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Isolated point theorems for uniform algebras on smooth manifolds

Volume 256 / 2021

Swarup N. Ghosh 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.

Authors

  • Swarup N. GhoshDepartment of Mathematics
    Southwestern Oklahoma State University
    Weatherford, OK 73096, U.S.A.
    e-mail

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