Geodesic
Notes on Derivations on Algebras of Measurable Operators
Matematičeskie zametki, Tome 87 (2010) no. 4, pp. 502-513

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Derivations on algebras of (unbounded) operators affiliated with a von Neumann algebra $\mathscr M$ are considered. Let $\mathscr A$ be one of the algebras of measurable operators, of locally measurable operators, and of $\tau$-measurable operators. The von Neumann algebras $\mathscr M$ of type I for which any derivation on $\mathscr A$ is inner are completely described in terms of properties of central projections. It is also shown that any derivation on the algebra $LS(\mathscr M)$ of all locally measurable operators affiliated with a properly infinite von Neumann algebra $\mathscr M$ vanishes on the center $LS(\mathscr M)$.
Keywords: operator algebra, von Neumann algebra, measurable operator algebra, derivation on an operator algebra, inner derivation, $*$-algebra.
Mots-clés : bimodule 
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     title = {Notes on {Derivations} on {Algebras} of {Measurable} {Operators}},
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A. F. Ber; B. De Pagter; F. A. Sukochev. Notes on Derivations on Algebras of Measurable Operators. Matematičeskie zametki, Tome 87 (2010) no. 4, pp. 502-513. http://geodesic.mathdoc.fr/item/MZM_2010_87_4_a2/