Positive block matrices and numerical ranges

Jean-Christophe Bourin; Antoine Mhanna

doi:10.1016/j.crma.2017.10.006

Functional analysis

Positive block matrices and numerical ranges
[Matrices par blocs positives et images numériques]

Présenté par : the Editorial Board

Jean-Christophe Bourin ¹ ; Antoine Mhanna ²

¹ Laboratoire de mathématiques de Besançon, Université Bourgogne Franche-Comté, CNRS UMR 6623, 16, route de Gray, 25030 Besançon, France
² Kfardebian, Lebanon

Comptes Rendus. Mathématique, Volume 355 (2017) no. 10, pp. 1077-1081.

Résumé
Abstract

Toute matrice positive partitionnée en quatre blocs de même taille satisfait l'inégalité en norme unitairement invariante $‖ M ‖ \leq ‖ M_{1, 1} + M_{2, 2} + ω I ‖$ , où ω est la largeur de l'image numérique de $M_{1, 2}$ .

Any positive matrix M partitioned in four n-by-n blocks satisfies the unitarily invariant norm inequality $‖ M ‖ \leq ‖ M_{1, 1} + M_{2, 2} + ω I ‖$ , where ω is the width of the numerical range of $M_{1, 2}$ . Some related inequalities and a reverse Lidskii majorization are given.

Reçu le : 2017-07-01
Accepté le : 2017-10-12
Publié le : 2017-10-01

DOI : 10.1016/j.crma.2017.10.006

Affiliations des auteurs :

Jean-Christophe Bourin ¹ ; Antoine Mhanna ²

¹ Laboratoire de mathématiques de Besançon, Université Bourgogne Franche-Comté, CNRS UMR 6623, 16, route de Gray, 25030 Besançon, France
² Kfardebian, Lebanon

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     title = {Positive block matrices and numerical ranges},
     journal = {Comptes Rendus. Math\'ematique},
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     language = {en},
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Jean-Christophe Bourin; Antoine Mhanna. Positive block matrices and numerical ranges. Comptes Rendus. Mathématique, Volume 355 (2017) no. 10, pp. 1077-1081. doi : 10.1016/j.crma.2017.10.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.10.006/

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