Nonlinear Maps Preserving the Jordan Triple 1- \(*\) -Product on Von Neumann Algebras

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• 作者：Changjing Li ; Fangyan Lu
• 关键词：Jordan triple \(*\) ; product ; Isomorphism ; Von Neumann algebras
• 刊名：Complex Analysis and Operator Theory
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：11
• 期：1
• 页码：109-117
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general; Operator Theory; Analysis;
• 出版者：Springer International Publishing
• ISSN：1661-8262
• 卷排序：11

文摘

In this paper, we investigate a bijective map \(\Phi \) between two von Neumann algebras, one of which has no central abelian projections, satisfying \(\Phi (A\bullet B\bullet C)=\Phi (A)\bullet \Phi (B)\bullet \Phi (C)\) for all A, B, C in the domain, where \(A\bullet B=AB+BA^{*}\) is the Jordan 1-\(*\)-product of A and B. It is showed that the map \(\Phi (I)\Phi \) is a sum of a linear \(*\)-isomorphism and a conjugate linear \(*\)-isomorphism, where \(\Phi (I)\) is a self-adjoint central element in the range with \(\Phi (I)^{2}=I\).