谱界等于增长界对应算子的一些性质  

Some Properties of the Operators Corresponding with Spectrum Determined Growth Condition

作　　者：孙丽丽 王丽洁 王辉[1] 张欣[3] 任寒景 SUN Lili;WANG Lijie;WANG Hui;ZHANG Xin;REN Hanjing(College of Mathematical Sciences,Harbin Normal University,Harbin 150025,China;College of Science,Harbin University of Science and Technology,Harbin 150080,China;Department of Basic Courses,Beijing Union University,Beijing 100101,China;School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China;Key Laboratory of Systems and Control,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China)

机构地区：[1]哈尔滨师范大学数学科学学院,哈尔滨150025 [2]哈尔滨理工大学理学院,哈尔滨150080 [3]北京联合大学基础课教学部,北京100101 [4]中国科学院大学数学科学学院,北京100049 [5]中国科学院数学与系统科学研究院系统控制实验室,北京100190

出　　处：《应用泛函分析学报》2019年第3期225-230,共6页Acta Analysis Functionalis Applicata

基　　金：黑龙江省自然科学基金(A201305);北京市教委科研计划项目(KM201811417013)

摘　　要：运用泛函分析方法和C0半群在有限维子空间上的展开的相关性质,通过分析谱界等于增长界的对应算子,证明了当谱界和增长界相等时,谱界上特征值的代数重等于几何重数.Using functional analytic methods and the related properties of the expan?sion of the C0 semigroup on the finite-dimensional subspace,we analyze the operators under spectrum determined growth condition.Then,we prove that the algebraic multiplicity of the eigenvalues on the spectral bound is equal to the geometrical multiplicity when the spectral bound and the growth bound are equal.

关 键 词：谱界 增长界 代数重数 几何重数 

分 类 号：O177.6[理学—数学]