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The Measure Spectrum of a Uniform Algebra and Subharmonicity

Published online by Cambridge University Press:  20 November 2018

Donna Kumagai
Donna Kumagai*
Affiliation:
The Pennsylvania State University, Reading, Pennsylvania
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Let A be a uniform algebra on a compact Hausdorff space X. The spectrum, or the maximal ideal space, MA, of A is given by

We define the measure spectrum, SA, of A by

SA is the set of all representing measures on X for all Φ ∈ MA. (A representing measure for Φ ∈ MA is a probability measure μ on X satisfying

The concept of representing measure continues to be an effective tool in the study of uniform algebras. See for example [12, Chapters 2 and 3], [5, pp. 15-22] and [3]. Most of the known results on the subject of representing measures, however, concern measures associated with a single homomorphism.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 34 , Issue 3 , 01 June 1982 , pp. 673 - 685
Copyright
Copyright © Canadian Mathematical Society 1982

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