Strong subdifferentiability and local Bishop–Phelps–Bollobás properties

Autores
Dantas, Sheldon; Kim, Sun Kwang; Lee, Han Ju; Mazzitelli, Martin Diego
Año de publicación
2020
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Some local versions of the Bishop–Phelps–Bollobás property for operators have been recently presented in Dantas et al. (J Math Anal Appl 468(1):304–323, 2018). In the present article, we continue studying these properties for multilinear mappings. We show some differences between the local and uniform versions of these and also provide some interesting examples which show that this study is not just a mere generalization of the linear case. As a consequence of our results, we get that, for 2 < p, q< ∞, the norm of the projective tensor product ℓp⊗ ^ πℓq is strongly subdifferentiable. Moreover, we present necessary and sufficient conditions for the norm of a Banach space Y to be strongly subdifferentiable through the study of these properties for bilinear mappings on ℓ1N×Y.
Fil: Dantas, Sheldon. Czech Technical University in Prague; República Checa
Fil: Kim, Sun Kwang. Chungbuk National University; Corea del Sur
Fil: Lee, Han Ju. Dongguk University, Seoul; Corea del Sur
Fil: Mazzitelli, Martin Diego. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Universidad Nacional de Cuyo; Argentina. Comisión Nacional de Energía Atómica. Fundación José A. Balseiro; Argentina
Materia
BANACH SPACE
BISHOP–PHELPS–BOLLOBÁS PROPERTY
NORM ATTAINING OPERATORS
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:11336/126401
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/126401
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Strong subdifferentiability and local Bishop–Phelps–Bollobás propertiesDantas, SheldonKim, Sun KwangLee, Han JuMazzitelli, Martin DiegoBANACH SPACEBISHOP–PHELPS–BOLLOBÁS PROPERTYNORM ATTAINING OPERATORShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Some local versions of the Bishop–Phelps–Bollobás property for operators have been recently presented in Dantas et al. (J Math Anal Appl 468(1):304–323, 2018). In the present article, we continue studying these properties for multilinear mappings. We show some differences between the local and uniform versions of these and also provide some interesting examples which show that this study is not just a mere generalization of the linear case. As a consequence of our results, we get that, for 2 < p, q< ∞, the norm of the projective tensor product ℓp⊗ ^ πℓq is strongly subdifferentiable. Moreover, we present necessary and sufficient conditions for the norm of a Banach space Y to be strongly subdifferentiable through the study of these properties for bilinear mappings on ℓ1N×Y.Fil: Dantas, Sheldon. Czech Technical University in Prague; República ChecaFil: Kim, Sun Kwang. Chungbuk National University; Corea del SurFil: Lee, Han Ju. Dongguk University, Seoul; Corea del SurFil: Mazzitelli, Martin Diego. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Universidad Nacional de Cuyo; Argentina. Comisión Nacional de Energía Atómica. Fundación José A. Balseiro; ArgentinaReal Acad Ciencias Exactas Fisicas & Naturales2020-01-02info: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/11336/126401Dantas, Sheldon; Kim, Sun Kwang; Lee, Han Ju; Mazzitelli, Martin Diego; Strong subdifferentiability and local Bishop–Phelps–Bollobás properties; Real Acad Ciencias Exactas Fisicas & Naturales; Revista de la Real Academia de Ciencias Exactas Fisicas y Naturales Serie A-matematicas; 114; 47; 2-1-2020; 1-161578-7303CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://link.springer.com/10.1007/s13398-019-00741-1info:eu-repo/semantics/altIdentifier/doi/10.1007/s13398-019-00741-1info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1905.08483info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T12:16:56Zoai:ri.conicet.gov.ar:11336/126401instacron: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 12:16:56.494CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Strong subdifferentiability and local Bishop–Phelps–Bollobás properties
title Strong subdifferentiability and local Bishop–Phelps–Bollobás properties
spellingShingle Strong subdifferentiability and local Bishop–Phelps–Bollobás properties
Dantas, Sheldon
BANACH SPACE
BISHOP–PHELPS–BOLLOBÁS PROPERTY
