一类线性算子半群的收敛性  

Convergence of a kind of linear operator semigroup

作　　者：禹晓红[1] 宋晓秋[1] 李玉霞[1] 

机构地区：[1]中国矿业大学理学院,江苏徐州221008

出　　处：《黑龙江科技学院学报》2011年第2期161-162,166,共3页Journal of Heilongjiang Institute of Science and Technology

基　　金：中央高校基本科研业务费专项资金资助项目(2010LKSX08)

摘　　要：为得到C0半群序列收敛于C0半群的条件,利用算子半群与无穷小生成元的关系,讨论了C0半群的收敛性和算子序列逼近问题。在Banach空间上,借助无穷小生成元的强收敛性得出其生成半群的强收敛性。借助定义有界线性算子Ln,将该结论推广到了一般的Banach空间序列上,进一步完善了Banach空间上算子半群的收敛性理论。Aimed at enabling C0 semigroup sequences to converge to C0 semigroup, this paper discus- ses the convergence and operator series approximation of Co semigroup using the relationship between op- erator semigroup and infinitesimal generator. In the space of Banach, the strong convergence of infinitesi- mal generator results in the strong convergence of the generated semigroup. Besides, using the definition of a bounded linear operator Ln, makes it possible to extend the conclusion to the general Banach space sequence, thus improving the convergence of semigroup in Banach space.

关 键 词：C0半群 半群序列 无穷小生成元 收敛性 算子序列逼近 抽象柯西问题 

分 类 号：O177.2[理学—数学]