Topological Wiener–Wintner theorems for amenable operator semigroups

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...

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Veröffentlicht in:Ergodic theory and dynamical systems 2014-10, Vol.34 (5), p.1674-1698
1. Verfasser: SCHREIBER, MARCO
Format: Artikel
Sprache:eng
Schlagworte:
Convergence
Dynamical systems
Ergodic processes
Group theory
Markov processes
Operators
Theorems
Topological manifolds
Topology
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Zusammenfassung: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.
ISSN:0143-3857
1469-4417
DOI:10.1017/etds.2013.14