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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$.


References [Enhancements On Off] (What's this?)

  • [A] R. Atalla, On the multiplicative behavior of regular matrices, Proc. Amer. Math. Soc. 26 (1970), 437-446. MR 42 #6633. MR 0271752 (42:6633)
  • [L] G. Leibowitz, Lectures on complex function algebras, Scott, Foresman, Glenview, Ill., 1970. MR 0428042 (55:1072)
  • [Ll] S. P. Lloyd, On certain projections in spaces of continuous functions, Pacific J. Math. 13 (1963), 171-175. MR 27 #2845. MR 0152873 (27:2845)
  • [P] R. R. Phelps, Lectures on Choquet's theorem, Van Nostrand, Princeton, N.J., 1966. MR 33 #1690. MR 0193470 (33:1690)
  • [Sem] Z. Semadeni, Banach spaces of continuous functions, Vol. I, PWN, Warsaw, 1971. MR 0296671 (45:5730)
  • [S] R. Sine, Geometric theory of a single Markov operator, Pacific J. Math. 27 (1968), 155-166. MR 39 #1630. MR 0240281 (39:1630)

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Additional Information

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

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