Hypercontractivity on the q-Araki-Woods Algebras |
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| Authors: | Hun Hee Lee Éric Ricard |
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| Affiliation: | 1.Department of Mathematics,Chungbuk National University,Cheongju,Korea;2.Laboratoire de Mathématiques,Université de Franche-Comté,Besan?on,France |
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| Abstract: | 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 L p to L 2 can occur if and only if the generator of the deformation is bounded. |
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