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Geometry in quotient reflexive 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:
Department of MathematicsThe University of Western Australia Nedlands, W. A. 6009, Australia
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Abstract

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The structure and geometry of Banach spaces with the property that E(4) = Ê** + E⊥ ⊥ are investigated: such spaces are called quotient reflexive spaces here. For these spaces, if E is very smooth, Ê is also very smooth, and if E* is weakly locally uniformly rotund (WLUR), E(4) is smooth on a certain (relatively) norm dense subset of Ê**. Consequently, for quotient reflexive spaces, WLUR and very-WLUR are equivalent in 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 2 , October 1983 , pp. 263 - 268
Copyright
Copyright © Australian Mathematical Society 1983

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