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Maximal one-sided ideals in Banach algebras

Published online by Cambridge University Press:  24 October 2008

Michael D. Green
Michael D. Green
Affiliation:
University of Newcastle-upon-Tyne
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Extract

In (1) Akemann and Rosenfeld introduced a property for Banach algebras which they called (*). A Banach algebra satisfies (*) if every maximal one-sided ideal in is closed. They proved that certain classes of Banach algebra with satisfy (*), and they mentioned a conjecture that if is a Banach algebra with , then satisfies (*). In this paper we show that, if is a Banach algebra with a bounded right (left) approximate identity, then maximal left (right) ideals in are closed, and we give a counter-example to the above conjecture. We also give an independent proof that C*-algebras satisfy (*).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 80 , Issue 1 , July 1976 , pp. 109 - 111
Copyright
Copyright © Cambridge Philosophical Society 1976

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References

REFERENCES

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