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On the l1-algebra of certain monoids

Published online by Cambridge University Press:  14 November 2011

M. J. Crabb  and
W. D. Munn
M. J. Crabb
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW, Scotland, U.K.
W. D. Munn
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW, Scotland, U.K.
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Abstract

The monoids considered are the free monoid Mx and the free monoid-with-involution MIx on a nonempty set X. In each case, relative to a simply-defined involution, an explicit construction is given for a separating family of continuous star matrix representations of the l1-algebra of the monoid and it is shown that this algebra admits a faithful trace. The results are based on earlier work by M. J. Crabb et al. concerning the complex semigroup algebras of Mx and MIx.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 128 , Issue 5 , 1998 , pp. 1023 - 1031
Copyright
Copyright © Royal Society of Edinburgh 1998

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References

1Barnes, B. A. and Duncan, J.. The Banach algebra l 1(S). J. Fund. Anal. 18 (1975), 96–113.CrossRefGoogle Scholar
2Bonsall, F. F. and Duncan, J.. Complete normed algebras (New York: Springer, 1973).CrossRefGoogle Scholar
3Chaudry, M. A., Crabb, M. J. and McGregor, C. M.. The primitivity of semigroup algebras of free products. Semigroup Forum 54 (1997), 221–9.CrossRefGoogle Scholar
4Crabb, M. J., McGregor, C. M., Munn, W. D. and Wassermann, S.. On the algebra of a free monoid. Proc. Roy. Soc. Edinburgh Sect. A 126 (1996), 939–45.CrossRefGoogle Scholar
5Easdown, D. and Munn, W. D.. On semigroups with involution. Bull. Austral. Math. Soc. 48 (1993), 93–100.CrossRefGoogle Scholar
6Goodearl, K. R. and Menal, P.. Free and residually finite-dimensional C*-algebras. J. Fund. Anal. 90 (1990), 391–410.CrossRefGoogle Scholar
7McGregor, C. M.. A representation for l(S). Bull. London Math. Soc. 8 (1976), 156–60.CrossRefGoogle Scholar
8McLean, R. G. and Kummer, H.. Representations of the Banach algebra ll(S). Semigroup Forum 37 (1988), 119–22.CrossRefGoogle Scholar