Non-regularity for Banach function algebras

J. F. Feinstein; D. W. B. Somerset

Non-regularity for Banach function algebras

Functional Analysis 2007-05-23 v2

Authors: J. F. Feinstein , D. W. B. Somerset

Abstract

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.

Cite

@article{arxiv.math/9811063,
  title  = {Non-regularity for Banach function algebras},
  author = {J. F. Feinstein and D. W. B. Somerset},
  journal= {arXiv preprint arXiv:math/9811063},
  year   = {2007}
}

Comments

17 pages plain TeX: expanded introduction and some extra examples

Non-regularity for Banach function algebras

Abstract

Cite

Comments

Related papers