Banach空间中线性算子核逆的一致有界性与收敛性  

The Uniform Boundedness and Convergence for the Core Inverses of Linear Operators in Banach Spaces

作　　者：赵亚媛 陈赛杰 朱兰萍[1] 黄强联[1] ZHAO Yayuan;CHEN Saijie;ZHU Lanping;HUANG Qianglian(School of Mathematical Sciences,Yangzhou University,Yangzhou 225002,China)

机构地区：[1]扬州大学数学科学学院,江苏扬州225002

出　　处：《应用数学》2021年第1期216-223,共8页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China (11771378,11871064,11971419);the Yangzhou University Foundation for Young Academic Leaders (2016zqn03);the Postgraduate Research and Practice Innovation Program of Yangzhou University (XKYCX19-057)。

摘　　要：本文主要研究Banach空间中线性算子核逆的一致有界性与收敛性之间的关系.首先证明核逆的一致有界性与收敛性的等价性,给出了核逆的表达式.其次,利用稳定扰动,证明核逆的稳定扰动与连续性是等价的.作为应用,我们还给出有限秩算子核逆的连续性特征,并给出扰动算子的核逆具有最简表达式的充分必要条件.The main topic of this paper is the relationship between uniform boundedness and convergence of the core inverses of linear operators in Banach spaces.We first obtain the equivalence of the uniform boundedness and convergence for core inverse and we give the expression of core inverse.Secondly,we investigate the stable perturbation for the core inverse and prove that the stable perturbation and the continuity of the core inverse are equivalent.As applications,we also give the continuity characterization for the core inverse of finite rank operators and derive the sufficient and necessary condition for the core inverse of the perturbed operator to have the simplest possible expression.

关 键 词：核逆 一致有界 收敛 广义逆 稳定扰动 

分 类 号：O177.91[理学—数学]