Distance to normal elements in 𝐶*-algebras of real rank zero

Kachkovskiy, Ilya; Safarov, Yuri

doi:10.1090/S0894-0347-2015-00823-2

Distance to normal elements in $C^*$-algebras of real rank zero
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by Ilya Kachkovskiy and Yuri Safarov

J. Amer. Math. Soc. 29 (2016), 61-80

DOI: https://doi.org/10.1090/S0894-0347-2015-00823-2

Published electronically: January 8, 2015

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Abstract:

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. A slightly modified estimate holds in a general $C^*$-algebra of real rank zero.

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