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arXiv · 1412.8303

Partial regularity and t-analytic sets for Banach function algebras

Joel Feinstein·Raymond Mortini
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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 $H^\infty$. 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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Joel Feinstein, Raymond Mortini. 2014-12-29. Partial regularity and t-analytic sets for Banach function algebras. https://doi.org/10.1007/s00209-011-0856-0

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