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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A tensor norm preserving unconditionality for $ \mathcal{L}_p$-spaces


Authors: Andreas Defant and David Pérez-García
Journal: Trans. Amer. Math. Soc. 360 (2008), 3287-3306
MSC (2000): Primary 46G25, 46M05, 47L20
Published electronically: January 10, 2008
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Abstract: We show that, for each $ n\in\mathbb{N}$, there is an $ n$-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 $ n$ arbitrary $ \mathcal{L}_{p_j}$-spaces $ Y_j$. In fact, $ \alpha$ is the tensor norm associated to the ideal of multiple $ 1$-summing $ n$-linear forms on Banach spaces.


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Additional Information

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: http://dx.doi.org/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
Published electronically: January 10, 2008
Additional Notes: This work was partially supported by Spanish projects MTM2005-00082 and MTM2005-08210
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.