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

J. Pitrik, D. Virosztek, Linear Algebra and Its Applications 609 (2020) 203–217.


Journal Article | Epub ahead of print | English
Author
Department
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 A#H-mean introduced by Kim, Lawson, and Lim.
Publishing Year
Date Published
2020-09-09
Journal Title
Linear Algebra and its Applications
Acknowledgement
The authors are grateful to Milán Mosonyi for fruitful discussions on the topic, and to the anonymous referee for his/her comments and suggestions.
Volume
609
Page
203-217
ISSN
IST-REx-ID

Cite this

Pitrik J, Virosztek D. A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means. Linear Algebra and its Applications. 2020;609:203-217. doi:10.1016/j.laa.2020.09.007
Pitrik, J., & Virosztek, D. (2020). A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means. Linear Algebra and Its Applications, 609, 203–217. https://doi.org/10.1016/j.laa.2020.09.007
Pitrik, József, and Daniel Virosztek. “A Divergence Center Interpretation of General Symmetric Kubo-Ando Means, and Related Weighted Multivariate Operator Means.” Linear Algebra and Its Applications 609 (2020): 203–17. https://doi.org/10.1016/j.laa.2020.09.007.
J. Pitrik and D. Virosztek, “A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means,” Linear Algebra and its Applications, vol. 609, pp. 203–217, 2020.
Pitrik J, Virosztek D. 2020. A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means. Linear Algebra and its Applications. 609, 203–217.
Pitrik, József, and Daniel Virosztek. “A Divergence Center Interpretation of General Symmetric Kubo-Ando Means, and Related Weighted Multivariate Operator Means.” Linear Algebra and Its Applications, vol. 609, Elsevier, 2020, pp. 203–17, doi:10.1016/j.laa.2020.09.007.
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