Real operator algebras:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
River Edge, NJ [u.a.]
World Scientific
2003
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 241 S. |
| ISBN: | 9812383808 |
Internformat
MARC
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| 100 | 1 | |a Li, Bing-Ren |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Real operator algebras |c Bingren Li |
| 264 | 1 | |a River Edge, NJ [u.a.] |b World Scientific |c 2003 | |
| 300 | |a XIII, 241 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Algèbres d'opérateurs | |
| 650 | 4 | |a Algèbres normées | |
| 650 | 4 | |a Banach, Algèbres de | |
| 650 | 4 | |a Banach algebras | |
| 650 | 4 | |a Operator algebras | |
| 650 | 0 | 7 | |a Operatoralgebra |0 (DE-588)4129366-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Operatoralgebra |0 (DE-588)4129366-6 |D s |
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Datensatz im Suchindex
| _version_ | 1804133341865181184 |
|---|---|
| adam_text | Contents
Preface v
1. Real Banach and Hubert Spaces 1
1.1 Complexification of real Banach and Hilbert spaces..... 1
1.2 Spectral decomposition theorem in real Hilbert spaces ... 9
2. Real Banach Algebras 15
2.1 Definition and complexification................ 15
2.2 Divisible real Banach algebras................. 20
2.3 The topological group of invertible elements and its principal
component ........................... 21
2.4 Radical............................. 22
2.5 Functional calculus....................... 25
2.6 Arens products......................... 26
2.7 Abelian real Banach algebras................. 28
3. Real Banach * Algebras 37
3.1 Some basic lemmas....................... 37
3.2 Abelian real Banach * algebras................ 40
3.3 Positive linear functionals and GNS construction...... 42
3.4 * Representations and topologically irreducible * represen-
tations .............................. 45
3.5 * Radical............................ 48
3.6 Symmetric real Banach * algebras .............. 51
4. Fundamentals of Real Von Neumann Algebras 59
xi
xii Real Operator Algebras
4.1 Banach spaces of operators on a real Hilbert space..... 59
4.2 Locally convex topologies in B(H).............. 61
4.3 Von Neumann s double commutation theorem ....... 63
4.4 Kaplansky s density theorem, tensor product commutation
theorem, and comparison of projections........... 68
4.5 Positive linear functionals................... 72
4.6 cr-Finite real VN algebras................... 76
5. Fundamentals of Real C*-Algebras 77
5.1 Definition and basic properties................ 77
5.2 Positive functionals and equivalent definition of real C*-
algebras............................. 83
5.3 Pure real states, their left kernels, and irreducible * repre-
sentations ............................ 88
5.4 Ideals, quotient algebras and extreme points......... 98
5.5 The bidual of a real C*-algebra................ 99
5.6 The uniqueness of * operation................. 104
5.7 Finite-dimensional real C*-algebras............. 108
5.8 The enveloping real C*-algebra of a hermitian real Banach
* algebra ............................ 110
5.9 * Representations of abelian real C*-algebras........ 120
6. Real W*-Algebras 123
6.1 Definition and basic properties................ 123
6.2 Normal linear functionals and singular linear functionals . . 130
6.3 Abelian real W-algebras................... 132
6.4 Unitaries and partial isometries................ 141
7. Gelfand-Naimark Conjecture in the Real Case 147
7.1 Real C*-equivalent algebras.................. 147
7.2 The closed unit ball of a unital real C*-algebra....... 152
7.3 Gelfand-Naimark conjecture in the real case......... 161
8. Classification of Real W-Algebras 167
8.1 Classification of real W*-algebras.............. 167
8.2 Finite real W*-algebras.................... 172
8.3 Properly infinite real W-algebras.............. 175
8.4 Semi-finite real W-algebras................. 176
Contents xiii
8.5 Purely infinite (type III) real W-algebras.......... 183
8.6 Properties on other classes of real W*-algebras....... 184
8.7 Real factors and tensor products............... 188
9. Real Reduction Theory 191
9.1 Real measurable fields of Hubert spaces........... 191
9.2 Real measurable fields of operators.............. 197
9.3 Real measurable fields of VN algebras............ 200
9.4 Real reduction theory..................... 205
10. (AF) Real C*-Algebras 211
10.1 Standard matrix unit ..................... 211
10.2 Technical lemmas........................ 218
10.3 Definition and basic properties................ 228
Bibliography 233
Notation Index 237
Index 239
|
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| id | DE-604.BV019834180 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T20:07:11Z |
| institution | BVB |
| isbn | 9812383808 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013159203 |
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| physical | XIII, 241 S. |
| publishDate | 2003 |
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| publisher | World Scientific |
| record_format | marc |
| spelling | Li, Bing-Ren Verfasser aut Real operator algebras Bingren Li River Edge, NJ [u.a.] World Scientific 2003 XIII, 241 S. txt rdacontent n rdamedia nc rdacarrier Algèbres d'opérateurs Algèbres normées Banach, Algèbres de Banach algebras Operator algebras Operatoralgebra (DE-588)4129366-6 gnd rswk-swf Operatoralgebra (DE-588)4129366-6 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013159203&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Li, Bing-Ren Real operator algebras Algèbres d'opérateurs Algèbres normées Banach, Algèbres de Banach algebras Operator algebras Operatoralgebra (DE-588)4129366-6 gnd |
| subject_GND | (DE-588)4129366-6 |
| title | Real operator algebras |
| title_auth | Real operator algebras |
| title_exact_search | Real operator algebras |
| title_full | Real operator algebras Bingren Li |
| title_fullStr | Real operator algebras Bingren Li |
| title_full_unstemmed | Real operator algebras Bingren Li |
| title_short | Real operator algebras |
| title_sort | real operator algebras |
| topic | Algèbres d'opérateurs Algèbres normées Banach, Algèbres de Banach algebras Operator algebras Operatoralgebra (DE-588)4129366-6 gnd |
| topic_facet | Algèbres d'opérateurs Algèbres normées Banach, Algèbres de Banach algebras Operator algebras Operatoralgebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013159203&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT libingren realoperatoralgebras |