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Analytic properties in the spectrum of certain Banach algebras

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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.

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  1. Department of Mathematics and Mathematical Statistics, Umeå University, 901 87, Umeå, Sweden

    Linus Carlsson

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  1. Linus Carlsson
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Carlsson, L. Analytic properties in the spectrum of certain Banach algebras. Math. Z. 261, 189–200 (2009). https://doi.org/10.1007/s00209-008-0322-9

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