扰动后算子广义逆连续的新特征  

Some New Continuity Characteristics of Generalized Inverses under Small Perturbations

作　　者：马吉溥[1] 

机构地区：[1]南京大学数学系,江苏南京210093

出　　处：《淮海工学院学报（自然科学版）》2005年第1期1-3,共3页Journal of Huaihai Institute of Technology:Natural Sciences Edition

基　　金：国家自然科学基金资助项目(10271053);教育部博士点基金资助项目(20020284026)

摘　　要：设B(E,F)表映Banach空间E到F 的有界线性算子全体.若A∈B(E,F)存在广义逆A+∈B(F,E),那么在A的邻近,哪些算子T,当‖T-A‖很小时,‖T+-A+‖也很小? 这是一个既有应用价值又具有理论意义的问题.近年来,许多这样的特征被提出,并在非线泛函分析和大范围分析的基础理论方面获得重要的应用.给出了两个新的特征,且举例以明其应用.相信和其它已知的特征一样,也将有重要的应用.Let B(E,F) denote all the bounded linear operators from Banach space E into another F. When A∈B(E,F) with a generalized inverse A^+∈B(F,E), which kind of the operators near A fulfill that there is a generalized inverse T^+of T near A such that (lim) T→A T^+=A^+. This is a very important problem with practical and theoretical significance. In recent years, many continuity characteristics of generalized inverses under small perturbations of operators in B(E,F) are presented and their applications to non-linear functional analysis and global analysis are given. In this paper, two new characteristics of such are introduced and illustrated by an example. They are very likely to have important applications as the given ones do.

关 键 词：广义逆扰动分析 秩定理 BANACH空间 

分 类 号：O177.91[理学—数学]