对偶空间上有界弱~* C-半群的扰动

纵观前人对算子半群理论的研究,无论是对于哪一类算子半群,所研究的基本上都是半群与其生成元之间的关系,半群的逼近以及扰动和半群的谱等问题。每一个拓扑向量空间的对偶空间上都存在弱*拓扑,并且在此拓扑下,定义在Banach空间上的强连续算子半群在其对偶空间上的对偶半群一般情况下不具有强连续性,但是在对偶空间上的弱*拓扑下是连续的。在对偶空间理论的基础上,根据已有的对偶空间上弱*连续算子半群以及C-半群的概念,引入了对偶空间上的弱*C-半群的概念及其生成元的定义,并且研究了对偶空间上弱*C-半群的基本性质。又结合C-半群的基本概念及其性质。利用C0-半群的扰动定理研究了对偶空间上的弱*C-半群的有界扰动。最后得出了对偶空间上的有界弱*C-半群的扰动定理。

Perturbation of weak~* C-semigroups on dual space

Throughout predecessors to semigroup of theory research,no matter what kind of operator semigroups,the research is almost focused on the relationship between semigroups and their generators,the approximation of semigroups,the perturbation of semigroups and the spectrum of semigroups.Every dual space of topology vector space has weak* topology,and in this topology,the dual semigroups of strong continuous semigroup in Banach space in its dual semigroups usually does not have strong continuity,but in the weak* topology of dual space it is continuous.This paper introduces the concept of weak* C-semigroups on dual space and the definition of its infinitisimal generator based on the theory of dual space and the existing weak* continuous operator semigroups on dual space and the concept of C-semigroups.Besides,the paper also researches the basic properties of weak* C-semigroups on the dual space and the perturbation of bounded weak* C-semigroups,combining with the basic concept and the property of C-semigroups and using the perturbation theorem of C0-semigroups on dual space.Finally,the perturbation theorem of bounded weak* C-semigroups on dual space is given.