Abstract: Let A be a unital algebra and M be a unital A-bimodule. A linear map δ:A → M is said to be Jordan derivable at a nontrivial idempotent P ∈ A if δ(A) ◦ B + A ◦ δ(B)=δ(A ◦ B) for any A, B ∈ A, with A ◦ B=P, here A ◦ B=AB + BA is the usual Jordan product. In this article, we show that if A=AlgN is a Hilbert space nest algebra and M=B(H), or A=M=B(X), then, a linear map δ:A → M is Jordan derivable at a nontrivial projection P ∈ N or an arbitrary but fixed nontrivial idempotent P ∈ B(X) if and only if it is a derivation. New equivalent characterization of derivations on these operator algebras was obtained.

Key words: Derivations, triangular algebras, subspace lattice algebras, Jordan derivable maps