2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/114106We investigate the transition semigroup of the solution to a stochastic evolution equation $dX(t) = AX(t)dt +dW_H(t)$, $t\ge 0,$ where $A$ is the generator of a $C_0$-semigroup $S$ on a separable real Banach space $E$ and $W_H$ is cylindrical white noise with values in a real Hilbert space $H$ which is continuously embedded in $E$. Various properties of these semigroups, such as the strong Feller property, the spectral gap property, and analyticity, are characterized in terms of the behaviour of $S$ in $H$. In particular we investigate the interplay between analyticity of the transition semigroup, $S$-invariance of $H$, and analyticity of the restricted semigroup $S_H$.This is an update of the published version of the paper. The proof of Theorem 9.1 has been correctedProbabilityFunctional Analysis35R15; 60H15; 47D03text