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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Additive mappings on rings of holomorphic functions


Authors: R. B. Burckel and Sadahiro Saeki
Journal: Proc. Amer. Math. Soc. 89 (1983), 79-85
MSC: Primary 30H05; Secondary 46E25
DOI: https://doi.org/10.1090/S0002-9939-1983-0706515-0
MathSciNet review: 706515
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0706515-0
Keywords: Additive maps, rings of holomorphic functions, derivations, homomorphisms
Article copyright: © Copyright 1983 American Mathematical Society