Optimal Holomorphic Hypercontractivity for CAR Algebras

摘要

We present a new proof of Janson's strong hypercontractivity inequality for the Ornstein-Uhlenbeck semigroup in holomorphic algebras associated with CAR (ca nonical anticommutation relations) algebras. In the one generator case we calculate op-timal bounds for t such that U_t is a contraction as a map L_2(H)→L_p(H) for arbitrary p ≥ 2. We also prove a logarithmic Sobolev inequality.