Pseudo-generalized inverse I

Abstract

The purpose of this paper is to introduce and study a new class of operators that we call pseudogeneralized 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.