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A general method for constructing essential uniform algebras

Volume 246 / 2019

J. F. Feinstein, Alexander J. Izzo Studia Mathematica 246 (2019), 47-61 MSC: Primary 46J10. DOI: 10.4064/sm170907-23-2 Published online: 7 September 2018

Abstract

A general method for constructing essential uniform algebras with prescribed properties is presented. Using the method, the following examples are constructed: an essential, natural, regular uniform algebra on the closed unit disc; an essential, natural counterexample to the peak point conjecture on each manifold-with-boundary of dimension at least three; and an essential, natural uniform algebra on the unit sphere in $\mathbb {C}^3$ containing the ball algebra and invariant under the action of the 3-torus. These examples show that a smoothness hypothesis in some results of Anderson and Izzo cannot be omitted.

Authors

  • J. F. FeinsteinSchool of Mathematical Sciences
    University of Nottingham
    University Park
    Nottingham NG7 2RD, UK
    e-mail
  • Alexander J. IzzoDepartment of Mathematics and Statistics
    Bowling Green State University
    Bowling Green, OH 43403, U.S.A.
    e-mail

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