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.
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}
}