Comparison of completely positive maps on Hilbert \(C^*\)-modules (Q432422)

The author studied the Stinespring construction associated to an operator-valued completely positive map on a full Hilbert \(C^*\)-module in [Cent. Eur. J. Math. 9, No. 4, 803--813 (2011; Zbl 1243.46049)]. In the present work, she introduces an equivalence relation on the collection of all operator-valued completely positive maps on a full Hilbert \(C^*\)-module \(X\), and shows that the Stinespring constructions associated to equivalent completely positive maps are unitarily equivalent. She also gives a preorder relation in the collection of all operator-valued completely positive maps on \(X\), and proves a Radon-Nikodym-type theorem for operator-valued completely positive maps on Hilbert \(C^*\)-modules.