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

Authors: Ilya Kachkovskiy and Yuri Safarov
Journal: J. Amer. Math. Soc. 29 (2016), 61-80
MSC (2010): Primary 47A05; Secondary 47L30, 15A27
Published electronically: January 8, 2015
MathSciNet review: 3402694
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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 $ \Vert[A,A^*]\Vert$ 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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Additional Information

Ilya Kachkovskiy
Affiliation: Department of Mathematics, University of California, Irvine, Irvine, California 92697-3875

Yuri Safarov
Affiliation: Department of Mathematics, King’s College London, Strand, London WC2R 2LS, United Kingdom

Keywords: Almost commuting operators, self-commutator, Brown-Douglas-Fillmore theorem.
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.
Article copyright: © Copyright 2015 American Mathematical Society

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