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Averaging sequences and abelian rank in amenable groups

Michael Hochman
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Abstract

We investigate the connection between the abelian rank of a countable amenable group and the existence of good averaging sequences (e.g. for the pointwise ergodic theorem). We show that if $G$ is a group of abelian rank $r(G)$ then any Tempel'man sequence must have constant at least $2^{r(G)}$ and if $G$ is abelian this constant is achieved. On the other hand, infinite rank excludes the existence of Tempel'man sequences and forces all tempered sequences to grow super-exponentially.

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Michael Hochman. 2006-01-18. Averaging sequences and abelian rank in amenable groups. https://doi.org/10.1007/s11856-007-0006-x

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