Generalized Inverse Operator for an Integrodifferential Operator in the Banach Space

By using the theory of generalized inversion of operators in Banach spaces, we establish conditions for the generalized invertibility of integrodifferential operators with degenerate kernels in Banach spaces. We obtain formulas for the construction of bounded projectors and the bounded generalized inverse operator for an integrodifferential operator with degenerate kernel in a Banach space. The results of investigations are illustrated by an example. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.