A note on strong skew Jordan product preserving maps on von Neumann algebras

被引：4

作者：

Taghavi, Ali ^{[1
]}

Kolivand, Farzaneh ^{[1
]}

机构：

[1] Univ Mazandaran, Fac Math Sci, Dept Math, POB 47416-1468, Babol Sar, Iran

来源：

PERIODICA MATHEMATICA HUNGARICA | 2017年 / 75卷 / 02期

关键词：

Factor von Neumann algebra; Strong commutativity; Skew Jordan product; LIE ISOMORPHISMS; LINEAR-MAPS; COMMUTATIVITY;

D O I：

10.1007/s10998-017-0202-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let A be a von Neumann algebra acting on the complex Hilbert space H and Phi : A -> A be a surjective map that satisfies the condition Phi(T) Phi(P) + Phi(P) Phi(T)* = T P + PT* for all T and all projections P in A. We characterize the concrete form of Phi on selfadjoint elements of A. Also when A is a factor von Neumann algebra, it is shown that Phi is either of the form Phi(T) = T + i tau(T) I or of the form Phi(T) = -T + i tau(T) I, where tau : A -> R is a real map.

引用

页码：330 / 335

页数：6

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