Abstract: The main aim of the present note is to consider bounded orthomorphisms between locally solid vector lattices. We establish a version of the remarkable Zannen theorem regarding equivalence between orthomorphisms and the underlying vector lattice for the case of all bounded orthomomorphisms. Furthermore, we investigate topological and ordered structures for these classes of orthomorphisms, as well. In particular, we show that each class of bounded orthomorphisms possesses the Levi or the \(AM\)-properties if and only if so is the underlying locally solid vector lattice. Moreover, we establish a similar result for the Lebesgue property, as well.

For citation: Sabbagh, R. and Zabeti, O. Bounded Orthomorphisms Between Locally Solid Vector Lattices, Vladikavkaz Math. J., 2021, vol. 23, no. 4, pp. 89-95.
DOI 10.46698/c1197-8093-8231-u

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