Optimization of some types of Rényi divergences between unitary orbits

In this article, we investigate explicitly the minimal and maximal values of the α-z-Rényi divergences and some other types of Rényi divergences between unitary orbits. Our main tools are the majorization theory of eigenvalues of matrices, and some matrix inequalities such as Golden–Thompson's and Araki–Lieb–Thirring's inequalities.