2015/08/15 by Antoine Mhanna, Mhanna, Antoine
Computer Science · Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Inequalities and Applications #Matrix Theory and Algorithms #Operator Algebras (math.OA) #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.1508.03754
openalex publication_date 2015/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For positive semi-definite block-matrix M, we say that M is P.S.D. and we write M=\beginpmatrix A & X X^* & B\endpmatrix ∈ \mathbbM_n+m+, with A∈ \mathbbM_n+, B ∈ \mathbbM_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‖≤ ‖A+B‖ for all symmetric norms.