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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
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 5 , Issue 4: Spectral problems. Issue dedicated to the memory of M. Birman , 2010 , pp. 317 - 339
Copyright
© EDP Sciences, 2010

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