Abstract
where (laf)(g)=f(ag) and (raf)(g)=f(ga). An invariant mean is a right and left invariant mean. Ml(G), [Mr(G)] c m(G)* will denote the set of left [right] invariant means and dim MIG = n will mean that the linear manifold spanned by Ml(G) c m(G)* is n-dimensional (see [5, ?2]). Q: 1l(G) -+ m(G)* will denote the natural mapping of the semigroup algebra 11(G) into m(G)*. The following is a result of I. S. Luthar (see [9]): A commutative semigroup G has a unique invariant mean (i.e., dim Ml(G) = 1) if and only if G contains a finite ideal. Luthar's proof also yields that the unique invariant mean has to belong to Q11(G). The main result of this paper is the following:
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