A theorem on holomorphic mappings into Banach spaces with basis
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- by Richard Aron and Joseph A. Cima PDF
- Proc. Amer. Math. Soc. 36 (1972), 289-292 Request permission
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
- Nelson Dunford, Uniformity in linear spaces, Trans. Amer. Math. Soc. 44 (1938), no. 2, 305–356. MR 1501971, DOI 10.1090/S0002-9947-1938-1501971-X
- Einar Hille and Ralph S. Phillips, Functional analysis and semi-groups, American Mathematical Society Colloquium Publications, Vol. 31, American Mathematical Society, Providence, R.I., 1957. rev. ed. MR 0089373
- Ivan Singer, Bases in Banach spaces. I, Die Grundlehren der mathematischen Wissenschaften, Band 154, Springer-Verlag, New York-Berlin, 1970. MR 0298399
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 36 (1972), 289-292
- MSC: Primary 46G20; Secondary 32A10
- DOI: https://doi.org/10.1090/S0002-9939-1972-0317046-7
- MathSciNet review: 0317046