Partial regularity and t-analytic sets for Banach function algebras
Feinstein, Joel and Mortini, Raymond (2011) Partial regularity and t-analytic sets for Banach function algebras. Mathematische Zeitschrift, 271 (1-2). pp. 139-155. ISSN 0025-5874
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 infinity. A description of all closed t-analytic sets for the disk-algebra is given. Moreover, we show that some of the assertions in  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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