In-betweenness: a geometric monotonicity property for operator means
Functional Analysis
2013-04-23 v1 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.1011.6313,
title = {In-betweenness: a geometric monotonicity property for operator means},
author = {Koenraad M. R. Audenaert},
journal= {arXiv preprint arXiv:1011.6313},
year = {2013}
}
Comments
15 pages; a preliminary version has been presented at the June 2010 ILAS Conference in Pisa, Italy