Trivial Jensen measures without regularity

Abstract

In this note we construct Swiss cheeses X such that R(X) is non-regular but such that R(X) has no non-trivial Jensen measures. We also construct a non-regular uniform algebra with compact, metrizable character space such that every point of the character space is a peak point.

6 pages plain tex

Cited by in corpus (7)

• A normal uniform algebra that fails to be strongly regular at a peak point
• Regularity of $R(X)$ does not pass to finite unions
• Extensions of uniform algebras
• Quasianalyticity in certain Banach function algebras
• A General Method for Constructing Essential Uniform Algebras
• A counterexample to a conjecture of S.E. Morris
• Swiss Cheeses and Their Applications