Monatshefte für Mathematik

, Volume 121, Issue 3, pp 189–197

Multiplicative derivations onC(X)

  • Helmut Goldmann
  • Peter Šemrl
Article

Abstract

LetX be a completely regular topological space satisfying the first axiom of countability with no isolated points, and letC(X) be the algebra of all continuous functions onX. A mappingd:C(X)→C(X) is called a multiplicative derivation ifd(fg)=fd(g)+gd(f) for every pair of functionsf, gC(X) (no linearity or continuity ofd is assumed). We obtain a complete description of such mappings and give examples to show that the above assumptions on the spaceX are essential.

1991 Mathematics Subject Classification

46E25 47B47 

Key words

Multiplicative derivation algebra of continuous functions 

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Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Helmut Goldmann
    • 1
  • Peter Šemrl
    • 2
  1. 1.Mathematisches Institut der Universität BayreuthBayreuthGermany
  2. 2.TF, University of MariborMariborSlovenia

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