A generalization of amenability and inner amenability of groups

Ghaffari, Ali

Czechoslovak Mathematical Journal, Tome 62 (2012) no. 3, pp. 729-742.

Résumé

Let $G$ be a locally compact group. We continue our work [A. Ghaffari: $\mathrm{\Gamma }$-amenability of locally compact groups, Acta Math. Sinica, English Series, 26 (2010), 2313–2324] in the study of $\mathrm{\Gamma }$-amenability of a locally compact group $G$ defined with respect to a closed subgroup $\mathrm{\Gamma }$ of $G\times G$. In this paper, among other things, we introduce and study a closed subspace $A_{\mathrm{\Gamma }}^p(G)$ of $L^{\mathrm{\infty }}(\mathrm{\Gamma })$ and then characterize the $\mathrm{\Gamma }$-amenability of $G$ using $A_{\mathrm{\Gamma }}^p(G)$. Various necessary and sufficient conditions are found for a locally compact group to possess a $\mathrm{\Gamma }$-invariant mean.

Détail

DOI : 10.1007/s10587-012-0043-4

Classification : 22D15, 43A60
Mots-clés : amenability; Banach algebra; inner amenability; locally compact group