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Automatically closed prime ideals

Published online by Cambridge University Press:  12 February 2007

PAUL LAWSON
PAUL LAWSON*
Affiliation:
Department of Pure Mathematics, University of Leeds, Leeds, LS2 9JT.
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Abstract

Let A be a Banach algebra, and let {xλ:λ ∈ Λ} be a collection of central elements of A. We show that the ideal is closed whenever it is prime. In particular, this shows that prime ideals generated by finitely many central elements of a Banach algebra are automatically closed.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 142 , Issue 1 , January 2007 , pp. 185 - 192
Copyright
Copyright © Cambridge Philosophical Society 2007

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References

REFERENCES

[1] Read, C. J.. All primes have closed range. Bull. London Math. Soc. 33 (2001), 341–346.CrossRefGoogle Scholar