Almost commuting unitary matrices

Exel, Ruy; Loring, Terry

doi:10.1090/S0002-9939-1989-0975641-9

Almost commuting unitary matrices
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by Ruy Exel and Terry Loring

Proc. Amer. Math. Soc. 106 (1989), 913-915

DOI: https://doi.org/10.1090/S0002-9939-1989-0975641-9

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Abstract:

A pair of square matrices is said to be almost commuting if their commutator is small in norm. We give an elementary proof of a theorem of Voiculescu showing that not all almost commuting pairs can be perturbed to a commuting pair.

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