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A Banach space with support homeomorphism is reflexive

Published online by Cambridge University Press:  17 April 2009

J.R. Giles
J.R. Giles
Affiliation:
The University of Newcastle, Newcastle, New South Wales.
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Abstract

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For every Banach space X there is a natural non-linear mapping from X into its dual X*. It is shown that if this mapping is a homeomorphism then it is onto X* and X is reflexive.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 5 , Issue 2 , October 1971 , pp. 187 - 189
Copyright
Copyright © Australian Mathematical Society 1971

References

[1]Bishop, Errett and Phelps, R.R., “A proof that every Banach space is subreflexive”, Bull. Amer. Math. Soc. 67 (1961), 97–98.CrossRefGoogle Scholar
[2]Cudia, Dennis F., “The geometry of Banach spaces. Smoothness”, Trans. Amer. Math. Soc. 110 (1964), 284–314.CrossRefGoogle Scholar
[3]Giles, J.R., “On a characterisation of differentiability of the norm of a normed linear space”, J. Austral. Math. Soc. 12 (1971), 106–114.CrossRefGoogle Scholar
[4]Giles, J.R., “On a differentiability condition for reflexivity of a Banach space”, J. Austral. Math. Soc. (to appear).Google Scholar
[5]Klee, Victor L. Jr, “Convex bodies and periodic homeomorphisms in Hilbert space”, Trans. Amer. Math. Soc. 74 (1953), 10–43.CrossRefGoogle Scholar