1Department of Mathematics and Statistics Miami University Oxford, OH 45056, U.S.A. 2Department of Mathematics University of Pittsburgh Pittsburgh, PA 15260, U.S.A. 3Department of Mathematics and Statistics Oakland University Rochester, MI 48309, U.S.A.
Studia Mathematica, Tome 154 (2003) no. 3, pp. 277-293
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.
Keywords:
basic sequence characterization relative weak compactness construct examples closed bounded convex subsets failing fixed point property nonexpansive self maps combining these results derive following characterization weak compactness closed bounded convex subsets weakly compact only its closed convex nonempty subsets have fixed point property nonexpansive mappings
Affiliations des auteurs :
P. N. Dowling
1
;
C. J. Lennard
2
;
B. Turett
3
1
Department of Mathematics and Statistics Miami University Oxford, OH 45056, U.S.A.
2
Department of Mathematics University of Pittsburgh Pittsburgh, PA 15260, U.S.A.
3
Department of Mathematics and Statistics Oakland University Rochester, MI 48309, U.S.A.
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title = {Characterizations of weakly compact sets
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P. N. Dowling; C. J. Lennard; B. Turett. Characterizations of weakly compact sets
and new fixed point free maps in $c_0$. Studia Mathematica, Tome 154 (2003) no. 3, pp. 277-293. doi: 10.4064/sm154-3-7
