2-Bilocal derivations

Let X be a Banach space and A be a unital subalgebra of B(X) containing all finite rank operators in B(X). A map δ:A→B(X) is called a 2-bilocal derivation if for A,B∈A, x∈X, there exists a derivation δA,B,x, such that δ(A)=δA,B,x(A)x and δ(B)x=δA,B,x(B)x. In this paper, we show that each 2-bilocal derivation on A is a derivation.