Generalized derivable mappings at zero point on some reflexive operator algebras

Let A be a subalgebra with the unit operator I in B(H), we say that a linear mapping ϕ from A into B(H) is a generalized derivable mapping at zero point if ϕ(ST) = ϕ(S)T + Sϕ(T) − Sϕ(I)T for any S, T∈A with ST = 0. In this paper, we show the following main result: every norm-continuous generalized derivable mapping at zero point on finite CSL algebras is a generalized derivation.