Description

• Title:
  Explicit models of ℓ_1-preduals and the weak* fixed point property in ℓ_1
• Creator:
  Casini, Emanuele;
  Miglierina, Enrico;
  Piasecki, Łukasz
• Description:
  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.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2024 Emanuele Casini, Enrico Miglierina, Łukasz Piasecki;
  https://creativecommons.org/licenses/by-nd/4.0
• Date:
  2024.03.10
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 63, No 1 (March 2024); 39 - 51;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/49317/37952 ;https://apcz.umk.pl/TMNA/article/view/49317/37953
• Subject:
  Nonexpansive mappings;
  w*-fixed point property;
  Lindenstrauss spaces;
  46B25, 47H10
• Identifier: https://apcz.umk.pl/TMNA/article/view/49317
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other