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Hypercontractivity of heat semigroups on free quantum groups (1511.02753v2)
Published 9 Nov 2015 in math.OA, math.FA, and math.PR
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.