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math.OA2025
On almost commuting unitary matrices
Adam Dor-On, Lucas Hall, Ilya Kachkovskiy
A question going back to Halmos asks when two approximately commuting matrices of a certain kind are close to exactly commuting matrices of the same kind. It has long been known th…
math.OA2011
Polynomials of almost-normal arguments in -algebras
Nikolay Filonov, Ilya Kachkovskiy
The functional calculus for normal elements in -algebras is an important tool of analysis. We consider polynomials for elements with small self-commutator norm…