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Journal of Operator Theory

Volume 59, Issue 2, Spring 2008  pp. 247-262.

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

Authors Pedro G. Massey
Author institution: Departamento de Matemática-FCE, Universidad Nacional de La Plata, La Plata (CC 172) and Instituto Argentino de Matemática-CONICET, Buenos Aires, Argentina

Summary:  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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