Improved arithmetic-geometric and Heinz means inequalities for Hilbert space operators

DOI10.5486/PMD.2012.5193zbMath1275.47038OpenAlexW2065729520MaRDI QIDQ2915412

Mario Krnić, Neda Lovričević, Fuad Kittaneh, Josip E. Pečarić

Publication date: 17 September 2012

Published in: Publicationes Mathematicae Debrecen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.5486/pmd.2012.5193

zbMATH Keywords

monotonicity Hilbert space refinement superadditivity converse geometric operator mean arithmetic operator mean positive invertible operator Heinz operator mean

Mathematics Subject Classification ID

Linear operator inequalities (47A63) Inequalities for sums, series and integrals (26D15) Operator means involving linear operators, shorted linear operators, etc. (47A64)

Related Items (26)

On the Heinz mean in multiple variables ⋮ Relative entropy and Tsallis entropy of two accretive operators ⋮ Reverses and variations of Heinz inequality ⋮ Reverse Young-type inequalities for matrices and operators ⋮ Operator iteration on the Young inequality ⋮ New ordering relations for the Heinz means via hyperbolic functions ⋮ Improved Heinz inequalities via the Jensen functional ⋮ FUNCTIONAL VERSIONS OF SOME REFINED AND REVERSED OPERATOR MEAN INEQUALITIES ⋮ The sharper version for generalized power mean inequalities with negative exponent ⋮ Refinements and reverses of means inequalities for Hilbert space operators ⋮ Unnamed Item ⋮ Generalized reverse Young and Heinz inequalities ⋮ More accurate classes of Jensen-type inequalities for convex and operator convex functions ⋮ Eigenvalue inequalities for differences of means of Hilbert space operators ⋮ Some refinements of the improved Young and its reverse inequalities ⋮ Generalized operator version of Bernoulli’s inequality ⋮ More accurate weak majorization relations for the Jensen and some related inequalities ⋮ On some Hölder-type inequalities with applications ⋮ Operator inequalities involving improved Young and its reverse inequalities ⋮ Quadratic weighted geometric mean in Hermitian unital Banach ∗-algebras ⋮ Refinements of the Heinz operator inequalities ⋮ Refining and reversing the weighted arithmetic-geometric mean inequality involving convex functionals and application for the functional entropy ⋮ Inequalities for weighted geometric mean in Hermitian unital Banach ∗-algebras via a result of Cartwright and Field ⋮ Some inequalities for Heinz operator mean ⋮ Refined Heinz operator inequalities ⋮ Further refinements and generalizations of the Young's and its reverse inequalities

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