id	sid	tid	token	lemma	pos
ejpam-2299	1	1	compile	compile	VERB
ejpam-2299	1	2	/	/	SYM
ejpam-2299	1	3	output.dvi	output.dvi	X
ejpam-2299	1	4	(	(	PUNCT
ejpam-2299	1	5	-1)-weak	-1)-weak	INTJ
ejpam-2299	1	6	amenability	amenability	NOUN
ejpam-2299	1	7	of	of	ADP
ejpam-2299	1	8	unitized	unitized	ADJ
ejpam-2299	1	9	banach	banach	NOUN
ejpam-2299	1	10	algebras	algebras	PROPN
ejpam-2299	1	11	s.	s.	PROPN
ejpam-2299	1	12	alireza	alireza	PROPN
ejpam-2299	1	13	hosseinioun1	hosseinioun1	PROPN
ejpam-2299	1	14	,	,	PUNCT
ejpam-2299	1	15	arezou	arezou	PROPN
ejpam-2299	1	16	valadkhani	valadkhani	PROPN
ejpam-2299	1	17	2,∗	2,∗	NUM
ejpam-2299	1	18	1	1	NUM
ejpam-2299	1	19	university	university	NOUN
ejpam-2299	1	20	of	of	ADP
ejpam-2299	1	21	arkansas	arkansas	PROPN
ejpam-2299	1	22	,	,	PUNCT
ejpam-2299	1	23	department	department	NOUN
ejpam-2299	1	24	of	of	ADP
ejpam-2299	1	25	mathematical	mathematical	ADJ
ejpam-2299	1	26	sciences	sciences	PROPN
ejpam-2299	1	27	,	,	PUNCT
ejpam-2299	1	28	fayetteville	fayetteville	PROPN
ejpam-2299	1	29	,	,	PUNCT
ejpam-2299	1	30	ar	ar	PROPN
ejpam-2299	1	31	72703	72703	NUM
ejpam-2299	1	32	,	,	PUNCT
ejpam-2299	1	33	usa	usa	PROPN
ejpam-2299	1	34	2	2	NUM
ejpam-2299	1	35	department	department	NOUN
ejpam-2299	1	36	of	of	ADP
ejpam-2299	1	37	mathematics	mathematic	NOUN
ejpam-2299	1	38	,	,	PUNCT
ejpam-2299	1	39	shahid	shahid	PROPN
ejpam-2299	1	40	beheshti	beheshti	PROPN
ejpam-2299	1	41	university	university	NOUN
ejpam-2299	1	42	,	,	PUNCT
ejpam-2299	1	43	tehran	tehran	PROPN
ejpam-2299	1	44	,	,	PUNCT
ejpam-2299	1	45	iran	iran	PROPN
ejpam-2299	1	46	abstract	abstract	ADJ
ejpam-2299	1	47	.	.	PUNCT
ejpam-2299	2	1	for	for	ADP
ejpam-2299	2	2	a	a	DET
ejpam-2299	2	3	banach	banach	NOUN
ejpam-2299	2	4	algebra	algebra	NOUN
ejpam-2299	2	5	a	a	PRON
ejpam-2299	2	6	,	,	PUNCT
ejpam-2299	2	7	its	its	PRON
ejpam-2299	2	8	second	second	ADJ
ejpam-2299	2	9	dual	dual	ADJ
ejpam-2299	2	10	a′′	a′′	NOUN
ejpam-2299	2	11	is	be	AUX
ejpam-2299	2	12	(	(	PUNCT
ejpam-2299	2	13	-1)-weakly	-1)-weakly	ADV
ejpam-2299	2	14	amenable	amenable	ADJ
ejpam-2299	2	15	if	if	SCONJ
ejpam-2299	2	16	a′	a′	PROPN
ejpam-2299	2	17	is	be	AUX
ejpam-2299	2	18	a	a	DET
ejpam-2299	2	19	banach	banach	NOUN
ejpam-2299	2	20	a′′bimodule	a′′bimodule	NOUN
ejpam-2299	2	21	and	and	CCONJ
ejpam-2299	2	22	the	the	DET
ejpam-2299	2	23	first	first	ADJ
ejpam-2299	2	24	cohomology	cohomology	NOUN
ejpam-2299	2	25	group	group	NOUN
ejpam-2299	2	26	of	of	ADP
ejpam-2299	2	27	a′′	a′′	NOUN
ejpam-2299	2	28	with	with	ADP
ejpam-2299	2	29	coefficients	coefficient	NOUN
ejpam-2299	2	30	in	in	ADP
ejpam-2299	2	31	a′	a′	PROPN
ejpam-2299	2	32	is	be	AUX
ejpam-2299	2	33	zero	zero	NUM
ejpam-2299	2	34	i.e.	i.e.	X
ejpam-2299	2	35	h1(a′′,a′	h1(a′′,a′	NOUN
ejpam-2299	2	36	)	)	PUNCT
ejpam-2299	3	1	=	=	PRON
ejpam-2299	3	2	{	{	PUNCT
ejpam-2299	3	3	0	0	NUM
ejpam-2299	3	4	}	}	PUNCT
ejpam-2299	3	5	.	.	PUNCT
ejpam-2299	4	1	we	we	PRON
ejpam-2299	4	2	first	first	ADV
ejpam-2299	4	3	show	show	VERB
ejpam-2299	4	4	that	that	SCONJ
ejpam-2299	4	5	under	under	ADP
ejpam-2299	4	6	certain	certain	ADJ
ejpam-2299	4	7	conditions	condition	NOUN
ejpam-2299	4	8	a′	a′	NOUN
ejpam-2299	4	9	is	be	AUX
ejpam-2299	4	10	a	a	DET
ejpam-2299	4	11	banach	banach	NOUN
ejpam-2299	4	12	a′′-bimodule	a′′-bimodule	NOUN
ejpam-2299	4	13	.	.	PUNCT
ejpam-2299	5	1	we	we	PRON
ejpam-2299	5	2	then	then	ADV
ejpam-2299	5	3	consider	consider	VERB
ejpam-2299	5	4	the	the	DET
ejpam-2299	5	5	relationships	relationship	NOUN
ejpam-2299	5	6	between	between	ADP
ejpam-2299	5	7	(	(	PUNCT
ejpam-2299	5	8	-1)-weak	-1)-weak	INTJ
ejpam-2299	5	9	amenability	amenability	NOUN
ejpam-2299	5	10	of	of	ADP
ejpam-2299	5	11	a	a	PRON
ejpam-2299	5	12	and	and	CCONJ
ejpam-2299	5	13	a	a	DET
ejpam-2299	5	14	#	#	NOUN
ejpam-2299	5	15	,	,	PUNCT
ejpam-2299	5	16	where	where	SCONJ
ejpam-2299	5	17	a	a	DET
ejpam-2299	5	18	#	#	NOUN
ejpam-2299	5	19	is	be	AUX
ejpam-2299	5	20	the	the	DET
ejpam-2299	5	21	unitization	unitization	NOUN
ejpam-2299	5	22	of	of	ADP
ejpam-2299	5	23	a.	a.	NOUN
ejpam-2299	5	24	2010	2010	NUM
ejpam-2299	5	25	mathematics	mathematic	NOUN
ejpam-2299	5	26	subject	subject	NOUN
ejpam-2299	5	27	classifications	classification	NOUN
ejpam-2299	5	28	:	:	PUNCT
ejpam-2299	5	29	46h25	46h25	NUM
ejpam-2299	5	30	key	key	ADJ
ejpam-2299	5	31	words	word	NOUN
ejpam-2299	5	32	and	and	CCONJ
ejpam-2299	5	33	phrases	phrase	NOUN
ejpam-2299	5	34	:	:	PUNCT
ejpam-2299	5	35	banach	banach	NOUN
ejpam-2299	5	36	algebra	algebra	NOUN
ejpam-2299	5	37	,	,	PUNCT
ejpam-2299	5	38	(	(	PUNCT
ejpam-2299	5	39	-1)-weak	-1)-weak	INTJ
ejpam-2299	5	40	amenability	amenability	NOUN
ejpam-2299	5	41	,	,	PUNCT
ejpam-2299	5	42	arens	aren	VERB
ejpam-2299	5	43	products	product	NOUN
ejpam-2299	5	44	unitization	unitization	NOUN
ejpam-2299	5	45	.	.	PUNCT
ejpam-2299	6	1	1	1	X
ejpam-2299	6	2	.	.	X
ejpam-2299	6	3	introduction	introduction	NOUN
ejpam-2299	6	4	let	let	VERB
ejpam-2299	6	5	a	a	PRON
ejpam-2299	6	6	be	be	AUX
ejpam-2299	6	7	a	a	DET
ejpam-2299	6	8	banach	banach	NOUN
ejpam-2299	6	9	algebra	algebra	NOUN
ejpam-2299	6	10	and	and	CCONJ
ejpam-2299	6	11	e	e	NOUN
ejpam-2299	6	12	be	be	AUX
ejpam-2299	6	13	a	a	DET
ejpam-2299	6	14	banach	banach	NOUN
ejpam-2299	6	15	a	a	DET
ejpam-2299	6	16	-	-	PUNCT
ejpam-2299	6	17	bimodule	bimodule	NOUN
ejpam-2299	6	18	,	,	PUNCT
ejpam-2299	6	19	then	then	ADV
ejpam-2299	6	20	a	a	DET
ejpam-2299	6	21	bounded	bounded	ADJ
ejpam-2299	6	22	derivation	derivation	NOUN
ejpam-2299	6	23	from	from	ADP
ejpam-2299	6	24	a	a	PRON
ejpam-2299	6	25	into	into	ADP
ejpam-2299	6	26	e	e	PROPN
ejpam-2299	6	27	is	be	AUX
ejpam-2299	6	28	a	a	DET
ejpam-2299	6	29	bounded	bounded	ADJ
ejpam-2299	6	30	linear	linear	NOUN
ejpam-2299	6	31	mapping	mapping	NOUN
ejpam-2299	7	1	d	d	NOUN
ejpam-2299	7	2	:	:	PUNCT
ejpam-2299	7	3	a	a	DET
ejpam-2299	7	4	−→	−→	NOUN
ejpam-2299	7	5	e	e	NOUN
ejpam-2299	7	6	such	such	ADJ
ejpam-2299	7	7	that	that	SCONJ
ejpam-2299	7	8	d(a	d(a	PROPN
ejpam-2299	7	9	·	·	PUNCT
ejpam-2299	7	10	b	b	X
ejpam-2299	7	11	)	)	PUNCT
ejpam-2299	7	12	=	=	SYM
ejpam-2299	7	13	da	da	PART
ejpam-2299	7	14	·	·	PUNCT
ejpam-2299	7	15	b	b	X
ejpam-2299	7	16	+	+	CCONJ
ejpam-2299	7	17	a	a	DET
ejpam-2299	7	18	·	·	SYM
ejpam-2299	7	19	db	db	NOUN
ejpam-2299	7	20	,	,	PUNCT
ejpam-2299	7	21	for	for	ADP
ejpam-2299	7	22	each	each	DET
ejpam-2299	7	23	a	a	NOUN
ejpam-2299	7	24	,	,	PUNCT
ejpam-2299	7	25	b	b	X
ejpam-2299	7	26	∈	∈	PROPN
ejpam-2299	7	27	a.	a.	NOUN
ejpam-2299	7	28	for	for	ADP
ejpam-2299	7	29	example	example	NOUN
ejpam-2299	7	30	let	let	VERB
ejpam-2299	7	31	x	x	SYM
ejpam-2299	7	32	∈	∈	PROPN
ejpam-2299	7	33	x	x	PUNCT
ejpam-2299	7	34	and	and	CCONJ
ejpam-2299	7	35	define	define	VERB
ejpam-2299	7	36	δx	δx	PROPN
ejpam-2299	7	37	:	:	PUNCT
ejpam-2299	7	38	a	a	DET
ejpam-2299	7	39	−→	−→	NOUN
ejpam-2299	7	40	e	e	NOUN
ejpam-2299	7	41	by	by	ADP
ejpam-2299	7	42	δx	δx	PROPN
ejpam-2299	7	43	a	a	DET
ejpam-2299	7	44	=	=	PUNCT
ejpam-2299	7	45	a	a	PRON
ejpam-2299	7	46	·	·	PUNCT
ejpam-2299	7	47	x	x	SYM
ejpam-2299	8	1	−	−	PROPN
ejpam-2299	8	2	x	x	SYM
ejpam-2299	8	3	·	·	PUNCT
ejpam-2299	8	4	a	a	X
ejpam-2299	8	5	,	,	PUNCT
ejpam-2299	8	6	then	then	ADV
ejpam-2299	8	7	δx	δx	VERB
ejpam-2299	8	8	is	be	AUX
ejpam-2299	8	9	a	a	DET
ejpam-2299	8	10	bounded	bounded	ADJ
ejpam-2299	8	11	derivation	derivation	NOUN
ejpam-2299	8	12	which	which	PRON
ejpam-2299	8	13	is	be	AUX
ejpam-2299	8	14	called	call	VERB
ejpam-2299	8	15	an	an	DET
ejpam-2299	8	16	inner	inner	ADJ
ejpam-2299	8	17	derivation	derivation	NOUN
ejpam-2299	8	18	.	.	PUNCT
ejpam-2299	9	1	let	let	VERB
ejpam-2299	9	2	z1(a	z1(a	PRON
ejpam-2299	9	3	,	,	PUNCT
ejpam-2299	9	4	e	e	NOUN
ejpam-2299	9	5	)	)	PUNCT
ejpam-2299	9	6	be	be	AUX
ejpam-2299	9	7	the	the	DET
ejpam-2299	9	8	space	space	NOUN
ejpam-2299	9	9	of	of	ADP
ejpam-2299	9	10	all	all	DET
ejpam-2299	9	11	bounded	bounded	ADJ
ejpam-2299	9	12	derivations	derivation	NOUN
ejpam-2299	9	13	from	from	ADP
ejpam-2299	9	14	a	a	PRON
ejpam-2299	9	15	into	into	ADP
ejpam-2299	9	16	e	e	NOUN
ejpam-2299	9	17	,	,	PUNCT
ejpam-2299	9	18	n1(a	n1(a	NOUN
ejpam-2299	9	19	,	,	PUNCT
ejpam-2299	9	20	e	e	NOUN
ejpam-2299	9	21	)	)	PUNCT
ejpam-2299	9	22	be	be	AUX
ejpam-2299	9	23	the	the	DET
ejpam-2299	9	24	space	space	NOUN
ejpam-2299	9	25	of	of	ADP
ejpam-2299	9	26	all	all	DET
ejpam-2299	9	27	inner	inner	ADJ
ejpam-2299	9	28	derivations	derivation	NOUN
ejpam-2299	9	29	from	from	ADP
ejpam-2299	9	30	a	a	PRON
ejpam-2299	9	31	into	into	ADP
ejpam-2299	9	32	e	e	NOUN
ejpam-2299	9	33	and	and	CCONJ
ejpam-2299	9	34	the	the	DET
ejpam-2299	9	35	first	first	ADJ
ejpam-2299	9	36	cohomology	cohomology	NOUN
ejpam-2299	9	37	group	group	NOUN
ejpam-2299	9	38	of	of	ADP
ejpam-2299	9	39	a	a	PRON
ejpam-2299	9	40	with	with	ADP
ejpam-2299	9	41	coefficients	coefficient	NOUN
ejpam-2299	9	42	in	in	ADP
ejpam-2299	9	43	e	e	NOUN
ejpam-2299	9	44	be	be	AUX
ejpam-2299	9	45	the	the	DET
ejpam-2299	9	46	quotient	quotient	NOUN
ejpam-2299	9	47	space	space	NOUN
ejpam-2299	9	48	h1(a	h1(a	PRON
ejpam-2299	9	49	,	,	PUNCT
ejpam-2299	9	50	x	x	X
ejpam-2299	9	51	)	)	PUNCT
ejpam-2299	10	1	=	=	SYM
ejpam-2299	10	2	z1(a	z1(a	NUM
ejpam-2299	10	3	,	,	PUNCT
ejpam-2299	10	4	x	x	PROPN
ejpam-2299	10	5	)	)	PUNCT
ejpam-2299	10	6	/n1(a	/n1(a	PUNCT
ejpam-2299	10	7	,	,	PUNCT
ejpam-2299	10	8	x	x	PROPN
ejpam-2299	10	9	)	)	PUNCT
ejpam-2299	10	10	.	.	PUNCT
ejpam-2299	11	1	a	a	DET
ejpam-2299	11	2	banach	banach	NOUN
ejpam-2299	11	3	algebra	algebra	NOUN
ejpam-2299	11	4	a	a	PRON
ejpam-2299	11	5	is	be	AUX
ejpam-2299	11	6	amenable	amenable	ADJ
ejpam-2299	11	7	if	if	SCONJ
ejpam-2299	11	8	h1(a	h1(a	PRON
ejpam-2299	11	9	,	,	PUNCT
ejpam-2299	11	10	e′	e′	ADJ
ejpam-2299	11	11	)	)	PUNCT
ejpam-2299	12	1	=	=	PRON
ejpam-2299	12	2	{	{	PUNCT
ejpam-2299	12	3	0	0	NUM
ejpam-2299	12	4	}	}	PUNCT
ejpam-2299	12	5	for	for	ADP
ejpam-2299	12	6	each	each	DET
ejpam-2299	12	7	banach	banach	NOUN
ejpam-2299	12	8	a	a	DET
ejpam-2299	12	9	-	-	PUNCT
ejpam-2299	12	10	bimodule	bimodule	NOUN
ejpam-2299	12	11	e	e	NOUN
ejpam-2299	12	12	,	,	PUNCT
ejpam-2299	12	13	this	this	DET
ejpam-2299	12	14	concept	concept	NOUN
ejpam-2299	12	15	was	be	AUX
ejpam-2299	12	16	introduced	introduce	VERB
ejpam-2299	12	17	by	by	ADP
ejpam-2299	12	18	b.	b.	PROPN
ejpam-2299	12	19	e.	e.	PROPN
ejpam-2299	12	20	johnson	johnson	PROPN
ejpam-2299	12	21	in	in	ADP
ejpam-2299	12	22	[	[	X
ejpam-2299	12	23	8	8	NUM
ejpam-2299	12	24	]	]	PUNCT
ejpam-2299	12	25	.	.	PUNCT
ejpam-2299	13	1	the	the	DET
ejpam-2299	13	2	notion	notion	NOUN
ejpam-2299	13	3	of	of	ADP
ejpam-2299	13	4	weak	weak	ADJ
ejpam-2299	13	5	amenability	amenability	NOUN
ejpam-2299	13	6	for	for	ADP
ejpam-2299	13	7	commutative	commutative	ADJ
ejpam-2299	13	8	banach	banach	NOUN
ejpam-2299	13	9	algebras	algebras	PROPN
ejpam-2299	13	10	was	be	AUX
ejpam-2299	13	11	introduced	introduce	VERB
ejpam-2299	13	12	by	by	ADP
ejpam-2299	13	13	w.	w.	PROPN
ejpam-2299	13	14	g.	g.	PROPN
ejpam-2299	13	15	bade	bade	PROPN
ejpam-2299	13	16	,	,	PUNCT
ejpam-2299	13	17	p.	p.	PROPN
ejpam-2299	13	18	c.	c.	PROPN
ejpam-2299	13	19	curtis	curtis	PROPN
ejpam-2299	13	20	and	and	CCONJ
ejpam-2299	13	21	h.	h.	PROPN
ejpam-2299	13	22	g.	g.	PROPN
ejpam-2299	13	23	dales	dales	PROPN
ejpam-2299	13	24	in	in	ADP
ejpam-2299	13	25	[	[	X
ejpam-2299	13	26	2	2	NUM
ejpam-2299	13	27	]	]	PUNCT
ejpam-2299	13	28	.	.	PUNCT
ejpam-2299	14	1	later	later	PROPN
ejpam-2299	14	2	johnson	johnson	PROPN
ejpam-2299	14	3	defined	define	VERB
ejpam-2299	14	4	weak	weak	ADJ
ejpam-2299	14	5	amenability	amenability	NOUN
ejpam-2299	14	6	for	for	ADP
ejpam-2299	14	7	arbitrary	arbitrary	ADJ
ejpam-2299	14	8	banach	banach	NOUN
ejpam-2299	14	9	algebras	algebra	NOUN
ejpam-2299	14	10	in	in	ADP
ejpam-2299	14	11	[	[	PUNCT
ejpam-2299	14	12	9	9	NUM
ejpam-2299	14	13	]	]	PUNCT
ejpam-2299	14	14	,	,	PUNCT
ejpam-2299	14	15	in	in	ADP
ejpam-2299	14	16	fact	fact	NOUN
ejpam-2299	14	17	a	a	DET
ejpam-2299	14	18	banach	banach	NOUN
ejpam-2299	14	19	algebra	algebra	NOUN
ejpam-2299	14	20	a	a	PRON
ejpam-2299	14	21	is	be	AUX
ejpam-2299	14	22	weakly	weakly	ADV
ejpam-2299	14	23	amenable	amenable	ADJ
ejpam-2299	14	24	if	if	SCONJ
ejpam-2299	14	25	h1(a	h1(a	PRON
ejpam-2299	14	26	,	,	PUNCT
ejpam-2299	14	27	a′	a′	ADJ
ejpam-2299	14	28	)	)	PUNCT
ejpam-2299	14	29	=	=	PRON
ejpam-2299	14	30	{	{	PUNCT
ejpam-2299	14	31	0	0	NUM
ejpam-2299	14	32	}	}	PUNCT
ejpam-2299	14	33	.	.	PUNCT
ejpam-2299	15	1	in	in	ADP
ejpam-2299	15	2	[	[	X
ejpam-2299	15	3	10	10	NUM
ejpam-2299	15	4	]	]	PUNCT
ejpam-2299	15	5	,	,	PUNCT
ejpam-2299	15	6	a.	a.	PROPN
ejpam-2299	15	7	medghalchi	medghalchi	PROPN
ejpam-2299	15	8	and	and	CCONJ
ejpam-2299	15	9	t.	t.	PROPN
ejpam-2299	15	10	yazdanpanah	yazdanpanah	PROPN
ejpam-2299	15	11	introduced	introduce	VERB
ejpam-2299	15	12	the	the	DET
ejpam-2299	15	13	notion	notion	NOUN
ejpam-2299	15	14	of	of	ADP
ejpam-2299	15	15	(	(	PUNCT
ejpam-2299	15	16	-1)-weak	-1)-weak	INTJ
ejpam-2299	15	17	amenability	amenability	NOUN
ejpam-2299	15	18	.	.	PUNCT
ejpam-2299	16	1	a	a	DET
ejpam-2299	16	2	banach	banach	NOUN
ejpam-2299	16	3	algebra	algebra	NOUN
ejpam-2299	16	4	a	a	PRON
ejpam-2299	16	5	is	be	AUX
ejpam-2299	16	6	(	(	PUNCT
ejpam-2299	16	7	-1)-weakly	-1)-weakly	ADV
ejpam-2299	16	8	amenable	amenable	ADJ
ejpam-2299	16	9	if	if	SCONJ
ejpam-2299	16	10	a′	a′	PROPN
ejpam-2299	16	11	is	be	AUX
ejpam-2299	16	12	a	a	DET
ejpam-2299	16	13	banach	banach	NOUN
ejpam-2299	16	14	a′′-bimodule	a′′-bimodule	NOUN
ejpam-2299	16	15	and	and	CCONJ
ejpam-2299	16	16	h1(a′′,a′	h1(a′′,a′	NOUN
ejpam-2299	16	17	)	)	PUNCT
ejpam-2299	17	1	=	=	PRON
ejpam-2299	17	2	{	{	PUNCT
ejpam-2299	17	3	0	0	NUM
ejpam-2299	17	4	}	}	PUNCT
ejpam-2299	17	5	.	.	PUNCT
ejpam-2299	18	1	there	there	PRON
ejpam-2299	18	2	are	be	VERB
ejpam-2299	18	3	some	some	DET
ejpam-2299	18	4	examples	example	NOUN
ejpam-2299	18	5	of	of	ADP
ejpam-2299	18	6	non	non	ADJ
ejpam-2299	18	7	(	(	PUNCT
ejpam-2299	18	8	-1)-weakly	-1)-weakly	ADP
ejpam-2299	18	9	amenable	amenable	ADJ
ejpam-2299	18	10	banach	banach	NOUN
ejpam-2299	18	11	algebras	algebra	VERB
ejpam-2299	18	12	.	.	PUNCT
ejpam-2299	19	1	for	for	ADP
ejpam-2299	19	2	instance	instance	NOUN
ejpam-2299	19	3	,	,	PUNCT
ejpam-2299	19	4	in	in	ADP
ejpam-2299	19	5	[	[	X
ejpam-2299	19	6	7	7	X
ejpam-2299	19	7	]	]	PUNCT
ejpam-2299	19	8	we	we	PRON
ejpam-2299	19	9	proved	prove	VERB
ejpam-2299	19	10	that	that	PRON
ejpam-2299	19	11	(	(	PUNCT
ejpam-2299	19	12	lipαk)′′	lipαk)′′	NOUN
ejpam-2299	19	13	for	for	ADP
ejpam-2299	19	14	α	α	PROPN
ejpam-2299	19	15	∈	∈	PROPN
ejpam-2299	19	16	(	(	PUNCT
ejpam-2299	19	17	0,1	0,1	NOUN
ejpam-2299	19	18	)	)	PUNCT
ejpam-2299	19	19	and	and	CCONJ
ejpam-2299	19	20	infinite	infinite	ADJ
ejpam-2299	19	21	compact	compact	ADJ
ejpam-2299	19	22	metric	metric	ADJ
ejpam-2299	19	23	space	space	NOUN
ejpam-2299	19	24	k	k	PROPN
ejpam-2299	19	25	is	be	AUX
ejpam-2299	19	26	not	not	PART
ejpam-2299	19	27	∗corresponding	∗corresponde	VERB
ejpam-2299	19	28	author	author	NOUN
ejpam-2299	19	29	.	.	PUNCT
ejpam-2299	20	1	email	email	NOUN
ejpam-2299	20	2	addresses	address	NOUN
ejpam-2299	20	3	:	:	PUNCT
ejpam-2299	20	4	ahosseinioun@yahoo.com	ahosseinioun@yahoo.com	X
ejpam-2299	20	5	(	(	PUNCT
ejpam-2299	20	6	s.	s.	PROPN
ejpam-2299	20	7	hosseinioun	hosseinioun	PROPN
ejpam-2299	20	8	)	)	PUNCT
ejpam-2299	20	9	,	,	PUNCT
ejpam-2299	20	10	arezou.valadkhani@yahoo.com	arezou.valadkhani@yahoo.com	X
ejpam-2299	20	11	(	(	PUNCT
ejpam-2299	20	12	a.	a.	NOUN
ejpam-2299	20	13	valadkhani	valadkhani	PROPN
ejpam-2299	20	14	)	)	PUNCT
ejpam-2299	20	15	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2299	21	1	231	231	NUM
ejpam-2299	21	2	c	c	NOUN
ejpam-2299	21	3	©	©	PROPN
ejpam-2299	21	4	2016	2016	NUM
ejpam-2299	21	5	ejpam	ejpam	VERB
ejpam-2299	21	6	all	all	DET
ejpam-2299	21	7	rights	right	NOUN
ejpam-2299	21	8	reserved	reserve	VERB
ejpam-2299	21	9	.	.	PUNCT
ejpam-2299	22	1	european	european	ADJ
ejpam-2299	22	2	journal	journal	PROPN
ejpam-2299	22	3	of	of	ADP
ejpam-2299	22	4	pure	pure	ADJ
ejpam-2299	22	5	and	and	CCONJ
ejpam-2299	22	6	applied	apply	VERB
ejpam-2299	22	7	mathematics	mathematic	NOUN
ejpam-2299	22	8	vol	vol	NOUN
ejpam-2299	22	9	.	.	PROPN
ejpam-2299	23	1	9	9	NUM
ejpam-2299	23	2	,	,	PUNCT
ejpam-2299	23	3	no	no	INTJ
ejpam-2299	23	4	.	.	NOUN
ejpam-2299	23	5	2	2	NUM
ejpam-2299	23	6	,	,	PUNCT
ejpam-2299	23	7	2016	2016	NUM
ejpam-2299	23	8	,	,	PUNCT
ejpam-2299	23	9	231	231	NUM
ejpam-2299	23	10	-	-	SYM
ejpam-2299	23	11	239	239	NUM
ejpam-2299	23	12	issn	issn	PROPN
ejpam-2299	23	13	1307	1307	NUM
ejpam-2299	23	14	-	-	SYM
ejpam-2299	23	15	5543	5543	NUM
ejpam-2299	23	16	–	–	PUNCT
ejpam-2299	23	17	www.ejpam.com	www.ejpam.com	X
ejpam-2299	23	18	s.	s.	PROPN
ejpam-2299	23	19	hosseinioun	hosseinioun	PROPN
ejpam-2299	23	20	,	,	PUNCT
ejpam-2299	23	21	a.	a.	NOUN
ejpam-2299	23	22	valadkhani	valadkhani	PROPN
ejpam-2299	23	23	/	/	SYM
ejpam-2299	23	24	eur	eur	PROPN
ejpam-2299	23	25	.	.	PUNCT
ejpam-2299	24	1	j.	j.	PROPN
ejpam-2299	24	2	pure	pure	PROPN
ejpam-2299	24	3	appl	appl	PROPN
ejpam-2299	24	4	.	.	PROPN
ejpam-2299	24	5	math	math	PROPN
ejpam-2299	24	6	,	,	PUNCT
ejpam-2299	24	7	9	9	NUM
ejpam-2299	24	8	(	(	PUNCT
ejpam-2299	24	9	2016	2016	NUM
ejpam-2299	24	10	)	)	PUNCT
ejpam-2299	24	11	,	,	PUNCT
ejpam-2299	24	12	231	231	NUM
ejpam-2299	24	13	-	-	SYM
ejpam-2299	24	14	239	239	NUM
ejpam-2299	24	15	232	232	NUM
ejpam-2299	24	16	(	(	PUNCT
ejpam-2299	24	17	-1)-weakly	-1)-weakly	ADV
ejpam-2299	24	18	amenable	amenable	ADJ
ejpam-2299	24	19	.	.	PUNCT
ejpam-2299	25	1	the	the	DET
ejpam-2299	25	2	space	space	NOUN
ejpam-2299	25	3	lp	lp	NOUN
ejpam-2299	25	4	for	for	ADP
ejpam-2299	25	5	1	1	NUM
ejpam-2299	25	6	<	<	X
ejpam-2299	25	7	p	p	X
ejpam-2299	25	8	<	<	X
ejpam-2299	25	9	∞	∞	PROPN
ejpam-2299	25	10	is	be	AUX
ejpam-2299	25	11	reflexive	reflexive	ADJ
ejpam-2299	25	12	and	and	CCONJ
ejpam-2299	25	13	weakly	weakly	ADV
ejpam-2299	25	14	amenable	amenable	ADJ
ejpam-2299	25	15	,	,	PUNCT
ejpam-2299	25	16	so	so	ADV
ejpam-2299	25	17	is	be	AUX
ejpam-2299	25	18	(	(	PUNCT
ejpam-2299	25	19	-1)-weakly	-1)-weakly	ADV
ejpam-2299	25	20	amenable	amenable	ADJ
ejpam-2299	25	21	which	which	PRON
ejpam-2299	25	22	is	be	AUX
ejpam-2299	25	23	not	not	PART
ejpam-2299	25	24	amenable	amenable	ADJ
ejpam-2299	25	25	since	since	SCONJ
ejpam-2299	25	26	it	it	PRON
ejpam-2299	25	27	does	do	VERB
ejpam-2299	25	28	n’t	not	PART
ejpam-2299	25	29	factor	factor	NOUN
ejpam-2299	25	30	.	.	PUNCT
ejpam-2299	26	1	furthermore	furthermore	ADV
ejpam-2299	26	2	,	,	PUNCT
ejpam-2299	26	3	the	the	DET
ejpam-2299	26	4	second	second	ADJ
ejpam-2299	26	5	dual	dual	ADJ
ejpam-2299	26	6	of	of	ADP
ejpam-2299	26	7	a	a	DET
ejpam-2299	26	8	c∗-algebra	c∗-algebra	PROPN
ejpam-2299	26	9	is	be	AUX
ejpam-2299	26	10	(	(	PUNCT
ejpam-2299	26	11	-1)-weakly	-1)-weakly	ADV
ejpam-2299	26	12	amenable	amenable	ADJ
ejpam-2299	26	13	and	and	CCONJ
ejpam-2299	26	14	in	in	ADP
ejpam-2299	26	15	the	the	DET
ejpam-2299	26	16	case	case	NOUN
ejpam-2299	26	17	a′′	a′′	NOUN
ejpam-2299	26	18	is	be	AUX
ejpam-2299	26	19	a	a	DET
ejpam-2299	26	20	non	non	ADJ
ejpam-2299	26	21	-	-	ADJ
ejpam-2299	26	22	nuclear	nuclear	ADJ
ejpam-2299	26	23	c∗-algebra	c∗-algebra	NOUN
ejpam-2299	26	24	,	,	PUNCT
ejpam-2299	26	25	we	we	PRON
ejpam-2299	26	26	can	can	AUX
ejpam-2299	26	27	conclude	conclude	VERB
ejpam-2299	26	28	that	that	PRON
ejpam-2299	26	29	a′′	a′′	NOUN
ejpam-2299	26	30	is	be	AUX
ejpam-2299	26	31	(	(	PUNCT
ejpam-2299	26	32	-1)-weakly	-1)-weakly	ADV
ejpam-2299	26	33	amenable	amenable	ADJ
ejpam-2299	26	34	which	which	PRON
ejpam-2299	26	35	is	be	AUX
ejpam-2299	26	36	not	not	PART
ejpam-2299	26	37	amenable	amenable	ADJ
ejpam-2299	26	38	.	.	PUNCT
ejpam-2299	27	1	therefore	therefore	ADV
ejpam-2299	27	2	,	,	PUNCT
ejpam-2299	27	3	the	the	DET
ejpam-2299	27	4	notion	notion	NOUN
ejpam-2299	27	5	of	of	ADP
ejpam-2299	27	6	(	(	PUNCT
ejpam-2299	27	7	-1)-weak	-1)-weak	ADJ
ejpam-2299	27	8	amenability	amenability	NOUN
ejpam-2299	27	9	is	be	AUX
ejpam-2299	27	10	different	different	ADJ
ejpam-2299	27	11	from	from	ADP
ejpam-2299	27	12	amenability	amenability	NOUN
ejpam-2299	27	13	.	.	PUNCT
ejpam-2299	28	1	for	for	ADP
ejpam-2299	28	2	more	more	ADJ
ejpam-2299	28	3	examples	example	NOUN
ejpam-2299	28	4	see	see	VERB
ejpam-2299	28	5	[	[	X
ejpam-2299	28	6	7	7	X
ejpam-2299	28	7	]	]	PUNCT
ejpam-2299	28	8	and	and	CCONJ
ejpam-2299	28	9	[	[	X
ejpam-2299	28	10	9	9	NUM
ejpam-2299	28	11	]	]	PUNCT
ejpam-2299	28	12	.	.	PUNCT
ejpam-2299	29	1	although	although	SCONJ
ejpam-2299	29	2	there	there	PRON
ejpam-2299	29	3	are	be	VERB
ejpam-2299	29	4	some	some	DET
