Spaces not containing l1 have weak approximate fixed point property

A nonempty closed convex bounded subset C of a Banach space is said to have the weak approximate fixed point property if for every continuous map f : C -> C there is a sequence {x(n)} in C such that x(n) - f (x(n)) converge weakly to 0. We prove in particular that C has this property whenever it contains no sequence equivalent to the standard basis of l(1). As a byproduct we obtain a characterization of Banach spaces not containing l(1) in terms of the weak topology. (c) 2010 Elsevier Inc. All rights reserved.