Order-continuous functionals in Boolean-valued models of set theory (Q1062675)

For terminology and notations see the review above [Zbl 0573.03022]. A linear positive operator T from a K-space X into a K-space Y is said to be a Maharam operator iff T is continuous and \(T([0,x])=[0,T(x)]\) for each positive \(x\in X\). The main theorem is about representation of Maharam operators with values in R by suitable functionals in \(V^{(B)}\) (with suitable Boolean algebra B). The theorem is used for the study of the structure of some operators - elements of \(L_ p(T)^*\) for a Maharam operator T - and for the desintegration formula: \(\partial (T\circ P)=T\circ \partial P\) for any sublinear P:E\(\to X\) and Maharam operator T:X\(\to Y\).