Geodesic
On multiplication operators and traces of commutators
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XIII, Tome 135 (1984), pp. 182-194

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Some new sufficient conditions on operators $A$, $B$ on Hilbert space are given in order that $\operatorname{trace}(AB-BA)=0$. 
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     author = {V. S. Shulman},
     title = {On multiplication operators and traces of commutators},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {182--194},
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     volume = {135},
     year = {1984},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_1984_135_a16/}
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V. S. Shulman. On multiplication operators and traces of commutators. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XIII, Tome 135 (1984), pp. 182-194. http://geodesic.mathdoc.fr/item/ZNSL_1984_135_a16/