摘要
称T∈B(X)满足Weyl定理新的变化性质——(z)性质,如果T的上半Weyl谱在T的谱集中的补集恰好为T的逼近点谱中孤立的有限重的特征值全体。讨论了(z)性质与其它Weyl型定理之间的关系,利用变化的本性逼近点谱给出了Banach空间中有界线性算子及其函数演算满足(z)性质的充要条件,考虑了(z)性质的可交换有限秩摄动。
An operator T∈B( X) defined on a Banach space X satisfies property( z),a newvariant of Weyl's theorem if the complement in the spectrum σ( T) of the upper semi-Weyl spectrum is the set of all isolated points of the approximate point spectrum which are eigenvalues of finite multiplicity. In this note,we first study the conditions between property( z) and other Weyl type theorem,then establish for a bounded linear operator and the calculus defined on a Banach space the sufficient and necessary conditions for which property( z) holds by means of the variant of essential approximate point spectrum. The perturbation of property( z) under finite rank operators is considered.
出处
《山东大学学报(理学版)》
CAS
CSCD
北大核心
2017年第2期60-65,72,共7页
Journal of Shandong University(Natural Science)
基金
国家自然科学基金资助项目(11501419)
渭南市科技计划项目(2016KYJ-3-3)
渭南师范学院人才项目(15ZRRC10)
渭南师范学院(数学)省重点扶持学科资助项目
渭南师范学院校级特色学科建设项目(14TSXK02)