7	the	the	DET
ejpam-441	64	8	main	main	ADJ
ejpam-441	64	9	result	result	NOUN
ejpam-441	64	10	of	of	ADP
ejpam-441	64	11	[	[	X
ejpam-441	64	12	4	4	NUM
ejpam-441	64	13	]	]	PUNCT
ejpam-441	64	14	.	.	PUNCT
ejpam-441	65	1	by	by	ADP
ejpam-441	65	2	lemma	lemma	PROPN
ejpam-441	65	3	1	1	NUM
ejpam-441	65	4	and	and	CCONJ
ejpam-441	65	5	theorem	theorem	VERB
ejpam-441	65	6	1	1	NUM
ejpam-441	65	7	we	we	PRON
ejpam-441	65	8	have	have	VERB
ejpam-441	65	9	the	the	DET
ejpam-441	65	10	following	following	NOUN
ejpam-441	65	11	.	.	PUNCT
ejpam-441	66	1	references	reference	NOUN
ejpam-441	66	2	577	577	NUM
ejpam-441	66	3	corollary	corollary	ADJ
ejpam-441	66	4	1	1	NUM
ejpam-441	66	5	(	(	PUNCT
ejpam-441	66	6	theorem	theorem	VERB
ejpam-441	66	7	7	7	NUM
ejpam-441	66	8	of	of	ADP
ejpam-441	66	9	4	4	NUM
ejpam-441	66	10	)	)	PUNCT
ejpam-441	66	11	.	.	PUNCT
ejpam-441	66	12	.	.	PUNCT
ejpam-441	67	1	if	if	SCONJ
ejpam-441	67	2	g1	g1	PROPN
ejpam-441	67	3	and	and	CCONJ
ejpam-441	67	4	g2	g2	PROPN
ejpam-441	67	5	are	be	AUX
ejpam-441	67	6	compact	compact	ADJ
ejpam-441	67	7	groups	group	NOUN
ejpam-441	67	8	,	,	PUNCT
ejpam-441	67	9	and	and	CCONJ
ejpam-441	67	10	if	if	SCONJ
ejpam-441	67	11	θ	θ	PROPN
ejpam-441	67	12	is	be	AUX
ejpam-441	67	13	an	an	DET
ejpam-441	67	14	isometric	isometric	ADJ
ejpam-441	67	15	isomorphism	isomorphism	NOUN
ejpam-441	67	16	from	from	ADP
ejpam-441	67	17	m(g1	m(g1	NOUN
ejpam-441	67	18	)	)	PUNCT
ejpam-441	67	19	∗∗	∗∗	NOUN
ejpam-441	67	20	onto	onto	ADP
ejpam-441	67	21	m(g2	m(g2	NOUN
ejpam-441	67	22	)	)	PUNCT
ejpam-441	68	1	∗∗	∗∗	PROPN
ejpam-441	68	2	,	,	PUNCT
ejpam-441	68	3	then	then	ADV
ejpam-441	68	4	θ	θ	X
ejpam-441	68	5	(	(	PUNCT
ejpam-441	68	6	l1(g1	l1(g1	PROPN
ejpam-441	68	7	)	)	PUNCT
ejpam-441	68	8	∗∗	∗∗	NOUN
ejpam-441	68	9	)	)	PUNCT
ejpam-441	68	10	=	=	SYM
ejpam-441	68	11	l1(g2	l1(g2	ADJ
ejpam-441	68	12	)	)	PUNCT
ejpam-441	68	13	∗∗.	∗∗.	NOUN
ejpam-441	68	14	since	since	SCONJ
ejpam-441	68	15	l1(g)∗∗	l1(g)∗∗	PROPN
ejpam-441	68	16	determines	determine	VERB
ejpam-441	68	17	g	g	PROPN
ejpam-441	68	18	[	[	X
ejpam-441	68	19	3	3	X
ejpam-441	68	20	]	]	PUNCT
ejpam-441	68	21	,	,	PUNCT
ejpam-441	68	22	then	then	ADV
ejpam-441	68	23	we	we	PRON
ejpam-441	68	24	have	have	VERB
ejpam-441	68	25	corollary	corollary	ADJ
ejpam-441	68	26	2	2	NUM
ejpam-441	68	27	.	.	PUNCT
ejpam-441	69	1	if	if	SCONJ
ejpam-441	69	2	g	g	PROPN
ejpam-441	69	3	is	be	AUX
ejpam-441	69	4	a	a	DET
ejpam-441	69	5	compact	compact	ADJ
ejpam-441	69	6	group	group	NOUN
ejpam-441	69	7	,	,	PUNCT
ejpam-441	69	8	then	then	ADV
ejpam-441	69	9	m(g)∗∗	m(g)∗∗	NOUN
ejpam-441	69	10	determines	determine	VERB
ejpam-441	69	11	g.	g.	PROPN
ejpam-441	69	12	references	reference	NOUN
ejpam-441	69	13	[	[	X
