Some majorization inequalities in Euclidean Jordan algebras

DOI10.1016/j.laa.2014.07.048zbMath1352.17032OpenAlexW2087836552MaRDI QIDQ406479

Lingchen Kong, Ziyan Luo, Jiyuan Tao, Nai-Hua Xiu

Publication date: 8 September 2014

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

Full work available at URL: https://doi.org/10.1016/j.laa.2014.07.048

zbMATH Keywords

majorizationEuclidean Jordan algebraThompson triangle inequality

Mathematics Subject Classification ID

Matrices over special rings (quaternions, finite fields, etc.) (15B33) Simple, semisimple Jordan algebras (17C20) Finite-dimensional structures of Jordan algebras (17C55)

Related Items (13)

A note on an inequality involving Jordan product in Euclidean Jordan algebras ⋮ Some log and weak majorization inequalities in Euclidean Jordan algebras ⋮ A Lie product type formula in Euclidean Jordan algebras ⋮ Weak majorization, doubly substochastic maps, and some related inequalities in Euclidean Jordan algebras ⋮ Some majorization inequalities induced by Schur products in Euclidean Jordan algebras ⋮ A Hölder type inequality and an interpolation theorem in Euclidean Jordan algebras ⋮ Unnamed Item ⋮ A generalization of the Craig-Sakamoto theorem to Euclidean Jordan algebras ⋮ Weak majorization and doubly substochastic operators on \(\ell^p(I)\) ⋮ Spectral sets and functions on Euclidean Jordan algebras ⋮ Positive and doubly stochastic maps, and majorization in Euclidean Jordan algebras ⋮ A Riesz-Thorin type interpolation theorem in Euclidean Jordan algebras ⋮ Refinements of Ky Fan's eigenvalue inequality for simple Euclidean Jordan algebras by using gradients of K-increasing functions

Cites Work

• Some inequalities of majorization type
• Some inequalities involving determinants, eigenvalues, and Schur complements in Euclidean Jordan algebras
• Some inertia theorems in Euclidean Jordan algebras
• Strict diagonal dominance and a Geršgorin type theorem in Euclidean Jordan algebras
• A representation theorem for (tr \(A^ p)^{1/p}\)
• Eigenvalues of sums of Hermitian matrices
• Some inequalities for the eigenvalues of the product of positive semidefinite Hermitian matrices
• Convex and concave functions of singular values of matrix sums
• The case of equality in the matrix-valued triangle inequality
• Matrix representations of octonions and their applications
• The Cauchy interlacing theorem in simple Euclidean Jordan algebras and some consequences
• The matrix valued triangle inequality:quaternion version
• Inequalities: theory of majorization and its applications
• Quaternions and matrices of quaternions
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