Derivations in commutative regular algebras (Q1889622)

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.