Generalized Log-Majorization and Multivariate Trace Inequalities

Fumio Hiai; Robert König; Marco Tomamichel

doi:10.1007/s00023-017-0569-y

Generalized Log-Majorization and Multivariate Trace Inequalities

Fumio Hiai, Robert König, Marco Tomamichel

Associate Professorship of Theory of Complex Quantum Systems

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8 Scopus citations

Abstract

We show that recent multivariate generalizations of the Araki–Lieb–Thirring inequality and the Golden–Thompson inequality (Sutter et al. in Commun Math Phys, 2016. doi:10.1007/s00220-016-2778-5) 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 regard to logarithmic integral averages of vectors of singular values.

Original language	English
Pages (from-to)	2499-2521
Number of pages	23
Journal	Annales Henri Poincare
Volume	18
Issue number	7
DOIs	https://doi.org/10.1007/s00023-017-0569-y
State	Published - 1 Jul 2017

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AU - Tomamichel, Marco

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Generalized Log-Majorization and Multivariate Trace Inequalities

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