Time regularity for generalized Mehler semigroups

We study continuity and Holder continuity of t bar right arrow P(t)f, where P-t is a generalized Mehler semigroup in C-b(X), the space of the continuous and bounded functions from a Banach space X to R, and f is an element of C-b(X). The generators L of such semigroups are realizations of a class of differential and pseudo-differential operators, both in finite and in infinite dimension. Examples of operators L to which this theory is applicable include Ornstein-Uhlenbeck operators with fractional diffusion in finite dimension, and Ornstein-Uhlenbeck operators with associated strong-Feller semigroups, in infinite dimension.