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 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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Citas:
---------- APA ----------
Carando, D. & Galicer, D.
(2011)
. Unconditionality in tensor products and ideals of polynomials, multilinear forms and operators. Quarterly Journal of Mathematics, 62(4), 845-869.
http://dx.doi.org/10.1093/qmath/haq024---------- CHICAGO ----------
Carando, D., Galicer, D.
"Unconditionality in tensor products and ideals of polynomials, multilinear forms and operators"
. Quarterly Journal of Mathematics 62, no. 4
(2011) : 845-869.
http://dx.doi.org/10.1093/qmath/haq024---------- MLA ----------
Carando, D., Galicer, D.
"Unconditionality in tensor products and ideals of polynomials, multilinear forms and operators"
. Quarterly Journal of Mathematics, vol. 62, no. 4, 2011, pp. 845-869.
http://dx.doi.org/10.1093/qmath/haq024---------- VANCOUVER ----------
Carando, D., Galicer, D. Unconditionality in tensor products and ideals of polynomials, multilinear forms and operators. Q. J. Math. 2011;62(4):845-869.
http://dx.doi.org/10.1093/qmath/haq024