, Volume 121, Issue 3, pp 189-197

Multiplicative derivations onC(X)

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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.

Supported by a grant from the Ministry of Science and Technology of Slovenia.