\(\Gamma \)-amenability of locally compact groups
The purpose of this paper is to study the notion of \(\Gamma \)-amenability of a locally compact group \(G\), where \(\Gamma \) is a closed subgroup of \(G\times G\). That notion was introduced by \textit{B. Li} and \textit{J.-P. Pier} in [Adv. Math., Beijing 21, No. 1, 97--112 (1992; Zbl 0763.43002)]. In case \(\Gamma =G\times\{e\}\) or \(\Gamma =\{e\}\times G\), \(\Gamma \)-amenability is amenability in the usual sense, and in case \(\Gamma =\text{diag}(G)\), \(\Gamma \)-amenability is equivalent to inner amenability. In this paper the author establishes various characterizations of \(\Gamma \)-amenable groups extending the well-known Følner's conditions. In the last section the author gives sufficient conditions for inner amenability in case of discrete groups.
scientific article; zbMATH DE number 5859368
scientific article