The τc -topology on locally compact foundation semigroups

Given a foundation locally compact Hausdorff topological semigroup S , we consider on Ma ( S )* the τc -topology, i.e. the weak topology under all right multipliers induced by measures in Ma ( S ). For such an arbitrary S the τc -topology is not weaker than the weak*-topology and not stronger than the norm topology on Ma ( S )*. However, a further investigation shows that for compact S the norm topology and τc -topology coincide on every norm bounded subset of Ma ( S ). Among the other results we mention that except for discrete S the τc -topology is always different from the norm-topology. Finally, we give some results about τc -almost periodic functionals.