Characterizing \(\xi\)-Lie multiplicative isomorphisms on von Neumann algebras. (English) Zbl 1469.46049

Song, Yamin; Hou, Jinchuan; Qi, Xiaofei

Abstr. Appl. Anal. 2014, Article ID 104272, 9 p. (2014).

Summary: Let \(\mathcal{M}\) and \(\mathcal{N}\) be von Neumann algebras without central summands of type \(I_1\). Assume that \(\xi \in \mathbb C\) with \(\xi \neq 1\). In this paper, all maps \(\Phi : \mathcal{M} \rightarrow \mathcal{N}\) satisfying \(\Phi \left(A B - \xi B A\right) = \Phi \left(A\right) \Phi \left(B\right) - \xi \Phi \left(B\right) \Phi(A)\) are characterized.

MSC:

46L10

General theory of von Neumann algebras

References:

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