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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.

References [Enhancements On Off] (What's this?)

  • [1] N. Dunford, Uniformity in linear spaces, Trans. Amer. Math. Soc. 44 (1938), 305-356. MR 1501971
  • [2] E. Hille and R. S. Phillips, Functional analysis and semi-groups, rev. ed., Amer. Math. Soc. Colloq. Publ., vol. 31, Amer. Math. Soc., Providence, R. I., 1957. MR 19, 664. MR 0089373 (19:664d)
  • [3] I. Singer, Bases in Banach space. I, Springer-Verlag, Berlin and New York, 1970. MR 0298399 (45:7451)

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Keywords: Banach spaces, basis, holomorphic functions, determining manifolds
Article copyright: © Copyright 1972 American Mathematical Society

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