Principles of functional analysis
By: Martin Schechter.
Edition: 2nd ed.
Series: Graduate studies in mathematics,; v. 36
Publisher: American Mathematical Society
Published: 2002
Place of publication: Providence, R.I
Language: eng
Number of pages: 425
Subjects: Functional analysis.
Notes: Includes bibliographical references and index.
Table of contents: title: Machine generated contents note: Chapter 1. BASIC NOTIONS; title: 1.1. A problem from differential equations; title: 1.2. An examination of the results; title: 1.3. Examples of Banach spaces; title: 1.4. Fourier series; title: 1.5. Problems; title: Chapter 2. DUALITY; title: 2.1. The Riesz representation theorem; title: 2.2. The Hahn-Banach theorem; title: 2.3. Consequences of the Hahn-Banach theorem; title: 2.4. Examples of dual spaces; title: 2.5. Problems; title: Chapter 3. LINEAR OPERATORS; title: 3.1. Basic properties; title: 3.2. The adjoint operator; title: 3.3. Annihilators; title: 3.4. The inverse operator; title: 3.5. Operators with closed ranges; title: 3.6. The uniform boundedness principle; title: 3.7. The open mapping theorem; title: 3.8. Problems; title: Chapter 4. THE RIESZ THEORY FOR COMPACT OPERATORS; title: 4.1. A type of integral equation; title: 4.2. Operators of finite rank; title: 4.3. Compact operators; title: 4.4. The adjoint of a compact operator; title: 4.5. Problems; title: Chapter 5. FREDHOLM OPERATORS; title: 5.1. Orientation; title: 5.2. Further properties; title: 5.3. Perturbation theory; title: 5.4. The adjoint operator; title: 5.5. A special case; title: 5.6. Semi-Fredholm operators; title: 5.7. Products of operators; title: 5.8. Problems; title: Chapter 6. SPECTRAL THEORY; title: 6.1. The spectrum and resolvent sets; title: 6.2. The spectral mapping theorem; title: 6.3. Operational calculus; title: 6.4. Spectral projections; title: 6.5. Complexification; title: 6.6. The complex Hahn-Banach theorem; title: 6.7. A geometric lemma; title: 6.8. Problems; title: Chapter 7. UNBOUNDED OPERATORS; title: 7.1. Unbounded Fredholm operators; title: 7.2. Further properties; title: 7.3. Operators with closed ranges; title: 7.4. Total subsets; title: 7.5. The essential spectrum; title: 7.6. Unbounded semi-Fredholm operators; title: 7.7. The adjoint of a product of operators; title: 7.8. Problems; title: Chapter 8. REFLEXIVE BANACH SPACES; title: 8.1. Properties of reflexive spaces; title: 8.2. Saturated subspaces; title: 8.3. Separable spaces; title: 8.4. Weak convergence; title: 8.5. Examples; title: 8.6. Completing a normed vector space; title: 8.7. Problems; title: Chapter 9. BANACH ALGEBRAS; title: 9.1. Introduction; title: 9.2. An example; title: 9.3. Commutative algebras; title: 9.4. Properties of maximal ideals; title: 9.5. Partially ordered sets; title: 9.6. Riesz operators; title: 9.7. Fredholm perturbations; title: 9.8. Semi-Fredholm perturbations; title: 9.9. Remarks; title: 9.10. Problems; title: Chapter 10. SEMIGROUPS; title: 10.1. A differential equation; title: 10.2. Uniqueness; title: 10.3. Unbounded operators; title: 10.4. The infinitesimal generator; title: 10.5. An approximation theorem; title: 10.6. Problems; title: Chapter 11. HILBERT SPACE; title: 11.1. When is a Banach space a Hilbert space?; title: 11.2. -Normal operators; title: 11.3. Approximation by operators of finite rank; title: 11.4. Integral operators; title: 11.5. Hyponormal operators; title: 11.6. Problems; title: Chapter 12. BILINEAR FORMS; title: 12.1. The numerical range; title: 12.2. The associated operator; title: 12.3. Symmetric forms; title: 12.4. Closed forms; title: 12.5. Closed extensions; title: 12.6. Closable operators; title: 12.7. Some proofs; title: 12.8. Some representation theorems; title: 12.9. Dissipative operators; title: 12.10. The case of a line or a strip; title: 12.11. Selfadjoint extensions; title: 12.12. Problems; title: Chapter 13. SELFADJOINT OPERATORS; title: 13.1. Orthogonal projections; title: 13.2. Square roots of operators; title: 13.3. A decomposition of operators; title: 13.4. Spectral resolution; title: 13.5. Some consequences; title: 13.6. Unbounded selfadjoint operators; title: 13.7. Problems; title: Chapter 14. MEASURES OF OPERATORS; title: 14.1. A seminorm; title: 14.2. Perturbation classes; title: 14.3. Related measures; title: 14.4. Measures of noncompactness; title: 14.5. The quotient space; title: 14.6. Strictly singular operators; title: 14.7. - Norm perturbations; title: 14.8. Perturbation functions; title: 14.9. Factored perturbation functions; title: 14.10. Problems; title: Chapter 15. EXAMPLES AND APPLICATIONS; title: 15.1. A few remarks; title: 15.2. A differential operator; title: 15.3. Does A have a closed extension?; title: 15.4. The closure of A; title: 15.5. Another approach; title: 15.6. The Fourier transform; title: 15.7. Multiplication by a function; title: 15.8. More general operators; title: 15.9. B-Compactness; title: 15.10. The adjoint of A; title: 15.11. An integral operator; title: 15.12. Problems; title: Appendix A. Glossary; title: Appendix B. Major Theorems; title: Bibliography; title: Index.