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arXiv · 1609.01999

Generalized Log-Majorization and Multivariate Trace Inequalities

Fumio Hiai·Robert Koenig·Marco Tomamichel
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Abstract

We show that recent multivariate generalizations of the Araki-Lieb-Thirring inequality and the Golden-Thompson inequality [Sutter, Berta, and Tomamichel, Comm. Math. Phys. (2016)] for Schatten norms hold more generally for all unitarily invariant norms and certain variations thereof. The main technical contribution is a generalization of the concept of log-majorization which allows us to treat majorization with regards to logarithmic integral averages of vectors of singular values.

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Fumio Hiai, Robert Koenig, Marco Tomamichel. 2016-09-07. Generalized Log-Majorization and Multivariate Trace Inequalities. https://doi.org/10.1007/s00023-017-0569-y

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