Ando-Hiai inequality and Furuta inequality

DOI10.1016/j.laa.2005.12.001zbMath1110.47011OpenAlexW2068340527MaRDI QIDQ2496625

Masatoshi Fujii, Eizaburo Kamei

Publication date: 20 July 2006

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

Full work available at URL: https://doi.org/10.1016/j.laa.2005.12.001

zbMATH Keywords

Furuta inequalitypositive operatorsLöwner-Heinz inequalitychaotic ordergrand Furuta inequalityoperator mean

Mathematics Subject Classification ID

Linear operator inequalities (47A63) Positive linear operators and order-bounded operators (47B65) Operator means involving linear operators, shorted linear operators, etc. (47A64)

Related Items (14)

Log-majorization Type Inequalities ⋮ Ando-Hiai Inequality: Extensions and Applications ⋮ Perspectives, Means and their Inequalities ⋮ Further generalizations of Bebiano-Lemos-Providência inequality ⋮ A satellite of the grand Furuta inequality and its application ⋮ Order automorphisms on positive definite operators and a few applications ⋮ A complement of the Ando--Hiai inequality ⋮ Some ways of constructing Furuta-type inequalities ⋮ An asymmetric Kadison's inequality ⋮ Variants of Ando-Hiai Inequality ⋮ A generalized Lemos-Soares norm inequality ⋮ Variants of Ando–Hiai inequality for operator power means ⋮ VARIANTS OF ANDO–HIAI TYPE INEQUALITIES FOR DEFORMED MEANS AND APPLICATIONS ⋮ Extensions of Lemos-Soares type log-majorization

Cites Work

• An elementary proof of an order preserving inequality
• Furuta's inequality and its application to Ando's theorem
• Means of positive linear operators
• Log majorization and complementary Golden-Thompson type inequalities
• Extension of the Furuta inequality and Ando-Hiai log-majorization
• $A \geq B \geq 0$ Assures $(B^r A^p B^r)^{1/q} \geq B^{(p+2r)/q$ for $r \geq 0$, $p \geq 0$, $q \geq 1$ with $(1 + 2r)q \geq p + 2r$
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