Coincidence of extendible vector-valued ideals with their minimal kernel

Autores
Galicer, Daniel Eric; Villafañe, Norberto Román
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We provide coincidence results for vector-valued ideals of multilinear operators. More precisely, if A is an ideal of n-linear mappings we give conditions for which the equality A(E1, ..., En; F) = Amin(E1, ..., En; F) holds isometrically. As an application, we obtain in many cases that the monomials form a Schauder basis of the space A(E1, ..., En; F). Several structural and geometric properties are also derived using this equality. We apply our results to the particular case where A is the classical ideal of extendible or Pietsch-integral multilinear operators. Similar statements are given for ideals of vector-valued homogeneous polynomials.
Fil: Galicer, Daniel Eric. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; Argentina
Fil: Villafañe, Norberto Román. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; Argentina
Materia
Multilinear Mappings
Radon-Nikodým Property
Polynomial Ideals
Metric Theory of Tensor Products
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/18864
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/18864
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Coincidence of extendible vector-valued ideals with their minimal kernelGalicer, Daniel EricVillafañe, Norberto RománMultilinear MappingsRadon-Nikodým PropertyPolynomial IdealsMetric Theory of Tensor Productshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We provide coincidence results for vector-valued ideals of multilinear operators. More precisely, if A is an ideal of n-linear mappings we give conditions for which the equality A(E1, ..., En; F) = Amin(E1, ..., En; F) holds isometrically. As an application, we obtain in many cases that the monomials form a Schauder basis of the space A(E1, ..., En; F). Several structural and geometric properties are also derived using this equality. We apply our results to the particular case where A is the classical ideal of extendible or Pietsch-integral multilinear operators. Similar statements are given for ideals of vector-valued homogeneous polynomials.Fil: Galicer, Daniel Eric. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; ArgentinaFil: Villafañe, Norberto Román. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; ArgentinaElsevier Inc2015-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/18864Galicer, Daniel Eric; Villafañe, Norberto Román; Coincidence of extendible vector-valued ideals with their minimal kernel; Elsevier Inc; Journal Of Mathematical Analysis And Applications; 421; 2; 1-2015; 1743-17660022-247XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmaa.2014.07.023info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0022247X14006660info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T14:23:41Zoai:ri.conicet.gov.ar:11336/18864instacron: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:34982025-10-15 14:23:41.366CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Coincidence of extendible vector-valued ideals with their minimal kernel
title Coincidence of extendible vector-valued ideals with their minimal kernel
spellingShingle Coincidence of extendible vector-valued ideals with their minimal kernel
Galicer, Daniel Eric
Multilinear Mappings
Radon-Nikodým Property
Polynomial Ideals
Metric Theory of Tensor Products
title_short Coincidence of extendible vector-valued ideals with their minimal kernel
title_full Coincidence of extendible vector-valued ideals with their minimal kernel
title_fullStr Coincidence of extendible vector-valued ideals with their minimal kernel
title_full_unstemmed Coincidence of extendible vector-valued ideals with their minimal kernel
title_sort Coincidence of extendible vector-valued ideals with their minimal kernel
dc.creator.none.fl_str_mv Galicer, Daniel Eric
Villafañe, Norberto Román
author Galicer, Daniel Eric
author_facet Galicer, Daniel Eric
Villafañe, Norberto Román
author_role author
author2 Villafañe, Norberto Román
author2_role author
dc.subject.none.fl_str_mv Multilinear Mappings
Radon-Nikodým Property
Polynomial Ideals
Metric Theory of Tensor Products
topic Multilinear Mappings
Radon-Nikodým Property
Polynomial Ideals
Metric Theory of Tensor Products
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We provide coincidence results for vector-valued ideals of multilinear operators. More precisely, if A is an ideal of n-linear mappings we give conditions for which the equality A(E1, ..., En; F) = Amin(E1, ..., En; F) holds isometrically. As an application, we obtain in many cases that the monomials form a Schauder basis of the space A(E1, ..., En; F). Several structural and geometric properties are also derived using this equality. We apply our results to the particular case where A is the classical ideal of extendible or Pietsch-integral multilinear operators. Similar statements are given for ideals of vector-valued homogeneous polynomials.
Fil: Galicer, Daniel Eric. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; Argentina
Fil: Villafañe, Norberto Román. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; Argentina
description We provide coincidence results for vector-valued ideals of multilinear operators. More precisely, if A is an ideal of n-linear mappings we give conditions for which the equality A(E1, ..., En; F) = Amin(E1, ..., En; F) holds isometrically. As an application, we obtain in many cases that the monomials form a Schauder basis of the space A(E1, ..., En; F). Several structural and geometric properties are also derived using this equality. We apply our results to the particular case where A is the classical ideal of extendible or Pietsch-integral multilinear operators. Similar statements are given for ideals of vector-valued homogeneous polynomials.
publishDate 2015
dc.date.none.fl_str_mv 2015-01
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/11336/18864
Galicer, Daniel Eric; Villafañe, Norberto Román; Coincidence of extendible vector-valued ideals with their minimal kernel; Elsevier Inc; Journal Of Mathematical Analysis And Applications; 421; 2; 1-2015; 1743-1766
0022-247X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/18864
identifier_str_mv Galicer, Daniel Eric; Villafañe, Norberto Román; Coincidence of extendible vector-valued ideals with their minimal kernel; Elsevier Inc; Journal Of Mathematical Analysis And Applications; 421; 2; 1-2015; 1743-1766
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.2014.07.023
info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0022247X14006660
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier Inc
publisher.none.fl_str_mv Elsevier Inc
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 13.22299

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