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Representations of the ℓ1-algebra of an inverse semigroup having the separation property†

Published online by Cambridge University Press:  18 May 2009

Bruce A. Barnes
Bruce A. Barnes
Affiliation:
University of Oregon, Eugene, Oregon
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Let S be a semigroup, and let ℓ1(S) denote the l1-semigroup algebra of S. Beginning with the fundamental paper of E. Hewitt and H. Zuckerman [5], there has been a considerable amount of research done concerning the Banach algebra ℓ1(S) in the case when S is abelian; see the bibliography [7]. However, until recently, there was very little information known concerning ℓ1(S) when S was nonabelian and infinite. Now for certain classes of infinite nonabelian semigroups with involution, recent progress has been made in the study of the Banach *-algebra ℓ1(S) and the *-representations of l1(S). In [2], B. Barnes and J. Duncan prove that ℓ1(S) is Jacobson semisimple, study the spectrum of elements in ℓ1(S), and construct and study *-representations of ℓ1(S) when S is the free semigroup with a finite or countably infinite set of generators (and also in some cases where the generators satisfy certain relations). In [1], the present author considered the representation theory of ℓ1(S) where S is an inverse semigroup. This paper is a sequel to [1].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 18 , Issue 2 , July 1977 , pp. 131 - 143
Copyright
Copyright © Glasgow Mathematical Journal Trust 1977

References

REFERENCES

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