Commutativity of the Arens product in lattice ordered algebras
type: Item
instance of: scholarly article
title: Commutativity of the Arens product in lattice ordered algebras
zbMATH Open document ID: 0945.46003
DOI: 10.1023/A:1009880911903
published in: Positivity
publication date: 2000-10-03T00:00:00Z
review text: A lattice ordered algebra \(A\) is considered, i.e. \(A\) is a vector lattice and an associative algebra such that \(xy\geq 0\) whenever \(x\geq 0\), \(y\geq 0\). Denote by \(A'\) the band of all order bounded linear functionals on \(A\) and by \((A')_n'\) the band of all order bounded order continuous linear functionals on \(A'\). The author shows that \((A')_n'\) is Abelian whenever \(A\) is Abelian. The proof is based on an approximation of positive elements in \((A')_n'\) by elements in the canonical image \(\widehat A\) of \(A\) in \((A')_n'\).
reviewed by: Beloslav Riečan
Mathematics Subject Classification ID: 46A40
Mathematics Subject Classification ID: 13J25
Mathematics Subject Classification ID: 46A20
Mathematics Subject Classification ID: 06F25
zbMATH DE Number: 1389560
zbMATH Keywords: order bounded linear functionals
zbMATH Keywords: lattice ordered algebra
zbMATH Keywords: order continuous linear functionals
author: Jacobus J. Grobler
MaRDI profile type: Publication
full work available at URL: a:1009880911903
OpenAlex ID: W344783515
description: scientific article; zbMATH DE number 1389560