Extension of vector-valued integral polynomials

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We study the extendibility of integral vector-valued polynomials on Banach spaces. We prove that an X-valued Pietsch-integral polynomial on E extends to an X-valued Pietsch-integral polynomial on any space F containing E, with the same integral norm. This is not the case for Grothendieck-integral po...

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Detalles Bibliográficos
Autores principales: Carando, D., Lassalle, S.
Formato: JOUR
Materias:
Extendibility
Integral polynomials
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_0022247X_v307_n1_p77_Carando
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_0022247X_v307_n1_p77_Carando
record_format dspace
spelling todo:paper_0022247X_v307_n1_p77_Carando2023-10-03T14:29:08Z Extension of vector-valued integral polynomials Carando, D. Lassalle, S. Extendibility Integral polynomials We study the extendibility of integral vector-valued polynomials on Banach spaces. We prove that an X-valued Pietsch-integral polynomial on E extends to an X-valued Pietsch-integral polynomial on any space F containing E, with the same integral norm. This is not the case for Grothendieck-integral polynomials: they do not always extend to X-valued Grothendieck-integral polynomials. However, they are extendible to X-valued polynomials. The Aron-Berner extension of an integral polynomial is also studied. A canonical integral representation is given for domains not containing ℓ1. © 2004 Elsevier Inc. All rights reserved. Fil:Carando, D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Lassalle, S. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_0022247X_v307_n1_p77_Carando
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Extendibility
Integral polynomials
spellingShingle Extendibility
Integral polynomials
Carando, D.
Lassalle, S.
Extension of vector-valued integral polynomials
topic_facet Extendibility
Integral polynomials
description We study the extendibility of integral vector-valued polynomials on Banach spaces. We prove that an X-valued Pietsch-integral polynomial on E extends to an X-valued Pietsch-integral polynomial on any space F containing E, with the same integral norm. This is not the case for Grothendieck-integral polynomials: they do not always extend to X-valued Grothendieck-integral polynomials. However, they are extendible to X-valued polynomials. The Aron-Berner extension of an integral polynomial is also studied. A canonical integral representation is given for domains not containing ℓ1. © 2004 Elsevier Inc. All rights reserved.
format JOUR
author Carando, D.
Lassalle, S.
author_facet Carando, D.
Lassalle, S.
author_sort Carando, D.
title Extension of vector-valued integral polynomials
title_short Extension of vector-valued integral polynomials
title_full Extension of vector-valued integral polynomials
title_fullStr Extension of vector-valued integral polynomials
title_full_unstemmed Extension of vector-valued integral polynomials
title_sort extension of vector-valued integral polynomials
url http://hdl.handle.net/20.500.12110/paper_0022247X_v307_n1_p77_Carando
work_keys_str_mv AT carandod extensionofvectorvaluedintegralpolynomials
AT lassalles extensionofvectorvaluedintegralpolynomials
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