Let X and Y be complex Banach spaces of dimension greater than 2. We show that every 2-local Lie isomorphism ϕ of B(X) onto B(Y) has the form ϕ = φ + τ, where φ is an isomorphism or the negative of an anti-isomorphism of B(X) onto B(Y), and τ is a homogeneous map from B(X) into ℂI vanishing on all finite sums of commutators.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm7864-12-2015,
author = {Lin Chen and Lizhong Huang and Fangyan Lu},
title = {2-local Lie isomorphisms of operator algebras on Banach spaces},
journal = {Studia Mathematica},
volume = {231},
year = {2015},
pages = {1-11},
zbl = {1337.47054},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm7864-12-2015}
}
Lin Chen; Lizhong Huang; Fangyan Lu. 2-local Lie isomorphisms of operator algebras on Banach spaces. Studia Mathematica, Tome 231 (2015) pp. 1-11. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm7864-12-2015/