Generalized Log-Majorization and Multivariate Trace Inequalities
Mathematical Physics
2017-12-12 v2 math.MP
Quantum Physics
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.
Keywords
Cite
@article{arxiv.1609.01999,
title = {Generalized Log-Majorization and Multivariate Trace Inequalities},
author = {Fumio Hiai and Robert Koenig and Marco Tomamichel},
journal= {arXiv preprint arXiv:1609.01999},
year = {2017}
}
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17 pages