Journal of Operator Theory
Volume 59, Issue 2, Spring 2008 pp. 247-262.
Refinements of spectral resolutions and modelling of operators in II1 factorsAuthors: 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 II1 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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