Refinements of spectral resolutions and modelling of operators in II$_1$ factors

Details Refinements of spectral resolutions and modelling of operators in II$_1$ factors Refinements of spectral resolutions and modelling of operators in II$_1$ factors

2006-05-02

arxiv.org/abs/math/0605070v1

Mathematics

Functional Analysis

Scientific paper

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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