A general method for constructing essential uniform algebras

被引：2
|
作者：
Feinstein, J. F. [1 ]
Izzo, Alexander J. [2 ]
机构：
[1] Univ Nottingham, Sch Math Sci, Univ Pk, Nottingham NG7 2RD, England
[2] Bowling Green State Univ, Dept Math & Stat, Bowling Green, OH 43403 USA
来源：
STUDIA MATHEMATICA | 2019年 / 246卷 / 01期
关键词：
essential uniform algebra; regular algebra; normal algebra; POLYNOMIAL-APPROXIMATION;
D O I：
10.4064/sm170907-23-2
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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 C-3 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.
引用
收藏
页码：47 / 61
页数：15
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