Conditions of solvability and representation of the solutions of equations with operator matrices
We propose new methods for the construction of generalized inverse operator matrices for the operator matrices in Banach spaces. The solvability criteria and the formulas for representations of the general solutions of operator equations with operator matrices are obtained. As an application, we con...
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| Date: | 2019 |
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| Main Authors: | , , , , , |
| Format: | Article |
| Language: | Russian |
| Published: |
Institute of Mathematics, NAS of Ukraine
2019
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/1452 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | We propose new methods for the construction of generalized inverse operator matrices for the operator matrices in Banach
spaces. The solvability criteria 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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