Symmetric Norm Inequalities And Positive Semi-Definite Block-Matrices
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.
Domains
Operator Algebras [math.OA]
Origin : Files produced by the author(s)
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