Topological Wiener-Wintner theorems for amenable operator semigroups

2012/09/29 by Marco Schreiber, Schreiber, Marco
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #math.DS #math.FA

paper · pdf · doi:10.48550/arxiv.1210.0108

26 pages, referee's suggestions incorporated, to appear in "Ergodic Theory and Dynamical Systems"

arxiv created 2013/01/29 · arxiv updated 2013/01/30

Abstract

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.

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