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 ON+ and the free permutation quantum group SN+. We show that these semigroups satisfy ultracontractivity and hypercontractivity estimates. We also give results regarding spectral gap and logarithmic Sobolev inequalities.
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