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2-local Lie isomorphisms of operator algebras on Banach spaces

Volume 229 / 2015

Lin Chen, Lizhong Huang, Fangyan Lu Studia Mathematica 229 (2015), 1-11 MSC: Primary 47B49; Secondary 16S50. DOI: 10.4064/sm7864-12-2015 Published online: 3 December 2015

Abstract

Let $X$ and $Y$ be complex Banach spaces of dimension greater than 2. We show that every 2-local Lie isomorphism $\phi $ of $B(X)$ onto $B(Y)$ has the form $\phi =\varphi +\tau $, where $\varphi $ is an isomorphism or the negative of an anti-isomorphism of $B(X)$ onto $B(Y)$, and $\tau $ is a homogeneous map from $B(X)$ into $\mathbb CI$ vanishing on all finite sums of commutators.

Authors

  • Lin ChenDepartment of Mathematics
    Soochow University
    Suzhou 215006, P.R. China
    and
    Department of Mathematics and Physics
    Anshun University
    Anshun 561000, P.R. China
    e-mail
  • Lizhong HuangDepartment of Mathematics
    Shanxi Datong University
    Datong 037009, P.R. China
    e-mail
  • Fangyan LuDepartment of Mathematics
    Soochow University
    Suzhou 215006, P.R. China
    e-mail

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