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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 still retains a capacity for many useful applications. Using recent results from the latter theory applied in noncommutative geometry, we derive applications to analogues of the classical Heinz inequality, a simplified proof of a famous inequality of Birman-Koplienko-Solomyak and also to the Connes-Moscovici inequality. Our methods are sufficiently strong to treat these inequalities in the setting of symmetric operator norms in general semifinite von Neumann algebras.

Keywords

double operator integrationunitarily invariant norm inequalitiesnoncommutative Lp-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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