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

Alexander J. Izzo

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

Complex Variables 2019-02-26 v1 Functional Analysis

Authors: Alexander J. Izzo

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.

Keywords

uniform algebra polynomial hull gleason part shilov boundary compact set invertible elements

Cite

@article{arxiv.1902.09050,
  title  = {A doubly generated uniform algebra with a one-point Gleason part off its Shilov boundary},
  author = {Alexander J. Izzo},
  journal= {arXiv preprint arXiv:1902.09050},
  year   = {2019}
}

Comments

The results of this paper are in a draft of the author's paper arXiv:1801.02252 but have been removed from the latest draft of that paper and given in this new paper at the suggestion of a referee

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

Abstract

Keywords

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