Spaces not containing l(1) have weak approximate fixed point property

作者：Kalenda Ondrej F K^*

来源：Journal of Mathematical Analysis and Applications, 2011, 373(1): 134-137.

DOI：10.1016/j.jmaa.2010.06.052

• Weak approximate fixed point property
• l(1)-sequence
• Frechet-Urysohn space

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.

• 出版日期2011-1-1