2006/01/23 by Jean-Christophe Bourin, Bourin, Jean-Christophe
Computer Science · Mathematics · #15A60 47A30 47A63 #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results #Mathematical Inequalities and Applications #Matrix Theory and Algorithms #Operator Algebras (math.OA) #math.FA #math.OA #msc:15A60 #msc:47A30 #msc:47A63
paper · pdf · doi:10.48550/arxiv.math/0601543
to appear in Linear Algebra Appl. (2006)
arxiv created 2006/01/23 · openalex publication_date 2006/01/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Some natural inequalities related to rearrangement in matrix products can also be regarded as extensions of classical inequalities for sequences or integrals. In particular, we show matrix versions of Chebyshev and Kantorovich type inequalities. The matrix approach may also provide simplified proofs and new results for classical inequalities. For instance, we show a link between Cassel's inequality and the basic rearrangement inequality for sequences of Hardy-Littlewood-Polya, and we state a reverse inequality to the Hardy-Littlewood-Polya inequality in which matrix technics are essential.