## 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.## References

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## Bibliographic Information

**Ilya Kachkovskiy**- Affiliation: Department of Mathematics, University of California, Irvine, Irvine, California 92697-3875
- MR Author ID: 862757
- Email: ikachkov@uci.edu
**Yuri Safarov**- Affiliation: Department of Mathematics, King’s College London, Strand, London WC2R 2LS, United Kingdom
- MR Author ID: 191381
- Email: yuri.safarov@kcl.ac.uk
- Received by editor(s): April 15, 2014
- Received by editor(s) in revised form: September 12, 2014
- Published electronically: January 8, 2015
- Additional Notes: The first author was supported by King’s Annual Fund and King’s Overseas ResearchStudentships, King’s College London, and partially by NSF Grant DMS-1101578.
- © Copyright 2015 American Mathematical Society
- Journal: J. Amer. Math. Soc.
**29**(2016), 61-80 - MSC (2010): Primary 47A05; Secondary 47L30, 15A27
- DOI: https://doi.org/10.1090/S0894-0347-2015-00823-2
- MathSciNet review: 3402694