✦ LIBER ✦

Nonlinear maps preserving Lie products on factor von Neumann algebras

✍ Scribed by Jian-Hua Zhang; Fang-Juan Zhang

Publisher: Elsevier Science
Year: 2008
Tongue: English
Weight: 149 KB
Volume: 429
Category: Article
ISSN: 0024-3795
DOI: 10.1016/j.laa.2008.01.031

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✦ Synopsis

In this paper, we prove that every bijective map preserving Lie products from a factor von Neumann algebra M into another factor von Neumann algebra N is of the form A → ψ(A) + ξ(A), where ψ : M → N is an additive isomorphism or the negative of an additive anti-isomorphism and ξ : M → CI is a map with ξ(AB -BA) = 0 for all A, B ∈ M.

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