Noncommutative dynamics and E-semigroups:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
2003
|
| Series: | Springer monographs in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 427 - 430 |
| Physical Description: | X, 434 S. 25 cm |
| ISBN: | 0387001514 |
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Record in the Search Index
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|---|---|
| adam_text | WILLIAM ARVESON NONCOMMUTATIVE DYNAMICS AND E-SEMIGROUPS SPRINGER
CONTENTS PREFACE V CHAPTER 1. DYNAMICAL ORIGINS 1 1.1. THE FLOW OF TIME
IN QUANTUM THEORY 1 1.2. CAUSALITY AND INTERACTIONS 5 1.3. SEMIGROUPS OF
ENDOMORPHISMS 9 1.4. EXISTENCE OF DYNAMICS 13 PART 1. INDEX AND
PERTURBATION THEORY 17 CHAPTER 2. ^-SEMIGROUPS 18 2.1. THE CAR/CCR FLOWS
19 27 31 33 41 45 53 56 59 64 66 67 70 72 74 77 83 87 93 99 101 101 112
116 117 121 125 2.2. 2.3. 2.4. 2.5. 2.6. 2.7. 2.8. 2.9. 2.10. CHAPTER
3.1. 3.2. 3.3. 3.4. 3.5. 3.6. 3.7. 3.8. 3.9. CHAPTER 4.1. 4.2. 4.3. 4.4.
4.5. 4.6. COCYCLE PERTURBATIONS MEASURABILITY AND CONTINUITY OF COCYCLES
CONCRETE PRODUCT SYSTEMS UNITS AND THE NUMERICAL INDEX COMPUTATION OF
THE INDEX TYPE AND DECOMPOSABILITY THE GAUGE GROUP G(A) PURE
I?O-SEMIGROUPS AND ABSORBING STATES NOTES AND REMARKS 3. CONTINUOUS
TENSOR PRODUCTS TENSOR PRODUCT SYSTEMS REPRESENTATIONS OF PRODUCT
SYSTEMS THE CONTINUOUS FOCK SPACE L 2 ( 1 ) MULTIPLIERS OF (0,OO) THE
CLASSIFYING SEMIGROUP E UNITS, DIMENSION, AND INDEX ADDITIVITY OF THE
INDEX AUTOMORPHISMS AND THE GAUGE GROUP NOTES AND REMARKS 4. SPECTRAL
C*-ALGEBRAS REGULAR REPRESENTATION OF C*(E) IRREDUCIBILITY NUCLEARITY
WIENER-HOPF PERTURBATIONS AND STABILIZATION AMENABILITY I AMENABILITY II
VIII CONTENTS 4.7. INFINITESIMAL DESCRIPTION OF C*(E) 130 4.8.
DECREASING WEIGHTS 133 4.9. STATE SPACE OF C*(E) 138 4.10. EXISTENCE OF
^O-SEMIGROUPS 145 4.11. SIMPLICITY 148 4.12. THE C*-ALGEBRAS W N 155
4.13. NOTES AND REMARKS 158 PART 2. CLASSIFICATION: TYPE I CASES 161
CHAPTER 5. PATH SPACES 162 5.1. DEFINITIONS AND EXAMPLES 162 5.2.
ADDITIVE FORMS AND THEIR EXPONENTIALS 166 5.3. EXACTNESS OF ADDITIVE
COCYCLES 172 5.4. STRONGLY SPANNING SETS 178 5.5. CLASSIFICATION OF
METRIC PATH SPACES 180 5.6. EXPONENTIALS OF METRIC PATH SPACES 196
CHAPTER 6. DECOMPOSABLE PRODUCT SYSTEMS 199 6.1. CONTINUITY OF THE
MODULUS 202 6.2. DECOMPOSABLE VECTORS 205 6.3. CONTINUITY AND
NORMALIZATION 207 6.4. CONTINUOUS LOGARITHMS 210 6.5. INFINITE
DIVISIBILITY 215 6.6. EXISTENCE OF MEASURABLE PROPAGATORS 223 6.7.
APPLICATIONS TO PRODUCT SYSTEMS 225 6.8. CLASSIFICATION OF O- SEM
IGROUPS 232 6.9. NOTES AND REMARKS 233 PART 3. NONCOMMUTATIVE LAPLACIANS
235 CHAPTER 7. CP-SEMIGROUPS 236 7.1. BASIC PROPERTIES 238 7.2. HARMONIC
ANALYSIS OF THE COMMUTATION RELATIONS 240 7.3. EXAMPLES: CCR HEAT FLOW,
CAUCHY FLOW 242 7.4. GENERATORS AND THE DOMAIN ALGEBRA 248 7.5. FURTHER
DISCUSSION OF EXAMPLES 252 7.6. NOTES AND REMARKS 253 CHAPTER 8.
C*-GENERATORS AND DILATION THEORY 254 8.1. DILATION AND COMPRESSION 255
8.2. MOMENT POLYNOMIALS 257 8.3. THE HIERARCHY OF DILATIONS 260 8.4.
GENERATORS OF C*-DYNAMICS 265 8.5. EXISTENCE OF C*-DILATIONS 269 8.6.
EXISTENCE OF W- -DILATIONS 274 8.7. EXAMPLES OF DILATIONS 279 8.8. TYPE
I PART OF AN 0 -SEMIGROUP 281 8.9. MORE ON MINIMALITY 284 8.10. UNITS
OF CP-SEMIGROUPS AND THEIR DILATIONS 293 CONTENTS LX 8.11. PURE
CP-SEMIGROUPS AND THEIR DILATIONS 299 8.12. NOTES AND REMARKS 302
CHAPTER 9. INDEX THEORY FOR CP-SEMIGROUPS 304 9.1. METRIC OPERATOR
SPACES 304 9.2. COMPOSITIONS OF COMPLETELY POSITIVE MAPS 308 9.3.
