Extension of vector-valued 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 po...

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Autores principales: Carando, Daniel German, Lassalle, Silvia Beatriz
Publicado: 2005
Materias:
Extendibility
Integral polynomials
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v307_n1_p77_Carando
http://hdl.handle.net/20.500.12110/paper_0022247X_v307_n1_p77_Carando
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_0022247X_v307_n1_p77_Carando
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spelling paper:paper_0022247X_v307_n1_p77_Carando2023-06-08T14:47:48Z Extension of vector-valued integral polynomials Carando, Daniel German Lassalle, Silvia Beatriz 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. 2005 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v307_n1_p77_Carando 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, Daniel German
Lassalle, Silvia Beatriz
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.
author Carando, Daniel German
Lassalle, Silvia Beatriz
author_facet Carando, Daniel German
Lassalle, Silvia Beatriz
author_sort Carando, Daniel German
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
publishDate 2005
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v307_n1_p77_Carando
http://hdl.handle.net/20.500.12110/paper_0022247X_v307_n1_p77_Carando
work_keys_str_mv AT carandodanielgerman extensionofvectorvaluedintegralpolynomials
AT lassallesilviabeatriz extensionofvectorvaluedintegralpolynomials
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