Geometry of state spaces of operator algebras:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
2003
|
| Series: | Mathematics: theory & applications
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. [451] - 458 |
| Physical Description: | XIII, 467 S.: graph. Darst. |
| ISBN: | 3764343192 0817643192 |
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Record in the Search Index
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|---|---|
| adam_text | ERIK M. ALFSEN FREDERIC W. SHULTZ GEOMETRY OF STATE SPACES OF OPERATOR
ALGEBRAS F; BIRKHAUSER- - ., - BOSTON * BASEL * BERLIN CONTENTS PREFACE
V PART I: JORDAN ALGEBRAS AND THEIR STATE SPACES 1 CHAPTER 1:
JB-ALGEBRAS 3 INTRODUCTION 3 QUOTIENTS OF JB-ALGEBRAS 16 PROJECTIONS AND
COMPRESSIONS IN JB-ALGEBRAS 22 OPERATOR COMMUTATIVITY 26 ORDER
DERIVATIONS ON JB-ALGEBRAS 30 APPENDIX: PROOF OF PROPOSITION 1.3 32
NOTES 34 CHAPTER 2: JBW-ALGEBRAS 37 INTRODUCTION 37 ORTHOGONALITY AND
RANGE PROJECTIONS 42 SPECTRAL RESOLUTIONS 46 THE LATTICES OF PROJECTIONS
AND COMPRESSIONS 48 CR-WEAKLY CLOSED HEREDITARY SUBALGEBRAS 54 CENTER OF
A JBW-ALGEBRA 55 THE BIDUAL OF A JB-ALGEBRA 58 THE PREDUAL OF A
JBW-ALGEBRA 62 JW-ALGEBRAS 70 ORDER AUTOMORPHISMS OF A JB-ALGEBRA 73
ABSTRACT CHARACTERIZATION OF COMPRESSIONS 75 NOTES 76 CHAPTER 3:
STRUCTURE OF JBW-ALGEBRAS 79 EQUIVALENCE OF PROJECTIONS 79 COMPARISON
THEORY 83 GLOBAL STRUCTURE OF TYPE I JBW-ALGEBRAS 85 CLASSIFICATION OF
TYPE I JBW-FACTORS 87 ATOMIC JBW-ALGEBRAS 96 NOTES 101 XII CONTENTS
CHAPTER 4: REPRESENTATIONS OF JB-ALGEBRAS 103 REPRESENTATIONS OF
JBW-FACTORS AS JW-ALGEBRAS 103 REPRESENTATIONS OF JB-ALGEBRAS AS JORDAN
OPERATOR ALGEBRAS . . 108 REVERSIBILITY 113 THE UNIVERSAL C*-ALGEBRA OF
A JB-ALGEBRA 120 CARTESIAN TRIPLES 127 NOTES 137 CHAPTER 5: STATE SPACES
OF JORDAN ALGEBRAS 139 CARRIER PROJECTIONS 139 THE LATTICE OF PROJECTIVE
FACES 143 DUAL MAPS OF JORDAN HOMOMORPHISMS 144 TRACES ON JB-ALGEBRAS
147 NORM CLOSED FACES OF JBW NORMAL STATE SPACES 157 THE HILBERT BALL
PROPERTY 168 THE (T-CONVEX HULL OF EXTREME POINTS . 172 TRACE CLASS
ELEMENTS OF ATOMIC JBW-ALGEBRAS 178 SYMMETRY AND ELLIPTICITY 183 NOTES
188 CHAPTER 6: DYNAMICAL CORRESPONDENCES 191 CONNES ORIENTATIONS 191
DYNAMICAL CORRESPONDENCES IN JB-ALGEBRAS 196 COMPARING NOTIONS OF
ORIENTATION 205 NOTES 206 PART II: CONVEXITY AND SPECTRAL THEORY 209
CHAPTER 7: GENERAL COMPRESSIONS 211 PROJECTIONS IN CONES 211 DEFINITION
OF GENERAL COMPRESSIONS 222 PROJECTIVE UNITS AND PROJECTIVE FACES 227
GEOMETRY OF PROJECTIVE FACES 241 NOTES 249 CHAPTER 8: SPECTRAL THEORY
251 THE LATTICE OF COMPRESSIONS 251 THE LATTICE OF COMPRESSIONS WHEN A =
V* 260 SPACES IN SPECTRAL DUALITY 271 SPECTRAL CONVEX SETS 291 APPENDIX.
