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arXiv · 1508.03754

Symmetric Norm Inequalities And Positive Semi-Definite Block-Matrices

Antoine Mhanna
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Abstract

For positive semi-definite block-matrix $M,$ we say that $M$ is P.S.D. and we write $M=\begin{pmatrix} A \& X\\ {X^*} \& B\end{pmatrix} \in {\mathbb{M}}\_{n+m}^+$, with $A\in {\mathbb{M}}\_n^+$, $B \in {\mathbb{M}}\_m^+.$ The focus is on studying the consequences of a decomposition lemma due to C.~Bourrin and the main result is extending the class of P.S.D. matrices $M$ written by blocks of same size that satisfies the inequality: $\|M\|\le \|A+B\|$ for all symmetric norms.

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Antoine Mhanna. 2015-08-15. Symmetric Norm Inequalities And Positive Semi-Definite Block-Matrices. https://arxiv.org/abs/1508.03754

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