Abstract
Orthogonally biadditive operators preserving disjointness are studied. It is proved that, that for a Dedekind complete vector lattice \(W\) and order ideals \(E\) and \(F\) in \(W\) , the set \(\mathfrak{N}(E,F;W)\) of all orthogonally biadditive operators commuting with projections is a band in the Dedekind complete vector lattice \(\mathcal{OBA}_r(E,F;W)\) of all regular orthogonally biadditive operators from the Cartesian product of \(E\) and \(F\) to \(W\) . A general form of the order projection onto this band is obtained, and an operator version of the Radon–Nikodym theorem for disjointness-preserving positive orthogonally biadditive operators is proved.
