Abstract:

Let X be a Banach space with dim X>1, and  ξ≠±1。 In this paper, we show that if a linear map φ:B(X)→B(X) satisfies φ(［A,B］ξ)=［φ(A),B］ξ+［A,φ(B)］ξ for all A,B∈B(X) with ABA=A, then φ is a derivation.

Key words: Banach space; ξ-Lie derivation; derivation