|
|||||
|
|
| 有限von Neumann代数上完全保迹秩的映射 | |
| 引用本文： | 侯晋川,张秀玲. 有限von Neumann代数上完全保迹秩的映射[J]. 太原理工大学学报, 2012, 43(3): 269-275 |
| 作者姓名： | 侯晋川 张秀玲 |
| 作者单位： | 1. 太原理工大学数学学院,太原,030024 2. 山西师范大学数计学院,山西临汾,041004 |
| 基金项目： | 国家自然科学基金资助项目(11171249) |
| 摘 要： | 从有限von Neumann代数的任意含0,±I的子集到该代数的以±I为不动点的每个完全迹秩不增(完全保迹秩)映射都可以延拓为该子集生成的子环上的可加可乘(单)映射,即(单射)环同态。特别地,矩阵代数上的以±I为不动点的完全秩不增映射必是环同态。 |
| 关 键 词： | von Neumann代数 同态 迹秩 |
Completely Trace-Rank Preserving Maps on Finite von Neumann Algebras |
|
| HOU Jinchuan , ZHANG Xiuling. Completely Trace-Rank Preserving Maps on Finite von Neumann Algebras[J]. Journal of Taiyuan University of Technology, 2012, 43(3): 269-275 | |
| Authors: | HOU Jinchuan ZHANG Xiuling |
| Affiliation: | 1.College of Mathematics,TUT,Taiyuan 030024,China; 2.College of Mathematics and Computer Science,Shanxi Normal University,Linfen 041004,China) |
| Abstract: | Every completely trace-rank nonincreasing(or completely trace-rank preserving) map from a subset containing 0,±I of a finite von N eumann algebra A into the algebra A with ±I as fixed points can be extended to an additive and multiplicative(injective) map, that is,(injective) ring homomorphism.In particular,every completely rank no nincreasing map from a matrix algebra into itself with ±I as fixed points must be a ring homomorphism. |
| Keywords: | von Neumann algebras homomorphisms trace-rank |
| 本文献已被 CNKI 万方数据 等数据库收录！ | |