Banach空间上正则半群的表示定理与范数连续  

Representation Theorem of Regular Semigroups in Banach Spaces and Norm Continuity

作　　者：段峰[1] 

机构地区：[1]铜陵职业技术学院基础教学部,安徽铜陵244061

出　　处：《合肥学院学报（自然科学版）》2016年第1期20-22,40,共4页Journal of Hefei University :Natural Sciences

基　　金：安徽省2015年省级质量工程项目"数学建模与高等数学课程教学改革"(2015jyxm516)资助

摘　　要：因为解析半群、可微半群、紧半群都是范数连续C0半群,故C0半群的范数连续性是讨论半群属性的必要条件之一。类似地,讨论正则半群的解析性、紧性等重要性质时,正则半群的范数连续性尤其重要。通过论证,引入指数有界正则半群新的表示定理,在Banach空间上,给出了一个正则半群范数连续的充分条件。Abstuact： Because the Analytic semigroups,Differentiable semigroups,Compact semigroups are the norm continuous CO -semigroups, the norm continuity of the Co -semigroups is one of the necessary conditions to discuss the semigroups property. Similarly, it is especially important to discuss the norm continuity of C-regularized semigroups when the important properties such as the analytical, compactness of the C-regularized semigroups are discussed. This paper will introduce a new representation method for the C-regularized semigroups of exponentially bounded C-regularized semigroups, and give a sufficient condition for a C-regularized semigroups norm continuous in Banach space.

关 键 词：正则半群 表示定理 范数连续 BANACH空间 

分 类 号：O177.2[理学—数学]