完全连续C-半群的生成和扰动

Generation and perturbation of completely continuous C-semigroups

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.