Isolated point theorems for uniform algebras on smooth manifolds
Volume 256 / 2021
Studia Mathematica 256 (2021), 187-196
MSC: 32E30, 46J10.
DOI: 10.4064/sm190513-5-1
Published online: 19 June 2020
Abstract
In 1957, Andrew Gleason conjectured that if $A$ is a uniform algebra on its maximal ideal space $X$ and every point of $X$ is a one-point Gleason part for $A$, then $A$ must contain all continuous functions on $X$. Gleason’s conjecture was disproved by Brian Cole in 1968. In this paper, we establish a strengthened form of Gleason’s conjecture for uniform algebras generated by real-analytic functions on compact subsets of real-analytic three-dimensional manifolds-with-boundary.
