HYPERGROUP ALGEBRAS AS TOPOLOGICAL ALGEBRAS

Let K be a locally compact hypergroup endowed with a left Haar measure and let L-1(K) be the usual Lebesgue space of K with respect to the left Haar measure. We investigate some properties of L1( K) under a locally convex topology beta(1). Among other things, the semireflexivity of (L-1(K),beta(1)) and of sequentially beta(1)-continuous functionals is studied. We also show that (L-1(K),beta(1)) with the convolution multiplication is always a complete semitopological algebra, whereas it is a topological algebra if and only if K is compact.