Characterizations of Nonlinear Lie Derivations ofB(X)

Let X be an infinite dimensional Banach space, and Φ:B(X)→B(X) is a nonlinear Lie derivation. Then Φ is the form δ+τ where δ is an additive derivation of B(X) and τ is a map from B(X) into its center ZB(X), which maps commutators into the zero