Babenko, I. K.; Bogatyi, S. A. The amenability of the substitution group of formal power series. (English. Russian original) Zbl 1228.43001 Izv. Math. 75, No. 2, 239-252 (2011); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 75, No. 2, 19-34 (2011). Summary: 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 \( C_{\text{u}}^*({\mathcal J}({\mathbf k}))\) 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. Cited in 4 Documents MSC: 43A07 Means on groups, semigroups, etc.; amenable groups 20E18 Limits, profinite groups 22A10 Analysis on general topological groups 46E15 Banach spaces of continuous, differentiable or analytic functions Keywords:topological group; group action; invariant mean PDFBibTeX XMLCite \textit{I. K. Babenko} and \textit{S. A. Bogatyi}, Izv. Math. 75, No. 2, 239--252 (2011; Zbl 1228.43001); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 75, No. 2, 19--34 (2011) Full Text: DOI