A reverse inequality for the weighted geometric mean due to Lawson--Lim

DOI10.1016/j.laa.2007.07.025zbMath1132.47016OpenAlexW2087670588MaRDI QIDQ2459971

Masatoshi Fujii, Masahiro Nakamura, Yuki Seo, Jun Ichi Fujii, Josip E. Pečarić

Publication date: 9 November 2007

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

Full work available at URL: https://doi.org/10.1016/j.laa.2007.07.025

zbMATH Keywords

positive operatorKantorovich constantreverse inequalitygeometric mean of \(n\)-operatorsSpecht ratio

Mathematics Subject Classification ID

Linear operator inequalities (47A63) Inequalities involving eigenvalues and eigenvectors (15A42) Positive linear operators and order-bounded operators (47B65) Operator means involving linear operators, shorted linear operators, etc. (47A64)

Related Items (17)

On the Lawson-Lim means and Karcher mean for positive invertible operators ⋮ On a new construction of geometric mean of \(n\)-operators ⋮ Weighted geometric mean of \(n\)-operators with \(n\)-parameters ⋮ On the Ando–Li–Mathias mean and the Karcher mean of positive definite matrices ⋮ Operator monotone functions on accretive matrices ⋮ Generalized Pólya-Szegő type inequalities for some non-commutative geometric means ⋮ Some refinements of operator inequalities for positive linear maps ⋮ Tensor product and Hadamard product for the Wasserstein means ⋮ Multidimensional Jensen's operator on a Hilbert space and applications ⋮ Multi-variable weighted geometric means of positive definite matrices ⋮ More accurate classes of Jensen-type inequalities for convex and operator convex functions ⋮ Inequalities of the Wasserstein mean with other matrix means ⋮ AN ANDERSON-TAYLOR TYPE INEQUALITY VIA THE SCHUR COMPLEMENT ⋮ Sherman's operator inequality ⋮ Generalized versions of reverse Young inequalities ⋮ Extension of the Kantorovich inequality for positive multilinear mappings ⋮ Some matrix power and Karcher means inequalities involving positive linear maps

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• Bounds for the ratio and difference between parallel sum and series via Mond-Pečarić method
• A general framework for extending means to higher orders
• Hilbert’s projective metric and iterated nonlinear maps
• Reverse inequalities on chaotically geometric mean via Specht ratio
• Geometrical significance of the Löwner-Heinz inequality

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