Derivations of nest algebras

Abstract

The results presented below are generalisations of some well known results about yon Neumann algebras. The first result, Theorem 2.1, yields a sufficient condition for automatic continuity of any derivation of an algebra of operators into a dual normal module. The theorem is followed by a corollary which shows that reflexive algebras with commutative subspace lattices have only continuous derivations into dual normal modules. The second result, Theorem 3.6, is quite independent of the former. In Section 3 we prove that, for any nest algebra ~¢ and any ultraweakly closed algebra ~ of operators, the first cohomology group Hl (d ,9~) always vanishes. We ought perhaps to mention, that nest algebras are reflexive and do have commutative lattices of invariant subspaces.