Extending polynomials in maximal and minimal ideals

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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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Autores principales: Carando, D., Galicer, D.
Formato: Artículo publishedVersion
Lenguaje:Inglés
Publicado: 2010
Materias:
Extension of polynomials
Polynomial ideals
Symmetric tensor products of banach spaces
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00345318_v46_n3_p669_Carando
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling paperaa:paper_00345318_v46_n3_p669_Carando2023-06-12T16:45:32Z Extending polynomials in maximal and minimal ideals Publ. Res. Inst. Math. Sci. 2010;46(3):669-680 Carando, D. Galicer, D. Extension of polynomials Polynomial ideals Symmetric tensor products of banach spaces 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. 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. 2010 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion application/pdf eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00345318_v46_n3_p669_Carando
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
language Inglés
orig_language_str_mv eng
topic Extension of polynomials
Polynomial ideals
Symmetric tensor products of banach spaces
spellingShingle Extension of polynomials
Polynomial ideals
Symmetric tensor products of banach spaces
Carando, D.
Galicer, D.
Extending polynomials in maximal and minimal ideals
topic_facet 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.
format Artículo
Artículo
publishedVersion
author Carando, D.
Galicer, D.
author_facet Carando, D.
Galicer, D.
author_sort Carando, D.
title Extending polynomials in maximal and minimal ideals
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
publishDate 2010
url http://hdl.handle.net/20.500.12110/paper_00345318_v46_n3_p669_Carando
work_keys_str_mv AT carandod extendingpolynomialsinmaximalandminimalideals
AT galicerd extendingpolynomialsinmaximalandminimalideals
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