Topological Brandt semigroups

Abstract

In the present paper, the properties of a locally compact Hausdorff topological Brandt semigroup, and the relation between its semigroup algebras and l1-Munn algebras over group algebras are investigated. It is proved that for each locally compact Hausdorff topological group G, and each index set I, there exists a locally compact Hausdorff topological Brandt semigroup S=B(G,I) such that the Banach algebras \(\mathcal {LM}_{I}(M(G))\) and \(\mathcal{LM}_{I}(L^{1}(G))\) are isometrically isomorphic to M(S)/l1({0}) and Ma(S)/l1({0}), respectively.