The matrix arithmetic-geometric mean inequality revisited

DOI10.1016/j.laa.2007.11.030zbMath1148.15014OpenAlexW2090537815MaRDI QIDQ2479524

Fuad Kittaneh, Rajendra Bhatia

Publication date: 26 March 2008

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

Full work available at URL: https://doi.org/10.1016/j.laa.2007.11.030

zbMATH Keywords

matrix inequalitiessingular valuespinchingarithmetic-geometric mean inequalityunitarily invariant normsmatrix monotone functions

Mathematics Subject Classification ID

Inequalities involving eigenvalues and eigenvectors (15A42) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Miscellaneous inequalities involving matrices (15A45)

Related Items (38)

Singular value inequalities for operators and matrices ⋮ Cauchy–Schwarz Operator and Norm Inequalities for Inner Product Type Transformers in Norm Ideals of Compact Operators, with Applications ⋮ More results on generalized singular number inequalities of \(\tau\)-measurable operators ⋮ Unification of the arithmetic-geometric mean and Hölder inequalities for unitarily invariant norms ⋮ Commutators and accretive operators ⋮ The singular values of \(A+B\) and \(A+iB\) ⋮ Singular value inequalities for accretive-dissipative normal operators ⋮ Norm inequalities for the spectral spread of Hermitian operators ⋮ On generalized singular number of positive matrix of τ measurable operators ⋮ Some singular value and unitarily invariant norm inequalities for Hilbert space operators ⋮ An arithmetic-geometric mean inequality for products of three matrices ⋮ Diagonal and off-diagonal blocks of positive definite partitioned matrices ⋮ On some inequalities for unitarily invariant norms and singular values ⋮ Better bounds on the numerical radii of Hilbert space operators ⋮ Singular value and norm inequalities involving the numerical radii of matrices ⋮ Norm inequalities for positive semidefinite matrices and a question of Bourin ⋮ Norm inequalities related to the matrix geometric mean ⋮ New lower bounds on the minimum singular value of a matrix ⋮ On a question of Bhatia and Kittaneh ⋮ On Schatten restricted norms ⋮ Some generalizations for singular value inequalities of compact operators ⋮ Refined Heinz-Kato-Löwner inequalities ⋮ Some extensions of the Young and Heinz inequalities for matrices ⋮ Singular value and unitarily invariant norm inequalities for sums and products of operators ⋮ New properties for certain positive semidefinite matrices ⋮ Singular value inequalities for compact operators ⋮ Generalized spectral radius and norm inequalities for Hilbert space operators ⋮ An arithmetic-geometric mean inequality for singular values and its applications ⋮ On Drury's solution of Bhatia \& Kittaneh's question ⋮ Interpolating inequalities for functions of positive semidefinite matrices ⋮ Tracial and majorisation Heinz mean-type inequalities for matrices ⋮ Singular value inequalities for commutators of Hilbert space operators ⋮ Inequalities related to 2 ✕ 2 block PPT matrices ⋮ Positive definiteness of functions with applications to operator norm inequalities ⋮ Singular value inequalities for the arithmetic, geometric and Heinz means of matrices ⋮ Rajendra Bhatia and his mathematical achievements ⋮ Extensions of the arithmetic–geometric means and Young's norm inequalities to accretive operators, with applications ⋮ Geometric-arithmetic master equation in large and fast open quantum systems

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