Order bounded orthosymmetric bilinear operator. (English) Zbl 1249.06048

The paper presents a new purely algebraic proof of the statement that every order-bounded orthosymmetric bilinear operator \(b\: E\times E\rightarrow F\), where \(E\), \(F\) are Archimedean vector lattices, is symmetric. As a conclusion, a new and short proof of the commutativity of Archimedean almost \(f\)-algebras is given.


06F25 Ordered rings, algebras, modules
06F20 Ordered abelian groups, Riesz groups, ordered linear spaces
46A40 Ordered topological linear spaces, vector lattices
47A65 Structure theory of linear operators
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