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A general method for constructing essential uniform algebras

Feinstein, Joel; Izzo, Alexander J.

Authors

Alexander J. Izzo



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. F., & 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 http://eprints.nottingham.ac.uk/id/eprint/50167
Publisher URL https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/studia-mathematica/all///112380/a-general-method-for-constructing-essential-uniform-algebras
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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