On orthosymmetric bilinear maps
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.
scientific article; zbMATH DE number 5692404
scientific article