Moore-Penrose inverse of some linear maps on infinite-dimensional vector spaces

Abstract

The aim of this work is to characterize linear maps of infinite-dimensional inner product spaces where the Moore-Penrose inverse exists. This MP inverse generalizes the well-known Moore-Penrose inverse of a matrix $A\in \text{Mat}_{n\times m} ({\mathbb C})$. Moreover, a method for the computation of the MP inverse of some endomorphisms on infinite-dimensional vector spaces is given. As an application, the least norm solution of an infinite linear system from the Moore-Penrose inverse offered is studied.