On p-compact mappings and the p-approximation property

The notion of p-compact sets arises naturally from Grothendieck's characterization of compact sets as those contained in the convex hull of a norm null sequence. The definition, due to Sinha and Karn (2002), leads to the concepts of p-approximation property and p-compact operators (which form a...

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Detalles Bibliográficos
Autor principal: Lassalle, Silvia Beatriz
Publicado: 2012
Materias:
Approximation properties
Holomorphic mappings
P-Compact sets
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v389_n2_p1204_Lassalle
http://hdl.handle.net/20.500.12110/paper_0022247X_v389_n2_p1204_Lassalle
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_0022247X_v389_n2_p1204_Lassalle
record_format dspace
spelling paper:paper_0022247X_v389_n2_p1204_Lassalle2023-06-08T14:47:55Z On p-compact mappings and the p-approximation property Lassalle, Silvia Beatriz Approximation properties Holomorphic mappings P-Compact sets The notion of p-compact sets arises naturally from Grothendieck's characterization of compact sets as those contained in the convex hull of a norm null sequence. The definition, due to Sinha and Karn (2002), leads to the concepts of p-approximation property and p-compact operators (which form an ideal with its ideal norm κ p). This paper examines the interaction between the p-approximation property and certain space of holomorphic functions, the p-compact analytic functions. In order to understand these functions we define a p-compact radius of convergence which allows us to give a characterization of the functions in the class. We show that p-compact holomorphic functions behave more like nuclear than compact maps. We use the ε-product of Schwartz, to characterize the p-approximation property of a Banach space in terms of p-compact homogeneous polynomials and in terms of p-compact holomorphic functions with range on the space. Finally, we show that p-compact holomorphic functions fit into the framework of holomorphy types which allows us to inspect the κ p-approximation property. Our approach also allows us to solve several questions posed by Aron, Maestre and Rueda (2010). © 2012 Elsevier Inc. Fil:Lassalle, S. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2012 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v389_n2_p1204_Lassalle http://hdl.handle.net/20.500.12110/paper_0022247X_v389_n2_p1204_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
Holomorphic mappings
P-Compact sets
spellingShingle Approximation properties
Holomorphic mappings
P-Compact sets
Lassalle, Silvia Beatriz
On p-compact mappings and the p-approximation property
topic_facet Approximation properties
Holomorphic mappings
P-Compact sets
description The notion of p-compact sets arises naturally from Grothendieck's characterization of compact sets as those contained in the convex hull of a norm null sequence. The definition, due to Sinha and Karn (2002), leads to the concepts of p-approximation property and p-compact operators (which form an ideal with its ideal norm κ p). This paper examines the interaction between the p-approximation property and certain space of holomorphic functions, the p-compact analytic functions. In order to understand these functions we define a p-compact radius of convergence which allows us to give a characterization of the functions in the class. We show that p-compact holomorphic functions behave more like nuclear than compact maps. We use the ε-product of Schwartz, to characterize the p-approximation property of a Banach space in terms of p-compact homogeneous polynomials and in terms of p-compact holomorphic functions with range on the space. Finally, we show that p-compact holomorphic functions fit into the framework of holomorphy types which allows us to inspect the κ p-approximation property. Our approach also allows us to solve several questions posed by Aron, Maestre and Rueda (2010). © 2012 Elsevier Inc.
author Lassalle, Silvia Beatriz
author_facet Lassalle, Silvia Beatriz
author_sort Lassalle, Silvia Beatriz
title On p-compact mappings and the p-approximation property
title_short On p-compact mappings and the p-approximation property
title_full On p-compact mappings and the p-approximation property
title_fullStr On p-compact mappings and the p-approximation property
title_full_unstemmed On p-compact mappings and the p-approximation property
title_sort on p-compact mappings and the p-approximation property
publishDate 2012
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v389_n2_p1204_Lassalle
http://hdl.handle.net/20.500.12110/paper_0022247X_v389_n2_p1204_Lassalle
work_keys_str_mv AT lassallesilviabeatriz onpcompactmappingsandthepapproximationproperty
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