Introduction to Hilbert space and the theory of spectral multiplicity:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Chelsea
1972
|
| Edition: | 2. ed., repr. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 114 S. |
| ISBN: | 0828400822 |
Staff View
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| 245 | 1 | 0 | |a Introduction to Hilbert space and the theory of spectral multiplicity |c by Paul R. Halmos |
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Record in the Search Index
| _version_ | 1804117267246481408 |
|---|---|
| adam_text | CONTENTS
Page
Preface 3
§0. Prerequisites and Notation 8
CHAPTER I
THE GEOMETRY OF HILBERT SPACE
§1. Linear Functionals 11
§2. Bilinear Functionals 12
§3. Quadratic Forms 12
§4. Inner Product and Norm 13
§5. The Inequalities of Bessel and Schwarz 14
§6. Hilbert Space 16
§7. Infinite Sums 17
§8. Conditions for Summability 19
§9. Examples of Hilbert Spaces 20
§10. Subspaces 21
§11. Vectors in and out of Subspaces 23
§12. Orthogonal Complements 24
§13. Vector Sums 25
§14. Bases 27
§15. A Non closed Vector Sum 28
§16. Dimension 29
§17. Boundedness 31
§18. Bounded Bilinear Functionals 32
CHAPTER II
THE ALGEBRA OF OPERATORS
§19. Operators 35
§20. Examples of Operators 36
§21. Inverses 37
§22. Adjoints 38
§23. Invariance 40
5
6 CONTENTS
§24. Hermitian Operators 41
§25. Normal and Unitary Operators 42
§26. Projections 43
§27. Projections and Subspaces 44
§28. Sums of Projections 46
§29. Products and Differences of Projections 47
§30. Infima and Suprema of Projections 49
§31. The Spectrum of an Operator 50
§32. Compactness of Spectra 52
§33. Transforms of Spectra , 53
§34. The Spectrum of a Hermitian Operator 54
§35. Spectral Heuristics 56
§36. Spectral Measures 58
§37. Spectral Integrals 60
§38. Regular Spectral Measures 61
§39. Real and Complex Spectral Measures 63
§40. Complex Spectral Integrals 65
§41. Description of the Spectral Subspaces 66
§42. Characterization of the Spectral Subspaces 68
§43. The Spectral Theorem for Hermitian Operators 69
§44. The Spectral Theorem for Normal Operators 71
CHAPTER III
THE ANALYSIS OF SPECTRAL MEASURES
§45. The Problem of Unitary Equivalence 74
§46. Multiplicity Functions in Finite dimensional Spaces 76
§47. Measures 77
§48. Boolean Operations on Measures 79
§49. Multiplicity Functions 80
§50. The Canonical Example of a Spectral Measure 83
§51. Finite dimensional Spectral Measures 84
§52. Simple Finite dimensional Spectral Measures 85
§53. The Commutator of a Set of Projections 87
§54. Pairs of Commutators 88
§55. Columns 89
§56. Rows 90
§57. Cycles 91
§58. Separable Projections 92
§59. Characterizations of Rows 93
CONTENTS 7
§60. Cycles and Rows 95
§61. The Existence of Rows 96
§62. Orthogonal Systems 97
§63. The Power of a Maximal Orthogonal System 99
§64. Multiplicities 100
§65. Measures from Vectors 102
§66. Subspaces from Measures 104
§67. The Multiplicity Function of a Spectral Measure 106
§68. Conclusion 108
References 109
Bibliography 112
|
| any_adam_object | 1 |
| author | Halmos, Paul R. 1916-2006 |
| author_GND | (DE-588)118746677 |
| author_facet | Halmos, Paul R. 1916-2006 |
| author_role | aut |
| author_sort | Halmos, Paul R. 1916-2006 |
| author_variant | p r h pr prh |
| building | Verbundindex |
| bvnumber | BV002976714 |
| classification_rvk | SK 600 |
| ctrlnum | (OCoLC)25565774 (DE-599)BVBBV002976714 |
| dewey-full | 515.7222 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.722 2 |
| dewey-search | 515.722 2 |
| dewey-sort | 3515.722 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed., repr. |
| format | Book |
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| id | DE-604.BV002976714 |
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| indexdate | 2024-07-09T15:51:41Z |
| institution | BVB |
| isbn | 0828400822 |
| language | English |
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| physical | 114 S. |
| publishDate | 1972 |
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| publisher | Chelsea |
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| spelling | Halmos, Paul R. 1916-2006 Verfasser (DE-588)118746677 aut Introduction to Hilbert space and the theory of spectral multiplicity by Paul R. Halmos 2. ed., repr. New York, NY Chelsea 1972 114 S. txt rdacontent n rdamedia nc rdacarrier Algèbres d'opérateurs ram Hilbert, Espaces de ram Théorie spectrale (mathématiques) ram Operatortheorie (DE-588)4075665-8 gnd rswk-swf Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Operator (DE-588)4130529-2 gnd rswk-swf Spektralmaß (DE-588)4182167-1 gnd rswk-swf Hilbert-Raum (DE-588)4159850-7 gnd rswk-swf Operatortheorie (DE-588)4075665-8 s DE-604 Operator (DE-588)4130529-2 s Spektraltheorie (DE-588)4116561-5 s 1\p DE-604 Hilbert-Raum (DE-588)4159850-7 s 2\p DE-604 Spektralmaß (DE-588)4182167-1 s 3\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001863610&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Halmos, Paul R. 1916-2006 Introduction to Hilbert space and the theory of spectral multiplicity Algèbres d'opérateurs ram Hilbert, Espaces de ram Théorie spectrale (mathématiques) ram Operatortheorie (DE-588)4075665-8 gnd Spektraltheorie (DE-588)4116561-5 gnd Operator (DE-588)4130529-2 gnd Spektralmaß (DE-588)4182167-1 gnd Hilbert-Raum (DE-588)4159850-7 gnd |
| subject_GND | (DE-588)4075665-8 (DE-588)4116561-5 (DE-588)4130529-2 (DE-588)4182167-1 (DE-588)4159850-7 |
| title | Introduction to Hilbert space and the theory of spectral multiplicity |
| title_auth | Introduction to Hilbert space and the theory of spectral multiplicity |
| title_exact_search | Introduction to Hilbert space and the theory of spectral multiplicity |
| title_full | Introduction to Hilbert space and the theory of spectral multiplicity by Paul R. Halmos |
| title_fullStr | Introduction to Hilbert space and the theory of spectral multiplicity by Paul R. Halmos |
| title_full_unstemmed | Introduction to Hilbert space and the theory of spectral multiplicity by Paul R. Halmos |
| title_short | Introduction to Hilbert space and the theory of spectral multiplicity |
| title_sort | introduction to hilbert space and the theory of spectral multiplicity |
| topic | Algèbres d'opérateurs ram Hilbert, Espaces de ram Théorie spectrale (mathématiques) ram Operatortheorie (DE-588)4075665-8 gnd Spektraltheorie (DE-588)4116561-5 gnd Operator (DE-588)4130529-2 gnd Spektralmaß (DE-588)4182167-1 gnd Hilbert-Raum (DE-588)4159850-7 gnd |
| topic_facet | Algèbres d'opérateurs Hilbert, Espaces de Théorie spectrale (mathématiques) Operatortheorie Spektraltheorie Operator Spektralmaß Hilbert-Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001863610&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT halmospaulr introductiontohilbertspaceandthetheoryofspectralmultiplicity |