ejpam-2299	29	5	main	main	ADJ
ejpam-2299	29	6	theorems	theorem	NOUN
ejpam-2299	29	7	and	and	CCONJ
ejpam-2299	29	8	examples	example	NOUN
ejpam-2299	29	9	which	which	PRON
ejpam-2299	29	10	may	may	AUX
ejpam-2299	29	11	suggest	suggest	VERB
ejpam-2299	29	12	that	that	SCONJ
ejpam-2299	29	13	the	the	DET
ejpam-2299	29	14	notion	notion	NOUN
ejpam-2299	29	15	of	of	ADP
ejpam-2299	29	16	(	(	PUNCT
ejpam-2299	29	17	-1)-weak	-1)-weak	ADJ
ejpam-2299	29	18	amenability	amenability	NOUN
ejpam-2299	29	19	is	be	AUX
ejpam-2299	29	20	close	close	ADJ
ejpam-2299	29	21	to	to	ADP
ejpam-2299	29	22	the	the	DET
ejpam-2299	29	23	notion	notion	NOUN
ejpam-2299	29	24	of	of	ADP
ejpam-2299	29	25	weak	weak	ADJ
ejpam-2299	29	26	amenability	amenability	NOUN
ejpam-2299	29	27	,	,	PUNCT
ejpam-2299	29	28	there	there	PRON
ejpam-2299	29	29	are	be	VERB
ejpam-2299	29	30	some	some	DET
ejpam-2299	29	31	examples	example	NOUN
ejpam-2299	29	32	which	which	PRON
ejpam-2299	29	33	prove	prove	VERB
ejpam-2299	29	34	that	that	SCONJ
ejpam-2299	29	35	these	these	DET
ejpam-2299	29	36	two	two	NUM
ejpam-2299	29	37	notions	notion	NOUN
ejpam-2299	29	38	are	be	AUX
ejpam-2299	29	39	different	different	ADJ
ejpam-2299	29	40	,	,	PUNCT
ejpam-2299	29	41	see	see	VERB
ejpam-2299	29	42	[	[	X
ejpam-2299	29	43	8	8	NUM
ejpam-2299	29	44	]	]	PUNCT
ejpam-2299	29	45	.	.	PUNCT
ejpam-2299	30	1	let	let	VERB
ejpam-2299	30	2	a	a	PRON
ejpam-2299	30	3	be	be	AUX
ejpam-2299	30	4	a	a	DET
ejpam-2299	30	5	banach	banach	NOUN
ejpam-2299	30	6	algebra	algebra	NOUN
ejpam-2299	30	7	and	and	CCONJ
ejpam-2299	30	8	a′′	a′′	NOUN
ejpam-2299	30	9	be	be	AUX
ejpam-2299	30	10	its	its	PRON
ejpam-2299	30	11	second	second	ADJ
ejpam-2299	30	12	dual	dual	ADJ
ejpam-2299	30	13	,	,	PUNCT
ejpam-2299	30	14	for	for	ADP
ejpam-2299	30	15	each	each	DET
ejpam-2299	30	16	a	a	NOUN
ejpam-2299	30	17	,	,	PUNCT
ejpam-2299	30	18	b	b	X
ejpam-2299	30	19	∈	∈	PROPN
ejpam-2299	30	20	a	a	X
ejpam-2299	30	21	,	,	PUNCT
ejpam-2299	30	22	f	f	PROPN
ejpam-2299	30	23	∈	∈	PROPN
ejpam-2299	30	24	a′	a′	PROPN
ejpam-2299	30	25	and	and	CCONJ
ejpam-2299	30	26	f	f	PROPN
ejpam-2299	30	27	,	,	PUNCT
ejpam-2299	30	28	g	g	PROPN
ejpam-2299	30	29	∈	∈	PROPN
ejpam-2299	30	30	a′′	a′′	NOUN
ejpam-2299	30	31	we	we	PRON
ejpam-2299	30	32	define	define	VERB
ejpam-2299	30	33	f	f	PROPN
ejpam-2299	30	34	·	·	PUNCT
ejpam-2299	30	35	a	a	X
ejpam-2299	30	36	,	,	PUNCT
ejpam-2299	30	37	a	a	DET
ejpam-2299	30	38	·	·	PUNCT
ejpam-2299	30	39	f	f	PROPN
ejpam-2299	30	40	and	and	CCONJ
ejpam-2299	30	41	f	f	PROPN
ejpam-2299	30	42	·	·	PUNCT
ejpam-2299	30	43	f	f	PROPN
ejpam-2299	30	44	,	,	PUNCT
ejpam-2299	30	45	f	f	PROPN
ejpam-2299	30	46	·	·	PUNCT
ejpam-2299	30	47	f	f	PROPN
ejpam-2299	30	48	∈	∈	PROPN
ejpam-2299	30	49	a′	a′	PROPN
ejpam-2299	30	50	by	by	ADP
ejpam-2299	30	51	f	f	PROPN
ejpam-2299	30	52	·	·	PUNCT
ejpam-2299	30	53	a(b	a(b	ADJ
ejpam-2299	30	54	)	)	PUNCT
ejpam-2299	31	1	=	=	SYM
ejpam-2299	31	2	f	f	X
ejpam-2299	31	3	(	(	PUNCT
ejpam-2299	31	4	a	a	DET
ejpam-2299	31	5	·	·	SYM
ejpam-2299	31	6	b	b	X
ejpam-2299	31	7	)	)	PUNCT
ejpam-2299	31	8	,	,	PUNCT
ejpam-2299	31	9	a	a	PRON
ejpam-2299	31	10	·	·	PUNCT
ejpam-2299	31	11	f	f	X
ejpam-2299	31	12	(	(	PUNCT
ejpam-2299	31	13	b	b	NOUN
ejpam-2299	31	14	)	)	PUNCT
ejpam-2299	31	15	=	=	SYM
ejpam-2299	31	16	f	f	X
ejpam-2299	31	17	(	(	PUNCT
ejpam-2299	31	18	b	b	PROPN
ejpam-2299	31	19	·	·	PUNCT
ejpam-2299	31	20	a	a	X
ejpam-2299	31	21	)	)	PUNCT
ejpam-2299	31	22	f	f	NOUN
ejpam-2299	31	23	·	·	PUNCT
ejpam-2299	31	24	f	f	X
ejpam-2299	31	25	(	(	PUNCT
ejpam-2299	31	26	a	a	X
ejpam-2299	31	27	)	)	PUNCT
ejpam-2299	31	28	=	=	SYM
ejpam-2299	31	29	f	f	X
ejpam-2299	31	30	(	(	PUNCT
ejpam-2299	31	31	f	f	X
ejpam-2299	31	32	·	·	PUNCT
ejpam-2299	31	33	a	a	X
ejpam-2299	31	34	)	)	PUNCT
ejpam-2299	31	35	,	,	PUNCT
ejpam-2299	31	36	f	f	PROPN
ejpam-2299	31	37	·	·	PUNCT
ejpam-2299	31	38	f(a	f(a	X
ejpam-2299	31	39	)	)	PUNCT
ejpam-2299	32	1	=	=	SYM
ejpam-2299	32	2	f(a	f(a	X
ejpam-2299	32	3	·	·	PUNCT
ejpam-2299	32	4	f	f	X
ejpam-2299	32	5	)	)	PUNCT
ejpam-2299	32	6	.	.	PUNCT
ejpam-2299	33	1	now	now	ADV
ejpam-2299	33	2	we	we	PRON
ejpam-2299	33	3	define	define	VERB
ejpam-2299	33	4	f	f	PROPN
ejpam-2299	33	5	·	·	PUNCT
ejpam-2299	33	6	g	g	NOUN
ejpam-2299	33	7	,	,	PUNCT
ejpam-2299	33	8	f	f	PROPN
ejpam-2299	33	9	×	×	NOUN
ejpam-2299	33	10	g	g	PROPN
ejpam-2299	33	11	∈	∈	PROPN
ejpam-2299	33	12	a′′	a′′	NOUN
ejpam-2299	33	13	as	as	SCONJ
ejpam-2299	33	14	follows	follow	VERB
ejpam-2299	33	15	f	f	PROPN
ejpam-2299	33	16	·	·	PUNCT
ejpam-2299	33	17	g	g	PROPN
ejpam-2299	33	18	(	(	PUNCT
ejpam-2299	33	19	f	f	NOUN
ejpam-2299	33	20	)	)	PUNCT
ejpam-2299	34	1	=	=	PUNCT
ejpam-2299	34	2	f(g	f(g	NOUN
ejpam-2299	34	3	·	·	PUNCT
ejpam-2299	34	4	f	f	X
ejpam-2299	34	5	)	)	PUNCT
ejpam-2299	34	6	,	,	PUNCT
ejpam-2299	34	7	f	f	PROPN
ejpam-2299	34	8	×	×	PROPN
ejpam-2299	34	9	g	g	PROPN
ejpam-2299	34	10	(	(	PUNCT
ejpam-2299	34	11	f	f	PROPN
ejpam-2299	34	12	)	)	PUNCT
ejpam-2299	35	1	=	=	SYM
ejpam-2299	35	2	g	g	PROPN
ejpam-2299	35	3	(	(	PUNCT
ejpam-2299	35	4	f	f	PROPN
ejpam-2299	35	5	·	·	PUNCT
ejpam-2299	35	6	f	f	X
ejpam-2299	35	7	)	)	PUNCT
ejpam-2299	35	8	.	.	PUNCT
ejpam-2299	36	1	then	then	ADV
ejpam-2299	36	2	a′′	a′′	PROPN
ejpam-2299	36	3	is	be	AUX
ejpam-2299	36	4	a	a	DET
ejpam-2299	36	5	banach	banach	NOUN
ejpam-2299	36	6	algebra	algebra	NOUN
ejpam-2299	36	7	with	with	ADP
ejpam-2299	36	8	respect	respect	NOUN
ejpam-2299	36	9	to	to	ADP
ejpam-2299	36	10	either	either	PRON
ejpam-2299	36	11	of	of	ADP
ejpam-2299	36	12	the	the	DET
ejpam-2299	36	13	products	product	NOUN
ejpam-2299	36	14	·	·	PUNCT
ejpam-2299	36	15	and	and	CCONJ
ejpam-2299	36	16	×.	×.	NOUN
ejpam-2299	36	17	these	these	DET
ejpam-2299	36	18	products	product	NOUN
ejpam-2299	36	19	are	be	AUX
ejpam-2299	36	20	called	call	VERB
ejpam-2299	36	21	the	the	DET
ejpam-2299	36	22	first	first	ADJ
ejpam-2299	36	23	and	and	CCONJ
ejpam-2299	36	24	the	the	DET
ejpam-2299	36	25	second	second	ADJ
ejpam-2299	36	26	arens	aren	NOUN
ejpam-2299	36	27	products	product	NOUN
ejpam-2299	36	28	on	on	ADP
ejpam-2299	36	29	a′′	a′′	PROPN
ejpam-2299	36	30	,	,	PUNCT
ejpam-2299	36	31	respectively	respectively	ADV
ejpam-2299	36	32	.	.	PUNCT
ejpam-2299	37	1	a	a	PRON
ejpam-2299	37	2	is	be	AUX
ejpam-2299	37	3	called	call	VERB
ejpam-2299	37	4	arens	aren	NOUN
ejpam-2299	37	5	regular	regular	ADJ
ejpam-2299	37	6	if	if	SCONJ
ejpam-2299	37	7	f	f	PROPN
ejpam-2299	37	8	·	·	PUNCT
ejpam-2299	37	9	g	g	NOUN
ejpam-2299	37	10	=	=	SYM
ejpam-2299	37	11	f	f	PROPN
ejpam-2299	37	12	×	×	NOUN
ejpam-2299	37	13	g	g	PROPN
ejpam-2299	37	14	,	,	PUNCT
ejpam-2299	37	15	for	for	ADP
ejpam-2299	37	16	all	all	DET
ejpam-2299	37	17	f	f	NOUN
ejpam-2299	37	18	,	,	PUNCT
ejpam-2299	37	19	g	g	PROPN
ejpam-2299	37	20	∈	∈	PROPN
ejpam-2299	37	21	a′′.	a′′.	PROPN
ejpam-2299	37	22	let	let	VERB
ejpam-2299	37	23	e	e	PRON
ejpam-2299	37	24	be	be	AUX
ejpam-2299	37	25	a	a	DET
ejpam-2299	37	26	banach	banach	NOUN
ejpam-2299	37	27	a	a	DET
ejpam-2299	37	28	-	-	PUNCT
ejpam-2299	37	29	bimodule	bimodule	NOUN
ejpam-2299	37	30	,	,	PUNCT
ejpam-2299	37	31	then	then	ADV
ejpam-2299	37	32	the	the	DET
ejpam-2299	37	33	iterated	iterated	ADJ
ejpam-2299	37	34	conjugates	conjugate	NOUN
ejpam-2299	37	35	of	of	ADP
ejpam-2299	37	36	e	e	NOUN
ejpam-2299	37	37	,	,	PUNCT
ejpam-2299	37	38	denoted	denote	VERB
ejpam-2299	37	39	by	by	ADP
ejpam-2299	37	40	e′	e′	PROPN
ejpam-2299	37	41	,	,	PUNCT
ejpam-2299	37	42	e′′	e′′	PROPN
ejpam-2299	37	43	,	,	PUNCT
ejpam-2299	37	44	e′′′	e′′′	PROPN
ejpam-2299	37	45	,	,	PUNCT
ejpam-2299	37	46	.	.	PUNCT
ejpam-2299	37	47	.	.	PUNCT
ejpam-2299	38	1	.	.	PUNCT
ejpam-2299	39	1	are	be	AUX
ejpam-2299	39	2	banach	banach	ADV
ejpam-2299	39	3	a	a	DET
ejpam-2299	39	4	-	-	PUNCT
ejpam-2299	39	5	bimodules	bimodule	NOUN
ejpam-2299	39	6	,	,	PUNCT
ejpam-2299	39	7	and	and	CCONJ
ejpam-2299	39	8	the	the	DET
ejpam-2299	39	9	map	map	NOUN
ejpam-2299	39	10	ρ	ρ	X
ejpam-2299	39	11	:	:	PUNCT
ejpam-2299	39	12	e′′′	e′′′	PROPN
ejpam-2299	39	13	−→	−→	NOUN
ejpam-2299	39	14	e′	e′	PROPN
ejpam-2299	39	15	with	with	ADP
ejpam-2299	39	16	ρ(γ	ρ(γ	NOUN
ejpam-2299	39	17	)	)	PUNCT
ejpam-2299	39	18	=	=	PUNCT
ejpam-2299	40	1	γ	γ	PROPN
ejpam-2299	40	2	|â	|â	NOUN
ejpam-2299	40	3	is	be	AUX
ejpam-2299	40	4	an	an	DET
ejpam-2299	40	5	a	a	DET
ejpam-2299	40	6	-	-	PUNCT
ejpam-2299	40	7	bimodule	bimodule	NOUN
ejpam-2299	40	8	homomorphism	homomorphism	NOUN
ejpam-2299	40	9	which	which	PRON
ejpam-2299	40	10	is	be	AUX
ejpam-2299	40	11	called	call	VERB
ejpam-2299	40	12	natural	natural	ADJ
ejpam-2299	40	13	projection	projection	NOUN
ejpam-2299	40	14	.	.	PUNCT
ejpam-2299	41	1	all	all	DET
ejpam-2299	41	2	concepts	concept	NOUN
ejpam-2299	41	3	and	and	CCONJ
ejpam-2299	41	4	definitions	definition	NOUN
ejpam-2299	41	5	which	which	PRON
ejpam-2299	41	6	are	be	AUX
ejpam-2299	41	7	not	not	PART
ejpam-2299	41	8	defined	define	VERB
ejpam-2299	41	9	in	in	ADP
ejpam-2299	41	10	this	this	DET
ejpam-2299	41	11	paper	paper	NOUN
ejpam-2299	41	12	may	may	AUX
ejpam-2299	41	13	be	be	AUX
ejpam-2299	41	14	found	find	VERB
ejpam-2299	41	15	in	in	ADP
ejpam-2299	41	16	[	[	X
ejpam-2299	41	17	4	4	NUM
ejpam-2299	41	18	]	]	PUNCT
ejpam-2299	41	19	.	.	PUNCT
ejpam-2299	42	1	2	2	X
ejpam-2299	42	2	.	.	X
ejpam-2299	42	3	when	when	SCONJ
ejpam-2299	42	4	a′	a′	PROPN
ejpam-2299	42	5	is	be	AUX
ejpam-2299	42	6	a	a	DET
ejpam-2299	42	7	banach	banach	NOUN
ejpam-2299	42	8	a′′-bimodule	a′′-bimodule	NOUN
ejpam-2299	42	9	?	?	PUNCT
ejpam-2299	43	1	in	in	ADP
ejpam-2299	43	2	the	the	DET
ejpam-2299	43	3	notion	notion	NOUN
ejpam-2299	43	4	of	of	ADP
ejpam-2299	43	5	(	(	PUNCT
ejpam-2299	43	6	-1)-weak	-1)-weak	INTJ
ejpam-2299	43	7	amenability	amenability	NOUN
ejpam-2299	43	8	,	,	PUNCT
ejpam-2299	43	9	a	a	DET
ejpam-2299	43	10	necessary	necessary	ADJ
ejpam-2299	43	11	condition	condition	NOUN
ejpam-2299	43	12	is	be	AUX
ejpam-2299	43	13	that	that	SCONJ
ejpam-2299	43	14	"	"	PUNCT
ejpam-2299	43	15	a′	a′	PROPN
ejpam-2299	43	16	is	be	AUX
ejpam-2299	43	17	a	a	DET
ejpam-2299	43	18	banach	banach	NOUN
ejpam-2299	43	19	a′′bimodule	a′′bimodule	NOUN
ejpam-2299	43	20	"	"	PUNCT
ejpam-2299	43	21	.	.	PUNCT
ejpam-2299	44	1	throughout	throughout	ADP
ejpam-2299	44	2	this	this	DET
ejpam-2299	44	3	paper	paper	NOUN
ejpam-2299	44	4	,	,	PUNCT
ejpam-2299	44	5	we	we	PRON
ejpam-2299	44	6	shall	shall	AUX
ejpam-2299	44	7	consider	consider	VERB
ejpam-2299	44	8	the	the	DET
ejpam-2299	44	9	second	second	ADJ
ejpam-2299	44	10	dual	dual	ADJ
ejpam-2299	44	11	a′′	a′′	NOUN
ejpam-2299	44	12	with	with	ADP
ejpam-2299	44	13	the	the	DET
ejpam-2299	44	14	first	first	ADJ
ejpam-2299	44	15	arens	aren	NOUN
ejpam-2299	44	16	product	product	NOUN
ejpam-2299	44	17	.	.	PUNCT
ejpam-2299	45	1	for	for	ADP
ejpam-2299	45	2	the	the	DET
ejpam-2299	45	3	relations	relation	NOUN
ejpam-2299	45	4	between	between	ADP
ejpam-2299	45	5	(	(	PUNCT
ejpam-2299	45	6	-1)-weak	-1)-weak	INTJ
ejpam-2299	45	7	amenability	amenability	NOUN
ejpam-2299	45	8	of	of	ADP
ejpam-2299	45	9	(	(	PUNCT
ejpam-2299	45	10	a′′	a′′	PROPN
ejpam-2299	45	11	,	,	PUNCT
ejpam-2299	45	12	·	·	PUNCT
ejpam-2299	45	13	)	)	PUNCT
ejpam-2299	45	14	and	and	CCONJ
ejpam-2299	45	15	(	(	PUNCT
ejpam-2299	45	16	a′′,×	a′′,×	NUM
ejpam-2299	45	17	)	)	PUNCT
ejpam-2299	45	18	,	,	PUNCT
ejpam-2299	45	19	see	see	VERB
ejpam-2299	45	20	[	[	X
ejpam-2299	45	21	9	9	NUM
ejpam-2299	45	22	]	]	PUNCT
ejpam-2299	45	23	.	.	PUNCT
ejpam-2299	46	1	theorem	theorem	NOUN
ejpam-2299	46	2	1	1	X
ejpam-2299	46	3	.	.	PUNCT
ejpam-2299	47	1	let	let	VERB
ejpam-2299	47	2	a	a	PRON
ejpam-2299	47	3	be	be	AUX
ejpam-2299	47	4	a	a	DET
ejpam-2299	47	5	banach	banach	NOUN
ejpam-2299	47	6	algebra	algebra	NOUN
ejpam-2299	47	7	.	.	PUNCT
ejpam-2299	48	1	then	then	ADV
ejpam-2299	48	2	in	in	ADP
ejpam-2299	48	3	each	each	PRON
ejpam-2299	48	4	of	of	ADP
ejpam-2299	48	5	the	the	DET
ejpam-2299	48	6	following	following	ADJ
ejpam-2299	48	7	cases	case	NOUN
ejpam-2299	48	8	,	,	PUNCT
ejpam-2299	48	9	a′	a′	PROPN
ejpam-2299	48	10	is	be	AUX
ejpam-2299	48	11	a	a	DET
ejpam-2299	48	12	banach	banach	NOUN
ejpam-2299	48	13	a′′-bimodule	a′′-bimodule	NOUN
ejpam-2299	48	14	:	:	PUNCT
ejpam-2299	48	15	(	(	PUNCT
ejpam-2299	48	16	1	1	X
ejpam-2299	48	17	)	)	PUNCT
ejpam-2299	48	18	a	a	PRON
ejpam-2299	48	19	is	be	AUX
ejpam-2299	48	20	arens	aren	NOUN
ejpam-2299	48	21	regular	regular	ADJ
ejpam-2299	48	22	;	;	PUNCT
ejpam-2299	48	23	(	(	PUNCT
ejpam-2299	48	24	2	2	X
ejpam-2299	48	25	)	)	PUNCT
ejpam-2299	48	26	â	â	X
ejpam-2299	48	27	is	be	AUX
ejpam-2299	48	28	a	a	DET
ejpam-2299	48	29	left	left	ADJ
ejpam-2299	48	30	ideal	ideal	NOUN
ejpam-2299	48	31	in	in	ADP
ejpam-2299	48	32	a′′	a′′	PROPN
ejpam-2299	48	33	;	;	PUNCT
ejpam-2299	48	34	(	(	PUNCT
ejpam-2299	48	35	3	3	X
ejpam-2299	48	36	)	)	PUNCT
ejpam-2299	48	37	â	â	X
ejpam-2299	48	38	is	be	AUX
ejpam-2299	48	39	a	a	DET
ejpam-2299	48	40	right	right	ADJ
ejpam-2299	48	41	ideal	ideal	NOUN
ejpam-2299	48	42	in	in	ADP
ejpam-2299	48	43	a′′	a′′	PROPN
ejpam-2299	48	44	and	and	CCONJ
ejpam-2299	48	45	a′′	a′′	PROPN
ejpam-2299	48	46	=	=	PROPN
ejpam-2299	48	47	a′′	a′′	PROPN
ejpam-2299	48	48	·	·	PUNCT
ejpam-2299	48	49	a.	a.	NOUN
ejpam-2299	48	50	proof	proof	NOUN
ejpam-2299	48	51	.	.	PUNCT
ejpam-2299	49	1	(	(	PUNCT
ejpam-2299	49	2	1	1	X
ejpam-2299	49	3	)	)	PUNCT
ejpam-2299	49	4	and	and	CCONJ
ejpam-2299	49	5	(	(	PUNCT
ejpam-2299	49	6	2	2	X
ejpam-2299	49	7	)	)	PUNCT
ejpam-2299	49	8	are	be	AUX
ejpam-2299	49	9	proved	prove	VERB
ejpam-2299	49	10	in	in	ADP
ejpam-2299	49	11	[	[	X
ejpam-2299	49	12	6	6	NUM
ejpam-2299	49	13	]	]	PUNCT
ejpam-2299	49	14	.	.	PUNCT
ejpam-2299	50	1	(	(	PUNCT
ejpam-2299	50	2	3	3	X
ejpam-2299	50	3	)	)	PUNCT
ejpam-2299	50	4	let	let	VERB
ejpam-2299	50	5	â	â	X
ejpam-2299	50	6	be	be	AUX
ejpam-2299	50	7	a	a	DET
ejpam-2299	50	8	right	right	ADJ
ejpam-2299	50	9	ideal	ideal	NOUN
ejpam-2299	50	10	in	in	ADP
ejpam-2299	50	11	a′′	a′′	PROPN
ejpam-2299	50	12	and	and	CCONJ
ejpam-2299	50	13	a′′	a′′	PROPN
ejpam-2299	50	14	·	·	PUNCT
ejpam-2299	50	15	a=	a=	PROPN
ejpam-2299	50	16	a′′.	a′′.	NOUN
ejpam-2299	50	17	let	let	VERB
ejpam-2299	50	18	a	a	DET
ejpam-2299	50	19	∈	∈	PROPN
ejpam-2299	50	20	a	a	PRON
ejpam-2299	50	21	,	,	PUNCT
ejpam-2299	50	22	f	f	X
ejpam-2299	50	23	,	,	PUNCT
ejpam-2299	50	24	g	g	PROPN
ejpam-2299	50	25	∈	∈	PROPN
ejpam-2299	50	26	a′′	a′′	NOUN
ejpam-2299	50	27	and	and	CCONJ
ejpam-2299	50	28	f	f	PROPN
ejpam-2299	50	29	∈	∈	PROPN
ejpam-2299	50	30	a′	a′	PROPN
ejpam-2299	50	31	,	,	PUNCT
ejpam-2299	50	32	then	then	ADV
ejpam-2299	50	33	there	there	PRON
ejpam-2299	50	34	exist	exist	VERB
ejpam-2299	50	35	f1	f1	ADJ
ejpam-2299	50	36	∈	∈	PROPN
ejpam-2299	50	37	a′′	a′′	NOUN
ejpam-2299	50	38	and	and	CCONJ
ejpam-2299	50	39	b	b	NOUN
ejpam-2299	50	40	,	,	PUNCT
ejpam-2299	50	41	c	c	PROPN
ejpam-2299	50	42	∈	∈	PROPN
ejpam-2299	50	43	a	a	DET
ejpam-2299	50	44	such	such	ADJ
ejpam-2299	50	45	that	that	SCONJ
ejpam-2299	50	46	f	f	PROPN
ejpam-2299	50	47	=	=	SYM
ejpam-2299	50	48	f1	f1	PROPN
ejpam-2299	50	49	·	·	PUNCT
ejpam-2299	50	50	b	b	PROPN
ejpam-2299	50	51	and	and	CCONJ
ejpam-2299	50	52	b	b	PROPN
ejpam-2299	50	53	·	·	PUNCT
ejpam-2299	50	54	g	g	NOUN
ejpam-2299	50	55	=	=	SYM
ejpam-2299	50	56	ĉ	ĉ	PROPN
ejpam-2299	50	57	,	,	PUNCT
ejpam-2299	50	58	so	so	SCONJ
ejpam-2299	50	59	we	we	PRON
ejpam-2299	50	60	have	have	VERB
ejpam-2299	50	61	(	(	PUNCT
ejpam-2299	50	62	f	f	X
ejpam-2299	50	63	·	·	PUNCT
ejpam-2299	50	64	f	f	X
ejpam-2299	50	65	)	)	PUNCT
ejpam-2299	50	66	·	·	PUNCT
ejpam-2299	50	67	g(a	g(a	PROPN
ejpam-2299	50	68	)	)	PUNCT
ejpam-2299	50	69	=	=	SYM
ejpam-2299	50	70	�	�	PROPN
ejpam-2299	50	71	f	f	PROPN
ejpam-2299	50	72	·	·	PUNCT
ejpam-2299	50	73	(	(	PUNCT
ejpam-2299	50	74	f1	f1	PROPN
ejpam-2299	50	75	·	·	SYM
ejpam-2299	50	76	b	b	X
ejpam-2299	50	77	)	)	PUNCT
ejpam-2299	50	78	�	�	PROPN
ejpam-2299	50	79	·	·	PUNCT
ejpam-2299	50	80	g(a	g(a	PROPN
ejpam-2299	50	81	)	)	PUNCT
ejpam-2299	51	1	=	=	PRON
ejpam-2299	51	2	(	(	PUNCT
ejpam-2299	51	3	f	f	X
ejpam-2299	51	4	·	·	PUNCT
ejpam-2299	51	5	f1	f1	NOUN
ejpam-2299	51	6	)	)	PUNCT
ejpam-2299	51	7	·	·	PUNCT
ejpam-2299	51	8	(	(	PUNCT
ejpam-2299	51	9	b	b	X
ejpam-2299	51	10	·	·	PUNCT
ejpam-2299	51	11	g)(a	g)(a	NOUN
ejpam-2299	51	12	)	)	PUNCT
ejpam-2299	51	13	=	=	PUNCT
ejpam-2299	52	1	(	(	PUNCT
ejpam-2299	52	2	f	f	X
ejpam-2299	52	3	·	·	PUNCT
ejpam-2299	52	4	f1	f1	NOUN
ejpam-2299	52	5	)	)	PUNCT
ejpam-2299	52	6	·	·	PUNCT
ejpam-2299	53	1	ĉ(a	ĉ(a	X
ejpam-2299	53	2	)	)	PUNCT
ejpam-2299	53	3	s.	s.	PROPN
ejpam-2299	53	4	hosseinioun	hosseinioun	PROPN
ejpam-2299	53	5	,	,	PUNCT
ejpam-2299	53	6	a.	a.	NOUN
ejpam-2299	53	7	valadkhani	valadkhani	PROPN
ejpam-2299	53	8	/	/	SYM
ejpam-2299	53	9	eur	eur	PROPN
ejpam-2299	53	10	.	.	PUNCT
ejpam-2299	54	1	j.	j.	PROPN
ejpam-2299	54	2	pure	pure	PROPN
ejpam-2299	54	3	appl	appl	PROPN
ejpam-2299	54	4	.	.	PROPN
ejpam-2299	54	5	math	math	PROPN
ejpam-2299	54	6	,	,	PUNCT
ejpam-2299	54	7	9	9	NUM
ejpam-2299	54	8	(	(	PUNCT
ejpam-2299	54	9	2016	2016	NUM
ejpam-2299	54	10	)	)	PUNCT
ejpam-2299	54	11	,	,	PUNCT
ejpam-2299	54	12	231	231	NUM
ejpam-2299	54	13	-	-	SYM
ejpam-2299	54	14	239	239	NUM
ejpam-2299	54	15	233	233	NUM
ejpam-2299	54	16	=	=	NOUN
ejpam-2299	54	17	ĉ(a	ĉ(a	X
ejpam-2299	54	18	·	·	PUNCT
ejpam-2299	54	19	(	(	PUNCT
ejpam-2299	54	20	f	f	X
ejpam-2299	54	21	·	·	PUNCT
ejpam-2299	54	22	f1	f1	NOUN
ejpam-2299	54	23	)	)	PUNCT
ejpam-2299	54	24	)	)	PUNCT
ejpam-2299	55	1	=	=	PUNCT
ejpam-2299	55	2	f	f	X
ejpam-2299	55	3	·	·	PUNCT
ejpam-2299	55	4	f1(c	f1(c	PROPN
ejpam-2299	55	5	·	·	PUNCT
ejpam-2299	55	6	a	a	X
ejpam-2299	55	7	)	)	PUNCT
ejpam-2299	55	8	=	=	SYM
ejpam-2299	55	9	f1	f1	NOUN
ejpam-2299	55	10	·	·	PUNCT
ejpam-2299	55	11	c(a	c(a	PROPN
ejpam-2299	55	12	·	·	PUNCT
ejpam-2299	55	13	f	f	X
ejpam-2299	55	14	)	)	PUNCT
ejpam-2299	55	15	=	=	SYM
ejpam-2299	55	16	�	�	PROPN
ejpam-2299	55	17	f1	f1	NOUN
ejpam-2299	55	18	·	·	PUNCT
ejpam-2299	55	19	(	(	PUNCT
ejpam-2299	55	20	b	b	X
ejpam-2299	55	21	·	·	SYM
ejpam-2299	55	22	g	g	NOUN
ejpam-2299	55	23	)	)	PUNCT
ejpam-2299	55	24	�	�	PROPN
ejpam-2299	55	25	(	(	PUNCT
ejpam-2299	55	26	a	a	DET
ejpam-2299	55	27	·	·	PUNCT
ejpam-2299	55	28	f	f	X
ejpam-2299	55	29	)	)	PUNCT
ejpam-2299	56	1	=	=	PUNCT
ejpam-2299	56	2	f	f	X
ejpam-2299	56	3	·	·	PUNCT
ejpam-2299	56	4	g(a	g(a	PROPN
ejpam-2299	56	5	·	·	PUNCT
ejpam-2299	56	6	f	f	X
ejpam-2299	56	7	)	)	PUNCT
ejpam-2299	57	1	=	=	PUNCT
ejpam-2299	57	2	f	f	X
ejpam-2299	57	3	·	·	PUNCT
ejpam-2299	57	4	(	(	PUNCT
ejpam-2299	57	5	f	f	X
ejpam-2299	57	6	·	·	PUNCT
ejpam-2299	57	7	g)(a	g)(a	PROPN
ejpam-2299	57	8	)	)	PUNCT
ejpam-2299	58	1	so	so	SCONJ
ejpam-2299	58	2	a′	a′	PROPN
ejpam-2299	58	3	is	be	AUX
ejpam-2299	58	4	a	a	DET
ejpam-2299	58	5	right	right	ADJ
ejpam-2299	58	6	a′′-module	a′′-module	NOUN
ejpam-2299	58	7	.	.	PUNCT
ejpam-2299	59	1	on	on	ADP
ejpam-2299	59	2	the	the	DET
ejpam-2299	59	3	other	other	ADJ
ejpam-2299	59	4	hand	hand	NOUN
ejpam-2299	59	5	,	,	PUNCT
ejpam-2299	59	6	there	there	PRON
ejpam-2299	59	7	exists	exist	VERB
ejpam-2299	59	8	d	d	PROPN
ejpam-2299	59	9	∈	∈	PROPN
ejpam-2299	59	10	a	a	DET
ejpam-2299	59	11	such	such	ADJ
ejpam-2299	59	12	that	that	SCONJ
ejpam-2299	59	13	a	a	DET
ejpam-2299	59	14	·	·	PUNCT
ejpam-2299	59	15	f	f	X
ejpam-2299	59	16	=	=	PUNCT
ejpam-2299	60	1	d̂	d̂	NOUN
ejpam-2299	61	1	and	and	CCONJ
ejpam-2299	61	2	we	we	PRON
ejpam-2299	61	3	have	have	VERB
ejpam-2299	61	4	�	�	PROPN
ejpam-2299	61	5	f	f	PROPN
ejpam-2299	61	6	·	·	PUNCT
ejpam-2299	61	7	f	f	X
ejpam-2299	61	8	)	)	PUNCT
ejpam-2299	61	9	·	·	PUNCT
ejpam-2299	62	1	g	g	X
ejpam-2299	62	2	�	�	PROPN
ejpam-2299	62	3	a	a	X
ejpam-2299	62	4	)	)	PUNCT
ejpam-2299	62	5	=	=	PROPN
ejpam-2299	62	6	g(a	g(a	PROPN
ejpam-2299	62	7	·	·	PUNCT
ejpam-2299	62	8	(	(	PUNCT
ejpam-2299	62	9	f	f	X
ejpam-2299	62	10	·	·	PUNCT
ejpam-2299	62	11	f	f	X
ejpam-2299	62	12	)	)	PUNCT
ejpam-2299	62	13	)	)	PUNCT
ejpam-2299	63	1	=	=	SYM
ejpam-2299	63	2	g((a	g((a	NOUN
ejpam-2299	63	3	·	·	PUNCT
ejpam-2299	64	1	f	f	X
ejpam-2299	64	2	)	)	PUNCT
ejpam-2299	64	3	·	·	PUNCT
ejpam-2299	64	4	f	f	X
ejpam-2299	64	5	)	)	PUNCT
ejpam-2299	65	1	=	=	PUNCT
ejpam-2299	65	2	g(d	g(d	X
ejpam-2299	65	3	·	·	PUNCT
ejpam-2299	65	4	f	f	X
ejpam-2299	65	5	)	)	PUNCT
ejpam-2299	66	1	=	=	X
ejpam-2299	66	2	d̂	d̂	PROPN
ejpam-2299	66	3	(	(	PUNCT
ejpam-2299	66	4	f	f	PROPN
ejpam-2299	66	5	·	·	PUNCT
ejpam-2299	66	6	g	g	NOUN
ejpam-2299	66	7	)	)	PUNCT
ejpam-2299	66	8	=	=	SYM
ejpam-2299	66	9	(	(	PUNCT
ejpam-2299	66	10	a	a	DET
ejpam-2299	66	11	·	·	SYM
ejpam-2299	66	12	f	f	X
ejpam-2299	66	13	)	)	PUNCT
ejpam-2299	66	14	(	(	PUNCT
ejpam-2299	66	15	f	f	X
