Title

On the matrix Heron means and Rényi divergences

Document Type

Article

Publication Date

1-1-2020

Subject Area

ARRAY(0x55c828811a70)

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 (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.

Publication Title

Linear and Multilinear Algebra

Digital Object Identifier (DOI)

10.1080/03081087.2020.1763239

ISSN

03081087

E-ISSN

15635139

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