Banach空间中度量广义逆的乘积扰动  

Multiplicative Perturbations of Metric Generalized Inverse in Banach Space

作　　者：杜法鹏[1] 薛以锋 Fa Peng DU;Yi Feng XUE(School of Mathematical Sciences,East China Normal University,Shanghai 200241,P.R.China;Research Center for Operator Algebras&Shanghai Key Laboratory of PMMP)

机构地区：[1]徐州工程学院数学与物理科学学院,徐州221008 [2]华东师范大学算子代数研究中心上海市核心数学与实践重点实验室华东师范大学数学科学学院,上海200241

出　　处：《数学学报（中文版）》2019年第6期939-948,共10页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11531003);上海市科学技术委员会项目(18dz2271000)

摘　　要：设X,Y为自反严格凸Banach空间.记A∈B(X,Y)为具有闭值域R(A)的有界线性算子,有界线性算子T=EAF∈B(X,Y)为A的乘积扰动.本文研究了有界线性算子A的Moore-Penrose度量广义逆的乘积扰动.在值域R(A)为α阶一致强唯一和零空间N(A)为β阶一致强唯一的条件下.给出了‖TM-AM‖的上界估计,作为应用,我们在Lp空间上讨论了Moore-Penrose度量广义逆的乘积扰动.Suppose X,Y are reflexive strictly convex Banach spaces.Let A∈B(X,Y)be a bounded linear operator with R(A)closed.T=EAF∈B(X,Y)is a multiplicative perturbation of A.In this paper,we investigate the multiplicative perturbations of the metric generalized inverse of A.We present the upper bound of‖TM-AM‖ under the condition that the range R(A)and the null space N(A)are uniformly strong unique of orderαand orderβ,respectively.As an application,we consider the multiplicative perturbation of metric generalized inverse in Lp space.

关 键 词：乘积扰动 Moore-Penrose度量广义逆 一致强唯一 

分 类 号：O177.2[理学—数学]