Lebesgue-type decomposition of positive operators

摘要

The present note is a revision of Ando's work with the same title. We give a new construction for the Lebesgue-decomposition of positive operators on Hilbert spaces with respect to each other. Our approach is similar to that of Kosaki: we use unbounded operator techniques and factorizations via two auxiliary Hilbert spaces associated to the positive operators in question.