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Optimal holomorphic hypercontractivity for CAR algebras

Królak I.

Bulletin of the Polish Academy of Sciences. Mathematics

2010

Vol. 58, no 1

79-90

We present a new proof of Janson's strong hypercontractivity inequality for the Ornstein-Uhlenbeck semigroup in holomorphic algebras associated with CAR (canonical anticommutation relations) algebras. In the one generator case we calculate optimal bounds for t such that Ut is a contraction as a map L2(H) → Lp(H) for arbitrary p ≥ 2. We also prove a logarithmic Sobolev inequality.