Time regularity for generalized Mehler semigroups

We study continuity and Hölder of t ? P f $t\mapsto P_tf$ , where $P_t$ is a generalized Mehler semigroup in C b ( X ) $C_b(X)$ the space continuous bounded functions from Banach to R $\mathbb {R}$ ? $f\in C_b(X)$ . The generators L such semigroups are realizations class differential pseudo-differential operators, both finite infinite dimension. Examples operators which this theory applicable include Ornstein–Uhlenbeck with fractional diffusion dimension, associated strong-Feller semigroups,