Non-regularity for Banach function algebras

1998/11/10 by J. F. Feinstein, Feinstein, J. F., D. W. B. Somerset +1
Mathematics · #46J20 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:46J20

paper · pdf · doi:10.48550/arxiv.math/9811063

17 pages plain TeX: expanded introduction and some extra examples

arxiv created 1999/09/21 · arxiv updated 2009/11/30

Abstract

Let A be a unital Banach function algebra with character space Φ_A. For x∈ 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∈Φ_A: M_x⊇ J_y\ has an infinite, connected subset. Various related results are given.

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