%0 Journal Article
%T Hypercontractivity of heat semigroups on free quantum groups
%A Uwe Franz
%A Guixiang Hong
%A Fran£żois Lemeux
%A Micha£żl Ulrich
%J Mathematics
%D 2015
%I arXiv
%X In this paper we study two semigroups of completely positive unital self-adjoint maps on the von Neumann algebras of the free orthogonal quantum group $O_N^+$ and the free permutation quantum group $S_N^+$. We show that these semigroups satisfy ultracontractivity and hypercontractivity estimates. We also give results regarding spectral gap and logarithmic Sobolev inequalities.
%U http://arxiv.org/abs/1511.02753v1