Antisymmetry and analytic structure in the spectrum of a uniform Fréchet algebra
type: Item
instance of: scholarly article
title: Antisymmetry and analytic structure in the spectrum of a uniform Fréchet algebra
zbMATH Open document ID: 0619.46050
DOI: 10.1007/BF01158048
author: Helmut Goldman
published in: Manuscripta Mathematica
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155247
review text: Let M be a \(C^{\infty}\)-smooth submanifold of a domain \(G\subset C^ n\). Denote by 0(M) the algebra of germs of holomorphic functions on M, that is, each \(f\in 0(M)\) is holomorphic in some neighbourhood of M, the neighbourhood dependent of f. Now define A(M) as the closure of 0(M) with respect to the topology of compact convergence on M. If M coincides with \(\sigma\) A(M), the spectrum of A(M), we give a necessary and sufficient condition for A(M) such that M is a complex manifold.
Mathematics Subject Classification ID: 46J10
Mathematics Subject Classification ID: 46E10
Mathematics Subject Classification ID: 46H05
zbMATH DE Number: 4004941
zbMATH Keywords: analytic structure in the spectrum of a uniform Fréchet algebra
zbMATH Keywords: antisymmetry
zbMATH Keywords: reflexivity
zbMATH Keywords: algebra of germs of holomorphic functions
zbMATH Keywords: topology of compact convergence
zbMATH Keywords: complex manifold
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4004941