Additive mappings on rings of holomorphic functions

Burckel, R. B.; Saeki, Sadahiro

doi:10.1090/S0002-9939-1983-0706515-0

Additive mappings on rings of holomorphic functions
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by R. B. Burckel and Sadahiro Saeki PDF

Proc. Amer. Math. Soc. 89 (1983), 79-85 Request permission

Abstract:

Additive maps $T$ between rings of holomorphic functions, which satisfy the multiplier-like condition $T(zf) = \phi T(f)$ for some $\phi$ and all $f$, are characterized. No linearity or continuity assumptions are made. Earlier results by L. Bers on homomorphisms and by J. Becker on derivations are corollaries.

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