Convex multivariate operator means

Frank Hansen

研究成果: Article査読

抄録

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.

本文言語English
ページ(範囲)209-224
ページ数16
ジャーナルLinear Algebra and Its Applications
564
DOI
出版ステータスPublished - 2019 3 1

ASJC Scopus subject areas

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

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