Maps preserving products XY-YX* on von Neumann algebras

被引：53

作者：

Bai, Zhaofang ^{[1
]}

Du, Shuanping ^{[1
]}

机构：

[1] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2012年 / 386卷 / 01期

关键词：

New products; Isomorphism; Von Neumann algebra; STANDARD OPERATOR-ALGEBRAS; LIE ISOMORPHISMS; JORDAN MAPS; CONJECTURES; ADDITIVITY; RINGS; MAPPINGS;

D O I：

10.1016/j.jmaa.2011.07.052

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let M, N be von Neumann algebras with no central summands of type I-1. For T, S is an element of M. define [T, S]* = TS - ST* a new product of T and S. In this note, it is proved that a not necessarily linear bijective map Phi : M -> N satisfies Phi([T, S](*)) = [Phi(T), Phi(S)](*) for all T, S is an element of M if and only if Phi is the direct sum of a linear *-isomorphism and a conjugate linear *-isomorphism. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：103 / 109

页数：7

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