\alpha-Amenable Hypergroups

TL;DR

This paper explores the concept of lpha-amenability in locally compact commutative hypergroups, establishing equivalences with hypergroup algebra properties and examining specific cases like hypergroup joins and polynomial hypergroups.

Contribution

It provides a characterization of lpha-amenability for hypergroups and links it to lpha-left amenability of the associated hypergroup algebra, including various classes of hypergroups.

Findings

lpha-amenability of hypergroups is equivalent to lpha-left amenability of their hypergroup algebra

Analysis of lpha-amenability in hypergroup joins and polynomial hypergroups

Extension of lpha-amenability concepts to multiple variables

Abstract

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