Refinements of spectral resolutions and modelling of operators in II factors
arXiv:math/0605070
Abstract
We study refinements between spectral resolutions in an arbitrary II factor $\M$ and obtain diffuse (maximal) refinements of spectral resolutions. We construct models of operators with respect to diffuse spectral resolutions. As an application we obtain new characterizations of sub-majorization and spectral preorder between positive operators in $\M$ and new versions of some known inequalities involving these preorders.