On the strong subdifferentiability of homogeneous polynomials and (symmetric) tensor products

Autores
Dantas, Sheldon; Jung, Mingu; Mazzitelli, Martin Diego; Rodríguez, Jorge Tomás
Año de publicación
2025
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study the (uniform) strong subdifferentiability of norms of Banach spaces P(N X, Y ∗) of all continuous N-homogeneous polynomials and tensor products of Banach spaces, namely X⊗b π· · · ⊗b πX and ⊗b πs,NX. Among other results, we characterize when the norms of spaces P(N'p, 'q), P(N lM1, lM2), and P(N d(w, p), lM2) are strongly subdifferentiable. Analogous results for multilinear mappings are also obtained. Since strong subdifferentiability of a dual space implies reflexivity, we improve some known results in [38, 48, 49] (in the spirit of Pitt's compactness theorem) on the reflexivity of spaces of N-homogeneous polynomials and N-linear mappings. Concerning the projective (symmetric) tensor norms, we provide positive results by considering the subsets U and Us of elementary tensors on the unit spheres of X⊗b π · · · ⊗b πX and ⊗b πs,N X, respectively. Specifically, we prove that the norms of ⊗b πs,N '2 and '2⊗b π · · · ⊗b π'2 are uniformly strongly subdifferentiable on Us and U, and that the norms of c0⊗b πs c0 and c0⊗b πc0 are strongly subdifferentiable on Us and U in the complex case.
Fil: Dantas, Sheldon. Universidad de Valencia; España. Universidad de Granada; España
Fil: Jung, Mingu. Korea Institute For Advanced Study; Corea del Sur
Fil: Mazzitelli, Martin Diego. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Cuyo; Argentina
Fil: Rodríguez, Jorge Tomás. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tandil; Argentina. Universidad Nacional del Centro de la Provincia de Buenos Aires; Argentina
Materia
TENSOR PRODUCT
SPACE OF MULTILINEAR FUNCTIONS AND POLYNOMIALS
STRONG SUBDIFFERENTIABILITY
BISHOP-PHELPS-BOLLOBÁS PROPERTY
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:11336/256352
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/256352
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling On the strong subdifferentiability of homogeneous polynomials and (symmetric) tensor productsDantas, SheldonJung, MinguMazzitelli, Martin DiegoRodríguez, Jorge TomásTENSOR PRODUCTSPACE OF MULTILINEAR FUNCTIONS AND POLYNOMIALSSTRONG SUBDIFFERENTIABILITYBISHOP-PHELPS-BOLLOBÁS PROPERTYhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study the (uniform) strong subdifferentiability of norms of Banach spaces P(N X, Y ∗) of all continuous N-homogeneous polynomials and tensor products of Banach spaces, namely X⊗b π· · · ⊗b πX and ⊗b πs,NX. Among other results, we characterize when the norms of spaces P(N'p, 'q), P(N lM1, lM2), and P(N d(w, p), lM2) are strongly subdifferentiable. Analogous results for multilinear mappings are also obtained. Since strong subdifferentiability of a dual space implies reflexivity, we improve some known results in [38, 48, 49] (in the spirit of Pitt's compactness theorem) on the reflexivity of spaces of N-homogeneous polynomials and N-linear mappings. Concerning the projective (symmetric) tensor norms, we provide positive results by considering the subsets U and Us of elementary tensors on the unit spheres of X⊗b π · · · ⊗b πX and ⊗b πs,N X, respectively. Specifically, we prove that the norms of ⊗b πs,N '2 and '2⊗b π · · · ⊗b π'2 are uniformly strongly subdifferentiable on Us and U, and that the norms of c0⊗b πs c0 and c0⊗b πc0 are strongly subdifferentiable on Us and U in the complex case.Fil: Dantas, Sheldon. Universidad de Valencia; España. Universidad de Granada; EspañaFil: Jung, Mingu. Korea Institute For Advanced Study; Corea del SurFil: Mazzitelli, Martin Diego. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Cuyo; ArgentinaFil: Rodríguez, Jorge Tomás. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tandil; Argentina. Universidad Nacional del Centro de la Provincia de Buenos Aires; ArgentinaUniversitat Autònoma de Barcelona2025-01info: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/11336/256352Dantas, Sheldon; Jung, Mingu; Mazzitelli, Martin Diego; Rodríguez, Jorge Tomás; On the strong subdifferentiability of homogeneous polynomials and (symmetric) tensor products; Universitat Autònoma de Barcelona; Publicacions Matematiques; 69; 1; 1-2025; 109-1450214-1493CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://raco.cat/index.php/PublicacionsMatematiques/article/view/433276info:eu-repo/semantics/altIdentifier/url/https://dialnet.unirioja.es/servlet/articulo?codigo=9869728info:eu-repo/semantics/altIdentifier/doi/10.5565/PUBLMAT6912505info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:54:27Zoai:ri.conicet.gov.ar:11336/256352instacron: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:34982025-10-22 11:54:28.066CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On the strong subdifferentiability of homogeneous polynomials and (symmetric) tensor products
title On the strong subdifferentiability of homogeneous polynomials and (symmetric) tensor products
spellingShingle On the strong subdifferentiability of homogeneous polynomials and (symmetric) tensor products
Dantas, Sheldon
TENSOR PRODUCT
