Semigroups of kernel operators

Abstract

We study several aspects of the asymptotic behavior of semigroups of kernel operators. On the one hand, we prove a mean ergodic theorem for Markovian transition semigroups on the space of measures. On the other hand, we deduce Doob"s stability theorem from the lattice structure of transition kernels and prove a Tauberian theorem for strong Feller semigroups.