Pseudo-generalized inverse II

Abstract

The purpose of this paper is to continue the study initiated in
[7] concerning the notion of pseudo-generalized
inverse. In this work, we are interested in investigating the
relationship between compactness, finite rank and pseudo-generalized
invertibility for bounded operators. The preserving properties of
products of pseudo-generalized invertible operators are also treated
and related results are given.
At the end of this paper, we discuss in some special cases the relationship
between the sets of n-left pseudo-generalized inverses of a
left pseudo-generalized invertible operator  T.