Multiplicative derivations onC(X)
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, g∈C(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 Classification46E25 47B47
Key wordsMultiplicative derivation algebra of continuous functions
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