J4 ›› 2013, Vol. 48 ›› Issue (8): 41-44.

• Articles • Previous Articles     Next Articles

Characterizations of ξ-Lie derivations of B(X)

LIU Dan, ZHANG Jian-hua*   

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, Shaanxi, China
  • Received:2012-12-24 Online:2013-08-20 Published:2013-08-21

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

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