# A general method for constructing essential uniform algebras

@article{Feinstein2015AGM, title={A general method for constructing essential uniform algebras}, author={Joel F. Feinstein and Alexander J. Izzo}, journal={Studia Mathematica}, year={2015} }

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 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…

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It was once conjectured that if $$A$$A is a uniform algebra on its maximal ideal space $$X$$X, and if each point of $$X$$X is a peak point for $$A$$A, then $$A = C(X)$$A=C(X). This peak-point…

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