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 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 , 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.