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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| Format: | Article |
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Instytut Matematyczny Polskiej Akademii Nauk
2019
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| Online Access: | https://eprints.nottingham.ac.uk/50167/ |
| Summary: | 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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