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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A theorem on holomorphic mappings into Banach spaces with basis


Authors: Richard Aron and Joseph A. Cima
Journal: Proc. Amer. Math. Soc. 36 (1972), 289-292
MSC: Primary 46G20; Secondary 32A10
MathSciNet review: 0317046
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Abstract: Let F be a mapping from a complex Banach space into another complex Banach space with a Schauder basis, such that each coordinate composition mapping is holomorphic. Necessary and sufficient conditions are given that F be holomorphic.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1972-0317046-7
PII: S 0002-9939(1972)0317046-7
Keywords: Banach spaces, basis, holomorphic functions, determining manifolds
Article copyright: © Copyright 1972 American Mathematical Society