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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Peak points for hypo-Dirichlet algebras


Author: S. J. Sidney
Journal: Proc. Amer. Math. Soc. 26 (1970), 431-436
MSC: Primary 46.55
MathSciNet review: 0264403
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Abstract: A proof is given of a theorem limiting the number of points not in the Choquet boundary for certain uniform algebras. In the hypo-Dirichlet case the argument reduces to a short proof that every point is in the Choquet boundary. Also, a lemma is presented which describes, for certain subalgebras of codimension one in a uniform algebra, a relation between certain spaces of real functions associated with the original algebra, and the corresponding spaces associated with the subalgebra.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1970-0264403-1
PII: S 0002-9939(1970)0264403-1
Keywords: Peak point, hypo-Dirichlet algebra, Choquet boundary, uniform algebra
Article copyright: © Copyright 1970 American Mathematical Society