A characterization of smooth functions defined on a Banach space
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- by Richard M. Hain PDF
- Proc. Amer. Math. Soc. 77 (1979), 63-67 Request permission
Abstract:
A sufficient condition for a function defined on a Banach space to be ${C^k}$ is given. This enables us to characterize the ${C^\infty }$ functions from one Banach space into another Banach space as those functions that, for each positive integer m, have the property that the composition of the function with each ${C^\infty }$ function from ${{\mathbf {R}}^m}$ into the domain of the function is ${C^\infty }$.References
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Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 77 (1979), 63-67
- MSC: Primary 58C20; Secondary 26E10
- DOI: https://doi.org/10.1090/S0002-9939-1979-0539632-8
- MathSciNet review: 539632