Optimal Holomorphic Hypercontractivity for CAR Algebras
Ilona Królak
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 58 (2010), p. 79-90 / Harvested from The Polish Digital Mathematics Library
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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 Ut is a contraction as a map L₂()→Lp() for arbitrary p ≥ 2. We also prove a logarithmic Sobolev inequality.

Publié le : 2010-01-01
EUDML-ID : urn:eudml:doc:281220 
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Ilona Królak. Optimal Holomorphic Hypercontractivity for CAR Algebras. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 58 (2010) pp. 79-90. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba58-1-9/