\(C^{\infty}\)-algebras from the functional analytic view point
type: Item
instance of: scholarly article
title: \(C^{\infty}\)-algebras from the functional analytic view point
zbMATH Open document ID: 0621.46046
DOI: 10.1016/0022-4049(87)90045-4
published in: Journal of Pure and Applied Algebra
publication date: 1987-01-01T00:00:00Z
review text: Roughly speaking a \(C^{\infty}\)-algebra is a commutative real algebra, in which one may not only evaluate polynomials but also \(C^{\infty}\)- functions. In this paper, we put a natural locally-m-convex topology on each \(C^{\infty}\)-algebra. This topology need not be Hausdorff, but if it is we derive nice results: The \(C^{\infty}\)-homomorphism are exactly the continuous algebra homomorphisms, countably generated Hausdorff \(C^{\infty}\)-algebras are nuclear, the action of smooth functions on Hausdorff \(C^{\infty}\)- algebras is smooth and continuous, and the coproduct equals the bornological tensor product in the most important cases. We also consider \(C^{\infty}\)-modules.
Mathematics Subject Classification ID: 46J05
Mathematics Subject Classification ID: 46J15
zbMATH DE Number: 4007001
zbMATH Keywords: C\({}^{\infty }\)-algebra
zbMATH Keywords: locally-m-convex topology
zbMATH Keywords: nuclear
zbMATH Keywords: coproduct
zbMATH Keywords: bornological tensor product
zbMATH Keywords: \(C^{\infty }\)-modules
Wikidata QID: Q62597204
author: Gerd Kainz
author: Andreas Kriegl
author: Peter W. Michor
MaRDI profile type: Publication
full work available at URL: 0022-4049(87)90045-4
OpenAlex ID: W2054452483
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description: scientific article; zbMATH DE number 4007001