A characterization of smooth functions defined on a Banach space

Journal Article

A sufficient condition for a function defined on a Banach space to be C k {C^k} is given. This enables us to characterize the C ∞ {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 ∞ {C^\infty } function from R m {{\mathbf {R}}^m} into the domain of the function is C ∞ {C^\infty } .

Full Text

Duke Authors

Cited Authors

  • Hain, RM

Published Date

  • 1979

Published In

Volume / Issue

  • 77 / 1

Start / End Page

  • 63 - 67

Published By

Electronic International Standard Serial Number (EISSN)

  • 1088-6826

International Standard Serial Number (ISSN)

  • 0002-9939

Digital Object Identifier (DOI)

  • 10.1090/s0002-9939-1979-0539632-8

Language

  • en