Convex multivariate operator means

Frank Hansen

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)209-224
Number of pages16
JournalLinear Algebra and Its Applications
Volume564
DOIs
Publication statusPublished - 2019 Mar 1

Keywords

  • Convex-log function
  • Geodesically convex function
  • Hyper-mean
  • Multivariate operator mean
  • Operator mean

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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