Bilinear forms, Schur multipliers, complete boundedness and duality

2023/01/12 by Erik Christensen, Christensen, Erik · 1 citation
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)

paper · pdf · doi:10.48550/arxiv.2301.05005

openalex publication_date 2023/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• The Schur multiplier norm and its dual norm

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