The relative operator entropy and the Karcher mean

DOI10.1016/j.laa.2016.11.018OpenAlexW2552933213MaRDI QIDQ2002767

Yuki Seo, Jun Ichi Fujii

Publication date: 12 July 2019

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

Full work available at URL: https://doi.org/10.1016/j.laa.2016.11.018

zbMATH Keywords

power meanoperator meanKarcher meanrelative operator entropyKarcher equation

Mathematics Subject Classification ID

Linear operator inequalities (47A63) Linear operator approximation theory (47A58) Measures of information, entropy (94A17) Operator means involving linear operators, shorted linear operators, etc. (47A64)

Related Items

Relative Operator Entropy ⋮ Estimates of Ando–Hiai-type inequalities on operator power means ⋮ The unique solution of the Karcher equation and the self-adjointness of the Karcher mean ⋮ Pusz-Woronowicz functional calculus and extended operator convex perspectives ⋮ Ando–Hiai type inequalities for multivariate operator means ⋮ Means for fixed rank PSD matrices

Cites Work

• Operator power means due to Lawson-Lim-Pálfia for \(1 < t < 2\)
• Matrix power means and the Karcher mean
• Riemannian geometry and matrix geometric means
• Form convex functions and the WYDL and other inequalities
• Operator means and range inclusion
• Functional calculus for sesquilinear forms and the purification map
• Relative entropy and the Wigner-Yanase-Dyson-Lieb concavity in an interpolation theory
• Means of positive linear operators
• Series and parallel addition of matrices
• On operator ranges
• Karcher means and Karcher equations of positive definite operators
• The Riemannian mean and matrix inequalities related to the Ando-Hiai inequality and chaotic order
• GEODESICS AND OPERATOR MEANS IN THE SPACE OF POSITIVE OPERATORS
• A note on the entropy for operator algebras
• On Majorization, Factorization, and Range Inclusion of Operators on Hilbert Space
• Conditional expectation in an operator algebra. IV. Entropy and information
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