The optimization problem to minimize the weighted sum of $\alpha$-z Bures-Wasserstein quantum divergences to given positive definite Hermitian matrices has been solved. We call the unique minimizer the $\alpha$-z weighted right mean, which provides a new non-commutative version of generalized mean (Hölder mean). We investigate its fundamental properties, and give many interesting operator inequalities with the matrix power mean including the Cartan mean. Moreover, we verify the trace inequality with the Wasserstein mean and provide bounds for the Hadamard product of two right means.
Miran Jeong
,
Jinmi Hwangm
,
Sejong Kim
. RIGHT MEAN FOR THE $\alpha$-z BURES-WASSERSTEIN QUANTUM DIVERGENCE*[J]. Acta mathematica scientia, Series B, 2023
, 43(5)
: 2320
-2332
.
DOI: 10.1007/s10473-023-0523-7
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