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A Dual characterization of Banach Spaces With the Convex Point-of-Continuity Property

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

Published online by Cambridge University Press:  20 November 2018

D. E. G. Hare
D. E. G. Hare*
Affiliation:
Department of Mathematics University of British Columbia Vancouver, Canada
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Abstract

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We introduce a new type of differentiability, called cofinite Fréchet differentiability. We show that the convex point-of-continuity property of Banach spaces is dual to the cofinite Fréchet differentiability of all equivalent norms. A corresponding result for dual spaces with the weak* convex point-of-continuity property is also established.

MSC classification

Secondary: 46B20: Geometry and structure of normed linear spaces
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 32 , Issue 3 , 01 September 1989 , pp. 274 - 280
Copyright
Copyright © Canadian Mathematical Society 1989

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