Topological Wiener-Wintner theorems for amenable operator semigroups

Inspired by topological Wiener-Wintner theorems we study the mean ergodicity of amenable semigroups of Markov operators on $C(K)$ and show the connection to the convergence of strong and weak ergodic nets. The results are then used to characterize mean ergodicity of Koopman semigroups corresponding to skew product actions on compact group extensions.Comment: 26 pages, referee's suggestions incorporated, to appear in "Ergodic Theory and Dynamical Systems

Relative ergodic properties of C*-dynamical systems

We study various ergodic properties of C*-dynamical systems inspired by unique ergodicity. In particular we work in a framework allowing for ergodic properties defined relative to various subspaces, and in terms of weighted means. Our main results are characterizations of such relative ergodic properties, ergodic theorems resulting from these properties, and examples exhibiting these properties.Comment: v1: 21 pages. v2: published version, 23 page