Remote Access Journal of the American Mathematical Society
Green Open Access

Journal of the American Mathematical Society

ISSN 1088-6834(online) ISSN 0894-0347(print)

Request Permissions   Purchase Content 
 

 

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
DOI: https://doi.org/10.1090/S0894-0347-2015-00823-2
Published electronically: January 8, 2015
MathSciNet review: 3402694
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Journal of the American Mathematical Society with MSC (2010): 47A05, 47L30, 15A27

Retrieve articles in all journals with MSC (2010): 47A05, 47L30, 15A27


Additional Information

Ilya Kachkovskiy
Affiliation: Department of Mathematics, University of California, Irvine, Irvine, California 92697-3875
Email: ikachkov@uci.edu

Yuri Safarov
Affiliation: Department of Mathematics, King’s College London, Strand, London WC2R 2LS, United Kingdom
Email: yuri.safarov@kcl.ac.uk

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