Extending polynomials in maximal and minimal ideals

Given a homogeneous polynomial on a Banach space E belonging to some maximal or minimal polynomial ideal, we consider its iterated extension to an ultrapower of E and prove that this extension remains in the ideal and has the same ideal norm. As a consequence, we show that the Aron-Berner extension...

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Detalles Bibliográficos
Autores: Carando, D., Galicer, D.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2010
País:Argentina
Institución:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
Repositorio:Biblioteca Digital (UBA-FCEN)
Idioma:inglés
OAI Identifier:paperaa:paper_00345318_v46_n3_p669_Carando
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00345318_v46_n3_p669_Carando
Access Level:acceso abierto
Palabra clave:Extension of polynomials
Polynomial ideals
Symmetric tensor products of banach spaces
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spelling Extending polynomials in maximal and minimal idealsCarando, D.Galicer, D.Extension of polynomialsPolynomial idealsSymmetric tensor products of banach spacesGiven a homogeneous polynomial on a Banach space E belonging to some maximal or minimal polynomial ideal, we consider its iterated extension to an ultrapower of E and prove that this extension remains in the ideal and has the same ideal norm. As a consequence, we show that the Aron-Berner extension is a well defined isometry for any maximal or minimal ideal of homogeneous polynomials. This allows us to obtain symmetric versions of some basic results of the metric theory of tensor products. © 2010 Research Institute for Mathematical Sciences, Kyoto University. All rights reserved.Fil:Carando, D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Fil:Galicer, D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.2010info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttp://hdl.handle.net/20.500.12110/paper_00345318_v46_n3_p669_CarandoPubl. Res. Inst. Math. Sci. 2010;46(3):669-680reponame:Biblioteca Digital (UBA-FCEN)instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesinstacron:UBA-FCENenginfo:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/2.5/ar2024-05-10T10:42:41Zpaperaa:paper_00345318_v46_n3_p669_CarandoInstitucionalhttps://digital.bl.fcen.uba.ar/Universidad públicaNo correspondehttps://digital.bl.fcen.uba.ar/cgi-bin/oaiserver.cgiana@bl.fcen.uba.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:18962024-05-10 10:42:42.955Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturalesfalse
dc.title.none.fl_str_mv Extending polynomials in maximal and minimal ideals
title Extending polynomials in maximal and minimal ideals
spellingShingle Extending polynomials in maximal and minimal ideals
Carando, D.
Extension of polynomials
Polynomial ideals
Symmetric tensor products of banach spaces
title_short Extending polynomials in maximal and minimal ideals
title_full Extending polynomials in maximal and minimal ideals
title_fullStr Extending polynomials in maximal and minimal ideals
title_full_unstemmed Extending polynomials in maximal and minimal ideals
title_sort Extending polynomials in maximal and minimal ideals
dc.creator.none.fl_str_mv Carando, D.
Galicer, D.
author Carando, D.
author_facet Carando, D.
Galicer, D.
author_role author
author2 Galicer, D.
author2_role author
dc.subject.none.fl_str_mv Extension of polynomials
Polynomial ideals
Symmetric tensor products of banach spaces
topic Extension of polynomials
Polynomial ideals
Symmetric tensor products of banach spaces
description Given a homogeneous polynomial on a Banach space E belonging to some maximal or minimal polynomial ideal, we consider its iterated extension to an ultrapower of E and prove that this extension remains in the ideal and has the same ideal norm. As a consequence, we show that the Aron-Berner extension is a well defined isometry for any maximal or minimal ideal of homogeneous polynomials. This allows us to obtain symmetric versions of some basic results of the metric theory of tensor products. © 2010 Research Institute for Mathematical Sciences, Kyoto University. All rights reserved.
publishDate 2010
dc.date.none.fl_str_mv 2010
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
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info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.12110/paper_00345318_v46_n3_p669_Carando
url http://hdl.handle.net/20.500.12110/paper_00345318_v46_n3_p669_Carando
dc.language.none.fl_str_mv eng
language eng
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by/2.5/ar
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by/2.5/ar
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv Publ. Res. Inst. Math. Sci. 2010;46(3):669-680
reponame:Biblioteca Digital (UBA-FCEN)
instname:Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron:UBA-FCEN
instname_str Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
instacron_str UBA-FCEN
institution UBA-FCEN
reponame_str Biblioteca Digital (UBA-FCEN)
collection Biblioteca Digital (UBA-FCEN)
repository.name.fl_str_mv Biblioteca Digital (UBA-FCEN) - Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales
repository.mail.fl_str_mv ana@bl.fcen.uba.ar
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