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...
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | JOUR |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00335606_v62_n4_p845_Carando |
| Aporte de: |
| id |
todo:paper_00335606_v62_n4_p845_Carando |
|---|---|
| record_format |
dspace |
| spelling |
todo:paper_00335606_v62_n4_p845_Carando2023-10-03T14:45:44Z Unconditionality in tensor products and ideals of polynomials, multilinear forms and operators Carando, D. Galicer, D. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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. |
| format |
JOUR |
| author |
Carando, D. Galicer, D. |
| spellingShingle |
Carando, D. Galicer, D. Unconditionality in tensor products and ideals of polynomials, multilinear forms and operators |
| author_facet |
Carando, D. Galicer, D. |
| author_sort |
Carando, D. |
| 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 |
| url |
http://hdl.handle.net/20.500.12110/paper_00335606_v62_n4_p845_Carando |
| work_keys_str_mv |
AT carandod unconditionalityintensorproductsandidealsofpolynomialsmultilinearformsandoperators AT galicerd unconditionalityintensorproductsandidealsofpolynomialsmultilinearformsandoperators |
| _version_ |
1807321028346511360 |