A general method for constructing essential uniform algebras

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...

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Main Authors: Feinstein, Joel F., Izzo, Alexander J.
Format: Article
Published: Instytut Matematyczny Polskiej Akademii Nauk 2019
Online Access:https://eprints.nottingham.ac.uk/50167/
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author Feinstein, Joel F.
Izzo, Alexander J.
author_facet Feinstein, Joel F.
Izzo, Alexander J.
author_sort Feinstein, Joel F.
building Nottingham Research Data Repository
collection Online Access
description 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.
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spelling nottingham-501672020-05-04T19:26:39Z https://eprints.nottingham.ac.uk/50167/ A general method for constructing essential uniform algebras Feinstein, Joel F. Izzo, Alexander J. 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. Instytut Matematyczny Polskiej Akademii Nauk 2019 Article PeerReviewed Feinstein, Joel F. and Izzo, Alexander J. (2019) A general method for constructing essential uniform algebras. Studia Mathematica, 246 . pp. 47-61. ISSN 0039-3223 https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/studia-mathematica/all/246/1/112380/a-general-method-for-constructing-essential-uniform-algebras 10.4064/sm170907-23-2 10.4064/sm170907-23-2 10.4064/sm170907-23-2
spellingShingle Feinstein, Joel F.
Izzo, Alexander J.
A general method for constructing essential uniform algebras
title A general method for constructing essential uniform algebras
title_full A general method for constructing essential uniform algebras
title_fullStr A general method for constructing essential uniform algebras
title_full_unstemmed A general method for constructing essential uniform algebras
title_short A general method for constructing essential uniform algebras
title_sort general method for constructing essential uniform algebras
url https://eprints.nottingham.ac.uk/50167/
https://eprints.nottingham.ac.uk/50167/
https://eprints.nottingham.ac.uk/50167/