Peak sets for the real part of a function algebra

Briem, Eggert

doi:10.1090/S0002-9939-1982-0647902-8

Peak sets for the real part of a function algebra
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Proc. Amer. Math. Soc. 85 (1982), 77-78 Request permission

Abstract:

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

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