Convex multivariate operator means
Mathematical Physics
2018-12-21 v2 math.MP
Abstract
The dominant method for defining multivariate operator means is to express them as fix-points under a contraction with respect to the Thompson metric. Although this method is powerful, it crucially depends on monotonicity. We are developing a technique to prove the existence of multivariate operator means that are not necessarily monotone. This gives rise to an entire new class of non-monotonic multivariate operator means.
Cite
@article{arxiv.1806.06570,
title = {Convex multivariate operator means},
author = {Frank Hansen},
journal= {arXiv preprint arXiv:1806.06570},
year = {2018}
}
Comments
We discovered that an argument in the proof of the last part of the last theorem in the first version of the paper is plainly wrong. Based on examples we still have ground to believe that the theorem is correct, but this is now only a conjecture. Some mean inequalities are added