An almost orthosymmetric bilinear map

In this paper, as a generalization of the concept of pseudo-almost f -algebra, we define a new concept of almost orthosymmetric bilinear map on a vector lattice and prove that the Arens triadjoint of a positive almost orthosymmetric bilinear map is positive almost orthosymmetric.This also extends results on the order bidual of pseudo-almost f -algebras.