Hypercontractivity on the q-Araki-Woods algebras
Lee, Hun Hee · Ricard, Éric
Original · EN
Extending a work of Carlen and Lieb, Biane has obtained the optimal hypercontractivity of the q-Ornstein-Uhlenbeck semigroup on the q-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 q-Araki-Woods algebras. We show that hypercontractivity from Lᵖ to L² can occur if and only if the generator of the deformation is bounded.
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