ejpam-441	69	14	1	1	NUM
ejpam-441	69	15	]	]	PUNCT
ejpam-441	69	16	r.	r.	PROPN
ejpam-441	69	17	arens	arens	PROPN
ejpam-441	69	18	,	,	PUNCT
ejpam-441	69	19	the	the	DET
ejpam-441	69	20	adjoint	adjoint	NOUN
ejpam-441	69	21	of	of	ADP
ejpam-441	69	22	a	a	DET
ejpam-441	69	23	bilinear	bilinear	NOUN
ejpam-441	69	24	operation	operation	NOUN
ejpam-441	69	25	,	,	PUNCT
ejpam-441	69	26	proc	proc	PROPN
ejpam-441	69	27	.	.	PUNCT
ejpam-441	70	1	amer	amer	PROPN
ejpam-441	70	2	.	.	PUNCT
ejpam-441	70	3	math	math	PROPN
ejpam-441	70	4	.	.	PUNCT
ejpam-441	71	1	soc	soc	PROPN
ejpam-441	71	2	.	.	PUNCT
ejpam-441	72	1	2(1951	2(1951	NUM
ejpam-441	72	2	)	)	PUNCT
ejpam-441	72	3	,	,	PUNCT
ejpam-441	73	1	839–848	839–848	NUM
ejpam-441	73	2	.	.	PUNCT
ejpam-441	74	1	[	[	X
ejpam-441	74	2	2	2	X
ejpam-441	74	3	]	]	PUNCT
ejpam-441	74	4	j.	j.	PROPN
ejpam-441	74	5	duncan	duncan	PROPN
ejpam-441	74	6	and	and	CCONJ
ejpam-441	74	7	s.	s.	PROPN
ejpam-441	74	8	a.	a.	PROPN
ejpam-441	74	9	hosseiniun	hosseiniun	PROPN
ejpam-441	74	10	,	,	PUNCT
ejpam-441	74	11	the	the	DET
ejpam-441	74	12	second	second	ADJ
ejpam-441	74	13	dual	dual	ADJ
ejpam-441	74	14	of	of	ADP
ejpam-441	74	15	banach	banach	NOUN
ejpam-441	74	16	algebra	algebra	NOUN
ejpam-441	74	17	,	,	PUNCT
ejpam-441	74	18	proc	proc	NOUN
ejpam-441	74	19	.	.	PUNCT
ejpam-441	75	1	roy	roy	PROPN
ejpam-441	75	2	.	.	PROPN
ejpam-441	75	3	soc	soc	PROPN
ejpam-441	75	4	.	.	PUNCT
ejpam-441	76	1	edinburgh	edinburgh	PROPN
ejpam-441	76	2	sect	sect	PROPN
ejpam-441	76	3	.	.	PUNCT
ejpam-441	77	1	a	a	DET
ejpam-441	77	2	84	84	NUM
ejpam-441	77	3	(	(	PUNCT
ejpam-441	77	4	1979	1979	NUM
ejpam-441	77	5	)	)	PUNCT
ejpam-441	77	6	,	,	PUNCT
ejpam-441	77	7	309–325	309–325	NUM
ejpam-441	77	8	.	.	PUNCT
ejpam-441	78	1	[	[	X
ejpam-441	78	2	3	3	NUM
ejpam-441	78	3	]	]	X
ejpam-441	78	4	f.	f.	PROPN
ejpam-441	78	5	ghahramani	ghahramani	PROPN
ejpam-441	78	6	and	and	CCONJ
ejpam-441	78	7	anthony	anthony	PROPN
ejpam-441	78	8	to	to	ADP
ejpam-441	78	9	-	-	PUNCT
ejpam-441	78	10	ming	ming	PROPN
ejpam-441	78	11	lau	lau	PROPN
ejpam-441	78	12	,	,	PUNCT
ejpam-441	78	13	multipliers	multiplier	NOUN
ejpam-441	78	14	and	and	CCONJ
ejpam-441	78	15	ideals	ideal	NOUN
ejpam-441	78	16	in	in	ADP
ejpam-441	78	17	second	second	ADJ
ejpam-441	78	18	conjugate	conjugate	ADJ
ejpam-441	78	19	algebras	algebra	NOUN
ejpam-441	78	20	related	relate	VERB
ejpam-441	78	21	to	to	ADP
ejpam-441	78	22	locally	locally	ADV
ejpam-441	78	23	compact	compact	ADJ
ejpam-441	78	24	groups	group	NOUN
ejpam-441	78	25	,	,	PUNCT
ejpam-441	78	26	journal	journal	NOUN
ejpam-441	78	27	of	of	ADP
ejpam-441	78	28	functional	functional	ADJ
ejpam-441	78	29	analysis	analysis	NOUN
ejpam-441	78	30	132	132	NUM
ejpam-441	78	31	(	(	PUNCT
