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On a problem of Barnes and Duncan

Published online by Cambridge University Press:  20 January 2009

R. G. McLean
R. G. McLean
Affiliation:
Department of MathematicsThe City UniversityNorthampton Square London EC1V 0HBUnited Kingdom
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Consider the free monoid on a non-empty set P, and let R be the quotient monoid determined by the relations:

Let R have its natural involution * in which each element of P is Hermitian. We show that the Banach *-algebra ℓ1(R) has a separating family of finite dimensional *-representations and consequently is *-semisimple. This generalizes a result of B. A. Barnes and J. Duncan (J. Funct. Anal.18 (1975), 96–113.) dealing with the case where P has two elements.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 34 , Issue 2 , June 1991 , pp. 321 - 323
Copyright
Copyright © Edinburgh Mathematical Society 1991

References

REFERENCES

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