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Holomorphic Generation of Continuous Inverse Algebras

Published online by Cambridge University Press:  20 November 2018

Harald Biller*
Affiliation:
Fachbereich Mathematik, Technische Universität Darmstadt, Schlossgartenstr. 7, 64289 Darmstadt, Germany e-mail: harald.biller@gmx.de
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Abstract

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We study complex commutative Banach algebras (and, more generally, continuous inverse algebras) in which the holomorphic functions of a fixed $n$-tuple of elements are dense. In particular, we characterize the compact subsets of ${{\mathbb{C}}^{n}}$ which appear as joint spectra of such $n$ -tuples. The characterization is compared with several established notions of holomorphic convexity by means of approximation conditions.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2007

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