Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

Request Permissions   Purchase Content 
 

 

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


Authors: Wojciech Bartoszek and Adam Śpiewak
Journal: Proc. Amer. Math. Soc. 145 (2017), 2997-3003
MSC (2010): Primary 47A35; Secondary 47D03, 43A65
DOI: https://doi.org/10.1090/proc/13495
Published electronically: December 30, 2016
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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), \Vert \cdot \Vert _{\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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 47A35, 47D03, 43A65

Retrieve articles in all journals with MSC (2010): 47A35, 47D03, 43A65


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

DOI: https://doi.org/10.1090/proc/13495
Keywords: Amenable Markov semigroups, Wiener-Wintner ergodic theorem.
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
Article copyright: © Copyright 2016 American Mathematical Society