A -compact mappings

For a fixed Banach operator ideal A, we use the notion of A-compact sets of Carl and Stephani to study A-compact polynomials and A-compact holomorphic mappings. Namely, those mappings g: X→ Y such that every x∈ X has a neighborhood V x such that g(V x ) is relatively A-compact. We show that the beha...

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Autor principal: Turco, P.
Formato: JOUR
Materias:
A-compact polynomials
A-compact sets
Holomorphic mappings
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_15787303_v110_n2_p863_Turco
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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_15787303_v110_n2_p863_Turco2023-10-03T16:27:38Z A -compact mappings Turco, P. A-compact polynomials A-compact sets Holomorphic mappings For a fixed Banach operator ideal A, we use the notion of A-compact sets of Carl and Stephani to study A-compact polynomials and A-compact holomorphic mappings. Namely, those mappings g: X→ Y such that every x∈ X has a neighborhood V x such that g(V x ) is relatively A-compact. We show that the behavior of A-compact polynomials is determined by its behavior in any neighborhood of any point. We transfer some known properties of A-compact operators to A-compact polynomials. In order to study A-compact holomorphic functions, we appeal to the A-compact radius of convergence which allows us to characterize the functions in this class. Under certain hypothesis on the ideal A, we give examples showing that our characterization is sharp. © 2015, Springer-Verlag Italia. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_15787303_v110_n2_p863_Turco
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic A-compact polynomials
A-compact sets
Holomorphic mappings
spellingShingle A-compact polynomials
A-compact sets
Holomorphic mappings
Turco, P.
A -compact mappings
topic_facet A-compact polynomials
A-compact sets
Holomorphic mappings
description For a fixed Banach operator ideal A, we use the notion of A-compact sets of Carl and Stephani to study A-compact polynomials and A-compact holomorphic mappings. Namely, those mappings g: X→ Y such that every x∈ X has a neighborhood V x such that g(V x ) is relatively A-compact. We show that the behavior of A-compact polynomials is determined by its behavior in any neighborhood of any point. We transfer some known properties of A-compact operators to A-compact polynomials. In order to study A-compact holomorphic functions, we appeal to the A-compact radius of convergence which allows us to characterize the functions in this class. Under certain hypothesis on the ideal A, we give examples showing that our characterization is sharp. © 2015, Springer-Verlag Italia.
format JOUR
author Turco, P.
author_facet Turco, P.
author_sort Turco, P.
title A -compact mappings
title_short A -compact mappings
title_full A -compact mappings
title_fullStr A -compact mappings
title_full_unstemmed A -compact mappings
title_sort -compact mappings
url http://hdl.handle.net/20.500.12110/paper_15787303_v110_n2_p863_Turco
work_keys_str_mv AT turcop acompactmappings
AT turcop compactmappings
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