First, we study the regularity of the heat semigroup generated by the OperatorH=L+VwhereVis a potential bounded from above, andLis the generator of the Ornstein-Uhlenbeck process ξwhich is the solution of the equation [ILM0001}whereB(t)is a cylindrical Brownian motion on a Hilbert spaceHA-2is an unbounded operator. In the final section, we study the regularity of the transition semigroup associated with the stochastic evolution equationwhereWis a vector field onH.