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arXiv · 1503.08875

Separable Lindenstrauss spaces whose duals lack the weak$^*$ fixed point property for nonexpansive mappings

Emanuele Casini·Enrico Miglierina·Łukasz Piasecki
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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 $X^*$.

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Emanuele Casini, Enrico Miglierina, Łukasz Piasecki. 2015-03-30. Separable Lindenstrauss spaces whose duals lack the weak$^*$ fixed point property for nonexpansive mappings. https://arxiv.org/abs/1503.08875

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