完全连续C-半群的生成和扰动  

Generation and perturbation of completely continuous C-semigroups

作　　者：刘瑞[1] 王盼[1] LIU Rui;WANG Pan(College of Mathematics and Computer Science,Yan’an University,Yan’an 716000,China)

机构地区：[1]延安大学数学与计算机科学学院,陕西延安716000

出　　处：《延安大学学报（自然科学版）》2024年第4期75-77,共3页Journal of Yan'an University：Natural Science Edition

基　　金：陕西省教育厅专项科研项目(20JK0984)。

摘　　要：为了丰富算子半群理论内容,在完全连续C-半群定义的基础上,利用C-半群的性质,讨论了算子A在稠定闭的条件下生成完全连续C-半群的问题以及C是一般的有界线性算子条件下完全连续C-半群的扰动问题,得到了完全连续C-半群的生成定理和扰动定理。研究结果推广了完全连续C-半群的内容,丰富了其应用领域,从而使算子半群理论更加完善。In order to enrich the theory of semigroups,based on the definition of completely continuous Csemigroups and the properties of C-semigroups,the problem of generating completely continuous C-semigroups with operator A under the condition of dense definite closure and the perturbed problem of completely continuous C-semigroups with C being a general bounded operator are discussed.The generation theorems and perturbation theorems of completely continuous C-semigroups are obtained.The research results extend the content of completely continuous C-semigroup,enrich its application field,and make the operator semigroup theory more perfect.

关 键 词：C-半群 无穷小生成元 完全连续算子 扰动 

分 类 号：O177[理学—数学]