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Holomorphic Generation of Continuous Inverse Algebras
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- Journal:
- Canadian Journal of Mathematics / Volume 59 / Issue 1 / 01 February 2007
- Published online by Cambridge University Press:
- 20 November 2018, pp. 3-35
- Print publication:
- 01 February 2007
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- Article
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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.
