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## On Symmetric Norm Inequalities And Hermitian Block-Matrices

(1)
1
Antoine Mhanna
• Function : Author

#### Abstract

The main purpose of this paper is to englobe some new and known types of Hermitian block-matrices $M=\begin{pmatrix} A & X\\ {X^*} & B\end{pmatrix}$ satisfying or not the inequality $\|M\|\le \|A+B\|$ for all symmetric norms. For positive definite block-matrices another inequality is established and it is shown that it can be sharper (for some symmetric norms) than the following holding inequality $\|M\|\le \|A\|+\|B\|$.

#### Domains

Mathematics [math] Operator Algebras [math.OA]

### Dates and versions

hal-01231860 , version 1 (21-11-2015)
hal-01231860 , version 2 (22-11-2015)
hal-01231860 , version 3 (27-05-2017)

### Identifiers

• HAL Id : hal-01231860 , version 3
• ARXIV :

### Cite

Antoine Mhanna. On Symmetric Norm Inequalities And Hermitian Block-Matrices. 2016. ⟨hal-01231860v3⟩

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