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Every nonreflexive subspace of |
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| Authors: | P. N. Dowling C. J. Lennard |
| Affiliation: | Department of Mathematics and Statistics, Miami University, Oxford, Ohio 45056 C. J. Lennard ; Department of Mathematics and Statistics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260 |
| Abstract: | The main result of this paper is that every nonreflexive subspace  of ![$L_{1}[0,1]$](http://www.ams.org/proc/1997-125-02/S0002-9939-97-03577-6/gif-abstract/img7.gif) fails the fixed point property for closed, bounded, convex subsets  of  and nonexpansive (or contractive) mappings on  . Combined with a theorem of Maurey we get that for subspaces  of ![$L_{1}[0,1]$](http://www.ams.org/proc/1997-125-02/S0002-9939-97-03577-6/gif-abstract/img12.gif) ,  is reflexive if and only if  has the fixed point property. For general Banach spaces the question as to whether reflexivity implies the fixed point property and the converse question are both still open. |
| Keywords: | Nonexpansive mapping contractive mapping asymptotically isometric copy of $ell_{1}$ closed bounded convex set fixed point property nonreflexive subspaces of $L_{1}[0 1]$ |
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