Log-majorizations related to the spectral geometric and Rényi means
摘要
In this article we study log-majorizations related to the spectral geometric and Rényi means. Our goal is to establish certain geometric properties for them with respect to the Thompson metric and Kim’s semi-metric on the cone of positive definite matrices. We also study geodesic in-betweenness type results for these two means and some Audenaert-type in-betweenness inequalities.