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We obtain an order sharp estimate for the distance from a given bounded operator $A$ on a Hilbert space to the set of normal operators in terms of $\|[A,A^*]\|$ and the distance to the set of invertible operators.
Brown L., Douglas R., Fillmore P., Unitary equivalence modulo the compact operators and extensions of C ∗ C^{*} -algebras, Proc. Conf. Operator Theory (Dalhousie Univ., Halifax, N. S. 1973), Lecture Notes in Math. 345, Springer, 1973, p. 58–128
1973
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2001
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2001
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Aleksandrov A., Peller V., Estimates of operator moduli of continuity
2011
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Filonov, N., Safarov, Y., On the relation between an operator and its self-commutator
2011
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Hastings M., Making almost commuting matrices commute
2011
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Aleksandrov A., Peller V., Operator and commutator moduli of continuity for normal operators
2012
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