Hypercontractivity of heat semigroups on free quantum groups
Operator Algebras
2019-09-20 v2 Functional Analysis
Probability
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 and the free permutation quantum group . We show that these semigroups satisfy ultracontractivity and hypercontractivity estimates. We also give results regarding spectral gap and logarithmic Sobolev inequalities.
Cite
@article{arxiv.1511.02753,
title = {Hypercontractivity of heat semigroups on free quantum groups},
author = {Uwe Franz and Guixiang Hong and François Lemeux and Michaël Ulrich and Haonan Zhang},
journal= {arXiv preprint arXiv:1511.02753},
year = {2019}
}
Comments
19 pages