Article contents
On the problem of non-smoothness of non-reflexive second conjugate spaces
Published online by Cambridge University Press: 17 April 2009
Abstract
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
- Copyright
- Copyright © Australian Mathematical Society 1975
References
- 6
- Cited by