有界线性算子的谱半径与扰动  

Spectral radius and perturbation of bounded linear operators

作　　者：赵静 王紫[1] ZHAO Jing;WANG Zi(School of Mathematics Science,Harbin Normal University,Harbin 150025,China)

机构地区：[1]哈尔滨师范大学数学科学学院,哈尔滨150025

出　　处：《哈尔滨商业大学学报（自然科学版）》2024年第3期346-349,377,共5页Journal of Harbin University of Commerce：Natural Sciences Edition

基　　金：国家自然科学基金项目(12061029,12001142)。

摘　　要：广义逆理论在数值线性代数、数值分析、最优化、控制论、数理统计、微分方程及应用数学中具有引人注目的应用,其中算子广义逆在求解线性算子方程的极值解、最小范数解与最佳逼近解时发挥重要作用.设X为Banach空间,T:X→X为具有闭值域的有界线性算子.利用谱半径代替范数作为刻画扰动算子的工具,在扰动算子是可交换的假设下,减弱了可逆算子方程的经典扰动结果和一般算子方程的最优扰动结果的前提条件.同时,也利用谱半径代替范数作为刻画扰动算子的工具,减弱了Banach空间有界线性算子T的广义逆的经典扰动结果的前提假设,获得了利用谱半径的更加精细的扰动误差估计.The generalized inverse theory has attracted much attention in numerical linear algebra,numerical analysis,optimization,control theory,mathematical statistics,differential equations and applied mathematics.The generalized inverse of operator plays an important role in solving the extremal solution,the minimum norm solution and the best approximation solution of linear operator equations.This paper used the spectral radius instead of the norm as a tool to characterize the perturbation operator,under the assumption that the perturbation operator was commutative,the preconditions for the classical perturbation results of the invertible operator equation and the optimal perturbation results of the general operator equation were weakened.At the same time,this paper used the spectral radius instead of the norm as a tool to characterize the perturbation operator,the preconditions for the classical perturbation results of the generalized inverse of the bounded linear operator in Banach space were weakened.A more precise perturbation error estimation using the spectral radius was also obtained.

关 键 词：谱半径 BANACH空间 有界线性算子 广义逆 扰动分析 

分 类 号：O177.2[理学—数学]