Non-regularity for Banach function algebras
J. Feinstein, D. Somerset (2000)
Studia Mathematica
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Let A be a unital Banach function algebra with character space . For , let and be the ideals of functions vanishing at x and in a neighbourhood of x, respectively. It is shown that the hull of is connected, and that if x does not belong to the Shilov boundary of A then the set has an infinite connected subset. Various related results are given.