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Non-regularity for Banach function algebras

J. F. Feinstein·D. W. B. Somerset
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Abstract

Let $A$ be a unital Banach function algebra with character space $Φ_A$. For $x\in Φ_A$, let $M_x$ and $J_x$ be the ideals of functions vanishing at $x$, and in a neighbourhood of $x$, respectively. It is shown that the hull of $J_x$ is connected, and that if $x$ does not belong to the Shilov boundary of $A$ then the set $\{y\inΦ_A: M_x\supseteq J_y\}$ has an infinite, connected subset. Various related results are given.

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J. F. Feinstein, D. W. B. Somerset. 1999-09-21. Non-regularity for Banach function algebras. https://arxiv.org/abs/math/9811063

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