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Proceedings of the American Mathematical Society

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Bump functions and differentiability in Banach spaces


Author: D. J. Ives
Journal: Proc. Amer. Math. Soc. 129 (2001), 3583-3588
MSC (2000): Primary 46G05; Secondary 46T20
DOI: https://doi.org/10.1090/S0002-9939-01-06086-5
Published electronically: April 24, 2001
MathSciNet review: 1860490
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Abstract:

We show that if a Banach space $E$ admits a continuous symmetrically Fréchet subdifferentiable bump function, then $E$ is an Asplund space.


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Additional Information

D. J. Ives
Affiliation: Department of Mathematics, University College London, Gower Street, London WC1E 6BT, United Kingdom
Email: dean@dps0.math.ucl.ac.uk

DOI: https://doi.org/10.1090/S0002-9939-01-06086-5
Received by editor(s): April 14, 2000
Published electronically: April 24, 2001
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2001 American Mathematical Society