Optimal Holomorphic Hypercontractivity for CAR Algebras
Volume 58 / 2010
Bulletin Polish Acad. Sci. Math. 58 (2010), 79-90
MSC: 81S05, 81R15.
DOI: 10.4064/ba58-1-9
Abstract
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 $U_t$ is a contraction as a map $L_2({\cal H})\to L_p({\cal H})$ for arbitrary $p\geq 2$. We also prove a logarithmic Sobolev inequality.
