Almost commuting unitary matrices

Author:

Exel Ruy,Loring Terry

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference6 articles.

1. Almost commuting matrices need not be nearly commuting;Choi, Man Duen;Proc. Amer. Math. Soc.,1988

2. Almost commuting Hermitian matrices;Davidson, Kenneth R.;Math. Scand.,1985

3. Some unsolved problems of unknown depth about operators on Hilbert space;Halmos, P. R.;Proc. Roy. Soc. Edinburgh Sect. A,1976

4. 𝐾-theory and asymptotically commuting matrices;Loring, Terry A.;Canad. J. Math.,1988

5. Remarks on the singular extension in the 𝐶*-algebra of the Heisenberg group;Voiculescu, Dan;J. Operator Theory,1981

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