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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Markov operators, peak points, and Choquet points


Author: Robert E. Atalla
Journal: Proc. Amer. Math. Soc. 41 (1973), 103-109
MSC: Primary 46E25; Secondary 47B99
DOI: https://doi.org/10.1090/S0002-9939-1973-0318861-7
MathSciNet review: 0318861
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Abstract: We deal with conditions on a closed subspace $ L$ of $ C(X)$ under which weak peak points are equivalent with Choquet points. If $ L$ satisfies a strengthened form of this equivalence ('weak peak sets = Choquet sets'--definitions are given below), then for any image of $ L$ under a Markov projection, weak peak points and Choquet points are equivalent. Conditions under which $ L$ satisfies the strengthened equivalence include (i) $ L$ interpolates its Shilov boundary, and (ii) $ L$ is the space of fixed points of a Markov operator $ T$ on $ C(X)$, where $ T$ is in an appropriate sense concentrated on the Shilov boundary of $ L$.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0318861-7
Keywords: Markov operator, projection, $ C(X)$, Shilov boundary, peak point, Choquet point, representing measure, fixed points of a Markov operator
Article copyright: © Copyright 1973 American Mathematical Society