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L1-spectrum of Banach space valued Ornstein-Uhlenbeck operators (1210.1287v1)
Published 4 Oct 2012 in math.CA, math.FA, and math.SP
Abstract: We characterize the $L1(E;\mu_\infty)$-spectrum of the Ornstein-Uhlenbeck operator, where $\mu_\infty$ 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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