Generalized Log-Majorization and Multivariate Trace Inequalities

  title={Generalized Log-Majorization and Multivariate Trace Inequalities},
  author={Fumio Hiai and Robert Koenig and Marco Tomamichel},
  journal={Annales Henri Poincar{\'e}},
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… CONTINUE READING


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