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.