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

• Autorzy: P. N. Dowling , C. J. Lennard , B. Turett
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47H09: Contraction-type mappings, nonexpansive mappings, A -proper mappings, etc.
• 46B45: Banach sequence spaces
• 47H10: Fixed-point theorems
• 46B50: Compactness in Banach (or normed) spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2003
• Tom: 154
• Numer: 3
• Strony: 277-293

Daty

wydano

2003

Twórcy

autor

P. N. Dowling

• Department of Mathematics and Statistics, Miami University, Oxford, OH 45056, U.S.A.

autor

C. J. Lennard

• Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, U.S.A.

autor

B. Turett

• Department of Mathematics and Statistics, Oakland University, Rochester, MI 48309, U.S.A.

Identyfikatory

DOI

10.4064/sm154-3-7