Interpolation of the continuity property for partially additive operators (Q1204692)

An operator \(T: X\to Y\) (\(X\) and \(Y\) are Banach lattices) is said to be partially additive if, for any disjoint elements \(x\), \(y\) in the domain of definition of \(T\), one has \(T(x+ y)= Tx+ Ty\). In this paper the authors consider the case when \(X\) and \(Y\) are generated by the \(K\)- method of interpolation and find some conditions for \(T\) to be continuous. The theorems presented are close to best possible for classical partially additive operators such as the substitution operator and the Hammerstein and Uryson operators.