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On single commutators in II$ _1$-factors


Authors: Ken Dykema and Anna Skripka
Journal: Proc. Amer. Math. Soc. 140 (2012), 931-940
MSC (2010): Primary 47B47, 47C15
DOI: https://doi.org/10.1090/S0002-9939-2011-10953-5
Published electronically: July 14, 2011
MathSciNet review: 2869077
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Abstract: We investigate the question of whether all elements of trace zero in a II$ _1$-factor are single commutators. We show that all nilpotent elements are single commutators, as are all normal elements of trace zero whose spectral distributions are discrete measures. Some other classes of examples are considered.


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Additional Information

Ken Dykema
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368
Email: kdykema@math.tamu.edu

Anna Skripka
Affiliation: Department of Mathematics, University of Central Florida, 4000 Central Florida Boulevard, P.O. Box 161364, Orlando, Florida 32816-1364
Email: skripka@math.ucf.edu

DOI: https://doi.org/10.1090/S0002-9939-2011-10953-5
Keywords: Commutators, II$_{1}$–factors
Received by editor(s): August 22, 2010
Received by editor(s) in revised form: December 16, 2010
Published electronically: July 14, 2011
Additional Notes: The first author’s research was supported in part by NSF grant DMS–0901220.
The second author’s research was supported in part by NSF grant DMS-0900870
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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