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17th "Summer" Conference on Topology and Applications
July 1-4, 2002
University of Auckland
Auckland, New Zealand

Organizers
David Gauld (University of Auckland), Sina Greenwood (University of Auckland), David McIntyre (University of Auckland), Warren Moors (Waikato University), Sidney Morris (University of South Australia), Vladimir Pestov (Victoria University Wellington), Ivan Reilly (University of Auckland), Des Robbie (University of Melbourne)

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A dual differentiation space without an equivalent locally uniformly rotund norm.
by
Warren Moors
The University of Waikato
Coauthors: Petar Kenderov (Bulgarian academy of sciences)

In this talk I will present an example of a Banach space of the form (C(K), ||·||\infty) which has the property that each equivalent norm on C(K) for which the Bishop-Phelps set (i.e., the set of continuous linear functions on C(K) that attain their norm) is residual in C(K)* has a dual norm which is Frechet differentiable on a dense subset of C(K)*, but which does not admit an equivalent locally uniformly rotund norm. Thus answering a question from 1997.

Date received: May 9, 2002

Copyright © 2002 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cait-10.