Derivations in commutative regular algebras. (English. Russian original) Zbl 1071.47036

Ber, A. F.; Sukochev, F. A.; Chilin, V. I.

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.

Reviewer: B. P. Duggal (Al Ain)

MSC:

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

Keywords:

commutative regular algebra; measurable operator; von Neumann algebra; atomic algebra; affiliation