On the alpha-Amenability of Hypergroups

Abstract

Let $UC(K)$ denote the Banach space of all bounded uniformly continuous functions on a hypergroup $K$. The main results of this article concern on the $\alpha$-amenability of $UC(K)$ and quotients and products of hypergroups. It is also shown that a Sturm-Liouville hypergroup with a positive index is $\alpha$-amenable if and only if $\alpha =1$.

15 pages; Keywords: Hypergroups: Sturm-Liouville, {Chébli-Trimèche}, Bessel-Kingman. $\alpha$-Amenable Hypergroups