A remark on supra-additive and supra-multiplicative operators on $C(X)$

Abstract: M. Radulescu proved the following result: Let $X$ be a compact Hausdorff topological space and ${\pi } C(X)\rightarrow C(X)$ a supra-additive and supra-multiplicative operator. Then ${\pi }$ is linear and multiplicative. We generalize this result to arbitrary topological spaces.

Keywords: $C(X)$-space, supra-additive, supra-multiplicative operator, realcompact

Classification (MSC2000): 46J10, 46E25

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