Abstract
Let A and B be two Archimedean vector lattices and let (A′)′n and (B′)′n be their order continuous order biduals. If Ψ: A × A → B is a positive orthosymmetric bimorphism, then the triadjoint Ψ***: (A′)′n × (A′)′n → (B′)′n of Ψ is inevitably orthosymmetric. This leads to a new and short proof of the commutativity of almost f-algebras.
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