Abstract
We provide a concrete isometric description of all the preduals of $\ell_1$ for which the standard basis in $\ell_1$ has a finite number of $w^*$-limit points. Then, we apply this result to give an example of an $\ell_1$-predual $X$ such that its dual $X^*$ lacks the weak$^*$ fixed point property for nonexpansive mappings (briefly, $w^*$-FPP), but $X$ does not contain an isometric copy of any hyperplane $W_{\alpha}$ of the space $c$ of convergent sequences such that $W_\alpha$ is a predual of $\ell_1$ and $W_\alpha^*$ lacks the $w^*$-FPP. This answers a question left open in the 2017 paper of the present authors.
Citation
Emanuele Casini. Enrico Miglierina. Łukasz Piasecki. "Explicit models of $\ell_1$-preduals and the weak* fixed point property in $\ell_1$." Topol. Methods Nonlinear Anal. 63 (1) 39 - 51, 2024. https://doi.org/10.12775/TMNA.2023.009
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