Li, Bingren; Pier, Jean-Paul Amenability with respect to a closed subgroup of a product group. (English) Zbl 0763.43002 Adv. Math., Beijing 21, No. 1, 97-112 (1992). The concept of \(\Gamma\)-amenability of locally compact groups is introduced, which is a generalization of the left amenability and the linear amenability in the usual sense. Let \(G\) be a locally compact group with unit element \(e\), and \(\Gamma\) be a closed subgroup of the product group \(G\times G\). The group \(G\) is said to be \(\Gamma\)-amenable if there exists a mean \(M\) on \(L^ \infty(G)\) such that \(M({_ af_ b})=M(f)\) for any \(f\in L^ \infty(G)\) and \((a,b)\in\Gamma\), where \({_ af_ b}(x)=f(a^{-1}xb)\) (\(x\in G\)). In the case \(\Gamma=G\times\{e\}\) and \(\Gamma=\{(x,x)\); \(x\in G\}\), \(\Gamma\)-amenability is equivalent to the left amenability and the inner amenability respectively. Various characterizations of \(\Gamma\)-amenability are established, which are analogous to the characterizations of amenability. Reviewer: K.Sakai (Kagoshima) Cited in 1 ReviewCited in 2 Documents MSC: 43A07 Means on groups, semigroups, etc.; amenable groups Keywords:\(\Gamma\)-amenability; locally compact groups; left amenability; linear amenability PDFBibTeX XMLCite \textit{B. Li} and \textit{J.-P. Pier}, Adv. Math., Beijing 21, No. 1, 97--112 (1992; Zbl 0763.43002)