Transactions of the American Mathematical Society

Author(s): Andreas Defant; David Pérez-García
Journal: Trans. Amer. Math. Soc. 360 (2008), 3287-3306.
MSC (2000): Primary 46G25, 46M05, 47L20
Posted: January 10, 2008
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Abstract: We show that, for each $n\in\mathbb{N}$ , there is an

-tensor norm $\alpha$ (in the sense of Grothendieck) with the surprising property that the $\alpha$ -tensor product $\tilde{\bigotimes}_\alpha(Y_1, \ldots, Y_n)$ has local unconditional structure for each choice of

arbitrary $\mathcal{L}_{p_j}$ -spaces

. In fact, $\alpha$ is the tensor norm associated to the ideal of multiple

-summing

-linear forms on Banach spaces.

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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 46G25, 46M05, 47L20

Andreas Defant
Affiliation: Fachbereich Mathematik, Universitaet Oldenburg, D--26111, Oldenburg, Germany
Email: defant@mathematik.uni-oldenburg.de

David Pérez-García
Affiliation: Área de Matemática Aplicada, Universidad Rey Juan Carlos, C/ Tulipan s/n, 28933 Móstoles (Madrid), Spain
Address at time of publication: Departamento de Análisis Matemático, Universidad Complutense de Madrid, 28040 Madrid, Spain
Email: david.perez.garcia@urjc.es, dperez@mat.ucm.es

DOI: 10.1090/S0002-9947-08-04428-0
PII: S 0002-9947(08)04428-0
Keywords: Unconditional bases, tensor products, $p$-summing operators, multilinear operators
Received by editor(s): September 15, 2005
Received by editor(s) in revised form: September 27, 2006
Posted: January 10, 2008
Additional Notes: This work was partially supported by Spanish projects MTM2005-00082 and MTM2005-08210
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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