PROOF OF THEOREM 8.87 303 NOTES 311 CONTENTS XIII PART III: STATE SPACE
CHARACTERIZATIONS 313 CHAPTER 9: CHARACTERIZATION OF JORDAN ALGEBRA
STATE SPACES 315 THE PURE STATE PROPERTIES 315 THE HILBERT BALL PROPERTY
319 ATOMICITY 323 THE TYPE I FACTOR CASE 325 CHARACTERIZATION OF STATE
SPACES OF JB-ALGEBRAS 339 CHARACTERIZATION OF NORMAL STATE SPACES OF JBW
ALGEBRAS . . . 343 NOTES 354 CHAPTER 10: CHARACTERIZATION OF NORMAL
STATE SPACES OF VON NEUMANN ALGEBRAS 357 THE NORMAL STATE SPACE OF B(H)
357 3-FRAMES, CARTESIAN TRIPLES, AND BLOWN UP 3-BALLS 358 THE
GENERALIZED 3-BALL PROPERTY 365 NOTES 373 CHAPTER 11: CHARACTERIZATION
OF C*-ALGEBRA STATE SPACES . 375 STATES AND REPRESENTATIONS OF
JB-ALGEBRAS 376 REVERSIBILITY OF JB-ALGEBRAS OF COMPLEX TYPE 382 THE
STATE SPACE OF THE UNIVERSAL C*-ALGEBRA OF A JB-ALGEBRA . . 393
ORIENTABILITY 402 CHARACTERIZATION OF C*-ALGEBRA STATE SPACES AMONG
JB-ALGEBRA STATE SPACES 406 CHARACTERIZATION OF C*-ALGEBRA STATE SPACES
AMONG CONVEX SETS 414 NOTES . 417 APPENDIX ; 41 9 BIBLIOGRAPHY 451 INDEX
459
|
| any_adam_object | 1 |
| author | Alfsen, Erik M. 1930- Shultz, Frederic W. 1945- |
| author_GND | (DE-588)123108330 (DE-588)123108284 |
| author_facet | Alfsen, Erik M. 1930- Shultz, Frederic W. 1945- |
| author_role | aut aut |
| author_sort | Alfsen, Erik M. 1930- |
| author_variant | e m a em ema f w s fw fws |
| building | Verbundindex |
| bvnumber | BV016481423 |
| callnumber-first | Q - Science |
| callnumber-label | QA10 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 600 SK 620 |
| ctrlnum | (OCoLC)50560356 (DE-599)BVBBV016481423 |
| dewey-full | 530.12/01/5113 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.12/01/5113 |
| dewey-search | 530.12/01/5113 |
| dewey-sort | 3530.12 11 45113 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| id | DE-604.BV016481423 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:11:01Z |
| institution | BVB |
| isbn | 3764343192 0817643192 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010188706 |
| oclc_num | 50560356 |
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| owner | DE-29T DE-355 DE-BY-UBR DE-824 DE-11 DE-20 |
| owner_facet | DE-29T DE-355 DE-BY-UBR DE-824 DE-11 DE-20 |
| physical | XIII, 467 S.: graph. Darst. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Birkhäuser |
| record_format | marc |
| series2 | Mathematics: theory & applications |
| spelling | Alfsen, Erik M. 1930- Verfasser (DE-588)123108330 aut Geometry of state spaces of operator algebras Erik M. Alfsen ; Frederic W. Shultz Boston [u.a.] Birkhäuser 2003 XIII, 467 S.: graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics: theory & applications Literaturverz. S. [451] - 458 Axiomatic set theory Functional analysis Jordan algebras Lattice theory Quantum logic Zustandsraum (DE-588)4132647-7 gnd rswk-swf Operatoralgebra (DE-588)4129366-6 gnd rswk-swf Operatoralgebra (DE-588)4129366-6 s Zustandsraum (DE-588)4132647-7 s DE-604 Shultz, Frederic W. 1945- Verfasser (DE-588)123108284 aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010188706&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Alfsen, Erik M. 1930- Shultz, Frederic W. 1945- Geometry of state spaces of operator algebras Axiomatic set theory Functional analysis Jordan algebras Lattice theory Quantum logic Zustandsraum (DE-588)4132647-7 gnd Operatoralgebra (DE-588)4129366-6 gnd |
| subject_GND | (DE-588)4132647-7 (DE-588)4129366-6 |
| title | Geometry of state spaces of operator algebras |
| title_auth | Geometry of state spaces of operator algebras |
| title_exact_search | Geometry of state spaces of operator algebras |
| title_full | Geometry of state spaces of operator algebras Erik M. Alfsen ; Frederic W. Shultz |
| title_fullStr | Geometry of state spaces of operator algebras Erik M. Alfsen ; Frederic W. Shultz |
| title_full_unstemmed | Geometry of state spaces of operator algebras Erik M. Alfsen ; Frederic W. Shultz |
| title_short | Geometry of state spaces of operator algebras |
| title_sort | geometry of state spaces of operator algebras |
| topic | Axiomatic set theory Functional analysis Jordan algebras Lattice theory Quantum logic Zustandsraum (DE-588)4132647-7 gnd Operatoralgebra (DE-588)4129366-6 gnd |
| topic_facet | Axiomatic set theory Functional analysis Jordan algebras Lattice theory Quantum logic Zustandsraum Operatoralgebra |
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