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Characterisation of normed linear spaces with Mazur's intersection property

Published online by Cambridge University Press:  17 April 2009

J.R. Giles ,
D.A. Gregory  and
Brailey Sims
J.R. Giles
Affiliation:
Department of Mathematics, University of Newcastle, Newcastle, New South Wales
D.A. Gregory
Affiliation:
Department of Mathematics, Queen's University, Kingston, Ontario, Canada;
Brailey Sims
Affiliation:
Department of Mathematics, University of New England, Armidale, New South Wales.
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Abstract

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Normed linear spaces possessing the euclidean space property that every bounded closed convex set is an intersection of closed balls, are characterised as those with dual ball having weak* denting points norm dense in the unit sphere. A characterisation of Banach spaces whose duals have a corresponding intersection property is established. The question of the density of the strongly exposed points of the ball is examined for spaces with such properties.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 18 , Issue 1 , February 1978 , pp. 105 - 123
Copyright
Copyright © Australian Mathematical Society 1978

References

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