Smooth extension of functions on a certain class of non-separable Banach spaces

Let us consider a Banach space X with the property that every real-valued Lipschitz function f can be uniformly approximated by a Lipschitz, C1-smooth function g with Lip(g)⩽CLip(f) (with C depending only on the space X). This is the case for a Banach space X bi-Lipschitz homeomorphic to a subset of...

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Detalles Bibliográficos
Autores: Jiménez Sevilla, María Del Mar, Sánchez González, Luis
Tipo de recurso: artículo
Fecha de publicación:2011
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/41997
Acceso en línea:https://hdl.handle.net/20.500.14352/41997
Access Level:acceso abierto
Palabra clave:517.98
Smooth extensions
Smooth approximations
Análisis funcional y teoría de operadores
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spelling Smooth extension of functions on a certain class of non-separable Banach spacesJiménez Sevilla, María Del MarSánchez González, Luis517.98Smooth extensionsSmooth approximationsAnálisis funcional y teoría de operadoresLet us consider a Banach space X with the property that every real-valued Lipschitz function f can be uniformly approximated by a Lipschitz, C1-smooth function g with Lip(g)⩽CLip(f) (with C depending only on the space X). This is the case for a Banach space X bi-Lipschitz homeomorphic to a subset of c0(Γ), for some set Γ, such that the coordinate functions of the homeomorphism are C1-smooth (Hájek and Johanis, 2010 . Then, we prove that for every closed subspace Y⊂X and every C1-smooth (Lipschitz) function f:Y→R, there is a C1-smooth (Lipschitz, respectively) extension of f to X. We also study C1-smooth extensions of real-valued functions defined on closed subsets of X. These results extend those given in Azagra et al. (2010) [4] to the class of non-separable Banach spaces satisfying the above property.ElsevierUniversidad Complutense de Madrid20112011-01-0120112011-01-01journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/41997reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/419972026-06-02T12:44:21Z
dc.title.none.fl_str_mv Smooth extension of functions on a certain class of non-separable Banach spaces
title Smooth extension of functions on a certain class of non-separable Banach spaces
spellingShingle Smooth extension of functions on a certain class of non-separable Banach spaces
Jiménez Sevilla, María Del Mar
517.98
Smooth extensions
Smooth approximations
Análisis funcional y teoría de operadores
title_short Smooth extension of functions on a certain class of non-separable Banach spaces
title_full Smooth extension of functions on a certain class of non-separable Banach spaces
title_fullStr Smooth extension of functions on a certain class of non-separable Banach spaces
title_full_unstemmed Smooth extension of functions on a certain class of non-separable Banach spaces
title_sort Smooth extension of functions on a certain class of non-separable Banach spaces
dc.creator.none.fl_str_mv Jiménez Sevilla, María Del Mar
Sánchez González, Luis
author Jiménez Sevilla, María Del Mar
author_facet Jiménez Sevilla, María Del Mar
Sánchez González, Luis
author_role author
author2 Sánchez González, Luis
author2_role author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 517.98
Smooth extensions
Smooth approximations
Análisis funcional y teoría de operadores
topic 517.98
Smooth extensions
Smooth approximations
Análisis funcional y teoría de operadores
description Let us consider a Banach space X with the property that every real-valued Lipschitz function f can be uniformly approximated by a Lipschitz, C1-smooth function g with Lip(g)⩽CLip(f) (with C depending only on the space X). This is the case for a Banach space X bi-Lipschitz homeomorphic to a subset of c0(Γ), for some set Γ, such that the coordinate functions of the homeomorphism are C1-smooth (Hájek and Johanis, 2010 . Then, we prove that for every closed subspace Y⊂X and every C1-smooth (Lipschitz) function f:Y→R, there is a C1-smooth (Lipschitz, respectively) extension of f to X. We also study C1-smooth extensions of real-valued functions defined on closed subsets of X. These results extend those given in Azagra et al. (2010) [4] to the class of non-separable Banach spaces satisfying the above property.
publishDate 2011
dc.date.none.fl_str_mv 2011
2011-01-01
2011
2011-01-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/41997
url https://hdl.handle.net/20.500.14352/41997
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,301603

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