On the perturbation of pseudo-generalized invertible operators

Abstract

This paper is a continuation of previous works Lahmar (Filomat 36:2551-2572, 2022), Lahmar (Filomat 36: 4575–4590, 2022), Lahmar (Preprint) where we defined a new class of operators called pseudo-generalized invertible operators that includes both the set of generalized invertible operators and the set of Drazin invertible operators. Here we focus essentially on the perturbation problem of pseudo-generalized invertible operators and the particular case of DPG invertibility.