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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/160871
Ver los metadatos del registro completo
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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 Técnicas2025-09-29T10:37:18Zoai: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:34982025-09-29 10:37:18.282CONICET 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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1844614392781471744 |
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13.070432 |