Optimal Holomorphic Hypercontractivity for CAR Algebras

• Autorzy: Ilona Królak
• Języki publikacji: EN

Abstrakty

EN

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 $L₂(𝓗) → L_p(𝓗)$ for arbitrary p ≥ 2. We also prove a logarithmic Sobolev inequality.

Kategorie tematyczne

• 81S05: Canonical quantization, commutation relations and statistics
• 81R15: Operator algebra methods

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2010
• Tom: 58
• Numer: 1
• Strony: 79-90

Daty

wydano

2010

Twórcy

autor

Ilona Królak

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

Identyfikatory

DOI

10.4064/ba58-1-9