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Towards the fixed point property for superreflexive spaces

Published online by Cambridge University Press:  17 April 2009

Andrzej Wiśnicki
Andrzej Wiśnicki
Affiliation:
Department of Mathematics, Maria Curie -Sklodowska University, 20–031 Lublin, Poland e-mail: awisnic@golem.umcs.lublin.pl
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Abstract

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A Banach space X is said to have property (Sm) if every metrically convex set A ⊂ X which lies on the unit sphere and has diameter not greater than one can be (weakly) separated from zero by a functional. We show that this geometrical condition is closely connected with the fixed point property for nonexpansive mappings in superreflexive spaces.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 64 , Issue 3 , December 2001 , pp. 435 - 444
Copyright
Copyright © Australian Mathematical Society 2001

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