Generalized Inversion of the Operator Matrices (Generalization of the Frobenius Theorem)

Generalized Inversion of the Operator Matrices (Generalization of the Frobenius Theorem)

We propose methods for the construction of the operator matrices generalized inverse to (2 × 2) operator matrices in Banach spaces. We obtain the condition of solvability and a formula for representation of at least one solution of the operator equation in terms of a (2 × 2) operator matrix. It is s...

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Veröffentlicht in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2024-02, Vol.278 (6), p.974-987
Hauptverfasser: Zhuravlev, V. P., Fomin, M. P.
Format: Artikel
Sprache:eng
Schlagworte:
Banach spaces
Generalized inverse
Mathematics
Mathematics and Statistics
Operators (mathematics)
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Zusammenfassung:We propose methods for the construction of the operator matrices generalized inverse to (2 × 2) operator matrices in Banach spaces. We obtain the condition of solvability and a formula for representation of at least one solution of the operator equation in terms of a (2 × 2) operator matrix. It is shown that the obtained formula for the generalized inverse operator matrix is related to the well-known Frobenius formula for the construction of the inverse matrix for a nondegenerate block matrix.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-024-06975-8