Geodesic
Structure of Lie derivations on algebras of measurable operators
Vladikavkazskij matematičeskij žurnal, Tome 14 (2012) no. 3, pp. 58-62

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We prove that every Lie derivation on algebras of measurable operators is of standard form, that is, it can be uniquely decomposed into the sum of a derivation and a center-valued trace. 
@article{VMJ_2012_14_3_a5,
     author = {I. M. Juraev},
     title = {Structure of {Lie} derivations on algebras of measurable operators},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {58--62},
     publisher = {mathdoc},
     volume = {14},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2012_14_3_a5/}
}
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I. M. Juraev. Structure of Lie derivations on algebras of measurable operators. Vladikavkazskij matematičeskij žurnal, Tome 14 (2012) no. 3, pp. 58-62. http://geodesic.mathdoc.fr/item/VMJ_2012_14_3_a5/