SPACE OF MULTILINEAR FUNCTIONS AND POLYNOMIALS
STRONG SUBDIFFERENTIABILITY
BISHOP-PHELPS-BOLLOBÁS PROPERTY
title_short On the strong subdifferentiability of homogeneous polynomials and (symmetric) tensor products
title_full On the strong subdifferentiability of homogeneous polynomials and (symmetric) tensor products
title_fullStr On the strong subdifferentiability of homogeneous polynomials and (symmetric) tensor products
title_full_unstemmed On the strong subdifferentiability of homogeneous polynomials and (symmetric) tensor products
title_sort On the strong subdifferentiability of homogeneous polynomials and (symmetric) tensor products
dc.creator.none.fl_str_mv Dantas, Sheldon
Jung, Mingu
Mazzitelli, Martin Diego
Rodríguez, Jorge Tomás
author Dantas, Sheldon
author_facet Dantas, Sheldon
Jung, Mingu
Mazzitelli, Martin Diego
Rodríguez, Jorge Tomás
author_role author
author2 Jung, Mingu
Mazzitelli, Martin Diego
Rodríguez, Jorge Tomás
author2_role author
author
author
dc.subject.none.fl_str_mv TENSOR PRODUCT
SPACE OF MULTILINEAR FUNCTIONS AND POLYNOMIALS
STRONG SUBDIFFERENTIABILITY
BISHOP-PHELPS-BOLLOBÁS PROPERTY
topic TENSOR PRODUCT
SPACE OF MULTILINEAR FUNCTIONS AND POLYNOMIALS
STRONG SUBDIFFERENTIABILITY
BISHOP-PHELPS-BOLLOBÁS PROPERTY
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 study the (uniform) strong subdifferentiability of norms of Banach spaces P(N X, Y ∗) of all continuous N-homogeneous polynomials and tensor products of Banach spaces, namely X⊗b π· · · ⊗b πX and ⊗b πs,NX. Among other results, we characterize when the norms of spaces P(N'p, 'q), P(N lM1, lM2), and P(N d(w, p), lM2) are strongly subdifferentiable. Analogous results for multilinear mappings are also obtained. Since strong subdifferentiability of a dual space implies reflexivity, we improve some known results in [38, 48, 49] (in the spirit of Pitt's compactness theorem) on the reflexivity of spaces of N-homogeneous polynomials and N-linear mappings. Concerning the projective (symmetric) tensor norms, we provide positive results by considering the subsets U and Us of elementary tensors on the unit spheres of X⊗b π · · · ⊗b πX and ⊗b πs,N X, respectively. Specifically, we prove that the norms of ⊗b πs,N '2 and '2⊗b π · · · ⊗b π'2 are uniformly strongly subdifferentiable on Us and U, and that the norms of c0⊗b πs c0 and c0⊗b πc0 are strongly subdifferentiable on Us and U in the complex case.
Fil: Dantas, Sheldon. Universidad de Valencia; España. Universidad de Granada; España
Fil: Jung, Mingu. Korea Institute For Advanced Study; Corea del Sur
Fil: Mazzitelli, Martin Diego. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Cuyo; Argentina
Fil: Rodríguez, Jorge Tomás. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tandil; Argentina. Universidad Nacional del Centro de la Provincia de Buenos Aires; Argentina
description We study the (uniform) strong subdifferentiability of norms of Banach spaces P(N X, Y ∗) of all continuous N-homogeneous polynomials and tensor products of Banach spaces, namely X⊗b π· · · ⊗b πX and ⊗b πs,NX. Among other results, we characterize when the norms of spaces P(N'p, 'q), P(N lM1, lM2), and P(N d(w, p), lM2) are strongly subdifferentiable. Analogous results for multilinear mappings are also obtained. Since strong subdifferentiability of a dual space implies reflexivity, we improve some known results in [38, 48, 49] (in the spirit of Pitt's compactness theorem) on the reflexivity of spaces of N-homogeneous polynomials and N-linear mappings. Concerning the projective (symmetric) tensor norms, we provide positive results by considering the subsets U and Us of elementary tensors on the unit spheres of X⊗b π · · · ⊗b πX and ⊗b πs,N X, respectively. Specifically, we prove that the norms of ⊗b πs,N '2 and '2⊗b π · · · ⊗b π'2 are uniformly strongly subdifferentiable on Us and U, and that the norms of c0⊗b πs c0 and c0⊗b πc0 are strongly subdifferentiable on Us and U in the complex case.
publishDate 2025
dc.date.none.fl_str_mv 2025-01
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/11336/256352
Dantas, Sheldon; Jung, Mingu; Mazzitelli, Martin Diego; Rodríguez, Jorge Tomás; On the strong subdifferentiability of homogeneous polynomials and (symmetric) tensor products; Universitat Autònoma de Barcelona; Publicacions Matematiques; 69; 1; 1-2025; 109-145
0214-1493
CONICET Digital
CONICET
url http://hdl.handle.net/11336/256352
identifier_str_mv Dantas, Sheldon; Jung, Mingu; Mazzitelli, Martin Diego; Rodríguez, Jorge Tomás; On the strong subdifferentiability of homogeneous polynomials and (symmetric) tensor products; Universitat Autònoma de Barcelona; Publicacions Matematiques; 69; 1; 1-2025; 109-145
0214-1493
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://raco.cat/index.php/PublicacionsMatematiques/article/view/433276
info:eu-repo/semantics/altIdentifier/url/https://dialnet.unirioja.es/servlet/articulo?codigo=9869728
info:eu-repo/semantics/altIdentifier/doi/10.5565/PUBLMAT6912505
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 Universitat Autònoma de Barcelona
publisher.none.fl_str_mv Universitat Autònoma de Barcelona
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 12.982451

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