Averaging sequences and abelian rank in amenable groups

Michael Hochman*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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 ergodic theorem). We show that if G is a group with finite abelian rank r(G), then 2r(G) is a lower bound on the constant associated to a Tempel'man sequence, and if G is abelain there is a Tempel'man sequence in G with this constant. On the other hand, infinite rank precludes the existence of Tempel'man sequences and forces all tempered sequences to grow super-exponentially.

Original languageAmerican English
Pages (from-to)119-128
Number of pages10
JournalIsrael Journal of Mathematics
Volume158
DOIs
StatePublished - Mar 2007

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