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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Detalles Bibliográficos
Publicado: 2016
Materias:
A-compact polynomials
A-compact sets
Holomorphic mappings
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15787303_v110_n2_p863_Turco
http://hdl.handle.net/20.500.12110/paper_15787303_v110_n2_p863_Turco
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_15787303_v110_n2_p863_Turco
record_format dspace
spelling paper:paper_15787303_v110_n2_p863_Turco2023-06-08T16:24:53Z A -compact mappings 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. 2016 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15787303_v110_n2_p863_Turco 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
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.
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
publishDate 2016
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15787303_v110_n2_p863_Turco
http://hdl.handle.net/20.500.12110/paper_15787303_v110_n2_p863_Turco
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