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For a pair of bounded linear Hilbert space operators $A$ and $B$ oneconsiders the Lebesgue type decompositions of $B$ with respect to $A$ into analmost dominated part and a singular part, analogous to the Lebesguedecomposition for a pair of measures (in which case one speaks of an absolutelycontinuous and a singular part). A complete parametrization of all Lebesguetype decompositions will be given, and the uniqueness of such decompositionswill be characterized. In addition, it will be shown that the almost dominatedpart of $B$ in a Lebesgue type decomposition has an abstract Radon-Nikodymderivative with respect to the operator $A$.

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