Normally solvable operator equations in a Banach space

DOI10.1007/s11253-013-0772-zzbMath1294.47018OpenAlexW1972442327MaRDI QIDQ384029

V. F. Zhuravlev, Oleksander Pokutnyi, Alexander A. Boichuk

Publication date: 25 November 2013

Published in: Ukrainian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11253-013-0772-z

zbMATH Keywords

solvabilityBanach spaceFredholm operatorgeneralized inverse operator, normally solvable operator equationSchmidt procedure

Mathematics Subject Classification ID

(Semi-) Fredholm operators; index theories (47A53) Equations and inequalities involving linear operators, with vector unknowns (47A50) General (adjoints, conjugates, products, inverses, domains, ranges, etc.) (47A05)

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General form of generalized invertible operators in Banach spaces ⋮ Bifurcation conditions for the solutions of weakly perturbed boundary-value problems for operator equations in Banach spaces ⋮ Solvability of linear integrodifferential equations with nondegenerate kernel in Hilbert spaces ⋮ Linear boundary-value problems for systems of integrodifferential equations with degenerate kernel. Resonance case for a weakly perturbed boundary-value problem ⋮ Generalized inversion of the operator matrices (generalization of the Frobenius theorem) ⋮ Generalized inverse operator for an integrodifferential operator in the Banach space ⋮ Weakly perturbed Fredholm integral equations with degenerate kernels in Banach spaces ⋮ Weakly perturbed operator equations in Banach spaces ⋮ Weakly nonlinear boundary-value problems for the Fredholm integral equations with degenerate kernels in Banach spaces ⋮ Conditions of solvability and representation of the solutions of equations with operator matrices ⋮ Generalized inversion of Fredholm integral operators with degenerate kernels in Banach spaces

Cites Work

• Generalized inverses. Theory and applications.
• COMPLEMENTED SUBSPACES IN BANACH SPACES
• A unified approach to generalized inverses of linear operators: I. Algebraic, topological and projectional properties
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