Mathematische Zeitschrift

, Volume 261, Issue 1, pp 189–200 | Cite as

Analytic properties in the spectrum of certain Banach algebras

Article

Abstract

We show a sufficient condition for a domain in \({\mathbb{C}^{n}}\) to be a H-domain of holomorphy. Furthermore if a domain \({\Omega \subset\subset \mathbb{C}^{n}}\) has the Gleason \({\mathcal{B}}\) property at a point \({p \in \Omega}\) and the projection of the n − 1th order generalized Shilov boundary does not coincide with Ω then \({\mathcal{M}^{B}}\) is schlicht. We also give two examples of pseudoconvex domains in which the spectrum is non-schlicht and satisfy several other interesting properties.

Keywords

Holomorphic functions Banach algebras Nebenhülle \({\overline\partial}\) -Problems Generalized Shilov boundary 

Mathematics Subject Classification (2000)

32A65 32W05 46J20 

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Department of Mathematics and Mathematical StatisticsUmeå UniversityUmeåSweden

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