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Double Operator Integrals and Submajorization

Published online by Cambridge University Press:  12 May 2010

D. Potapov and
F. Sukochev
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Abstract

We present a user-friendly version of a double operator integration theory which stillretains a capacity for many useful applications. Using recent results from the lattertheory applied in noncommutative geometry, we derive applications to analogues of theclassical Heinz inequality, a simplified proof of a famous inequality ofBirman-Koplienko-Solomyak and also to the Connes-Moscovici inequality. Our methods aresufficiently strong to treat these inequalities in the setting of symmetric operator normsin general semifinite von Neumann algebras.

Keywords

double operator integrationunitarily invariant norm inequalitiesnoncommutative L p -spaces

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