Existence of optimal subspaces in reflexive Banach spaces

Autores
Cuenya, Hector Hugo; Levis, Fabián Eduardo
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Given a finite set Y in a  reflexive Banach space F and a family C of closed subspaces of F, we study the problem of finding a subspace W in C that best approximates the data Y in the sense that sum_{f  in Y} d(f,W) = min_{V in C} sum_{f  in Y} d(f,V), where d is the distance function on F. In this paper, we give necessary conditions and sufficient conditions over C for which such a best approximation exists. In particular, when F has finite dimension a characterization on C is given.
Fil: Cuenya, Hector Hugo. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas, Físico-Químicas y Naturales. Departamento de Matemática; Argentina
Fil: Levis, Fabián Eduardo. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas, Físico-Químicas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Optimal Subspaces
Existence
Reflexive Banach Space
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:11336/47263
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Existence of optimal subspaces in reflexive Banach spacesCuenya, Hector HugoLevis, Fabián EduardoOptimal SubspacesExistenceReflexive Banach Spacehttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Given a finite set Y in a  reflexive Banach space F and a family C of closed subspaces of F, we study the problem of finding a subspace W in C that best approximates the data Y in the sense that sum_{f  in Y} d(f,W) = min_{V in C} sum_{f  in Y} d(f,V), where d is the distance function on F. In this paper, we give necessary conditions and sufficient conditions over C for which such a best approximation exists. In particular, when F has finite dimension a characterization on C is given.Fil: Cuenya, Hector Hugo. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas, Físico-Químicas y Naturales. Departamento de Matemática; ArgentinaFil: Levis, Fabián Eduardo. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas, Físico-Químicas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaDuke University Press2015-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/47263Cuenya, Hector Hugo; Levis, Fabián Eduardo; Existence of optimal subspaces in reflexive Banach spaces; Duke University Press; Annals of Functional Analysis; 6; 2; 2-2015; 69-772008-8752CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://projecteuclid.org/euclid.afa/1418997767info:eu-repo/semantics/altIdentifier/doi/10.15352/afa/06-2-7info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:22:19Zoai:ri.conicet.gov.ar:11336/47263instacron: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:34982025-09-10 13:22:19.272CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Existence of optimal subspaces in reflexive Banach spaces
title Existence of optimal subspaces in reflexive Banach spaces
spellingShingle Existence of optimal subspaces in reflexive Banach spaces
Cuenya, Hector Hugo
Optimal Subspaces
Existence
Reflexive Banach Space
title_short Existence of optimal subspaces in reflexive Banach spaces
title_full Existence of optimal subspaces in reflexive Banach spaces
title_fullStr Existence of optimal subspaces in reflexive Banach spaces
title_full_unstemmed Existence of optimal subspaces in reflexive Banach spaces
title_sort Existence of optimal subspaces in reflexive Banach spaces
dc.creator.none.fl_str_mv Cuenya, Hector Hugo
Levis, Fabián Eduardo
author Cuenya, Hector Hugo
author_facet Cuenya, Hector Hugo
Levis, Fabián Eduardo
author_role author
author2 Levis, Fabián Eduardo
author2_role author
dc.subject.none.fl_str_mv Optimal Subspaces
Existence
Reflexive Banach Space
topic Optimal Subspaces
Existence
Reflexive Banach Space
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Given a finite set Y in a  reflexive Banach space F and a family C of closed subspaces of F, we study the problem of finding a subspace W in C that best approximates the data Y in the sense that sum_{f  in Y} d(f,W) = min_{V in C} sum_{f  in Y} d(f,V), where d is the distance function on F. In this paper, we give necessary conditions and sufficient conditions over C for which such a best approximation exists. In particular, when F has finite dimension a characterization on C is given.
Fil: Cuenya, Hector Hugo. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas, Físico-Químicas y Naturales. Departamento de Matemática; Argentina
Fil: Levis, Fabián Eduardo. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas, Físico-Químicas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description Given a finite set Y in a  reflexive Banach space F and a family C of closed subspaces of F, we study the problem of finding a subspace W in C that best approximates the data Y in the sense that sum_{f  in Y} d(f,W) = min_{V in C} sum_{f  in Y} d(f,V), where d is the distance function on F. In this paper, we give necessary conditions and sufficient conditions over C for which such a best approximation exists. In particular, when F has finite dimension a characterization on C is given.
publishDate 2015
dc.date.none.fl_str_mv 2015-02
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/11336/47263
Cuenya, Hector Hugo; Levis, Fabián Eduardo; Existence of optimal subspaces in reflexive Banach spaces; Duke University Press; Annals of Functional Analysis; 6; 2; 2-2015; 69-77
2008-8752
CONICET Digital
CONICET
url http://hdl.handle.net/11336/47263
identifier_str_mv Cuenya, Hector Hugo; Levis, Fabián Eduardo; Existence of optimal subspaces in reflexive Banach spaces; Duke University Press; Annals of Functional Analysis; 6; 2; 2-2015; 69-77
2008-8752
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://projecteuclid.org/euclid.afa/1418997767
info:eu-repo/semantics/altIdentifier/doi/10.15352/afa/06-2-7
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
dc.publisher.none.fl_str_mv Duke University Press
publisher.none.fl_str_mv Duke University Press
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 12.493442

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