… In this section, we introduce a notion of an orthogonally biadditive operator and prove that
the vector space of all regular orthogonally biadditive operators defined on the Cartesian …

… of positive orthogonally bi-additive operators several results … that a positive order bounded
orthogonally bi-additive map \(T:{\… we prove that a positive orthogonally bi-additive operator \(T:…

… vector lattices and orthogonally additive and biadditive operators, as well as basic examples
of OBOs. In Sec. 4, we introduce a special class of orthogonally biadditive operators, namely…

… In this paper we consider the generalization of the orthogonality … In this case we will consider
biadditive mappings instead of … Now we introduce some theory of the adjoint operator on …

… operators on complex vector lattices. We establish the Riesz-Kantorovich type calculus for
regular orthogonally additive operators … We prove that a regular orthogonally additive operator …

… We study orthogonally additive operators on Riesz spaces. … (E, F) for which every orthogonally
additive operator from E to F is … operators to the setting of orthogonally additive operators. …

… for a homogeneous orthogonality which still ensure the existence of an additive/quadratic
representation. Actually, we can reduce the question of orthogonally additive mappings to …

… the bi-additive s-functional inequalities (1) and (2) and prove the Hyers-Ulam stability of the
bi-additive … and unital C∗algebras associated with the bi-additive s-functional inequalities (1) …

… operators that are not adjointable. … a-biadditive orthogonality preserving mapping on K ×
K . In addition, we show that if F is a fully complemented submodule of E and f is orthogonally …

… operator (see §2) mapping C(5) into X. We will show (see Lemma 3.4) that additive operators
… In this section we shall represent an additive operator in terms of a family of measures {jdh}…