General Form of Generalized Invertible Operators in Banach Spaces

Abstract

We prove theorems on the general form of generalized invertible operators in Banach spaces in the case where the operators are topologically Noetherian or topologically Fredholm. These theorems generalize the well-known Nikol’skii theorem on the general form of Fredholm operators and the Atkinson theorem on the general form of Noetherian operators in function spaces.