On null sequences for Banach operator ideals, trace duality and approximation properties

Let A be a Banach operator ideal and X be a Banach space. We undertake the study of the vector space of A-null sequences of Carl and Stephani on X, c0,A(X), from a unified point of view after we introduce a norm which makes it a Banach space. To give accurate results we consider local versions of th...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autor principal:	Lassalle, Silvia Beatriz
Publicado:	2017
Materias:	46B45; Secondary: 46B28 46B50 approximation properties compact sets null sequences Operator ideals Primary: 46B04
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0025584X_v290_n14-15_p2308_Lassalle http://hdl.handle.net/20.500.12110/paper_0025584X_v290_n14-15_p2308_Lassalle
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_0025584X_v290_n14-15_p2308_Lassalle
record_format	dspace
spelling	paper:paper_0025584X_v290_n14-15_p2308_Lassalle2025-07-30T17:35:09Z On null sequences for Banach operator ideals, trace duality and approximation properties Lassalle, Silvia Beatriz 46B45; Secondary: 46B28 46B50 approximation properties compact sets null sequences Operator ideals Primary: 46B04 Let A be a Banach operator ideal and X be a Banach space. We undertake the study of the vector space of A-null sequences of Carl and Stephani on X, c0,A(X), from a unified point of view after we introduce a norm which makes it a Banach space. To give accurate results we consider local versions of the different types of accessibility of Banach operator ideals. We show that in the most common situations, when A is right-accessible for (ℓ1;X),c0,A(X) behaves much alike c0(X). When this is the case we give a geometric tensor product representation of c0,A(X). On the other hand, we show an example where the representation fails. Also, via a trace duality formula, we characterize the dual space of c0,A(X). We apply our results to study some problems related with the KA -approximation property giving a trace condition which is used to solve the remaining case (p=1) of a problem posed by Kim (2015). Namely, we prove that if a dual space has the K1 -approximation property then the space has the Ku,1 -approximation property. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim Fil:Lassalle, S. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2017 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0025584X_v290_n14-15_p2308_Lassalle http://hdl.handle.net/20.500.12110/paper_0025584X_v290_n14-15_p2308_Lassalle
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	46B45; Secondary: 46B28 46B50 approximation properties compact sets null sequences Operator ideals Primary: 46B04
spellingShingle	46B45; Secondary: 46B28 46B50 approximation properties compact sets null sequences Operator ideals Primary: 46B04 Lassalle, Silvia Beatriz On null sequences for Banach operator ideals, trace duality and approximation properties
topic_facet	46B45; Secondary: 46B28 46B50 approximation properties compact sets null sequences Operator ideals Primary: 46B04
description	Let A be a Banach operator ideal and X be a Banach space. We undertake the study of the vector space of A-null sequences of Carl and Stephani on X, c0,A(X), from a unified point of view after we introduce a norm which makes it a Banach space. To give accurate results we consider local versions of the different types of accessibility of Banach operator ideals. We show that in the most common situations, when A is right-accessible for (ℓ1;X),c0,A(X) behaves much alike c0(X). When this is the case we give a geometric tensor product representation of c0,A(X). On the other hand, we show an example where the representation fails. Also, via a trace duality formula, we characterize the dual space of c0,A(X). We apply our results to study some problems related with the KA -approximation property giving a trace condition which is used to solve the remaining case (p=1) of a problem posed by Kim (2015). Namely, we prove that if a dual space has the K1 -approximation property then the space has the Ku,1 -approximation property. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
author	Lassalle, Silvia Beatriz
author_facet	Lassalle, Silvia Beatriz
author_sort	Lassalle, Silvia Beatriz
title	On null sequences for Banach operator ideals, trace duality and approximation properties
title_short	On null sequences for Banach operator ideals, trace duality and approximation properties
title_full	On null sequences for Banach operator ideals, trace duality and approximation properties
title_fullStr	On null sequences for Banach operator ideals, trace duality and approximation properties
title_full_unstemmed	On null sequences for Banach operator ideals, trace duality and approximation properties
title_sort	on null sequences for banach operator ideals, trace duality and approximation properties
publishDate	2017
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0025584X_v290_n14-15_p2308_Lassalle http://hdl.handle.net/20.500.12110/paper_0025584X_v290_n14-15_p2308_Lassalle
work_keys_str_mv	AT lassallesilviabeatriz onnullsequencesforbanachoperatoridealstracedualityandapproximationproperties
_version_	1840323896672256000

On null sequences for Banach operator ideals, trace duality and approximation properties

Ejemplares similares