Convex multivariate operator means
Copyright policy )Convex multivariate operator means
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.
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
- University of Copenhagen Denmark
- University of Copenhagen Denmark
convex-log function, multivariate operator mean, Hyper-mean, Operator mean, operator mean, FOS: Physical sciences, Mathematical Physics (math-ph), Global Riemannian geometry, including pinching, geodesically convex function, Geodesically convex function, Operator means involving linear operators, shorted linear operators, etc., Multivariate operator mean, Convex-log function, hyper-mean, Linear operator inequalities, Mathematical Physics, 47A64, 53C20, 47A63
convex-log function, multivariate operator mean, Hyper-mean, Operator mean, operator mean, FOS: Physical sciences, Mathematical Physics (math-ph), Global Riemannian geometry, including pinching, geodesically convex function, Geodesically convex function, Operator means involving linear operators, shorted linear operators, etc., Multivariate operator mean, Convex-log function, hyper-mean, Linear operator inequalities, Mathematical Physics, 47A64, 53C20, 47A63
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