强不可约算子理论及其应用(英文)  

Theory of Strongly Irreducible Operators and Its Applications

作　　者：蒋春澜[1] 纪奎[1] 

机构地区：[1]河北师范大学数学与信息科学学院,石家庄河北050016

出　　处：《数学进展》2011年第4期385-392,共8页Advances in Mathematics（China）

基　　金：supported by NSFC(No.10731020);NSFC(No.10901046)

摘　　要：在有限维空间的矩阵理论中,著名的约当标准型定理充分揭示了矩阵的内在结构.在这篇综述中,我们给出复可分的无穷维希尔伯特空间上类似的约当标准型定理.同时也展示了该理论在其它数学分支中的应用。In the matrix theory of finite dimensional space, the famous Jordan canonical form theorem sufficiently reveals the internal structure of matrices. In the survey, we will give similar Jordan canonical form theorems of operator theory in a complex, separable, infinite dimensional Hilbert space. By the way, we also show their applications in other mathematical branches.

关 键 词：强不可约算子 相似等价 K0-群 von—Neumann代数 因子 TOEPLITZ算子 

分 类 号：O177.1[理学—数学]