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...
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todo:paper_0025584X_v290_n14-15_p2308_Lassalle2023-10-03T14:36:21Z On null sequences for Banach operator ideals, trace duality and approximation properties Lassalle, S. Turco, P. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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, S. Turco, P. 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 |
| format |
JOUR |
| author |
Lassalle, S. Turco, P. |
| author_facet |
Lassalle, S. Turco, P. |
| author_sort |
Lassalle, S. |
| 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 |
| url |
http://hdl.handle.net/20.500.12110/paper_0025584X_v290_n14-15_p2308_Lassalle |
| work_keys_str_mv |
AT lassalles onnullsequencesforbanachoperatoridealstracedualityandapproximationproperties AT turcop onnullsequencesforbanachoperatoridealstracedualityandapproximationproperties |
| _version_ |
1807317048282316800 |