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: | , |
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| Formato: | JOUR |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00335606_v62_n4_p845_Carando |
| Aporte de: |
| Sumario: | 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. |
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