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arXiv:1111.7292 [math.DS]AbstractReferencesReviewsResources

Norm convergence of multiple ergodic averages on amenable groups

Pavel Zorin-Kranich

Published 2011-11-30, updated 2013-12-18Version 8

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.

Comments: v8: 16 p., with improved notation and a new introduction
Categories: math.DS
Subjects: 37A30
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