Amenability notions of hypergroups and some applications to locally compact groups

Abstract

Different notions of amenability on hypergroups and their relations are studied. Developing Leptin's theorem for discrete hypergroups, we characterize the existence of a bounded approximate identity for hypergroup Fourier algebras. We study the Leptin condition for discrete hypergroups derived from the representation theory of some classes of compact groups. Studying amenability of the hypergroup algebras for discrete commutative hypergroups, we obtain some results on amenability properties of some central Banach algebras on compact and discrete groups.Comment: Significant revisions to the paper. Abstract revised, some typos corrected, some references added. The exposition has been improved while the paper has been shortened significantly. An error in the proof of the Leptin theorem is corrected by restricting the case to discrete hypergroup