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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 Ma(S) be the space of all measures 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 Ma(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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