| Popis: |
Let $K$ be a hypergroup. The purpose of this article is to study the notions of amenability of the hypergroup algebras $L(K)$ , $M(K)$ , and $L(K)^{**}$ . Among other results, we obtain a characterization of approximate amenability of $L(K)^{**}$ . Moreover, we introduce the Banach space $L_{\infty}(K,L(K))$ and prove that the dual of a Banach hypergroup algebra $L(K)$ can be identified with $L_{\infty}(K,L(K))$ . In particular, $L(K)$ is an $F$ -algebra. By using this fact, we give necessary and sufficient conditions for $K$ to be left-amenable. |
