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.

Casini, E., Miglierina, E., Piasecki, L., Popescu, R., Stability constants of the weak⁎ fixed point property for the space ℓ1, <<JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS>>, 2017; 452 (1): 673-684. [doi:10.1016/j.jmaa.2017.02.039] [http://hdl.handle.net/10807/98025]

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

Miglierina, Enrico
Secondo
;
Piasecki, Lukasz
Penultimo
;
2017

Abstract

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.
Inglese
Casini, E., Miglierina, E., Piasecki, L., Popescu, R., Stability constants of the weak⁎ fixed point property for the space ℓ1, <<JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS>>, 2017; 452 (1): 673-684. [doi:10.1016/j.jmaa.2017.02.039] [http://hdl.handle.net/10807/98025]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10807/98025
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