A proof via operator means of an order preserving inequality

DOI10.1016/0024-3795(89)90291-7zbMath0770.47003OpenAlexW1973395267MaRDI QIDQ1813210

Takayuki Furuta

Publication date: 25 June 1992

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

Full work available at URL: https://doi.org/10.1016/0024-3795(89)90291-7

zbMATH Keywords

operator inequalityoperator meansmeans of linear operators

Mathematics Subject Classification ID

Norms (inequalities, more than one norm, etc.) of linear operators (47A30) Linear operator inequalities (47A63) Functional calculus for linear operators (47A60)

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Extension of the Furuta inequality and Ando-Hiai log-majorization ⋮ Complements to the Furuta inequality ⋮ Generalizations of Kosaki trace inequalities and related trace inequalities on chaotic order ⋮ Equivalence relations among Reid, Löwner-Heinz and Heinz-Kato inequalities, and extensions of these inequalities ⋮ Further extensions of Aluthge transformation on \(p\)-hyponormal operators ⋮ Some further results on Hermitian-matrix inequalities ⋮ Characterization of chaotic order and its applications to furuta's type operator inequalities ⋮ Furuta's inequality and its application to Ando's theorem ⋮ Operator functions associated with Furuta's inequality ⋮ Mean theoretic approach to the grand Furuta inequality ⋮ Generalized Aluthge transformation on 𝑝-hyponormal operators

Cites Work

• Unnamed Item
• Means of positive linear operators
• Shorter Notes: Some Operator Monotone Functions
• $A \geq B \geq 0$ 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 $(1 + 2r)q \geq p + 2r$