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

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Dowling P. , Lennard C. , Turett B.

Studia Mathematica

2003

tom 154

nr 3

277-293

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.

New fixed point free nonexpansive maps on weakly compact, convex subsets of L¹[0,1]

100%

Dowling P. , Lennard C. , Turett B.

Studia Mathematica

2007

tom 180

nr 3

271-284

We show that every subset of L¹[0,1] that contains the nontrivial intersection of an order interval and finitely many hyperplanes fails to have the fixed point property for nonexpansive mappings.