A course in operator theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Math. Soc.
2000
|
| Series: | Graduate studies in mathematics
21 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 372 S. |
| ISBN: | 0821820656 9780821820650 |
Staff View
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| 245 | 1 | 0 | |a A course in operator theory |c John B. Conway |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 2000 | |
| 300 | |a XV, 372 S. | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface xiii
Chapter 1. Introduction to C* Algebras 1
§1. Definition and examples 1
§2. Abelian C* algebras and the Functional Calculus 7
§3. The positive elements in a C* algebra 12
§4. Approximate identities 17
§5. Ideals in a C* algebra 21
§6. Representations of a C* algebra 24
§7. Positive linear functionals and the GNS construction 29
Chapter 2. Normal Operators 37
§8. Some topologies on B(7i) 37
§9. Spectral measures 41
§10. The Spectral Theorem 47
§11. Star cyclic normal operators 51
§12. The commutant 55
§13. Von Neumann algebras 60
§14. Abelian von Neumann algebras 62
§15. The functional calculus for normal operators 65
Chapter 3. Compact Operators 71
§16. C* algebras of compact operators 71
ix
x Contents
§17. Ideals of operators 82
§18. Trace class and Hilbert Schmidt operators 86
§19. The dual spaces of the compact operators and the trace class 93
§20. The weak star topology 95
§21. Inflation and the topologies 99
Chapter 4. Some Non Normal Operators 105
§22. Algebras and lattices 105
§23. Isometries 111
§24. Unilateral and bilateral shifts 118
§25. Some results on Hardy spaces 126
§26. The functional calculus for the unilateral shift 132
§27. Weighted shifts 136
§28. The Volterra operator 143
§29. Bergman operators 147
§30. Subnormal operators 157
§31. Essentially normal operators 170
Chapter 5. More on C* Algebras 181
§32. Irreducible representations 181
§33. Positive maps 187
§34. Completely positive maps 190
§35. An application: Spectral sets and the Sz. Nagy Dilation
Theorem 198
§36. Quasicentral approximate identitites 204
Chapter 6. Compact Perturbations 207
§37. Behavior of the spectrum under a compact perturbation 207
§38. Bp perturbations of hermitian operators 211
§39. The Weyl von Neumann Berg Theorem 214
§40. Voiculescu s Theorem 220
§41. Approximately equivalent representations 229
§42. Some applications 236
Chapter 7. Introduction to Von Neumann Algebras 241
§43. Elementary properties and examples 242
§44. The Kaplansky Density Theorem 250
Contents xi
§45. The Pedersen Up Down Theorem 253
§46. Normal homomorphisms and ideals 258
§47. Equivalence of projections 265
§48. Classification of projections 270
§49. Properties of projections 278
§50. The structure of Type I algebras 282
§51. The classification of Type I algebras 289
§52. Operator valued measurable functions 294
§53. Some structure theory for continuous algebras 301
§54. Weak star continuous linear functional revisited 305
§55. The center valued trace 311
Chapter 8. Reflexivity 319
§56. Fundamentals and examples 319
§57. Reflexive operators on finite dimensional spaces 323
§58. Hyperreflexive subspaces 327
§59. Reflexivity and duality 335
§60. Hypereflexive von Neumann algebras 342
§61. Some examples of operators 348
Bibliography 355
Index 367
List of Symbols 371
|
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| id | DE-604.BV013156375 |
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| indexdate | 2024-07-09T18:40:00Z |
| institution | BVB |
| isbn | 0821820656 9780821820650 |
| language | English |
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| physical | XV, 372 S. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | American Math. Soc. |
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| series | Graduate studies in mathematics |
| series2 | Graduate studies in mathematics |
| spelling | Conway, John B. 1939- Verfasser (DE-588)110699882 aut A course in operator theory John B. Conway Providence, RI American Math. Soc. 2000 XV, 372 S. txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 21 Operatortheorie Operatortheorie (DE-588)4075665-8 gnd rswk-swf Operatortheorie (DE-588)4075665-8 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-2076-5 Graduate studies in mathematics 21 (DE-604)BV009739289 21 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008963921&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Conway, John B. 1939- A course in operator theory Graduate studies in mathematics Operatortheorie Operatortheorie (DE-588)4075665-8 gnd |
| subject_GND | (DE-588)4075665-8 |
| title | A course in operator theory |
| title_auth | A course in operator theory |
| title_exact_search | A course in operator theory |
| title_full | A course in operator theory John B. Conway |
| title_fullStr | A course in operator theory John B. Conway |
| title_full_unstemmed | A course in operator theory John B. Conway |
| title_short | A course in operator theory |
| title_sort | a course in operator theory |
| topic | Operatortheorie Operatortheorie (DE-588)4075665-8 gnd |
| topic_facet | Operatortheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008963921&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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