Extension of linear 0-continuous operators (Q1099030)

A generalization of the classical Kantorovitch linear positive operator extension theorem is presented. The authors omit the assumption that the original domain (of the operator \(A_ 0)\) \(X_ 0\) majorises the whole space X. The main tool is the possibility to contruct to every \(x\in X\) \(+\) a sequence \((x_ n)_ n\subset X_ 0\) such that \(x_ n\nearrow x\) and \((A_ 0(x_ n))_ n\) is bounded.