Geodesic
On a certain class of operator algebras and their derivations
Eurasian mathematical journal, Tome 5 (2014) no. 1, pp. 82-94.

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Given a von Neumann algebra $M$ with a faithful normal finite trace, we introduce the so-called finite tracial algebra $M_f$ as the intersection of $L_p$-spaces $L_p(M,\mu)$ over all $p\geqslant1$ and over all faithful normal finite traces $\mu$ on $M$. Basic algebraic and topological properties of finite tracial algebras are studied. We prove that all derivations on these algebras are inner. 
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Sh. A. Ayupov; R. Z. Abdullaev; K. K. Kudaybergenov. On a certain class of operator algebras and their derivations. Eurasian mathematical journal, Tome 5 (2014) no. 1, pp. 82-94. http://geodesic.mathdoc.fr/item/EMJ_2014_5_1_a2/

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