## A note on a Wiener-Wintner theorem for mean ergodic Markov amenable semigroups

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- by Wojciech Bartoszek and Adam Śpiewak PDF
- Proc. Amer. Math. Soc.
**145**(2017), 2997-3003 Request permission

## Abstract:

We prove a Wiener-Wintner ergodic type theorem for a Markov representation $\mathcal {S} = \{ S_g : g\in G \}$ of a right amenable semitopological semigroup $G$. We assume that $\mathcal {S}$ is mean ergodic as a semigroup of linear Markov operators acting on $(C(K), \| \cdot \|_{\sup })$, where $K$ is a fixed Hausdorff, compact space. The main result of the paper is necessary and sufficient conditions for mean ergodicity of a distorted semigroup $\{ \chi (g)S_g : g\in G \}$, where $\chi$ is a semigroup character. Such conditions were obtained before under the additional assumption that $\mathcal {S}$ is uniquely ergodic.## References

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## Additional Information

**Wojciech Bartoszek**- Affiliation: Department of Probability and Biomathematics, Gdańsk University of Technology, ul. Narutowicza 11/12, 80 233 Gdańsk, Poland
- Email: bartowk@mifgate.mif.pg.gda.pl
**Adam Śpiewak**- Affiliation: Department of Probability and Biomathematics, Gdańsk University of Technology, ul. Narutowicza 11/12, 80 233 Gdańsk, Poland
- Email: adspiewak@gmail.com
- Received by editor(s): July 3, 2015
- Received by editor(s) in revised form: June 27, 2016, July 30, 2016, and August 11, 2016
- Published electronically: December 30, 2016
- Additional Notes: The first author is the corresponding author
- Communicated by: Nimish Shah
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**145**(2017), 2997-3003 - MSC (2010): Primary 47A35; Secondary 47D03, 43A65
- DOI: https://doi.org/10.1090/proc/13495
- MathSciNet review: 3637947