双连续正则预解算子族的生成及逼近定理  

The Generation and Approximation Theorems for Bi-Continuous Regularized Resolvent Operator Families

作　　者：陈藏[1] 葛世刚[2] 刘海生[2] 仓定帮[2] 

机构地区：[1]华北科技学院教务处,北京101601 [2]华北科技学院基础部,北京101601

出　　处：《四川师范大学学报（自然科学版）》2014年第6期844-849,共6页Journal of Sichuan Normal University（Natural Science）

基　　金：中央高校基本科研资助基金(3142014039;3142013039和3142014127)资助项目

摘　　要：传统的半群理论研究很多时候要求半群是Banach空间上的强连续半群,在实际研究中发现有些问题所对应的半群并不是强连续的,可以在Banach空间上赋予一个比范数拓扑粗的局部凸拓扑τ,使得半群在拓扑τ下强连续.基于此在给出了Banach空间上双连续正则预解算子族概念及其性质的基础上,重点讨论双连续正则预解算子族的生成及逼近定理.For many applications of operator semigroups,strong continuity with respect to the norm of a Banach space is a too strong requirement.In fact,there exists a class operator semigroups which the usual strong continuity fails to hold and then the concept of bi-continuous semigroups is introduced.Based on the theories of bi-continuous semigroups and regularized resolvent operator families,the concept of bi-continuous regularized resolvent operator families is presented,then the generation and approximation theorems for bi-continuous regularized resolvent operator families are studied especially.

关 键 词：双连续正则预解算子族 生成定理 逼近定理 

分 类 号：O177.2[理学—数学]