Bilinear forms, Schur multipliers, complete boundedness and duality
Copyright policy )Bilinear forms, Schur multipliers, complete boundedness and duality
Grothendieck's inequalities for operators and bilinear forms imply some factorization results for complex $m \times n$ matrices. Based on the theory of operator spaces and completely bounded maps 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 bilinear forms and of Schur multipliers are conjugate duals to each other with respect to their completely bounded norms.
- University of Copenhagen Denmark
- University of Copenhagen Denmark
Mathematics - Operator Algebras, Schur product, Functional Analysis (math.FA), Mathematics - Functional Analysis, 15A23, 46B25, 46L07 (Primary) 15A60, 15A63, 47A30, 47L25 (Secondary), Grothendieck's inequality, Algebras of operators on Banach spaces and other topological linear spaces, factorisation, FOS: Mathematics, Operator spaces and completely bounded maps, Norms of matrices, numerical range, applications of functional analysis to matrix theory, Operator Algebras (math.OA)
Mathematics - Operator Algebras, Schur product, Functional Analysis (math.FA), Mathematics - Functional Analysis, 15A23, 46B25, 46L07 (Primary) 15A60, 15A63, 47A30, 47L25 (Secondary), Grothendieck's inequality, Algebras of operators on Banach spaces and other topological linear spaces, factorisation, FOS: Mathematics, Operator spaces and completely bounded maps, Norms of matrices, numerical range, applications of functional analysis to matrix theory, Operator Algebras (math.OA)
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