Operator algebras and quantum statistical mechanics: 1 C*- and W*-algebras, symmetry groups, decomposition of states
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York ; Berlin ; Heidelberg
Springer
1979
|
| Schriftenreihe: | Texts and monographs in physics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 500 Seiten |
| ISBN: | 0387091874 3540091874 |
Internformat
MARC
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| 245 | 1 | 0 | |a Operator algebras and quantum statistical mechanics |n 1 |p C*- and W*-algebras, symmetry groups, decomposition of states |c Ola Bratteli ; Derek W. Robinson |
| 264 | 1 | |a New York ; Berlin ; Heidelberg |b Springer |c 1979 | |
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Datensatz im Suchindex
| _version_ | 1804141429352562688 |
|---|---|
| adam_text | Contents Volume 1
Introduction 1
Notes and Remarks 16
C* Algebras and von Newmann Algebras 17
2.1. C* Algebras 19
2.1.1. Basic Definitions and Structure 19
2.2. Functional and Spectral Analysis 25
2.2.1. Resolvents, Spectra, and Spectral Radius 25
2.2.2. Positive Elements 32
2.2.3. Approximate Identities and Quotient Algebras 39
2.3. Representations and States 42
2.3.1. Representations 42
2.3.2. States 48
2.3.3. Construction of Representations 54
2.3.4. Existence of Representations 58
2.3.5. Commutative C* Algebras 61
vii
viii Contents
2.4. von Neumann Algebras 65
2.4.1. Topologies on if (§) 65
2.4.2. Definition and Elementary Properties of von Neumann Algebras 71
2.4.3. Normal States and the Predual 75
2.4.4. Quasi Equivalence of Representations 79
2.5. Tomita Takesaki Modular Theory and Standard Forms of von Neumann
Algebras 83
2.5.1. ff Finite von Neumann Algebras 84
2.5.2. The Modular Group 86
2.5.3. Integration and Analytic Elements for One Parameter Groups of
Isometries on Banach Spaces 97
2.5.4. Self Dual Cones and Standard Forms 102
2.6. Quasi Local Algebras 118
2.6.1. Cluster Properties 118
2.6.2. Topological Properties 129
2.6.3. Algebraic Properties 133
2.7. Miscellaneous Results and Structure 136
2.7.1. Dynamical Systems and Crossed Products 136
2.7.2. Tensor Products of Operator Algebras 142
2.7.3. Weights on Operator Algebras; Self Dual Cones of General von
Neumann Algebras; Duality and Classification of Factors;
Classification of C* Algebras 145
Notes and Remarks 152
Groups, Semigroups, and Generators 157
3.1. Banach Space Theory 159
3.1.1. Uniform Continuity 161
3.1.2. Strong, Weak, and Weak* Continuity 163
3.1.3. Convergence Properties 183
3.1.4. Perturbation Theory 189
3.1.5. Approximation Theory 198
3.2. Algebraic Theory 205
3.2.1. Positive Linear Maps and Jordan Morphisms 205
3.2.2. General Properties of Derivations 228
Contents ix
3.2.3. Spectral Theory and Bounded Derivations 244
3.2.4. Derivations and Automorphism Groups 259
3.2.5. Spatial Derivations and Invariant States 263
3.2.6. Approximation Theory for Automorphism Groups 285
Notes and Remarks 298
Decomposition Theory 309
4.1. General Theory 311
4.1.1. Introduction 311
4.1.2. Barycentric Decompositions 315
4.1.3. Orthogonal Measures 333
4.1.4. Borel Structure of States 344
4.2. Extremal, Central, and Subcentral Decompositions 353
4.2.1. Extremal Decompositions 353
4.2.2. Central and Subcentral Decompositions 362
4.3. Invariant States 367
4.3.1. Ergodic Decompositions 367
4.3.2. Ergodic States 386
4.3.3. Locally Compact Abelian Groups 400
4.3.4. Broken Symmetry 416
4.4. Spatial Decomposition 432
4.4.1. General Theory 433
4.4.2. Spatial Decomposition and Decomposition of States 442
Notes and Remarks 451
References 459
Books and Monographs 461
Articles 464
List of Symbols 481
Subject Index 487
|
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| indexdate | 2024-07-09T22:15:44Z |
| institution | BVB |
| isbn | 0387091874 3540091874 |
| language | English |
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| physical | XII, 500 Seiten |
| publishDate | 1979 |
| publishDateSearch | 1979 |
| publishDateSort | 1979 |
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| spelling | Bratteli, Ola 1946-2015 (DE-588)1292586575 aut Operator algebras and quantum statistical mechanics 1 C*- and W*-algebras, symmetry groups, decomposition of states Ola Bratteli ; Derek W. Robinson New York ; Berlin ; Heidelberg Springer 1979 XII, 500 Seiten txt rdacontent n rdamedia nc rdacarrier Texts and monographs in physics Operatoralgebra (DE-588)4129366-6 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Statistische Mechanik (DE-588)4056999-8 gnd rswk-swf Algebra (DE-588)4001156-2 gnd rswk-swf Quantenstatistik (DE-588)4047991-2 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Operatoralgebra (DE-588)4129366-6 s Quantenstatistik (DE-588)4047991-2 s DE-604 Algebra (DE-588)4001156-2 s Statistik (DE-588)4056995-0 s Statistische Mechanik (DE-588)4056999-8 s Quantenmechanik (DE-588)4047989-4 s Robinson, Derek W. 1935- (DE-588)107889455 aut (DE-604)BV002354703 1 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019212286&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bratteli, Ola 1946-2015 Robinson, Derek W. 1935- Operator algebras and quantum statistical mechanics Operatoralgebra (DE-588)4129366-6 gnd Statistik (DE-588)4056995-0 gnd Statistische Mechanik (DE-588)4056999-8 gnd Algebra (DE-588)4001156-2 gnd Quantenstatistik (DE-588)4047991-2 gnd Quantenmechanik (DE-588)4047989-4 gnd |
| subject_GND | (DE-588)4129366-6 (DE-588)4056995-0 (DE-588)4056999-8 (DE-588)4001156-2 (DE-588)4047991-2 (DE-588)4047989-4 |
| title | Operator algebras and quantum statistical mechanics |
| title_auth | Operator algebras and quantum statistical mechanics |
| title_exact_search | Operator algebras and quantum statistical mechanics |
| title_full | Operator algebras and quantum statistical mechanics 1 C*- and W*-algebras, symmetry groups, decomposition of states Ola Bratteli ; Derek W. Robinson |
| title_fullStr | Operator algebras and quantum statistical mechanics 1 C*- and W*-algebras, symmetry groups, decomposition of states Ola Bratteli ; Derek W. Robinson |
| title_full_unstemmed | Operator algebras and quantum statistical mechanics 1 C*- and W*-algebras, symmetry groups, decomposition of states Ola Bratteli ; Derek W. Robinson |
| title_short | Operator algebras and quantum statistical mechanics |
| title_sort | operator algebras and quantum statistical mechanics c and w algebras symmetry groups decomposition of states |
| topic | Operatoralgebra (DE-588)4129366-6 gnd Statistik (DE-588)4056995-0 gnd Statistische Mechanik (DE-588)4056999-8 gnd Algebra (DE-588)4001156-2 gnd Quantenstatistik (DE-588)4047991-2 gnd Quantenmechanik (DE-588)4047989-4 gnd |
| topic_facet | Operatoralgebra Statistik Statistische Mechanik Algebra Quantenstatistik Quantenmechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019212286&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002354703 |
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