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A renorming theorem for dual spaces

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

Published online by Cambridge University Press:  09 April 2009

A. C. Yorke
A. C. Yorke
Affiliation:
School of Mathematical and Physical SciencesMurdoch UniversityMurdoch WesternAustralia6150
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Abstract

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If the second dual of a Banach space E is smooth at each point of a certain norm dense subset, then its first dual admits a long sequence of norm one projections, and these projections have ranges which are suitable for a transfinite induction argument. This leads to the construction of an equivalent locally uniformly rotund norm and a Markuschevich basis for E*.

MSC classification

Secondary: 46B99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 35 , Issue 3 , December 1983 , pp. 334 - 337
Copyright
Copyright © Australian Mathematical Society 1983

References

Amir, D. and Lindenstrauss, J. (1968), ‘The structure of weakly compact sets in Banach spaces’, Ann. of Math. (2) 88, 35–46.CrossRefGoogle Scholar
Diestel, J. (1975), Geometry of Banach spaces—selected topics (Springer-Verlag, Berlin, Heidelberg, New York).CrossRefGoogle Scholar
Giles, J. R. (1975), ‘On smoothness of the Banach space embedding’, Bull. Austral. Math. Soc. 13, 69–74.CrossRefGoogle Scholar
John, K. and Zizler, V. (1974), ‘Smoothness and its equivalents in weakly compactly generated Banach spaces’, J. Functional Analysis 15, 1–11.CrossRefGoogle Scholar
John, K. and Zizler, V. (1975), ‘Markuschevich bases in some dual spaces’, Proc. Amer. Math. Soc. 50, 293–296.Google Scholar
Tacon, D. G. (1970), ‘The conjugate of a smooth Banach space’, Bull. Austral. Math. Soc. 2, 415–425.CrossRefGoogle Scholar
Troyanski, S. L. (1971), ‘On locally uniformaly convex and differentiable norms in certain non-separable Banach spaces’, Studia Math. 37, 173–180.CrossRefGoogle Scholar
Yorke, A. C. (1977), ‘Weakly rotundity in Banach spaces’, J. Austral. Math. Soc. Ser. A 24, 224–233.CrossRefGoogle Scholar
Yorke, A. C. (1979), ‘Differentiability and local rotundity’, J. Austral. Math. Soc. Ser. A 28, 205–213.CrossRefGoogle Scholar