On a Revisited Moore-Penrose Inverse of a Linear Operator on Hilbert Spaces

Abstract

For two given Hilbert spaces H and K and a given bounded linear operator A \in L(H,K) having closed range, it is well known that the Moore-Penrose inverse of A is a reflexive 1-inverse G \in L(K,H)
of A which is both minimum norm and least squares. In this paper, weaker equivalent conditions for an operator G to be the Moore-Penrose inverse of A are investigated in terms of normal, EP, bi-normal, bi-EP, l-quasi-normal and r-quasi-normal and l-quasi-EP and r-quasi-EP operators.