Polynomials and holomorphic functions on A-compact sets in Banach spaces

Autores
Lassalle, Silvia Beatriz; Turco, Pablo Alejandro
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we study the behavior of holomorphic mappings on A-compact sets. Motivated by the recent work of Aron, Çalişkan, García and Maestre (2016), we give several conditions (on the holomorphic mappings and on the λ-Banach operator ideal A) under which A-compact sets are preserved. Appealing to the notion of tensor stability for operator ideals, we first address the question in the polynomial setting. Then, we define a radius of (A;B)-compactification that permits us to tackle the analytic case. Our approach, for instance, allows us to show that the image of any (p,r)-compact set under any holomorphic function (defined on any open set of a Banach space) is again (p,r)-compact.
Fil: Lassalle, Silvia Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Turco, Pablo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Materia
A-COMPACT SETS
BANACH SPACES
HOLOMORPHIC FUNCTIONS
HOMOGENEOUS POLYNOMIALS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/89056
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Polynomials and holomorphic functions on A-compact sets in Banach spacesLassalle, Silvia BeatrizTurco, Pablo AlejandroA-COMPACT SETSBANACH SPACESHOLOMORPHIC FUNCTIONSHOMOGENEOUS POLYNOMIALShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we study the behavior of holomorphic mappings on A-compact sets. Motivated by the recent work of Aron, Çalişkan, García and Maestre (2016), we give several conditions (on the holomorphic mappings and on the λ-Banach operator ideal A) under which A-compact sets are preserved. Appealing to the notion of tensor stability for operator ideals, we first address the question in the polynomial setting. Then, we define a radius of (A;B)-compactification that permits us to tackle the analytic case. Our approach, for instance, allows us to show that the image of any (p,r)-compact set under any holomorphic function (defined on any open set of a Banach space) is again (p,r)-compact.Fil: Lassalle, Silvia Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Turco, Pablo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaAcademic Press Inc Elsevier Science2018-07info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/89056Lassalle, Silvia Beatriz; Turco, Pablo Alejandro; Polynomials and holomorphic functions on A-compact sets in Banach spaces; Academic Press Inc Elsevier Science; Journal of Mathematical Analysis and Applications; 463; 2; 7-2018; 1092-11080022-247XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmaa.2018.03.070info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0022247X18302828info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-05T10:30:17Zoai:ri.conicet.gov.ar:11336/89056instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-11-05 10:30:17.5CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Polynomials and holomorphic functions on A-compact sets in Banach spaces
title Polynomials and holomorphic functions on A-compact sets in Banach spaces
spellingShingle Polynomials and holomorphic functions on A-compact sets in Banach spaces
Lassalle, Silvia Beatriz
A-COMPACT SETS
BANACH SPACES
HOLOMORPHIC FUNCTIONS
HOMOGENEOUS POLYNOMIALS
title_short Polynomials and holomorphic functions on A-compact sets in Banach spaces
title_full Polynomials and holomorphic functions on A-compact sets in Banach spaces
title_fullStr Polynomials and holomorphic functions on A-compact sets in Banach spaces
title_full_unstemmed Polynomials and holomorphic functions on A-compact sets in Banach spaces
title_sort Polynomials and holomorphic functions on A-compact sets in Banach spaces
dc.creator.none.fl_str_mv Lassalle, Silvia Beatriz
Turco, Pablo Alejandro
author Lassalle, Silvia Beatriz
author_facet Lassalle, Silvia Beatriz
Turco, Pablo Alejandro
author_role author
author2 Turco, Pablo Alejandro
author2_role author
dc.subject.none.fl_str_mv A-COMPACT SETS
BANACH SPACES
HOLOMORPHIC FUNCTIONS
HOMOGENEOUS POLYNOMIALS
topic A-COMPACT SETS
BANACH SPACES
HOLOMORPHIC FUNCTIONS
HOMOGENEOUS POLYNOMIALS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this paper we study the behavior of holomorphic mappings on A-compact sets. Motivated by the recent work of Aron, Çalişkan, García and Maestre (2016), we give several conditions (on the holomorphic mappings and on the λ-Banach operator ideal A) under which A-compact sets are preserved. Appealing to the notion of tensor stability for operator ideals, we first address the question in the polynomial setting. Then, we define a radius of (A;B)-compactification that permits us to tackle the analytic case. Our approach, for instance, allows us to show that the image of any (p,r)-compact set under any holomorphic function (defined on any open set of a Banach space) is again (p,r)-compact.
Fil: Lassalle, Silvia Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Turco, Pablo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
description In this paper we study the behavior of holomorphic mappings on A-compact sets. Motivated by the recent work of Aron, Çalişkan, García and Maestre (2016), we give several conditions (on the holomorphic mappings and on the λ-Banach operator ideal A) under which A-compact sets are preserved. Appealing to the notion of tensor stability for operator ideals, we first address the question in the polynomial setting. Then, we define a radius of (A;B)-compactification that permits us to tackle the analytic case. Our approach, for instance, allows us to show that the image of any (p,r)-compact set under any holomorphic function (defined on any open set of a Banach space) is again (p,r)-compact.
publishDate 2018
dc.date.none.fl_str_mv 2018-07
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/89056
Lassalle, Silvia Beatriz; Turco, Pablo Alejandro; Polynomials and holomorphic functions on A-compact sets in Banach spaces; Academic Press Inc Elsevier Science; Journal of Mathematical Analysis and Applications; 463; 2; 7-2018; 1092-1108
0022-247X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/89056
identifier_str_mv Lassalle, Silvia Beatriz; Turco, Pablo Alejandro; Polynomials and holomorphic functions on A-compact sets in Banach spaces; Academic Press Inc Elsevier Science; Journal of Mathematical Analysis and Applications; 463; 2; 7-2018; 1092-1108
0022-247X
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmaa.2018.03.070
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0022247X18302828
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Academic Press Inc Elsevier Science
publisher.none.fl_str_mv Academic Press Inc Elsevier Science
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.087074

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