Double Operator Integrals and Submajorization

School of Mathematics and Statistics, University of NSW, Kensington NSW 2052, Australia

^* Corresponding author. E-mail: f.sukochev@unsw.edu.au.

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.