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Proper cocycles and weak forms of amenability

Paul Jolissaint — 2015

Colloquium Mathematicae

Let G and H be locally compact, second countable groups. Assume that G acts in a measure class preserving way on a standard space (X,μ) such that L ( X , μ ) has an invariant mean and that there is a Borel cocycle α: G × X → H which is proper in the sense of Jolissaint (2000) and Knudby (2014). We show that if H has one of the three properties: Haagerup property (a-T-menability), weak amenability or weak Haagerup property, then so does G. In particular, we show that if Γ and Δ are measure equivalent discrete...

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