Regularity points and Jensen measures for R(X)

Feinstein, Joel and Yang, H. (2016) Regularity points and Jensen measures for R(X). Studia Mathematica . ISSN 1730-6337 (In Press)

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We discuss two types of `regularity point', points of continuity and R-points for Banach function algebras, which were introduced by the first author and Somerset in [16]. We show that, even for the natural uniform algebras R(X) (for compact plane sets X), these two types of regularity point can be different. We then give a new method for constructing Swiss cheese sets X such that R(X) is not regular, but such that R(X) has no non-trivial Jensen measures. The original construction appears in the first author's previous work. Our new approach to constructing such sets is more general, and allows us to obtain additional properties. In particular, we use our construction to give an example of such a Swiss cheese set X with the property that the set of points of discontinuity for R(X) has positive area.

Item Type: Article
Keywords: swiss cheeses, uniform algebras, regularity of R(X)
Schools/Departments: University of Nottingham UK Campus > Faculty of Science > School of Mathematical Sciences
Depositing User: Eprints, Support
Date Deposited: 19 Jul 2016 08:39
Last Modified: 15 Sep 2016 00:53

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