Mathematische Zeitschrift

, Volume 261, Issue 1, pp 189–200

Analytic properties in the spectrum of certain Banach algebras

Authors

    • Department of Mathematics and Mathematical StatisticsUmeå University
Article

DOI: 10.1007/s00209-008-0322-9

Cite this article as:
Carlsson, L. Math. Z. (2009) 261: 189. doi:10.1007/s00209-008-0322-9

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 functionsBanach algebrasNebenhülle\({\overline\partial}\) -ProblemsGeneralized Shilov boundary

Mathematics Subject Classification (2000)

32A6532W0546J20

Copyright information

© Springer-Verlag 2008