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Characterizations of weakly compact sets and new fixed point free maps in c₀

P. N. Dowling, C. J. Lennard, B. Turett (2003)

Studia Mathematica

We give a basic sequence characterization of relative weak compactness in c₀ and we construct new examples of closed, bounded, convex subsets of c₀ failing the fixed point property for nonexpansive self-maps. Combining these results, we derive the following characterization of weak compactness for closed, bounded, convex subsets C of c₀: such a C is weakly compact if and only if all of its closed, convex, nonempty subsets have the fixed point property for nonexpansive mappings.

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