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On the problem of non-smoothness of non-reflexive second conjugate spaces

Published online by Cambridge University Press:  17 April 2009

Ivan Singer
Ivan Singer
Affiliation:
Département d'Informatique, Université de Montréal, Canada; Institute of Mathematics, Calea Grivitei 21, Bucuresti, Romania.
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Abstract

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We prove that if E is a Banach space which has a subspace G such that the conjugate space G* contains a proper norm closed linear subspace V of characteristic 1, then E** is not smooth and there exist in πE(E) points of non-smoothness for E**, where πE: E → E** is the canonical embedding. We show that the spaces E having such a subspace G constitute a large proper subfamily of the family of all non-reflexive Banach spaces.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 12 , Issue 3 , June 1975 , pp. 407 - 416
Copyright
Copyright © Australian Mathematical Society 1975

References

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