Shlyakhtenko's algebras and ultracontractivity of Ornstein-Uhlenbeck semigroup

Abstract: The Ornstein-Uhlenbeck semigroup is defined on L^p-spaces associated with Shlyakhtenko's algebras alias free Araki-Woods algebras (even their Yang-Baxter deformations). We show how the ultracontractivity of the semigroup holds (or does not hold) depending on U_t, the one-parameter group of orthogonal transformations defining the algebra.