Stable perturbations of operators and related topics / Yifeng Xue.

Format:

Book

Author/Creator:

Xue, Yifeng.

Language:

English

Subjects (All):

Integral operators.

Physical Description:

1 online resource (305 p.)

Edition:

1st ed.

Place of Publication:

Singapore : World Scientific Pub. Co., 2012.

Language Note:

English

Summary:

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 t

Contents:

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 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; 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

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9786613646835

9781280669903

128066990X

9789814383608

9814383600

OCLC:

794328409