Separable Lindenstrauss spaces whose duals lack the weak∗ fixed point property for nonexpansive mappings

Emanuele Casini; Enrico Miglierina; Łukasz Piasecki; Lukasz Piasecki

doi:10.4064/sm8237-12-2016

Separable Lindenstrauss spaces whose duals lack the weak∗ fixed point property for nonexpansive mappings

Emanuele Casini
, Enrico Miglierina
, Łukasz Piasecki
, Lukasz Piasecki

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

We study the w∗-fixed point property for nonexpansive mappings. First we show that the dual space X∗ lacks the w∗-fixed point property whenever X contains an isometric copy of c. Then, the main result of our paper provides several characterizations of weak-star topologies that fail the fixed point property for nonexpansive mappings in ℓ1. This result allows us to obtain a characterization of all separable Lindenstrauss spaces X with X∗ failing the w∗-fixed point property.

Original language	English
Pages (from-to)	1-16
Number of pages	16
Journal	Studia Mathematica
Volume	238
DOIs	https://doi.org/10.4064/sm8237-12-2016
Publication status	Published - 2017

Keywords

nonexpansive mappings, w*-fixed point property, Lindenstrauss spaces

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10.4064/sm8237-12-2016

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abstract = "We study the w∗-fixed point property for nonexpansive mappings. First we show that the dual space X∗ lacks the w∗-fixed point property whenever X contains an isometric copy of c. Then, the main result of our paper provides several characterizations of weak-star topologies that fail the fixed point property for nonexpansive mappings in ℓ1. This result allows us to obtain a characterization of all separable Lindenstrauss spaces X with X∗ failing the w∗-fixed point property.",

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AU - Casini, Emanuele

AU - Miglierina, Enrico

AU - Piasecki, Łukasz

AU - Piasecki, Lukasz

PY - 2017

Y1 - 2017

N2 - We study the w∗-fixed point property for nonexpansive mappings. First we show that the dual space X∗ lacks the w∗-fixed point property whenever X contains an isometric copy of c. Then, the main result of our paper provides several characterizations of weak-star topologies that fail the fixed point property for nonexpansive mappings in ℓ1. This result allows us to obtain a characterization of all separable Lindenstrauss spaces X with X∗ failing the w∗-fixed point property.

AB - We study the w∗-fixed point property for nonexpansive mappings. First we show that the dual space X∗ lacks the w∗-fixed point property whenever X contains an isometric copy of c. Then, the main result of our paper provides several characterizations of weak-star topologies that fail the fixed point property for nonexpansive mappings in ℓ1. This result allows us to obtain a characterization of all separable Lindenstrauss spaces X with X∗ failing the w∗-fixed point property.

KW - nonexpansive mappings, w-fixed point property, Lindenstrauss spaces

UR - http://hdl.handle.net/10807/98026

UR - https://www.impan.pl/en/publishing-house/journals-and-series/studia-mathematica/all/238/1/92118/separable-lindenstrauss-spaces-whose-duals-lack-the-weak-fixed-point-property-for-nonexpansive-mappings

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DO - 10.4064/sm8237-12-2016

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VL - 238

SP - 1

EP - 16

JO - Studia Mathematica

JF - Studia Mathematica

ER -

Separable Lindenstrauss spaces whose duals lack the weak∗ fixed point property for nonexpansive mappings

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