算子及其函数的(R)性质的判定

摘要：

令H为无限维复可分的Hilbert空间,H上有界线性算子的全体为B(H).用σ(T),σab(T)和σa(T)分别表示为算子T∈B(H)的谱集,Browder本质逼近点谱和逼近点谱.称算子T∈B(H)满足(R)性质,若σa(T)\σab(T)=π00(T),其中π00(T)={λ∈isoσ(T)∶0<n(T-λI)<∞}.主要借助新的谱集给出了算子满足(R)性质新的判定,并进一步得出了算子函数满足(R)性质的充分必要条件.

Let H be an infinite dimensional separable complex Hilbert space and the totality of bounded operators on H is B(H).σ(T),σab(T)andσa(T)denote the spectrum,the Browder essential approximate spectrum and approximate point spectrum of T∈B(H)respectively.T∈B(H)satisfies the property(R)ifσa(T)\σab(T)=π00(T),whereπ00(T)={λ∈isoσ(T)∶0<n(T-λI)<∞}.In this paper,we give a new judgment for operators for which property(R)holds by means of the new spectral set.In addition,the necessary and sufficient conditions for operator functions to satisfy(R)property are explored.

作者：

胡添翼 窦艳妮

Hu Tianyi;Dou Yanni(College of Mathematics and Statistics,Shaanxi Normal University,Xi'an 710119,China)

机构地区：

陕西师范大学数学与统计学院

出处：

《Betway官方客服学报：自然科学版》 CAS 北大核心  2023年第2期63-69,共7页

Journal of Henan Normal University(Natural Science Edition)

基金：

陕西省自然科学基金(2021JM-189).

关键词：

(R)性质 算子函数 谱

property(R) function of operator spectrum

分类号：

O177.2 [理学—基础数学] 

算子及其函数的(R)性质的判定.pdf