Characterizations of weakly compact sets and new fixed point free maps in $c_0$

Volume 154 / 2003

P. N. Dowling, C. J. Lennard, B. Turett Studia Mathematica 154 (2003), 277-293 MSC: 47H10, 47H09, 46B50, 46B45. DOI: 10.4064/sm154-3-7

Abstract

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.

Authors

  • P. N. DowlingDepartment of Mathematics and Statistics
    Miami University
    Oxford, OH 45056, U.S.A.
    e-mail
  • C. J. LennardDepartment of Mathematics
    University of Pittsburgh
    Pittsburgh, PA 15260, U.S.A.
    e-mail
  • B. TurettDepartment of Mathematics and Statistics
    Oakland University
    Rochester, MI 48309, U.S.A.
    e-mail

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