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arXiv · 1011.6313

In-betweenness: a geometric monotonicity property for operator means

Koenraad M. R. Audenaert
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Abstract

We introduce the notions of in-betweenness and monotonicity with respect to a metric, for operator means. These notions can be seen as generalising their natural counterpart for scalar means, and as a relaxation of the notion of geodesity. We exhibit two classes of non-trivial means that are monotonic with respect to the Euclidean metric. We also show that all Kubo-Ando means are monotonic with respect to the trace metric, which is the natural metric for the geometric mean.

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BibTeXRIS

Koenraad M. R. Audenaert. 2010-11-29. In-betweenness: a geometric monotonicity property for operator means. https://doi.org/10.1016/j.laa.2011.02.051

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