First, we study the regularity of the heat semigroup generated by the OperatorH=L+Vwhere Vis a potential bounded from above, and Lis the generator of the Ornstein-Uhlenbeck process ξwhich is the solution of the equation [ILM0001where B(t)is a cylindrical Brownian motion on a Hilbert space HA^-2is an unbounded operator. In the final section, we study the regularity of the transition semigroup associated with the stochastic evolution equation   where Wis a vector field on H.