Generalized derivable mappings at zero point on some reflexive operator algebras

Abstract

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.