Lebesgue type decompositions and Radon–Nikodym derivatives for pairs of bounded linear operators

Abstract For a pair of bounded linear Hilbert space operators A and B one considers the Lebesgue type decompositions with respect to into an almost dominated part singular part, analogous decomposition for measures in which case speaks absolutely continuous part. complete parametrization all will be given, uniqueness such characterized. In addition, it shown that has abstract Radon–Nikodym derivative operator .