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Weakly prime compact convex sets and uniform algebras

Published online by Cambridge University Press:  24 October 2008

A. J. Ellis
A. J. Ellis
Affiliation:
University College of Swansea
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Extract

1. Introduction. We introduce the notion of a weakly prime compact convex set, and we develop a reduction theory for spaces A(K). The notion is less restrictive in general than the prime compact convex sets of Chu, but gives a finer reduction than the Bishop and Silov decompositions forA(K) (12). The natural analogue for uniform algebras is related to the concept of weakly analytic sets due to Arenson, but unlike maximal weakly analytic sets the maximal weakly prime sets are always generalized peak sets; the uniform algebra can always be retrieved from the restrictions of the algebra to the maximal weakly prime sets.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 81 , Issue 2 , March 1977 , pp. 225 - 232
Copyright
Copyright © Cambridge Philosophical Society 1977

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References

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