Properties WORTH and WORTH\(^*\), \((1+\delta)\) embeddings in Banach spaces with 1-unconditional basis and wFPP
type: Item
instance of: scholarly article
title: Properties WORTH and WORTH\(^*\), \((1+\delta)\) embeddings in Banach spaces with 1-unconditional basis and wFPP
zbMATH Open document ID: 1217.46011
DOI: 10.1155/2010/342691
author: Berta Gamboa de Buen
author: Helga Fetter
published in: Fixed Point Theory and Applications
publication date: 2010-04-13T00:00:00Z
full work available at URL: https://eudml.org/doc/231755
review text: The authors show that a Banach space \(X\) that \((1+\delta)\) embeds in a subspace \(X_\delta\) of a Banach space \(Y\) with a \(1\)-unconditional basis has the weak fixed point property for nonexpansive mappings. In fact, such a space has the property AMC introduced by \textit{J. García Falset} and \textit{E. Lloréns-Fuster} [J. Math. Anal. Appl. 172, No.~1, 39--52 (1993; Zbl 0780.47039)]. Applying this to the result proved by \textit{S. R. Cowell} and \textit{N. J. Kalton} [Q. J. Math. 61, No.~2, 217--240 (2010; Zbl 1215.46010)], they can show that if \(X\) is a reflexive Banach space and has the property WORTH, then \(X\) and its dual \(X^*\) have the fixed point property for nonexpansive mappings.
reviewed by: Satit Saejung
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 5692322
zbMATH Keywords: fixed point property
zbMATH Keywords: weak orthogonality
zbMATH Keywords: nonexpansive mapping
MaRDI profile type: Publication
OpenAlex ID: W1550756844
Wikidata QID: Q59219765
cites work: Q4205971
cites work: Q4039048
cites work: A class of spaces with weak normal structure
cites work: The effect of the dual on a Banach space and the weak fixed point propery
cites work: ASYMPTOTIC UNCONDITIONALITY
cites work: A geometric property of Banach spaces related to the fixed point property
cites work: Unconditional bases and fixed points of nonexpansive mappings
description: scientific article; zbMATH DE number 5692322