Non-regularity for Banach function algebras

Details Non-regularity for Banach function algebras Non-regularity for Banach function algebras

1998-11-10

arxiv.org/abs/math/9811063v2

Mathematics

Functional Analysis

17 pages plain TeX: expanded introduction and some extra examples

Scientific paper

Let $A$ be a unital Banach function algebra with character space $\Phi_A$. For $x\in \Phi_A$, 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 $\{y\in\Phi_A: M_x\supseteq J_y\}$ has an infinite, connected subset. Various related results are given.

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