Derivations on Certain CSL Algebras II

Abstract

Let A be a CSL algebra on a Hilbert space. Sufficient conditions are given so that all derivations of A into A are inner. The conditions are determined by an order relationship between the core projection of A. The proofs are based on a result of E.C. Lance which shows that the nth cohomology spaces for a nest algebra are trivial. Reflexive algebras whose invariant subspace lattice is an infinite ordinal direct sum of commutative subspace lattices satisfy the sufficient conditions. A nest subalgebra A of a von Neumann algebra which is a CSL algebra is also shown to have only inner derivations.