Peak Sets for the Real Part of a Function Algebra

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 May 1982Publisher:JSTORJournal:Proceedings of the American Mathematical Society, volume 85, page 77 (issn: 0002-9939,

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Authors: Briem, Eggert;

doi: 10.2307/2043286 , 10.1090/s0002-9939-1982-0647902-8

Peak Sets for the Real Part of a Function Algebra

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Abstract

We show that if A A is a function algebra with the property that every peak set for re A A is an interpolation set for A A then A = C ( X ) A = C(X) .

Keywords

compact convex sets, function algebra, Banach algebras of continuous functions, function algebras, interpolation set, Convex sets in topological linear spaces; Choquet theory, facial structure, simplex, peak set, space of continuous affine functions

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