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arXiv · 1902.09050

A doubly generated uniform algebra with a one-point Gleason part off its Shilov boundary

Alexander J. Izzo
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Abstract

It is shown that there exists a compact set $X$ in ${\mathbb C}^2$ with a nontrivial polynomial hull $\widehat X$ such that some point of $\widehat X \setminus X$ is a one-point Gleason part for $P(X)$. Furthermore, $X$ can chosen so that $P(X)$ has a dense set of invertible elements.

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Alexander J. Izzo. 2019-02-25. A doubly generated uniform algebra with a one-point Gleason part off its Shilov boundary. https://arxiv.org/abs/1902.09050

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