COMPACTNESS OF MARKOV AND SCHRÖ DINGER SEMI-GROUPS : A PROBABILISTIC APPROACH

It is proved if an irreducible, strong Feller symmetric Markov process possesses a tightness property, then its semi-group is an L^2-compact operator. In this paper, applying this fact, we prove probabilistically the compactness of Dirichlet-Laplacians and Schrödinger operators