Optimal Holomorphic Hypercontractivity for CAR Algebras

Volume 58 / 2010

Ilona Królak Bulletin Polish Acad. Sci. Math. 58 (2010), 79-90 MSC: 81S05, 81R15. DOI: 10.4064/ba58-1-9


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.


  • Ilona KrólakInstitute of Mathematics
    Wrocław University
    Pl. Grunwaldzki 2/4
    50-384 Wrocław, Poland

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