A general method for constructing essential uniform algebras
Volume 246 / 2019
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.
