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

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.