Strict topology on locally compact semigroups

Abstract

Let S be a locally compact Hausdorff semigroup, and \(\mathfrak {A}\) a solid subalgebra of measure algebra M(S). In this paper, among other results, we find necessary and sufficient conditions on S that implies \(\mathfrak {A}\) is a semi-topological or a topological algebra with respect to the strict topology on M(S). Applications to discrete semigroups, Brandt semigroups and Clifford semigroups are given. An example establishes negatively the open question of Maghsoudi (Semigroup Forum 86:133–139, 2012). Also, we give a correct proof of Proposition 2.1 of Maghsoudi (2012).