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On the l1-algebra of certain monoids

  • M. J. Crabb (a1) and W. D. Munn (a1)

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.

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1Barnes, B. A. and Duncan, J.. The Banach algebra l 1(S). J. Fund. Anal. 18 (1975), 96113.
2Bonsall, F. F. and Duncan, J.. Complete normed algebras (New York: Springer, 1973).
3Chaudry, M. A., Crabb, M. J. and McGregor, C. M.. The primitivity of semigroup algebras of free products. Semigroup Forum 54 (1997), 221–9.
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.
5Easdown, D. and Munn, W. D.. On semigroups with involution. Bull. Austral. Math. Soc. 48 (1993), 93100.
6Goodearl, K. R. and Menal, P.. Free and residually finite-dimensional C*-algebras. J. Fund. Anal. 90 (1990), 391410.
7McGregor, C. M.. A representation for l(S). Bull. London Math. Soc. 8 (1976), 156–60.
8McLean, R. G. and Kummer, H.. Representations of the Banach algebra ll(S). Semigroup Forum 37 (1988), 119–22.

On the l1-algebra of certain monoids

  • M. J. Crabb (a1) and W. D. Munn (a1)

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