Jensen and Minkowski inequalities for operator means and anti-norms
| Affiliation auteurs | Affiliation ok |
| Titre | Jensen and Minkowski inequalities for operator means and anti-norms |
| Type de publication | Journal Article |
| Year of Publication | 2014 |
| Auteurs | Bourin J-C, Hiai F |
| Journal | LINEAR ALGEBRA AND ITS APPLICATIONS |
| Volume | 456 |
| Pagination | 22-53 |
| Date Published | SEP 1 |
| Type of Article | Article |
| ISSN | 0024-3795 |
| Mots-clés | Anti-norm, Concave function, Convex function, Majorization, Matrix, Operator mean, Positive linear map, Schur product, Symmetric norm |
| Résumé | Jensen inequalities for positive linear maps of Choi and Hansen-Pedersen type are established for a large class of operator/matrix means such as some p-means and some Kubo-Ando means. These results are also extensions of the Minkowski determinantal inequality. To this end we develop the study of anti-norms, a notion parallel to the symmetric norms in matrix analysis, including functionals like Schatten q-norms for a parameter q is an element of (-infinity, 1] and the Minkowski functional det(1/n) A. (C) 2014 Elsevier Inc. All rights reserved. |
| DOI | 10.1016/j.laa.2014.05.030 |