Non-regularity for Banach function algebras

J. Feinstein; D. Somerset

ArticleOriginal scientific text

Title

Non-regularity for Banach function algebras

Authors ¹, ²

Affiliations

School of Mathematical Sciences, University of Nottingham, NG7 2RD, U.K.
Department of Mathematical Sciences, University of Aberdeen, AB24 3UE, U.K.

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 \in Φ_{A} : M_{x} \supseteq J_{y}}

has an infinite connected subset. Various related results are given.

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Title

Non-regularity for Banach function algebras

Affiliations

Abstract

Bibliography