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Proceedings of the American Mathematical Society

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An example concerning core measures


Author: S. J. Sidney
Journal: Proc. Amer. Math. Soc. 26 (1970), 428-430
MSC: Primary 46.55
DOI: https://doi.org/10.1090/S0002-9939-1970-0264402-X
MathSciNet review: 0264402
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Abstract: We shall construct a uniform algebra having a multiplicative linear functional whose space of representing measures is infinite-dimensional but nevertheless has a core measure. This answers in the negative an open question in Gamelin's book [1, p. 106].


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DOI: https://doi.org/10.1090/S0002-9939-1970-0264402-X
Keywords: Core measure, uniform algebra, multiplicative linear functional, Poisson kernel
Article copyright: © Copyright 1970 American Mathematical Society