Recent developments of the operator Kantorovich inequality

DOI10.1016/j.exmath.2012.08.007zbMath1259.26029OpenAlexW1984481090MaRDI QIDQ1931419

Mohammad Sal Moslehian

Publication date: 14 January 2013

Published in: Expositiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.exmath.2012.08.007

zbMATH Keywords

operator inequalitycovarianceKantorovich inequalityoperator mean\(C^{\ast }\)-algebravariance inequalitysemi-inner product \(C^{\ast }\)-module

Mathematics Subject Classification ID

Generalizations of inner products (semi-inner products, partial inner products, etc.) (46C50) Norms (inequalities, more than one norm, etc.) of linear operators (47A30) Linear operator inequalities (47A63) (C^*)-modules (46L08) General theory of (C^*)-algebras (46L05) Inequalities for sums, series and integrals (26D15)

Related Items (8)

Certain integral inequalities involving tensor products, positive linear maps, and operator means ⋮ A note on a conjecture about Wielandt’s inequality ⋮ A note on a Wielandt type norm inequality ⋮ On condition numbers of symmetric and nonsymmetric domain decomposition methods ⋮ Developed matrix inequalities via positive multilinear mappings ⋮ Matrix power means and the information monotonicity ⋮ Complementary to Jensen's operator inequalities in external formulas ⋮ Extension of the Kantorovich inequality for positive multilinear mappings

Cites Work

• Cauchy-Schwarz inequality in semi-inner product \(C^{\ast}\)-modules via polar decomposition
• A treatment of the Cauchy-Schwarz inequality in \(C^{*}\)-modules
• A Grüss inequality for \(n\)-positive linear maps
• Matrix versions of the Cauchy and Kantorovich inequalities
• New inequalities of the Kantorovich type for bounded linear operators in Hilbert spaces
• Grüss' inequality for positive linear functionals
• Matrix inequalities for convex functions
• Some comments on six inequalities associated with the inefficiency of ordinary least squares with one regressor
• Operator inequalities associated with Hölder-McCarthy and Kantorovich inequalities
• Geometric means
• Operator inequalities related to Cauchy-Schwarz and Hölder-McCarthy inequalities
• Several matrix Kantorovich-type inequalities
• Reverse of the grand Furuta inequality and its applications
• An extension of Kantorovich inequality to \(n\)-operators via the geometric mean by Ando--Li--Mathias
• Matrix versions of some classical inequalities
• Some matrix inequalities
• Conditional expectation in an operator algebra
• Equivalence of the wielandt inequality and the kantorovich inequality
• A Diaz-Metcalf type inequality for positive linear maps and its applications
• On a Generalization of an Inequality of L. V. Kantorovich
• On the Kantorovich Inequality
• Bounds for the ratio and difference between parallel sum and series via Mond-Pečarić method
• Kantorovich type inequalities for ordered linear spaces
• A matrix version of the Ky Fan generalization of the kantorovich inequality
• Operator versions of the Kantorovich inequality
• Inequalities on Singular Values of Block Triangular Matrices
• Bloomfield-Watson-Knott type inequalities for eigenvalues
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