【作者】 孙爽；

【导师】 王玉文；

【作者基本信息】 哈尔滨师范大学 ， 应用数学， 2010， 硕士

【摘要】 Banach空间有界线性算子广义逆的扰动分析在算子理论的实际应用领域起到非常重要的作用,并且已经广泛应用于统计,优化,控制等学科.但由于度量广义逆一般为有界齐性的非线性算子,所以其扰动定理的证明与线性广义逆的扰动定理完全不同.在本文中,我们更深入的研究了Banach空间中有界线性算子的Moore-Penrose(单值)度量广义逆的扰动分析.我们给出了在特定条件下的(单值)度量广义逆的形式表示,及在这种条件下的范数估计和误差界估计.首先应用度量稳定扰动的定义及广义正交分解定理,给出在特定条件下有界线性算子的Moore-Penrose单值度量广义逆的误差界估计,并推导出其度量广义逆扰动的范数估计.接下来我们在上述定理的基础上,应用度量投影算子的连续性,以及度量广义逆算子的拟可加性,给出了Moore-Penrose单值度量广义逆的形式表示,及其稳定扰动的范数估计和误差估计.本文仅讨论了Banach有界线性算子的单值度量广义逆的扰动的范数估计及误差估计界.对于单值度量广义逆的稳定扰动的等价条件,集值度量广义逆的扰动,还有待进一步探究.更多还原

【Abstract】 Perturbation analysis of Moore-Penrose metric generalizedinverse of linear op-erators in Banach space play an very important role in the actual application do-main of operator theory, and have already been applied to Statistics, Optimizes and Control. Because the Moore-Penrose metric generalized inverse is a bounded homogeneous nonlinear operator in general, the proof of its perturbation theorem is completely different from that of linear generalized inverse perturbation theorem.In this paper, we further study the perturbation analysis for Moore-Penrose (single-valued) metric generalized inverse of bounded linear operators in Banach space. We give the complete description of (single-valued) metric generalized inverse under norm, and the norm estimate and the error bound estimate are also given.Firstly, we apply the definition of stable perturbation and generalized orthog-onal decomposition theorem to give the Moore-Penrose metric generalized inverse error bound estimate under norm, and derive the norm estimate of the perturbation of Moore-Penrose metric generalized inverse. Next, by means of the above theorem, the continuity of the metric projection operator and the pseudo-additivity of metric generalized inverse, we give a complete description of Moore-Penrose single-valued metric generalized inverse, and the norm estimation and error estimation is also given in this paper.In this paper, we only discuss the norm estimation and error estimation of perturbation for Moore-Penrose single-valued metric generalized inverse of bounded linear operators in Banach space. But the equivalent condition of the stable pertur-bation of single-valued metric generalized inverse, and the perturbation of set-valued metric generalized inverse still need further studies.更多还原