NORM ATTAINING OPERATORS
title_short Strong subdifferentiability and local Bishop–Phelps–Bollobás properties
title_full Strong subdifferentiability and local Bishop–Phelps–Bollobás properties
title_fullStr Strong subdifferentiability and local Bishop–Phelps–Bollobás properties
title_full_unstemmed Strong subdifferentiability and local Bishop–Phelps–Bollobás properties
title_sort Strong subdifferentiability and local Bishop–Phelps–Bollobás properties
dc.creator.none.fl_str_mv Dantas, Sheldon
Kim, Sun Kwang
Lee, Han Ju
Mazzitelli, Martin Diego
author Dantas, Sheldon
author_facet Dantas, Sheldon
Kim, Sun Kwang
Lee, Han Ju
Mazzitelli, Martin Diego
author_role author
author2 Kim, Sun Kwang
Lee, Han Ju
Mazzitelli, Martin Diego
author2_role author
author
author
dc.subject.none.fl_str_mv BANACH SPACE
BISHOP–PHELPS–BOLLOBÁS PROPERTY
NORM ATTAINING OPERATORS
topic BANACH SPACE
BISHOP–PHELPS–BOLLOBÁS PROPERTY
NORM ATTAINING OPERATORS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Some local versions of the Bishop–Phelps–Bollobás property for operators have been recently presented in Dantas et al. (J Math Anal Appl 468(1):304–323, 2018). In the present article, we continue studying these properties for multilinear mappings. We show some differences between the local and uniform versions of these and also provide some interesting examples which show that this study is not just a mere generalization of the linear case. As a consequence of our results, we get that, for 2 < p, q< ∞, the norm of the projective tensor product ℓp⊗ ^ πℓq is strongly subdifferentiable. Moreover, we present necessary and sufficient conditions for the norm of a Banach space Y to be strongly subdifferentiable through the study of these properties for bilinear mappings on ℓ1N×Y.
Fil: Dantas, Sheldon. Czech Technical University in Prague; República Checa
Fil: Kim, Sun Kwang. Chungbuk National University; Corea del Sur
Fil: Lee, Han Ju. Dongguk University, Seoul; Corea del Sur
Fil: Mazzitelli, Martin Diego. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Universidad Nacional de Cuyo; Argentina. Comisión Nacional de Energía Atómica. Fundación José A. Balseiro; Argentina
description Some local versions of the Bishop–Phelps–Bollobás property for operators have been recently presented in Dantas et al. (J Math Anal Appl 468(1):304–323, 2018). In the present article, we continue studying these properties for multilinear mappings. We show some differences between the local and uniform versions of these and also provide some interesting examples which show that this study is not just a mere generalization of the linear case. As a consequence of our results, we get that, for 2 < p, q< ∞, the norm of the projective tensor product ℓp⊗ ^ πℓq is strongly subdifferentiable. Moreover, we present necessary and sufficient conditions for the norm of a Banach space Y to be strongly subdifferentiable through the study of these properties for bilinear mappings on ℓ1N×Y.
publishDate 2020
dc.date.none.fl_str_mv 2020-01-02
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/11336/126401
Dantas, Sheldon; Kim, Sun Kwang; Lee, Han Ju; Mazzitelli, Martin Diego; Strong subdifferentiability and local Bishop–Phelps–Bollobás properties; Real Acad Ciencias Exactas Fisicas & Naturales; Revista de la Real Academia de Ciencias Exactas Fisicas y Naturales Serie A-matematicas; 114; 47; 2-1-2020; 1-16
1578-7303
CONICET Digital
CONICET
url http://hdl.handle.net/11336/126401
identifier_str_mv Dantas, Sheldon; Kim, Sun Kwang; Lee, Han Ju; Mazzitelli, Martin Diego; Strong subdifferentiability and local Bishop–Phelps–Bollobás properties; Real Acad Ciencias Exactas Fisicas & Naturales; Revista de la Real Academia de Ciencias Exactas Fisicas y Naturales Serie A-matematicas; 114; 47; 2-1-2020; 1-16
1578-7303
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://link.springer.com/10.1007/s13398-019-00741-1
info:eu-repo/semantics/altIdentifier/doi/10.1007/s13398-019-00741-1
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1905.08483
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 Real Acad Ciencias Exactas Fisicas & Naturales
publisher.none.fl_str_mv Real Acad Ciencias Exactas Fisicas & Naturales
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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