Far Eastern Mathematical Journal

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Lie derivations on the algebra of measurable operators affiliated with a type I finite von Neumann algebra

Ilkhom M. Juraev

2013, issue 1, Ñ. 43-51

Let $M$ be a type I finite von Neumann algebra and let $S(M)$ be the algebra of all measurable operators affiliated with M. We prove that every Lie derivation on $S(M)$ has standard form, that is, it is decomposed into the sum of a derivation and a center-valued trace.

von Neumann algebra, measurable operator, type I von Neumann algebra, derivation, inner derivation, Lie derivation, center-valued trace

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