Extending polynomials in maximal and minimal ideals

Autores
Carando, Daniel Germán; Galicer, Daniel Eric
Año de publicación
2010
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
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.
Fil: Carando, Daniel Germán. 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
Fil: Galicer, Daniel Eric. 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
Materia
EXTENSION OF POLYNOMIALS
POLYNOMIAL IDEALS
SYMMETRIC TENSOR PRODUCTS OF BANACH SPACES
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:11336/69129
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Extending polynomials in maximal and minimal idealsCarando, Daniel GermánGalicer, Daniel EricEXTENSION OF POLYNOMIALSPOLYNOMIAL IDEALSSYMMETRIC TENSOR PRODUCTS OF BANACH SPACEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Given 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.Fil: Carando, Daniel Germán. 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"; ArgentinaFil: Galicer, Daniel Eric. 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"; ArgentinaKyoto Univeristy2010-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/69129Carando, Daniel Germán; Galicer, Daniel Eric; Extending polynomials in maximal and minimal ideals; Kyoto Univeristy; Publications Of The Research Institute For Mathematical Sciences; 46; 3; 3-2010; 669-6800034-53181663-4926CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/0910.3888info:eu-repo/semantics/altIdentifier/url/https://www.ems-ph.org/journals/show_abstract.php?issn=0034-5318&vol=46&iss=3&rank=8info:eu-repo/semantics/altIdentifier/doi/10.2977/PRIMS/21info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:12:28Zoai:ri.conicet.gov.ar:11336/69129instacron: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 10:12:28.291CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
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, Daniel Germán
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, Daniel Germán
Galicer, Daniel Eric
author Carando, Daniel Germán
author_facet Carando, Daniel Germán
Galicer, Daniel Eric
author_role author
author2 Galicer, Daniel Eric
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
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 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.
Fil: Carando, Daniel Germán. 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
Fil: Galicer, Daniel Eric. 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
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.
publishDate 2010
dc.date.none.fl_str_mv 2010-03
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/11336/69129
Carando, Daniel Germán; Galicer, Daniel Eric; Extending polynomials in maximal and minimal ideals; Kyoto Univeristy; Publications Of The Research Institute For Mathematical Sciences; 46; 3; 3-2010; 669-680
0034-5318
1663-4926
CONICET Digital
CONICET
url http://hdl.handle.net/11336/69129
identifier_str_mv Carando, Daniel Germán; Galicer, Daniel Eric; Extending polynomials in maximal and minimal ideals; Kyoto Univeristy; Publications Of The Research Institute For Mathematical Sciences; 46; 3; 3-2010; 669-680
0034-5318
1663-4926
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://arxiv.org/abs/0910.3888
info:eu-repo/semantics/altIdentifier/url/https://www.ems-ph.org/journals/show_abstract.php?issn=0034-5318&vol=46&iss=3&rank=8
info:eu-repo/semantics/altIdentifier/doi/10.2977/PRIMS/21
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
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Kyoto Univeristy
publisher.none.fl_str_mv Kyoto Univeristy
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 13.070432

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