Convex multivariate operator means

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningfagfællebedømt

We prove that a trace function, generated by the functional calculus, is geodesically convex in the Riemannian manifold of positive definite matrices, if and only if it is geodesically convex in positive numbers. The analysis of multivariate operator means is facilitated by the study of classes of means that are fix-points under a contraction with respect to the Thompson metric. Although such methods are powerful, they crucially depend on monotonicity. We develop new techniques to prove existence of multivariate operator means that are not necessarily monotone.

TidsskriftLinear Algebra and Its Applications
Sider (fra-til)209-224
Antal sider16
StatusUdgivet - 2019


ID: 240199297