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On a Characterisation of Differentiability of the Norm of a Normed Linear Space

Published online by Cambridge University Press:  09 April 2009

J. R. Giles
J. R. Giles
Affiliation:
The University of Newcastle, N.S.W.
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The purpose of this paper is to show that the various differentiability conditions for the norm of a normed linear space can be characterised by continuity conditions for a certain mapping from the space into its dual. Differentiability properties of the norm are often more easily handled using this characterisation and to demonstrate this we give somewhat more direct proofs of the reflexivity of a Banach space whose dual norm is strongly differentiable, and the duality of uniform rotundity and uniform strong differentiability of the norm for a Banach space.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 12 , Issue 1 , February 1971 , pp. 106 - 114
Copyright
Copyright © Australian Mathematical Society 1971

References

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