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...
| Main Authors: | , |
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| Format: | Article |
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Instytut Matematyczny Polskiej Akademii Nauk
2019
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| Online Access: | https://eprints.nottingham.ac.uk/50167/ |
| _version_ | 1848798173923901440 |
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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. |
| first_indexed | 2025-11-14T20:15:34Z |
| format | Article |
| id | nottingham-50167 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T20:15:34Z |
| publishDate | 2019 |
| publisher | Instytut Matematyczny Polskiej Akademii Nauk |
| recordtype | eprints |
| repository_type | Digital Repository |
| 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/ |