Abstract
In this paperwestudy the Arens triadjoints of some bilinear maps on vector lattices. In particular, we prove that, for Archimedean vector lattices A and B, the Arens triadjoint i) T*** : A" x A" ? B" of a positive orthosymmetric bilinear map T:A x A ? B is positive orthosymmetric, and ii) T***: A" x A" ? A" of a bi-orthomorphism T : A x A ? A is a bi-orthomorphism. These generalize results on the order bidual of f -algebras and almost f-algebras in [4].
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