Abstract
Bhatia, Lim, and Yamazaki studied the norm minimality of several Kubo-Ando means of positive semidefinite matrices. Recently, Hiai proved a norm minimality result involving the the weighted geometric mean and its ‘naïve’ extension given by , which is a matrix function in the definition of the quantum α-z-Rényi divergence. In connection to these results, for positive semidefinite matrices, we show that the inequality holds for p = 1, 2, , and , among other related inequalities.
Disclosure statement
No potential conflict of interest was reported by the author(s).