Comptes Rendus
no. 5
Functional analysis
On some eigenvalue inequalities for Schatten–von Neumann operators
[Sur quelques inégalités pour les valeurs propres d'opérateurs de Schatten–von Neumann]

Présenté par : the Editorial Board

Minghua Lin1
1 Department of Mathematics, Shanghai University, Shanghai, 200444, China
Comptes Rendus. Mathématique, Volume 356 (2018) no. 5, pp. 517-522.

Dans les articles [J. Funct. Anal. 267 (2014) 3500–3506] et [Commun. Contemp. Math. 18 (2016) 1550022], Michael Gil' a récemment obtenu des bornes pour les valeurs propres d'opérateurs de Schatten–von Neumann qui améliorent des énoncés classiques dans ce contexte. Nous reprenons ces résultats et en donnons des preuves véritablement différentes (par exemple, en utilisant la transformation d'Aluthge, la majoration). Au fil des arguments, nous obtenons de nouveaux résultats.

Michael Gil' recently obtained some bounds for eigenvalues in [J. Funct. Anal. 267 (2014) 3500–3506] and [Commun. Contemp. Math. 18 (2016) 1550022], which improve some classical results related to this aspect. We revisit these results by providing genuinely different arguments (e.g., using Aluthge transform, majorization). New results are derived along our discussions.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2018.04.004
Minghua Lin 1

1 Department of Mathematics, Shanghai University, Shanghai, 200444, China 
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Minghua Lin. On some eigenvalue inequalities for Schatten–von Neumann operators. Comptes Rendus. Mathématique, Volume 356 (2018) no. 5, pp. 517-522. doi : 10.1016/j.crma.2018.04.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.04.004/

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