Very important in matrix/operator theory and its applications are not only the (linear) algebraic and the analytic aspects but also the geometric aspect and the order (or conic) structure. Geometric approaches have been playing vital roles in matrix theory. For instance, the Thompson metric, the monotone Riemannian metrics due to Petz, the operator means due to Kubo-Ando, in particular, the geometric (or Karcher) operator mean and its several variable extension have been forming the basis of recent development of matrix theory. There are different order concepts for Hermitian matrices/operators, e.g., positive semidefiniteness order (the central notion in the Löwner theory), the spectral order, majorization order, etc., corresponding to which different types of matrix inequalities have been developed. In particular, the majorization technique is very strong to obtain symmetric norm and trace inequalities for matrices.
The aim of this contributed minisymposium is aimed to exchange new developments and ideas on geometry of matrices, various contraction properties of matrices, matrix/operator means, various matrix/operator inequalities, and their applications to quantum information etc. The scope of the minisymposium has some overlaps with that of the invited minisymposium "Matrix Inequalities and Operator Means." A multiple effect for both would be expected by collaboration.
Tuesday 12/07, 10:30–12:30
- Tue 10:30–11:00, Room AV 03.12A two variables norm functional, Jean-Christophe Bourin (Universite de Franche-Comte).
- Tue 11:00–11:30, Room AV 03.12Quotient metrics and the cone of positive invertible matrices, Gabriel Larotonda (CONICET (Argentina)).
- Tue 11:30–12:00, Room AV 03.12On some results related to positive definite matrices by means of matrix means, Osman Kan (Selcuk University Science Faculty).
- Tue 12:00–12:30, Room AV 03.12Some inequalities of Levinson's type for Lipschitzian mappings between two Banach spaces, Jadranka Micic Hot (University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture).
Wednesday 13/07, 10:30–12:30
- Wed 10:30–11:00, SW RaadzaalCharacterizations of interpolational means and an application, Takeaki Yamazaki (Toyo University).
- Wed 11:00–11:30, SW RaadzaalA two parameter operator mean made from the power mean, Yoichi Udagawa (Tokyo University of Science).
- Wed 11:30–12:00, SW RaadzaalHadamard product for the weighted Karcher means, Sejong Kim (Chungbuk National University).
- Wed 12:00–12:30, SW RaadzaalThe relative operator entropy and Karcher means, Yuki Seo (Osaka Kyoiku University).
Friday 15/07, 10:30–12:30
- Fri 10:30–11:00, Room AV 03.12Some operator inequalities which characterize operator means, Hiroyuki Osaka (Ritsumeikan University).
- Fri 11:00–11:30, Room AV 03.12Application of Schur multipliers to a problem of perturbation, Clément Coine (University of Franche-Comté).
- Fri 11:30–12:00, Room AV 03.12A generalization of Araki's log-majorization, Fumio Hiai (Tohoku University).
- Fri 12:00–12:30, Room AV 03.12Update on a few permanent conjectures, Fuzhen Zhang (Nova Southeastern University).