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Keywords:
vector lattice; positive bilinear operator; orthosymmetric bilinear operator; lattice bimorphism
vector lattice; positive bilinear operator; orthosymmetric bilinear operator; lattice bimorphism
Summary:
It is proved by an order theoretical and purely algebraic method that any order bounded orthosymmetric bilinear operator $b\colon E\times E\rightarrow F$ where $E$ and $F$ are Archimedean vector lattices is symmetric. This leads to a new and short proof of the commutativity of Archimedean almost $f$-algebras.
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