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Published June 2009 | Submitted
Journal Article Open

L^1-spectrum of Banach space valued Ornstein-Uhlenbeck operators

Abstract

We characterize the L^1(E,μ_∞)-spectrum of the Ornstein–Uhlenbeck operator Lf(x) = (1/2)TrQD^(2) + , where μ_∞ is the invariant measure for the Ornstein–Uhlenbeck semigroup generated by L. The main result covers the general case of an infinite-dimensional Banach space E under the assumption that the point spectrum of A* is nonempty and extends several recent related results.

Additional Information

© 2009 Springer. Received: 28 March 2008 Accepted: 25 May 2008 Published online: 19 June 2008. The author would like to thank J.M.A.M. van Neerven and Rostyslav O. Hryniv for helpful remarks.

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Created:
August 21, 2023
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