Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-24T11:10:07.475Z Has data issue: false hasContentIssue false
  • English
  • Français

Strong differentiability of the norm and rotundity of the dual

Part of: Normed linear spaces and Banach spaces; Banach lattices

Published online by Cambridge University Press:  09 April 2009

J. R. Giles
J. R. Giles
Affiliation:
University of Newcastle N.S.W. 2308 Australia University of Washington Seattle, WA 98195 U.S.A.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

For normed linear spaces two similar characterizations of strong differentiability of the norm and rotundity of the dual space are established, but it is shown that in general there is no causal relation between these two concepts.

MSC classification

Secondary: 46B10: Duality and reflexivity
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 26 , Issue 3 , November 1978 , pp. 302 - 308
Copyright
Copyright © Australian Mathematical Society 1978

References

Brown, A. L. (1974), “A rotund reflexive space having a subspace of codimension two with a discontinuous metric projection”, Michigan Math. J. 21, 145–151.CrossRefGoogle Scholar
Day, M. M. (1973), Normed Linear Spaces, 3rd ed. (Springer).CrossRefGoogle Scholar
Giles, J. R. (1971), “On a characterization of differentiability of the norm of a normed linear space”, J. Austral. Math. Soc. 12, 106–114.CrossRefGoogle Scholar
Giles, J. R. (1976), “Uniformly weak differentiability of the norm and a condition of Vlasov”, J. Austral. Math. Soc. 21,(A) 393–409.CrossRefGoogle Scholar
Klee, V. L. (1959), “Some new results on smoothness and rotundity in normed linear spaces”, Math. Ann. 139, 51–63.CrossRefGoogle Scholar
Phelps, R. R. (1960), “A representation theorem for bounded convex sets”, Proc. Amer. Math. Soc. 11, 976–983.CrossRefGoogle Scholar
Vlasov, L. P. (1970), “Almost convex and Chebychev sets”, Math. Notes Acad. Sci. USSR 8, 776–779.CrossRefGoogle Scholar