Sur les espaces test pour la moyennabilité

Details Sur les espaces test pour la moyennabilité Sur les espaces test pour la moyennabilité

2010-06-25

arxiv.org/abs/1006.5058v6

C. R. Math. Acad. Sci. Soc. R. Canada, Vol.33 (2011), No. 3, pp. 65-77

Mathematics

Group Theory

12 pages, French language, Latex 2e. The final submission to C.R. Math. Rep. Acad. Sci. Canada. taking into account referee's

Scientific paper

We observe that a Polish group $G$ is amenable if and only if every continuous action of $G$ on the Hilbert cube admits an invariant probability measure. This generalizes a result of Bogatyi and Fedorchuk. We also show that actions on the Cantor space can be used to detect amenability and extreme amenability of Polish non-archimedean groups as well as amenability at infinity of discrete countable groups. As corollary, the latter property can also be tested by actions on the Hilbert cube. These results generalize a criterion due to Giordano and de la Harpe.

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