M-structures in vector-valued polynomial spaces

Autores
Dimant, Veronica Isabel; Lassalle, Silvia Beatriz
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
This paper is concerned with the study of M-structures in spaces of polynomials. More precisely, we discuss for E and F Banach spaces, whether the class of weakly continuous on bounded sets n-homogeneous polynomials, Pw(nE; F), is an M-ideal in the space of continuous n-homogeneous polynomials P(nE; F). We show that there is some hope for this to happen only for a finite range of values of n. We establish sufficient conditions under which the problem has positive and negative answers and use the obtained results to study the particular cases when E = lp and F = lq or F is a Lorentz sequence space d(w; q). We extend to our setting the notion of property (M) introduced by Kalton which allows us to lift M-structures from the linear to the vector-valued polynomial context. Also, when Pw(nE; F) is an M-ideal in P(nE; F) we prove a Bishop-Phelps type result for vector-valued polynomials and relate norm-attaining polynomials with farthest points and remotal sets.
Fil: Dimant, Veronica Isabel. Universidad de San Andrés; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Lassalle, Silvia Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Materia
M-ideals
homogeneous polynomials
weakly continuous on bounded sets polynomials
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:11336/160871
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/160871
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling M-structures in vector-valued polynomial spacesDimant, Veronica IsabelLassalle, Silvia BeatrizM-idealshomogeneous polynomialsweakly continuous on bounded sets polynomialshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1This paper is concerned with the study of M-structures in spaces of polynomials. More precisely, we discuss for E and F Banach spaces, whether the class of weakly continuous on bounded sets n-homogeneous polynomials, Pw(nE; F), is an M-ideal in the space of continuous n-homogeneous polynomials P(nE; F). We show that there is some hope for this to happen only for a finite range of values of n. We establish sufficient conditions under which the problem has positive and negative answers and use the obtained results to study the particular cases when E = lp and F = lq or F is a Lorentz sequence space d(w; q). We extend to our setting the notion of property (M) introduced by Kalton which allows us to lift M-structures from the linear to the vector-valued polynomial context. Also, when Pw(nE; F) is an M-ideal in P(nE; F) we prove a Bishop-Phelps type result for vector-valued polynomials and relate norm-attaining polynomials with farthest points and remotal sets.Fil: Dimant, Veronica Isabel. Universidad de San Andrés; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Lassalle, Silvia Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaHeldermann Verlag2012-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/160871Dimant, Veronica Isabel; Lassalle, Silvia Beatriz; M-structures in vector-valued polynomial spaces; Heldermann Verlag; Journal Of Convex Analysis; 19; 3; 12-2012; 685-7110944-65322363-6394CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.heldermann.de/JCA/JCA19/JCA193/jca19037.htminfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T12:09:25Zoai:ri.conicet.gov.ar:11336/160871instacron: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 12:09:25.641CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv M-structures in vector-valued polynomial spaces
title M-structures in vector-valued polynomial spaces
spellingShingle M-structures in vector-valued polynomial spaces
Dimant, Veronica Isabel
M-ideals
homogeneous polynomials
weakly continuous on bounded sets polynomials
title_short M-structures in vector-valued polynomial spaces
title_full M-structures in vector-valued polynomial spaces
title_fullStr M-structures in vector-valued polynomial spaces
title_full_unstemmed M-structures in vector-valued polynomial spaces
title_sort M-structures in vector-valued polynomial spaces
dc.creator.none.fl_str_mv Dimant, Veronica Isabel
Lassalle, Silvia Beatriz
author Dimant, Veronica Isabel
author_facet Dimant, Veronica Isabel
Lassalle, Silvia Beatriz
author_role author
author2 Lassalle, Silvia Beatriz
author2_role author
dc.subject.none.fl_str_mv M-ideals
homogeneous polynomials
weakly continuous on bounded sets polynomials
topic M-ideals
homogeneous polynomials
weakly continuous on bounded sets polynomials
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv This paper is concerned with the study of M-structures in spaces of polynomials. More precisely, we discuss for E and F Banach spaces, whether the class of weakly continuous on bounded sets n-homogeneous polynomials, Pw(nE; F), is an M-ideal in the space of continuous n-homogeneous polynomials P(nE; F). We show that there is some hope for this to happen only for a finite range of values of n. We establish sufficient conditions under which the problem has positive and negative answers and use the obtained results to study the particular cases when E = lp and F = lq or F is a Lorentz sequence space d(w; q). We extend to our setting the notion of property (M) introduced by Kalton which allows us to lift M-structures from the linear to the vector-valued polynomial context. Also, when Pw(nE; F) is an M-ideal in P(nE; F) we prove a Bishop-Phelps type result for vector-valued polynomials and relate norm-attaining polynomials with farthest points and remotal sets.
Fil: Dimant, Veronica Isabel. Universidad de San Andrés; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Lassalle, Silvia Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
description This paper is concerned with the study of M-structures in spaces of polynomials. More precisely, we discuss for E and F Banach spaces, whether the class of weakly continuous on bounded sets n-homogeneous polynomials, Pw(nE; F), is an M-ideal in the space of continuous n-homogeneous polynomials P(nE; F). We show that there is some hope for this to happen only for a finite range of values of n. We establish sufficient conditions under which the problem has positive and negative answers and use the obtained results to study the particular cases when E = lp and F = lq or F is a Lorentz sequence space d(w; q). We extend to our setting the notion of property (M) introduced by Kalton which allows us to lift M-structures from the linear to the vector-valued polynomial context. Also, when Pw(nE; F) is an M-ideal in P(nE; F) we prove a Bishop-Phelps type result for vector-valued polynomials and relate norm-attaining polynomials with farthest points and remotal sets.
publishDate 2012
dc.date.none.fl_str_mv 2012-12
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/11336/160871
Dimant, Veronica Isabel; Lassalle, Silvia Beatriz; M-structures in vector-valued polynomial spaces; Heldermann Verlag; Journal Of Convex Analysis; 19; 3; 12-2012; 685-711
0944-6532
2363-6394
CONICET Digital
CONICET
url http://hdl.handle.net/11336/160871
identifier_str_mv Dimant, Veronica Isabel; Lassalle, Silvia Beatriz; M-structures in vector-valued polynomial spaces; Heldermann Verlag; Journal Of Convex Analysis; 19; 3; 12-2012; 685-711
0944-6532
2363-6394
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://www.heldermann.de/JCA/JCA19/JCA193/jca19037.htm
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 Heldermann Verlag
publisher.none.fl_str_mv Heldermann Verlag
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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