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arXiv · 1110.1080

On algebras of holomorphic functions of a given type

Santiago Muro
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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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Santiago Muro. 2011-10-05. On algebras of holomorphic functions of a given type. https://arxiv.org/abs/1110.1080

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