Partial regularity and t-analytic sets for Banach function algebras

Feinstein, Joel; Mortini, Raymond

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 infinity. A description of all closed t-analytic sets for the disk-algebra is given. Moreover, we show that some of the assertions in [8] 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.

Citation

Feinstein, J., & Mortini, R. (2012). Partial regularity and t-analytic sets for Banach function algebras. Mathematische Zeitschrift, 271(1-2), https://doi.org/10.1007/s00209-011-0856-0

• Journal Article Type: Article
• Acceptance Date: Feb 1, 2011
• Online Publication Date: Mar 19, 2011
• Publication Date: Jun 1, 2012
• Deposit Date: Jan 29, 2015
• Publicly Available Date: Jan 29, 2015
• Journal: Mathematische Zeitschrift
• Print ISSN: 0025-5874
• Electronic ISSN: 1432-1823
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 271
• Issue: 1-2
• DOI: https://doi.org/10.1007/s00209-011-0856-0
• Public URL: https://nottingham-repository.worktribe.com/output/1007295
• Publisher URL: http://link.springer.com/article/10.1007%2Fs00209-011-0856-0
• Additional Information: The final publication is available at Springer via http://dx.doi.org/10.1007/s00209-011-0856-0
• Contract Date: Jan 29, 2015