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Vietnam Journal of Mathematics 35:1(2007) 33-41

 Amenable Locally Compact Foundation Semigroups

Ali Ghaffari

Abstract.  Let S be a locally compact Hausdorff topological semigroup, and M(S) be the Banach algebra of all bounded regular Borel measures on S. Let M_a(S) be the space of all measures µ M(S) such that both mapping and from S into M(S) are weakly continuous.

In this paper, we present a few results in the theory of amenable foundation semigroups. A number of theorems are established about left invariant mean of a foundation semigroup. In particular, we establish theorems which show that M_a(S)* has a left invariant mean. Some results were previously known for groups.

2000 Mathematics Subject Classification: 22A20, 43A60.

Keywords: Banach algebras, locally compact semigroup, topologically left invariant mean, fixed point.

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