Refinements of spectral resolutions and modelling of operators in II₁ factors
classification
🧮 math.FA
math.OA
keywords
spectralresolutionsoperatorsrefinementsdiffuseobtainapplicationarbitrary
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We study refinements between spectral resolutions in an arbitrary II$_1$ 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.
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