Characterizations of Nonlinear Lie Derivations of B ( X )

Abstract

Let $X$ be an infinite dimensional Banach space, and $\mathrm{\Phi }:B(X)\to B(X)$ is a nonlinear Lie derivation. Then Φ is the form $\delta +\tau$ where $\delta$ is an additive derivation of $B(X)$ and $\tau$ is a map from $B(X)$ into its center $Z_{B(X)}$, which maps commutators into the zero.