Unbounded operator algebras and representation theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel u.a.
Birkhäuser
1990
|
| Series: | Operator theory
37 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Lizenz d. Akad.-Verl., Berlin |
| Physical Description: | 380 S. |
| ISBN: | 3764323213 0817623213 |
Staff View
MARC
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| 100 | 1 | |a Schmüdgen, Konrad |d 1947- |e Verfasser |0 (DE-588)115774599 |4 aut | |
| 245 | 1 | 0 | |a Unbounded operator algebras and representation theory |c Konrad Schmüdgen |
| 264 | 1 | |a Basel u.a. |b Birkhäuser |c 1990 | |
| 300 | |a 380 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Operator theory |v 37 | |
| 500 | |a Lizenz d. Akad.-Verl., Berlin | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
1. Preliminaries 13
1.1. Locally Convex Spaces 13
1.2. Spaces of Linear Mappings and Spaces of Sesquilinear Forms 16
1.3. Ordered * Vector Spaces 19
1.4. * Algebras and Topological * Algebras 21
1.5. The Topologies xF, rn, r0 and rp, x , r° 22
1.6. Operators on Hilbert Space 27
1.7. Lie Groups, Lie Algebras and Enveloping Algebras 31
Notes 32
Part I. 0# Algebras and Topologies 33
2. O Families and Their Graph Topologies 35
2.1. O Families, O* Families and O* Algebras 35
2.2. The Graph Topology 39
2.3. The Locally Convex Space 3)^ 44
2.4. Bounded Sets in Quasi Frechet Domains 50
2.5. Examples and Counter Examples 54
2.6. The Positive Cone of an O* Algebra 59
Notes 63
3. Spaces of Linear Mappings Associated with O Families and Their Topologization 64
3.1. The Algebras B(2 2, 3 x) and 2(2)% 2 A) 64
3.2. The Vector Space 2(2)A, 2)$) 70
3.3. Topologies Generalizing the Operator Norm Topology 75
3.4. Some Density Results 86
3.5. The Weak and Strong Operator Topologies and the Ultraweak and Ultrastrong To¬
pologies 91
3.6. Continuity of * Representations 95
Notes 100
4. Topologies for O Families with Metrizable Graph Topologies 101
4.1. 0 Neighbourhood Bases for the Topologies x%, xjr, Xq and t*, v^, xc 101
4.2. Bounded Sets for the Topologies xb and rln 106
4.3. Commutatively Dominated Frechet Domains 108
4.4. General Results about the Topologies r , Xjy, xg 114
4.5. Topologies on Countably Generated O* Algebras 118
Notes 122
Contents 11
5. Ultra weakly Continuous Linear Functionals and Duality Theory 123
5.1. The Predual 123
5.2. The Generalized Trace 133
5.3. Representation of Linear Functionals by Density Matrices 138
5.4. The Duality Theorem 143
5.5. Characterizations of Montel Domains 149
Notes 153
6. The Generalized Calkin Algebra and the * Algebra f+(2 ) 155
6.1. Completely Continuous Linear Mappings 155
6.2. Faithful * Representations of the Generalized Calkin Algebra 161
6.3. Derivations and * Automorphisms of jt+(3 ) 166
6.4. Atomic * AIgebra8 170
Notes 174
7. Commutants 175
7.1. Some Results on Strongly Commuting Self Adjoint Operators 175
7.2. Unbounded and Bounded Commutants of O* Algebras 178
7.3. Commutants of Strictly Self Adjoint O* Algebras 187
7.4. A Class of Subspaces of 2(2 m #jj) 193
Notes 198
Part II: ? Representations 199
8. Basics of ^ Representations 201
8.1. Representations and * Representations 201
8.2. Intertwining Operators 210
8.3. Invariant and Reducing Subspaces 213
8.4. Similarity, Unitary Equivalence and Disjointness of Representations 219
8.5. Induced Extensions 222
8.6. The Gelfand Neumark Segal Construction 227
Notes 234
9. Sell Adjoint Representations of Commutative * Algebras 236
9.1. Integrable Representations of Commutative * Algebras 236
9.2. Decomposition of Integrable Representations as Direct Sums of Cyclic Represen¬
tations 242
9.3. Two Classes of Couples of Self Adjoint Operators 244
9.4. Construction of Non Integrable Self Adjoint Representations of CfXj, x2] .... 252
Notes 258
10. Integrable Representations of Enveloping Algebras 260
10.1. The Infinitesimal Representation of a Unitary Representation 261
10.2. Elliptic Elements in the Enveloping Algebra 267
10.3. Analytic Vectors and Analytic Domination of Families of Operators 274
10.4. Analytic Vectors for • Representations of Enveloping Algebras 282
10.5. Exponentiation of * Representations of Enveloping Algebras 290
10.6. Decomposition of G Integrable Representations as Direct Sums of Cyclic Represen¬
tations 296
