On orthosymmetric bilinear maps
type: Item
instance of: scholarly article
title: On orthosymmetric bilinear maps
zbMATH Open document ID: 1204.06010
author: Fethi Ben Amor
published in: Positivity
publication date: 2010-04-13T00:00:00Z
review text: In this paper the author proves, among other things, the following two result: the first one states that if \(A\) is an Archimedean almost \(f\)-algebra and if \(D\) is an order-bounded derivation on \(A\), then \(D(abc)=0\) and \((D(ab))^3=0\) for all \(a, b, c \in A\). This result has been obtained independently by \textit{A. Toumi} and \textit{M. A. Toumi} [Positivity 14, No.~2, 239--245 (2010; Zbl 1213.06014)]. The second result deals with the symmetry of orthosymmetric bilinear maps. More precisely, the author proves that if \(A,B\) are two Archimedean vector lattices then any (\(r\)-\(u\)) continuous orthosymmetric bilinear map \(:A\times A\rightarrow B\) is symmetric. This leads to a generalization of a Buskes-Kusraev result.
Mathematics Subject Classification ID: 06F25
Mathematics Subject Classification ID: 46A40
Mathematics Subject Classification ID: 47B47
Mathematics Subject Classification ID: 47B65
zbMATH DE Number: 5692404
zbMATH Keywords: order-bounded derivation
zbMATH Keywords: orthosymmetric bilinear map
zbMATH Keywords: Archimedean almost \(f\)-algebra
zbMATH Keywords: Archimedean vector lattice
reviewed by: Mohamed Ali Toumi
MaRDI profile type: Publication
full work available at URL: s11117-009-0009-4
OpenAlex ID: W2096989892
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DOI: 10.1007/S11117-009-0009-4
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description: scientific article; zbMATH DE number 5692404