Stable Perturbations of operators and related topics

• Main Author: Xue, Yifeng
• 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: Algebraic functions; Analyse fonctionnelle; Fonctions algébriques; Functional analysis; Integral operators; Inverse problems (Differential equations); Linear operators; Numerical & Computational Mathematics; Opérateurs linéaires; Pure Mathematics; Drazin Inverse; Generalized Inverse; Moore-Penrose Inverse; Stable Perturbation
• ISBN: 9789814383592; 9814383597
• DOI: 10.1142/8365

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...

Table of Contents:

• 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