no. 10
Functional analysis
Positive block matrices and numerical ranges
[Matrices par blocs positives et images numériques]

Présenté par : the Editorial Board

Bourin, Jean-Christophe1 ; Mhanna, Antoine2
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, Tome 355 (2017) no. 10, pp. 1077-1081.

Toute matrice positive partitionnée en quatre blocs de même taille satisfait l'inégalité en norme unitairement invariante ‖M‖≤‖M1,1+M2,2+ωI‖, où ω est la largeur de l'image numérique de M1,2.

Any positive matrix M partitioned in four n-by-n blocks satisfies the unitarily invariant norm inequality ‖M‖≤‖M1,1+M2,2+ωI‖, where ω is the width of the numerical range of M1,2. Some related inequalities and a reverse Lidskii majorization are given.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2017.10.006
Bourin, Jean-Christophe 1 ; Mhanna, Antoine 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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Bourin, Jean-Christophe; Mhanna, Antoine. Positive block matrices and numerical ranges. Comptes Rendus. Mathématique, Tome 355 (2017) no. 10, pp. 1077-1081. doi : 10.1016/j.crma.2017.10.006. http://www.numdam.org/articles/10.1016/j.crma.2017.10.006/

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