The fixed point property of unital abelian Banach algebras
type: Item
instance of: scholarly article
title: The fixed point property of unital abelian Banach algebras
zbMATH Open document ID: 1201.46045
DOI: 10.1155/2010/362829
author: W. Fupinwong
author: S. Dhompongsa
published in: Fixed Point Theory and Applications
publication date: 2010-04-13T00:00:00Z
full work available at URL: https://eudml.org/doc/225315
review text: Let \(X\) be an infinite-dimensional unital abelian Banach algebra. It is shown that \(X\) does not have the fixed point property for nonexpansive mappings (fpp) if the character \(\tau\) on \(X\) and the spectral radius \(r(x)\) of \(x \in X\) satisfy the following conditions: (i) if \(|\tau(x)| \leq |\tau(y)|\), \(x,y \in X\), then \(||x|| \leq ||y||\); and (ii) inf \(\{r(x) : x \in X, ||x|| = 1 \} > 0\). Examples of algebras which fail the fpp are given, including algebras of continuous functions on compact sets.
reviewed by: Srinivasa Swaminathan
Mathematics Subject Classification ID: 46J10
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 46B20
zbMATH DE Number: 5692324
Wikidata QID: Q59251220
MaRDI profile type: Publication
OpenAlex ID: W1970195376
cites work: A Fixed Point Free Nonexpansive Map
cites work: Fixed point property and normal structure for Banach spaces associated to locally compact groups
cites work: Fixed points of nonexpansive mappings in spaces of continuous functions
cites work: Fixed point properties of \(C^{*}\)-algebras
cites work: Q4223155
cites work: Q3997462
description: scientific article; zbMATH DE number 5692324