Strong skew commutativity preserving maps on von Neumann algebras

被引：27

作者：

Qi, Xiaofei ^{[1
]}

Hou, Jinchuan ^{[1
,2
]}

机构：

[1] Shanxi Univ, Dept Math, Taiyuan 030006, Peoples R China

[2] Taiyuan Univ Technol, Dept Math, Taiyuan 030024, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2013年 / 397卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Von Neumann algebras; Prime rings; General preserving maps; Skew Lie products; POLYNOMIAL XY; PRODUCT; YX;

D O I：

10.1016/j.jmaa.2012.07.036

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let M be a von Neumann algebra without central summands of type I-1. Assume that Phi : M -> M is a surjective map. It is shown that Phi is strong skew commutativity preserving (that is, satisfies Phi(A)Phi(B) - Phi(B)Phi(A)(*) = AB - BA(*) for all A, B is an element of M) if and only if there exists some self-adjoint element Z in the center of M with Z(2) = I such that Phi(A) = ZA for all A is an element of M. The strong skew commutativity preserving maps on prime involution rings and prime involution algebras are also characterized. (C) 2012 Published by Elsevier Inc.

引用

页码：362 / 370

页数：9

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