Stability constants of the weak⁎ fixed point property for the space ℓ1
Journal of Mathematical Analysis and Applications(2017)
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 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.
更多查看译文
关键词
Weak⁎ fixed point property,Stability of weak⁎ fixed point property,Lindenstrauss spaces,ℓ1 space,Renorming
AI 理解论文
溯源树
样例
![](https://originalfileserver.aminer.cn/sys/aminer/pubs/mrt_preview.jpeg)
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要