Geodesic
Optimal Holomorphic Hypercontractivity for CAR Algebras
Ilona Królak1
1 Institute of Mathematics Wrocław University Pl. Grunwaldzki 2/4 50-384 Wrocław, Poland
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 58 (2010) no. 1, pp. 79-90

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/ba58-1-9
Keywords: present proof jansons strong hypercontractivity inequality ornstein uhlenbeck semigroup holomorphic algebras associated car canonical anticommutation relations algebras generator calculate optimal bounds contraction map cal cal arbitrary geq prove logarithmic sobolev inequality

Ilona Królak 1

1 Institute of Mathematics Wrocław University Pl. Grunwaldzki 2/4 50-384 Wrocław, Poland 
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Ilona Królak. Optimal Holomorphic Hypercontractivity for CAR Algebras. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 58 (2010) no. 1, pp. 79-90. doi: 10.4064/ba58-1-9

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