Algebras of Measures on a Locally Compact Semigroup Iii

Topologically left invariant means on semigroup algebras

“…We say that S is semifoundation if there is a measure ν ∈ M 0 (S) such that the map x → δ x * ν from S into M(S) is continuous. It is clear that every foundation semigroup is also a semifoundation semigroup (for more on foundation semigroups, the reader is referred to [2] and [5]). We recall that a mean M is left invariant if M, f δ x = M, f for any x ∈ S and f ∈ M(S) * .…”

“…Thus {Ω f ; f ∈ M(S) * } has the finite intersection property, as required. So (1) is equivalent to (2).…”

The topological centers of LUC(S)* and M a (S)** of certain foundation semigroups

“…Recall also that on a locally compact Hausdor and jointly continuous topological semigroup S, M a S (orL S ) [2], [5], [7] denotes the space of all measures " P M S (the space of all bounded complex Radon measures on S) for which the mappings x U 3 À " j j à x (where x denotes the Dirac measure at x) and x U 3 À x à " j j from S into M S are weakly continuous. It is well known that M a S is a closed two-sided L-ideal of M S .…”

Certain semigroups embeddabable in topological groups

“…For various results on M a (S) for the case where S is locally compact we refer the interested reader to Baker (1970 and1972), Dzinotyiweyi (1978b), Dzinotyiweyi and Sleijpen (1979), and Sleijpen (1976 and1978).…”