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Derivations in commutative regular algebras. (English. Russian original) Zbl 1071.47036
Math. Notes 75, No. 3, 418-419 (2004); translation from Mat. Zametki 75, No. 3, 453-454 (2004).
Let \(L(M)\) denote the algebra of all measurable operators affiliated with a commutative regular algebra \(M\). In this note, the authors announce some results on derivations for the algebra \(L(M)\), in particular, that (i) a commutative von Neumann algebra \(M\) can have non-inner derivations on \(L(M)\) and (ii) derivations on \(L(M)\) are (in general) not continuous in the topology of convergence in measure.

47B47 Commutators, derivations, elementary operators, etc.
13N15 Derivations and commutative rings
46L05 General theory of \(C^*\)-algebras
46L10 General theory of von Neumann algebras
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