All-derivable points in continuous nest algebras

Let A be an operator algebra on a Hilbert space. We say that an element G ∈ A is an all-derivable point of A for the strong operator topology if every strong operator topology continuous derivable linear mapping ϕ at G (i.e. ϕ(ST ) = ϕ(S)T +Sϕ(T ) for any S,T ∈ algN with ST = G) is a derivation. Let N be a continuous nest on a complex and separable Hilbert space H. We show in this paper that every orthogonal projection operator P(M) (0 =M ∈N) is an all-derivable point of algN for the strong operator topology. © 2007 Elsevier Inc. All rights reserved