Some norm inequalities for matrix means

DOI10.1016/j.laa.2016.03.018zbMath1334.15052OpenAlexW2308466522MaRDI QIDQ273132

Yongdo Lim, Takeaki Yamazaki, Rajendra Bhatia

Publication date: 21 April 2016

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

Full work available at URL: https://doi.org/10.1016/j.laa.2016.03.018

zbMATH Keywords

positive definite matrixunitarily invariant normpower meanmatrix mean

Mathematics Subject Classification ID

Norms (inequalities, more than one norm, etc.) of linear operators (47A30) Inequalities involving eigenvalues and eigenvectors (15A42) Eigenvalues, singular values, and eigenvectors (15A18) Operator means involving linear operators, shorted linear operators, etc. (47A64)

Related Items (18)

Log-majorization Type Inequalities ⋮ Some geometric properties of matrix means with respect to different metrics ⋮ Some trace inequalities for matrix means ⋮ On the matrix Heron means and Rényi divergences ⋮ On a conjecture of Bhatia, Lim and Yamazaki ⋮ New log-majorization results concerning eigenvalues and singular values and a complement of a norm inequality ⋮ Weak log-majorization and inequalities of power means ⋮ Spectral inequalities for Kubo-Ando operator means ⋮ The Rényi power means of matrices ⋮ On an eigenvalue inequality involving the Hadamard product ⋮ Some log-majorizations and an extension of a determinantal inequality ⋮ Inequalities for the Wasserstein mean of positive definite matrices ⋮ Non-linear interpolation of the harmonic-geometric-arithmetic matrix means ⋮ Some inequalities for the matrix Heron mean ⋮ Inequalities of the Wasserstein mean with other matrix means ⋮ The Ando-Hiai inequalities for the solution of the generalized Karcher equation and related results ⋮ Weighted Hellinger distance and in-betweenness property ⋮ Rajendra Bhatia and his mathematical achievements

Cites Work

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• Norm inequalities related to the matrix geometric mean
• Matrix power means and the Karcher mean
• Interpolating the arithmetic--geometric mean inequality and its operator version
• Means of positive linear operators
• Log majorization and complementary Golden-Thompson type inequalities
• Riemannian metrics on positive definite matrices related to means. II
• The Riemannian mean and matrix inequalities related to the Ando-Hiai inequality and chaotic order
• Trace inequalities for multiple products of two matrices
• $A \geq B \geq 0$ 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 $(1 + 2r)q \geq p + 2r$

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