On the alpha-Amenability of Hypergroups

Details On the alpha-Amenability of Hypergroups On the alpha-Amenability of Hypergroups

2007-04-23

arxiv.org/abs/0704.2976v3

Mathematics

Functional Analysis

15 pages; Keywords: Hypergroups: Sturm-Liouville, {Ch\'{e}bli-Trim\`{e}che}, Bessel-Kingman. $\alpha$-Amenable Hypergroups

Scientific paper

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 $\alpha=1$.

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