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Finite sums of commutators
Author(s):
Ciprian
Pop
Journal:
Proc. Amer. Math. Soc.
130
(2002),
3039-3041.
MSC (2000):
Primary 46L05
Posted:
March 14, 2002
MathSciNet review:
1908928
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Abstract:
We show that elements of unital  -algebras without tracial states are finite sums of commutators. Moreover, the number of commutators involved is bounded, depending only on the given  -algebra.
References:
-
- 1.
- Thierry Fack, Finite sums of commutators in
 -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
 -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
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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:
cpop@math.tamu.edu
DOI:
10.1090/S0002-9939-02-06484-5
PII:
S 0002-9939(02)06484-5
Received by editor(s):
February 20, 2001
Received by editor(s) in revised form:
May 29, 2001
Posted:
March 14, 2002
Communicated by:
David R. Larson
Copyright of article:
Copyright
2002,
American Mathematical Society
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