| Banach空间中度量广义逆的乘积扰动 |
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| 引用本文： | 杜法鹏,薛以锋.Banach空间中度量广义逆的乘积扰动[J].数学学报,2019,62(6):939-948. |
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| 作者姓名： | 杜法鹏 薛以锋 |
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| 作者单位： | 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 |
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| 基金项目： | 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） |
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| 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‖T~M-A~M‖的上界估计,作为应用,我们在L~p空间上讨论了Moore-Penrose度量广义逆的乘积扰动.
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| 关 键 词： | 乘积扰动 Moore-Penrose度量广义逆 一致强唯一 |
Multiplicative Perturbations of Metric Generalized Inverse in Banach Space |
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| Fa Peng DU,Yi Feng XUE.Multiplicative Perturbations of Metric Generalized Inverse in Banach Space[J].Acta Mathematica Sinica,2019,62(6):939-948. |
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| Authors: | Fa Peng DU Yi Feng XUE |
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| Institution: | 1. School of Mathematical&Physical Sciences, Xuzhou University of Technology, Xuzhou 221008, P. R. China;
2. Research Center for Operator Algebras&Shanghai Key Laboratory of PMMP;School of Mathematical Sciences, East China Normal University, Shanghai 200241, P. R. China |
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| Abstract: | 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 order α and order β, respectively. As an application, we consider the multiplicative perturbation of metric generalized inverse in Lp space. |
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| Keywords: | multiplicative perturbation metric generalized inverse uniformly strong unique |
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