Unconditional bases and fixed points of nonexpansive mappings
type: Item
instance of: scholarly article
title: Unconditional bases and fixed points of nonexpansive mappings
zbMATH Open document ID: 0566.47038
author: Pei-Kee Lin
published in: Pacific Journal of Mathematics
publication date: 1985-01-01T00:00:00Z
review text: Using Maurey's ultraproduct techniques, the author has proved the following two theorems: Theorem 1. Let X be a Banach space with an unconditional basis. If the unconditional constant \(\lambda <(\sqrt{33}-3)/2\), then every weakly compact convex subset of X has the fixed point property for nonexpansive mappings. Theorem 2. Let X be a superreflexive space with a suppression unconditional basis. Then every weakly compact convex subset of X has the fixed point property for nonexpansive mappings. But the following problem is still open: Problem. Let X be a (superreflexive) Banach space with an unconditional basis. Does every weakly compact convex subset of X have the fixed point property for nonexpansive mappings?
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 46B15
Mathematics Subject Classification ID: 03C20
zbMATH DE Number: 3903393
zbMATH Keywords: Maurey's ultraproduct techniques
zbMATH Keywords: Banach space with an unconditional basis
zbMATH Keywords: unconditional constant
zbMATH Keywords: fixed point property for nonexpansive mappings
zbMATH Keywords: superreflexive space with a suppression unconditional basis
zbMATH Keywords: weakly compact convex subset
MaRDI profile type: Publication
full work available at URL: pjm.1985.116.69
OpenAlex ID: W2142960374
DOI: 10.2140/PJM.1985.116.69
description: scientific article; zbMATH DE number 3903393