Convex multivariate operator means

DOI10.1016/j.laa.2018.11.032OpenAlexW2807943206WikidataQ128824529 ScholiaQ128824529MaRDI QIDQ1715845

Frank Hansen

Publication date: 29 January 2019

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.06570

zbMATH Keywords

operator meanconvex-log functiongeodesically convex functionhyper-meanmultivariate operator mean

Mathematics Subject Classification ID

Linear operator inequalities (47A63) Global Riemannian geometry, including pinching (53C20) Operator means involving linear operators, shorted linear operators, etc. (47A64)

Related Items (2)

Operator geodesically convex functions and their applications ⋮ Nonhomogeneous Karcher equations with vector fields on positive definite matrices

Cites Work

• The fast track to Löwner's theorem
• Regular operator mappings and multivariate geometric means
• Monotonicity of the matrix geometric mean
• Matrix power means and the Karcher mean
• Riemannian geometry and matrix geometric means
• Operator means of probability measures and generalized Karcher equations
• Riemannian metrics on positive definite matrices related to means
• Concavity of certain maps on positive definite matrices and applications to Hadamard products
• The Golden-Thompson trace inequality is complemented
• Log majorization and complementary Golden-Thompson type inequalities
• Geometric means
• Perturbation formulas for traces on \(C^*\)-algebras
• Trace functions with applications in quantum physics
• Extensions of Lieb's concavity theorem
• Karcher means and Karcher equations of positive definite operators
• Interpolation by completely positive maps
• JENSEN'S OPERATOR INEQUALITY
• Weighted means and Karcher equations of positive operators
• A Differential Geometric Approach to the Geometric Mean of Symmetric Positive-Definite Matrices

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