Problems in operator theory:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, R.I.
American Math. Soc.
2002
|
| Series: | Graduate studies in mathematics
51 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 386 S. graph. Darst. |
| ISBN: | 0821821474 9780821821473 |
Staff View
MARC
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| 100 | 1 | |a Abramovich, Yuri A. |d 1945-2003 |e Verfasser |0 (DE-588)120117967 |4 aut | |
| 245 | 1 | 0 | |a Problems in operator theory |c Y. A. Abramovich ; C. D. Aliprantis |
| 264 | 1 | |a Providence, R.I. |b American Math. Soc. |c 2002 | |
| 300 | |a XII, 386 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate studies in mathematics |v 51 | |
| 650 | 7 | |a Análise funcional (problemas e exercícios) |2 larpcal | |
| 650 | 7 | |a Operadores (problemas e exercícios) |2 larpcal | |
| 650 | 4 | |a Opérateurs, Théorie des - Problèmes et exercices | |
| 650 | 4 | |a Operator theory |v Problems, exercises, etc | |
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Record in the Search Index
| _version_ | 1804129319787692032 |
|---|---|
| adam_text | Contents
Foreword xi
Chapter 1. Odds and Ends 1
§1.1. Banach Spaces, Operators, and Linear Functional 1
§1.2. Banach Lattices and Positive Operators 20
§1.3. Bases in Banach Spaces 31
§1.4. Ultrapowers of Banach Spaces 44
§1.5. Vector valued Functions 48
§1.6. Fundamentals of Measure Theory 51
Chapter 2. Basic Operator Theory 63
§2.1. Bounded Below Operators 63
§2.2. The Ascent and Descent of an Operator 68
§2.3. Banach Lattices with Order Continuous Norms 71
§2.4. Compact and Weakly Compact Positive Operators 78
Chapter 3. Operators on AL and AM spaces 87
§3.1. AL and AM spaces 87
§3.2. Complex Banach Lattices 96
§3.3. The Center of a Banach Lattice 105
§3.4. The Predual of a Principal Ideal 111
Chapter 4. Special Classes of Operators 119
§4.1. Finite rank Operators 119
§4.2. Multiplication Operators 125
vii
viii Contents
§4.3. Lattice and Algebraic Homomorphisms 129
§4.4. Fredholm Operators 134
§4.5. Strictly Singular Operators 139
Chapter 5. Integral Operators 145
§5.1. The Basics of Integral Operators 145
§5.2. Abstract Integral Operators 154
§5.3. Conditional Expectations and Positive Projections 169
§5.4. Positive Projections and Lattice subspaces 180
Chapter 6. Spectral Properties 189
§6.1. The Spectrum of an Operator 189
§6.2. Special Points of the Spectrum 197
§6.3. The Resolvent of a Positive Operator 201
§6.4. Functional Calculus 205
Chapter 7. Some Special Spectra 215
§7.1. The Spectrum of a Compact Operator 215
§7.2. Turning Approximate Eigenvalues into Eigenvalues 222
§7.3. The Spectrum of a Lattice Homomorphism 230
§7.4. The Order Spectrum of an Order Bounded Operator 232
§7.5. The Essential Spectrum of a Bounded Operator 237
Chapter 8. Positive Matrices 243
§8.1. The Banach Lattices Mn(R) and Mn(C) 243
§8.2. Operators on Finite Dimensional Spaces 251
§8.3. Matrices with Non negative Entries 262
§8.4. Irreducible Matrices 265
§8.5. The Perron Frobenius Theorem 268
Chapter 9. Irreducible Operators 273
§9.1. Irreducible and Expanding Operators 273
§9.2. Ideal Irreducibility and the Spectral Radius 283
§9.3. Band Irreducibility and the Spectral Radius 290
§9.4. Krein Operators and C(fi) spaces 293
Chapter 10. Invariant Subspaces 299
§10.1. A Smorgasbord of Invariant Subspaces 299
§10.2. The Lomonosov Invariant Subspace Theorem 307
Contents ix
§10.3. Invariant Ideals for Positive Operators 310
§10.4. Invariant Subspaces of Families of Positive Operators 317
§10.5. Compact friendly Operators 320
§10.6. Positive Operators on Banach Spaces with Bases 329
§10.7. Non transitive Algebras 331
Chapter 11. The Daugavet Equation 335
§11.1. The Daugavet Equation and Uniform Convexity 335
§11.2. The Daugavet Property in AL and AM spaces 352
§11.3. The Daugavet Property in Banach Spaces 356
§11.4. The Daugavet Property in C(fi) spaces 359
§11.5. Slices and the Daugavet Property 365
§11.6. Narrow Operators 369
§11.7. Some Applications of the Daugavet Equation 372
Bibliography 375
Index 379
|
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| spelling | Abramovich, Yuri A. 1945-2003 Verfasser (DE-588)120117967 aut Problems in operator theory Y. A. Abramovich ; C. D. Aliprantis Providence, R.I. American Math. Soc. 2002 XII, 386 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 51 Análise funcional (problemas e exercícios) larpcal Operadores (problemas e exercícios) larpcal Opérateurs, Théorie des - Problèmes et exercices Operator theory Problems, exercises, etc Operatortheorie (DE-588)4075665-8 gnd rswk-swf Operatortheorie (DE-588)4075665-8 s DE-604 Aliprantis, Charalambos D. 1946-2009 Verfasser (DE-588)121199010 aut Erscheint auch als Online-Ausgabe 978-1-4704-2100-7 Graduate studies in mathematics 51 (DE-604)BV009739289 51 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009887906&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Abramovich, Yuri A. 1945-2003 Aliprantis, Charalambos D. 1946-2009 Problems in operator theory Graduate studies in mathematics Análise funcional (problemas e exercícios) larpcal Operadores (problemas e exercícios) larpcal Opérateurs, Théorie des - Problèmes et exercices Operator theory Problems, exercises, etc Operatortheorie (DE-588)4075665-8 gnd |
| subject_GND | (DE-588)4075665-8 |
| title | Problems in operator theory |
| title_auth | Problems in operator theory |
| title_exact_search | Problems in operator theory |
| title_full | Problems in operator theory Y. A. Abramovich ; C. D. Aliprantis |
| title_fullStr | Problems in operator theory Y. A. Abramovich ; C. D. Aliprantis |
| title_full_unstemmed | Problems in operator theory Y. A. Abramovich ; C. D. Aliprantis |
| title_short | Problems in operator theory |
| title_sort | problems in operator theory |
| topic | Análise funcional (problemas e exercícios) larpcal Operadores (problemas e exercícios) larpcal Opérateurs, Théorie des - Problèmes et exercices Operator theory Problems, exercises, etc Operatortheorie (DE-588)4075665-8 gnd |
| topic_facet | Análise funcional (problemas e exercícios) Operadores (problemas e exercícios) Opérateurs, Théorie des - Problèmes et exercices Operator theory Problems, exercises, etc Operatortheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009887906&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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