Complete rank theorem of advanced calculus and singularities of bounded linear operators
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Publication:942957
DOI10.1007/s11464-008-0019-8zbMath1176.47049OpenAlexW2060980407MaRDI QIDQ942957
Publication date: 8 September 2008
Published in: Frontiers of Mathematics in China (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s11464-008-0019-8
perturbation analysisgeneralized inverse operatorslocal linearisationrank theoremFredholm and semi-Fredholm operators
Theory of matrix inversion and generalized inverses (15A09) Perturbation theory of linear operators (47A55) Global submanifolds (53C40) Continuous and differentiable maps in nonlinear functional analysis (46T20) Abstract inverse mapping and implicit function theorems involving nonlinear operators (47J07)
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Cites Work
- Three classes of smooth Banach submanifolds in \(B(E, F)\)
- A rank theorem of operators between Banach spaces
- Characters and derived length in groups of odd order
- (1. 2) inverses of operators between Banach spaces and local conjugacy theorem
- Convergence of Newton-like methods for singular operator equations using outer inverses
- Perturbation analysis for the operator equation \(Tx=b\) in Banach spaces
- Local conjugacy theorem, rank theorems in advanced calculus and a generalized principle for constructing Banach manifolds
- A generalized preimage theorem in global analysis
- Perturbation analysis of generalized inverses of linear operators in Banach spaces
- Rank theorems of operators between Banach spaces
- A generalized transversality in global analysis
- Topological and geometric property of matrix algebra
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