Perturbation Analysis Of Moore-penrose Metric Generalized Inverse Of Linear Operators In Banach Space

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.