A general method for constructing essential uniform algebras

Feinstein, Joel; Izzo, Alexander J.

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 C3 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.

Citation

Feinstein, J., & Izzo, A. J. (2019). A general method for constructing essential uniform algebras. Studia Mathematica, 246, 47-61. https://doi.org/10.4064/sm170907-23-2

• Journal Article Type: Article
• Acceptance Date: Jan 12, 2018
• Online Publication Date: Sep 7, 2018
• Publication Date: Jan 1, 2019
• Deposit Date: Mar 5, 2018
• Publicly Available Date: Sep 7, 2018
• Journal: Studia Mathematica
• Print ISSN: 0039-3223
• Electronic ISSN: 1730-6337
• Publisher: Polskiej Akademii Nauk, Instytut Matematyczny
• Peer Reviewed: Peer Reviewed
• Volume: 246
• Pages: 47-61
• DOI: https://doi.org/10.4064/sm170907-23-2
• Public URL: https://nottingham-repository.worktribe.com/output/904473
• Publisher URL: https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/studia-mathematica/all///112380/a-general-method-for-constructing-essential-uniform-algebras
• Contract Date: Mar 5, 2018