Stability constants of the weak⁎ fixed point property for the space ℓ1

Enrico Miglierina, Lukasz Piasecki, Emanuele Casini, Łukasz Piasecki, Roxana Popescu

Risultato della ricerca: Contributo in rivistaArticolo in rivista

6 Citazioni (Scopus)


The main aim of the paper is to study some quantitative aspects of the stability of the weak⁎ fixed point property for nonexpansive mappings in ℓ1 (shortly, w⁎-fpp). We focus on two complementary approaches to this topic. First, given a predual X of ℓ1 such that the σ(ℓ1,X)-fpp holds, we precisely establish how far, with respect to the Banach–Mazur distance, we can move from X without losing the w⁎-fpp. The interesting point to note here is that our estimate depends only on the smallest radius of the ball in ℓ1 containing all σ(ℓ1,X)-cluster points of the extreme points of the unit ball. Second, we pass to consider the stability of the w⁎-fpp in the restricted framework of preduals of ℓ1. Namely, we show that every predual X of ℓ1 with a distance from c0 strictly less than 3, induces a weak⁎ topology on ℓ1 such that the σ(ℓ1,X)-fpp holds.
Lingua originaleEnglish
pagine (da-a)673-684
Numero di pagine12
RivistaJournal of Mathematical Analysis and Applications
Stato di pubblicazionePubblicato - 2017


  • Analysis
  • Applied Mathematics
  • Lindenstrauss spaces
  • Renorming
  • Stability of weak⁎ fixed point property
  • Weak⁎ fixed point property
  • ℓ1 space


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