ejpam-2299	66	16	·	·	PUNCT
ejpam-2299	66	17	g	g	NOUN
ejpam-2299	66	18	)	)	PUNCT
ejpam-2299	67	1	=	=	SYM
ejpam-2299	67	2	f	f	X
ejpam-2299	67	3	·	·	PUNCT
ejpam-2299	67	4	(	(	PUNCT
ejpam-2299	67	5	f	f	X
ejpam-2299	67	6	·	·	PUNCT
ejpam-2299	67	7	g)(a	g)(a	PROPN
ejpam-2299	67	8	)	)	PUNCT
ejpam-2299	67	9	.	.	PUNCT
ejpam-2299	68	1	therefore	therefore	ADV
ejpam-2299	68	2	a′	a′	PROPN
ejpam-2299	68	3	is	be	AUX
ejpam-2299	68	4	a	a	DET
ejpam-2299	68	5	banach	banach	NOUN
ejpam-2299	68	6	a′′-bimodule	a′′-bimodule	NOUN
ejpam-2299	68	7	.	.	PUNCT
ejpam-2299	69	1	remark	remark	PROPN
ejpam-2299	69	2	1	1	NUM
ejpam-2299	69	3	.	.	PUNCT
ejpam-2299	70	1	dales	dale	NOUN
ejpam-2299	70	2	,	,	PUNCT
ejpam-2299	70	3	rodrigues	rodrigue	NOUN
ejpam-2299	70	4	-	-	PUNCT
ejpam-2299	70	5	palacios	palacio	NOUN
ejpam-2299	70	6	and	and	CCONJ
ejpam-2299	70	7	velasco	velasco	PROPN
ejpam-2299	70	8	in	in	ADP
ejpam-2299	70	9	[	[	X
ejpam-2299	70	10	5	5	NUM
ejpam-2299	70	11	]	]	PUNCT
ejpam-2299	70	12	proved	prove	VERB
ejpam-2299	70	13	that	that	SCONJ
ejpam-2299	70	14	for	for	ADP
ejpam-2299	70	15	a	a	DET
ejpam-2299	70	16	banach	banach	NOUN
ejpam-2299	70	17	algebra	algebra	NOUN
ejpam-2299	70	18	a	a	PRON
ejpam-2299	70	19	,	,	PUNCT
ejpam-2299	70	20	a′	a′	PROPN
ejpam-2299	70	21	is	be	AUX
ejpam-2299	70	22	an	an	DET
ejpam-2299	70	23	a′′-submodule	a′′-submodule	NOUN
ejpam-2299	70	24	of	of	ADP
ejpam-2299	70	25	a′′′	a′′′	PROPN
ejpam-2299	71	1	if	if	SCONJ
ejpam-2299	71	2	and	and	CCONJ
ejpam-2299	71	3	only	only	ADV
ejpam-2299	71	4	if	if	SCONJ
ejpam-2299	71	5	a	a	PRON
ejpam-2299	71	6	is	be	AUX
ejpam-2299	71	7	arens	aren	NOUN
ejpam-2299	71	8	regular	regular	ADJ
ejpam-2299	71	9	.	.	PUNCT
ejpam-2299	72	1	so	so	ADV
ejpam-2299	72	2	under	under	ADP
ejpam-2299	72	3	the	the	DET
ejpam-2299	72	4	condition	condition	NOUN
ejpam-2299	72	5	”	"	PUNCT
ejpam-2299	72	6	a′	a′	PROPN
ejpam-2299	72	7	is	be	AUX
ejpam-2299	72	8	a	a	DET
ejpam-2299	72	9	banach	banach	NOUN
ejpam-2299	72	10	a′′-bimodule	a′′-bimodule	NOUN
ejpam-2299	72	11	”	"	PUNCT
ejpam-2299	72	12	we	we	PRON
ejpam-2299	72	13	can	can	AUX
ejpam-2299	72	14	consider	consider	VERB
ejpam-2299	72	15	a	a	DET
ejpam-2299	72	16	larger	large	ADJ
ejpam-2299	72	17	class	class	NOUN
ejpam-2299	72	18	of	of	ADP
ejpam-2299	72	19	banach	banach	NOUN
ejpam-2299	72	20	algebras	algebra	NOUN
ejpam-2299	72	21	.	.	PUNCT
ejpam-2299	72	22	example	example	NOUN
ejpam-2299	73	1	1	1	NUM
ejpam-2299	73	2	.	.	PUNCT
ejpam-2299	74	1	in	in	ADP
ejpam-2299	74	2	each	each	PRON
ejpam-2299	74	3	of	of	ADP
ejpam-2299	74	4	the	the	DET
ejpam-2299	74	5	following	following	ADJ
ejpam-2299	74	6	cases	case	NOUN
ejpam-2299	74	7	by	by	ADP
ejpam-2299	74	8	using	use	VERB
ejpam-2299	74	9	theorem	theorem	NOUN
ejpam-2299	74	10	1	1	NUM
ejpam-2299	74	11	,	,	PUNCT
ejpam-2299	74	12	a′	a′	PROPN
ejpam-2299	74	13	is	be	AUX
ejpam-2299	74	14	a	a	DET
ejpam-2299	74	15	banach	banach	NOUN
ejpam-2299	74	16	a′′-bimodule	a′′-bimodule	NOUN
ejpam-2299	74	17	.	.	PUNCT
ejpam-2299	75	1	(	(	PUNCT
ejpam-2299	75	2	1	1	X
ejpam-2299	75	3	)	)	PUNCT
ejpam-2299	75	4	let	let	VERB
ejpam-2299	75	5	a	a	PRON
ejpam-2299	75	6	be	be	AUX
ejpam-2299	75	7	a	a	DET
ejpam-2299	75	8	c∗-algebra	c∗-algebra	PROPN
ejpam-2299	75	9	,	,	PUNCT
ejpam-2299	75	10	then	then	ADV
ejpam-2299	75	11	a	a	PRON
ejpam-2299	75	12	is	be	AUX
ejpam-2299	75	13	arens	aren	NOUN
ejpam-2299	75	14	regular	regular	ADJ
ejpam-2299	75	15	and	and	CCONJ
ejpam-2299	75	16	a′	a′	NOUN
ejpam-2299	75	17	is	be	AUX
ejpam-2299	75	18	a	a	DET
ejpam-2299	75	19	banach	banach	NOUN
ejpam-2299	75	20	a′′-bimodule	a′′-bimodule	NOUN
ejpam-2299	76	1	[	[	X
ejpam-2299	76	2	3	3	NUM
ejpam-2299	76	3	]	]	PUNCT
ejpam-2299	76	4	.	.	PUNCT
ejpam-2299	77	1	(	(	PUNCT
ejpam-2299	77	2	2	2	X
ejpam-2299	77	3	)	)	PUNCT
ejpam-2299	77	4	let	let	VERB
ejpam-2299	77	5	a=	a=	ADV
ejpam-2299	77	6	l1(n	l1(n	NOUN
ejpam-2299	77	7	)	)	PUNCT
ejpam-2299	77	8	with	with	ADP
ejpam-2299	77	9	product	product	NOUN
ejpam-2299	77	10	f	f	X
ejpam-2299	77	11	·	·	PUNCT
ejpam-2299	77	12	g	g	PROPN
ejpam-2299	77	13	=	=	SYM
ejpam-2299	77	14	f	f	PROPN
ejpam-2299	77	15	(	(	PUNCT
ejpam-2299	77	16	1)g	1)g	PROPN
ejpam-2299	77	17	.	.	PUNCT
ejpam-2299	78	1	then	then	ADV
ejpam-2299	78	2	a	a	PRON
ejpam-2299	78	3	is	be	AUX
ejpam-2299	78	4	a	a	DET
ejpam-2299	78	5	banach	banach	NOUN
ejpam-2299	78	6	algebra	algebra	NOUN
ejpam-2299	78	7	with	with	ADP
ejpam-2299	78	8	l1	l1	PROPN
ejpam-2299	78	9	-	-	PUNCT
ejpam-2299	78	10	norm	norm	NOUN
ejpam-2299	78	11	and	and	CCONJ
ejpam-2299	78	12	a	a	PRON
ejpam-2299	78	13	is	be	AUX
ejpam-2299	78	14	a	a	DET
ejpam-2299	78	15	left	left	ADJ
ejpam-2299	78	16	ideal	ideal	NOUN
ejpam-2299	78	17	in	in	ADP
ejpam-2299	78	18	a′′.	a′′.	PROPN
ejpam-2299	78	19	so	so	SCONJ
ejpam-2299	78	20	a′	a′	PROPN
ejpam-2299	78	21	is	be	AUX
ejpam-2299	78	22	a	a	DET
ejpam-2299	78	23	banach	banach	NOUN
ejpam-2299	78	24	a′′-bimodule	a′′-bimodule	NOUN
ejpam-2299	79	1	[	[	X
ejpam-2299	79	2	6	6	NUM
ejpam-2299	79	3	]	]	PUNCT
ejpam-2299	79	4	.	.	PUNCT
ejpam-2299	80	1	(	(	PUNCT
ejpam-2299	80	2	3	3	X
ejpam-2299	80	3	)	)	PUNCT
ejpam-2299	80	4	let	let	VERB
ejpam-2299	80	5	s	s	PRON
ejpam-2299	80	6	be	be	AUX
ejpam-2299	80	7	an	an	DET
ejpam-2299	80	8	infinite	infinite	NOUN
ejpam-2299	80	9	set	set	VERB
ejpam-2299	80	10	with	with	ADP
ejpam-2299	80	11	product	product	NOUN
ejpam-2299	80	12	s	s	PART
ejpam-2299	80	13	·	·	PUNCT
ejpam-2299	80	14	t	t	PROPN
ejpam-2299	80	15	=	=	SYM
ejpam-2299	80	16	t	t	PROPN
ejpam-2299	80	17	for	for	ADP
ejpam-2299	80	18	all	all	DET
ejpam-2299	80	19	s	s	PROPN
ejpam-2299	80	20	,	,	PUNCT
ejpam-2299	80	21	t	t	PROPN
ejpam-2299	80	22	∈	∈	PROPN
ejpam-2299	80	23	s.	s.	PROPN
ejpam-2299	80	24	then	then	ADV
ejpam-2299	80	25	l1(s	l1(s	PROPN
ejpam-2299	80	26	)	)	PUNCT
ejpam-2299	80	27	is	be	AUX
ejpam-2299	80	28	a	a	DET
ejpam-2299	80	29	left	left	ADJ
ejpam-2299	80	30	ideal	ideal	NOUN
ejpam-2299	80	31	in	in	ADP
ejpam-2299	80	32	(	(	PUNCT
ejpam-2299	80	33	l1(s))′′	l1(s))′′	PROPN
ejpam-2299	80	34	and	and	CCONJ
ejpam-2299	80	35	so	so	ADV
ejpam-2299	80	36	(	(	PUNCT
ejpam-2299	80	37	l1(s))′	l1(s))′	PROPN
ejpam-2299	80	38	is	be	AUX
ejpam-2299	80	39	a	a	DET
ejpam-2299	80	40	banach	banach	NOUN
ejpam-2299	80	41	(	(	PUNCT
ejpam-2299	80	42	l1(s))′′	l1(s))′′	PROPN
ejpam-2299	80	43	-bimodule	-bimodule	NOUN
ejpam-2299	80	44	.	.	PUNCT
ejpam-2299	81	1	but	but	CCONJ
ejpam-2299	81	2	l1(s	l1(s	PROPN
ejpam-2299	81	3	)	)	PUNCT
ejpam-2299	81	4	is	be	AUX
ejpam-2299	81	5	not	not	PART
ejpam-2299	81	6	a	a	DET
ejpam-2299	81	7	right	right	ADJ
ejpam-2299	81	8	ideal	ideal	NOUN
ejpam-2299	81	9	in	in	ADP
ejpam-2299	81	10	(	(	PUNCT
ejpam-2299	81	11	l1(s))′′	l1(s))′′	PROPN
ejpam-2299	81	12	[	[	X
ejpam-2299	81	13	6	6	NUM
ejpam-2299	81	14	]	]	PUNCT
ejpam-2299	81	15	(	(	PUNCT
ejpam-2299	81	16	so	so	ADV
ejpam-2299	81	17	the	the	DET
ejpam-2299	81	18	third	third	ADJ
ejpam-2299	81	19	condition	condition	NOUN
ejpam-2299	81	20	in	in	ADP
ejpam-2299	81	21	theorem	theorem	NOUN
ejpam-2299	81	22	1	1	NUM
ejpam-2299	81	23	is	be	AUX
ejpam-2299	81	24	not	not	PART
ejpam-2299	81	25	a	a	DET
ejpam-2299	81	26	necessary	necessary	ADJ
ejpam-2299	81	27	condition	condition	NOUN
ejpam-2299	81	28	)	)	PUNCT
ejpam-2299	81	29	.	.	PUNCT
ejpam-2299	82	1	(	(	PUNCT
ejpam-2299	82	2	4	4	X
ejpam-2299	82	3	)	)	PUNCT
ejpam-2299	82	4	we	we	PRON
ejpam-2299	82	5	know	know	VERB
ejpam-2299	82	6	that	that	SCONJ
ejpam-2299	82	7	for	for	SCONJ
ejpam-2299	82	8	each	each	DET
ejpam-2299	82	9	semisimple	semisimple	ADJ
ejpam-2299	82	10	annihilator	annihilator	PROPN
ejpam-2299	82	11	banach	banach	PROPN
ejpam-2299	82	12	algebra	algebra	VERB
ejpam-2299	82	13	a	a	PRON
ejpam-2299	82	14	,	,	PUNCT
ejpam-2299	82	15	a	a	PRON
ejpam-2299	82	16	is	be	AUX
ejpam-2299	82	17	an	an	DET
ejpam-2299	82	18	ideal	ideal	NOUN
ejpam-2299	82	19	in	in	ADP
ejpam-2299	82	20	a′′	a′′	NOUN
ejpam-2299	82	21	[	[	X
ejpam-2299	82	22	13	13	NUM
ejpam-2299	82	23	]	]	PUNCT
ejpam-2299	82	24	.	.	PUNCT
ejpam-2299	83	1	so	so	ADV
ejpam-2299	83	2	a′	a′	PROPN
ejpam-2299	83	3	is	be	AUX
ejpam-2299	83	4	a	a	DET
ejpam-2299	83	5	banach	banach	NOUN
ejpam-2299	83	6	a′′-bimodule	a′′-bimodule	NOUN
ejpam-2299	83	7	and	and	CCONJ
ejpam-2299	83	8	we	we	PRON
ejpam-2299	83	9	have	have	VERB
ejpam-2299	83	10	the	the	DET
ejpam-2299	83	11	following	follow	VERB
ejpam-2299	83	12	assertion	assertion	NOUN
ejpam-2299	83	13	:	:	PUNCT
ejpam-2299	83	14	•	•	NOUN
ejpam-2299	83	15	let	let	VERB
ejpam-2299	83	16	g	g	PRON
ejpam-2299	83	17	be	be	AUX
ejpam-2299	83	18	an	an	DET
ejpam-2299	83	19	infinite	infinite	ADJ
ejpam-2299	83	20	compact	compact	ADJ
ejpam-2299	83	21	group	group	NOUN
ejpam-2299	83	22	,	,	PUNCT
ejpam-2299	83	23	then	then	ADV
ejpam-2299	83	24	l1(g	l1(g	PROPN
ejpam-2299	83	25	)	)	PUNCT
ejpam-2299	83	26	is	be	AUX
ejpam-2299	83	27	not	not	PART
ejpam-2299	83	28	arens	aren	NOUN
ejpam-2299	83	29	regular	regular	ADJ
ejpam-2299	83	30	but	but	CCONJ
ejpam-2299	83	31	l1(g	l1(g	PRON
ejpam-2299	83	32	)	)	PUNCT
ejpam-2299	83	33	is	be	AUX
ejpam-2299	83	34	an	an	DET
ejpam-2299	83	35	ideal	ideal	NOUN
ejpam-2299	83	36	in	in	ADP
ejpam-2299	83	37	�	�	PROPN
ejpam-2299	83	38	l1(g	l1(g	PROPN
ejpam-2299	83	39	)	)	PUNCT
ejpam-2299	83	40	�	�	PROPN
ejpam-2299	83	41	′′	′′	PROPN
ejpam-2299	83	42	.	.	PUNCT
ejpam-2299	84	1	so	so	ADV
ejpam-2299	84	2	�	�	PROPN
ejpam-2299	84	3	l1(g	l1(g	PROPN
ejpam-2299	84	4	)	)	PUNCT
ejpam-2299	84	5	�	�	PROPN
ejpam-2299	84	6	′	′	NUM
ejpam-2299	84	7	is	be	AUX
ejpam-2299	84	8	a	a	DET
ejpam-2299	84	9	banach	banach	NOUN
ejpam-2299	84	10	�	�	PROPN
ejpam-2299	84	11	l1(g	l1(g	PROPN
ejpam-2299	84	12	)	)	PUNCT
ejpam-2299	84	13	�	�	PROPN
ejpam-2299	84	14	′′	′′	NOUN
ejpam-2299	84	15	-bimodule	-bimodule	NOUN
ejpam-2299	84	16	,	,	PUNCT
ejpam-2299	84	17	whereas	whereas	SCONJ
ejpam-2299	84	18	l1(g	l1(g	PROPN
ejpam-2299	84	19	)	)	PUNCT
ejpam-2299	84	20	is	be	AUX
ejpam-2299	84	21	not	not	PART
ejpam-2299	84	22	arens	aren	NOUN
ejpam-2299	84	23	regular	regular	ADJ
ejpam-2299	84	24	(	(	PUNCT
ejpam-2299	84	25	so	so	ADV
ejpam-2299	84	26	the	the	DET
ejpam-2299	84	27	first	first	ADJ
ejpam-2299	84	28	condition	condition	NOUN
ejpam-2299	84	29	in	in	ADP
ejpam-2299	84	30	theorem	theorem	NOUN
ejpam-2299	84	31	1	1	NUM
ejpam-2299	84	32	is	be	AUX
ejpam-2299	84	33	not	not	PART
ejpam-2299	84	34	a	a	DET
ejpam-2299	84	35	necessary	necessary	ADJ
ejpam-2299	84	36	condition	condition	NOUN
ejpam-2299	84	37	)	)	PUNCT
ejpam-2299	84	38	.	.	PUNCT
ejpam-2299	85	1	•	•	INTJ
ejpam-2299	85	2	let	let	VERB
ejpam-2299	85	3	g	g	NOUN
ejpam-2299	85	4	be	be	AUX
ejpam-2299	85	5	an	an	DET
ejpam-2299	85	6	finite	finite	ADJ
ejpam-2299	85	7	group	group	NOUN
ejpam-2299	85	8	then	then	ADV
ejpam-2299	85	9	m(g	m(g	PROPN
ejpam-2299	85	10	)	)	PUNCT
ejpam-2299	85	11	is	be	AUX
ejpam-2299	85	12	an	an	DET
ejpam-2299	85	13	ideal	ideal	NOUN
ejpam-2299	85	14	in	in	ADP
ejpam-2299	85	15	m(g)′′.	m(g)′′.	PROPN
ejpam-2299	85	16	so	so	PROPN
ejpam-2299	85	17	m(g)′	m(g)′	PROPN
ejpam-2299	85	18	is	be	AUX
ejpam-2299	85	19	a	a	DET
ejpam-2299	85	20	banach	banach	NOUN
ejpam-2299	85	21	m(g)′′-bimodule	m(g)′′-bimodule	NOUN
ejpam-2299	86	1	[	[	X
ejpam-2299	86	2	11	11	NUM
ejpam-2299	86	3	]	]	PUNCT
ejpam-2299	86	4	and	and	CCONJ
ejpam-2299	86	5	[	[	X
ejpam-2299	86	6	12	12	NUM
ejpam-2299	86	7	]	]	PUNCT
ejpam-2299	86	8	.	.	PUNCT
ejpam-2299	87	1	(	(	PUNCT
ejpam-2299	87	2	5	5	X
ejpam-2299	87	3	)	)	PUNCT
ejpam-2299	87	4	let	let	VERB
ejpam-2299	87	5	x	x	PRON
ejpam-2299	87	6	be	be	AUX
ejpam-2299	87	7	a	a	DET
ejpam-2299	87	8	reflexive	reflexive	ADJ
ejpam-2299	87	9	banach	banach	NOUN
ejpam-2299	87	10	space	space	NOUN
ejpam-2299	87	11	and	and	CCONJ
ejpam-2299	87	12	k	k	NOUN
ejpam-2299	87	13	l(x	l(x	PROPN
ejpam-2299	87	14	)	)	PUNCT
ejpam-2299	87	15	be	be	AUX
ejpam-2299	87	16	the	the	DET
ejpam-2299	87	17	algebra	algebra	NOUN
ejpam-2299	87	18	of	of	ADP
ejpam-2299	87	19	compact	compact	ADJ
ejpam-2299	87	20	operators	operator	NOUN
ejpam-2299	87	21	on	on	ADP
ejpam-2299	87	22	x	x	X
ejpam-2299	87	23	.	.	PUNCT
ejpam-2299	88	1	then	then	ADV
ejpam-2299	88	2	k	k	PROPN
ejpam-2299	88	3	l(x	l(x	PROPN
ejpam-2299	88	4	)	)	PUNCT
ejpam-2299	88	5	is	be	AUX
ejpam-2299	88	6	an	an	DET
ejpam-2299	88	7	ideal	ideal	NOUN
ejpam-2299	88	8	in	in	ADP
ejpam-2299	88	9	k	k	PROPN
ejpam-2299	88	10	l(x	l(x	PROPN
ejpam-2299	88	11	)	)	PUNCT
ejpam-2299	88	12	′′	′′	PROPN
ejpam-2299	88	13	and	and	CCONJ
ejpam-2299	88	14	so	so	ADV
ejpam-2299	88	15	(	(	PUNCT
ejpam-2299	88	16	k	k	NOUN
ejpam-2299	88	17	l(x	l(x	PROPN
ejpam-2299	88	18	)	)	PUNCT
ejpam-2299	88	19	)	)	PUNCT
ejpam-2299	89	1	′	′	NUM
ejpam-2299	89	2	is	be	AUX
ejpam-2299	89	3	a	a	DET
ejpam-2299	89	4	banach	banach	NOUN
ejpam-2299	89	5	(	(	PUNCT
ejpam-2299	89	6	k	k	NOUN
ejpam-2299	89	7	l(x	l(x	PROPN
ejpam-2299	89	8	)	)	PUNCT
ejpam-2299	89	9	)	)	PUNCT
ejpam-2299	89	10	′′-bimodule	′′-bimodule	NOUN
ejpam-2299	89	11	.	.	PUNCT
ejpam-2299	90	1	note	note	VERB
ejpam-2299	90	2	that	that	SCONJ
ejpam-2299	90	3	in	in	ADP
ejpam-2299	90	4	the	the	DET
ejpam-2299	90	5	case	case	NOUN
ejpam-2299	90	6	x	x	PRON
ejpam-2299	90	7	has	have	AUX
ejpam-2299	90	8	not	not	PART
ejpam-2299	90	9	approximation	approximation	VERB
ejpam-2299	90	10	property	property	NOUN
ejpam-2299	90	11	k	k	PROPN
ejpam-2299	90	12	l(x	l(x	PROPN
ejpam-2299	90	13	)	)	PUNCT
ejpam-2299	90	14	is	be	AUX
ejpam-2299	90	15	not	not	PART
ejpam-2299	90	16	an	an	DET
ejpam-2299	90	17	annihilator	annihilator	NOUN
ejpam-2299	90	18	algebra	algebra	NOUN
ejpam-2299	90	19	[	[	X
ejpam-2299	90	20	1	1	NUM
ejpam-2299	90	21	]	]	PUNCT
ejpam-2299	90	22	.	.	PUNCT
ejpam-2299	91	1	now	now	ADV
ejpam-2299	91	2	we	we	PRON
ejpam-2299	91	3	give	give	VERB
ejpam-2299	91	4	an	an	DET
ejpam-2299	91	5	example	example	NOUN
ejpam-2299	91	6	of	of	ADP
ejpam-2299	91	7	a	a	DET
ejpam-2299	91	8	banach	banach	NOUN
ejpam-2299	91	9	algebra	algebra	NOUN
ejpam-2299	91	10	a	a	PRON
ejpam-2299	91	11	for	for	ADP
ejpam-2299	91	12	which	which	PRON
ejpam-2299	91	13	a′	a′	NOUN
ejpam-2299	91	14	is	be	AUX
ejpam-2299	91	15	not	not	PART
ejpam-2299	91	16	a	a	DET
ejpam-2299	91	17	banach	banach	NOUN
ejpam-2299	91	18	a′′-bimodule	a′′-bimodule	NOUN
ejpam-2299	91	19	.	.	PUNCT
ejpam-2299	92	1	example	example	NOUN
ejpam-2299	92	2	2	2	NUM
ejpam-2299	92	3	.	.	X
ejpam-2299	92	4	consider	consider	VERB
ejpam-2299	92	5	a	a	DET
ejpam-2299	92	6	=	=	SYM
ejpam-2299	92	7	(	(	PUNCT
ejpam-2299	92	8	l1,∗	l1,∗	NOUN
ejpam-2299	92	9	)	)	PUNCT
ejpam-2299	92	10	for	for	ADP
ejpam-2299	92	11	n	n	CCONJ
ejpam-2299	92	12	,	,	PUNCT
ejpam-2299	92	13	m	m	PROPN
ejpam-2299	92	14	∈	∈	PROPN
ejpam-2299	92	15	n.	n.	NOUN
ejpam-2299	92	16	set	set	VERB
ejpam-2299	92	17	an	an	DET
ejpam-2299	92	18	=	=	X
ejpam-2299	92	19	δ22n	δ22n	ADV
ejpam-2299	92	20	,	,	PUNCT
ejpam-2299	92	21	bm	bm	PROPN
ejpam-2299	92	22	=	=	NOUN
ejpam-2299	92	23	δ22m+1−1	δ22m+1−1	PROPN
ejpam-2299	92	24	and	and	CCONJ
ejpam-2299	92	25	x	x	X
ejpam-2299	92	26	=	=	PUNCT
ejpam-2299	92	27	δ1	δ1	NOUN
ejpam-2299	92	28	that	that	DET
ejpam-2299	92	29	(	(	PUNCT
ejpam-2299	92	30	an)n	an)n	PROPN
ejpam-2299	92	31	,	,	PUNCT
ejpam-2299	92	32	(	(	PUNCT
ejpam-2299	92	33	bm)m	bm)m	PROPN
ejpam-2299	92	34	are	be	AUX
ejpam-2299	92	35	bounded	bound	VERB
ejpam-2299	92	36	sequences	sequence	NOUN
ejpam-2299	92	37	in	in	ADP
ejpam-2299	92	38	l1	l1	PROPN
ejpam-2299	92	39	.	.	PUNCT
ejpam-2299	93	1	there	there	PRON
ejpam-2299	93	2	are	be	VERB
ejpam-2299	93	3	f	f	X
ejpam-2299	93	4	,	,	PUNCT
ejpam-2299	93	5	g	g	PROPN
ejpam-2299	93	6	∈	∈	PROPN
ejpam-2299	93	7	a′′	a′′	NOUN
ejpam-2299	93	8	for	for	ADP
ejpam-2299	93	9	which	which	PRON
ejpam-2299	93	10	f	f	PROPN
ejpam-2299	93	11	=	=	PROPN
ejpam-2299	93	12	w∗	w∗	PROPN
ejpam-2299	93	13	−	−	PROPN
ejpam-2299	94	1	limn	limn	PROPN
ejpam-2299	94	2	ân	ân	PROPN
ejpam-2299	94	3	,	,	PUNCT
ejpam-2299	94	4	g	g	PROPN
ejpam-2299	94	5	=	=	PROPN
ejpam-2299	94	6	w∗	w∗	PROPN
ejpam-2299	94	7	−	−	PROPN
ejpam-2299	94	8	limm	limm	NOUN
ejpam-2299	94	9	b̂m	b̂m	PRON
ejpam-2299	94	10	.	.	PUNCT
ejpam-2299	95	1	now	now	ADV
ejpam-2299	95	2	,	,	PUNCT
ejpam-2299	95	3	let	let	VERB
ejpam-2299	95	4	s	s	PRON
ejpam-2299	95	5	=	=	VERB
ejpam-2299	95	6	�	�	PROPN
ejpam-2299	95	7	22n	22n	X
ejpam-2299	95	8	+	+	CCONJ
ejpam-2299	95	9	22m+1	22m+1	NUM
ejpam-2299	95	10	:	:	PUNCT
ejpam-2299	95	11	n	n	CCONJ
ejpam-2299	95	12	,	,	PUNCT
ejpam-2299	95	13	m	m	VERB
ejpam-2299	95	14	∈	∈	PROPN
ejpam-2299	95	15	n	n	CCONJ
ejpam-2299	95	16	,	,	PUNCT
ejpam-2299	95	17	n	n	CCONJ
ejpam-2299	95	18	<	<	X
ejpam-2299	95	19	m	m	PROPN
ejpam-2299	95	20	s.	s.	PROPN
ejpam-2299	95	21	hosseinioun	hosseinioun	PROPN
ejpam-2299	95	22	,	,	PUNCT
ejpam-2299	95	23	a.	a.	NOUN
ejpam-2299	95	24	valadkhani	valadkhani	PROPN
ejpam-2299	95	25	/	/	SYM
ejpam-2299	95	26	eur	eur	PROPN
ejpam-2299	95	27	.	.	PUNCT
ejpam-2299	96	1	j.	j.	PROPN
ejpam-2299	96	2	pure	pure	PROPN
ejpam-2299	96	3	appl	appl	PROPN
ejpam-2299	96	4	.	.	PROPN
ejpam-2299	96	5	math	math	PROPN
ejpam-2299	96	6	,	,	PUNCT
ejpam-2299	96	7	9	9	NUM
ejpam-2299	96	8	(	(	PUNCT
ejpam-2299	96	9	2016	2016	NUM
ejpam-2299	96	10	)	)	PUNCT
ejpam-2299	96	11	,	,	PUNCT
ejpam-2299	96	12	231	231	NUM
ejpam-2299	96	13	-	-	SYM
ejpam-2299	96	14	239	239	NUM
ejpam-2299	96	15	234	234	NUM
ejpam-2299	96	16	and	and	CCONJ
ejpam-2299	96	17	set	set	VERB
ejpam-2299	96	18	λ	λ	PROPN
ejpam-2299	96	19	=	=	SYM
ejpam-2299	96	20	χs	χs	PROPN
ejpam-2299	96	21	,	,	PUNCT
ejpam-2299	96	22	where	where	SCONJ
ejpam-2299	96	23	χs	χs	PROPN
ejpam-2299	96	24	is	be	AUX
ejpam-2299	96	25	characteristic	characteristic	ADJ
ejpam-2299	96	26	function	function	NOUN
ejpam-2299	96	27	on	on	ADP
ejpam-2299	96	28	s.	s.	PROPN
ejpam-2299	97	1	so	so	ADV
ejpam-2299	97	2	(	(	PUNCT
ejpam-2299	97	3	bm	bm	PROPN
ejpam-2299	97	4	∗	∗	PROPN
ejpam-2299	97	5	x	x	PROPN
ejpam-2299	97	6	)	)	PUNCT
ejpam-2299	97	7	∗	∗	NOUN
ejpam-2299	97	8	an	an	DET
ejpam-2299	97	9	=	=	NOUN
ejpam-2299	97	10	δ22n+22m+1	δ22n+22m+1	NOUN
ejpam-2299	98	1	and	and	CCONJ
ejpam-2299	98	2	we	we	PRON
ejpam-2299	98	3	have	have	VERB
ejpam-2299	98	4	lim	lim	PROPN
ejpam-2299	98	5	n→∞	n→∞	X
ejpam-2299	98	6	λ(bm	λ(bm	PROPN
ejpam-2299	98	7	∗	∗	NOUN
ejpam-2299	98	8	x	x	X
ejpam-2299	98	9	∗	∗	NOUN
ejpam-2299	98	10	an	an	NOUN
ejpam-2299	98	11	)	)	PUNCT
ejpam-2299	98	12	=	=	SYM
ejpam-2299	98	13	0	0	NUM
ejpam-2299	98	14	,	,	PUNCT
ejpam-2299	98	15	lim	lim	PROPN
ejpam-2299	98	16	m→∞	m→∞	NOUN
ejpam-2299	98	17	λ(bm	λ(bm	PROPN
ejpam-2299	98	18	∗	∗	NOUN
ejpam-2299	98	19	x	x	X
ejpam-2299	98	20	∗	∗	NOUN
ejpam-2299	98	21	an	an	NOUN
ejpam-2299	98	22	)	)	PUNCT
ejpam-2299	99	1	=	=	SYM
ejpam-2299	99	2	1	1	X
ejpam-2299	99	3	.	.	PUNCT
ejpam-2299	100	1	so	so	ADV
ejpam-2299	100	2	,	,	PUNCT
ejpam-2299	100	3	(	(	PUNCT
ejpam-2299	100	4	f	f	PROPN
ejpam-2299	100	5	·	·	SYM
ejpam-2299	100	6	λ	λ	NOUN
ejpam-2299	100	7	)	)	PUNCT
ejpam-2299	101	1	·	·	PUNCT
ejpam-2299	101	2	g(x	g(x	NOUN
ejpam-2299	101	3	)	)	PUNCT
ejpam-2299	102	1	=	=	X
ejpam-2299	102	2	g(x	g(x	X
ejpam-2299	102	3	·	·	PUNCT
ejpam-2299	102	4	(	(	PUNCT
ejpam-2299	102	5	f	f	X
ejpam-2299	102	6	·	·	SYM
ejpam-2299	102	7	λ	λ	NOUN
ejpam-2299	102	8	)	)	PUNCT
ejpam-2299	102	9	)	)	PUNCT
ejpam-2299	103	1	=	=	SYM
ejpam-2299	104	1	lim	lim	PROPN
ejpam-2299	104	2	m	m	VERB
ejpam-2299	104	3	f(λ	f(λ	PROPN
ejpam-2299	104	4	·	·	PUNCT
ejpam-2299	104	5	(	(	PUNCT
ejpam-2299	104	6	bm	bm	PROPN
ejpam-2299	104	7	∗	∗	PROPN
ejpam-2299	104	8	x	x	NOUN
ejpam-2299	104	9	)	)	PUNCT
ejpam-2299	104	10	)	)	PUNCT
ejpam-2299	105	1	=	=	SYM
ejpam-2299	106	1	lim	lim	PROPN
ejpam-2299	106	2	m	m	PROPN
ejpam-2299	106	3	lim	lim	PROPN
ejpam-2299	106	4	n	n	PROPN
ejpam-2299	106	5	λ(bm	λ(bm	PROPN
ejpam-2299	106	6	∗	∗	NOUN
ejpam-2299	106	7	x	x	X
ejpam-2299	106	8	∗	∗	NOUN
ejpam-2299	106	9	an	an	NOUN
ejpam-2299	106	10	)	)	PUNCT
ejpam-2299	106	11	=	=	NOUN
ejpam-2299	106	12	0	0	X
ejpam-2299	106	13	.	.	PUNCT
ejpam-2299	107	1	on	on	ADP
ejpam-2299	107	2	the	the	DET
ejpam-2299	107	3	other	other	ADJ
ejpam-2299	107	4	hand	hand	NOUN
ejpam-2299	107	5	,	,	PUNCT
ejpam-2299	107	6	f	f	X
ejpam-2299	107	7	·	·	PUNCT
ejpam-2299	107	8	(	(	PUNCT
ejpam-2299	107	9	λ	λ	X
ejpam-2299	107	10	·	·	PUNCT
ejpam-2299	107	11	g)(x	g)(x	PROPN
ejpam-2299	107	12	)	)	PUNCT
ejpam-2299	107	13	=	=	NOUN
ejpam-2299	107	14	f((λ	f((λ	NOUN
ejpam-2299	107	15	·	·	PUNCT
ejpam-2299	107	16	g	g	NOUN
ejpam-2299	107	17	)	)	PUNCT
ejpam-2299	107	18	·	·	PUNCT
ejpam-2299	108	1	x	x	X
ejpam-2299	108	2	)	)	PUNCT
ejpam-2299	108	3	=	=	SYM
ejpam-2299	108	4	lim	lim	PROPN
ejpam-2299	108	5	n	n	CCONJ
ejpam-2299	108	6	λ	λ	PROPN
ejpam-2299	108	7	·	·	PUNCT
ejpam-2299	108	8	g(x	g(x	PROPN
