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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
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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 ${C}\sp{\ast}$ -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


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