算子演算的a-Browder定理和(ω1)性质的等价性

J4 ›› 2011, Vol. 46 ›› Issue (4): 108-112.

算子演算的a-Browder定理和(ω₁)性质的等价性

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:2010-03-31 发布日期:2011-04-21
通讯作者: 曹小红(1972- )，女，教授，研究方向为算子理论. Email: xiaohongcao@snnu.edu.cn
作者简介:张鹤佳（1986- ）,女，硕士研究生，研究方向为算子理论. Email: zhj-8.6@stu.snnu.edu.cn
基金资助:
陕西师范大学中央高校基本科研业务费专项资金资助项目(GK200901015);陕西师范大学研究生培养创新基金资助项目(2010CXS022)

The equivalence of a-Browder theorem and property (ω₁) for operational calculus of operators

ZHANG He-jia, CAO Xiao-hong*

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

Received:2010-03-31 Published:2011-04-21

摘要/Abstract

摘要：

根据一致可逆性质定义的一种新谱集σ₂(·)。通过它与变化的本质逼近点谱σ₁(·)之间的关系, 给出了算子演算满足a-Browder定理和有(ω₁)性质的充要条件。研究了a-Browder定理和(ω₁) 性质对算子及其共轭的算子演算同时成立的条件,描述了H(P)类算子的算子演算的(ω₁)性质。

关键词: 谱; a-Browder定理; (ω₁) 性质

Abstract:

The sufficient and necessary conditions are given for an operational calculus which satisfies a-Browder theorem and has property (ω₁) by the variant of the essential approximate point spectrum σ₁(·) and the spectrum σ₂(·) defined in terms of the property of consistency in invertibility. Then the relation is considered between a-Browder theorem holding for an operational calculus and its conjugate having property (ω₁). Besides, we research the condition of the operational calculus of an H(P) operator having property (ω₁).

Key words: spectrum; a-Browder theorem; property (ω₁)

张鹤佳，曹小红*. 算子演算的a-Browder定理和(ω₁)性质的等价性[J]. J4, 2011, 46(4): 108-112.

ZHANG He-jia, CAO Xiao-hong*. The equivalence of a-Browder theorem and property (ω₁) for operational calculus of operators[J]. J4, 2011, 46(4): 108-112.

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算子演算的a-Browder定理和(ω₁)性质的等价性

The equivalence of a-Browder theorem and property (ω₁) for operational calculus of operators

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