2023/01/12 by Erik Christensen, Christensen, Erik · 2 citations
Mathematics · #15A23 #15A63 #46B25 #46L07 (Primary) 15A60 #47A30 #47L25 (Secondary) #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical Inequalities and Applications #Operator Algebras (math.OA) #math.FA #math.OA #msc:15A23 #msc:15A60 #msc:15A63 #msc:46B25 #msc:46L07 #msc:47A30 #msc:47L25
paper · pdf · doi:10.48550/arxiv.2301.05005
A part of this was previously announced on the arXiv as the first half of the article "Norm optimal factorizations of scalar and block matrices", arXiv:2211.00591. Later results have forced a division of the article. The part on block matrices will appear separately
arxiv created 2023/01/12 · openalex publication_date 2023/01/12 · arxiv updated 2023/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Grothendieck's inequalities for operators and bilinear forms imply some factorization results for complex m x n matrices. Based on the theory of operator spaces and completely bounded mappings we present norm optimal versions of these results and two norm optimal factorization results related to the Schur product. We show that the spaces of respectively bilinear forms and Schur multipliers are conjugate duals to each other with respect to their completely bounded norms.