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Stable Perturbations of Operators and Related Topics : Essays in Honour of Jia-an Yan.
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...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Singapore :
World Scientific,
2012.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Preface; Contents; 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 Perturbation3.1 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 kernel4.5 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-mapping6. Some Related Topics; 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 TheoremAppendix 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.