Conditions of solvability and submission of solutions of equations with operator matrix in banach spaces

Abstract

The paper proposed methods for constructing a generalized inverse operator matrices to operator matrices in Banach spaces. Solvability criteria and formulas for representations of general solutions of operator equations with operator matrices are obtained. As an application, the relationship obtained formulas with the well-known Frobenius formula for constructing the inverse matrices to a non-degenerate block matrix.