A quantitative version of the commutator theorem for zero trace matrices

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Abstract

Let A be an m × m complex matrix with zero trace and let ε > 0. Then there are m × m matrices B and C such that A = [B,C] and ||B||||C|| ≤ Kεmε||A|| where K ε depends only on ε. Moreover, the matrix B can be taken to be normal.

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Johnson, W. B., Ozawa, N., & Schechtman, G. (2013). A quantitative version of the commutator theorem for zero trace matrices. Proceedings of the National Academy of Sciences of the United States of America, 110(48), 19251–19255. https://doi.org/10.1073/pnas.1202411109

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