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A nontrivial uniform algebra Dirichlet on its maximal ideal space
Alexander J. Izzo
It is shown that there exists a nontrivial uniform algebra that is Dirichlet on its maximal ideal space and has a dense set of elements that are exponentials. This answers a 65-yea…
A nontrivial uniform algebra regular on the Cantor set
J. F. Feinstein, Alexander J. Izzo
We prove the existence of a nontrivial uniform algebra that is logmodular and regular on the Cantor set. As a consequence, we obtain that for every compact metrizable space X witho…
Weakly strongly regular uniform algebras
J. F. Feinstein, Alexander J. Izzo
Given a uniform algebra A on a compact Hausdorff space X and a point x in X, denote by M_x the ideal of functions in A that vanish at x and by J_x the ideal of functions in A that…
A sharper Swiss cheese
Alexander J. Izzo
It is shown that there exists a compact planar set K such that the uniform algebra R(K) is nontrivial and strongly regular. This settles an issue raised by Donald Wilken 55 years a…