广义Kato型算子及具有广义(ω)性质算子的摄动  

Generalized Kato Type Operators and Perturbations for Operators with Generalized Property(ω)

作　　者：刘爱芳[1] 曹小红[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,西安710062

出　　处：《吉林大学学报（理学版）》2012年第2期201-207,共7页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:10871224);陕西师范大学中央高校基本科研业务费项目(批准号:GK200901015)

摘　　要：给出了广义Kato型算子的定义,并根据广义Kato型算子的性质定义了算子的一种新谱,通过该谱给出了Hilbert空间上有界线性算子满足广义(ω)性质的充要条件,并得到了Hilbert空间上有界线性算子在有限秩算子和幂有限秩算子摄动下满足广义(ω)性质的充要条件.We gave the definition of generalized Kato type oper ators and defined the new spectrum in view of the property of generalized Kato o perators.We establish the sufficient and necessary conditions for a bounded lin ear operator defined on a Hilbert space under which generalized property（ω） holds,and obtained the sufficient and necessary conditions for a bounded linear operator on a Hilbert space,which has generalized property（ω） under pe rturbations by finite rank operators and power finite rank operators.

关 键 词：广义Kato型算子 广义(ω)性质 摄动 

分 类 号：O177.2[理学—数学]