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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Vydáno v:Journal of mathematical analysis and applications Ročník 389; číslo 2; s. 792 - 811
Hlavní autor: Muro, Santiago
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Inc 15.05.2012
Témata:
Fréchet algebras
Holomorphy types
Polynomial ideals
Riemann domains
Holomorphy types
Polynomial ideals
Fréchet algebras
Riemann domains
ISSN:0022-247X, 1096-0813
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Popis
Shrnutí: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