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Analytic properties in the spectrum of certain Banach algebras

Authors:	Linus Carlsson

Institution:	1.Department of Mathematics and Mathematical Statistics,Ume? University,Ume?,Sweden

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" target="_blank">gif" alt="$${\overline\partial}$$" align="middle" border="0"> -Problems Generalized Shilov boundary
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