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Partial regularity and t-analytic sets for Banach function algebras

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Abstract

In this note we introduce the notion of t-analytic sets. Using this concept, we construct a class of closed prime ideals in Banach function algebras and discuss some problems related to Alling’s conjecture in H ∞. A description of all closed t-analytic sets for the disk-algebra is given. Moreover, we show that some of the assertions in Daoui et al. (Proc. Am. Math. Soc. 131:3211–3220, 2003) concerning the O-analyticity and S-regularity of certain Banach function algebras are not correct. We also determine the largest set on which a Douglas algebra is pointwise regular.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK

    Joel Feinstein

  2. Département de Mathématiques, LMAM, UMR 7122, Université Paul Verlaine, Ile du Saulcy, 57045, Metz, France

    Raymond Mortini

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  1. Joel Feinstein
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  2. Raymond Mortini
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Correspondence to Raymond Mortini.

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Feinstein, J., Mortini, R. Partial regularity and t-analytic sets for Banach function algebras. Math. Z. 271, 139–155 (2012). https://doi.org/10.1007/s00209-011-0856-0

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