This is an announcement for the paper "Spaces not containing $\ell_1$ have weak aproximate fixed point property" by Ondrej F.K. Kalenda.

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 $f:C\to C$ 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 $\ell_1$. As a byproduct we obtain a characterization of Banach spaces not containing $\ell_1$ in terms of the weak topology.

Archive classification: math.FA

Remarks: 5 pages

Submitted from: kalenda@karlin.mff.cuni.cz

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1005.1218

or

http://arXiv.org/abs/1005.1218