Ring derivations on algebras of continuous functions
type: Item
instance of: scholarly article
title: Ring derivations on algebras of continuous functions
zbMATH Open document ID: 0892.46059
DOI: 10.1007/BF01196575
author: Helmut Goldmann
published in: Archiv der Mathematik
publication date: 1995-08-22T00:00:00Z
review text: A ringderivation on a topological algebra \(A\) is a map \(D\) from \(A\) to \(A\) satisfying the conditions 1) \(D(a+b)=D(a) +D(b)\) and 2) \(D(ab)=aD(b)+D(a)b\). Let \(G\) be an open subset of the real line or the complex plane and let \(A\) be one of the algebras (real or complex) \(C(G)\), \(C^{\infty}(G)\) or \(H(G)\) (holomorphic functions on \(G\)) equipped with the topology of uniform convergence on compact subsets of \(G\). The author gives a simple proof of the automatic continuity of every ringderivation on \(A\), a proof which can be extended to a large class of topological algebras.
reviewed by: E. Briem
Mathematics Subject Classification ID: 46H40
zbMATH DE Number: 779019
zbMATH Keywords: derivation
zbMATH Keywords: ringderivation
zbMATH Keywords: topological algebra
MaRDI profile type: Publication
cites work: A note on derivations of algebras of analytic functions.
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description: scientific article; zbMATH DE number 779019