posted on 2024-07-16, 11:20authored byRaluca Dumitru, Jose A. Franco
Bhatia, Lim and Yamazaki obtained results on the norm minimality of the Kubo-Ando Heinz means of positive semidefinite matrices. Namely, they proved that
for , in the case of the Schatten 1-norm or 2-norm. In this article, we refine these results via the matrix function in the definition of the Rényi divergence. We show that four different types of inequalities hold, under certain conditions, for Schatten 1- and 2-norms.