Nonsymmetric Ornstein–Uhlenbeck Semigroups in Banach Spaces

LetEbe a separable real Banach space and letQ∈L(E*, E) be positive and symmetric. LetS={S(t)}t⩾0be aC0-semigroup onEWe study the relations between the reproducing kernel Hilbert spaces associated with the operatorsQt :=∫t0 S(s) QS*(s) ds. Under the assumption that these operators are the covariances of centered Gaussian measuresμtonE, we also study equivalenceμt∼μsfor different values of s and t, and we calculate their Radon–Nikodym derivatives.