Hypercontractivity on the -Araki-Woods algebras
arXiv:1008.5286 · doi:10.1007/s00220-011-1221-1
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.
17 pages