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Smoothability, Strong Smoothability and Dentability in Banach Spaces1

Published online by Cambridge University Press:  20 November 2018

R. Anantharaman ,
T. Lewis  and
J. H. M. Whitfield
R. Anantharaman
Affiliation:
Suny College at old Westbury, Old WestburyLong Island, New York
T. Lewis
Affiliation:
University of Alberta, Edmonton, Alberta, Canada, T6G 2G1
J. H. M. Whitfield
Affiliation:
Lakehead University, Thunder Bay, Ontario, Canada., P7B 5E1
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Abstract

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It is shown that dentability of the unit ball of a conjugate Banach space X* does not imply smoothability of the unit ball of X, answering a question raised by Kemp. A property called strong smoothability is introduced and is shown to be dual to dentability. The results are used to provide new proofs of the facts that X is an Asplund space whenever it has an equivalent Fréchet differentiable norm, or whenever X* has the Radon-Nikodym Property.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 24 , Issue 1 , 01 March 1981 , pp. 59 - 68
Copyright
Copyright © Canadian Mathematical Society 1981

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