Separable Lindenstrauss spaces whose duals lack the weak∗ fixed point property for nonexpansive mappings

Enrico Miglierina, Lukasz Piasecki, Emanuele Casini, Łukasz Piasecki

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

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 ℓ1. This result allows us to obtain a characterization of all separable Lindenstrauss spaces X with X∗ failing the w∗-fixed point property.
Original languageEnglish
Pages (from-to)1-16
Number of pages16
JournalStudia Mathematica
Volume238
DOIs
Publication statusPublished - 2017

Keywords

  • nonexpansive mappings, w*-fixed point property, Lindenstrauss spaces

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