Hecke *-algebras on locally compact hypergroups

In this paper, for a discrete hypergroup K and its subhypergroup H, we initiate the related Hecke *-algebra which is an extension of the classical one, and study its basic properties. Especially, we give a necessary and sufficient condition (named (beta)) for this algebra to be associative. Also, we show that this new structure is an associative *-algebra if and only if K is a locally compact group.