Pseudo-generalized inverse I

Abstract

The purpose of this paper is to introduce and study a new class
of operators that we call pseudo-generalized invertible operators.
This class includes both the class of generalized invertible
operators and the class of Drazin invertible operators. Some
results connected with ascent and essential ascent are also obtained
for this new class. The relationship between pseudo-generalized
invertible operators, semi-Fredholm operators and generalized
invertible operators is explored.