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Abstract
We prove hypercontractivity of nonsymmetric Ornstein-Uhlenbeck semigroups in Hilbert spaces, using direct probabilistic arguments. Our results imply exponential convergence at infinity for the semigroup. We show by examples that in our setting logarithmic Sobolev inequalities do not hold in general
*Partally supported by Itlian MURST 60% research funds. Tis work was undertaken wile the author was Scuola Normale Superiore Pisa
*Partally supported by Itlian MURST 60% research funds. Tis work was undertaken wile the author was Scuola Normale Superiore Pisa
Notes
*Partally supported by Itlian MURST 60% research funds. Tis work was undertaken wile the author was Scuola Normale Superiore Pisa