Characterizations of Lie derivations of B (X)

Document Type

Article

Publication Date

1-1-2010

Abstract

Let X be a Banach space of dimension greater than 2. We prove that if ? : B (X) ? B (X) is a linear map satisfying? ([A, B]) = [? (A), B] + [A, ? (B)]for any A, B ? B (X) with AB = 0 (resp. AB = P, where P is a fixed nontrivial idempotent), then ? = d + ?, where d is a derivation of B (X) and ? : B (X) ? C I is a linear map vanishing at commutators [A, B] with AB = 0 (resp. AB = P). © 2009 Elsevier Inc. All rights reserved.

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