Mappings Preserving Sum of Products a ο b - ba* on Factor von Neumann Algebras

被引：0
|
作者：
da Motta Ferreira, Joao Carlos [1 ]
Bruno Marietto, Maria das Gracas [1 ]
机构：
[1] Fed Univ ABC, Ctr Math Computat & Cognit, Ave Estados 5001, BR-09210580 Santo Andre, SP, Brazil
来源：
BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY | 2021年 / 47卷 / 03期
关键词：
*-Ring isomorphisms; Factor von Neumann algebras; JORDAN MAPS; ADDITIVITY;
D O I：
10.1007/s41980-020-00406-5
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let A and B be two factor von Neumann algebras. In this paper, we proved that a bijective mapping phi: A -> B satisfies phi(a circle b - ba*) = phi(a) circle phi(b) - phi(b)phi(a)* (where circle is the special Jordan product on A and B, respectively), for all elementsa,b is an element of A, if and only if phi is a*-ring isomorphism. In particular, if the von Neumann algebras A and B are type I factors, then phi is a unitary isomorphism or a conjugate unitary isomorphism.
引用
收藏
页码：679 / 688
页数：10
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