Notes 298
12 Contents
11. n Positivity and Complete Positlvity of ^Representations 300
11.1. ra Positive and Completely Positive Maps of Matrix Ordered Spaces 301
11.2. re Positive and Completely Positive Maps of * Algebras 305
11.3. A First Application: Integrable Extensions of * Representations of Commutative
? Algebras 310
11.4. A Second Application: Integrable Extensions of * Representations of Enveloping
Algebras 315
11.5. A Third Application: Completely Centrally Positive Operators 318
11.6. Strongly 1 Positive * Representations which are not Strongly 2 Positive 324
Notes 329
12. Integral Decompositions of * Representations and States 330
12.1. Decomposable Closed Operators 331
12.2. Localization of Decomposable Operators 336
12.3. Decomposition of * Representations 340
12.4. Integral Representation of Positive Linear Punctionals 345
12.5. The Moment Problem over Nuclear Spaces 354
Notes 360
Bibliography 362
Symbol Index 374
Subject Index 378
|
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| author_GND | (DE-588)115774599 |
| author_facet | Schmüdgen, Konrad 1947- |
| author_role | aut |
| author_sort | Schmüdgen, Konrad 1947- |
| author_variant | k s ks |
| building | Verbundindex |
| bvnumber | BV001881869 |
| classification_rvk | SK 600 SK 620 |
| classification_tum | MAT 467f |
| ctrlnum | (OCoLC)260155357 (DE-599)BVBBV001881869 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV001881869 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:36:58Z |
| institution | BVB |
| isbn | 3764323213 0817623213 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001241021 |
| oclc_num | 260155357 |
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| physical | 380 S. |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Operator theory |
| series2 | Operator theory |
| spelling | Schmüdgen, Konrad 1947- Verfasser (DE-588)115774599 aut Unbounded operator algebras and representation theory Konrad Schmüdgen Basel u.a. Birkhäuser 1990 380 S. txt rdacontent n rdamedia nc rdacarrier Operator theory 37 Lizenz d. Akad.-Verl., Berlin Hilbert-Raum (DE-588)4159850-7 gnd rswk-swf Algebra mit Involution (DE-588)4236038-9 gnd rswk-swf Darstellungstheorie (DE-588)4148816-7 gnd rswk-swf Operatoralgebra (DE-588)4129366-6 gnd rswk-swf Unbeschränkter Operator (DE-588)4236037-7 gnd rswk-swf Operatoralgebra (DE-588)4129366-6 s DE-604 Algebra mit Involution (DE-588)4236038-9 s Unbeschränkter Operator (DE-588)4236037-7 s Hilbert-Raum (DE-588)4159850-7 s Darstellungstheorie (DE-588)4148816-7 s Operator theory 37 (DE-604)BV000000970 37 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001241021&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schmüdgen, Konrad 1947- Unbounded operator algebras and representation theory Operator theory Hilbert-Raum (DE-588)4159850-7 gnd Algebra mit Involution (DE-588)4236038-9 gnd Darstellungstheorie (DE-588)4148816-7 gnd Operatoralgebra (DE-588)4129366-6 gnd Unbeschränkter Operator (DE-588)4236037-7 gnd |
| subject_GND | (DE-588)4159850-7 (DE-588)4236038-9 (DE-588)4148816-7 (DE-588)4129366-6 (DE-588)4236037-7 |
| title | Unbounded operator algebras and representation theory |
| title_auth | Unbounded operator algebras and representation theory |
| title_exact_search | Unbounded operator algebras and representation theory |
| title_full | Unbounded operator algebras and representation theory Konrad Schmüdgen |
| title_fullStr | Unbounded operator algebras and representation theory Konrad Schmüdgen |
| title_full_unstemmed | Unbounded operator algebras and representation theory Konrad Schmüdgen |
| title_short | Unbounded operator algebras and representation theory |
| title_sort | unbounded operator algebras and representation theory |
| topic | Hilbert-Raum (DE-588)4159850-7 gnd Algebra mit Involution (DE-588)4236038-9 gnd Darstellungstheorie (DE-588)4148816-7 gnd Operatoralgebra (DE-588)4129366-6 gnd Unbeschränkter Operator (DE-588)4236037-7 gnd |
| topic_facet | Hilbert-Raum Algebra mit Involution Darstellungstheorie Operatoralgebra Unbeschränkter Operator |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001241021&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000970 |
| work_keys_str_mv | AT schmudgenkonrad unboundedoperatoralgebrasandrepresentationtheory |