English

A General Method for Constructing Essential Uniform Algebras

Functional Analysis 2018-03-06 v2

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 of dimension at least three; and an essential, natural uniform algebra on the unit sphere in 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.

Keywords

Cite

@article{arxiv.1512.08069,
  title  = {A General Method for Constructing Essential Uniform Algebras},
  author = {J. F. Feinstein and Alexander J. Izzo},
  journal= {arXiv preprint arXiv:1512.08069},
  year   = {2018}
}
R2 v1 2026-06-22T12:18:09.702Z