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The Choquet boundary for uniform algebras

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1757)

Abstract

By a uniform algebra (or function algebra) in C c(Y) (Y compact Hausdorff) we mean any uniformly closed subalgebra of C c(Y) which contains the constant functions and separates points of Y. For metrizable Y, the Choquet boundary of a uniform algebra A has a particularly simple description (Bishop [8]): It consists of the peak points for A, i.e., of those y in Y for which there exists a function f in A with the property that |f(x)| < |f(y)| if xy. This result is a special case of a characterization (for arbitrary Y) due to Bishop and de Leeuw [9], which is the main theorem of this section.

Keywords

  • Peak Point
  • Function Algebra
  • Smooth Point
  • Uniform Algebra
  • Maximum Modulus Principle

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 2001 Springer-Verlag Berlin Heidelberg

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(2001). The Choquet boundary for uniform algebras. In: Phelps, R.R. (eds) Lectures on Choquet’s Theorem. Lecture Notes in Mathematics, vol 1757. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48719-0_8

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  • DOI: https://doi.org/10.1007/3-540-48719-0_8

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41834-4

  • Online ISBN: 978-3-540-48719-7

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