This is an announcement for the paper "On a conjecture of Pisier on the analyticity of semigroups" by Cedric Arhancet.

Abstract: We show that the analyticity of some semigroups $(T_t)_{t \geq 0}$ of 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.

Archive classification: math.FA

Remarks: 10 pages; comments are welcome

Submitted from: cedric.arhancet@univ-fcomte.fr

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1403.6737

or

http://arXiv.org/abs/1403.6737