The Banach ideal of A-compact operators and related approximation properties

We use the notion of A-compact sets (determined by an operator ideal A), introduced by Carl and Stephani (1984), to show that many known results of certain approximation properties and several ideals of compact operators can be systematically studied under this framework. For Banach operator ideals...

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Detalles Bibliográficos
Autores principales:	Lassalle, S., Turco, P.
Formato:	JOUR
Materias:	Approximation properties Compact sets Operator ideals
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_00221236_v265_n10_p2452_Lassalle
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

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spelling	todo:paper_00221236_v265_n10_p2452_Lassalle2023-10-03T14:27:17Z The Banach ideal of A-compact operators and related approximation properties Lassalle, S. Turco, P. Approximation properties Compact sets Operator ideals We use the notion of A-compact sets (determined by an operator ideal A), introduced by Carl and Stephani (1984), to show that many known results of certain approximation properties and several ideals of compact operators can be systematically studied under this framework. For Banach operator ideals A, we introduce a way to measure the size of A-compact sets and use it to give a norm on KA, the ideal of A-compact operators. Then, we study two types of approximation properties determined by A-compact sets. We focus our attention on an approximation property which makes use of the norm defined on KA. This notion fits the definition of the A-approximation property, recently introduced by Oja (2012), with KA instead of A. We exemplify the power of the Carl-Stephani theory and the geometric structure introduced here by appealing to some recent developments on p-compactness. © 2013 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_00221236_v265_n10_p2452_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	Approximation properties Compact sets Operator ideals
spellingShingle	Approximation properties Compact sets Operator ideals Lassalle, S. Turco, P. The Banach ideal of A-compact operators and related approximation properties
topic_facet	Approximation properties Compact sets Operator ideals
description	We use the notion of A-compact sets (determined by an operator ideal A), introduced by Carl and Stephani (1984), to show that many known results of certain approximation properties and several ideals of compact operators can be systematically studied under this framework. For Banach operator ideals A, we introduce a way to measure the size of A-compact sets and use it to give a norm on KA, the ideal of A-compact operators. Then, we study two types of approximation properties determined by A-compact sets. We focus our attention on an approximation property which makes use of the norm defined on KA. This notion fits the definition of the A-approximation property, recently introduced by Oja (2012), with KA instead of A. We exemplify the power of the Carl-Stephani theory and the geometric structure introduced here by appealing to some recent developments on p-compactness. © 2013 Elsevier Inc.
format	JOUR
author	Lassalle, S. Turco, P.
author_facet	Lassalle, S. Turco, P.
author_sort	Lassalle, S.
title	The Banach ideal of A-compact operators and related approximation properties
title_short	The Banach ideal of A-compact operators and related approximation properties
title_full	The Banach ideal of A-compact operators and related approximation properties
title_fullStr	The Banach ideal of A-compact operators and related approximation properties
title_full_unstemmed	The Banach ideal of A-compact operators and related approximation properties
title_sort	banach ideal of a-compact operators and related approximation properties
url	http://hdl.handle.net/20.500.12110/paper_00221236_v265_n10_p2452_Lassalle
work_keys_str_mv	AT lassalles thebanachidealofacompactoperatorsandrelatedapproximationproperties AT turcop thebanachidealofacompactoperatorsandrelatedapproximationproperties AT lassalles banachidealofacompactoperatorsandrelatedapproximationproperties AT turcop banachidealofacompactoperatorsandrelatedapproximationproperties
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The Banach ideal of A-compact operators and related approximation properties

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