ejpam-2299	108	9	∗	∗	NOUN
ejpam-2299	108	10	an	an	NOUN
ejpam-2299	108	11	)	)	PUNCT
ejpam-2299	109	1	=	=	SYM
ejpam-2299	109	2	lim	lim	PROPN
ejpam-2299	109	3	n	n	PROPN
ejpam-2299	109	4	lim	lim	PROPN
ejpam-2299	109	5	m	m	PROPN
ejpam-2299	109	6	λ(bm	λ(bm	PROPN
ejpam-2299	109	7	∗	∗	NOUN
ejpam-2299	109	8	x	x	X
ejpam-2299	109	9	∗	∗	NOUN
ejpam-2299	109	10	an	an	NOUN
ejpam-2299	109	11	)	)	PUNCT
ejpam-2299	109	12	=	=	SYM
ejpam-2299	109	13	1	1	X
ejpam-2299	109	14	.	.	PUNCT
ejpam-2299	110	1	therefore	therefore	ADV
ejpam-2299	110	2	a′	a′	PROPN
ejpam-2299	110	3	is	be	AUX
ejpam-2299	110	4	not	not	PART
ejpam-2299	110	5	a	a	DET
ejpam-2299	110	6	banach	banach	NOUN
ejpam-2299	110	7	a′′-bimodule	a′′-bimodule	NOUN
ejpam-2299	110	8	and	and	CCONJ
ejpam-2299	110	9	so	so	ADV
ejpam-2299	110	10	a′′	a′′	NOUN
ejpam-2299	110	11	is	be	AUX
ejpam-2299	110	12	not	not	PART
ejpam-2299	110	13	(	(	PUNCT
ejpam-2299	110	14	-1)-weakly	-1)-weakly	ADV
ejpam-2299	110	15	amenable	amenable	ADJ
ejpam-2299	110	16	.	.	PUNCT
ejpam-2299	111	1	question	question	NOUN
ejpam-2299	111	2	.	.	PUNCT
ejpam-2299	112	1	is	be	AUX
ejpam-2299	112	2	there	there	PRON
ejpam-2299	112	3	any	any	DET
ejpam-2299	112	4	banach	banach	NOUN
ejpam-2299	112	5	algebra	algebra	NOUN
ejpam-2299	112	6	a	a	DET
ejpam-2299	112	7	such	such	ADJ
ejpam-2299	112	8	that	that	SCONJ
ejpam-2299	112	9	a	a	PRON
ejpam-2299	112	10	is	be	AUX
ejpam-2299	112	11	amenable	amenable	ADJ
ejpam-2299	112	12	but	but	CCONJ
ejpam-2299	112	13	a′	a′	NOUN
ejpam-2299	112	14	is	be	AUX
ejpam-2299	112	15	not	not	PART
ejpam-2299	112	16	a′′-bimodule	a′′-bimodule	NOUN
ejpam-2299	112	17	?	?	PUNCT
ejpam-2299	113	1	3	3	X
ejpam-2299	113	2	.	.	X
ejpam-2299	113	3	unitization	unitization	NOUN
ejpam-2299	113	4	let	let	VERB
ejpam-2299	113	5	a	a	PRON
ejpam-2299	113	6	has	have	VERB
ejpam-2299	113	7	not	not	PART
ejpam-2299	113	8	unit	unit	NOUN
ejpam-2299	113	9	element	element	NOUN
ejpam-2299	113	10	and	and	CCONJ
ejpam-2299	113	11	a	a	DET
ejpam-2299	113	12	#	#	NOUN
ejpam-2299	113	13	=	=	SYM
ejpam-2299	113	14	a⊕ce	a⊕ce	PROPN
ejpam-2299	113	15	be	be	AUX
ejpam-2299	113	16	the	the	DET
ejpam-2299	113	17	unitization	unitization	NOUN
ejpam-2299	113	18	of	of	ADP
ejpam-2299	113	19	a.	a.	NOUN
ejpam-2299	113	20	for	for	ADP
ejpam-2299	113	21	e	e	PROPN
ejpam-2299	113	22	∈	∈	PROPN
ejpam-2299	113	23	a	a	DET
ejpam-2299	113	24	#	#	NOUN
ejpam-2299	113	25	,	,	PUNCT
ejpam-2299	113	26	by	by	ADP
ejpam-2299	113	27	hahn	hahn	NOUN
ejpam-2299	113	28	-	-	PUNCT
ejpam-2299	113	29	banach	banach	NOUN
ejpam-2299	113	30	theorem	theorem	NOUN
ejpam-2299	113	31	there	there	PRON
ejpam-2299	113	32	exists	exist	VERB
ejpam-2299	113	33	e′	e′	X
ejpam-2299	113	34	∈	∈	PROPN
ejpam-2299	113	35	a#′	a#′	VERB
ejpam-2299	113	36	such	such	ADJ
ejpam-2299	113	37	that	that	PRON
ejpam-2299	113	38	e′(e	e′(e	NOUN
ejpam-2299	113	39	)	)	PUNCT
ejpam-2299	113	40	=	=	SYM
ejpam-2299	113	41	1	1	NUM
ejpam-2299	113	42	and	and	CCONJ
ejpam-2299	113	43	e′(a	e′(a	PROPN
ejpam-2299	113	44	)	)	PUNCT
ejpam-2299	113	45	=	=	SYM
ejpam-2299	113	46	0	0	NUM
ejpam-2299	113	47	for	for	ADP
ejpam-2299	113	48	each	each	PRON
ejpam-2299	113	49	a	a	DET
ejpam-2299	113	50	∈	∈	PROPN
ejpam-2299	113	51	a	a	PRON
ejpam-2299	113	52	,	,	PUNCT
ejpam-2299	113	53	and	and	CCONJ
ejpam-2299	113	54	we	we	PRON
ejpam-2299	113	55	can	can	AUX
ejpam-2299	113	56	extend	extend	VERB
ejpam-2299	113	57	λ	λ	PROPN
ejpam-2299	113	58	∈	∈	PROPN
ejpam-2299	113	59	a′	a′	NOUN
ejpam-2299	113	60	to	to	ADP
ejpam-2299	113	61	an	an	DET
ejpam-2299	113	62	element	element	NOUN
ejpam-2299	113	63	of	of	ADP
ejpam-2299	113	64	a#′	a#′	PROPN
ejpam-2299	113	65	with	with	ADP
ejpam-2299	113	66	λ(e	λ(e	NOUN
ejpam-2299	113	67	)	)	PUNCT
ejpam-2299	113	68	=	=	SYM
ejpam-2299	113	69	1	1	X
ejpam-2299	113	70	.	.	PUNCT
ejpam-2299	114	1	so	so	ADV
ejpam-2299	114	2	a#′	a#′	PROPN
ejpam-2299	114	3	=	=	SYM
ejpam-2299	114	4	ce′⊕∞a′	ce′⊕∞a′	NOUN
ejpam-2299	114	5	and	and	CCONJ
ejpam-2299	114	6	‖αe′+λ‖=max{|α|,‖λ‖	‖αe′+λ‖=max{|α|,‖λ‖	PROPN
ejpam-2299	114	7	}	}	PUNCT
ejpam-2299	114	8	for	for	ADP
ejpam-2299	114	9	α	α	PRON
ejpam-2299	114	10	∈	∈	PROPN
ejpam-2299	114	11	c	c	PROPN
ejpam-2299	114	12	and	and	CCONJ
ejpam-2299	114	13	λ	λ	PROPN
ejpam-2299	114	14	∈	∈	PROPN
ejpam-2299	114	15	a′.	a′.	NOUN
ejpam-2299	114	16	moreover	moreover	ADV
ejpam-2299	114	17	,	,	PUNCT
ejpam-2299	114	18	a#′	a#′	PROPN
ejpam-2299	114	19	is	be	AUX
ejpam-2299	114	20	a	a	DET
ejpam-2299	114	21	banach	banach	NOUN
ejpam-2299	114	22	space	space	NOUN
ejpam-2299	114	23	and	and	CCONJ
ejpam-2299	114	24	is	be	AUX
ejpam-2299	114	25	a	a	DET
ejpam-2299	114	26	banach	banach	NOUN
ejpam-2299	114	27	a#-bimodule	a#-bimodule	NOUN
ejpam-2299	114	28	by	by	ADP
ejpam-2299	114	29	module	module	NOUN
ejpam-2299	114	30	multiplications	multiplication	NOUN
ejpam-2299	114	31	(	(	PUNCT
ejpam-2299	114	32	αe+	αe+	NOUN
ejpam-2299	114	33	a	a	NOUN
ejpam-2299	114	34	)	)	PUNCT
ejpam-2299	114	35	·	·	PUNCT
ejpam-2299	115	1	(	(	PUNCT
ejpam-2299	115	2	γe′	γe′	X
ejpam-2299	115	3	+	+	ADJ
ejpam-2299	115	4	λ	λ	NOUN
ejpam-2299	115	5	)	)	PUNCT
ejpam-2299	115	6	=(	=(	NOUN
ejpam-2299	115	7	αγ+λ(a))e′	αγ+λ(a))e′	NOUN
ejpam-2299	116	1	+	+	NOUN
ejpam-2299	116	2	αλ+	αλ+	PROPN
ejpam-2299	116	3	a	a	DET
ejpam-2299	116	4	·	·	PUNCT
ejpam-2299	116	5	λ	λ	X
ejpam-2299	116	6	(	(	PUNCT
ejpam-2299	116	7	γe′	γe′	X
ejpam-2299	116	8	+	+	NOUN
ejpam-2299	116	9	λ	λ	NOUN
ejpam-2299	116	10	)	)	PUNCT
ejpam-2299	116	11	·	·	PUNCT
ejpam-2299	116	12	(	(	PUNCT
ejpam-2299	116	13	αe+	αe+	NOUN
ejpam-2299	116	14	a	a	X
ejpam-2299	116	15	)	)	PUNCT
ejpam-2299	116	16	=(	=(	NOUN
ejpam-2299	116	17	αγ+λ(a))e′	αγ+λ(a))e′	NOUN
ejpam-2299	117	1	+	+	PRON
ejpam-2299	117	2	αλ+λ	αλ+λ	ADJ
ejpam-2299	117	3	·	·	PUNCT
ejpam-2299	117	4	a	a	DET
ejpam-2299	117	5	where	where	SCONJ
ejpam-2299	117	6	α	α	NOUN
ejpam-2299	117	7	,	,	PUNCT
ejpam-2299	117	8	γ	γ	PROPN
ejpam-2299	117	9	∈	∈	PROPN
ejpam-2299	117	10	c	c	NOUN
ejpam-2299	117	11	,	,	PUNCT
ejpam-2299	117	12	a	a	DET
ejpam-2299	117	13	∈	∈	PROPN
ejpam-2299	117	14	a	a	PRON
ejpam-2299	117	15	and	and	CCONJ
ejpam-2299	117	16	λ	λ	PROPN
ejpam-2299	117	17	∈	∈	NOUN
ejpam-2299	117	18	a′.	a′.	NOUN
ejpam-2299	117	19	let	let	VERB
ejpam-2299	117	20	ê	ê	PROPN
ejpam-2299	117	21	∈	∈	VERB
ejpam-2299	117	22	a′′	a′′	NOUN
ejpam-2299	117	23	with	with	ADP
ejpam-2299	117	24	ê(λ	ê(λ	NOUN
ejpam-2299	117	25	)	)	PUNCT
ejpam-2299	117	26	=	=	PUNCT
ejpam-2299	118	1	λ(e	λ(e	PROPN
ejpam-2299	118	2	)	)	PUNCT
ejpam-2299	118	3	,	,	PUNCT
ejpam-2299	118	4	then	then	ADV
ejpam-2299	118	5	(	(	PUNCT
ejpam-2299	118	6	a#)′′	a#)′′	PROPN
ejpam-2299	118	7	=	=	SYM
ejpam-2299	118	8	a′′	a′′	NOUN
ejpam-2299	118	9	⊕cê.	⊕cê.	NOUN
ejpam-2299	118	10	for	for	ADP
ejpam-2299	118	11	more	more	ADJ
ejpam-2299	118	12	details	detail	NOUN
ejpam-2299	118	13	see	see	VERB
ejpam-2299	118	14	[	[	X
ejpam-2299	118	15	4	4	NUM
ejpam-2299	118	16	]	]	PUNCT
ejpam-2299	118	17	.	.	PUNCT
ejpam-2299	119	1	lemma	lemma	PROPN
ejpam-2299	119	2	1	1	X
ejpam-2299	119	3	.	.	PUNCT
ejpam-2299	120	1	let	let	VERB
ejpam-2299	120	2	a	a	DET
ejpam-2299	120	3	be	be	AUX
ejpam-2299	120	4	an	an	DET
ejpam-2299	120	5	arens	aren	NOUN
ejpam-2299	120	6	regular	regular	ADJ
ejpam-2299	120	7	banach	banach	NOUN
ejpam-2299	120	8	algebra	algebra	NOUN
ejpam-2299	120	9	.	.	PUNCT
ejpam-2299	121	1	then	then	ADV
ejpam-2299	121	2	a′	a′	PROPN
ejpam-2299	121	3	and	and	CCONJ
ejpam-2299	121	4	a#′	a#′	PROPN
ejpam-2299	121	5	are	be	AUX
ejpam-2299	121	6	banach	banach	ADV
ejpam-2299	121	7	a#′′-bimodule	a#′′-bimodule	ADJ
ejpam-2299	121	8	.	.	PUNCT
ejpam-2299	122	1	proof	proof	NOUN
ejpam-2299	122	2	.	.	PUNCT
ejpam-2299	123	1	the	the	DET
ejpam-2299	123	2	proof	proof	NOUN
ejpam-2299	123	3	is	be	AUX
ejpam-2299	123	4	straightforward	straightforward	ADJ
ejpam-2299	123	5	.	.	PUNCT
ejpam-2299	124	1	theorem	theorem	NOUN
ejpam-2299	124	2	2	2	NUM
ejpam-2299	124	3	.	.	PUNCT
ejpam-2299	125	1	let	let	VERB
ejpam-2299	125	2	a	a	DET
ejpam-2299	125	3	be	be	AUX
ejpam-2299	125	4	an	an	DET
ejpam-2299	125	5	arens	aren	NOUN
ejpam-2299	125	6	regular	regular	ADJ
ejpam-2299	125	7	banach	banach	NOUN
ejpam-2299	125	8	algebra	algebra	NOUN
ejpam-2299	125	9	and	and	CCONJ
ejpam-2299	125	10	a′′2	a′′2	PROPN
ejpam-2299	125	11	=	=	NOUN
ejpam-2299	125	12	a′′.	a′′.	PROPN
ejpam-2299	125	13	if	if	SCONJ
ejpam-2299	125	14	a′′	a′′	NOUN
ejpam-2299	125	15	is	be	AUX
ejpam-2299	125	16	(	(	PUNCT
ejpam-2299	125	17	-1)-weakly	-1)-weakly	ADV
ejpam-2299	125	18	amenable	amenable	ADJ
ejpam-2299	125	19	,	,	PUNCT
ejpam-2299	125	20	then	then	ADV
ejpam-2299	125	21	a′′	a′′	NOUN
ejpam-2299	125	22	#	#	NOUN
ejpam-2299	125	23	is	be	AUX
ejpam-2299	125	24	(	(	PUNCT
ejpam-2299	125	25	-1)-weakly	-1)-weakly	ADV
ejpam-2299	125	26	amenable	amenable	ADJ
ejpam-2299	125	27	.	.	PUNCT
ejpam-2299	126	1	proof	proof	NOUN
ejpam-2299	126	2	.	.	PUNCT
ejpam-2299	127	1	suppose	suppose	VERB
ejpam-2299	127	2	that	that	SCONJ
ejpam-2299	127	3	a	a	PRON
ejpam-2299	127	4	has	have	AUX
ejpam-2299	127	5	not	not	PART
ejpam-2299	127	6	unit	unit	NOUN
ejpam-2299	127	7	element	element	NOUN
ejpam-2299	127	8	and	and	CCONJ
ejpam-2299	127	9	a	a	DET
ejpam-2299	127	10	#	#	NOUN
ejpam-2299	127	11	=	=	PRON
ejpam-2299	127	12	a⊕	a⊕	X
ejpam-2299	127	13	ce	ce	AUX
ejpam-2299	127	14	be	be	AUX
ejpam-2299	127	15	its	its	PRON
ejpam-2299	127	16	unitization	unitization	NOUN
ejpam-2299	127	17	.	.	PUNCT
ejpam-2299	128	1	by	by	ADP
ejpam-2299	128	2	the	the	DET
ejpam-2299	128	3	previous	previous	ADJ
ejpam-2299	128	4	lemma	lemma	PROPN
ejpam-2299	128	5	,	,	PUNCT
ejpam-2299	128	6	a′	a′	PROPN
ejpam-2299	128	7	is	be	AUX
ejpam-2299	128	8	a	a	DET
ejpam-2299	128	9	banach	banach	NOUN
ejpam-2299	128	10	a′′-bimodule	a′′-bimodule	NOUN
ejpam-2299	128	11	and	and	CCONJ
ejpam-2299	128	12	a#′	a#′	PROPN
ejpam-2299	128	13	is	be	AUX
ejpam-2299	128	14	a	a	DET
ejpam-2299	128	15	banach	banach	NOUN
ejpam-2299	128	16	a#′′-bimodule	a#′′-bimodule	ADV
ejpam-2299	128	17	.	.	PUNCT
ejpam-2299	129	1	since	since	SCONJ
ejpam-2299	129	2	a′′	a′′	NOUN
ejpam-2299	129	3	#	#	PROPN
ejpam-2299	129	4	is	be	AUX
ejpam-2299	129	5	a	a	DET
ejpam-2299	129	6	unital	unital	ADJ
ejpam-2299	129	7	banach	banach	NOUN
ejpam-2299	129	8	algebra	algebra	NOUN
ejpam-2299	129	9	and	and	CCONJ
ejpam-2299	129	10	a′	a′	NOUN
ejpam-2299	129	11	#	#	NOUN
ejpam-2299	129	12	is	be	AUX
ejpam-2299	129	13	a	a	DET
ejpam-2299	129	14	unital	unital	ADJ
ejpam-2299	129	15	a′′#-bimodule	a′′#-bimodule	ADJ
ejpam-2299	129	16	and	and	CCONJ
ejpam-2299	129	17	a′′	a′′	NOUN
ejpam-2299	129	18	is	be	AUX
ejpam-2299	129	19	a	a	DET
ejpam-2299	129	20	maximal	maximal	ADJ
ejpam-2299	129	21	ideal	ideal	NOUN
ejpam-2299	129	22	of	of	ADP
ejpam-2299	129	23	codimension	codimension	NOUN
ejpam-2299	129	24	one	one	NUM
ejpam-2299	129	25	in	in	ADP
ejpam-2299	129	26	a′′	a′′	NOUN
ejpam-2299	129	27	#	#	NOUN
ejpam-2299	129	28	,	,	PUNCT
ejpam-2299	129	29	by	by	ADP
ejpam-2299	129	30	2.8.23	2.8.23	NUM
ejpam-2299	129	31	(	(	PUNCT
ejpam-2299	129	32	iii	iii	NOUN
ejpam-2299	129	33	)	)	PUNCT
ejpam-2299	129	34	in	in	ADP
ejpam-2299	129	35	[	[	X
ejpam-2299	129	36	4	4	X
ejpam-2299	129	37	]	]	PUNCT
ejpam-2299	129	38	we	we	PRON
ejpam-2299	129	39	can	can	AUX
ejpam-2299	129	40	conclude	conclude	VERB
ejpam-2299	129	41	that	that	PRON
ejpam-2299	129	42	h1(a#′′,a#′	h1(a#′′,a#′	NOUN
ejpam-2299	129	43	)	)	PUNCT
ejpam-2299	129	44	=	=	SYM
ejpam-2299	129	45	h1(a′′,a#′	h1(a′′,a#′	PROPN
ejpam-2299	129	46	)	)	PUNCT
ejpam-2299	129	47	.	.	PUNCT
ejpam-2299	130	1	let	let	VERB
ejpam-2299	130	2	d	d	NOUN
ejpam-2299	130	3	:	:	PUNCT
ejpam-2299	130	4	a′′	a′′	NOUN
ejpam-2299	130	5	−→	−→	NOUN
ejpam-2299	130	6	a#′	a#′	PROPN
ejpam-2299	130	7	be	be	VERB
ejpam-2299	130	8	a	a	DET
ejpam-2299	130	9	bounded	bounded	ADJ
ejpam-2299	130	10	derivation	derivation	NOUN
ejpam-2299	130	11	.	.	PUNCT
ejpam-2299	131	1	we	we	PRON
ejpam-2299	131	2	define	define	VERB
ejpam-2299	131	3	s.	s.	PROPN
ejpam-2299	131	4	hosseinioun	hosseinioun	PROPN
ejpam-2299	131	5	,	,	PUNCT
ejpam-2299	131	6	a.	a.	NOUN
ejpam-2299	131	7	valadkhani	valadkhani	PROPN
ejpam-2299	131	8	/	/	SYM
ejpam-2299	131	9	eur	eur	PROPN
ejpam-2299	131	10	.	.	PUNCT
ejpam-2299	132	1	j.	j.	PROPN
ejpam-2299	132	2	pure	pure	PROPN
ejpam-2299	132	3	appl	appl	PROPN
ejpam-2299	132	4	.	.	PROPN
ejpam-2299	132	5	math	math	PROPN
ejpam-2299	132	6	,	,	PUNCT
ejpam-2299	132	7	9	9	NUM
ejpam-2299	132	8	(	(	PUNCT
ejpam-2299	132	9	2016	2016	NUM
ejpam-2299	132	10	)	)	PUNCT
ejpam-2299	132	11	,	,	PUNCT
ejpam-2299	132	12	231	231	NUM
ejpam-2299	132	13	-	-	SYM
ejpam-2299	132	14	239	239	NUM
ejpam-2299	132	15	235	235	NUM
ejpam-2299	132	16	d	d	NOUN
ejpam-2299	132	17	:	:	PUNCT
ejpam-2299	132	18	a′′	a′′	NOUN
ejpam-2299	132	19	−→	−→	NOUN
ejpam-2299	132	20	a′	a′	PROPN
ejpam-2299	132	21	by	by	ADP
ejpam-2299	132	22	d(f	d(f	NOUN
ejpam-2299	132	23	)	)	PUNCT
ejpam-2299	132	24	=	=	SYM
ejpam-2299	132	25	df	df	PROPN
ejpam-2299	132	26	|a×{0	|a×{0	VERB
ejpam-2299	132	27	}	}	PUNCT
ejpam-2299	132	28	,	,	PUNCT
ejpam-2299	132	29	for	for	ADP
ejpam-2299	132	30	each	each	DET
ejpam-2299	132	31	f	f	PROPN
ejpam-2299	132	32	∈	∈	PROPN
ejpam-2299	132	33	a′′.	a′′.	PROPN
ejpam-2299	133	1	then	then	ADV
ejpam-2299	133	2	d	d	PROPN
ejpam-2299	133	3	is	be	AUX
ejpam-2299	133	4	a	a	DET
ejpam-2299	133	5	bounded	bounded	ADJ
ejpam-2299	133	6	derivation	derivation	NOUN
ejpam-2299	133	7	(	(	PUNCT
ejpam-2299	133	8	note	note	VERB
ejpam-2299	133	9	that	that	PRON
ejpam-2299	133	10	df(a	df(a	PUNCT
ejpam-2299	133	11	)	)	PUNCT
ejpam-2299	134	1	=	=	SYM
ejpam-2299	134	2	df(a+	df(a+	PROPN
ejpam-2299	134	3	0e	0e	NOUN
ejpam-2299	134	4	)	)	PUNCT
ejpam-2299	134	5	.	.	PUNCT
ejpam-2299	135	1	so	so	ADV
ejpam-2299	135	2	df	df	PROPN
ejpam-2299	135	3	∈	∈	PROPN
ejpam-2299	135	4	a′	a′	PROPN
ejpam-2299	135	5	)	)	PUNCT
ejpam-2299	135	6	.	.	PUNCT
ejpam-2299	136	1	by	by	ADP
ejpam-2299	136	2	(	(	PUNCT
ejpam-2299	136	3	-1)-weakly	-1)-weakly	ADV
ejpam-2299	136	4	amenability	amenability	NOUN
ejpam-2299	136	5	of	of	ADP
ejpam-2299	136	6	a′′	a′′	NOUN
ejpam-2299	136	7	,	,	PUNCT
ejpam-2299	136	8	there	there	PRON
ejpam-2299	136	9	exists	exist	VERB
ejpam-2299	136	10	f0	f0	PROPN
ejpam-2299	136	11	∈	∈	PROPN
ejpam-2299	136	12	a′	a′	NOUN
ejpam-2299	136	13	such	such	ADJ
ejpam-2299	136	14	that	that	PRON
ejpam-2299	136	15	for	for	ADP
ejpam-2299	136	16	each	each	DET
ejpam-2299	136	17	f	f	PROPN
ejpam-2299	136	18	∈	∈	PROPN
ejpam-2299	136	19	a′′	a′′	PROPN
ejpam-2299	136	20	,	,	PUNCT
ejpam-2299	136	21	df	df	PROPN
ejpam-2299	136	22	=	=	SYM
ejpam-2299	136	23	δ	δ	PROPN
ejpam-2299	136	24	f0	f0	PROPN
ejpam-2299	136	25	f	f	PROPN
ejpam-2299	136	26	.	.	PUNCT
ejpam-2299	137	1	let	let	VERB
ejpam-2299	137	2	d1	d1	PROPN
ejpam-2299	137	3	=	=	PUNCT
ejpam-2299	138	1	d	d	NOUN
ejpam-2299	138	2	−	−	PROPN
ejpam-2299	138	3	d	d	NOUN
ejpam-2299	138	4	,	,	PUNCT
ejpam-2299	138	5	then	then	ADV
ejpam-2299	138	6	d1	d1	PROPN
ejpam-2299	138	7	is	be	AUX
ejpam-2299	138	8	a	a	DET
ejpam-2299	138	9	bounded	bounded	ADJ
ejpam-2299	138	10	derivation	derivation	NOUN
ejpam-2299	138	11	.	.	PUNCT
ejpam-2299	139	1	now	now	ADV
ejpam-2299	139	2	we	we	PRON
ejpam-2299	139	3	show	show	VERB
ejpam-2299	139	4	that	that	SCONJ
ejpam-2299	139	5	d1	d1	PROPN
ejpam-2299	139	6	=	=	SYM
ejpam-2299	139	7	0	0	PUNCT
ejpam-2299	139	8	(	(	PUNCT
ejpam-2299	139	9	consider	consider	VERB
ejpam-2299	139	10	df	df	NOUN
ejpam-2299	139	11	as	as	ADP
ejpam-2299	139	12	an	an	DET
ejpam-2299	139	13	element	element	NOUN
ejpam-2299	139	14	in	in	ADP
ejpam-2299	139	15	a′	a′	NOUN
ejpam-2299	139	16	with	with	ADP
ejpam-2299	139	17	its	its	PRON
ejpam-2299	139	18	extension	extension	NOUN
ejpam-2299	139	19	)	)	PUNCT
ejpam-2299	139	20	.	.	PUNCT
ejpam-2299	140	1	for	for	ADP
ejpam-2299	140	2	f	f	PROPN
ejpam-2299	140	3	,	,	PUNCT
ejpam-2299	140	4	g	g	PROPN
ejpam-2299	140	5	∈	∈	PROPN
ejpam-2299	140	6	a′′	a′′	NOUN
ejpam-2299	140	7	,	,	PUNCT
ejpam-2299	140	8	there	there	PRON
ejpam-2299	140	9	is	be	VERB
ejpam-2299	140	10	(	(	PUNCT
ejpam-2299	140	11	b	b	PROPN
ejpam-2299	140	12	j	j	PROPN
ejpam-2299	140	13	)	)	PUNCT
ejpam-2299	140	14	j	j	PROPN
ejpam-2299	140	15	in	in	ADP
ejpam-2299	140	16	a	a	DET
ejpam-2299	140	17	with	with	ADP
ejpam-2299	140	18	b̂	b̂	NOUN
ejpam-2299	140	19	j	j	PROPN
ejpam-2299	140	20	w∗	w∗	PROPN
ejpam-2299	140	21	−→	−→	ADV
ejpam-2299	140	22	g	g	PROPN
ejpam-2299	140	23	,	,	PUNCT
ejpam-2299	140	24	then	then	ADV
ejpam-2299	140	25	e′	e′	NOUN
ejpam-2299	140	26	·	·	PUNCT
ejpam-2299	140	27	g(a+αe	g(a+αe	PROPN
ejpam-2299	140	28	)	)	PUNCT
ejpam-2299	140	29	=	=	SYM
ejpam-2299	141	1	g((a+αe)(0	g((a+αe)(0	PROPN
ejpam-2299	141	2	+	+	SYM
ejpam-2299	141	3	e′	e′	NOUN
ejpam-2299	141	4	)	)	PUNCT
ejpam-2299	141	5	)	)	PUNCT
ejpam-2299	142	1	=	=	SYM
ejpam-2299	142	2	g(αe′	g(αe′	NOUN
ejpam-2299	142	3	)	)	PUNCT
ejpam-2299	143	1	=	=	PROPN
ejpam-2299	143	2	lim	lim	PROPN
ejpam-2299	143	3	j	j	PROPN
ejpam-2299	143	4	b̂	b̂	NOUN
ejpam-2299	143	5	j(αe′	j(αe′	PROPN
ejpam-2299	143	6	)	)	PUNCT
ejpam-2299	144	1	=	=	VERB
ejpam-2299	145	1	lim	lim	PROPN
ejpam-2299	145	2	j	j	PROPN
ejpam-2299	145	3	αe′(b	αe′(b	PROPN
ejpam-2299	145	4	j	j	PROPN
ejpam-2299	145	5	)	)	PUNCT
ejpam-2299	146	1	=	=	PUNCT
ejpam-2299	146	2	0	0	X
ejpam-2299	146	3	.	.	PUNCT
ejpam-2299	147	1	on	on	ADP
ejpam-2299	147	2	the	the	DET
ejpam-2299	147	3	other	other	ADJ
ejpam-2299	147	4	hand	hand	NOUN
ejpam-2299	147	5	,	,	PUNCT
ejpam-2299	147	6	since	since	SCONJ
ejpam-2299	147	7	d	d	NOUN
ejpam-2299	147	8	:	:	PUNCT
ejpam-2299	147	9	a′′	a′′	NOUN
ejpam-2299	147	10	−→	−→	NOUN
ejpam-2299	147	11	a#′	a#′	PROPN
ejpam-2299	147	12	and	and	CCONJ
ejpam-2299	147	13	a#′	a#′	ADJ
ejpam-2299	147	14	=	=	PUNCT
ejpam-2299	147	15	a′	a′	PROPN
ejpam-2299	147	16	⊕	⊕	PROPN
ejpam-2299	147	17	ce′	ce′	PROPN
ejpam-2299	147	18	,	,	PUNCT
ejpam-2299	147	19	for	for	ADP
ejpam-2299	147	20	each	each	DET
ejpam-2299	147	21	f	f	PROPN
ejpam-2299	147	22	∈	∈	PROPN
ejpam-2299	147	23	a′′	a′′	NOUN
ejpam-2299	147	24	there	there	PRON
ejpam-2299	147	25	are	be	VERB
ejpam-2299	147	26	unique	unique	ADJ
ejpam-2299	147	27	elements	element	NOUN
ejpam-2299	147	28	,	,	PUNCT
ejpam-2299	147	29	λf	λf	PROPN
ejpam-2299	147	30	∈	∈	PROPN
ejpam-2299	147	31	a′	a′	NOUN
ejpam-2299	147	32	and	and	CCONJ
ejpam-2299	147	33	αf	αf	ADP
ejpam-2299	147	34	∈	∈	PROPN
ejpam-2299	147	35	c	c	NOUN
ejpam-2299	147	36	such	such	ADJ
ejpam-2299	147	37	that	that	DET
ejpam-2299	147	38	df	df	NOUN
ejpam-2299	148	1	=	=	PUNCT
ejpam-2299	148	2	λf	λf	PROPN
ejpam-2299	149	1	+	+	CCONJ
ejpam-2299	149	2	αf	αf	VERB
ejpam-2299	149	3	e′.	e′.	NOUN
ejpam-2299	149	4	since	since	SCONJ
ejpam-2299	149	5	df	df	PROPN
ejpam-2299	149	6	=	=	PUNCT
ejpam-2299	149	7	df	df	PROPN
ejpam-2299	149	8	|a×{0	|a×{0	VERB
ejpam-2299	149	9	}	}	PUNCT
ejpam-2299	149	10	,	,	PUNCT
ejpam-2299	149	11	and	and	CCONJ
ejpam-2299	149	12	df	df	PROPN
ejpam-2299	149	13	=	=	SYM
ejpam-2299	150	1	λf	λf	PROPN
ejpam-2299	150	2	then	then	ADV
ejpam-2299	150	3	d1f	d1f	NOUN
ejpam-2299	150	4	=	=	NOUN
ejpam-2299	150	5	αf	αf	VERB
ejpam-2299	150	6	e′.	e′.	NOUN
ejpam-2299	151	1	so	so	SCONJ
ejpam-2299	151	2	we	we	PRON
ejpam-2299	151	3	have	have	AUX
ejpam-2299	151	4	d1(f	d1(f	PROPN
ejpam-2299	151	5	·	·	PUNCT
ejpam-2299	151	6	g	g	NOUN
ejpam-2299	151	7	)	)	PUNCT
ejpam-2299	151	8	=	=	NOUN
ejpam-2299	152	1	d1f	d1f	NOUN
ejpam-2299	152	2	·	·	PUNCT
ejpam-2299	152	3	g	g	PROPN
ejpam-2299	152	4	+	+	CCONJ
ejpam-2299	152	5	f	f	PROPN
ejpam-2299	152	6	·	·	PUNCT
ejpam-2299	152	7	d1	d1	NOUN
ejpam-2299	152	8	g	g	NOUN
ejpam-2299	152	9	=	=	SYM
ejpam-2299	152	10	αf	αf	X
ejpam-2299	152	11	(	(	PUNCT
ejpam-2299	152	12	e	e	NOUN
ejpam-2299	152	13	′	′	NUM
ejpam-2299	152	14	·	·	PUNCT
ejpam-2299	152	15	g	g	X
ejpam-2299	152	16	)	)	PUNCT
ejpam-2299	152	17	+	+	NOUN
ejpam-2299	152	18	αg(f	αg(f	X
ejpam-2299	152	19	·	·	PUNCT
ejpam-2299	152	20	e	e	X
ejpam-2299	152	21	′	′	NUM
ejpam-2299	152	22	)	)	PUNCT
ejpam-2299	152	23	=	=	SYM
ejpam-2299	153	1	0	0	X
ejpam-2299	153	2	.	.	PUNCT
ejpam-2299	154	1	since	since	SCONJ
ejpam-2299	154	2	d1	d1	PROPN
ejpam-2299	154	3	is	be	AUX
ejpam-2299	154	4	bounded	bound	VERB
ejpam-2299	154	5	then	then	ADV
ejpam-2299	154	6	d1|a′′2	d1|a′′2	PROPN
ejpam-2299	154	7	=	=	SYM
ejpam-2299	154	8	0	0	X
ejpam-2299	154	9	.	.	PUNCT
ejpam-2299	155	1	so	so	ADV
ejpam-2299	155	2	by	by	ADP
ejpam-2299	155	3	the	the	DET
ejpam-2299	155	4	essentiality	essentiality	NOUN
ejpam-2299	155	5	of	of	ADP
ejpam-2299	155	6	a′′	a′′	NOUN
ejpam-2299	155	7	,	,	PUNCT
ejpam-2299	155	8	d1	d1	PROPN
ejpam-2299	155	9	=	=	SYM
ejpam-2299	155	10	0	0	NUM
ejpam-2299	155	11	,	,	PUNCT
