广义C-半群的生成元和性质

C-半群是有界线性算子强连续半群的一个有意义的推广,这一概念最早是由Davies与Pang引入的。后来,R.delaubenfels对其中生成元的定义作了改进。高文华为解决广义动态经济问题提出了广义C0-半群的定义,王宗毅对其进行了进一步研究,刘嫚提出了广义C-半群的定义。文章在此基础上给出了广义C-半群生成元及其弱生成元的定义,并且对其生成元的强弱性进行了研究,证明了其生成元的强弱等价性。另外,王宗毅在传统C0-半群的基础上,给出了广义C0-半群的定义,并且研究了它的一些性质,得到了一些有意义的结果,文章在此基础上进一步探讨了广义C-半群生成元的若干性质。

Generator and some properties of generalized C-semigroups

Bounded linear operator semigroup is significant promotion of strong continuous semigroup.This concept was first introduced by Davies and Pang.Later,the definition of generating element was improved by R.delaubenfels.Gao Wen-hua gave the definition of generalized semigroups to solve generalized dynamic economy problem.Wang Zong-yi has carried on the further research.Liu Man proposed a generalized semigroups.This paper gives a generalized semigroup generator and its weak generative element,and studies the generating element intensity,proves that the weak equivalence in addition,In addition,Wang Zongyi gave the generalized semigroups on the foundation of semigroup,and studied its properties,and obtained some meaningful results.On this basis,this paper further explores the generalized semigroup generator and its properties.