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 and its 'naïve' extension given by , which is a matrix function in the definition of...

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Bibliographic Details
Published in:Linear & multilinear algebra 2022-05, Vol.70 (8), p.1442-1450
Main Authors: Hoa Dinh, Trung, Dumitru, Raluca, Franco, Jose A.
Format: Article
Language:English
Subjects:
Heron means
interpolation of means
Kubo-Ando means
Mathematical analysis
Matrices (mathematics)
Renyi divergences
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Summary: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.
ISSN:0308-1087
1563-5139
DOI:10.1080/03081087.2020.1763239