Weaker relatives of the bounded approximation property for a Banach operator ideal

Fixed a Banach operator ideal A, we introduce and investigate two new approximation properties, which are strictly weaker than the bounded approximation property (BAP) for A of Lima et al. (2010). We call them the weak BAP for A and the local BAP for A, showing that the latter is in turn strictly we...

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Detalles Bibliográficos
Autor principal: Lassalle, Silvia Beatriz
Publicado: 2016
Materias:
Banach operator ideals
Bounded approximation properties
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00219045_v205_n_p25_Lassalle
http://hdl.handle.net/20.500.12110/paper_00219045_v205_n_p25_Lassalle
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00219045_v205_n_p25_Lassalle
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spelling paper:paper_00219045_v205_n_p25_Lassalle2023-06-08T14:43:04Z Weaker relatives of the bounded approximation property for a Banach operator ideal Lassalle, Silvia Beatriz Banach operator ideals Bounded approximation properties Fixed a Banach operator ideal A, we introduce and investigate two new approximation properties, which are strictly weaker than the bounded approximation property (BAP) for A of Lima et al. (2010). We call them the weak BAP for A and the local BAP for A, showing that the latter is in turn strictly weaker than the former. Under this framework, we address the question of approximation properties passing from dual spaces to underlying spaces. We relate the weak and local BAPs for A with approximation properties given by tensor norms and show that the Saphar BAP of order p is the weak BAP for the ideal of absolutely p*-summing operators, 1≤p≤∞, 1/p+1/p*=1. © 2016 Elsevier Inc. Fil:Lassalle, S. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2016 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00219045_v205_n_p25_Lassalle http://hdl.handle.net/20.500.12110/paper_00219045_v205_n_p25_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 Banach operator ideals
Bounded approximation properties
spellingShingle Banach operator ideals
Bounded approximation properties
Lassalle, Silvia Beatriz
Weaker relatives of the bounded approximation property for a Banach operator ideal
topic_facet Banach operator ideals
Bounded approximation properties
description Fixed a Banach operator ideal A, we introduce and investigate two new approximation properties, which are strictly weaker than the bounded approximation property (BAP) for A of Lima et al. (2010). We call them the weak BAP for A and the local BAP for A, showing that the latter is in turn strictly weaker than the former. Under this framework, we address the question of approximation properties passing from dual spaces to underlying spaces. We relate the weak and local BAPs for A with approximation properties given by tensor norms and show that the Saphar BAP of order p is the weak BAP for the ideal of absolutely p*-summing operators, 1≤p≤∞, 1/p+1/p*=1. © 2016 Elsevier Inc.
author Lassalle, Silvia Beatriz
author_facet Lassalle, Silvia Beatriz
author_sort Lassalle, Silvia Beatriz
title Weaker relatives of the bounded approximation property for a Banach operator ideal
title_short Weaker relatives of the bounded approximation property for a Banach operator ideal
title_full Weaker relatives of the bounded approximation property for a Banach operator ideal
title_fullStr Weaker relatives of the bounded approximation property for a Banach operator ideal
title_full_unstemmed Weaker relatives of the bounded approximation property for a Banach operator ideal
title_sort weaker relatives of the bounded approximation property for a banach operator ideal
publishDate 2016
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00219045_v205_n_p25_Lassalle
http://hdl.handle.net/20.500.12110/paper_00219045_v205_n_p25_Lassalle
work_keys_str_mv AT lassallesilviabeatriz weakerrelativesoftheboundedapproximationpropertyforabanachoperatorideal
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