Left cancellative and left shiffable hypergroups

Abstract

Many of interesting results on a locally compact group G heavily depend on. the fact that epsilon(x).vertical bar m vertical bar = vertical bar epsilon(x).m vertical bar for every x is an element of G and m is an element of C-b(G)*. In the present paper, by introducing the two notions of left cancellative and left shiftable hypergroups and investigating their properties, we have been able (among other results) to prove that if K is a locally compact hypergroup for which x * y is a finite set for every x, y is an element of K, then epsilon(x).vertical bar m vertical bar = vertical bar epsilon(x).m vertical bar for every x is an element of K and m is an element of C-b(K)* if and only if K is a group.