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Smooth bump functions and geomentry of Banach spaces

Part of: Normed linear spaces and Banach spaces; Banach lattices

Published online by Cambridge University Press:  26 February 2010

R. Deville ,
G. Godefroy  and
V. Zizler
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.

MSC classification

Secondary: 46B03: Isomorphic theory (including renorming) of Banach spaces
Type
Research Article
Information
Mathematika , Volume 40 , Issue 2 , December 1993 , pp. 305 - 321
Copyright
Copyright © University College London 1993

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