[1]费秀海,张建华.von Neumann代数上保持投影的映射[J].南京师范大学学报(自然科学版),2016,39(04):0.[doi:10.3969/j.issn.1001-4616.2016.04.002]
　Fei Xiuhai,Zhang Jianhua.Maps Preserving Projections on von Neumann Algebras[J].Journal of Nanjing Normal University(Natural Science Edition),2016,39(04):0.[doi:10.3969/j.issn.1001-4616.2016.04.002]
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von Neumann代数上保持投影的映射()
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《南京师范大学学报》（自然科学版）[ISSN:1001-4616/CN:32-1239/N]

卷:
第39卷
期数:
2016年04期
页码:
0
栏目:
·数学与计算机科学·
出版日期:
2016-12-30

文章信息/Info

Title:
Maps Preserving Projections on von Neumann Algebras
文章编号:
1001-4616(2016)04-0005-03
作者:
费秀海1; 2; 张建华2
(1.滇西科技师范学院数学系,云南 临沧 677000)(2.陕西师范大学数学与信息科学学院,陕西 西安 710062)
Author(s):
Fei Xiuhai1; 2; Zhang Jianhua2
(1.Department of Mathematics,Dianxi Science and Technology Normal University,Lincang 677000,China)(2. College of Mathematics and Information Science,Shaanxi Normal University,Xi’an 710062,China)
关键词:
von Neumann代数; 投影; Jordan同构
Keywords:
von Neumann algebra; projection; Jordan isomorphism
分类号:
O177.1
DOI:
10.3969/j.issn.1001-4616.2016.04.002
文献标志码:
A
摘要:
设A是复Hilbert空间H上的一个von Neumann代数,P(A)表示A中投影的全体. 本文证明了连续满射Φ:A→A如果满足A+λB∈P(A)Φ(A)+λΦ(B)∈P(A),A,B∈A和λ∈C,则Φ是A上的一个Jordan同构.
Abstract:
Let A be a von Neumann algebra over complex Hilbert space H,and P(A)denote all projections of A. In this paper,we prove that a continuous surjective mapping Φ:A→A if satisfies A+λB∈P(A)Φ(A)+λΦ(B)∈P(A),A,B∈A and λ∈C,then Φ is a Jordan isomorphism on A.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:2016-05-29.
基金项目:国家自然科学基金(11471199)、陕西省自然科学基础研究计划资助项目(2014JQ1015).
通讯联系人:费秀海,博士生,研究方向:算子代数与算子理论. E-mail:xiuhaifei@snnu.edu.cn
更新日期/Last Update: 2016-12-31