Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



Finite sums of commutators

Author: Ciprian Pop
Journal: Proc. Amer. Math. Soc. 130 (2002), 3039-3041
MSC (2000): Primary 46L05
Published electronically: March 14, 2002
MathSciNet review: 1908928
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: 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.

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

  • Thierry Fack, Finite sums of commutators in $C^{\ast } $-algebras, Ann. Inst. Fourier (Grenoble) 32 (1982), no. 1, vii, 129–137 (English, with French summary). MR 658946
  • 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
  • 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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 46L05

Retrieve articles in all journals with MSC (2000): 46L05

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

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
Article copyright: © Copyright 2002 American Mathematical Society