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Smooth bump functions and geomentry of Banach spaces

Published online by Cambridge University Press:  26 February 2010

R. Deville
Affiliation:
Université de Franche-Comté, Besaçon, France
G. Godefroy
Affiliation:
Equipe d'Analyse, Université Paris VI, F-75252-Paris, Cedex 05, France
V. Zizler
Affiliation:
Department of Mathematics, University of Alberta, 632 Central Academic Building, Edmonton, Alberta, Canada
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Abstract

Norms with moduli of smoothness of power type are constructed on spaces with the Radon-Nikodym property that admit pointwise Lipschitz bump functions with pointwise moduli of smoothness of power type. It is shown that no norms with pointwise moduli of rotundity of power type can exist on nonsuperreflexive spaces. A new smoothness characterization of spaces isomorphic to Hilbert spaces is given.

Type
Research Article
Copyright
Copyright © University College London 1993

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