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Locally uniformly rotund norms and Markuschevich bases

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 MathematicsUniversity of New EnglandArmidale, N.S.W. 2351, Australia
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Abstract

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If a Banach space E admits a Markuschevich basis, then E can be renormed to be locally uniformly rotund. When the coefficient space of the basis is 1-norming, and this norm is very smooth, E is weakly compactly generated.

MSC classification

Secondary: 46B99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 27 , Issue 3 , May 1979 , pp. 371 - 377
Copyright
Copyright © Australian Mathematical Society 1979

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