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Unique Matrix Factorizations associated to Bilinear Forms and Schur Multipliers (2309.17092v1)
Published 29 Sep 2023 in math.FA, math.OA, and math.RA
Abstract: Grothendieck's inequalities for operators and bilinear forms imply some factorization results for complex m x n matrices. The theory of operator spaces provides a set up which describes 4 norm optimal factorizations of Grothendieck's sort. It is shown that 3 of the optimal factorizations are uniquely determined and the remaining one is unique in some cases.