Norm convergence of multiple ergodic averages on amenable groups
Dynamical Systems
2016-11-28 v8
Abstract
We apply Walsh's method for proving norm convergence of multiple ergodic averages to arbitrary amenable groups. We obtain convergence in the uniform Ces\`aro sense for their polynomial actions and for ``triangular'' averages associated to commuting homomorphic actions. The latter generalizes a result due to Bergelson, McCutcheon, and Zhang in the case of two actions.
Keywords
Cite
@article{arxiv.1111.7292,
title = {Norm convergence of multiple ergodic averages on amenable groups},
author = {Pavel Zorin-Kranich},
journal= {arXiv preprint arXiv:1111.7292},
year = {2016}
}
Comments
v8: 16 p., with improved notation and a new introduction