Geodesic
The amenability of the substitution group of formal power series
Izvestiya. Mathematics , Tome 75 (2011) no. 2, pp. 239-252

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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.
Keywords: topological group, invariant mean.
Mots-clés : group action 
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     author = {I. K. Babenko and S. A. Bogatyi},
     title = {The amenability of the substitution group of formal power series},
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     pages = {239--252},
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     number = {2},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2011_75_2_a1/}
}
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I. K. Babenko; S. A. Bogatyi. The amenability of the substitution group of formal power series. Izvestiya. Mathematics , Tome 75 (2011) no. 2, pp. 239-252. http://geodesic.mathdoc.fr/item/IM2_2011_75_2_a1/