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Smooth bump functions and geomentry of Banach spaces

  • R. Deville (a1), G. Godefroy (a2) and V. Zizler (a3)

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.

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Smooth bump functions and geomentry of Banach spaces

  • R. Deville (a1), G. Godefroy (a2) and V. Zizler (a3)

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