Arens regularity of semigroup algebras with certain locally convex topologies

The authors have recently introduced and studied a locally convex topology beta(1)(S) on the semigroup algebra M-a(S) of a locally compact semigroup S; as the main result, they showed that the strong dual of (M-a(S),beta(1)(S)) can be identified with the Banach space L-0(infinity) (S, M-a(S)) for a large class of locally compact semigroups S. Here, an application of this result is made to define and investigate an Arens multiplication on the second dual of (M-a(S),beta(1)(S)).