Moore-Penrose Inverse Of The Partitioned Operators

This paper consists of four parts: Basic knowledge about the Hilbert C~*-modules, particular formulae for the Moore-Penrose inverses of the partitioned bounded linear operators on the Hilbert spaces, general formulae for the Moore-Penrose inverses of the partitioned adjointable operators on the Hilbert C~*-modules, the relationship between the weighted Moore-Penrose inverses and its application in the perturbation estimations.In the first chapter, we will recall some basic knowledge about the Hilbert C~*-modules.In the second chapter, we will focus on the study of the particular formulae for the Moore-Penrose inverses of the 1×2 partitioned bounded linear operators on the Hilbert spaces, and will generalize the main results of [2] from the matrix case to the case of bounded linear operators on the Hilbert spaces.In the third chapter, we will study the weighted Moore-Penrose inverses of the 1×2 partitioned adjointable operators on the Hilbert C~*-modules, and will provide seven different formulae for the weighted Moore-Penrose inverses.In the fourth chapter, we will study the relationship between the weighted Moore-Penrose inverses and derive an important formula. Based on this formula, some perturbation estimations for the weighted Moore-Penrose inverses are carried out.