Non-trivial derivations on commutative regular algebras. (English) Zbl 1129.46056
The paper is concerned with the question of describing derivations of the algebra \(L(M)\) of all operators affiliated with a commutative von Neumann algebra \(M\). It is shown that there exists a nonzero derivation on \(L(M)\) if and only if the Boolean algebra of all projections in \(M\) is not atomic. In fact, the authors are able to deal with a general class of commutative algebras containing \(L(M)\) as a special case.
Reviewer: Armando R. Villena (Granada)
MSC:
46L57 | Derivations, dissipations and positive semigroups in \(C^*\)-algebras |
46H40 | Automatic continuity |
46L51 | Noncommutative measure and integration |
47B47 | Commutators, derivations, elementary operators, etc. |