ejpam-2299	155	12	so	so	ADV
ejpam-2299	155	13	d	d	NOUN
ejpam-2299	155	14	=	=	SYM
ejpam-2299	155	15	δ	δ	PROPN
ejpam-2299	155	16	f0	f0	PROPN
ejpam-2299	155	17	where	where	SCONJ
ejpam-2299	155	18	f0	f0	PROPN
ejpam-2299	155	19	=	=	SYM
ejpam-2299	155	20	f0	f0	PROPN
ejpam-2299	156	1	+	+	CCONJ
ejpam-2299	156	2	0e′	0e′	NUM
ejpam-2299	156	3	∈	∈	PROPN
ejpam-2299	156	4	a′	a′	NOUN
ejpam-2299	156	5	⊕ce′	⊕ce′	NOUN
ejpam-2299	156	6	=	=	PUNCT
ejpam-2299	156	7	a#′.	a#′.	ADJ
ejpam-2299	156	8	therefore	therefore	ADV
ejpam-2299	156	9	h1(a#′′,a#′	h1(a#′′,a#′	NOUN
ejpam-2299	156	10	)	)	PUNCT
ejpam-2299	156	11	=	=	SYM
ejpam-2299	156	12	h1(a′′,a#′	h1(a′′,a#′	PROPN
ejpam-2299	156	13	)	)	PUNCT
ejpam-2299	156	14	=	=	PUNCT
ejpam-2299	156	15	{	{	PUNCT
ejpam-2299	156	16	0	0	NUM
ejpam-2299	156	17	}	}	PUNCT
ejpam-2299	156	18	.	.	PUNCT
ejpam-2299	157	1	theorem	theorem	NOUN
ejpam-2299	157	2	3	3	X
ejpam-2299	157	3	.	.	PUNCT
ejpam-2299	158	1	let	let	VERB
ejpam-2299	158	2	a	a	DET
ejpam-2299	158	3	be	be	AUX
ejpam-2299	158	4	an	an	DET
ejpam-2299	158	5	arens	aren	NOUN
ejpam-2299	158	6	regular	regular	ADJ
ejpam-2299	158	7	banach	banach	NOUN
ejpam-2299	158	8	algebra	algebra	NOUN
ejpam-2299	158	9	,	,	PUNCT
ejpam-2299	158	10	a#′′	a#′′	PROPN
ejpam-2299	158	11	be	be	VERB
ejpam-2299	158	12	(	(	PUNCT
ejpam-2299	158	13	-1)-weakly	-1)-weakly	ADV
ejpam-2299	158	14	amenable	amenable	ADJ
ejpam-2299	158	15	and	and	CCONJ
ejpam-2299	158	16	h2(a′′,c0	h2(a′′,c0	NOUN
ejpam-2299	158	17	)	)	PUNCT
ejpam-2299	158	18	=	=	SYM
ejpam-2299	158	19	(	(	PUNCT
ejpam-2299	158	20	0	0	NUM
ejpam-2299	158	21	)	)	PUNCT
ejpam-2299	158	22	.	.	PUNCT
ejpam-2299	159	1	then	then	ADV
ejpam-2299	159	2	a′′	a′′	PROPN
ejpam-2299	159	3	is	be	AUX
ejpam-2299	159	4	(	(	PUNCT
ejpam-2299	159	5	-1)-weakly	-1)-weakly	ADV
ejpam-2299	159	6	amenable	amenable	ADJ
ejpam-2299	159	7	.	.	PUNCT
ejpam-2299	160	1	proof	proof	NOUN
ejpam-2299	160	2	.	.	PUNCT
ejpam-2299	161	1	we	we	PRON
ejpam-2299	161	2	may	may	AUX
ejpam-2299	161	3	suppose	suppose	VERB
ejpam-2299	161	4	that	that	SCONJ
ejpam-2299	161	5	a	a	PRON
ejpam-2299	161	6	has	have	AUX
ejpam-2299	161	7	not	not	PART
ejpam-2299	161	8	unit	unit	NOUN
ejpam-2299	161	9	element	element	NOUN
ejpam-2299	161	10	and	and	CCONJ
ejpam-2299	161	11	a	a	DET
ejpam-2299	161	12	#	#	NOUN
ejpam-2299	161	13	=	=	SYM
ejpam-2299	161	14	a⊕c0e	a⊕c0e	PROPN
ejpam-2299	161	15	.	.	PUNCT
ejpam-2299	162	1	then	then	ADV
ejpam-2299	162	2	σ	σ	X
ejpam-2299	162	3	:	:	PUNCT
ejpam-2299	162	4	0	0	NUM
ejpam-2299	163	1	−→	−→	NOUN
ejpam-2299	163	2	a−→	a−→	PRON
ejpam-2299	163	3	a	a	DET
ejpam-2299	163	4	#	#	NOUN
ejpam-2299	163	5	−→	−→	NOUN
ejpam-2299	163	6	c0	c0	NOUN
ejpam-2299	163	7	−→	−→	NOUN
ejpam-2299	163	8	0	0	NUM
ejpam-2299	163	9	is	be	AUX
ejpam-2299	163	10	an	an	DET
ejpam-2299	163	11	admissible	admissible	ADJ
ejpam-2299	163	12	short	short	ADJ
ejpam-2299	163	13	exact	exact	ADJ
ejpam-2299	163	14	sequence	sequence	NOUN
ejpam-2299	163	15	and	and	CCONJ
ejpam-2299	163	16	hence	hence	ADV
ejpam-2299	163	17	so	so	ADV
ejpam-2299	163	18	is	be	AUX
ejpam-2299	163	19	its	its	PRON
ejpam-2299	163	20	dual	dual	ADJ
ejpam-2299	163	21	,	,	PUNCT
ejpam-2299	163	22	σ′	σ′	PUNCT
ejpam-2299	163	23	:	:	PUNCT
ejpam-2299	163	24	0	0	NUM
ejpam-2299	164	1	−→	−→	NOUN
ejpam-2299	164	2	c0	c0	NOUN
ejpam-2299	164	3	−→	−→	NOUN
ejpam-2299	164	4	a#′	a#′	VERB
ejpam-2299	164	5	−→	−→	NOUN
ejpam-2299	164	6	a′	a′	NOUN
ejpam-2299	164	7	−→	−→	NOUN
ejpam-2299	164	8	0	0	NUM
ejpam-2299	164	9	.	.	PUNCT
ejpam-2299	165	1	using	use	VERB
ejpam-2299	165	2	2.8.25	2.8.25	NUM
ejpam-2299	165	3	in	in	ADP
ejpam-2299	165	4	[	[	X
ejpam-2299	165	5	4	4	X
ejpam-2299	165	6	]	]	PUNCT
ejpam-2299	165	7	we	we	PRON
ejpam-2299	165	8	have	have	VERB
ejpam-2299	165	9	exact	exact	ADJ
ejpam-2299	165	10	sequence	sequence	NOUN
ejpam-2299	165	11	s	s	PART
ejpam-2299	165	12	:	:	PUNCT
ejpam-2299	165	13	.	.	PUNCT
ejpam-2299	165	14	.	.	PUNCT
ejpam-2299	165	15	.	.	PUNCT
ejpam-2299	166	1	−→	−→	ADJ
ejpam-2299	166	2	h1(a′′,c0	h1(a′′,c0	SYM
ejpam-2299	166	3	)	)	PUNCT
ejpam-2299	166	4	−→	−→	NOUN
ejpam-2299	166	5	h1(a′′,a#′	h1(a′′,a#′	NOUN
ejpam-2299	166	6	)	)	PUNCT
ejpam-2299	166	7	−→	−→	NOUN
ejpam-2299	166	8	h1(a′′,a′	h1(a′′,a′	NOUN
ejpam-2299	166	9	)	)	PUNCT
ejpam-2299	166	10	−→	−→	NOUN
ejpam-2299	166	11	h2(a′′,c0	h2(a′′,c0	NOUN
ejpam-2299	166	12	)	)	PUNCT
ejpam-2299	166	13	−→	−→	NOUN
ejpam-2299	166	14	.	.	PUNCT
ejpam-2299	166	15	.	.	PUNCT
ejpam-2299	166	16	.	.	PUNCT
ejpam-2299	167	1	,	,	PUNCT
ejpam-2299	167	2	from	from	ADP
ejpam-2299	167	3	2.8.23	2.8.23	NUM
ejpam-2299	167	4	(	(	PUNCT
ejpam-2299	167	5	iii	iii	NOUN
ejpam-2299	167	6	)	)	PUNCT
ejpam-2299	167	7	in	in	ADP
ejpam-2299	167	8	[	[	X
ejpam-2299	167	9	4	4	NUM
ejpam-2299	167	10	]	]	PUNCT
ejpam-2299	167	11	,	,	PUNCT
ejpam-2299	167	12	h1(a′′,a#′	h1(a′′,a#′	NOUN
ejpam-2299	167	13	)	)	PUNCT
ejpam-2299	167	14	=	=	SYM
ejpam-2299	167	15	h1(a′′#,a#′	h1(a′′#,a#′	PROPN
ejpam-2299	167	16	)	)	PUNCT
ejpam-2299	167	17	=	=	SYM
ejpam-2299	167	18	(	(	PUNCT
ejpam-2299	167	19	0	0	NUM
ejpam-2299	167	20	)	)	PUNCT
ejpam-2299	167	21	,	,	PUNCT
ejpam-2299	167	22	since	since	SCONJ
ejpam-2299	167	23	a′′	a′′	NOUN
ejpam-2299	167	24	#	#	NOUN
ejpam-2299	167	25	is	be	AUX
ejpam-2299	167	26	(	(	PUNCT
ejpam-2299	167	27	-1)-weakly	-1)-weakly	ADV
ejpam-2299	167	28	amenable	amenable	ADJ
ejpam-2299	167	29	.	.	PUNCT
ejpam-2299	168	1	moreover	moreover	ADV
ejpam-2299	168	2	h2(a′′,c0	h2(a′′,c0	NOUN
ejpam-2299	168	3	)	)	PUNCT
ejpam-2299	168	4	=	=	SYM
ejpam-2299	168	5	(	(	PUNCT
ejpam-2299	168	6	0	0	NUM
ejpam-2299	168	7	)	)	PUNCT
ejpam-2299	168	8	,	,	PUNCT
ejpam-2299	168	9	so	so	CCONJ
ejpam-2299	168	10	in	in	ADP
ejpam-2299	168	11	the	the	DET
ejpam-2299	168	12	exact	exact	ADJ
ejpam-2299	168	13	sequence	sequence	NOUN
ejpam-2299	168	14	s	s	PART
ejpam-2299	168	15	,	,	PUNCT
ejpam-2299	168	16	h1(a′′,a#′	h1(a′′,a#′	NOUN
ejpam-2299	168	17	)	)	PUNCT
ejpam-2299	169	1	=	=	PUNCT
ejpam-2299	169	2	h2(a′′,c0	h2(a′′,c0	NOUN
ejpam-2299	169	3	)	)	PUNCT
ejpam-2299	170	1	=	=	SYM
ejpam-2299	170	2	(	(	PUNCT
ejpam-2299	170	3	0	0	NUM
ejpam-2299	170	4	)	)	PUNCT
ejpam-2299	170	5	then	then	ADV
ejpam-2299	170	6	h1(a′′,a′	h1(a′′,a′	NUM
ejpam-2299	170	7	)	)	PUNCT
ejpam-2299	171	1	=	=	PRON
ejpam-2299	171	2	(	(	PUNCT
ejpam-2299	171	3	0	0	NUM
ejpam-2299	171	4	)	)	PUNCT
ejpam-2299	171	5	.	.	PUNCT
ejpam-2299	172	1	remark	remark	NOUN
ejpam-2299	172	2	2	2	NUM
ejpam-2299	172	3	.	.	PUNCT
ejpam-2299	173	1	the	the	DET
ejpam-2299	173	2	condition	condition	NOUN
ejpam-2299	173	3	h2(a′′,c0	h2(a′′,c0	NOUN
ejpam-2299	173	4	)	)	PUNCT
ejpam-2299	173	5	=	=	SYM
ejpam-2299	173	6	(	(	PUNCT
ejpam-2299	173	7	0	0	NUM
ejpam-2299	173	8	)	)	PUNCT
ejpam-2299	173	9	in	in	ADP
ejpam-2299	173	10	theorem	theorem	NOUN
ejpam-2299	173	11	3	3	NUM
ejpam-2299	173	12	is	be	AUX
ejpam-2299	173	13	not	not	PART
ejpam-2299	173	14	trivial	trivial	ADJ
ejpam-2299	173	15	.	.	PUNCT
ejpam-2299	174	1	to	to	ADP
ejpam-2299	174	2	this	this	DET
ejpam-2299	174	3	end	end	NOUN
ejpam-2299	174	4	,	,	PUNCT
ejpam-2299	174	5	let	let	VERB
ejpam-2299	174	6	b	b	NOUN
ejpam-2299	174	7	=	=	SYM
ejpam-2299	174	8	�	�	PROPN
ejpam-2299	174	9	f	f	PROPN
ejpam-2299	174	10	∈	∈	PROPN
ejpam-2299	174	11	a(d	a(d	PROPN
ejpam-2299	174	12	)	)	PUNCT
ejpam-2299	174	13	:	:	PUNCT
ejpam-2299	175	1	f	f	X
ejpam-2299	175	2	(	(	PUNCT
ejpam-2299	175	3	0	0	NUM
ejpam-2299	175	4	)	)	PUNCT
ejpam-2299	175	5	=	=	SYM
ejpam-2299	175	6	f	f	PROPN
ejpam-2299	175	7	′(0	′(0	PROPN
ejpam-2299	175	8	)	)	PUNCT
ejpam-2299	176	1	=	=	SYM
ejpam-2299	176	2	0	0	PUNCT
ejpam-2299	177	1	then	then	ADV
ejpam-2299	177	2	b	b	PROPN
ejpam-2299	177	3	is	be	AUX
ejpam-2299	177	4	a	a	DET
ejpam-2299	177	5	closed	closed	ADJ
ejpam-2299	177	6	subalgebra	subalgebra	NOUN
ejpam-2299	177	7	of	of	ADP
ejpam-2299	177	8	the	the	DET
ejpam-2299	177	9	disc	disc	NOUN
ejpam-2299	177	10	algebra	algebra	PROPN
ejpam-2299	177	11	a(d	a(d	PROPN
ejpam-2299	177	12	)	)	PUNCT
ejpam-2299	177	13	.	.	PUNCT
ejpam-2299	178	1	consider	consider	VERB
ejpam-2299	178	2	c0	c0	NOUN
ejpam-2299	178	3	as	as	ADP
ejpam-2299	178	4	the	the	DET
ejpam-2299	178	5	annihilator	annihilator	PROPN
ejpam-2299	178	6	b	b	PROPN
ejpam-2299	178	7	-	-	PUNCT
ejpam-2299	178	8	module	module	NOUN
ejpam-2299	178	9	i.e.	i.e.	X
ejpam-2299	178	10	b	b	NOUN
ejpam-2299	178	11	acts	act	VERB
ejpam-2299	178	12	trivially	trivially	ADV
ejpam-2299	178	13	on	on	ADP
ejpam-2299	178	14	the	the	DET
ejpam-2299	178	15	left	left	NOUN
ejpam-2299	178	16	and	and	CCONJ
ejpam-2299	178	17	right	right	ADV
ejpam-2299	178	18	on	on	ADP
ejpam-2299	178	19	c0	c0	PROPN
ejpam-2299	178	20	.	.	PUNCT
ejpam-2299	179	1	now	now	ADV
ejpam-2299	179	2	we	we	PRON
ejpam-2299	179	3	define	define	VERB
ejpam-2299	179	4	µ	µ	X
ejpam-2299	179	5	:	:	PUNCT
ejpam-2299	179	6	b	b	NUM
ejpam-2299	179	7	×	×	NOUN
ejpam-2299	179	8	b	b	PROPN
ejpam-2299	179	9	−→	−→	ADJ
ejpam-2299	179	10	c0	c0	NOUN
ejpam-2299	179	11	,	,	PUNCT
ejpam-2299	179	12	by	by	ADP
ejpam-2299	179	13	(	(	PUNCT
ejpam-2299	179	14	f	f	PROPN
ejpam-2299	179	15	,	,	PUNCT
ejpam-2299	179	16	g	g	PROPN
ejpam-2299	179	17	)	)	PUNCT
ejpam-2299	179	18	7→	7→	NUM
ejpam-2299	180	1	f	f	PROPN
ejpam-2299	180	2	′′′(0)g	′′′(0)g	PROPN
ejpam-2299	180	3	′′′(0	′′′(0	PROPN
ejpam-2299	180	4	)	)	PUNCT
ejpam-2299	180	5	.	.	PUNCT
ejpam-2299	181	1	then	then	ADV
ejpam-2299	181	2	µ	µ	X
ejpam-2299	181	3	is	be	AUX
ejpam-2299	181	4	a	a	DET
ejpam-2299	181	5	continuous	continuous	ADJ
ejpam-2299	181	6	functional	functional	NOUN
ejpam-2299	181	7	for	for	ADP
ejpam-2299	181	8	which	which	PRON
ejpam-2299	181	9	µ	µ	X
ejpam-2299	181	10	(	(	PUNCT
ejpam-2299	181	11	f	f	PROPN
ejpam-2299	181	12	,	,	PUNCT
ejpam-2299	181	13	g	g	NOUN
ejpam-2299	181	14	)	)	PUNCT
ejpam-2299	181	15	=	=	SYM
ejpam-2299	181	16	µ(g	µ(g	PROPN
ejpam-2299	181	17	,	,	PUNCT
ejpam-2299	181	18	f	f	PROPN
ejpam-2299	181	19	)	)	PUNCT
ejpam-2299	181	20	.	.	PUNCT
ejpam-2299	182	1	if	if	SCONJ
ejpam-2299	182	2	h2(b	h2(b	PROPN
ejpam-2299	182	3	,	,	PUNCT
ejpam-2299	182	4	c0	c0	NOUN
ejpam-2299	182	5	)	)	PUNCT
ejpam-2299	182	6	=	=	PUNCT
ejpam-2299	182	7	{	{	PUNCT
ejpam-2299	182	8	0	0	NUM
ejpam-2299	182	9	}	}	PUNCT
ejpam-2299	182	10	,	,	PUNCT
ejpam-2299	182	11	then	then	ADV
ejpam-2299	182	12	for	for	ADP
ejpam-2299	182	13	some	some	DET
ejpam-2299	182	14	λ	λ	PROPN
ejpam-2299	182	15	∈	∈	PROPN
ejpam-2299	182	16	b′	b′	NOUN
ejpam-2299	182	17	we	we	PRON
ejpam-2299	182	18	have	have	VERB
ejpam-2299	182	19	µ=	µ=	PRON
ejpam-2299	182	20	δ1(λ	δ1(λ	NOUN
ejpam-2299	182	21	)	)	PUNCT
ejpam-2299	182	22	where	where	SCONJ
ejpam-2299	182	23	δ1(λ	δ1(λ	X
ejpam-2299	182	24	)	)	PUNCT
ejpam-2299	182	25	(	(	PUNCT
ejpam-2299	182	26	f	f	PROPN
ejpam-2299	182	27	,	,	PUNCT
ejpam-2299	182	28	g	g	NOUN
ejpam-2299	182	29	)	)	PUNCT
ejpam-2299	182	30	=	=	SYM
ejpam-2299	182	31	f	f	X
ejpam-2299	182	32	·	·	PUNCT
ejpam-2299	182	33	λg	λg	PROPN
ejpam-2299	182	34	−λ	−λ	PROPN
ejpam-2299	182	35	(	(	PUNCT
ejpam-2299	182	36	f	f	PROPN
ejpam-2299	182	37	·	·	PUNCT
ejpam-2299	182	38	g	g	NOUN
ejpam-2299	182	39	)	)	PUNCT
ejpam-2299	183	1	+	+	NOUN
ejpam-2299	183	2	λ	λ	X
ejpam-2299	183	3	f	f	X
ejpam-2299	183	4	·	·	PUNCT
ejpam-2299	183	5	g.	g.	PROPN
ejpam-2299	183	6	(	(	PUNCT
ejpam-2299	183	7	1	1	X
ejpam-2299	183	8	)	)	PUNCT
ejpam-2299	183	9	s.	s.	PROPN
ejpam-2299	183	10	hosseinioun	hosseinioun	PROPN
ejpam-2299	183	11	,	,	PUNCT
ejpam-2299	183	12	a.	a.	NOUN
ejpam-2299	183	13	valadkhani	valadkhani	PROPN
ejpam-2299	183	14	/	/	SYM
ejpam-2299	183	15	eur	eur	PROPN
ejpam-2299	183	16	.	.	PUNCT
ejpam-2299	184	1	j.	j.	PROPN
ejpam-2299	184	2	pure	pure	PROPN
ejpam-2299	184	3	appl	appl	PROPN
ejpam-2299	184	4	.	.	PROPN
ejpam-2299	184	5	math	math	PROPN
ejpam-2299	184	6	,	,	PUNCT
ejpam-2299	184	7	9	9	NUM
ejpam-2299	184	8	(	(	PUNCT
ejpam-2299	184	9	2016	2016	NUM
ejpam-2299	184	10	)	)	PUNCT
ejpam-2299	184	11	,	,	PUNCT
ejpam-2299	184	12	231	231	NUM
ejpam-2299	184	13	-	-	SYM
ejpam-2299	184	14	239	239	NUM
ejpam-2299	184	15	236	236	NUM
ejpam-2299	184	16	if	if	SCONJ
ejpam-2299	184	17	for	for	ADP
ejpam-2299	184	18	z	z	PROPN
ejpam-2299	184	19	∈	∈	PROPN
ejpam-2299	185	1	d	d	X
ejpam-2299	185	2	we	we	PRON
ejpam-2299	185	3	define	define	VERB
ejpam-2299	185	4	f	f	PROPN
ejpam-2299	185	5	,	,	PUNCT
ejpam-2299	185	6	g	g	PROPN
ejpam-2299	185	7	,	,	PUNCT
ejpam-2299	185	8	h	h	NOUN
ejpam-2299	185	9	∈	∈	PROPN
ejpam-2299	185	10	b	b	PROPN
ejpam-2299	185	11	by	by	ADP
ejpam-2299	185	12	f	f	PROPN
ejpam-2299	185	13	(	(	PUNCT
ejpam-2299	185	14	z	z	NOUN
ejpam-2299	185	15	)	)	PUNCT
ejpam-2299	185	16	=	=	SYM
ejpam-2299	185	17	z2	z2	PROPN
ejpam-2299	185	18	,	,	PUNCT
ejpam-2299	185	19	g(z	g(z	PROPN
ejpam-2299	185	20	)	)	PUNCT
ejpam-2299	185	21	=	=	SYM
ejpam-2299	185	22	z4	z4	NOUN
ejpam-2299	185	23	and	and	CCONJ
ejpam-2299	185	24	h(z	h(z	NOUN
ejpam-2299	185	25	)	)	PUNCT
ejpam-2299	185	26	=	=	SYM
ejpam-2299	186	1	z3	z3	PROPN
ejpam-2299	186	2	then	then	ADV
ejpam-2299	186	3	f	f	PROPN
ejpam-2299	186	4	′′′(z	′′′(z	PROPN
ejpam-2299	186	5	)	)	PUNCT
ejpam-2299	186	6	=	=	SYM
ejpam-2299	186	7	0	0	NUM
ejpam-2299	186	8	,	,	PUNCT
ejpam-2299	186	9	g	g	PROPN
ejpam-2299	186	10	′′′(z	′′′(z	PROPN
ejpam-2299	186	11	)	)	PUNCT
ejpam-2299	186	12	=	=	SYM
ejpam-2299	186	13	24z	24z	NOUN
ejpam-2299	186	14	,	,	PUNCT
ejpam-2299	186	15	h′′′(z	h′′′(z	PROPN
ejpam-2299	186	16	)	)	PUNCT
ejpam-2299	186	17	=	=	SYM
ejpam-2299	186	18	6	6	NUM
ejpam-2299	186	19	and	and	CCONJ
ejpam-2299	186	20	we	we	PRON
ejpam-2299	186	21	have	have	VERB
ejpam-2299	186	22	µ	µ	NUM
ejpam-2299	186	23	(	(	PUNCT
ejpam-2299	186	24	f	f	PROPN
ejpam-2299	186	25	,	,	PUNCT
ejpam-2299	186	26	g	g	NOUN
ejpam-2299	186	27	)	)	PUNCT
ejpam-2299	186	28	=	=	SYM
ejpam-2299	187	1	f	f	PROPN
ejpam-2299	187	2	′′′(0)g	′′′(0)g	PROPN
ejpam-2299	187	3	′′′(0	′′′(0	PROPN
ejpam-2299	187	4	)	)	PUNCT
ejpam-2299	187	5	=	=	SYM
ejpam-2299	187	6	0	0	NUM
ejpam-2299	187	7	and	and	CCONJ
ejpam-2299	187	8	µ(h	µ(h	PROPN
ejpam-2299	187	9	,	,	PUNCT
ejpam-2299	187	10	h	h	NOUN
ejpam-2299	187	11	)	)	PUNCT
ejpam-2299	187	12	=	=	SYM
ejpam-2299	188	1	36	36	NUM
ejpam-2299	188	2	.	.	PUNCT
ejpam-2299	189	1	since	since	SCONJ
ejpam-2299	189	2	c	c	PROPN
ejpam-2299	189	3	is	be	AUX
ejpam-2299	189	4	an	an	DET
ejpam-2299	189	5	annihilator	annihilator	PROPN
ejpam-2299	189	6	b	b	NOUN
ejpam-2299	189	7	-	-	PUNCT
ejpam-2299	189	8	module	module	NOUN
ejpam-2299	189	9	then	then	ADV
ejpam-2299	189	10	f	f	PROPN
ejpam-2299	189	11	·	·	PUNCT
ejpam-2299	189	12	λg	λg	X
ejpam-2299	189	13	=	=	SYM
ejpam-2299	189	14	λ	λ	X
ejpam-2299	189	15	f	f	X
ejpam-2299	189	16	·	·	PUNCT
ejpam-2299	189	17	g	g	NOUN
ejpam-2299	189	18	=	=	NOUN
ejpam-2299	189	19	0	0	PROPN
ejpam-2299	189	20	.	.	PUNCT
ejpam-2299	190	1	on	on	ADP
ejpam-2299	190	2	the	the	DET
ejpam-2299	190	3	other	other	ADJ
ejpam-2299	190	4	hand	hand	NOUN
ejpam-2299	190	5	by	by	ADP
ejpam-2299	190	6	(	(	PUNCT
ejpam-2299	190	7	1	1	X
ejpam-2299	190	8	)	)	PUNCT
ejpam-2299	190	9	we	we	PRON
ejpam-2299	190	10	have	have	AUX
ejpam-2299	190	11	µ	µ	NUM
ejpam-2299	190	12	(	(	PUNCT
ejpam-2299	190	13	f	f	PROPN
ejpam-2299	190	14	,	,	PUNCT
ejpam-2299	190	15	g	g	NOUN
ejpam-2299	190	16	)	)	PUNCT
ejpam-2299	190	17	=	=	NOUN
ejpam-2299	190	18	δ1(λ	δ1(λ	X
ejpam-2299	190	19	)	)	PUNCT
ejpam-2299	190	20	(	(	PUNCT
ejpam-2299	190	21	f	f	X
ejpam-2299	190	22	,	,	PUNCT
ejpam-2299	190	23	g	g	PROPN
ejpam-2299	190	24	)	)	PUNCT
ejpam-2299	190	25	=	=	SYM
ejpam-2299	190	26	−λ	−λ	PROPN
ejpam-2299	190	27	(	(	PUNCT
ejpam-2299	190	28	f	f	PROPN
ejpam-2299	190	29	·	·	PUNCT
ejpam-2299	190	30	g	g	NOUN
ejpam-2299	190	31	)	)	PUNCT
ejpam-2299	190	32	,	,	PUNCT
ejpam-2299	190	33	µ(h	µ(h	PROPN
ejpam-2299	190	34	,	,	PUNCT
ejpam-2299	190	35	h	h	NOUN
ejpam-2299	190	36	)	)	PUNCT
ejpam-2299	190	37	=	=	SYM
ejpam-2299	190	38	δ1(λ)(h	δ1(λ)(h	PROPN
ejpam-2299	190	39	,	,	PUNCT
ejpam-2299	190	40	h	h	NOUN
ejpam-2299	190	41	)	)	PUNCT
ejpam-2299	190	42	=	=	SYM
ejpam-2299	190	43	−λ(h	−λ(h	X
ejpam-2299	190	44	·	·	PUNCT
ejpam-2299	190	45	h	h	NOUN
ejpam-2299	190	46	)	)	PUNCT
ejpam-2299	190	47	.	.	PUNCT
ejpam-2299	191	1	so	so	ADV
ejpam-2299	191	2	λ	λ	PROPN
ejpam-2299	191	3	(	(	PUNCT
ejpam-2299	191	4	f	f	PROPN
ejpam-2299	191	5	·	·	PUNCT
ejpam-2299	191	6	g	g	NOUN
ejpam-2299	191	7	)	)	PUNCT
ejpam-2299	191	8	=	=	SYM
ejpam-2299	191	9	0	0	NUM
ejpam-2299	192	1	and	and	CCONJ
ejpam-2299	192	2	λ(h	λ(h	ADJ
ejpam-2299	192	3	·	·	SYM
ejpam-2299	192	4	h	h	NOUN
ejpam-2299	192	5	)	)	PUNCT
ejpam-2299	192	6	=	=	PUNCT
ejpam-2299	192	7	−36	−36	X
ejpam-2299	192	8	.	.	PUNCT
ejpam-2299	193	1	but	but	CCONJ
ejpam-2299	193	2	f	f	X
ejpam-2299	193	3	·	·	PUNCT
ejpam-2299	193	4	g(z	g(z	ADJ
ejpam-2299	193	5	)	)	PUNCT
ejpam-2299	193	6	=	=	SYM
ejpam-2299	193	7	z2	z2	PROPN
ejpam-2299	193	8	·	·	SYM
ejpam-2299	193	9	z4	z4	PROPN
ejpam-2299	193	10	=	=	SYM
ejpam-2299	193	11	z6	z6	PROPN
ejpam-2299	193	12	=	=	SYM
ejpam-2299	193	13	h	h	NOUN
ejpam-2299	193	14	·	·	PUNCT
ejpam-2299	193	15	h(z	h(z	NOUN
ejpam-2299	193	16	)	)	PUNCT
ejpam-2299	193	17	,	,	PUNCT
ejpam-2299	193	18	which	which	PRON
ejpam-2299	193	19	is	be	AUX
ejpam-2299	193	20	a	a	DET
ejpam-2299	193	21	contradiction	contradiction	NOUN
ejpam-2299	193	22	.	.	PUNCT
ejpam-2299	194	1	so	so	ADV
ejpam-2299	194	2	h2(b	h2(b	PROPN
ejpam-2299	194	3	,	,	PUNCT
ejpam-2299	194	4	c0	c0	NOUN
ejpam-2299	194	5	)	)	PUNCT
ejpam-2299	194	6	6=	6=	PUNCT
ejpam-2299	194	7	{	{	PUNCT
ejpam-2299	194	8	0	0	NUM
ejpam-2299	194	9	}	}	PUNCT
ejpam-2299	194	10	.	.	PUNCT
ejpam-2299	195	1	now	now	ADV
ejpam-2299	195	2	consider	consider	VERB
ejpam-2299	195	3	µ′′	µ′′	NOUN
ejpam-2299	195	4	:	:	PUNCT
ejpam-2299	195	5	b′′×b′′	b′′×b′′	PROPN
ejpam-2299	195	6	−→	−→	ADJ
ejpam-2299	195	7	c0	c0	NOUN
ejpam-2299	195	8	,	,	PUNCT
ejpam-2299	195	9	and	and	CCONJ
ejpam-2299	195	10	suppose	suppose	VERB
ejpam-2299	195	11	that	that	SCONJ
ejpam-2299	195	12	for	for	ADP
ejpam-2299	195	13	some	some	DET
ejpam-2299	195	14	λ	λ	PROPN
ejpam-2299	195	15	∈	∈	NOUN
ejpam-2299	195	16	b′′′	b′′′	NOUN
ejpam-2299	195	17	we	we	PRON
ejpam-2299	195	18	have	have	VERB
ejpam-2299	195	19	µ′′	µ′′	NOUN
ejpam-2299	195	20	=	=	SYM
ejpam-2299	195	21	δ1(λ	δ1(λ	X
ejpam-2299	195	22	)	)	PUNCT
ejpam-2299	195	23	and	and	CCONJ
ejpam-2299	195	24	soλ(õf	soλ(õf	NOUN
ejpam-2299	195	25	·	·	SYM
ejpam-2299	196	1	g	g	X
ejpam-2299	196	2	)	)	PUNCT
ejpam-2299	196	3	=	=	SYM
ejpam-2299	196	4	0	0	NUM
ejpam-2299	196	5	andλ	andλ	PROPN
ejpam-2299	196	6	(	(	PUNCT
ejpam-2299	196	7	ˆh	ˆh	NOUN
ejpam-2299	196	8	·	·	PUNCT
ejpam-2299	196	9	h	h	NOUN
ejpam-2299	196	10	)	)	PUNCT
ejpam-2299	196	11	=	=	PUNCT
ejpam-2299	196	12	−36	−36	X
ejpam-2299	196	13	,	,	PUNCT
ejpam-2299	196	14	but	but	CCONJ
ejpam-2299	196	15	f	f	X
ejpam-2299	196	16	·	·	PUNCT
ejpam-2299	196	17	g	g	NOUN
ejpam-2299	196	18	=	=	PUNCT
ejpam-2299	196	19	h·h	h·h	NOUN
ejpam-2299	196	20	.	.	PUNCT
ejpam-2299	197	1	so	so	ADV
ejpam-2299	197	2	there	there	PRON
ejpam-2299	197	3	is	be	VERB
ejpam-2299	197	4	noλ	noλ	NOUN
ejpam-2299	197	5	∈	∈	NOUN
ejpam-2299	197	6	b′′′	b′′′	NOUN
ejpam-2299	197	7	with	with	ADP
ejpam-2299	197	8	µ′′	µ′′	NOUN
ejpam-2299	197	9	=	=	SYM
ejpam-2299	197	10	δ1(λ	δ1(λ	X
ejpam-2299	197	11	)	)	PUNCT
ejpam-2299	197	12	.	.	PUNCT
ejpam-2299	198	1	therefore	therefore	ADV
ejpam-2299	198	2	h2(b′′,c0	h2(b′′,c0	NOUN
ejpam-2299	198	3	)	)	PUNCT
ejpam-2299	198	4	6=	6=	PUNCT
ejpam-2299	198	5	{	{	PUNCT
ejpam-2299	198	6	0	0	NUM
ejpam-2299	198	7	}	}	PUNCT
ejpam-2299	198	8	.	.	PUNCT
ejpam-2299	199	1	the	the	DET
ejpam-2299	199	2	ext	ext	PROPN
ejpam-2299	199	3	example	example	NOUN
ejpam-2299	199	4	shows	show	VERB
ejpam-2299	199	5	that	that	SCONJ
ejpam-2299	199	6	the	the	DET
ejpam-2299	199	7	converse	converse	NOUN
ejpam-2299	199	8	of	of	ADP
ejpam-2299	199	9	theorem	theorem	NOUN
ejpam-2299	199	10	1	1	NUM
ejpam-2299	199	11	is	be	AUX
ejpam-2299	199	12	not	not	PART
ejpam-2299	199	13	true	true	ADJ
ejpam-2299	199	14	.	.	PUNCT
ejpam-2299	200	1	example	example	NOUN
ejpam-2299	201	1	3	3	NUM
ejpam-2299	201	2	.	.	PUNCT
ejpam-2299	201	3	by	by	ADP
ejpam-2299	201	4	4.1.42	4.1.42	NUM
ejpam-2299	201	5	in	in	ADP
ejpam-2299	201	6	[	[	X
ejpam-2299	201	7	4	4	NUM
ejpam-2299	201	8	]	]	PUNCT
ejpam-2299	201	9	,	,	PUNCT
ejpam-2299	201	10	h2(lp	h2(lp	PROPN
ejpam-2299	201	11	,	,	PUNCT
ejpam-2299	201	12	c0	c0	NOUN
ejpam-2299	201	13	)	)	PUNCT
ejpam-2299	201	14	6=	6=	ADP
ejpam-2299	201	15	{	{	PUNCT
ejpam-2299	201	16	0	0	NUM
ejpam-2299	201	17	}	}	PUNCT
ejpam-2299	201	18	for	for	ADP
ejpam-2299	201	19	p	p	NOUN
ejpam-2299	201	20	>	>	SYM
ejpam-2299	201	21	1	1	NUM
ejpam-2299	201	22	and	and	CCONJ
ejpam-2299	201	23	lp	lp	NOUN
