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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Autor principal:	Lassalle, Silvia Beatriz
Publicado:	2013
Materias:	Approximation properties Compact sets Operator ideals
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00221236_v265_n10_p2452_Lassalle 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

id	paper:paper_00221236_v265_n10_p2452_Lassalle
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spelling	paper:paper_00221236_v265_n10_p2452_Lassalle2023-06-08T14:46:26Z The Banach ideal of A-compact operators and related approximation properties Lassalle, Silvia Beatriz 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. 2013 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00221236_v265_n10_p2452_Lassalle 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, Silvia Beatriz 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.
author	Lassalle, Silvia Beatriz
author_facet	Lassalle, Silvia Beatriz
author_sort	Lassalle, Silvia Beatriz
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
publishDate	2013
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00221236_v265_n10_p2452_Lassalle http://hdl.handle.net/20.500.12110/paper_00221236_v265_n10_p2452_Lassalle
work_keys_str_mv	AT lassallesilviabeatriz thebanachidealofacompactoperatorsandrelatedapproximationproperties AT lassallesilviabeatriz banachidealofacompactoperatorsandrelatedapproximationproperties
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The Banach ideal of A-compact operators and related approximation properties

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