This is an announcement for the paper "Separable Lindenstrauss spaces whose duals lack the weak$^*$ fixed point property for nonexpansive mappings" by Emanuele Casini, Enrico Miglierina, and Lukasz Piasecki.

Abstract: In this paper we study the $w^*$-fixed point property for nonexpansive mappings. First we show that the dual space $X^*$ lacks the $w^*$-fixed point property whenever $X$ contains an isometric copy of the space $c$. Then, the main result of our paper provides several characterizations of weak-star topologies that fail the fixed point property for nonexpansive mappings in $\ell_1$ space. This result allows us to obtain a characterization of all separable Lindenstrauss spaces $X$ inducing the failure of $w^*$-fixed point property in $X^*$.

Archive classification: math.FA

Mathematics Subject Classification: Primary 47H09, Secondary 46B25

Submitted from: enrico.miglierina@unicatt.it

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

http://front.math.ucdavis.edu/1503.08875

or

http://arXiv.org/abs/1503.08875