# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## 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.

#### Autorzy

• 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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