Unique Matrix Factorizations associated to Bilinear Forms and Schur Multipliers
arXiv:2309.17092 · doi:10.1016/j.laa.2024.02.019
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.