On the Uniform Boundedness and Convergence of Generalized, Moore-Penrose and Group Inverses

Abstract

This paper concerns the relationship between the uniform boundedness and convergence of various generalized inverses. Using the stable perturbation of generalized inverse and the gap between closed linear subspaces, we prove the equivalence for the uniform boundedness and convergence of generalized inverse. Based on this, we consider the case for the Moore-Penrose inverse and group inverse. Some new and concise expression and convergence theorems are provided. The results obtained in this paper extend and improve many known results in operator theory and matrix theory.