α-Amenable Hypergroups
Abstract
Description
Let $K$ denote a locally compact commutative hypergroup,
$L^1(K)$ the hypergroup algebra, and $α$ a real-valued hermitian character of $K$. We show that $K$ is $α$-amenable if and only if $L^1(K)$ is $α$-left amenable. We also consider the $α$-amenability of hypergroup joins and polynomial hypergroups in several variables as well as a single variable.