Derivations of certain operator algebras (Q1586742)

Summary: Let \({\mathcal N}\) be a nest and let \({\mathcal A}\) be a subalgebra of \(L(H)\) all rank one operators of \(\text{alg }{\mathcal N}\). We give several conditions under which any derivation \(\delta\) from \({\mathcal A}\) into \(L(H)\) must be inner. The conditions include (1) \(H_-\neq H\), (2) \(0_+\neq 0\), (3) there is a nontrivial projection in \({\mathcal N}\) which is in \({\mathcal A}\), and (4) \(\delta\) is norm continuous. We also give some applications.