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On a differentiability condition for reflexivity of a Banach space

Published online by Cambridge University Press:  09 April 2009

J. R. Giles
Affiliation:
The University of Newcastle, N.S.W.
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In studying the geometry of normed linear space it is useful to draw attention to the following mapping.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1971

References

[1]Bishop, E. and Phelps, R. R., ‘A proof that every Banach space is subreflexive’, Bull. Amer. Math. Soc. 67 (1961), 9798.Google Scholar
[2]Cudia, D. F., ‘The geometry of Banach spaces. Smoothness’, Trans. Amer. Math. Soc. 110 (1964), 284314.Google Scholar
[3]Giles, J. R., ‘On a characterisation of differentiability of the norm of a normed linear space’, J. Aust. Math. Soc. 12 (1971), 106114.CrossRefGoogle Scholar
[4]Kelley, J. L. and Namioka, I., ‘Linear Topological Spaces’ (Van Nostrand, Princeton, 1963).Google Scholar
[5]Lovaglia, A. R., ‘Locally uniformly convex Banach spaces’, Trans. Amer. Math. Soc. 78 (1955), 225238.Google Scholar
[6]Phelps, R. R., ‘Subreflexive normed linear spaces’, Arch. Math. 8 (1957), 444450.CrossRefGoogle Scholar
[7]Wilansky, A., ‘Functional Analysis’ (Blaisdell, Waltham, Mass., 1964).Google Scholar