The amenability of the substitution group of formal power series

I. K. Babenko ; S. A. Bogatyi

Izvestiya. Mathematics , Tome 75 (2011) no. 2, pp. 239-252.

Résumé

We study the amenability property for the group $\mathcal{J}(\mathbf{k})$ of formal power series in one variable with coefficients in a commutative ring $\mathbf{k}$ with identity. We show that there exists an invariant mean on the space $C_{\mathrm{u}}^*(\mathcal{J}(\mathbf{k}))$ of uniformly continuous bounded functions on this group. This is equivalent to the fact that every continuous action of $\mathcal{J}(\mathbf{k})$ on every compact space has an invariant probability measure.

Détail

Keywords: topological group, invariant mean.
Mots-clés : group action

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