Unconditionality in tensor products and ideals of polynomials, multilinear forms and operators

We study tensor norms that destroy unconditionality in the following sense: for every Banach space E with unconditional basis, the n-fold tensor product of E (with the corresponding tensor norm) does not have unconditional basis. We establish an easy criterion to check whether a tensor norm destroys...

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Autores principales: Carando, Daniel German, Galicer, Daniel Eric
Publicado: 2011
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00335606_v62_n4_p845_Carando
http://hdl.handle.net/20.500.12110/paper_00335606_v62_n4_p845_Carando
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00335606_v62_n4_p845_Carando
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spelling paper:paper_00335606_v62_n4_p845_Carando2023-06-08T15:00:33Z Unconditionality in tensor products and ideals of polynomials, multilinear forms and operators Carando, Daniel German Galicer, Daniel Eric We study tensor norms that destroy unconditionality in the following sense: for every Banach space E with unconditional basis, the n-fold tensor product of E (with the corresponding tensor norm) does not have unconditional basis. We establish an easy criterion to check whether a tensor norm destroys unconditionality or not. Using this test we get that all injective and projective tensor norms different from ε and destroy unconditionality, both in full and symmetric tensor products. We present applications to polynomial ideals: we show that many usual polynomial ideals never have the Gordon-Lewis property. In some cases we even obtain that the monomial basic sequence can never be unconditional. Analogous problems for multilinear ideals are addressed, and noteworthy differences between the 2-fold and the n-fold (n ≥ 3) theory are obtained. © 2010 Published by Oxford University Press. 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. 2011 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00335606_v62_n4_p845_Carando http://hdl.handle.net/20.500.12110/paper_00335606_v62_n4_p845_Carando
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description We study tensor norms that destroy unconditionality in the following sense: for every Banach space E with unconditional basis, the n-fold tensor product of E (with the corresponding tensor norm) does not have unconditional basis. We establish an easy criterion to check whether a tensor norm destroys unconditionality or not. Using this test we get that all injective and projective tensor norms different from ε and destroy unconditionality, both in full and symmetric tensor products. We present applications to polynomial ideals: we show that many usual polynomial ideals never have the Gordon-Lewis property. In some cases we even obtain that the monomial basic sequence can never be unconditional. Analogous problems for multilinear ideals are addressed, and noteworthy differences between the 2-fold and the n-fold (n ≥ 3) theory are obtained. © 2010 Published by Oxford University Press. All rights reserved.
author Carando, Daniel German
Galicer, Daniel Eric
spellingShingle Carando, Daniel German
Galicer, Daniel Eric
Unconditionality in tensor products and ideals of polynomials, multilinear forms and operators
author_facet Carando, Daniel German
Galicer, Daniel Eric
author_sort Carando, Daniel German
title Unconditionality in tensor products and ideals of polynomials, multilinear forms and operators
title_short Unconditionality in tensor products and ideals of polynomials, multilinear forms and operators
title_full Unconditionality in tensor products and ideals of polynomials, multilinear forms and operators
title_fullStr Unconditionality in tensor products and ideals of polynomials, multilinear forms and operators
title_full_unstemmed Unconditionality in tensor products and ideals of polynomials, multilinear forms and operators
title_sort unconditionality in tensor products and ideals of polynomials, multilinear forms and operators
publishDate 2011
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00335606_v62_n4_p845_Carando
http://hdl.handle.net/20.500.12110/paper_00335606_v62_n4_p845_Carando
work_keys_str_mv AT carandodanielgerman unconditionalityintensorproductsandidealsofpolynomialsmultilinearformsandoperators
AT galicerdanieleric unconditionalityintensorproductsandidealsofpolynomialsmultilinearformsandoperators
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