算子乘积的本质谱

J4 ›› 2010, Vol. 45 ›› Issue (10): 83-88.

算子乘积的本质谱

赵玲玲，张鹤佳，曹小红*

陕西师范大学数学与信息科学学院, 陕西西安 710062

收稿日期:2009-06-15 出版日期:2010-10-16 发布日期:2010-10-19
通讯作者: 曹小红(1972-),女，教授，研究方向为算子理论.
作者简介:赵玲玲（1983-),女，硕士，研究方向为算子理论. Email: lingling8383@163.com
基金资助:
国家自然科学基金资助项目（10726043）；教育部新世纪优秀人才支持计划资助项目（2006);中央高校基本科研业务费专项基金资助项目

Essential spectrum of the products of operators

ZHAO Ling-ling, ZHANG He-jia, CAO Xiao-hong*

College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, Shaanxi, China

Received:2009-06-15 Online:2010-10-16 Published:2010-10-19

摘要/Abstract

摘要：

设A为Hilbert空间H上的有界线性算子, 若任给B∈B(H),有 σ_e(AB)=σ_e(BA),则称 A为一个一致Fredholm算子(简写为CF算子)或者称算子A具有CF性质, 其中σ_e(·)表示本质谱。给出了算子具有CF性质的充要条件, 并且考虑了算子的紧摄动的CF性质；研究了算子矩阵的CF性质。

关键词: Fredholm算子; 半Fredholm算子; 谱

Abstract:

Let A be a bounded linear operator on a Hilbert space H. A∈B(H) is called a consistent in Fredholm (briefly CF operator) or A has property CF if σ_e(AB)=σ_e(BA) for every B∈B(H), where σ_e(·) denotes the essential spectrum. In this note, sufficient and necessary conditions for property CF are given, and the property CF for compact perturbation of A is considered. Finally, the properties CF of operator matrices are studied.

Key words: Fredholm operator; semi-Fredholm operator; spectrum

赵玲玲，张鹤佳，曹小红*. 算子乘积的本质谱[J]. J4, 2010, 45(10): 83-88.

ZHAO Ling-ling, ZHANG He-jia, CAO Xiao-hong*. Essential spectrum of the products of operators[J]. J4, 2010, 45(10): 83-88.

参考文献

多维度评价

Viewed

Full text

Abstract

Cited

Shared

Discussed