## Abstract and Applied Analysis

### Characterizing $\xi$-Lie Multiplicative Isomorphisms on Von Neumann Algebras

#### Abstract

Let $\scr M$ and $\mathrm{\scr N}$ be von Neumann algebras without central summands of type ${I}_{1}$. Assume that $\xi \in \Bbb C$ with $\xi \ne 1$. In this paper, all maps $\mathrm{\Phi }:\scr M\to \mathrm{\scr N}$ satisfying $\mathrm{\Phi }(AB-\xi BA)=\mathrm{\Phi }(A)\mathrm{\Phi }(B)-\xi \mathrm{\Phi }(B)\mathrm{\Phi }(A)$ are characterized.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 104272, 9 pages.

Dates
First available in Project Euclid: 26 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1395857996

Digital Object Identifier
doi:10.1155/2014/104272

Mathematical Reviews number (MathSciNet)
MR3166558

Zentralblatt MATH identifier
07021742

#### Citation

Song, Yamin; Hou, Jinchuan; Qi, Xiaofei. Characterizing $\xi$ -Lie Multiplicative Isomorphisms on Von Neumann Algebras. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 104272, 9 pages. doi:10.1155/2014/104272. https://projecteuclid.org/euclid.aaa/1395857996

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