中文摘要：

利用了广义C0半群的定义、生成元的概念、性质、C0半群所具有的耗散算子的结论,主要得到了广义C0半群与生成元之间的关系,线性算子的耗散性刻画了广义C0半群以及压缩的广义C0生成元的充要条件,进而得到耗散的线性算子与广义C0半群的生成元之间的关系,耗散算子与共轭之间的关系,给出了耗散算子的一些性质。Banach空间中耗散算子是一类应用背景极强的算子,该工作对研究Banach空间下的无穷维动力系统的长期行为意义极大。将C0半群中的耗散算子的性质广泛推广到了广义C0半群,极大的丰富了广义C0半群的内容。

英文摘要：

In this paper,using the definition of generalized C0-semigroup,the concept and characteristics of generator,the theorey of C0-semigroup and dissipation operator,the author gave the relationship between a generalized C0-semigroup and generators.The dissipation of linear operator depicted generalized C0-semigroup,necessary and sufficient condition between generalized compression C0-semigroups and generators,and the author gave the relationship of dissipative linear operator and generalized C0-semigroup generators,and the relationship of the dissipative linear operator and conjugation,and some characteristics of dissipative operator.We all know,Banach space compresses a class of dissipative operators which have strong application background.The work of the study of infinite dimensional Banach space under the long-term behavior of dynamical systems is significant.The author promoted properties of dissipative C0-semigroup operators to general C0-semigroups,which greatly enriched the content of the generalized C0-semigroup.