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arXiv · 2002.11678

A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means

József Pitrik·Dániel Virosztek
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Abstract

It is well known that special Kubo-Ando operator means admit divergence center interpretations, moreover, they are also mean squared error estimators for certain metrics on positive definite operators. In this paper we give a divergence center interpretation for every symmetric Kubo-Ando mean. This characterization of the symmetric means naturally leads to a definition of weighted and multivariate versions of a large class of symmetric Kubo-Ando means. We study elementary properties of these weighted multivariate means, and note in particular that in the special case of the geometric mean we recover the weighted $\mathcal{A} \# \mathcal{H}$-mean introduced by Kim, Lawson, and Lim.

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József Pitrik, Dániel Virosztek. 2020-02-26. A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means. https://doi.org/10.1016/j.laa.2020.09.007

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