Stable Perturbations of operators and related topics
This book provides a broad introduction to the generalized inverses, Moore–Penrose inverses, Drazin inverses and T–S outer generalized inverses and their perturbation analyses in the spaces of infinite-dimensional. This subject has many applications in operator theory, operator algebras, global anal...
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| Main Author | |
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| Format | eBook Book |
| Language | English |
| Published |
New Jersey
World Scientific Publishing Co. Pte. Ltd
2012
World Scientific World Scientific Publishing Company WORLD SCIENTIFIC WSPC |
| Edition | 1 |
| Subjects | |
| Online Access | Get full text |
| ISBN | 9789814383592 9814383597 |
| DOI | 10.1142/8365 |
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| Abstract | This book provides a broad introduction to the generalized inverses, Moore–Penrose inverses, Drazin inverses and T–S outer generalized inverses and their perturbation analyses in the spaces of infinite-dimensional. This subject has many applications in operator theory, operator algebras, global analysis and approximation theory and so on. |
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| AbstractList | This book provides a broad introduction to the generalized inverses, Moore–Penrose inverses, Drazin inverses and T–S outer generalized inverses and their perturbation analyses in the spaces of infinite-dimensional. This subject has many applications in operator theory, operator algebras, global analysis and approximation theory and so on. This book provides a broad introduction to the generalized inverses, Moore-Penrose inverses, Drazin inverses and T-S outer generalized inverses and their perturbation analyses in the spaces of infinite-dimensional. This subject has many applications in operator theory, operator algebras, global analysis and approximation theory and so on.Stable Perturbations of Operators and Related Topics is self-contained and unified in presentation. It may be used as an advanced textbook by graduate students. It is also suitable for researchers as a reference. The proofs of statements and explanations in the book are detailed enough that interested readers can study it by themselves.Contents: Basics in Functional AnalysisStable Perturbation of Densely-Defined Closed OperatorsMoore-Penrose Inverse and Its Stable PerturbationDrazin Inverses, T-S Generalized Inverses and Their PerturbationsMiscellaneous ApplicationsSome Related TopicsReadership: Graduate students and researchers in analysis and differential equations, numerical analysis and computational mathematics, algebra. |
| Author | Xue, Yifeng |
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| Keywords | Drazin Inverse Generalized Inverse Moore-Penrose Inverse Stable Perturbation |
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| Notes | Includes bibliographical references and index |
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| Snippet | This book provides a broad introduction to the generalized inverses, Moore–Penrose inverses, Drazin inverses and T–S outer generalized inverses and their... This book provides a broad introduction to the generalized inverses, Moore-Penrose inverses, Drazin inverses and T-S outer generalized inverses and their... |
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| SubjectTerms | Algebraic functions Analyse fonctionnelle Fonctions algébriques Functional analysis Integral operators Inverse problems (Differential equations) Linear operators Numerical & Computational Mathematics Opérateurs linéaires Pure Mathematics |
| SubjectTermsDisplay | Algebraic functions Analyse fonctionnelle Fonctions algébriques Functional analysis Inverse problems (Differential equations) Linear operators Opérateurs linéaires |
| TableOfContents | Stable perturbations of operators and related topics -- Preface -- Contents -- Chapter 1: Basics in Functional Analysis -- Chapter 2: Stable Perturbation of Densely-Defined Closed Operators -- Chapter 3: Moore-Penrose Inverse and Its Stable Perturbation -- Chapter 4: Drazin Inverses, T-S Generalized Inverses and Their Perturbations -- Chapter 5: Miscellaneous Applications -- Chapter 6: Some Related Topics -- Appendix A: Some Results From Topology and Analysis -- Appendix B: More On C* - Algebras -- Bibliography -- Index 6.1 Perturbation of reduced minimum modulus -- 6.2 Perturbation analysis for the consistent operator equation on Banach spaces -- 6.3 Fredholm elements relative to a homomorphism and their indices -- 6.4 Lifting a Moore-Penrose inverse from quotient C*-algebras -- 6.5 Approximate polar decomposition in C*-algebras -- 6.6 The reduced minimum modulus relative to a quotient C*- algebra -- 6.7 Notes -- Appendix A Some Results From Topology And Analysis -- A.1 Some topological results -- A.2 Holomorphic vector-valued functions -- A.3 Inverse Function Theorem -- Appendix B More On C*-Algebras -- B.1 Some basic results in C*-algebras -- B.2 Lifting problems about projections -- B.3 K-theory for C*-algebras -- Bibliography -- Index Intro -- Contents -- Preface -- 1. Basics in Functional Analysis -- 1.1 Banach spaces and Hilbert spaces -- 1.2 Reduced minimum moduli of densely-defined operators -- 1.3 The gap function of subspaces -- 1.4 Banach algebras -- 1.5 C*-algebras -- 1.6 Notes -- 2. Stable Perturbation of Densely-Defined Closed Operators -- 2.1 Generalized inverses of linear operators on Banach spaces -- 2.2 Stable perturbation of operators -- 2.3 Perturbation analysis of the operator equation Ax = b -- 2.4 Generalized inverses in Banach algebras -- 2.5 Some applications of stable perturbations -- 2.6 Notes -- 3. Moore-Penrose Inverse And Its Stable Perturbation -- 3.1 The Moore-Penrose inverse -- 3.2 The reverse order law of the Moore-Penrose inverses -- 3.3 Stable perturbation of closed operators in Hilbert spaces -- 3.4 The representations of certain Moore-Penrose inverses -- 3.5 Moore-Penrose inverses in C*-algebras -- 3.6 Notes -- 4. Drazin Inverses, T -S Generalized Inverses And Their Perturbations -- 4.1 Drazin inverses on Banach spaces -- 4.2 The outer generalized inverse with prescribed range and kernel -- 4.3 The stable perturbation of Drazin inverses -- 4.4 The perturbation analysis of the outer generalized inverse with prescribed range and kernel -- 4.5 Drazin inverses and generalized Drazin inverses in Banach algebras -- 4.6 Stable perturbation of Drazin inverses -- 4.7 Representations for the Drazin inverses of sums, products and block matrices -- 4.8 Notes -- 5. Miscellaneous Applications -- 5.1 The Generalized Bott-Duffin inverse of an operator on a Hilbert Space -- 5.2 Some applications of Moore-Penrose inverses in frame theory -- 5.3 Generalized Cowen-Douglas mappings -- 5.4 Condition numbers related to Moore-Penrose inverses and Drazin inverses -- 5.5 The local conjugacy of a C1-mapping -- 6. Some Related Topics |
| Title | Stable Perturbations of operators and related topics |
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