Weak compactness is equivalent to the Fixed Point Property in $c_0$

Abstract: In 1981, B. Maurey proved that nonempty, weakly compact, convex subsets of $c_0$ have the

fixed point property for nonexpansive mappings.

A characterization for closed bounded convex subsets in $c_0$ having the Fixed Point Property was

obtained in 2004 when P.N Dowling, C.J. Lennard and B. Turret showed that for any such set that is

non-weakly compact, there exists a contractive mapping that is fixed point free.

We will discuss the construction presented of such mapping in the latter paper.