On the matrix Heron means and Rényi divergences
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 (Formula presented.) and its ‘naïve’ extension given by (Formula presented.), 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 (Formula presented.) holds for p = 1, 2, (Formula presented.), and (Formula presented.), among other related inequalities.
Linear and Multilinear Algebra
Digital Object Identifier (DOI)
Trung Hoa Dinh, Raluca Dumitru & Jose A. Franco (2020) On the matrix Heron means and Rényi divergences, Linear and Multilinear Algebra, DOI: 10.1080/03081087.2020.1763239