On a conjecture of Pisier on the analyticity of semigroups

Abstract

We show that the analyticity of semigroups $(T_t{)}_{t\ge 0}$ 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.

12 pages; many minors changes

References in corpus (1)

• $H^{\infty }$ functional calculus and maximal inequalities for semigroups of contractions on vector-valued $L_p$-spaces