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Nilpotent elements of operator ideals as single commutators


Authors: Ken Dykema and Amudhan Krishnaswamy–Usha
Journal: Proc. Amer. Math. Soc. 146 (2018), 3031-3037
MSC (2010): Primary 47B47; Secondary 47L20
DOI: https://doi.org/10.1090/proc/13987
Published electronically: February 28, 2018
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Abstract: For an arbitrary operator ideal $ \mathcal {I}$, every nilpotent element of $ \mathcal {I}$ is a single commutator of operators from $ \mathcal {I}^{\,t}$ for an exponent $ t$ that depends on the degree of nilpotency.


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Additional Information

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

Amudhan Krishnaswamy–Usha
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
Email: amudhan@math.tamu.edu

DOI: https://doi.org/10.1090/proc/13987
Keywords: Operator ideals, commutators, nilpotent operators
Received by editor(s): June 12, 2017
Received by editor(s) in revised form: October 15, 2017, and August 24, 2017
Published electronically: February 28, 2018
Communicated by: Stephan Ramon Garcia
Article copyright: © Copyright 2018 American Mathematical Society

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