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Holomorphic Generation of Continuous Inverse Algebras

Published online by Cambridge University Press:  20 November 2018

Harald Biller
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.

Keywords

46H3032A3832E3041A2046J15holomorphic functional calculuscommutative continuous inverse algebraholomorphic convexityStein compactameromorphic convexityholomorphic approximation
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 59 , Issue 1 , 01 February 2007 , pp. 3 - 35
Copyright
Copyright © Canadian Mathematical Society 2007

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