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Principles of functional analysis

By: Schechter, Martin.
Material type: materialTypeLabelBookSeries: Graduate studies in mathematics, v. 36. Publisher: Providence, R.I. : American Mathematical Society, ©2002Edition: 2nd ed.Description: xxi, 425 p. : ill. ; 26 cm.ISBN: 9780821848562.Subject(s): Functional analysisOnline resources: Table of contents
Contents:
Machine generated contents note: Chapter 1. BASIC NOTIONS -- 1.1. A problem from differential equations -- 1.2. An examination of the results -- 1.3. Examples of Banach spaces -- 1.4. Fourier series -- 1.5. Problems -- Chapter 2. DUALITY -- 2.1. The Riesz representation theorem -- 2.2. The Hahn-Banach theorem -- 2.3. Consequences of the Hahn-Banach theorem -- 2.4. Examples of dual spaces -- 2.5. Problems -- Chapter 3. LINEAR OPERATORS -- 3.1. Basic properties -- 3.2. The adjoint operator -- 3.3. Annihilators -- 3.4. The inverse operator -- 3.5. Operators with closed ranges -- 3.6. The uniform boundedness principle -- 3.7. The open mapping theorem -- 3.8. Problems -- Chapter 4. THE RIESZ THEORY FOR COMPACT OPERATORS -- 4.1. A type of integral equation -- 4.2. Operators of finite rank -- 4.3. Compact operators -- 4.4. The adjoint of a compact operator -- 4.5. Problems -- Chapter 5. FREDHOLM OPERATORS -- 5.1. Orientation -- 5.2. Further properties -- 5.3. Perturbation theory -- 5.4. The adjoint operator -- 5.5. A special case -- 5.6. Semi-Fredholm operators -- 5.7. Products of operators -- 5.8. Problems -- Chapter 6. SPECTRAL THEORY -- 6.1. The spectrum and resolvent sets -- 6.2. The spectral mapping theorem -- 6.3. Operational calculus -- 6.4. Spectral projections -- 6.5. Complexification -- 6.6. The complex Hahn-Banach theorem -- 6.7. A geometric lemma -- 6.8. Problems -- Chapter 7. UNBOUNDED OPERATORS -- 7.1. Unbounded Fredholm operators -- 7.2. Further properties -- 7.3. Operators with closed ranges -- 7.4. Total subsets -- 7.5. The essential spectrum -- 7.6. Unbounded semi-Fredholm operators -- 7.7. The adjoint of a product of operators -- 7.8. Problems -- Chapter 8. REFLEXIVE BANACH SPACES -- 8.1. Properties of reflexive spaces -- 8.2. Saturated subspaces -- 8.3. Separable spaces -- 8.4. Weak convergence -- 8.5. Examples -- 8.6. Completing a normed vector space -- 8.7. Problems -- Chapter 9. BANACH ALGEBRAS -- 9.1. Introduction -- 9.2. An example -- 9.3. Commutative algebras -- 9.4. Properties of maximal ideals -- 9.5. Partially ordered sets -- 9.6. Riesz operators -- 9.7. Fredholm perturbations -- 9.8. Semi-Fredholm perturbations -- 9.9. Remarks -- 9.10. Problems -- Chapter 10. SEMIGROUPS -- 10.1. A differential equation -- 10.2. Uniqueness -- 10.3. Unbounded operators -- 10.4. The infinitesimal generator -- 10.5. An approximation theorem -- 10.6. Problems -- Chapter 11. HILBERT SPACE -- 11.1. When is a Banach space a Hilbert space? -- 11.2. -Normal operators -- 11.3. Approximation by operators of finite rank -- 11.4. Integral operators -- 11.5. Hyponormal operators -- 11.6. Problems -- Chapter 12. BILINEAR FORMS -- 12.1. The numerical range -- 12.2. The associated operator -- 12.3. Symmetric forms -- 12.4. Closed forms -- 12.5. Closed extensions -- 12.6. Closable operators -- 12.7. Some proofs -- 12.8. Some representation theorems -- 12.9. Dissipative operators -- 12.10. The case of a line or a strip -- 12.11. Selfadjoint extensions -- 12.12. Problems -- Chapter 13. SELFADJOINT OPERATORS -- 13.1. Orthogonal projections -- 13.2. Square roots of operators -- 13.3. A decomposition of operators -- 13.4. Spectral resolution -- 13.5. Some consequences -- 13.6. Unbounded selfadjoint operators -- 13.7. Problems -- Chapter 14. MEASURES OF OPERATORS -- 14.1. A seminorm -- 14.2. Perturbation classes -- 14.3. Related measures -- 14.4. Measures of noncompactness -- 14.5. The quotient space -- 14.6. Strictly singular operators -- 14.7. - Norm perturbations -- 14.8. Perturbation functions -- 14.9. Factored perturbation functions -- 14.10. Problems -- Chapter 15. EXAMPLES AND APPLICATIONS -- 15.1. A few remarks -- 15.2. A differential operator -- 15.3. Does A have a closed extension? -- 15.4. The closure of A -- 15.5. Another approach -- 15.6. The Fourier transform -- 15.7. Multiplication by a function -- 15.8. More general operators -- 15.9. B-Compactness -- 15.10. The adjoint of A -- 15.11. An integral operator -- 15.12. Problems -- Appendix A. Glossary -- Appendix B. Major Theorems -- Bibliography -- Index.
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515.7 LIM-F Functional analysis 515.7 MAC-E Elementary functional analysis 515.7 SAX-B Beginning functional analysis 515.7 SCH-P Principles of functional analysis 515.7 SHI-E Elementary functional analysis 515.7 SUH-F Functional analysis 515.7 YOS-F Functional analysis

Includes bibliographical references and index.

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

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