Structure of Lie derivations on algebras of measurable operators
Vladikavkazskij matematičeskij žurnal, Tome 14 (2012) no. 3, pp. 58-62 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
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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/

[1] Albeverio S., Ayupov Sh. A., Kudaybergenov K. K., “Structure of derivations on various algebras of measurable operators for type I von Neumann algebras”, J. Func. Anal., 256 (2009), 2917–2943 | DOI | MR | Zbl

[2] Herstein I. N., “Lie and Jordan structures in simple, associative rings”, Bull. Amer. Math. Soc., 67 (1961), 517–531 | DOI | MR | Zbl

[3] Johnson B. E., “Symmetric amenability and the nonexistence of Lie and Jordan derivatuons”, Math. Proc. Cambridge Philos. Soc., 120 (1996), 455–473 | DOI | MR | Zbl

[4] Martindale W. S., “Lie derivations of primitive rings”, Mich. Math. J., 11 (1964), 183–187 | DOI | MR | Zbl

[5] Mathieu M., Villena A. R., “Lie derivations on $C^*$-algebras”, J. Func. Anal., 202 (2003), 504–525 | DOI | MR | Zbl

[6] Villena A. R., “Lie derivations on Banach algebras”, J. Algebra, 226 (2000), 390–409 | DOI | MR | Zbl

[7] Robert Miers C., “Lie derivations of von Neumann algebras”, J. Math., 40 (1972), 403–409 | MR

[8] Segal I., “A non-commutative extension of abstract integration”, Ann. of Math., 57 (1953), 401–457 | DOI | MR | Zbl

[9] Sakai S., “Derivations of $W^*$-algebras”, Ann. of Math., 83 (1966), 273–279 | DOI | MR | Zbl