119The semigroup algebra of a foundation semigroup with locally convex topologies and its Arens regularity
R. Farokhzad, Mahmoud Filali · 2025
In this paper, we deal with the dual of the semigroup algebras M a ( S ) for an extensive class of locally compact semigroups S under certain locally convex topologies. We introduce a locally convex topology τ LUC on M a ( S ) under which the strong dual of ( M a ( S ) , τ LUC ) is identified with the Banach space LUC ( S ) of all bounded left uniformly continuous functions on S . We then make an application of this result to define and investigate the first Arens product on the second dual of ( M a ( S ) , τ LUC ) .