Cores for Feller semigroups with an invariant measure

Let be an elliptic differential operator with unbounded coefficients on RN and assume that the associated Feller semigroup (T(t))t⩾0 has an invariant measure μ. Then (T(t))t⩾0 extends to a strongly continuous semigroup (Tp(t))t⩾0 on Lp(μ)=Lp(RN,μ) for every 1⩽p<∞. We prove that, under mild conditions on the coefficients of A, the space of test functions is a core for the generator (Ap,Dp) of (Tp(t))t⩾0 in Lp(μ) for 1⩽p<∞.