Some remarks on orthogonally additive operators

We study orthogonally additive operators on Riesz spaces. Our first result gives necessary and sufficient conditions on a pair of Riesz spaces (E, F) for which every orthogonally additive operator from E to F is laterally-to-order bounded. Second result extends an analogue of Pitt's compactness theorem obtained by the second and third named authors for narrow linear operators to the setting of orthogonally additive operators. Third result provides sufficient conditions on a pair of orthogonally additive operators S and T to have S ? T, as well as to have S? T without any assumption on the domain and range spaces. Finally we prove an analogue of Meyer's theorem on the existence of modules of disjointness preserving operator for orthogonally additive operators.