Hypercontractivity of heat semigroups on free quantum groups

Abstract

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.

19 pages

Cited by in corpus (2)

• Hardy-Littlewood inequalities on compact quantum groups of Kac type
• Property RD and hypercontractivity for orthogonal free quantum groups