Conditions of Solvability and Representation of the Solutions of Equations with Operator Matrices
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We propose new methods for the construction of generalized inverse operator matrices for the operator matrices in Banach spaces. The criteria of solvability and the formulas for representations of the general solutions of operator equations with operator matrices are obtained. As an application, we consider the relationship between the obtained formulas and the well-known Frobenius formula for the construction of the matrix inverse to a nondegenerate block matrix.
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