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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm154-3-7,
author = {P. N. Dowling and C. J. Lennard and B. Turett},
title = {Characterizations of weakly compact sets and new fixed point free maps in c0},
journal = {Studia Mathematica},
volume = {157},
year = {2003},
pages = {277-293},
zbl = {1037.47039},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm154-3-7}
}
P. N. Dowling; C. J. Lennard; B. Turett. Characterizations of weakly compact sets and new fixed point free maps in c₀. Studia Mathematica, Tome 157 (2003) pp. 277-293. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm154-3-7/