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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Autores principales: Lassalle, S., Oja, E., Turco, P.
Formato: JOUR
Materias:
Banach operator ideals
Bounded approximation properties
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00219045_v205_n_p25_Lassalle
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_00219045_v205_n_p25_Lassalle2023-10-03T14:22:39Z Weaker relatives of the bounded approximation property for a Banach operator ideal Lassalle, S. Oja, E. Turco, P. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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, S.
Oja, E.
Turco, P.
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.
format JOUR
author Lassalle, S.
Oja, E.
Turco, P.
author_facet Lassalle, S.
Oja, E.
Turco, P.
author_sort Lassalle, S.
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
url http://hdl.handle.net/20.500.12110/paper_00219045_v205_n_p25_Lassalle
work_keys_str_mv AT lassalles weakerrelativesoftheboundedapproximationpropertyforabanachoperatorideal
AT ojae weakerrelativesoftheboundedapproximationpropertyforabanachoperatorideal
AT turcop weakerrelativesoftheboundedapproximationpropertyforabanachoperatorideal
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