Separable Lindenstrauss spaces whose duals lack the weak$^*$ fixed point property for nonexpansive mappings
Volume 238 / 2017
Studia Mathematica 238 (2017), 1-16
MSC: Primary 47H09; Secondary 46B25.
DOI: 10.4064/sm8237-12-2016
Published online: 24 March 2017
Abstract
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 $c$. Then, the main result of our paper provides several characterizations of weak-star topologies that fail the fixed point property for nonexpansive mappings in $\ell _1$. This result allows us to obtain a characterization of all separable Lindenstrauss spaces $X$ with $X^*$ failing the $w^*$-fixed point property.