ejpam-2299	201	24	is	be	AUX
ejpam-2299	201	25	weakly	weakly	ADV
ejpam-2299	201	26	amenable	amenable	ADJ
ejpam-2299	201	27	and	and	CCONJ
ejpam-2299	201	28	reflexive	reflexive	ADJ
ejpam-2299	201	29	.	.	PUNCT
ejpam-2299	202	1	so	so	ADV
ejpam-2299	202	2	lp	lp	ADV
ejpam-2299	202	3	is	be	AUX
ejpam-2299	202	4	(	(	PUNCT
ejpam-2299	202	5	-1)-weakly	-1)-weakly	ADV
ejpam-2299	202	6	amenable	amenable	ADJ
ejpam-2299	202	7	.	.	PUNCT
ejpam-2299	203	1	since	since	SCONJ
ejpam-2299	203	2	lp	lp	NOUN
ejpam-2299	203	3	has	have	VERB
ejpam-2299	203	4	an	an	DET
ejpam-2299	203	5	approximate	approximate	ADJ
ejpam-2299	203	6	identity	identity	NOUN
ejpam-2299	203	7	,	,	PUNCT
ejpam-2299	203	8	then	then	ADV
ejpam-2299	203	9	lp	lp	ADV
ejpam-2299	203	10	=	=	SYM
ejpam-2299	203	11	(	(	PUNCT
ejpam-2299	203	12	lp)2	lp)2	PROPN
ejpam-2299	203	13	and	and	CCONJ
ejpam-2299	203	14	by	by	ADP
ejpam-2299	203	15	theorem	theorem	NOUN
ejpam-2299	203	16	2	2	NUM
ejpam-2299	203	17	,	,	PUNCT
ejpam-2299	203	18	(	(	PUNCT
ejpam-2299	203	19	lp	lp	NOUN
ejpam-2299	203	20	)	)	PUNCT
ejpam-2299	203	21	#	#	NOUN
ejpam-2299	203	22	is	be	AUX
ejpam-2299	203	23	(	(	PUNCT
ejpam-2299	203	24	-1)-weakly	-1)-weakly	ADV
ejpam-2299	203	25	amenable	amenable	ADJ
ejpam-2299	203	26	(	(	PUNCT
ejpam-2299	203	27	note	note	VERB
ejpam-2299	203	28	that	that	SCONJ
ejpam-2299	203	29	(	(	PUNCT
ejpam-2299	203	30	lp	lp	NOUN
ejpam-2299	203	31	)	)	PUNCT
ejpam-2299	203	32	#	#	NOUN
ejpam-2299	203	33	′′	′′	NOUN
ejpam-2299	203	34	=	=	SYM
ejpam-2299	203	35	(	(	PUNCT
ejpam-2299	203	36	lp)′′	lp)′′	X
ejpam-2299	203	37	#	#	NOUN
ejpam-2299	203	38	≃	≃	NOUN
ejpam-2299	203	39	lp	lp	NOUN
ejpam-2299	203	40	#	#	NOUN
ejpam-2299	203	41	)	)	PUNCT
ejpam-2299	203	42	.	.	PUNCT
ejpam-2299	204	1	a	a	DET
ejpam-2299	204	2	normed	normed	ADJ
ejpam-2299	204	3	algebra	algebra	NOUN
ejpam-2299	204	4	a	a	PRON
ejpam-2299	204	5	has	have	VERB
ejpam-2299	204	6	π	π	NOUN
ejpam-2299	204	7	-	-	NOUN
ejpam-2299	204	8	property	property	NOUN
ejpam-2299	204	9	if	if	SCONJ
ejpam-2299	204	10	there	there	PRON
ejpam-2299	204	11	is	be	VERB
ejpam-2299	204	12	a	a	DET
ejpam-2299	204	13	constant	constant	ADJ
ejpam-2299	204	14	c	c	NOUN
ejpam-2299	204	15	>	>	X
ejpam-2299	204	16	0	0	PUNCT
ejpam-2299	204	17	with	with	ADP
ejpam-2299	204	18	9a9π	9a9π	NOUN
ejpam-2299	204	19	≤	≤	NUM
ejpam-2299	204	20	c‖a‖	c‖a‖	NOUN
ejpam-2299	204	21	,	,	PUNCT
ejpam-2299	204	22	for	for	ADP
ejpam-2299	204	23	a	a	DET
ejpam-2299	204	24	∈	∈	PROPN
ejpam-2299	204	25	a2	a2	NOUN
ejpam-2299	204	26	,	,	PUNCT
ejpam-2299	204	27	where	where	SCONJ
ejpam-2299	204	28	9a9π	9a9π	NOUN
ejpam-2299	204	29	=	=	SYM
ejpam-2299	204	30	inf	inf	PROPN
ejpam-2299	204	31	¦	¦	PROPN
ejpam-2299	205	1	∑∞	∑∞	X
ejpam-2299	205	2	j=1	j=1	PROPN
ejpam-2299	205	3	‖a	‖a	PUNCT
ejpam-2299	205	4	j‖‖b	j‖‖b	NOUN
ejpam-2299	205	5	j‖	j‖	NOUN
ejpam-2299	205	6	:	:	PUNCT
ejpam-2299	205	7	a	a	DET
ejpam-2299	205	8	=	=	PUNCT
ejpam-2299	205	9	∑∞	∑∞	NOUN
ejpam-2299	205	10	j=1	j=1	PROPN
ejpam-2299	205	11	a	a	DET
ejpam-2299	205	12	j	j	PROPN
ejpam-2299	205	13	b	b	PROPN
ejpam-2299	205	14	j	j	PROPN
ejpam-2299	205	15	©	©	PROPN
ejpam-2299	205	16	,	,	PUNCT
ejpam-2299	205	17	for	for	ADP
ejpam-2299	205	18	more	more	ADJ
ejpam-2299	205	19	details	detail	NOUN
ejpam-2299	205	20	see	see	VERB
ejpam-2299	205	21	[	[	X
ejpam-2299	205	22	4	4	NUM
ejpam-2299	205	23	]	]	PUNCT
ejpam-2299	205	24	.	.	PUNCT
ejpam-2299	206	1	by	by	ADP
ejpam-2299	206	2	2.8.21	2.8.21	NUM
ejpam-2299	206	3	in	in	ADP
ejpam-2299	206	4	[	[	PUNCT
ejpam-2299	206	5	4	4	NUM
ejpam-2299	206	6	]	]	PUNCT
ejpam-2299	206	7	,	,	PUNCT
ejpam-2299	206	8	a	a	DET
ejpam-2299	206	9	banach	banach	NOUN
ejpam-2299	206	10	algebra	algebra	NOUN
ejpam-2299	206	11	with	with	ADP
ejpam-2299	206	12	h2(a	h2(a	PROPN
ejpam-2299	206	13	,	,	PUNCT
ejpam-2299	206	14	c0	c0	NOUN
ejpam-2299	206	15	)	)	PUNCT
ejpam-2299	206	16	=	=	PUNCT
ejpam-2299	206	17	{	{	PUNCT
ejpam-2299	206	18	0	0	NUM
ejpam-2299	206	19	}	}	PUNCT
ejpam-2299	206	20	hasπ	hasπ	NOUN
ejpam-2299	206	21	-	-	PUNCT
ejpam-2299	206	22	property	property	NOUN
ejpam-2299	206	23	.	.	PUNCT
ejpam-2299	207	1	now	now	ADV
ejpam-2299	207	2	,	,	PUNCT
ejpam-2299	207	3	by	by	ADP
ejpam-2299	207	4	using	use	VERB
ejpam-2299	207	5	theorem	theorem	NOUN
ejpam-2299	207	6	3	3	NUM
ejpam-2299	207	7	we	we	PRON
ejpam-2299	207	8	have	have	VERB
ejpam-2299	207	9	the	the	DET
ejpam-2299	207	10	following	follow	VERB
ejpam-2299	207	11	corollary	corollary	NOUN
ejpam-2299	207	12	.	.	PUNCT
ejpam-2299	208	1	corollary	corollary	ADJ
ejpam-2299	208	2	1	1	NUM
ejpam-2299	208	3	.	.	PUNCT
ejpam-2299	209	1	let	let	VERB
ejpam-2299	209	2	a	a	PRON
ejpam-2299	209	3	be	be	AUX
ejpam-2299	209	4	a	a	DET
ejpam-2299	209	5	banach	banach	NOUN
ejpam-2299	209	6	algebra	algebra	NOUN
ejpam-2299	209	7	for	for	ADP
ejpam-2299	209	8	which	which	PRON
ejpam-2299	209	9	a′′	a′′	NOUN
ejpam-2299	209	10	has	have	VERB
ejpam-2299	209	11	π	π	NOUN
ejpam-2299	209	12	-	-	NOUN
ejpam-2299	209	13	property	property	NOUN
ejpam-2299	209	14	.	.	PUNCT
ejpam-2299	210	1	if	if	SCONJ
ejpam-2299	210	2	a#′′	a#′′	NOUN
ejpam-2299	210	3	is	be	AUX
ejpam-2299	210	4	(	(	PUNCT
ejpam-2299	210	5	-1)-weakly	-1)-weakly	ADV
ejpam-2299	210	6	amenable	amenable	ADJ
ejpam-2299	210	7	,	,	PUNCT
ejpam-2299	210	8	then	then	ADV
ejpam-2299	210	9	a′′	a′′	NOUN
ejpam-2299	210	10	is	be	AUX
ejpam-2299	210	11	(	(	PUNCT
ejpam-2299	210	12	-1)-weakly	-1)-weakly	ADV
ejpam-2299	210	13	amenable	amenable	ADJ
ejpam-2299	210	14	.	.	PUNCT
ejpam-2299	211	1	theorem	theorem	NOUN
ejpam-2299	211	2	4	4	NUM
ejpam-2299	211	3	.	.	PUNCT
ejpam-2299	212	1	let	let	VERB
ejpam-2299	212	2	a	a	DET
ejpam-2299	212	3	be	be	AUX
ejpam-2299	212	4	an	an	DET
ejpam-2299	212	5	arens	aren	NOUN
ejpam-2299	212	6	regular	regular	ADJ
ejpam-2299	212	7	banach	banach	NOUN
ejpam-2299	212	8	algebra	algebra	NOUN
ejpam-2299	212	9	and	and	CCONJ
ejpam-2299	212	10	a′′	a′′	NOUN
ejpam-2299	212	11	#	#	NOUN
ejpam-2299	212	12	is	be	AUX
ejpam-2299	212	13	(	(	PUNCT
ejpam-2299	212	14	-1)-weakly	-1)-weakly	ADV
ejpam-2299	212	15	amenable	amenable	ADJ
ejpam-2299	212	16	.	.	PUNCT
ejpam-2299	213	1	if	if	SCONJ
ejpam-2299	213	2	g(df	g(df	NUM
ejpam-2299	213	3	)	)	PUNCT
ejpam-2299	213	4	=	=	SYM
ejpam-2299	213	5	−f(dg	−f(dg	PROPN
ejpam-2299	213	6	)	)	PUNCT
ejpam-2299	213	7	,	,	PUNCT
ejpam-2299	213	8	for	for	ADP
ejpam-2299	213	9	each	each	DET
ejpam-2299	213	10	d	d	PROPN
ejpam-2299	213	11	∈	∈	PROPN
ejpam-2299	213	12	z1(a′′,a′	z1(a′′,a′	NOUN
ejpam-2299	213	13	)	)	PUNCT
ejpam-2299	213	14	and	and	CCONJ
ejpam-2299	213	15	each	each	DET
ejpam-2299	213	16	f	f	NOUN
ejpam-2299	213	17	,	,	PUNCT
ejpam-2299	213	18	g	g	PROPN
ejpam-2299	213	19	∈	∈	PROPN
ejpam-2299	213	20	a′′.	a′′.	PROPN
ejpam-2299	213	21	then	then	ADV
ejpam-2299	213	22	a′′	a′′	PROPN
ejpam-2299	213	23	is	be	AUX
ejpam-2299	213	24	(	(	PUNCT
ejpam-2299	213	25	-1)-weakly	-1)-weakly	ADV
ejpam-2299	213	26	amenable	amenable	ADJ
ejpam-2299	213	27	.	.	PUNCT
ejpam-2299	214	1	proof	proof	NOUN
ejpam-2299	214	2	.	.	PUNCT
ejpam-2299	215	1	let	let	VERB
ejpam-2299	215	2	d	d	X
ejpam-2299	215	3	∈	∈	PROPN
ejpam-2299	215	4	z1(a′′,a′	z1(a′′,a′	NOUN
ejpam-2299	215	5	)	)	PUNCT
ejpam-2299	215	6	.	.	PUNCT
ejpam-2299	216	1	we	we	PRON
ejpam-2299	216	2	define	define	VERB
ejpam-2299	216	3	d	d	NOUN
ejpam-2299	216	4	#	#	NOUN
ejpam-2299	216	5	:	:	PUNCT
ejpam-2299	216	6	a′′	a′′	NOUN
ejpam-2299	216	7	−→a#′	−→a#′	X
ejpam-2299	216	8	d#(f)(αe+	d#(f)(αe+	VERB
ejpam-2299	216	9	a	a	PRON
ejpam-2299	216	10	)	)	PUNCT
ejpam-2299	216	11	:	:	PUNCT
ejpam-2299	217	1	=	=	X
ejpam-2299	217	2	d(f)(a	d(f)(a	NUM
ejpam-2299	217	3	)	)	PUNCT
ejpam-2299	217	4	.	.	PUNCT
ejpam-2299	218	1	we	we	PRON
ejpam-2299	218	2	prove	prove	VERB
ejpam-2299	218	3	d	d	NOUN
ejpam-2299	218	4	#	#	NOUN
ejpam-2299	218	5	is	be	AUX
ejpam-2299	218	6	a	a	DET
ejpam-2299	218	7	derivation	derivation	NOUN
ejpam-2299	218	8	.	.	PUNCT
ejpam-2299	219	1	let	let	VERB
ejpam-2299	219	2	f	f	X
ejpam-2299	219	3	,	,	PUNCT
ejpam-2299	219	4	g	g	PROPN
ejpam-2299	219	5	∈	∈	PROPN
ejpam-2299	219	6	a′′	a′′	NOUN
ejpam-2299	219	7	,	,	PUNCT
ejpam-2299	219	8	then	then	ADV
ejpam-2299	219	9	there	there	PRON
ejpam-2299	219	10	are	be	VERB
ejpam-2299	219	11	nets	net	NOUN
ejpam-2299	219	12	(	(	PUNCT
ejpam-2299	219	13	ai)i	ai)i	NOUN
ejpam-2299	219	14	and	and	CCONJ
ejpam-2299	219	15	(	(	PUNCT
ejpam-2299	219	16	b	b	PROPN
ejpam-2299	219	17	j	j	PROPN
ejpam-2299	219	18	)	)	PUNCT
ejpam-2299	219	19	j	j	PROPN
ejpam-2299	219	20	in	in	ADP
ejpam-2299	219	21	a	a	DET
ejpam-2299	219	22	such	such	ADJ
ejpam-2299	219	23	that	that	SCONJ
ejpam-2299	219	24	ai	ai	AUX
ejpam-2299	219	25	w∗	w∗	PROPN
ejpam-2299	219	26	−→	−→	PROPN
ejpam-2299	219	27	f	f	PROPN
ejpam-2299	219	28	and	and	CCONJ
ejpam-2299	219	29	b	b	PROPN
ejpam-2299	219	30	j	j	PROPN
ejpam-2299	219	31	w∗	w∗	PROPN
ejpam-2299	219	32	−→	−→	NOUN
ejpam-2299	219	33	g	g	PROPN
ejpam-2299	219	34	and	and	CCONJ
ejpam-2299	219	35	for	for	ADP
ejpam-2299	219	36	each	each	DET
ejpam-2299	219	37	α	α	NOUN
ejpam-2299	219	38	∈	∈	PROPN
ejpam-2299	219	39	c	c	NOUN
ejpam-2299	219	40	,	,	PUNCT
ejpam-2299	219	41	a	a	DET
ejpam-2299	219	42	∈	∈	PROPN
ejpam-2299	219	43	a	a	PRON
ejpam-2299	219	44	we	we	PRON
ejpam-2299	219	45	have	have	VERB
ejpam-2299	219	46	d#f	d#f	PROPN
ejpam-2299	219	47	·	·	PUNCT
ejpam-2299	219	48	g(αe+	g(αe+	NOUN
ejpam-2299	219	49	a	a	NOUN
ejpam-2299	219	50	)	)	PUNCT
ejpam-2299	219	51	=	=	NOUN
ejpam-2299	219	52	g((αe+	g((αe+	PROPN
ejpam-2299	219	53	a	a	NOUN
ejpam-2299	219	54	)	)	PUNCT
ejpam-2299	219	55	·	·	PUNCT
ejpam-2299	219	56	d#f	d#f	PROPN
ejpam-2299	219	57	)	)	PUNCT
ejpam-2299	219	58	=	=	PROPN
ejpam-2299	219	59	lim	lim	PROPN
ejpam-2299	219	60	j	j	PROPN
ejpam-2299	219	61	�	�	PROPN
ejpam-2299	219	62	(	(	PUNCT
ejpam-2299	219	63	αe+	αe+	NOUN
ejpam-2299	219	64	a	a	NOUN
ejpam-2299	219	65	)	)	PUNCT
ejpam-2299	219	66	·	·	PUNCT
ejpam-2299	220	1	d#f	d#f	PROPN
ejpam-2299	220	2	�	�	PROPN
ejpam-2299	220	3	(	(	PUNCT
ejpam-2299	220	4	b	b	PROPN
ejpam-2299	220	5	j	j	NOUN
ejpam-2299	220	6	)	)	PUNCT
ejpam-2299	221	1	=	=	PROPN
ejpam-2299	221	2	lim	lim	PROPN
ejpam-2299	221	3	j	j	PROPN
ejpam-2299	221	4	df(αb	df(αb	PROPN
ejpam-2299	221	5	j	j	PROPN
ejpam-2299	221	6	+	+	CCONJ
ejpam-2299	221	7	b	b	PROPN
ejpam-2299	221	8	ja	ja	PROPN
ejpam-2299	221	9	)	)	PUNCT
ejpam-2299	222	1	=	=	PROPN
ejpam-2299	222	2	lim	lim	PROPN
ejpam-2299	222	3	j	j	PROPN
ejpam-2299	223	1	α	α	PROPN
ejpam-2299	223	2	·	·	PUNCT
ejpam-2299	223	3	b̂	b̂	NOUN
ejpam-2299	223	4	j(df	j(df	PROPN
ejpam-2299	223	5	)	)	PUNCT
ejpam-2299	224	1	+	+	CCONJ
ejpam-2299	224	2	lim	lim	PROPN
ejpam-2299	224	3	j	j	PROPN
ejpam-2299	224	4	b̂	b̂	PROPN
ejpam-2299	224	5	j(a	j(a	PROPN
ejpam-2299	224	6	·	·	PUNCT
ejpam-2299	224	7	df	df	PROPN
ejpam-2299	224	8	)	)	PUNCT
ejpam-2299	224	9	.	.	PUNCT
ejpam-2299	225	1	so	so	ADV
ejpam-2299	225	2	�	�	PROPN
ejpam-2299	225	3	d#f	d#f	PROPN
ejpam-2299	225	4	·	·	PUNCT
ejpam-2299	225	5	g	g	NOUN
ejpam-2299	225	6	)	)	PUNCT
ejpam-2299	225	7	�	�	PROPN
ejpam-2299	225	8	αe+	αe+	NOUN
ejpam-2299	225	9	a	a	X
ejpam-2299	225	10	)	)	PUNCT
ejpam-2299	225	11	=	=	SYM
ejpam-2299	225	12	αg(df	αg(df	VERB
ejpam-2299	225	13	)	)	PUNCT
ejpam-2299	226	1	+	+	CCONJ
ejpam-2299	226	2	g(a	g(a	PROPN
ejpam-2299	226	3	·	·	PUNCT
ejpam-2299	226	4	df	df	PROPN
ejpam-2299	226	5	)	)	PUNCT
ejpam-2299	226	6	and	and	CCONJ
ejpam-2299	226	7	similarly	similarly	ADV
ejpam-2299	226	8	�	�	PROPN
ejpam-2299	226	9	f	f	PROPN
ejpam-2299	226	10	·	·	PUNCT
ejpam-2299	226	11	d#g	d#g	PROPN
ejpam-2299	226	12	�	�	PROPN
ejpam-2299	226	13	(	(	PUNCT
ejpam-2299	226	14	αe+	αe+	NOUN
ejpam-2299	226	15	a	a	X
ejpam-2299	226	16	)	)	PUNCT
ejpam-2299	226	17	=	=	SYM
ejpam-2299	226	18	αf(dg	αf(dg	PROPN
ejpam-2299	226	19	)	)	PUNCT
ejpam-2299	227	1	+	+	CCONJ
ejpam-2299	227	2	f(dg	f(dg	PROPN
ejpam-2299	227	3	·	·	PUNCT
ejpam-2299	227	4	a	a	X
ejpam-2299	227	5	)	)	PUNCT
ejpam-2299	227	6	.	.	PUNCT
ejpam-2299	228	1	s.	s.	PROPN
ejpam-2299	228	2	hosseinioun	hosseinioun	PROPN
ejpam-2299	228	3	,	,	PUNCT
ejpam-2299	228	4	a.	a.	NOUN
ejpam-2299	228	5	valadkhani	valadkhani	PROPN
ejpam-2299	228	6	/	/	SYM
ejpam-2299	228	7	eur	eur	PROPN
ejpam-2299	228	8	.	.	PUNCT
ejpam-2299	229	1	j.	j.	PROPN
ejpam-2299	229	2	pure	pure	PROPN
ejpam-2299	229	3	appl	appl	PROPN
ejpam-2299	229	4	.	.	PROPN
ejpam-2299	229	5	math	math	PROPN
ejpam-2299	229	6	,	,	PUNCT
ejpam-2299	229	7	9	9	NUM
ejpam-2299	229	8	(	(	PUNCT
ejpam-2299	229	9	2016	2016	NUM
ejpam-2299	229	10	)	)	PUNCT
ejpam-2299	229	11	,	,	PUNCT
ejpam-2299	229	12	231	231	NUM
ejpam-2299	229	13	-	-	SYM
ejpam-2299	229	14	239	239	NUM
ejpam-2299	229	15	237	237	NUM
ejpam-2299	229	16	then	then	ADV
ejpam-2299	229	17	we	we	PRON
ejpam-2299	229	18	have	have	VERB
ejpam-2299	229	19	�	�	NOUN
ejpam-2299	229	20	d#f	d#f	PROPN
ejpam-2299	229	21	·	·	PUNCT
ejpam-2299	229	22	g	g	PROPN
ejpam-2299	230	1	+	+	CCONJ
ejpam-2299	230	2	f	f	PROPN
ejpam-2299	230	3	·	·	PUNCT
ejpam-2299	230	4	d#g	d#g	PROPN
ejpam-2299	230	5	�	�	PROPN
ejpam-2299	230	6	(	(	PUNCT
ejpam-2299	230	7	αe+	αe+	NOUN
ejpam-2299	230	8	a	a	X
ejpam-2299	230	9	)	)	PUNCT
ejpam-2299	230	10	=	=	NOUN
ejpam-2299	230	11	αg(df	αg(df	VERB
ejpam-2299	230	12	)	)	PUNCT
ejpam-2299	231	1	+	+	CCONJ
ejpam-2299	231	2	g(a	g(a	PROPN
ejpam-2299	231	3	·	·	PUNCT
ejpam-2299	231	4	df	df	PROPN
ejpam-2299	231	5	)	)	PUNCT
ejpam-2299	231	6	+	+	NOUN
ejpam-2299	231	7	αf(dg	αf(dg	NUM
ejpam-2299	231	8	)	)	PUNCT
ejpam-2299	232	1	+	+	CCONJ
ejpam-2299	232	2	f(dg	f(dg	PROPN
ejpam-2299	232	3	·	·	PUNCT
ejpam-2299	232	4	a	a	X
ejpam-2299	232	5	)	)	PUNCT
ejpam-2299	233	1	=	=	NOUN
ejpam-2299	233	2	α	α	NOUN
ejpam-2299	233	3	(	(	PUNCT
ejpam-2299	233	4	g(df	g(df	PROPN
ejpam-2299	233	5	)	)	PUNCT
ejpam-2299	233	6	+	+	CCONJ
ejpam-2299	233	7	f(dg	f(dg	NOUN
ejpam-2299	233	8	)	)	PUNCT
ejpam-2299	233	9	)	)	PUNCT
ejpam-2299	234	1	+	+	CCONJ
ejpam-2299	234	2	f	f	X
ejpam-2299	234	3	·	·	PUNCT
ejpam-2299	234	4	dg(a	dg(a	X
ejpam-2299	234	5	)	)	PUNCT
ejpam-2299	235	1	+	+	CCONJ
ejpam-2299	235	2	df	df	PROPN
ejpam-2299	235	3	·	·	PUNCT
ejpam-2299	235	4	g(a	g(a	PROPN
ejpam-2299	235	5	)	)	PUNCT
ejpam-2299	235	6	=(	=(	NOUN
ejpam-2299	235	7	f	f	X
ejpam-2299	235	8	·	·	PUNCT
ejpam-2299	235	9	dg	dg	PROPN
ejpam-2299	235	10	+	+	CCONJ
ejpam-2299	235	11	df	df	PROPN
ejpam-2299	235	12	·	·	PUNCT
ejpam-2299	235	13	g)(a	g)(a	PROPN
ejpam-2299	235	14	)	)	PUNCT
ejpam-2299	236	1	=	=	SYM
ejpam-2299	236	2	d#(f	d#(f	NOUN
ejpam-2299	236	3	·	·	PUNCT
ejpam-2299	236	4	g)(a+αe	g)(a+αe	PROPN
ejpam-2299	236	5	)	)	PUNCT
ejpam-2299	236	6	.	.	PUNCT
ejpam-2299	237	1	therefore	therefore	ADV
ejpam-2299	237	2	d	d	X
ejpam-2299	237	3	#	#	NOUN
ejpam-2299	237	4	is	be	AUX
ejpam-2299	237	5	a	a	DET
ejpam-2299	237	6	bounded	bounded	ADJ
ejpam-2299	237	7	derivation	derivation	NOUN
ejpam-2299	237	8	and	and	CCONJ
ejpam-2299	237	9	there	there	PRON
ejpam-2299	237	10	exists	exist	VERB
ejpam-2299	237	11	λ1	λ1	ADJ
ejpam-2299	237	12	=	=	SYM
ejpam-2299	237	13	λ0	λ0	NOUN
ejpam-2299	237	14	+	+	CCONJ
ejpam-2299	237	15	α0e′	α0e′	NOUN
ejpam-2299	237	16	∈	∈	NOUN
ejpam-2299	237	17	a#′	a#′	PROPN
ejpam-2299	237	18	such	such	ADJ
ejpam-2299	237	19	that	that	DET
ejpam-2299	237	20	d#(f	d#(f	PROPN
ejpam-2299	237	21	)	)	PUNCT
ejpam-2299	237	22	=	=	SYM
ejpam-2299	237	23	δλ1	δλ1	NOUN
ejpam-2299	237	24	(	(	PUNCT
ejpam-2299	237	25	f	f	NOUN
ejpam-2299	237	26	)	)	PUNCT
ejpam-2299	237	27	,	,	PUNCT
ejpam-2299	237	28	for	for	ADP
ejpam-2299	237	29	f	f	PROPN
ejpam-2299	237	30	∈	∈	PROPN
ejpam-2299	237	31	a′′	a′′	NOUN
ejpam-2299	237	32	(	(	PUNCT
ejpam-2299	237	33	note	note	VERB
ejpam-2299	237	34	that	that	SCONJ
ejpam-2299	237	35	since	since	SCONJ
ejpam-2299	237	36	a#′	a#′	NOUN
ejpam-2299	237	37	=	=	PUNCT
ejpam-2299	237	38	a′	a′	NOUN
ejpam-2299	237	39	⊕ce′	⊕ce′	NOUN
ejpam-2299	237	40	,	,	PUNCT
ejpam-2299	237	41	λ0	λ0	NOUN
ejpam-2299	237	42	∈	∈	NOUN
ejpam-2299	237	43	a′	a′	NOUN
ejpam-2299	237	44	and	and	CCONJ
ejpam-2299	237	45	α0	α0	PROPN
ejpam-2299	237	46	∈	∈	PROPN
ejpam-2299	237	47	c	c	NOUN
ejpam-2299	237	48	are	be	AUX
ejpam-2299	237	49	unique	unique	ADJ
ejpam-2299	237	50	and	and	CCONJ
ejpam-2299	237	51	h1(a′′,a#′	h1(a′′,a#′	NOUN
ejpam-2299	237	52	)	)	PUNCT
ejpam-2299	237	53	=	=	SYM
ejpam-2299	238	1	h1(a′′#,a#′	h1(a′′#,a#′	PROPN
ejpam-2299	238	2	)	)	PUNCT
ejpam-2299	238	3	=	=	SYM
ejpam-2299	238	4	(	(	PUNCT
ejpam-2299	238	5	0	0	NUM
ejpam-2299	238	6	)	)	PUNCT
ejpam-2299	238	7	)	)	PUNCT
ejpam-2299	238	8	.	.	PUNCT
ejpam-2299	239	1	we	we	PRON
ejpam-2299	239	2	show	show	VERB
ejpam-2299	239	3	that	that	SCONJ
ejpam-2299	239	4	d	d	NOUN
ejpam-2299	239	5	=	=	PUNCT
ejpam-2299	239	6	δλ0	δλ0	X
ejpam-2299	239	7	.	.	PUNCT
ejpam-2299	240	1	toward	toward	ADP
ejpam-2299	240	2	this	this	DET
ejpam-2299	240	3	end	end	NOUN
ejpam-2299	240	4	,	,	PUNCT
ejpam-2299	240	5	let	let	VERB
ejpam-2299	240	6	f	f	PROPN
ejpam-2299	240	7	∈	∈	PROPN
ejpam-2299	240	8	a′′	a′′	NOUN
ejpam-2299	240	9	and	and	CCONJ
ejpam-2299	240	10	a	a	DET
ejpam-2299	240	11	∈	∈	PROPN
ejpam-2299	240	12	a	a	X
ejpam-2299	240	13	,	,	PUNCT
ejpam-2299	240	14	we	we	PRON
ejpam-2299	240	15	have	have	VERB
ejpam-2299	240	16	(	(	PUNCT
ejpam-2299	240	17	df)(a	df)(a	PROPN
ejpam-2299	240	18	)	)	PUNCT
ejpam-2299	241	1	=	=	VERB
ejpam-2299	241	2	d#f(a+	d#f(a+	PROPN
ejpam-2299	241	3	0e	0e	NOUN
ejpam-2299	241	4	)	)	PUNCT
ejpam-2299	241	5	=	=	SYM
ejpam-2299	241	6	δλ1	δλ1	NOUN
ejpam-2299	241	7	(	(	PUNCT
ejpam-2299	241	8	f)(a+	f)(a+	NOUN
ejpam-2299	241	9	0e	0e	NOUN
ejpam-2299	241	10	)	)	PUNCT
ejpam-2299	241	11	=	=	SYM
ejpam-2299	242	1	(	(	PUNCT
ejpam-2299	242	2	f	f	X
ejpam-2299	242	3	·	·	PUNCT
ejpam-2299	242	4	λ1	λ1	ADJ
ejpam-2299	242	5	−λ1	−λ1	PROPN
ejpam-2299	242	6	·	·	PUNCT
ejpam-2299	242	7	f)(a+	f)(a+	NOUN
ejpam-2299	242	8	0e	0e	NOUN
ejpam-2299	242	9	)	)	PUNCT
ejpam-2299	243	1	=	=	NOUN
ejpam-2299	243	2	f(λ1	f(λ1	NOUN
ejpam-2299	243	3	·	·	PUNCT
ejpam-2299	243	4	(	(	PUNCT
ejpam-2299	243	5	a+	a+	X
ejpam-2299	243	6	0e)−	0e)−	NUM
ejpam-2299	243	7	(	(	PUNCT
ejpam-2299	243	8	a+	a+	X
ejpam-2299	243	9	0e	0e	NOUN
ejpam-2299	243	10	)	)	PUNCT
ejpam-2299	243	11	·	·	PUNCT
ejpam-2299	243	12	λ1	λ1	ADJ
ejpam-2299	243	13	)	)	PUNCT
ejpam-2299	243	14	=	=	PROPN
ejpam-2299	243	15	f	f	PROPN
ejpam-2299	243	16	�	�	PROPN
ejpam-2299	243	17	(	(	PUNCT
ejpam-2299	243	18	λ0	λ0	NOUN
ejpam-2299	243	19	+	+	NOUN
ejpam-2299	243	20	α0e′)(a+	α0e′)(a+	PROPN
ejpam-2299	243	21	0e)−	0e)−	NOUN
ejpam-2299	243	22	(	(	PUNCT
ejpam-2299	243	23	a+	a+	X
ejpam-2299	243	24	0e)(λ0	0e)(λ0	NUM
ejpam-2299	243	25	+	+	NOUN
ejpam-2299	243	26	α0e′	α0e′	NOUN
ejpam-2299	243	27	)	)	PUNCT
ejpam-2299	243	28	�	�	NOUN
ejpam-2299	243	29	=	=	SYM
ejpam-2299	243	30	f(λ0	f(λ0	NOUN
ejpam-2299	243	31	·	·	PUNCT
ejpam-2299	243	32	a−	a−	PROPN
ejpam-2299	243	33	a	a	DET
ejpam-2299	243	34	·	·	SYM
ejpam-2299	243	35	λ0	λ0	NOUN
ejpam-2299	243	36	)	)	PUNCT
ejpam-2299	243	37	=	=	SYM
ejpam-2299	243	38	(	(	PUNCT
ejpam-2299	243	39	f	f	X
ejpam-2299	243	40	·	·	PUNCT
ejpam-2299	243	41	λ0	λ0	NOUN
ejpam-2299	243	42	−λ0	−λ0	ADV
ejpam-2299	243	43	·	·	PUNCT
ejpam-2299	243	44	f)(a	f)(a	NUM
ejpam-2299	243	45	)	)	PUNCT
ejpam-2299	244	1	=	=	PUNCT
ejpam-2299	244	2	δλ0	δλ0	INTJ
ejpam-2299	244	3	(	(	PUNCT
ejpam-2299	244	4	f)(a	f)(a	NOUN
ejpam-2299	244	5	)	)	PUNCT
ejpam-2299	244	6	.	.	PUNCT
ejpam-2299	245	1	so	so	ADV
ejpam-2299	246	1	d	d	NOUN
ejpam-2299	246	2	=	=	PUNCT
ejpam-2299	247	1	δλ0	δλ0	INTJ
ejpam-2299	247	2	.	.	PUNCT
ejpam-2299	248	1	therefore	therefore	ADV
ejpam-2299	248	2	a′′	a′′	PROPN
ejpam-2299	248	3	is	be	AUX
ejpam-2299	248	4	(	(	PUNCT
ejpam-2299	248	5	-1)-weakly	-1)-weakly	ADV
ejpam-2299	248	6	amenable	amenable	ADJ
ejpam-2299	248	7	.	.	PUNCT
ejpam-2299	249	1	the	the	DET
ejpam-2299	249	2	following	follow	VERB
ejpam-2299	249	3	example	example	NOUN
ejpam-2299	249	4	shows	show	VERB
ejpam-2299	249	5	that	that	SCONJ
ejpam-2299	249	6	the	the	DET
ejpam-2299	249	7	condition	condition	NOUN
ejpam-2299	249	8	in	in	ADP
ejpam-2299	249	9	theorem	theorem	NOUN
ejpam-2299	249	10	4	4	NUM
ejpam-2299	249	11	,	,	PUNCT
ejpam-2299	249	12	is	be	AUX
ejpam-2299	249	13	not	not	PART
ejpam-2299	249	14	trivial	trivial	ADJ
ejpam-2299	249	15	.	.	PUNCT
ejpam-2299	250	1	example	example	NOUN
ejpam-2299	251	1	4	4	NUM
ejpam-2299	251	2	.	.	PUNCT
ejpam-2299	251	3	let	let	VERB
ejpam-2299	251	4	t	t	PROPN
ejpam-2299	251	5	be	be	AUX
ejpam-2299	251	6	the	the	DET
ejpam-2299	251	7	unit	unit	NOUN
ejpam-2299	251	8	circle	circle	NOUN
ejpam-2299	251	9	and	and	CCONJ
ejpam-2299	251	10	a=	a=	PROPN
ejpam-2299	251	11	l	l	X
ejpam-2299	251	12	ipαt	ipαt	PROPN
ejpam-2299	251	13	.	.	PUNCT
ejpam-2299	252	1	let	let	VERB
