Functional analysis
A norm inequality for positive block matrices
Comptes Rendus. Mathématique, Volume 356 (2018) no. 7, pp. 818-822.

Any positive matrix M=(Mi,j)i,j=1m with each block Mi,j square satisfies the symmetric norm inequality Mi=1mMi,i+i=1m1ωiI, where ωi (i=1,,m1) are quantities involving the width of numerical ranges. This extends the main theorem of Bourin and Mhanna (2017) [4] to a higher number of blocks.

Toute matrice positive M=(Mi,j)i,j=1m écrite en blocs carrés Mi,j satisfait Mi=1mMi,i+i=1m1ωiI, où les quantités ωi, i=1,,m1, font intervenir la largeur du domaine des valeurs numériques. Ceci étend le théorème principal de Bourin, Mhanna (2017) [4] aux matrices écrites avec un nombre de blocs arbitraire.

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DOI: 10.1016/j.crma.2018.05.006
Lin, Minghua 1

1 Department of Mathematics, Shanghai University, Shanghai, 200444, China
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Lin, Minghua. A norm inequality for positive block matrices. Comptes Rendus. Mathématique, Volume 356 (2018) no. 7, pp. 818-822. doi : 10.1016/j.crma.2018.05.006. http://www.numdam.org/articles/10.1016/j.crma.2018.05.006/

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