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Local and 2-Local Lie Derivations of Operator Algebras on Banach Spaces

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Abstract

Let X be a Banach space of dimension > 2. We show that every local Lie derivation of B(X) is a Lie derivation, and that a map of B(X) is a 2-local Lie derivation if and only if it has the form \({A \mapsto AT - TA + \psi(A)}\), where \({T \in B(X)}\) and ψ is a homogeneous map from B(X) into \({\mathbb{F}I}\) satisfying \({\psi(A + B) = \psi(A)}\) for \({A, B \in B(X)}\) with B being a sum of commutators.

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Authors and Affiliations

  1. Department of Mathematics, Soochow Univrsity, Suzhou, 215006, People’s Republic of China

    Lin Chen, Fangyan Lu & Ting Wang

  2. Department of Mathematics and Computer Science, Anshun Univrsity, Anshun, 561000, People’s Republic of China

    Lin Chen

  3. Department of Mathematics, Nanyang Normal Univrsity, Nanyang, 473000, People’s Republic of China

    Ting Wang

Authors
  1. Lin Chen
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  2. Fangyan Lu
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  3. Ting Wang
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Correspondence to Fangyan Lu.

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Chen, L., Lu, F. & Wang, T. Local and 2-Local Lie Derivations of Operator Algebras on Banach Spaces. Integr. Equ. Oper. Theory 77, 109–121 (2013). https://doi.org/10.1007/s00020-013-2074-0

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  • DOI: https://doi.org/10.1007/s00020-013-2074-0

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