All-derivable points in nest algebras

Suppose that A is an operator algebra on a Hilbert space H. An element V in A is called an all-derivable point of A for the strong operator topology if every strong operator topology continuous derivable mapping φ at V is a derivation. Let N be a complete nest on a complex and separable Hilbert space H. Suppose that M belongs to N with {0}≠M≠H and write for M or M⊥. Our main result is: for any with , if is invertible in , then Ω is an all-derivable point in for the strong operator topology.