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arXiv · 0906.3253

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

Daniel Carando·Daniel Galicer
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Abstract

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 weather a tensor norm destroys unconditionality or not. Using this test we get that all injective and projective tensor norms different from $\varepsilon$ and $π$ destroy unconditionality, both in full and symmetric tensor products. We present applications to polynomial ideals: we show that many usual polynomial ideals never enjoy the Gordon-Lewis property. We also consider the unconditionality of the monomial basic sequence. Analogous problems for multilinear and operator ideals are addressed.

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Daniel Carando, Daniel Galicer. 2010-02-08. Unconditionality in tensor products and ideals of polynomials, multilinear forms and operators. https://doi.org/10.1093/qmath/haq024

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