Characterizations of weakly compact sets and new fixed point free maps in $c_0$
Tom 154 / 2003
Studia Mathematica 154 (2003), 277-293
MSC: 47H10, 47H09, 46B50, 46B45.
DOI: 10.4064/sm154-3-7
Streszczenie
We give a basic sequence characterization of relative weak compactness in $c_{0}$ and we construct new examples of closed, bounded, convex subsets of $c_{0}$ 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 $c_{0}$: 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.
