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

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?)

  • 1. Thierry Fack, Finite sums of commutators in ${C}\sp{\ast} $-algebras, Ann. Inst. Fourier (Grenoble) 32 (1982), no. 1, vii, 129-137. MR 83g:46051
  • 2. Thierry Fack and Pierre de la Harpe, Sommes de commutateurs dans les algèbres de von Neumann finies continues, Ann. Inst. Fourier (Grenoble) 30 (1980), no. 3, 49-73. MR 81m:46085
  • 3. Uffe Haagerup, Quasitraces on exact ${C}^*$-algebras are traces, Manuscript distributed at the Operator Algebra Conference in Istanbul, July 1991.
  • 4. Mikael Rørdam, On sums of finite projections, Operator algebras and operator theory (Shanghai, 1997) Contemporary Math. 228, Amer. Math. Soc., Providence, RI, 1998, pp. 327-340. MR 2000a:46098

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