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

Volume 238 / 2017

Emanuele Casini, Enrico Miglierina, Łukasz Piasecki 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.

Authors

  • Emanuele CasiniDipartimento di Scienza e Alta Tecnologia
    Università dell’Insubria
    via Valleggio 11
    22100 Como, Italy
    e-mail
  • Enrico MiglierinaDipartimento di Discipline Matematiche
    Finanza Matematica ed Econometria
    Università Cattolica del Sacro Cuore
    Via Necchi 9, 20123 Milano, Italy
    e-mail
  • Łukasz PiaseckiInstytut Matematyki
    Uniwersytet Marii Curie-Skłodowskiej
    Pl. Marii Curie-Skłodowskiej 1
    20-031 Lublin, Poland
    e-mail

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