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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Finite sums of commutators
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by Ciprian Pop PDF
Proc. Amer. Math. Soc. 130 (2002), 3039-3041 Request permission


We show that elements of unital $C^*$-algebras without tracial states are finite sums of commutators. Moreover, the number of commutators involved is bounded, depending only on the given $C^*$-algebra.
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  • Th. Fack and P. de la Harpe, Sommes de commutateurs dans les algèbres de von Neumann finies continues, Ann. Inst. Fourier (Grenoble) 30 (1980), no. 3, 49–73 (French). MR 597017, DOI 10.5802/aif.792
  • Uffe Haagerup, Quasitraces on exact ${C}^*$-algebras are traces, Manuscript distributed at the Operator Algebra Conference in Istanbul, July 1991.
  • Mikael Rørdam, On sums of finite projections, Operator algebras and operator theory (Shanghai, 1997) Contemp. Math., vol. 228, Amer. Math. Soc., Providence, RI, 1998, pp. 327–340. MR 1667668, DOI 10.1090/conm/228/03295
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Additional Information
  • Ciprian Pop
  • Affiliation: I.M.A.R., CP 1–764, Bucharest, Romania
  • Address at time of publication: Department of Mathematics, Texas A&M University, College Station, Texas 77843–3368
  • Email:
  • Received by editor(s): February 20, 2001
  • Received by editor(s) in revised form: May 29, 2001
  • Published electronically: March 14, 2002
  • Communicated by: David R. Larson
  • © Copyright 2002 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 130 (2002), 3039-3041
  • MSC (2000): Primary 46L05
  • DOI:
  • MathSciNet review: 1908928