Let AlgL be a reflexive algebra on a Hilbert space H. Let P be a non-triavial idempotent in AlgL with P( H) ∈ L and δ : AlgL → AlgL be a continuous linear map with the property that A,B ∈ AlgL, AB + BA = P ⇒ 2Aδ(B) + 2Bδ(A) = δ(P), In this article, we characterize δ. Then we apply the main results to CSL-algebras, irreducible CDC algebras and nest algebras on a Hilbert space H.