ejpam-2299	252	2	(	(	PUNCT
ejpam-2299	252	3	f̂(n))n∈z	f̂(n))n∈z	X
ejpam-2299	252	4	and	and	CCONJ
ejpam-2299	252	5	(	(	PUNCT
ejpam-2299	252	6	ĝ(n))n∈z	ĝ(n))n∈z	PROPN
ejpam-2299	252	7	are	be	AUX
ejpam-2299	252	8	the	the	DET
ejpam-2299	252	9	fourier	fourier	ADJ
ejpam-2299	252	10	coefficients	coefficient	NOUN
ejpam-2299	252	11	of	of	ADP
ejpam-2299	252	12	f	f	PROPN
ejpam-2299	252	13	∈	∈	PROPN
ejpam-2299	252	14	lipαt	lipαt	PROPN
ejpam-2299	252	15	and	and	CCONJ
ejpam-2299	252	16	g	g	PROPN
ejpam-2299	252	17	∈	∈	PROPN
ejpam-2299	252	18	l	l	NOUN
ejpam-2299	252	19	ipαt	ipαt	NOUN
ejpam-2299	252	20	.	.	PUNCT
ejpam-2299	253	1	we	we	PRON
ejpam-2299	253	2	define	define	VERB
ejpam-2299	253	3	d	d	NOUN
ejpam-2299	253	4	as	as	SCONJ
ejpam-2299	253	5	follows	follow	VERB
ejpam-2299	253	6	d	d	NOUN
ejpam-2299	253	7	:	:	PUNCT
ejpam-2299	253	8	a′′→	a′′→	X
ejpam-2299	253	9	a′	a′	NOUN
ejpam-2299	253	10	df(g	df(g	PUNCT
ejpam-2299	253	11	)	)	PUNCT
ejpam-2299	253	12	=	=	PUNCT
ejpam-2299	254	1	+	+	PUNCT
ejpam-2299	254	2	∞∑	∞∑	NUM
ejpam-2299	254	3	n=−∞	n=−∞	NUM
ejpam-2299	254	4	nĝ(n)f̂(n	nĝ(n)f̂(n	NOUN
ejpam-2299	254	5	)	)	PUNCT
ejpam-2299	254	6	.	.	PUNCT
ejpam-2299	255	1	so	so	ADV
ejpam-2299	255	2	d	d	PRON
ejpam-2299	255	3	is	be	AUX
ejpam-2299	255	4	a	a	DET
ejpam-2299	255	5	derivation	derivation	NOUN
ejpam-2299	255	6	which	which	PRON
ejpam-2299	255	7	is	be	AUX
ejpam-2299	255	8	not	not	PART
ejpam-2299	255	9	inner	inner	ADJ
ejpam-2299	255	10	.	.	PUNCT
ejpam-2299	256	1	since	since	SCONJ
ejpam-2299	256	2	(	(	PUNCT
ejpam-2299	256	3	l	l	PROPN
ejpam-2299	256	4	ipαt	ipαt	NOUN
ejpam-2299	256	5	)	)	PUNCT
ejpam-2299	256	6	′′	′′	PROPN
ejpam-2299	256	7	=	=	SYM
ejpam-2299	256	8	lipαt	lipαt	PROPN
ejpam-2299	256	9	,	,	PUNCT
ejpam-2299	256	10	then	then	ADV
ejpam-2299	256	11	for	for	ADP
ejpam-2299	256	12	f	f	PROPN
ejpam-2299	256	13	,	,	PUNCT
ejpam-2299	256	14	g	g	PROPN
ejpam-2299	256	15	∈	∈	PROPN
ejpam-2299	256	16	lipαt	lipαt	PROPN
ejpam-2299	256	17	there	there	PRON
ejpam-2299	256	18	are	be	VERB
ejpam-2299	256	19	(	(	PUNCT
ejpam-2299	256	20	fα)α	fα)α	PROPN
ejpam-2299	256	21	and	and	CCONJ
ejpam-2299	256	22	(	(	PUNCT
ejpam-2299	256	23	gβ)β	gβ)β	PROPN
ejpam-2299	256	24	in	in	ADP
ejpam-2299	256	25	l	l	PROPN
ejpam-2299	256	26	ipαt	ipαt	NOUN
ejpam-2299	257	1	such	such	ADJ
ejpam-2299	257	2	that	that	SCONJ
ejpam-2299	257	3	f	f	PROPN
ejpam-2299	257	4	=	=	SYM
ejpam-2299	257	5	w∗	w∗	PROPN
ejpam-2299	257	6	−	−	PROPN
ejpam-2299	257	7	limα	limα	PROPN
ejpam-2299	257	8	f̂α	f̂α	PROPN
ejpam-2299	257	9	and	and	CCONJ
ejpam-2299	257	10	g	g	PROPN
ejpam-2299	257	11	=	=	PROPN
ejpam-2299	257	12	w∗	w∗	PROPN
ejpam-2299	257	13	−	−	PROPN
ejpam-2299	257	14	limβ	limβ	ADJ
ejpam-2299	257	15	ĝβ	ĝβ	NOUN
ejpam-2299	257	16	.	.	PUNCT
ejpam-2299	258	1	then	then	ADV
ejpam-2299	258	2	we	we	PRON
ejpam-2299	258	3	have	have	VERB
ejpam-2299	258	4	dfα(gβ	dfα(gβ	NOUN
ejpam-2299	258	5	)	)	PUNCT
ejpam-2299	258	6	=	=	PUNCT
ejpam-2299	259	1	+	+	ADP
ejpam-2299	259	2	∞∑	∞∑	NUM
ejpam-2299	259	3	n=−∞	n=−∞	NUM
ejpam-2299	259	4	nĝβ	nĝβ	PROPN
ejpam-2299	259	5	(	(	PUNCT
ejpam-2299	259	6	n	n	CCONJ
ejpam-2299	259	7	)	)	PUNCT
ejpam-2299	259	8	f̂α(−n	f̂α(−n	NOUN
ejpam-2299	259	9	)	)	PUNCT
ejpam-2299	259	10	=	=	PUNCT
ejpam-2299	260	1	+	+	ADJ
ejpam-2299	260	2	∞∑	∞∑	NUM
ejpam-2299	260	3	n=−∞	n=−∞	INTJ
ejpam-2299	260	4	(	(	PUNCT
ejpam-2299	260	5	−n	−n	NOUN
ejpam-2299	260	6	)	)	PUNCT
ejpam-2299	260	7	ĝβ(−n	ĝβ(−n	NOUN
ejpam-2299	260	8	)	)	PUNCT
ejpam-2299	260	9	f̂α(n	f̂α(n	NOUN
ejpam-2299	260	10	)	)	PUNCT
ejpam-2299	261	1	=	=	NOUN
ejpam-2299	261	2	−	−	X
ejpam-2299	261	3	+	+	NOUN
ejpam-2299	261	4	∞∑	∞∑	NUM
ejpam-2299	261	5	n=−∞	n=−∞	NUM
ejpam-2299	261	6	nĝβ	nĝβ	PROPN
ejpam-2299	261	7	(	(	PUNCT
ejpam-2299	261	8	−n	−n	ADV
ejpam-2299	261	9	)	)	PUNCT
ejpam-2299	261	10	·	·	PUNCT
ejpam-2299	261	11	f̂α(n	f̂α(n	NOUN
ejpam-2299	261	12	)	)	PUNCT
ejpam-2299	261	13	=	=	PUNCT
ejpam-2299	261	14	−(dgβ	−(dgβ	NOUN
ejpam-2299	261	15	)	)	PUNCT
ejpam-2299	261	16	(	(	PUNCT
ejpam-2299	261	17	fα	fα	NOUN
ejpam-2299	261	18	)	)	PUNCT
ejpam-2299	261	19	.	.	PUNCT
ejpam-2299	262	1	on	on	ADP
ejpam-2299	262	2	the	the	DET
ejpam-2299	262	3	other	other	ADJ
ejpam-2299	262	4	hand	hand	NOUN
ejpam-2299	262	5	lim	lim	PROPN
ejpam-2299	262	6	β	β	PROPN
ejpam-2299	262	7	lim	lim	PROPN
ejpam-2299	262	8	α	α	PROPN
ejpam-2299	262	9	d	d	X
ejpam-2299	262	10	fα(gβ	fα(gβ	PROPN
ejpam-2299	262	11	)	)	PUNCT
ejpam-2299	263	1	=	=	PROPN
ejpam-2299	263	2	lim	lim	PROPN
ejpam-2299	263	3	β	β	PROPN
ejpam-2299	263	4	df(gβ	df(gβ	PROPN
ejpam-2299	263	5	)	)	PUNCT
ejpam-2299	264	1	=	=	PUNCT
ejpam-2299	264	2	lim	lim	PROPN
ejpam-2299	264	3	β	β	PROPN
ejpam-2299	264	4	ĝβdf	ĝβdf	PROPN
ejpam-2299	265	1	=	=	SYM
ejpam-2299	266	1	g(df	g(df	PROPN
ejpam-2299	266	2	)	)	PUNCT
ejpam-2299	267	1	,	,	PUNCT
ejpam-2299	267	2	lim	lim	PROPN
ejpam-2299	267	3	β	β	PROPN
ejpam-2299	267	4	lim	lim	PROPN
ejpam-2299	267	5	α	α	PROPN
ejpam-2299	267	6	dgβ	dgβ	PROPN
ejpam-2299	267	7	(	(	PUNCT
ejpam-2299	267	8	fα	fα	NOUN
ejpam-2299	267	9	)	)	PUNCT
ejpam-2299	268	1	=	=	SYM
ejpam-2299	269	1	lim	lim	PROPN
ejpam-2299	269	2	α	α	PROPN
ejpam-2299	269	3	lim	lim	PROPN
ejpam-2299	269	4	β	β	PROPN
ejpam-2299	269	5	dgβ	dgβ	PROPN
ejpam-2299	269	6	(	(	PUNCT
ejpam-2299	269	7	fα	fα	NOUN
ejpam-2299	269	8	)	)	PUNCT
ejpam-2299	269	9	=	=	VERB
ejpam-2299	270	1	lim	lim	PROPN
ejpam-2299	270	2	α	α	PROPN
ejpam-2299	270	3	dg	dg	PROPN
ejpam-2299	270	4	(	(	PUNCT
ejpam-2299	270	5	fα	fα	NOUN
ejpam-2299	270	6	)	)	PUNCT
ejpam-2299	270	7	=	=	SYM
ejpam-2299	270	8	f(dg	f(dg	PROPN
ejpam-2299	270	9	)	)	PUNCT
ejpam-2299	270	10	.	.	PUNCT
ejpam-2299	271	1	so	so	ADV
ejpam-2299	271	2	f(dg	f(dg	NOUN
ejpam-2299	271	3	)	)	PUNCT
ejpam-2299	271	4	=	=	PUNCT
ejpam-2299	271	5	−g(df	−g(df	PROPN
ejpam-2299	271	6	)	)	PUNCT
ejpam-2299	271	7	where	where	SCONJ
ejpam-2299	271	8	d	d	NOUN
ejpam-2299	271	9	is	be	AUX
ejpam-2299	271	10	a	a	DET
ejpam-2299	271	11	non	non	ADJ
ejpam-2299	271	12	-	-	ADJ
ejpam-2299	271	13	inner	inner	ADJ
ejpam-2299	271	14	derivation	derivation	NOUN
ejpam-2299	271	15	.	.	PUNCT
ejpam-2299	272	1	s.	s.	PROPN
ejpam-2299	272	2	hosseinioun	hosseinioun	PROPN
ejpam-2299	272	3	,	,	PUNCT
ejpam-2299	272	4	a.	a.	NOUN
ejpam-2299	272	5	valadkhani	valadkhani	PROPN
ejpam-2299	272	6	/	/	SYM
ejpam-2299	272	7	eur	eur	PROPN
ejpam-2299	272	8	.	.	PUNCT
ejpam-2299	273	1	j.	j.	PROPN
ejpam-2299	273	2	pure	pure	PROPN
ejpam-2299	273	3	appl	appl	PROPN
ejpam-2299	273	4	.	.	PROPN
ejpam-2299	273	5	math	math	PROPN
ejpam-2299	273	6	,	,	PUNCT
ejpam-2299	273	7	9	9	NUM
ejpam-2299	273	8	(	(	PUNCT
ejpam-2299	273	9	2016	2016	NUM
ejpam-2299	273	10	)	)	PUNCT
ejpam-2299	273	11	,	,	PUNCT
ejpam-2299	273	12	231	231	NUM
ejpam-2299	273	13	-	-	SYM
ejpam-2299	273	14	239	239	NUM
ejpam-2299	273	15	238	238	NUM
ejpam-2299	273	16	theorem	theorem	NOUN
ejpam-2299	273	17	5	5	NUM
ejpam-2299	273	18	.	.	PUNCT
ejpam-2299	273	19	let	let	VERB
ejpam-2299	273	20	a	a	PRON
ejpam-2299	273	21	be	be	AUX
ejpam-2299	273	22	a	a	DET
ejpam-2299	273	23	unital	unital	ADJ
ejpam-2299	273	24	banach	banach	NOUN
ejpam-2299	273	25	algebra	algebra	NOUN
ejpam-2299	273	26	and	and	CCONJ
ejpam-2299	273	27	a′′	a′′	NOUN
ejpam-2299	273	28	is	be	AUX
ejpam-2299	273	29	commutative	commutative	ADJ
ejpam-2299	273	30	and	and	CCONJ
ejpam-2299	273	31	(	(	PUNCT
ejpam-2299	273	32	-1)-weakly	-1)-weakly	ADV
ejpam-2299	273	33	amenable	amenable	ADJ
ejpam-2299	273	34	.	.	PUNCT
ejpam-2299	274	1	then	then	ADV
ejpam-2299	274	2	z1(a′′	z1(a′′	PROPN
ejpam-2299	274	3	,	,	PUNCT
ejpam-2299	274	4	e	e	NOUN
ejpam-2299	274	5	)	)	PUNCT
ejpam-2299	274	6	=	=	SYM
ejpam-2299	274	7	(	(	PUNCT
ejpam-2299	274	8	0	0	NUM
ejpam-2299	274	9	)	)	PUNCT
ejpam-2299	274	10	,	,	PUNCT
ejpam-2299	274	11	for	for	ADP
ejpam-2299	274	12	each	each	DET
ejpam-2299	274	13	banach	banach	NOUN
ejpam-2299	274	14	a′′-module	a′′-module	NOUN
ejpam-2299	274	15	e.	e.	PROPN
ejpam-2299	274	16	proof	proof	PROPN
ejpam-2299	274	17	.	.	PUNCT
ejpam-2299	275	1	let	let	VERB
ejpam-2299	275	2	e	e	PRON
ejpam-2299	275	3	be	be	AUX
ejpam-2299	275	4	a	a	DET
ejpam-2299	275	5	banach	banach	NOUN
ejpam-2299	275	6	left	leave	VERB
ejpam-2299	275	7	a′′-module	a′′-module	NOUN
ejpam-2299	275	8	and	and	CCONJ
ejpam-2299	275	9	define	define	VERB
ejpam-2299	275	10	x	x	X
ejpam-2299	275	11	·	·	PUNCT
ejpam-2299	275	12	f	f	X
ejpam-2299	276	1	=	=	NOUN
ejpam-2299	276	2	:	:	PUNCT
ejpam-2299	276	3	f	f	X
ejpam-2299	276	4	·	·	PUNCT
ejpam-2299	276	5	x	x	PUNCT
ejpam-2299	276	6	for	for	ADP
ejpam-2299	276	7	each	each	DET
ejpam-2299	276	8	f	f	PROPN
ejpam-2299	276	9	∈	∈	PROPN
ejpam-2299	276	10	a′′	a′′	NOUN
ejpam-2299	276	11	and	and	CCONJ
ejpam-2299	276	12	x	x	PROPN
ejpam-2299	276	13	∈	∈	PROPN
ejpam-2299	276	14	e.	e.	PROPN
ejpam-2299	276	15	then	then	ADV
ejpam-2299	276	16	e	e	PROPN
ejpam-2299	276	17	is	be	AUX
ejpam-2299	276	18	a	a	DET
ejpam-2299	276	19	banach	banach	ADV
ejpam-2299	276	20	right	right	ADJ
ejpam-2299	276	21	a′′-module	a′′-module	NOUN
ejpam-2299	276	22	and	and	CCONJ
ejpam-2299	276	23	commutativity	commutativity	NOUN
ejpam-2299	276	24	of	of	ADP
ejpam-2299	276	25	a′′	a′′	NOUN
ejpam-2299	276	26	implies	imply	VERB
ejpam-2299	276	27	that	that	SCONJ
ejpam-2299	276	28	e	e	NOUN
ejpam-2299	276	29	is	be	AUX
ejpam-2299	276	30	a	a	DET
ejpam-2299	276	31	banach	banach	NOUN
ejpam-2299	276	32	a′′-bimodule	a′′-bimodule	NOUN
ejpam-2299	276	33	(	(	PUNCT
ejpam-2299	276	34	of	of	ADP
ejpam-2299	276	35	course	course	NOUN
ejpam-2299	276	36	e	e	NOUN
ejpam-2299	276	37	is	be	AUX
ejpam-2299	276	38	an	an	DET
ejpam-2299	276	39	a	a	DET
ejpam-2299	276	40	-	-	PUNCT
ejpam-2299	276	41	bimodule	bimodule	NOUN
ejpam-2299	276	42	and	and	CCONJ
ejpam-2299	276	43	e′	e′	NOUN
ejpam-2299	276	44	is	be	AUX
ejpam-2299	276	45	an	an	DET
ejpam-2299	276	46	a′′-bimodule	a′′-bimodule	NOUN
ejpam-2299	276	47	)	)	PUNCT
ejpam-2299	276	48	.	.	PUNCT
ejpam-2299	277	1	let	let	VERB
ejpam-2299	277	2	e	e	PRON
ejpam-2299	277	3	be	be	AUX
ejpam-2299	277	4	the	the	DET
ejpam-2299	277	5	unit	unit	NOUN
ejpam-2299	277	6	element	element	NOUN
ejpam-2299	277	7	in	in	ADP
ejpam-2299	277	8	a	a	PRON
ejpam-2299	277	9	,	,	PUNCT
ejpam-2299	277	10	and	and	CCONJ
ejpam-2299	277	11	let	let	VERB
ejpam-2299	277	12	d	d	PRON
ejpam-2299	277	13	be	be	AUX
ejpam-2299	277	14	a	a	DET
ejpam-2299	277	15	non	non	ADJ
ejpam-2299	277	16	-	-	ADJ
ejpam-2299	277	17	zero	zero	ADJ
ejpam-2299	277	18	derivation	derivation	NOUN
ejpam-2299	277	19	in	in	ADP
ejpam-2299	277	20	z1(a′′	z1(a′′	PROPN
ejpam-2299	277	21	,	,	PUNCT
ejpam-2299	277	22	e	e	NOUN
ejpam-2299	277	23	)	)	PUNCT
ejpam-2299	277	24	.	.	PUNCT
ejpam-2299	278	1	then	then	ADV
ejpam-2299	278	2	for	for	ADP
ejpam-2299	278	3	some	some	DET
ejpam-2299	278	4	f0	f0	PROPN
ejpam-2299	278	5	∈	∈	PROPN
ejpam-2299	278	6	a′′	a′′	NOUN
ejpam-2299	278	7	,	,	PUNCT
ejpam-2299	278	8	we	we	PRON
ejpam-2299	278	9	have	have	AUX
ejpam-2299	278	10	df0	df0	ADJ
ejpam-2299	278	11	6=	6=	NUM
ejpam-2299	278	12	0	0	NUM
ejpam-2299	278	13	,	,	PUNCT
ejpam-2299	278	14	so	so	SCONJ
ejpam-2299	278	15	there	there	PRON
ejpam-2299	278	16	exists	exist	VERB
ejpam-2299	278	17	λ	λ	PROPN
ejpam-2299	278	18	∈	∈	PROPN
ejpam-2299	278	19	e′	e′	NOUN
ejpam-2299	279	1	such	such	ADJ
ejpam-2299	279	2	that	that	SCONJ
ejpam-2299	279	3	λ(df0	λ(df0	NOUN
ejpam-2299	279	4	)	)	PUNCT
ejpam-2299	279	5	=	=	SYM
ejpam-2299	279	6	1	1	X
ejpam-2299	279	7	.	.	X
ejpam-2299	279	8	we	we	PRON
ejpam-2299	279	9	define	define	VERB
ejpam-2299	279	10	r	r	NOUN
ejpam-2299	279	11	:	:	PUNCT
ejpam-2299	279	12	e	e	NOUN
ejpam-2299	279	13	−→a′	−→a′	PROPN
ejpam-2299	279	14	r(x)(a	r(x)(a	NOUN
ejpam-2299	279	15	)	)	PUNCT
ejpam-2299	280	1	=	=	X
ejpam-2299	280	2	λ(â	λ(â	NOUN
ejpam-2299	280	3	·	·	PUNCT
ejpam-2299	280	4	x	x	X
ejpam-2299	280	5	)	)	PUNCT
ejpam-2299	280	6	,	,	PUNCT
ejpam-2299	280	7	(	(	PUNCT
ejpam-2299	280	8	a	a	DET
ejpam-2299	280	9	∈	∈	PROPN
ejpam-2299	280	10	a	a	PRON
ejpam-2299	280	11	,	,	PUNCT
ejpam-2299	280	12	x	x	SYM
ejpam-2299	280	13	∈	∈	NOUN
ejpam-2299	280	14	x	x	X
ejpam-2299	280	15	)	)	PUNCT
ejpam-2299	280	16	.	.	PUNCT
ejpam-2299	281	1	r	r	NOUN
ejpam-2299	281	2	is	be	AUX
ejpam-2299	281	3	a	a	DET
ejpam-2299	281	4	bounded	bounded	ADJ
ejpam-2299	281	5	linear	linear	PROPN
ejpam-2299	281	6	map	map	NOUN
ejpam-2299	281	7	.	.	PUNCT
ejpam-2299	282	1	now	now	ADV
ejpam-2299	282	2	r	r	VERB
ejpam-2299	282	3	◦	◦	NOUN
ejpam-2299	282	4	d	d	NOUN
ejpam-2299	282	5	:	:	PUNCT
ejpam-2299	282	6	a′′	a′′	NOUN
ejpam-2299	282	7	−→	−→	PROPN
ejpam-2299	282	8	a′	a′	PROPN
ejpam-2299	282	9	is	be	AUX
ejpam-2299	282	10	a	a	DET
ejpam-2299	282	11	bounded	bounded	ADJ
ejpam-2299	282	12	derivation	derivation	NOUN
ejpam-2299	282	13	since	since	SCONJ
ejpam-2299	282	14	r	r	NOUN
ejpam-2299	282	15	◦	◦	NOUN
ejpam-2299	282	16	d(f	d(f	NOUN
ejpam-2299	282	17	·	·	PUNCT
ejpam-2299	282	18	g)(a	g)(a	VERB
ejpam-2299	282	19	)	)	PUNCT
ejpam-2299	283	1	=	=	NOUN
ejpam-2299	283	2	r(df	r(df	X
ejpam-2299	283	3	·	·	PUNCT
ejpam-2299	284	1	g	g	PROPN
ejpam-2299	284	2	+	+	CCONJ
ejpam-2299	284	3	f	f	PROPN
ejpam-2299	284	4	·	·	PUNCT
ejpam-2299	284	5	dg)(a	dg)(a	PROPN
ejpam-2299	284	6	)	)	PUNCT
ejpam-2299	285	1	=	=	PUNCT
ejpam-2299	285	2	λ(â	λ(â	NOUN
ejpam-2299	285	3	·	·	PUNCT
ejpam-2299	285	4	(	(	PUNCT
ejpam-2299	285	5	df	df	PROPN
ejpam-2299	285	6	·	·	PUNCT
ejpam-2299	285	7	g	g	NOUN
ejpam-2299	285	8	)	)	PUNCT
ejpam-2299	285	9	+	+	CCONJ
ejpam-2299	285	10	â	â	X
ejpam-2299	285	11	·	·	PUNCT
ejpam-2299	285	12	(	(	PUNCT
ejpam-2299	285	13	f	f	X
ejpam-2299	285	14	·	·	PUNCT
ejpam-2299	285	15	dg	dg	PROPN
ejpam-2299	285	16	)	)	PUNCT
ejpam-2299	285	17	)	)	PUNCT
ejpam-2299	286	1	=	=	NOUN
ejpam-2299	286	2	g	g	NOUN
ejpam-2299	286	3	·	·	SYM
ejpam-2299	286	4	λ(â	λ(â	NOUN
ejpam-2299	286	5	·	·	PUNCT
ejpam-2299	286	6	df	df	NOUN
ejpam-2299	286	7	)	)	PUNCT
ejpam-2299	286	8	+	+	CCONJ
ejpam-2299	286	9	f	f	X
ejpam-2299	286	10	·	·	PUNCT
ejpam-2299	286	11	λ(â	λ(â	NOUN
ejpam-2299	286	12	·	·	PUNCT
ejpam-2299	286	13	dg	dg	NOUN
ejpam-2299	286	14	)	)	PUNCT
ejpam-2299	286	15	.	.	PUNCT
ejpam-2299	287	1	on	on	ADP
ejpam-2299	287	2	the	the	DET
ejpam-2299	287	3	other	other	ADJ
ejpam-2299	287	4	hand	hand	NOUN
ejpam-2299	287	5	for	for	ADP
ejpam-2299	287	6	g	g	NOUN
ejpam-2299	287	7	=	=	SYM
ejpam-2299	287	8	w∗−	w∗−	NOUN
ejpam-2299	287	9	limα	limα	PROPN
ejpam-2299	287	10	b̂α	b̂α	NOUN
ejpam-2299	287	11	and	and	CCONJ
ejpam-2299	287	12	x	x	SYM
ejpam-2299	287	13	∈	∈	PROPN
ejpam-2299	287	14	e	e	NOUN
ejpam-2299	287	15	,	,	PUNCT
ejpam-2299	287	16	the	the	DET
ejpam-2299	287	17	net	net	NOUN
ejpam-2299	287	18	(	(	PUNCT
ejpam-2299	287	19	b̂α	b̂α	PROPN
ejpam-2299	287	20	·	·	PUNCT
ejpam-2299	287	21	x)α	x)α	X
ejpam-2299	287	22	is	be	AUX
ejpam-2299	287	23	a	a	DET
ejpam-2299	287	24	bounded	bounded	ADJ
ejpam-2299	287	25	net	net	NOUN
ejpam-2299	287	26	in	in	ADP
ejpam-2299	287	27	e′′	e′′	PROPN
ejpam-2299	287	28	,	,	PUNCT
ejpam-2299	287	29	so	so	ADV
ejpam-2299	287	30	×bα	×bα	ADJ
ejpam-2299	287	31	·	·	PUNCT
ejpam-2299	287	32	x	x	SYM
ejpam-2299	287	33	w∗	w∗	VERB
ejpam-2299	287	34	−→	−→	NOUN
ejpam-2299	287	35	g	g	PROPN
ejpam-2299	287	36	·	·	PUNCT
ejpam-2299	287	37	x	x	X
ejpam-2299	287	38	,	,	PUNCT
ejpam-2299	287	39	especially	especially	ADV
ejpam-2299	287	40	λ(g	λ(g	NOUN
ejpam-2299	287	41	·	·	PUNCT
ejpam-2299	288	1	x	x	X
ejpam-2299	288	2	)	)	PUNCT
ejpam-2299	288	3	=	=	SYM
ejpam-2299	288	4	limλ	limλ	PROPN
ejpam-2299	288	5	(	(	PUNCT
ejpam-2299	288	6	b̂α	b̂α	NOUN
ejpam-2299	288	7	·	·	PUNCT
ejpam-2299	288	8	x	x	X
ejpam-2299	288	9	)	)	PUNCT
ejpam-2299	288	10	and	and	CCONJ
ejpam-2299	288	11	we	we	PRON
ejpam-2299	288	12	have	have	AUX
ejpam-2299	288	13	(	(	PUNCT
ejpam-2299	288	14	r(df	r(df	NUM
ejpam-2299	288	15	)	)	PUNCT
ejpam-2299	288	16	·	·	PUNCT
ejpam-2299	288	17	g	g	NOUN
ejpam-2299	288	18	)	)	PUNCT
ejpam-2299	288	19	(	(	PUNCT
ejpam-2299	288	20	a	a	X
ejpam-2299	288	21	)	)	PUNCT
ejpam-2299	289	1	=	=	SYM
ejpam-2299	289	2	lim	lim	PROPN
ejpam-2299	289	3	α	α	PROPN
ejpam-2299	289	4	(	(	PUNCT
ejpam-2299	289	5	r(df	r(df	PROPN
ejpam-2299	289	6	)	)	PUNCT
ejpam-2299	289	7	·	·	PUNCT
ejpam-2299	289	8	a)(bα	a)(bα	X
ejpam-2299	289	9	)	)	PUNCT
ejpam-2299	289	10	=	=	SYM
ejpam-2299	289	11	lim	lim	PROPN
ejpam-2299	289	12	α	α	PROPN
ejpam-2299	289	13	r(df)(a	r(df)(a	PROPN
ejpam-2299	289	14	·	·	PUNCT
ejpam-2299	289	15	bα	bα	NOUN
ejpam-2299	289	16	)	)	PUNCT
ejpam-2299	289	17	=	=	SYM
ejpam-2299	290	1	lim	lim	PROPN
ejpam-2299	290	2	α	α	X
ejpam-2299	290	3	λ(ôa	λ(ôa	X
ejpam-2299	290	4	·	·	PUNCT
ejpam-2299	290	5	bα	bα	PROPN
ejpam-2299	290	6	·	·	PUNCT
ejpam-2299	290	7	df	df	NOUN
ejpam-2299	290	8	)	)	PUNCT
ejpam-2299	290	9	=	=	SYM
ejpam-2299	290	10	λ	λ	X
ejpam-2299	290	11	·	·	PUNCT
ejpam-2299	290	12	g(â	g(â	X
ejpam-2299	290	13	·	·	PUNCT
ejpam-2299	290	14	df	df	NOUN
ejpam-2299	290	15	)	)	PUNCT
ejpam-2299	290	16	=	=	SYM
ejpam-2299	291	1	g	g	PROPN
ejpam-2299	291	2	·	·	PUNCT
ejpam-2299	291	3	λ(â	λ(â	NOUN
ejpam-2299	291	4	·	·	PUNCT
ejpam-2299	291	5	df	df	PROPN
ejpam-2299	291	6	)	)	PUNCT
ejpam-2299	291	7	.	.	PUNCT
ejpam-2299	292	1	similarly	similarly	ADV
ejpam-2299	292	2	(	(	PUNCT
ejpam-2299	292	3	f	f	X
ejpam-2299	292	4	·	·	PUNCT
ejpam-2299	292	5	r(dg	r(dg	PROPN
ejpam-2299	292	6	)	)	PUNCT
ejpam-2299	292	7	)	)	PUNCT
ejpam-2299	293	1	(	(	PUNCT
ejpam-2299	293	2	a	a	X
ejpam-2299	293	3	)	)	PUNCT
ejpam-2299	293	4	=	=	SYM
ejpam-2299	293	5	f	f	X
ejpam-2299	293	6	·	·	PUNCT
ejpam-2299	293	7	λ(a	λ(a	PROPN
ejpam-2299	293	8	·	·	SYM
ejpam-2299	293	9	dg	dg	NOUN
ejpam-2299	293	10	)	)	PUNCT
ejpam-2299	293	11	.	.	PUNCT
ejpam-2299	294	1	therefore	therefore	ADV
ejpam-2299	294	2	r	r	NOUN
ejpam-2299	294	3	◦	◦	NOUN
ejpam-2299	294	4	d	d	NOUN
ejpam-2299	294	5	is	be	AUX
ejpam-2299	294	6	a	a	DET
ejpam-2299	294	7	derivation	derivation	NOUN
ejpam-2299	294	8	in	in	ADP
ejpam-2299	294	9	z1(a′′,a′	z1(a′′,a′	NOUN
ejpam-2299	294	10	)	)	PUNCT
ejpam-2299	294	11	.	.	PUNCT
ejpam-2299	295	1	now	now	ADV
ejpam-2299	295	2	,	,	PUNCT
ejpam-2299	295	3	since	since	SCONJ
ejpam-2299	295	4	a′′	a′′	NOUN
ejpam-2299	295	5	is	be	AUX
ejpam-2299	295	6	(	(	PUNCT
ejpam-2299	295	7	-1)-weakly	-1)-weakly	ADV
ejpam-2299	295	8	amenable	amenable	ADJ
ejpam-2299	295	9	and	and	CCONJ
ejpam-2299	295	10	commutative	commutative	ADJ
ejpam-2299	295	11	then	then	ADV
ejpam-2299	295	12	r	r	NOUN
ejpam-2299	295	13	◦	◦	NOUN
ejpam-2299	296	1	d	d	X
ejpam-2299	297	1	=	=	NOUN
ejpam-2299	298	1	0	0	PROPN
ejpam-2299	298	2	.	.	PUNCT
ejpam-2299	299	1	but	but	CCONJ
ejpam-2299	299	2	r	r	NOUN
ejpam-2299	299	3	◦	◦	NOUN
ejpam-2299	299	4	d(f0)(e	d(f0)(e	NOUN
ejpam-2299	299	5	)	)	PUNCT
ejpam-2299	299	6	=	=	SYM
ejpam-2299	299	7	r(df0)(e	r(df0)(e	X
ejpam-2299	299	8	)	)	PUNCT
ejpam-2299	299	9	=	=	SYM
ejpam-2299	300	1	λ(e	λ(e	PROPN
ejpam-2299	300	2	·	·	PUNCT
ejpam-2299	300	3	df0	df0	ADJ
ejpam-2299	300	4	)	)	PUNCT
ejpam-2299	300	5	=	=	SYM
ejpam-2299	300	6	1	1	NUM
ejpam-2299	300	7	,	,	PUNCT
ejpam-2299	300	8	which	which	PRON
ejpam-2299	300	9	is	be	AUX
ejpam-2299	300	10	a	a	DET
ejpam-2299	300	11	contradiction	contradiction	NOUN
ejpam-2299	300	12	.	.	PUNCT
ejpam-2299	301	1	so	so	ADV
ejpam-2299	301	2	d	d	X
ejpam-2299	301	3	=	=	SYM
ejpam-2299	301	4	0	0	PUNCT
ejpam-2299	302	1	and	and	CCONJ
ejpam-2299	302	2	we	we	PRON
ejpam-2299	302	3	have	have	VERB
ejpam-2299	302	4	z1(a′′	z1(a′′	NOUN
ejpam-2299	302	5	,	,	PUNCT
ejpam-2299	302	6	e	e	NOUN
ejpam-2299	302	7	)	)	PUNCT
ejpam-2299	302	8	=	=	SYM
ejpam-2299	302	9	0	0	NUM
ejpam-2299	303	1	now	now	ADV
ejpam-2299	303	2	we	we	PRON
ejpam-2299	303	3	recall	recall	VERB
ejpam-2299	303	4	some	some	DET
ejpam-2299	303	5	theorems	theorem	NOUN
ejpam-2299	303	6	which	which	PRON
ejpam-2299	303	7	are	be	AUX
ejpam-2299	303	8	used	use	VERB
ejpam-2299	303	9	in	in	ADP
ejpam-2299	303	10	the	the	DET
ejpam-2299	303	11	following	follow	VERB
ejpam-2299	303	12	corollaries	corollary	NOUN
ejpam-2299	303	13	.	.	PUNCT
ejpam-2299	304	1	theorem	theorem	VERB
ejpam-2299	304	2	6	6	NUM
ejpam-2299	304	3	.	.	PUNCT
ejpam-2299	304	4	for	for	ADP
ejpam-2299	304	5	a	a	DET
ejpam-2299	304	6	commutative	commutative	ADJ
ejpam-2299	304	7	banach	banach	NOUN
ejpam-2299	304	8	algebra	algebra	NOUN
ejpam-2299	305	1	a	a	PRON
ejpam-2299	305	2	,	,	PUNCT
ejpam-2299	305	3	if	if	SCONJ
ejpam-2299	305	4	a	a	PRON
ejpam-2299	305	5	is	be	AUX
ejpam-2299	305	6	weakly	weakly	ADV
ejpam-2299	305	7	amenable	amenable	ADJ
ejpam-2299	305	8	,	,	PUNCT
ejpam-2299	305	9	then	then	ADV
ejpam-2299	305	10	z1(a	z1(a	NUM
ejpam-2299	305	11	,	,	PUNCT
ejpam-2299	305	12	e	e	NOUN
ejpam-2299	305	13	)	)	PUNCT
ejpam-2299	305	14	=	=	SYM
ejpam-2299	305	15	(	(	PUNCT
