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, 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.
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Supported by a grant from the Ministry of Science and Technology of Slovenia.
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Goldmann, H., Šemrl, P. Multiplicative derivations onC(X) . Monatshefte für Mathematik 121, 189–197 (1996). https://doi.org/10.1007/BF01298949
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DOI: https://doi.org/10.1007/BF01298949