English

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

R2 v1 2026-06-21T19:44:15.882Z