ejpam-441	78	32	1995	1995	NUM
ejpam-441	78	33	)	)	PUNCT
ejpam-441	78	34	170–191	170–191	NUM
ejpam-441	78	35	.	.	PUNCT
ejpam-441	79	1	[	[	X
ejpam-441	79	2	4	4	NUM
ejpam-441	79	3	]	]	PUNCT
ejpam-441	79	4	f.	f.	PROPN
ejpam-441	79	5	ghahramani	ghahramani	PROPN
ejpam-441	79	6	and	and	CCONJ
ejpam-441	79	7	j.	j.	PROPN
ejpam-441	79	8	p.	p.	PROPN
ejpam-441	79	9	mcclure	mcclure	PROPN
ejpam-441	79	10	,	,	PUNCT
ejpam-441	79	11	the	the	DET
ejpam-441	79	12	second	second	ADJ
ejpam-441	79	13	dual	dual	ADJ
ejpam-441	79	14	algebra	algebra	NOUN
ejpam-441	79	15	of	of	ADP
ejpam-441	79	16	the	the	DET
ejpam-441	79	17	measure	measure	NOUN
ejpam-441	79	18	algebra	algebra	NOUN
ejpam-441	79	19	of	of	ADP
ejpam-441	79	20	a	a	DET
ejpam-441	79	21	compact	compact	ADJ
ejpam-441	79	22	group	group	NOUN
ejpam-441	79	23	,	,	PUNCT
ejpam-441	79	24	bull	bull	PROPN
ejpam-441	79	25	.	.	PUNCT
ejpam-441	80	1	london	london	PROPN
ejpam-441	80	2	math	math	PROPN
ejpam-441	80	3	.	.	PUNCT
ejpam-441	81	1	soc	soc	PROPN
ejpam-441	81	2	.	.	PUNCT
ejpam-441	82	1	29	29	NUM
ejpam-441	82	2	(	(	PUNCT
ejpam-441	82	3	1997	1997	NUM
ejpam-441	82	4	)	)	PUNCT
ejpam-441	83	1	223–226	223–226	NUM
ejpam-441	83	2	.	.	PUNCT
ejpam-441	84	1	[	[	X
ejpam-441	84	2	5	5	NUM
ejpam-441	84	3	]	]	PUNCT
ejpam-441	84	4	b.	b.	PROPN
ejpam-441	84	5	e.	e.	PROPN
ejpam-441	84	6	johnson	johnson	PROPN
ejpam-441	84	7	,	,	PUNCT
ejpam-441	84	8	isometric	isometric	ADJ
ejpam-441	84	9	isomorphisms	isomorphism	NOUN
ejpam-441	84	10	of	of	ADP
ejpam-441	84	11	measure	measure	NOUN
ejpam-441	84	12	algebras	algebra	NOUN
ejpam-441	84	13	,	,	PUNCT
ejpam-441	84	14	proc	proc	PROPN
ejpam-441	84	15	.	.	PUNCT
ejpam-441	85	1	amer	amer	PROPN
ejpam-441	85	2	.	.	PUNCT
ejpam-441	85	3	math	math	PROPN
ejpam-441	85	4	.	.	PUNCT
ejpam-441	86	1	soc	soc	PROPN
ejpam-441	86	2	.	.	PUNCT
ejpam-441	87	1	15(1964	15(1964	NUM
ejpam-441	87	2	)	)	PUNCT
ejpam-441	87	3	,	,	PUNCT
ejpam-441	88	1	186–188	186–188	NUM
ejpam-441	88	2	.	.	PUNCT
ejpam-441	89	1	[	[	X
ejpam-441	89	2	6	6	NUM
ejpam-441	89	3	]	]	PUNCT
ejpam-441	89	4	j.	j.	PROPN
ejpam-441	89	5	g.	g.	PROPN
ejpam-441	89	6	wendel	wendel	PROPN
ejpam-441	89	7	,	,	PUNCT
ejpam-441	89	8	left	leave	VERB
ejpam-441	89	9	centralizers	centralizer	NOUN
ejpam-441	89	10	and	and	CCONJ
ejpam-441	89	11	isomorphisms	isomorphism	NOUN
ejpam-441	89	12	of	of	ADP
ejpam-441	89	13	group	group	NOUN
ejpam-441	89	14	algebras	algebra	NOUN
ejpam-441	89	15	,	,	PUNCT
ejpam-441	89	16	pacific	pacific	PROPN
ejpam-441	89	17	j.	j.	PROPN
ejpam-441	89	18	math	math	PROPN
ejpam-441	89	19	.	.	PUNCT
ejpam-441	90	1	2	2	NUM
ejpam-441	90	2	(	(	PUNCT
ejpam-441	90	3	1952	1952	NUM
ejpam-441	90	4	)	)	PUNCT
ejpam-441	91	1	251–256	251–256	NUM
ejpam-441	91	2	.	.	PUNCT