Jordanian Canonical Form of Quasinormal Operator

被引：0
|
作者：
徐新军
王鹏辉
纪友清
机构：
[1] Changchun
[2] Institute of Mathematics
[3] Jilin University
来源：
Communications in Mathematical Research | 2004年 / 02期
关键词：
strongly irreducible; (SI) decomposition; quasinormal operator; pure operator;
D O I：
10.13447/j.1674-5647.2004.02.011
中图分类号：
O177.5 [巴拿赫代数（赋范代数）、拓扑代数、抽象调和分析];
学科分类号：
070104 ;
摘要：
An operator on a Hilbert space is said to have (SI) decomposition if it is similar to the orthogonal direct sum of some (SI) operators. In this paper, we prove that every operator, which is similar to a quasinormal operator, has (SI)decomposition if and only if it is similar to D ( 0≤j<N λjS), where D is a diagonaloperator, λj is a positive number, N is a natural number or ∞, and S is the unilateral shift.
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页码：200 / 206
页数：7
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