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A Non-Reflexive Banach Space has Non-Smooth Third Conjugate Space

Published online by Cambridge University Press:  20 November 2018

J. R. Giles
J. R. Giles*
Affiliation:
The University Of Newcastle, N.S.W. 2308, Australia
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J. Dixmier has observed [3, p. 1070] that a non-reflexive Banach space has non-rotund fourth conjugate space. It is the aim of this paper to improve Dixmier’s result by showing that a non-reflexive Banach space already has non-smooth third conjugate space in that the images under natural embedding of the continuous linear functionals which do not attain their norm on the unit sphere are non-smooth points of the third conjugate space.

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 1 , 01 March 1974, pp. 117 - 119
Copyright
Copyright © Canadian Mathematical Society 1974

References

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