ejpam-2299	305	16	0	0	NUM
ejpam-2299	305	17	)	)	PUNCT
ejpam-2299	305	18	for	for	ADP
ejpam-2299	305	19	each	each	DET
ejpam-2299	305	20	banach	banach	NOUN
ejpam-2299	305	21	a	a	DET
ejpam-2299	305	22	-	-	PUNCT
ejpam-2299	305	23	module	module	NOUN
ejpam-2299	305	24	e.	e.	PROPN
ejpam-2299	305	25	theorem	theorem	PROPN
ejpam-2299	305	26	7	7	PROPN
ejpam-2299	305	27	.	.	PUNCT
ejpam-2299	306	1	let	let	VERB
ejpam-2299	306	2	a	a	PRON
ejpam-2299	306	3	be	be	AUX
ejpam-2299	306	4	a	a	DET
ejpam-2299	306	5	commutative	commutative	ADJ
ejpam-2299	306	6	banach	banach	NOUN
ejpam-2299	306	7	algebra	algebra	NOUN
ejpam-2299	306	8	.	.	PUNCT
ejpam-2299	307	1	then	then	ADV
ejpam-2299	307	2	a	a	PRON
ejpam-2299	307	3	is	be	AUX
ejpam-2299	307	4	weakly	weakly	ADV
ejpam-2299	307	5	amenable	amenable	ADJ
ejpam-2299	307	6	if	if	SCONJ
ejpam-2299	307	7	and	and	CCONJ
ejpam-2299	307	8	only	only	ADV
ejpam-2299	307	9	if	if	SCONJ
ejpam-2299	307	10	a	a	DET
ejpam-2299	307	11	#	#	NOUN
ejpam-2299	307	12	is	be	AUX
ejpam-2299	307	13	weakly	weakly	ADV
ejpam-2299	307	14	amenable	amenable	ADJ
ejpam-2299	307	15	.	.	PUNCT
ejpam-2299	308	1	see	see	VERB
ejpam-2299	308	2	[	[	X
ejpam-2299	308	3	2	2	X
ejpam-2299	308	4	]	]	PUNCT
ejpam-2299	308	5	and	and	CCONJ
ejpam-2299	308	6	[	[	X
ejpam-2299	308	7	4	4	X
ejpam-2299	308	8	]	]	PUNCT
ejpam-2299	308	9	for	for	ADP
ejpam-2299	308	10	proofs	proof	NOUN
ejpam-2299	308	11	of	of	ADP
ejpam-2299	308	12	theorems	theorem	NOUN
ejpam-2299	308	13	6	6	NUM
ejpam-2299	308	14	and	and	CCONJ
ejpam-2299	308	15	7	7	NUM
ejpam-2299	308	16	,	,	PUNCT
ejpam-2299	308	17	respectively	respectively	ADV
ejpam-2299	308	18	.	.	PUNCT
ejpam-2299	309	1	corollary	corollary	ADJ
ejpam-2299	309	2	2	2	NUM
ejpam-2299	309	3	.	.	PUNCT
ejpam-2299	310	1	let	let	VERB
ejpam-2299	310	2	a	a	DET
ejpam-2299	310	3	be	be	AUX
ejpam-2299	310	4	an	an	DET
ejpam-2299	310	5	arens	aren	NOUN
ejpam-2299	310	6	regular	regular	ADJ
ejpam-2299	310	7	commutative	commutative	ADJ
ejpam-2299	310	8	banach	banach	NOUN
ejpam-2299	310	9	algebra	algebra	NOUN
ejpam-2299	310	10	.	.	PUNCT
ejpam-2299	311	1	then	then	ADV
ejpam-2299	311	2	a#′′	a#′′	PROPN
ejpam-2299	311	3	is	be	AUX
ejpam-2299	311	4	(	(	PUNCT
ejpam-2299	311	5	-1)-weakly	-1)-weakly	ADV
ejpam-2299	311	6	amenable	amenable	ADJ
ejpam-2299	311	7	if	if	SCONJ
ejpam-2299	311	8	and	and	CCONJ
ejpam-2299	311	9	only	only	ADV
ejpam-2299	311	10	if	if	SCONJ
ejpam-2299	311	11	a′′	a′′	NOUN
ejpam-2299	311	12	is	be	AUX
ejpam-2299	311	13	weakly	weakly	ADV
ejpam-2299	311	14	amenable	amenable	ADJ
ejpam-2299	311	15	.	.	PUNCT
ejpam-2299	312	1	proof	proof	NOUN
ejpam-2299	312	2	.	.	PUNCT
ejpam-2299	313	1	let	let	VERB
ejpam-2299	313	2	a′′	a′′	NOUN
ejpam-2299	313	3	be	be	AUX
ejpam-2299	313	4	weakly	weakly	ADV
ejpam-2299	313	5	amenable	amenable	ADJ
ejpam-2299	313	6	then	then	ADV
ejpam-2299	313	7	by	by	ADP
ejpam-2299	313	8	theorem	theorem	NOUN
ejpam-2299	313	9	7	7	NUM
ejpam-2299	313	10	,	,	PUNCT
ejpam-2299	313	11	a	a	DET
ejpam-2299	313	12	#	#	NOUN
ejpam-2299	313	13	is	be	AUX
ejpam-2299	313	14	weakly	weakly	ADV
ejpam-2299	313	15	amenable	amenable	ADJ
ejpam-2299	313	16	.	.	PUNCT
ejpam-2299	314	1	since	since	SCONJ
ejpam-2299	314	2	a	a	PRON
ejpam-2299	314	3	is	be	AUX
ejpam-2299	314	4	arens	aren	NOUN
ejpam-2299	314	5	regular	regular	ADJ
ejpam-2299	314	6	then	then	ADV
ejpam-2299	314	7	by	by	ADP
ejpam-2299	314	8	lemma	lemma	PROPN
ejpam-2299	314	9	1	1	NUM
ejpam-2299	314	10	,	,	PUNCT
ejpam-2299	314	11	a#′	a#′	PROPN
ejpam-2299	314	12	is	be	AUX
ejpam-2299	314	13	a	a	DET
ejpam-2299	314	14	banach	banach	NOUN
ejpam-2299	314	15	a#′′-bimodul	a#′′-bimodul	NOUN
ejpam-2299	314	16	,	,	PUNCT
ejpam-2299	314	17	so	so	SCONJ
ejpam-2299	314	18	h1(a#′′,a#′	h1(a#′′,a#′	PROPN
ejpam-2299	314	19	)	)	PUNCT
ejpam-2299	314	20	=	=	SYM
ejpam-2299	314	21	{	{	PUNCT
ejpam-2299	314	22	0	0	NUM
ejpam-2299	314	23	}	}	PUNCT
ejpam-2299	314	24	.	.	PUNCT
ejpam-2299	315	1	for	for	ADP
ejpam-2299	315	2	the	the	DET
ejpam-2299	315	3	converse	converse	NOUN
ejpam-2299	315	4	,	,	PUNCT
ejpam-2299	315	5	let	let	VERB
ejpam-2299	315	6	a#′′	a#′′	PROPN
ejpam-2299	315	7	is	be	AUX
ejpam-2299	315	8	(	(	PUNCT
ejpam-2299	315	9	-1)-weakly	-1)-weakly	ADV
ejpam-2299	315	10	amenable	amenable	ADJ
ejpam-2299	315	11	.	.	PUNCT
ejpam-2299	316	1	using	use	VERB
ejpam-2299	316	2	theorem	theorem	NOUN
ejpam-2299	316	3	5	5	NUM
ejpam-2299	316	4	,	,	PUNCT
ejpam-2299	316	5	a#′′	a#′′	NOUN
ejpam-2299	316	6	is	be	AUX
ejpam-2299	316	7	weakly	weakly	ADV
ejpam-2299	316	8	amenable	amenable	ADJ
ejpam-2299	316	9	,	,	PUNCT
ejpam-2299	316	10	so	so	ADV
ejpam-2299	316	11	by	by	ADP
ejpam-2299	316	12	theorem	theorem	NOUN
ejpam-2299	316	13	7	7	NUM
ejpam-2299	316	14	,	,	PUNCT
ejpam-2299	316	15	a′′	a′′	NOUN
ejpam-2299	316	16	is	be	AUX
ejpam-2299	316	17	weakly	weakly	ADV
ejpam-2299	316	18	amenable	amenable	ADJ
ejpam-2299	316	19	.	.	PUNCT
ejpam-2299	317	1	references	reference	NOUN
ejpam-2299	317	2	239	239	NUM
ejpam-2299	317	3	corollary	corollary	ADJ
ejpam-2299	317	4	3	3	NUM
ejpam-2299	317	5	.	.	PUNCT
ejpam-2299	318	1	let	let	VERB
ejpam-2299	318	2	a	a	PRON
ejpam-2299	318	3	be	be	AUX
ejpam-2299	318	4	a	a	DET
ejpam-2299	318	5	banach	banach	NOUN
ejpam-2299	318	6	algebra	algebra	NOUN
ejpam-2299	318	7	and	and	CCONJ
ejpam-2299	318	8	a′′	a′′	NOUN
ejpam-2299	318	9	be	be	AUX
ejpam-2299	318	10	commutative	commutative	ADJ
ejpam-2299	318	11	and	and	CCONJ
ejpam-2299	318	12	(	(	PUNCT
ejpam-2299	318	13	-1)-weakly	-1)-weakly	ADV
ejpam-2299	318	14	amenable	amenable	ADJ
ejpam-2299	318	15	,	,	PUNCT
ejpam-2299	318	16	for	for	ADP
ejpam-2299	318	17	which	which	PRON
ejpam-2299	318	18	a′′	a′′	NOUN
ejpam-2299	318	19	·	·	PUNCT
ejpam-2299	318	20	a=	a=	PROPN
ejpam-2299	318	21	a′′.	a′′.	PROPN
ejpam-2299	318	22	then	then	ADV
ejpam-2299	318	23	a′′	a′′	PROPN
ejpam-2299	318	24	is	be	AUX
ejpam-2299	318	25	(	(	PUNCT
ejpam-2299	318	26	-1)-weakly	-1)-weakly	ADV
ejpam-2299	318	27	amenable	amenable	ADJ
ejpam-2299	318	28	if	if	SCONJ
ejpam-2299	318	29	and	and	CCONJ
ejpam-2299	318	30	only	only	ADV
ejpam-2299	318	31	if	if	SCONJ
ejpam-2299	318	32	a#′′	a#′′	NOUN
ejpam-2299	318	33	is	be	AUX
ejpam-2299	318	34	(	(	PUNCT
ejpam-2299	318	35	-1)-weakly	-1)-weakly	ADV
ejpam-2299	318	36	amenable	amenable	ADJ
ejpam-2299	318	37	.	.	PUNCT
ejpam-2299	319	1	proof	proof	NOUN
ejpam-2299	319	2	.	.	PUNCT
ejpam-2299	320	1	if	if	SCONJ
ejpam-2299	320	2	a′′	a′′	NOUN
ejpam-2299	320	3	is	be	AUX
ejpam-2299	320	4	commutative	commutative	ADJ
ejpam-2299	320	5	and	and	CCONJ
ejpam-2299	320	6	(	(	PUNCT
ejpam-2299	320	7	-1)-weakly	-1)-weakly	ADV
ejpam-2299	320	8	amenable	amenable	ADJ
ejpam-2299	320	9	,	,	PUNCT
ejpam-2299	320	10	and	and	CCONJ
ejpam-2299	320	11	also	also	ADV
ejpam-2299	320	12	a′′	a′′	NOUN
ejpam-2299	320	13	·	·	SYM
ejpam-2299	321	1	a=	a=	PROPN
ejpam-2299	322	1	a′′	a′′	NOUN
ejpam-2299	323	1	then	then	ADV
ejpam-2299	323	2	it	it	PRON
ejpam-2299	323	3	is	be	AUX
ejpam-2299	323	4	proved	prove	VERB
ejpam-2299	323	5	that	that	SCONJ
ejpam-2299	323	6	z1(a′′	z1(a′′	NOUN
ejpam-2299	323	7	,	,	PUNCT
ejpam-2299	323	8	e	e	NOUN
ejpam-2299	323	9	)	)	PUNCT
ejpam-2299	323	10	=	=	SYM
ejpam-2299	323	11	0	0	NUM
ejpam-2299	323	12	for	for	ADP
ejpam-2299	323	13	each	each	DET
ejpam-2299	323	14	banach	banach	NOUN
ejpam-2299	323	15	a′′-module	a′′-module	NOUN
ejpam-2299	323	16	e.	e.	PROPN
ejpam-2299	323	17	now	now	ADV
ejpam-2299	323	18	use	use	VERB
ejpam-2299	323	19	theorems	theorem	NOUN
ejpam-2299	323	20	6	6	NUM
ejpam-2299	323	21	and	and	CCONJ
ejpam-2299	323	22	7	7	NUM
ejpam-2299	323	23	.	.	NUM
ejpam-2299	323	24	references	reference	NOUN
ejpam-2299	323	25	[	[	X
ejpam-2299	323	26	1	1	NUM
ejpam-2299	323	27	]	]	PUNCT
ejpam-2299	323	28	f.	f.	PROPN
ejpam-2299	323	29	e.	e.	PROPN
ejpam-2299	323	30	alexander	alexander	PROPN
ejpam-2299	323	31	.	.	PUNCT
ejpam-2299	324	1	some	some	DET
ejpam-2299	324	2	algebraic	algebraic	ADJ
ejpam-2299	324	3	properties	property	NOUN
ejpam-2299	324	4	of	of	ADP
ejpam-2299	324	5	f(x	f(x	PROPN
ejpam-2299	324	6	)	)	PUNCT
ejpam-2299	324	7	and	and	CCONJ
ejpam-2299	324	8	k(x	k(x	PROPN
ejpam-2299	324	9	)	)	PUNCT
ejpam-2299	324	10	,	,	PUNCT
ejpam-2299	324	11	proceedings	proceeding	NOUN
ejpam-2299	324	12	of	of	ADP
ejpam-2299	324	13	the	the	DET
ejpam-2299	324	14	edinburgh	edinburgh	PROPN
ejpam-2299	324	15	mathematical	mathematical	PROPN
ejpam-2299	324	16	society	society	PROPN
ejpam-2299	324	17	,	,	PUNCT
ejpam-2299	324	18	19	19	NUM
ejpam-2299	324	19	,	,	PUNCT
ejpam-2299	324	20	353–361	353–361	NUM
ejpam-2299	324	21	.	.	PUNCT
ejpam-2299	324	22	1975	1975	NUM
ejpam-2299	324	23	.	.	PUNCT
ejpam-2299	325	1	[	[	X
ejpam-2299	325	2	2	2	X
ejpam-2299	325	3	]	]	PUNCT
ejpam-2299	325	4	w.	w.	PROPN
ejpam-2299	325	5	g.	g.	PROPN
ejpam-2299	325	6	bade	bade	PROPN
ejpam-2299	325	7	,	,	PUNCT
ejpam-2299	325	8	p.	p.	PROPN
ejpam-2299	325	9	c.	c.	PROPN
ejpam-2299	325	10	curtis	curtis	PROPN
ejpam-2299	325	11	,	,	PUNCT
ejpam-2299	325	12	and	and	CCONJ
ejpam-2299	325	13	h.	h.	PROPN
ejpam-2299	325	14	g.	g.	PROPN
ejpam-2299	325	15	dales	dales	PROPN
ejpam-2299	325	16	.	.	PUNCT
ejpam-2299	326	1	amenability	amenability	NOUN
ejpam-2299	326	2	and	and	CCONJ
ejpam-2299	326	3	weak	weak	ADJ
ejpam-2299	326	4	amenability	amenability	NOUN
ejpam-2299	326	5	for	for	ADP
ejpam-2299	326	6	beurling	beurling	NOUN
ejpam-2299	326	7	and	and	CCONJ
ejpam-2299	326	8	lipschits	lipschit	NOUN
ejpam-2299	326	9	algebra	algebra	NOUN
ejpam-2299	326	10	,	,	PUNCT
ejpam-2299	326	11	proceedings	proceeding	NOUN
ejpam-2299	326	12	of	of	ADP
ejpam-2299	326	13	the	the	DET
ejpam-2299	326	14	london	london	PROPN
ejpam-2299	326	15	mathematical	mathematical	ADJ
ejpam-2299	326	16	society	society	NOUN
ejpam-2299	326	17	,	,	PUNCT
ejpam-2299	326	18	3(55	3(55	NUM
ejpam-2299	326	19	)	)	PUNCT
ejpam-2299	326	20	,	,	PUNCT
ejpam-2299	326	21	359–377	359–377	NUM
ejpam-2299	326	22	.	.	PUNCT
ejpam-2299	326	23	1987	1987	NUM
ejpam-2299	326	24	.	.	PUNCT
ejpam-2299	327	1	[	[	X
ejpam-2299	327	2	3	3	NUM
ejpam-2299	327	3	]	]	PUNCT
ejpam-2299	327	4	m.	m.	NOUN
ejpam-2299	327	5	c.	c.	PROPN
ejpam-2299	327	6	f.	f.	PROPN
ejpam-2299	327	7	berglund	berglund	PROPN
ejpam-2299	327	8	.	.	PUNCT
ejpam-2299	327	9	ideal	ideal	PROPN
ejpam-2299	327	10	c∗-algebras	c∗-algebras	PROPN
ejpam-2299	327	11	,	,	PUNCT
ejpam-2299	327	12	duke	duke	PROPN
ejpam-2299	327	13	mathematical	mathematical	PROPN
ejpam-2299	327	14	journal	journal	PROPN
ejpam-2299	327	15	,	,	PUNCT
ejpam-2299	327	16	40	40	NUM
ejpam-2299	327	17	,	,	PUNCT
ejpam-2299	327	18	241–257	241–257	NUM
ejpam-2299	327	19	.	.	NOUN
ejpam-2299	327	20	1973	1973	NUM
ejpam-2299	327	21	.	.	PUNCT
ejpam-2299	328	1	[	[	X
ejpam-2299	328	2	4	4	X
ejpam-2299	328	3	]	]	PUNCT
ejpam-2299	328	4	h.	h.	PROPN
ejpam-2299	328	5	g.	g.	PROPN
ejpam-2299	328	6	dales	dales	PROPN
ejpam-2299	328	7	.	.	PUNCT
ejpam-2299	329	1	banach	banach	NOUN
ejpam-2299	329	2	algebra	algebra	NOUN
ejpam-2299	329	3	and	and	CCONJ
ejpam-2299	329	4	automatic	automatic	ADJ
ejpam-2299	329	5	continuity	continuity	NOUN
ejpam-2299	329	6	,	,	PUNCT
ejpam-2299	329	7	oxford	oxford	PROPN
ejpam-2299	329	8	university	university	PROPN
ejpam-2299	329	9	press	press	NOUN
ejpam-2299	329	10	,	,	PUNCT
ejpam-2299	329	11	2000	2000	NUM
ejpam-2299	329	12	.	.	PUNCT
ejpam-2299	330	1	[	[	X
ejpam-2299	330	2	5	5	X
ejpam-2299	330	3	]	]	PUNCT
ejpam-2299	330	4	h.	h.	PROPN
ejpam-2299	330	5	g.	g.	PROPN
ejpam-2299	330	6	dales	dales	PROPN
ejpam-2299	330	7	,	,	PUNCT
ejpam-2299	330	8	a.	a.	NOUN
ejpam-2299	330	9	rodriguez	rodriguez	NOUN
ejpam-2299	330	10	-	-	PUNCT
ejpam-2299	330	11	palacios	palacio	NOUN
ejpam-2299	330	12	,	,	PUNCT
ejpam-2299	330	13	and	and	CCONJ
ejpam-2299	330	14	m.	m.	NOUN
ejpam-2299	330	15	v.	v.	PROPN
ejpam-2299	330	16	velasco	velasco	PROPN
ejpam-2299	330	17	.	.	PUNCT
ejpam-2299	331	1	the	the	DET
ejpam-2299	331	2	second	second	ADJ
ejpam-2299	331	3	transpose	transpose	NOUN
ejpam-2299	331	4	of	of	ADP
ejpam-2299	331	5	a	a	DET
ejpam-2299	331	6	derivation	derivation	NOUN
ejpam-2299	331	7	,	,	PUNCT
ejpam-2299	331	8	journal	journal	NOUN
ejpam-2299	331	9	of	of	ADP
ejpam-2299	331	10	the	the	DET
ejpam-2299	331	11	london	london	PROPN
ejpam-2299	331	12	mathematical	mathematical	ADJ
ejpam-2299	331	13	society	society	NOUN
ejpam-2299	331	14	,	,	PUNCT
ejpam-2299	331	15	2(64	2(64	NUM
ejpam-2299	331	16	)	)	PUNCT
ejpam-2299	331	17	,	,	PUNCT
ejpam-2299	331	18	707–721	707–721	NUM
ejpam-2299	331	19	.	.	PUNCT
ejpam-2299	331	20	2001	2001	NUM
ejpam-2299	331	21	.	.	PUNCT
ejpam-2299	332	1	[	[	X
ejpam-2299	332	2	6	6	NUM
ejpam-2299	332	3	]	]	PUNCT
ejpam-2299	332	4	j.	j.	PROPN
ejpam-2299	332	5	duncan	duncan	PROPN
ejpam-2299	332	6	and	and	CCONJ
ejpam-2299	332	7	s.	s.	PROPN
ejpam-2299	332	8	a.	a.	PROPN
ejpam-2299	332	9	hosseiniun	hosseiniun	PROPN
ejpam-2299	332	10	,	,	PUNCT
ejpam-2299	332	11	the	the	DET
ejpam-2299	332	12	second	second	ADJ
ejpam-2299	332	13	dual	dual	ADJ
ejpam-2299	332	14	of	of	ADP
ejpam-2299	332	15	banach	banach	NOUN
ejpam-2299	332	16	algeba	algeba	NOUN
ejpam-2299	332	17	.	.	PUNCT
ejpam-2299	333	1	proceedings	proceeding	NOUN
ejpam-2299	333	2	of	of	ADP
ejpam-2299	333	3	the	the	DET
ejpam-2299	333	4	royal	royal	ADJ
ejpam-2299	333	5	society	society	NOUN
ejpam-2299	333	6	of	of	ADP
ejpam-2299	333	7	edinburgh	edinburgh	PROPN
ejpam-2299	333	8	,	,	PUNCT
ejpam-2299	333	9	section	section	NOUN
ejpam-2299	333	10	a	a	PRON
ejpam-2299	333	11	,	,	PUNCT
ejpam-2299	333	12	84	84	NUM
ejpam-2299	333	13	,	,	PUNCT
ejpam-2299	333	14	309–325	309–325	NUM
ejpam-2299	333	15	.	.	PUNCT
ejpam-2299	333	16	1979	1979	NUM
ejpam-2299	333	17	.	.	PUNCT
ejpam-2299	334	1	[	[	X
ejpam-2299	334	2	7	7	X
ejpam-2299	334	3	]	]	X
ejpam-2299	334	4	m.	m.	PROPN
ejpam-2299	334	5	eshaghi	eshaghi	PROPN
ejpam-2299	334	6	,	,	PUNCT
ejpam-2299	334	7	s.	s.	PROPN
ejpam-2299	334	8	a.	a.	PROPN
ejpam-2299	334	9	r.	r.	PROPN
ejpam-2299	334	10	hosseinioun	hosseinioun	PROPN
ejpam-2299	334	11	,	,	PUNCT
ejpam-2299	334	12	and	and	CCONJ
ejpam-2299	334	13	a.	a.	NOUN
ejpam-2299	334	14	valadkhani	valadkhani	PROPN
ejpam-2299	334	15	.	.	PUNCT
ejpam-2299	335	1	on	on	ADP
ejpam-2299	335	2	(	(	PUNCT
ejpam-2299	335	3	-1)-weak	-1)-weak	INTJ
ejpam-2299	335	4	amenability	amenability	NOUN
ejpam-2299	335	5	of	of	ADP
ejpam-2299	335	6	banach	banach	NOUN
ejpam-2299	335	7	algebras	algebra	NOUN
ejpam-2299	335	8	,	,	PUNCT
ejpam-2299	335	9	mathematical	mathematical	ADJ
ejpam-2299	335	10	reports	report	NOUN
ejpam-2299	335	11	,	,	PUNCT
ejpam-2299	335	12	15(3	15(3	NUM
ejpam-2299	335	13	)	)	PUNCT
ejpam-2299	335	14	,	,	PUNCT
ejpam-2299	335	15	271–279	271–279	NUM
ejpam-2299	335	16	.	.	PUNCT
ejpam-2299	335	17	2013	2013	NUM
ejpam-2299	335	18	.	.	PUNCT
ejpam-2299	336	1	[	[	X
ejpam-2299	336	2	8	8	NUM
ejpam-2299	336	3	]	]	X
ejpam-2299	336	4	b.	b.	PROPN
ejpam-2299	336	5	e.	e.	PROPN
ejpam-2299	336	6	johnson	johnson	PROPN
ejpam-2299	336	7	.	.	PUNCT
ejpam-2299	337	1	cohomology	cohomology	PROPN
ejpam-2299	337	2	in	in	ADP
ejpam-2299	337	3	banach	banach	NOUN
ejpam-2299	337	4	algebras	algebra	NOUN
ejpam-2299	337	5	,	,	PUNCT
ejpam-2299	337	6	memoirs	memoir	NOUN
ejpam-2299	337	7	of	of	ADP
ejpam-2299	337	8	the	the	DET
ejpam-2299	337	9	american	american	PROPN
ejpam-2299	337	10	mathematical	mathematical	PROPN
ejpam-2299	337	11	society	society	NOUN
ejpam-2299	337	12	,	,	PUNCT
ejpam-2299	337	13	127	127	NUM
ejpam-2299	337	14	,	,	PUNCT
ejpam-2299	337	15	96	96	NUM
ejpam-2299	337	16	.	.	NOUN
ejpam-2299	337	17	1972	1972	NUM
ejpam-2299	337	18	.	.	PUNCT
ejpam-2299	338	1	[	[	X
ejpam-2299	338	2	9	9	NUM
ejpam-2299	338	3	]	]	PUNCT
ejpam-2299	338	4	b.	b.	PROPN
ejpam-2299	338	5	e.	e.	PROPN
ejpam-2299	338	6	johnson	johnson	PROPN
ejpam-2299	338	7	.	.	PUNCT
ejpam-2299	339	1	weak	weak	ADJ
ejpam-2299	339	2	amenability	amenability	NOUN
ejpam-2299	339	3	of	of	ADP
ejpam-2299	339	4	group	group	NOUN
ejpam-2299	339	5	algebras	algebra	NOUN
ejpam-2299	339	6	,	,	PUNCT
ejpam-2299	339	7	bulletin	bulletin	NOUN
ejpam-2299	339	8	of	of	ADP
ejpam-2299	339	9	the	the	DET
ejpam-2299	339	10	london	london	PROPN
ejpam-2299	339	11	mathematical	mathematical	ADJ
ejpam-2299	339	12	society	society	NOUN
ejpam-2299	339	13	,	,	PUNCT
ejpam-2299	339	14	23	23	NUM
ejpam-2299	339	15	,	,	PUNCT
ejpam-2299	339	16	281–284	281–284	NUM
ejpam-2299	339	17	.	.	NOUN
ejpam-2299	339	18	1991	1991	NUM
ejpam-2299	339	19	.	.	PUNCT
ejpam-2299	340	1	[	[	X
ejpam-2299	340	2	10	10	NUM
ejpam-2299	340	3	]	]	X
ejpam-2299	340	4	a.	a.	NOUN
ejpam-2299	340	5	medghalchi	medghalchi	PROPN
ejpam-2299	340	6	and	and	CCONJ
ejpam-2299	340	7	t.	t.	PROPN
ejpam-2299	340	8	yazdanpanah	yazdanpanah	PROPN
ejpam-2299	340	9	.	.	PUNCT
ejpam-2299	341	1	problems	problem	NOUN
ejpam-2299	341	2	concerning	concern	VERB
ejpam-2299	341	3	n	n	CCONJ
ejpam-2299	341	4	-	-	PUNCT
ejpam-2299	341	5	weak	weak	ADJ
ejpam-2299	341	6	amenability	amenability	NOUN
ejpam-2299	341	7	of	of	ADP
ejpam-2299	341	8	banach	banach	NOUN
ejpam-2299	341	9	algebras	algebra	NOUN
ejpam-2299	341	10	,	,	PUNCT
ejpam-2299	341	11	czechoslovak	czechoslovak	ADJ
ejpam-2299	341	12	mathematical	mathematical	ADJ
ejpam-2299	341	13	journal	journal	NOUN
ejpam-2299	341	14	,	,	PUNCT
ejpam-2299	341	15	55(4	55(4	PROPN
ejpam-2299	341	16	)	)	PUNCT
ejpam-2299	341	17	,	,	PUNCT
ejpam-2299	341	18	863–876	863–876	NUM
ejpam-2299	341	19	.	.	PUNCT
ejpam-2299	341	20	2005	2005	NUM
ejpam-2299	341	21	.	.	PUNCT
ejpam-2299	342	1	[	[	X
ejpam-2299	342	2	11	11	NUM
ejpam-2299	342	3	]	]	PUNCT
ejpam-2299	342	4	s.	s.	PROPN
ejpam-2299	342	5	watanabe	watanabe	PROPN
ejpam-2299	342	6	.	.	PUNCT
ejpam-2299	343	1	a	a	DET
ejpam-2299	343	2	banach	banach	NOUN
ejpam-2299	343	3	algebra	algebra	NOUN
ejpam-2299	343	4	which	which	PRON
ejpam-2299	343	5	is	be	AUX
ejpam-2299	343	6	an	an	DET
ejpam-2299	343	7	ideal	ideal	NOUN
ejpam-2299	343	8	in	in	ADP
ejpam-2299	343	9	the	the	DET
ejpam-2299	343	10	second	second	ADJ
ejpam-2299	343	11	dual	dual	ADJ
ejpam-2299	343	12	space	space	NOUN
ejpam-2299	343	13	,	,	PUNCT
ejpam-2299	343	14	science	science	NOUN
ejpam-2299	343	15	reports	report	NOUN
ejpam-2299	343	16	of	of	ADP
ejpam-2299	343	17	niigata	niigata	PROPN
ejpam-2299	343	18	university	university	PROPN
ejpam-2299	343	19	,	,	PUNCT
ejpam-2299	343	20	series	series	NOUN
ejpam-2299	343	21	a	a	NOUN
ejpam-2299	343	22	,	,	PUNCT
ejpam-2299	343	23	11	11	NUM
ejpam-2299	343	24	,	,	PUNCT
ejpam-2299	343	25	95–101	95–101	NUM
ejpam-2299	343	26	.	.	PUNCT
ejpam-2299	343	27	1974	1974	NUM
ejpam-2299	343	28	.	.	PUNCT
ejpam-2299	344	1	[	[	X
ejpam-2299	344	2	12	12	NUM
ejpam-2299	344	3	]	]	X
ejpam-2299	344	4	s.	s.	PROPN
ejpam-2299	344	5	watanabe	watanabe	PROPN
ejpam-2299	344	6	.	.	PUNCT
ejpam-2299	345	1	a	a	DET
ejpam-2299	345	2	banach	banach	NOUN
ejpam-2299	345	3	algebra	algebra	NOUN
ejpam-2299	345	4	which	which	PRON
ejpam-2299	345	5	is	be	AUX
ejpam-2299	345	6	an	an	DET
ejpam-2299	345	7	ideal	ideal	NOUN
ejpam-2299	345	8	in	in	ADP
ejpam-2299	345	9	the	the	DET
ejpam-2299	345	10	second	second	ADJ
ejpam-2299	345	11	dual	dual	ADJ
ejpam-2299	345	12	space	space	NOUN
ejpam-2299	345	13	ii	ii	PROPN
ejpam-2299	345	14	,	,	PUNCT
ejpam-2299	345	15	science	science	NOUN
ejpam-2299	345	16	reports	report	NOUN
ejpam-2299	345	17	of	of	ADP
ejpam-2299	345	18	niigata	niigata	PROPN
ejpam-2299	345	19	university	university	PROPN
ejpam-2299	345	20	,	,	PUNCT
ejpam-2299	345	21	series	series	NOUN
ejpam-2299	345	22	a	a	NOUN
ejpam-2299	345	23	,	,	PUNCT
ejpam-2299	345	24	13	13	NUM
ejpam-2299	345	25	,	,	PUNCT
ejpam-2299	345	26	43–48	43–48	NUM
ejpam-2299	345	27	.	.	PUNCT
ejpam-2299	345	28	1976	1976	NUM
ejpam-2299	345	29	.	.	PUNCT
ejpam-2299	346	1	[	[	X
ejpam-2299	346	2	13	13	NUM
ejpam-2299	346	3	]	]	PUNCT
ejpam-2299	346	4	p.	p.	PROPN
ejpam-2299	346	5	k.	k.	PROPN
ejpam-2299	346	6	wong	wong	PROPN
ejpam-2299	346	7	.	.	PUNCT
ejpam-2299	347	1	on	on	ADP
ejpam-2299	347	2	the	the	DET
ejpam-2299	347	3	arens	aren	NOUN
ejpam-2299	347	4	product	product	NOUN
ejpam-2299	347	5	and	and	CCONJ
ejpam-2299	347	6	certain	certain	ADJ
ejpam-2299	347	7	banach	banach	NOUN
ejpam-2299	347	8	algebras	algebra	NOUN
ejpam-2299	347	9	,	,	PUNCT
ejpam-2299	347	10	transactions	transaction	NOUN
ejpam-2299	347	11	of	of	ADP
ejpam-2299	347	12	the	the	DET
ejpam-2299	347	13	american	american	PROPN
ejpam-2299	347	14	mathematical	mathematical	PROPN
ejpam-2299	347	15	society	society	NOUN
ejpam-2299	347	16	,	,	PUNCT
ejpam-2299	347	17	37	37	NUM
ejpam-2299	347	18	,	,	PUNCT
ejpam-2299	347	19	111–113	111–113	NUM
ejpam-2299	347	20	.	.	NOUN
ejpam-2299	347	21	1973	1973	NUM
ejpam-2299	347	22	.	.	PUNCT