Geodesic
K-Theory and Asymptotically Commuting Matrices
Canadian journal of mathematics, Tome 40 (1988) no. 1, pp. 197-216

Voir la notice de l'article provenant de la source Cambridge University Press

To shed light on the following unsolved problem, several authors have considered related problems. The problem is that of finding commuting approximants to pairs of asymptotically commuting self-adjoint matrices:Suppose that Hn and Kn are self-adjoint matrices of dimension m(n), with ║Hn ║, ║Kn ║ ≦ 1, which commute asymptotically in the sense that Must there then exist commuting self-adjoint matrices H′n and K′n for which One may alter the conditions imposed on Hn and Kn , for example, by requiring Hn to be normal and Kn to be self-adjoint, and ask whether commuting approximants H′n and K′n can be found satisfying the same conditions. Some of these related problems have been solved. This paper will examine their solutions from a K-theoretic point of view, illustrating the difficulty inherent in modifying them to work for the original problem. 
Loring, Terry A. K-Theory and Asymptotically Commuting Matrices. Canadian journal of mathematics, Tome 40 (1988) no. 1, pp. 197-216. doi: 10.4153/CJM-1988-008-9
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