Abstract
In this article we continue investigation of the lateral order on complex vector lattices started in [10,39]. We extend some of main results of [35] and [32] to the setting of operators on complex vector lattices. We establish the Riesz-Kantorovich type calculus for regular orthogonally additive operators defined on the complexification EC of an uniformly complete vector lattice E with the principal projection property and taking values in Dedekind complete vector lattice F. We prove that a regular orthogonally additive operator T:EC→F from the complexfication EC of an uniformly complete vector lattice E with the principal projection property to a Banach lattice F with an order continuous norm is narrow if and only if the modulus |T|:EC→F is.
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