On algebras of holomorphic functions of a given type

Details On algebras of holomorphic functions of a given type On algebras of holomorphic functions of a given type

2011-10-05

arxiv.org/abs/1110.1080v1

Mathematics

Functional Analysis

30 pages

Scientific paper

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 Fr\'echet 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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