Hypercontractivity on the $q$-Araki-Woods algebras
Operator Algebras
2015-05-19 v1 Functional Analysis
Abstract
Extending a work of Carlen and Lieb, Biane has obtained the optimal hypercontractivity of the -Ornstein-Uhlenbeck semigroup on the -deformation of the free group algebra. In this note, we look for an extension of this result to the type III situation, that is for the -Araki-Woods algebras. We show that hypercontractivity from to can occur if and only if the generator of the deformation is bounded.
Cite
@article{arxiv.1008.5286,
title = {Hypercontractivity on the $q$-Araki-Woods algebras},
author = {Hun Hee Lee and Éric Ricard},
journal= {arXiv preprint arXiv:1008.5286},
year = {2015}
}
Comments
17 pages