Module Connes amenability of hypergroup measure algebras (Q317744)

In this paper, the author firstly gives general facts on dual Banach algebras and Banach modules and studies module diagonals. Let \(K_{0}\) be a closed subhypergroup of a locally compact measured hypergroup \(K\). He shows that \(M(K)\) is a dual Banach algebra and a dual Banach \(M(K_{0})\)-bimodule with compatible actions for each hypergroup \(K\). He finds formulas for the corresponding multiplication operator and its first and second conjugates. Also, he gives several examples of hypergroups. As a main theorem, he shows that if \(M(K)\) has a normal module virtual diagonal, then \(K\) is amenable.