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arXiv · 1210.1287

L1-spectrum of Banach space valued Ornstein-Uhlenbeck operators

Rostyslav Kozhan
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Abstract

We characterize the $L^1(E;μ_\infty)$-spectrum of the Ornstein-Uhlenbeck operator, where $μ_\infty$ is the invariant measure for the Ornstein-Uhlenbeck semigroup. The main result covers the general case of an infinite-dimensional Banach space E under the assumption that the point spectrum of drift operator $A^*$ is nonempty. This extends several recent related results.

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BibTeXRIS

Rostyslav Kozhan. 2012-10-04. L1-spectrum of Banach space valued Ornstein-Uhlenbeck operators. https://doi.org/10.1007/s00233-008-9088-y

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