NUMERICAL INDEX 312 9.4. INDEX OF THE DILATION 319 9.5. NOTES AND
REMARKS 323 CHAPTER 10. BOUNDED GENERATORS 324 10.1. GEOMETRY OF THE
SYMBOL 324 10.2. PERTURBATIONS, RANK OF THE SYMBOL 333 10.3. COMPUTATION
OF UNITS 338 10.4. COMPLETENESS OF THE COVARIANCE FUNCTION 345 10.5.
SUBORDINATE CP-SEMIGROUPS 348 10.6. TYPE OF THE MINIMAL DILATION 351
10.7. NOTES AND REMARKS 354 PART 4. CAUSALITY AND DYNAMICS 355 CHAPTER
11. PURE PERTURBATIONS OF CAR/CCR FLOWS 356 11.1. CONSTRUCTIONS IN
MATRIX ALGEBRAS 357 11.2. ERGODICITY VERSUS PURITY IN MATRIX ALGEBRAS
363 11.3. EXISTENCE OF COCYCLE PERTURBATIONS 367 11.4. NOTES AND REMARKS
372 CHAPTER 12. INTERACTION THEORY 374 12.1. INDEX AND THE EXISTENCE OF
DYNAMICS 374 12.2. EIGENVALUE LISTS OF NORMAL STATES 376 12.3. TOWERS:
CONVERGENCE OF EIGENVALUE LISTS 378 12.4. THE INTERACTION INEQUALITY 385
12.5. NOTES, REMARKS, PROBLEMS 387 PART 5. TYPE III EXAMPLES 389 CHAPTER
13. POWERS EXAMPLES 390 13.1. QUASI-FREE STATES OF THE CAR ALGEBRA 390
13.2. EXAMPLES BASED ON QUASI-FREE STATES 393 13.3. ROLE OF TOEPLITZ AND
HANKEL OPERATORS 397 13.4. A TRACE FORMULA 402 13.5. ALMOST INVARIANT
SUBSPACES 403 13.6. THE NONEXISTENCE OF UNITS 406 13.7. NOTES AND
REMARKS 411 CHAPTER 14. TSIRELSON-VERSHIK PRODUCT SYSTEMS 412 14.1.
CORRELATION FUNCTIONS AND QUASI-ORTHOGONALITY 412 14.2. GAUSSIAN SPACES
415 14.3. EQUIVALENCE OPERATORS ON GAUSSIAN SPACES 417 14.4. THE L 2
SPACE OF A MEASURE CLASS 419 X CONTENTS 14.5. PRODUCT SYSTEMS OF TYPE
III 423 14.6. NOTES AND REMARKS 425 BIBLIOGRAPHY 427 INDEX 431
|
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| indexdate | 2024-07-09T19:16:24Z |
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| spelling | Arveson, William 1934- Verfasser (DE-588)128603577 aut Noncommutative dynamics and E-semigroups William Arveson New York [u.a.] Springer 2003 X, 434 S. 25 cm txt rdacontent n rdamedia nc rdacarrier Springer monographs in mathematics Literaturverz. S. 427 - 430 Algèbres non commutatives Endomorphismes (Théorie des groupes) Semi-groupes Endomorphisms (Group theory) Noncommutative algebras Semigroups Operatorhalbgruppe (DE-588)4172620-0 gnd rswk-swf Nichtkommutative Algebra (DE-588)4304013-5 gnd rswk-swf Endomorphismus (DE-588)4280121-7 gnd rswk-swf Operatortheorie (DE-588)4075665-8 gnd rswk-swf Nichtkommutative Algebra (DE-588)4304013-5 s Endomorphismus (DE-588)4280121-7 s Operatorhalbgruppe (DE-588)4172620-0 s Operatortheorie (DE-588)4075665-8 s DE-604 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010431053&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Arveson, William 1934- Noncommutative dynamics and E-semigroups Algèbres non commutatives Endomorphismes (Théorie des groupes) Semi-groupes Endomorphisms (Group theory) Noncommutative algebras Semigroups Operatorhalbgruppe (DE-588)4172620-0 gnd Nichtkommutative Algebra (DE-588)4304013-5 gnd Endomorphismus (DE-588)4280121-7 gnd Operatortheorie (DE-588)4075665-8 gnd |
| subject_GND | (DE-588)4172620-0 (DE-588)4304013-5 (DE-588)4280121-7 (DE-588)4075665-8 |
| title | Noncommutative dynamics and E-semigroups |
| title_auth | Noncommutative dynamics and E-semigroups |
| title_exact_search | Noncommutative dynamics and E-semigroups |
| title_full | Noncommutative dynamics and E-semigroups William Arveson |
| title_fullStr | Noncommutative dynamics and E-semigroups William Arveson |
| title_full_unstemmed | Noncommutative dynamics and E-semigroups William Arveson |
| title_short | Noncommutative dynamics and E-semigroups |
| title_sort | noncommutative dynamics and e semigroups |
| topic | Algèbres non commutatives Endomorphismes (Théorie des groupes) Semi-groupes Endomorphisms (Group theory) Noncommutative algebras Semigroups Operatorhalbgruppe (DE-588)4172620-0 gnd Nichtkommutative Algebra (DE-588)4304013-5 gnd Endomorphismus (DE-588)4280121-7 gnd Operatortheorie (DE-588)4075665-8 gnd |
| topic_facet | Algèbres non commutatives Endomorphismes (Théorie des groupes) Semi-groupes Endomorphisms (Group theory) Noncommutative algebras Semigroups Operatorhalbgruppe Nichtkommutative Algebra Endomorphismus Operatortheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010431053&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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