On algebras of holomorphic functions of a given type

We show that several spaces of holomorphic functions on a Riemann domain over a Banach space, including the nuclear and Hilbert–Schmidt bounded type, are locally m-convex Fréchet algebras. We prove that the spectrum of these algebras has a natural analytic structure, which we use to characterize the...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2012-05, Vol.389 (2), p.792-811
Main Author: Muro, Santiago
Format: Article
Language:English
Subjects:
Fréchet algebras
Holomorphy types
Polynomial ideals
Riemann domains
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Summary:We show that several spaces of holomorphic functions on a Riemann domain over a Banach space, including the nuclear and Hilbert–Schmidt bounded type, are locally m-convex Fréchet algebras. We prove that the spectrum of these algebras has a natural analytic structure, which we use to characterize the envelope of holomorphy. We also show a Cartan–Thullen type theorem.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2011.12.022