G. Da Prato, Scuola Normale Superiore di Pisa, Piazza dei Cavalieri 7, I-56126 Pisa, Italy, e-mail: daprato@sns.it; L. Tubaro, Department of Mathematics, University of Trento, via Sommarive 14, I-38050 Povo (Trento), Italy, e-mail: tubaro@science.unitn.it
Abstract: Given a Hilbert space $H$ with a Borel probability measure $\nu$, we prove the $m$-dissipativity in $L^1(H, \nu)$ of a Kolmogorov operator $K$ that is a perturbation, not necessarily of gradient type, of an Ornstein-Uhlenbeck operator.
Keywords: Kolmogorov equations, invatiant measures, $m$-dissipativity
Classification (MSC 2000): 47B25, 81S20, 37L40, 35K57, 70H15
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