Refinements of spectral resolutions and modelling of operators in II1 factors
Abstract
We study refinements between spectral resolutions in an arbitrary II1 factor 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 and new versions of some known inequalities involving these preorders.
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