Prof. Markus Kunze “A monotone convergence Theorem for strong Feller semigroups”

Let T_n be an increasing sequence of sub Markovian kernel operators
over a Polish space E that satisfy the strong Feller property, i.e. they
map bounded and measurable functions on E to bounded and
continuous functions on E. Denote the limit semigroup by T. We prove
that T also satisfies the strong Feller property whenever the Laplace
transform of T maps the function 1 to a continuous function. We apply
this result to strongly elliptic operators on R^d with unbounded
coefficients under fairly mild regularity assumptions. Some counterexamples will be discussed as well.

This is joint work with Christian Budde, Alexander Dobrick and Jochen Glück.