@article { , title = {A general method for constructing essential uniform algebras}, 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.}, doi = {10.4064/sm170907-23-2}, eissn = {1730-6337}, issn = {0039-3223}, journal = {Studia Mathematica}, pages = {47-61}, publicationstatus = {Published}, publisher = {Polskiej Akademii Nauk, Instytut Matematyczny}, url = {https://nottingham-repository.worktribe.com/output/904473}, volume = {246}, year = {2019}, author = {Feinstein, Joel and Izzo, Alexander J.} }