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arXiv · 1403.6737

On a conjecture of Pisier on the analyticity of semigroups

Cédric Arhancet
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Abstract

We show that the analyticity of semigroups $(T_t)_{t \geq 0}$ of selfadjoint contractive Fourier multipliers on $L^p$-spaces of compact abelian groups is preserved by the tensorisation of the identity operator of a Banach space for a large class of K-convex Banach spaces, answering partially a conjecture of Pisier. We also give versions of this result for some semigroups of Schur multipliers and Fourier multipliers on noncommutative $L^p$-spaces. Finally, we give a precise description of semigroups of Schur multipliers to which the result of this paper can be applied.

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Cédric Arhancet. 2014-03-26. On a conjecture of Pisier on the analyticity of semigroups. https://arxiv.org/abs/1403.6737

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