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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:452

Article

Casini, Emanuele¹  Miglierina, Enrico²  Piasecki, Lukasz³  Popescu, Roxana⁴ 

[1] Univ Insubria, Dipartimento Sci & Alta Tecnol, Via Valleggio 11, I-22100 Como, Italy

[2] Univ Cattolica Sacro Cuore, Dipartimento Discipline Matemat Finanza Matemat &, Via Necchi 9, I-20123 Milan, Italy

[3] Uniwersytet Marii Curie Sklodowskiej, Inst Matemat, Pl Marii Curie Sklodowskiej 1, PL-20031 Lublin, Poland

[4] Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA

关键词: Weak fixed point property;    Stability of weak* fixed point property;    Lindenstrauss spaces;    l(1) space;    Reforming;   

DOI  :  10.1016/j.jmaa.2017.02.039

来源: Elsevier

【 摘 要 】

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 l(1) (shortly, w*-fpp). We focus on two complementary approaches to this topic. First, given a predual X of l(1) such that the sigma(l(1), 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 l(1) containing all sigma(l(1), 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 l(1). Namely, we show that every predual X of l(1) with a distance from c(0)-strictly less than 3, induces a weak* topology on l(1) such that the sigma(l(1), X)-fpp holds. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free