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Article

Ghaffari, Ali
A generalization of amenability and inner amenability of groups. (English). Czechoslovak Mathematical Journal, vol. 62 (2012), issue 3, pp. 729-742
MSC: 22D15, 43A60 | MR 2984632 | Zbl 1265.43003 | DOI: 10.1007/s10587-012-0043-4
Keywords:
amenability; Banach algebra; inner amenability; locally compact group
Summary:
Let $G$ be a locally compact group. We continue our work [A. Ghaffari: $\Gamma $-amenability of locally compact groups, Acta Math. Sinica, English Series, 26 (2010), 2313–2324] in the study of $\Gamma $-amenability of a locally compact group $G$ defined with respect to a closed subgroup $\Gamma $ of $G\times G$. In this paper, among other things, we introduce and study a closed subspace $A_\Gamma ^p(G)$ of $L^\infty (\Gamma )$ and then characterize the $\Gamma $-amenability of $G$ using $A_\Gamma ^p(G)$. Various necessary and sufficient conditions are found for a locally compact group to possess a $\Gamma $-invariant mean.
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