A doubly generated uniform algebra with a one-point Gleason part off its Shilov boundary
Volume 252 / 2020
Studia Mathematica 252 (2020), 311-319
MSC: Primary 32E20; Secondary 46J10, 46J15.
DOI: 10.4064/sm190224-7-6
Published online: 11 February 2020
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 be chosen so that $P(X)$ has a dense set of invertible elements.
