An invitation to operator theory:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Math. Soc.
2002
|
| Series: | Graduate studies in mathematics
50 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 530 S. graph. Darst. |
| ISBN: | 0821821466 9780821821466 |
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 An invitation to operator theory |c Y. A. Abramovich ; C. D. Aliprantis |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 2002 | |
| 300 | |a XIV, 530 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 50 | |
| 650 | 7 | |a Análise funcional |2 larpcal | |
| 650 | 4 | |a Opérateurs, Théorie des | |
| 650 | 7 | |a Álgebras de operadores |2 larpcal | |
| 650 | 4 | |a Operator theory | |
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| 700 | 1 | |a Aliprantis, Charalambos D. |d 1946-2009 |e Verfasser |0 (DE-588)121199010 |4 aut | |
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Record in the Search Index
| _version_ | 1804129324110970880 |
|---|---|
| adam_text | Contents
Foreword ix
Chapter 1. Odds and Ends 1
§1.1. Banach Spaces, Operators, and Linear Functional 1
§1.2. Banach Lattices and Positive Operators 13
§1.3. Bases in Banach Spaces 27
§1.4. Ultrapowers of Banach Spaces 37
§1.5. Vector valued Functions 44
§1.6. Fundamentals of Measure Theory 52
Chapter 2. Basic Operator Theory 69
§2.1. Bounded Below Operators 69
§2.2. The Ascent and Descent of an Operator 79
§2.3. Banach Lattices with Order Continuous Norms 84
§2.4. Compact and Weakly Compact Positive Operators 88
Chapter 3. Operators on AL and AM spaces 93
§3.1. AL and AM spaces 94
§3.2. Complex Banach Lattices 103
§3.3. The Center of a Banach Lattice 112
§3.4. The Predual of a Principal Ideal 119
Chapter 4. Special Classes of Operators 123
§4.1. Finite rank Operators 123
§4.2. Multiplication Operators 135
v
vi Contents
§4.3. Lattice and Algebraic Homomorphisms 142
§4.4. Fredholm Operators 155
§4.5. Strictly Singular Operators 170
Chapter 5. Integral Operators 179
§5.1. The Basics of Integral Operators 180
§5.2. Abstract Integral Operators 193
§5.3. Conditional Expectations and Positive Projections 211
§5.4. Positive Projections and Lattice subspaces 228
Chapter 6. Spectral Properties 237
§6.1. The Spectrum of an Operator 237
§6.2. Special Points of the Spectrum 248
§6.3. The Resolvent of a Positive Operator 253
§6.4. Functional Calculus 256
Chapter 7. Some Special Spectra 271
§7.1. The Spectrum of a Compact Operator 272
§7.2. Turning Approximate Eigenvalues into Eigenvalues 281
§7.3. The Spectrum of a Lattice Homomorphism 287
§7.4. The Order Spectrum of an Order Bounded Operator 291
§7.5. The Essential Spectrum of a Bounded Operator 298
Chapter 8. Positive Matrices 315
§8.1. The Banach Lattices Mn(R) and Mn(C) 316
§8.2. Operators on Finite Dimensional Spaces 320
§8.3. Matrices with Non negative Entries 329
§8.4. Irreducible Matrices 332
§8.5. The Perron Frobenius Theorem 339
Chapter 9. Irreducible Operators 347
§9.1. Irreducible and Expanding Operators 347
§9.2. Ideal Irreducibility and the Spectral Radius 357
§9.3. Band Irreducibility and the Spectral Radius 365
§9.4. Krein Operators on C(Q) spaces 370
Chapter 10. Invariant Subspaces 381
§10.1. A Smorgasbord of Invariant Subspaces 383
§10.2. The Lomonosov Invariant Subspace Theorem 393
Contents vii
§10.3. Invariant Ideals for Positive Operators 398
§10.4. Invariant Subspaces of Families of Positive Operators 409
§10.5. Compact friendly Operators 425
§10.6. Positive Operators on Banach Spaces with Bases 436
§10.7. A Characterization of Non transitive Algebras 440
§10.8. Comments on the Invariant Subspace Problem 449
Chapter 11. The Daugavet Equation 455
§11.1. The Daugavet Equation and Uniform Convexity 456
§11.2. The Daugavet Property in AL and vlM spaces 467
§11.3. The Daugavet Property in Banach Spaces 471
§11.4. The Daugavet Property in C(fi) spaces 477
§11.5. Slices and the Daugavet Property 487
§11.6. Narrow Operators 493
§11.7. Some Applications of the Daugavet Equation 500
Bibliography 505
Index 521
|
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.724 515.724 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| indexdate | 2024-07-09T19:03:19Z |
| institution | BVB |
| isbn | 0821821466 9780821821466 |
| language | English |
| lccn | 2002074420 |
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| physical | XIV, 530 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
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| publisher | American Math. Soc. |
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| series | Graduate studies in mathematics |
| series2 | Graduate studies in mathematics |
| spelling | Abramovich, Yuri A. 1945-2003 Verfasser (DE-588)120117967 aut An invitation to operator theory Y. A. Abramovich ; C. D. Aliprantis Providence, RI American Math. Soc. 2002 XIV, 530 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 50 Análise funcional larpcal Opérateurs, Théorie des Álgebras de operadores larpcal Operator theory 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 978-1-4704-2099-4 Graduate studies in mathematics 50 (DE-604)BV009739289 50 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009890666&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Abramovich, Yuri A. 1945-2003 Aliprantis, Charalambos D. 1946-2009 An invitation to operator theory Graduate studies in mathematics Análise funcional larpcal Opérateurs, Théorie des Álgebras de operadores larpcal Operator theory Operatortheorie (DE-588)4075665-8 gnd |
| subject_GND | (DE-588)4075665-8 |
| title | An invitation to operator theory |
| title_auth | An invitation to operator theory |
| title_exact_search | An invitation to operator theory |
| title_full | An invitation to operator theory Y. A. Abramovich ; C. D. Aliprantis |
| title_fullStr | An invitation to operator theory Y. A. Abramovich ; C. D. Aliprantis |
| title_full_unstemmed | An invitation to operator theory Y. A. Abramovich ; C. D. Aliprantis |
| title_short | An invitation to operator theory |
| title_sort | an invitation to operator theory |
| topic | Análise funcional larpcal Opérateurs, Théorie des Álgebras de operadores larpcal Operator theory Operatortheorie (DE-588)4075665-8 gnd |
| topic_facet | Análise funcional Opérateurs, Théorie des Álgebras de operadores Operator theory Operatortheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009890666&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV009739289 |
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