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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.
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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