Inverses Of Linear Operators Research Articles

Continuity of generalized inverses of linear operators in Banach spaces and its applications

The perturbation problem of generalized inverse is studied. And some new stability characteristics of generalized inverses were presented. It was also proved that the stability characteristics of generalized inverses were independent of the choice of the generalized inverse. Based on this result, two sufficient and necessary conditions for the lower semi-continuity of generalized inverses as the set-valued mappings are given.

The Basic Principles for Stable Approximations to Orthogonal Generalized Inverses of Linear Operators in Hilbert Spaces

ABSTRACT This work presents some basic principles concerned with two general settings for stable approximating orthogonal generalized inverses in Hilbert spaces. In these two settings, perfect convergence and perfect uniform convergence are two important concepts for making theoretical or numerical analysis. Our basic principles characterize the two important concepts by some necessary conditions: stability with other compensated conditions. These basic principles include as simple corollaries some well-known results.

Metric Generalized Inverse of Linear Operator in Banach Space

The Moore–Penrose metric generalized inverse T+ of linear operator T in Banach space is systematically investigated in this paper. Unlike the case in Hilbert space, even T is a linear operator in Banach Space, the Moore-Penrose metric generalized inverse T+ is usually homogeneous and nonlinear in general. By means of the methods of geometry of Banach Space, the necessary and sufficient conditions for existence, continuity, linearity and minimum property of the Moore-Penrose metric generalized inverse T+ will be given, and some properties of T+ will be investigated in this paper.

The representation and approximation of the W-weighted Drazin inverse of linear operators in Hilbert space

We present a unified representation theorem for the W-weighted Drazin inverse of linear operators in Hilbert space and a general error bound. Five specific expressions, computational procedures, and their error bounds for the W-weighted Drazin inverse are uniformly derived from the unified representation theorem.

Inversion of linear operators perturbed on the spectrum

Inversion of linear operators perturbed on the spectrum

The inversion of linear operators acting on distributions. I

The inversion of linear operators acting on distributions. I

The inversion of linear operators acting on distributions. II

The inversion of linear operators acting on distributions. II