MS-10 Matrix Analysis: Inequalities, Means, and Majorization (Matrix Inequalities)

Organizers: Fumio Hiai (Tohoku University, Japan) and Yongdo Lim (Sungkyunkwan University, Korea)

A core concept in Matrix Analysis is order structure constituting different notions of positive semidefiniteness order (or Loewner order), spectral and majorization order for eigenvalues, etc. Correspondingly, different types of matrix/operator inequalities have become a big research field with wide applications. In particular, various majorization results have played vital roles in matrix norm inequalities for unitarily invariant norms. A subject strongly connected to these order relations is theory of matrix/operator means, whose multivariate extensions have recently been developed extensively. In particular, the extension of the geometric mean in Riemannian geometry approach is remarkable. This mini-symposium is aimed to exchange new developments and ideas in topics including matrix (norm) inequalities, matrix/operator means, and majorizations for matrices.


Man-Duen Choi, Some assorted inequalities for positive linear maps

Douglas Farenick, Isometries and contractions of density operators relative to the Bures metric

Frank Hansen, Peierls-Bogolyubov's inequality for deformed exponentials

Fumio Hiai, Log-majorization and Lie-Trotter formula for the Cartan barycenter

Masatoshi Ito, Estimations of power difference mean by Heron mean

Sejong Kim, An order inequality characterizing Cartan barycenters of positive definite matrices

Fuad Kittaneh, A generalization of the Ando-Hiai-Okubo trace inequalities

Seung-Hyeok Kye, Separability of three qubit X-states

Jimmie Lawson, The Karcher Barycentric Map for Positive Operator Probability Measures on Hilbert Space

Yongdo Lim, Multiplicative Geometric Means

Lajos Molnar, Order automorphisms in matrix algebras and in operator algebras and their applications

Takashi Sano, On classes of non-normal matrices/operators

Takeaki Yamazaki, Properties of weighted operator means via generalized relative operator entropy

Pingping Zhang, Remarks on two determinantal inequalities