Generalized derivations and bilocal Jordan derivations of nest algebras (Q539394)

Summary: Let \(H\) be a complex Hilbert space and \(B(H)\) the collection of all linear bounded operators, \(\mathfrak A\) be a closed subspace lattice including 0 on \(H\), then \(\mathfrak A\) is a nest, accordingly \(\text{alg}\,\mathfrak A = \{ T\in B(H): TN \subseteq N\;\forall N \in\mathfrak A \}\) is a nest algebra. It is shown that for nest algebras, generalized derivations are generalized inner derivations, and bilocal Jordan derivations are inner derivations.