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ISSN 1088-6850(e) ISSN 0002-9947(p)

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

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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