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Cover Art
PRINTED BOOKS
Author Schechter, Martin.

Title Principles of functional analysis / Martin Schechter.

Published Providence, R.I. : American Mathematical Society, 2001.

Copies

Location Call No. Status
 UniM ERC  515.7 SCHE    CLMS RETD
Edition 2nd ed.
Physical description xxi, 425 pages.
Series Graduate studies in mathematics, 1065-7339 ; v. 36.
Graduate studies in mathematics. 1065-7339 ; v. 36.
Bibliography Includes bibliographical references and index.
Contents Chapter 1. Basic Notions 1 -- 1.1. A problem from differential equations 1 -- 1.2. An examination of the results 6 -- 1.3. Examples of Banach spaces 9 -- 1.4. Fourier series 17 -- Chapter 2. Duality 29 -- 2.1. Riesz representation theorem 29 -- 2.2. Hahn-Banach theorem 33 -- 2.3. Consequences of the Hahn-Banach theorem 36 -- 2.4. Examples of dual spaces 39 -- Chapter 3. Linear Operators 55 -- 3.1. Basic properties 55 -- 3.2. Adjoint operator 57 -- 3.3. Annihilators 59 -- 3.4. Inverse operator 60 -- 3.5. Operators with closed ranges 66 -- 3.6. Uniform boundedness principle 71 -- 3.7. Open mapping theorem 71 -- Chapter 4. Riesz Theory for Compact Operators 77 -- 4.1. A type of integral equation 77 -- 4.2. Operators of finite rank 85 -- 4.3. Compact operators 88 -- 4.4. Adjoint of a compact operator 95 -- Chapter 5. Fredholm Operators 101 -- 5.2. Further properties 105 -- 5.3. Perturbation theory 109 -- 5.4. Adjoint operator 112 -- 5.5. A special case 114 -- 5.6. Semi-Fredholm operators 117 -- 5.7. Products of operators 123 -- Chapter 6. Spectral Theory 129 -- 6.1. Spectrum and resolvent sets 129 -- 6.2. Spectral mapping theorem 133 -- 6.3. Operational calculus 134 -- 6.4. Spectral projections 141 -- 6.5. Complexification 147 -- 6.6. Complex Hahn-Banach theorem 148 -- 6.7. A geometric lemma 150 -- Chapter 7. Unbounded Operators 155 -- 7.1. Unbounded Fredholm operators 155 -- 7.2. Further properties 161 -- 7.3. Operators with closed ranges 164 -- 7.4. Total subsets 169 -- 7.5. Essential spectrum 171 -- 7.6. Unbounded semi-Fredholm operators 173 -- 7.7. Adjoint of a product of operators 177 -- Chapter 8. Reflexive Banach Spaces 183 -- 8.1. Properties of reflexive spaces 183 -- 8.2. Saturated subspaces 185 -- 8.3. Separable spaces 188 -- 8.4. Weak convergence 190 -- 8.6. Completing a normed vector space 196 -- Chapter 9. Banach Algebras 201 -- 9.3. Commutative algebras 206 -- 9.4. Properties of maximal ideals 209 -- 9.5. Partially ordered sets 211 -- 9.6. Riesz operators 213 -- 9.7. Fredholm perturbations 215 -- 9.8. Semi-Fredholm perturbations 216 -- Chapter 10. Semigroups 225 -- 10.1. A differential equation 225 -- 10.2. Uniqueness 228 -- 10.3. Unbounded operators 229 -- 10.4. Infinitesimal generator 235 -- 10.5. An approximation theorem 238 -- Chapter 11. Hilbert Space 243 -- 11.1. When is a Banach space a Hilbert space? 243 -- 11.2. Normal operators 246 -- 11.3. Approximation by operators of finite rank 252 -- 11.4. Integral operators 253 -- 11.5. Hyponormal operators 257 -- Chapter 12. Bilinear forms 265 -- 12.1. Numerical range 265 -- 12.2. Associated operator 266 -- 12.3. Symmetric forms 268 -- 12.4. Closed forms 270 -- 12.5. Closed extensions 274 -- 12.6. Closable operators 278 -- 12.7. Some proofs 281 -- 12.8. Some representation theorems 284 -- 12.9. Dissipative operators 285 -- 12.10. Case of a line or a strip 290 -- 12.11. Selfadjoint extensions 294 -- Chapter 13. Selfadjoint Operators 297 -- 13.1. Orthogonal projections 297 -- 13.2. Square roots of operators 299 -- 13.3. A decomposition of operators 304 -- 13.4. Spectral resolution 306 -- 13.5. Some consequences 311 -- 13.6. Unbounded selfadjoint operators 314 -- Chapter 14. Measures of Operators 325 -- 14.1. A seminorm 325 -- 14.2. Perturbation classes 329 -- 14.3. Related measures 332 -- 14.4. Measures of noncompactness 339 -- 14.5. Quotient space 341 -- 14.6. Strictly singular operators 342 -- 14.7. Norm perturbations 345 -- 14.8. Perturbation functions 350 -- 14.9. Factored perturbation functions 354 -- Chapter 15. Examples and Applications 359 -- 15.1. A few remarks 359 -- 15.2. A differential operator 360 -- 15.3. Does A have a closed extension? 363 -- 15.4. Closure of A 364 -- 15.5. Another approach 369 -- 15.6. Fourier transform 372 -- 15.7. Multiplication by a function 374 -- 15.8. More general operators 378 -- 15.9. B-Compactness 381 -- 15.10. Adjoint of A 383 -- 15.11. An integral operator 384 -- Appendix B. Major Theorems 405.
Subject Functional analysis.
ISBN 0821828959 (alk. paper)