Advanced Studies: Euro-Tbilisi Mathematical Journal

On amenability of hypergroup algebras

A. Ghaffari, M. Mohammadi, M. Sheiban

In this paper, among the other things, we prove a variety of characterizations of amenable hypergroups. We give sufficient conditions and some necessary conditions for H to have a left invariant mean. We know that every topologically left invariant mean on L^∞(H) is also left invariant mean. Sufficient conditions on a left invariant mean to be a topologically left invariant mean are given. One of the main results of this paper implies that, if φ ∈ P¹(H) is left invariant mean, then H is compact.


Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 18(2) (2025), pp. 107-118