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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| Published in: | Journal of mathematical analysis and applications Vol. 389; no. 2; pp. 792 - 811 |
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| Format: | Journal Article |
| Language: | English |
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15.05.2012
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| ISSN: | 0022-247X, 1096-0813 |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Muro, Santiago |
| Author_xml | – sequence: 1 givenname: Santiago surname: Muro fullname: Muro, Santiago email: smuro@dm.uba.ar organization: Departamento de Matemática – Pab I, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina |
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| Keywords | Holomorphy types Polynomial ideals Fréchet algebras Riemann domains |
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| Title | On algebras of holomorphic functions of a given type |
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