Publication at Faculty of Mathematics and Physics |
2011
Abstract
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 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.