Representations of *-algebras, locally compact groups, and Banach *-algebraic bundles: 2 Banach *-algebraic bundles, induced representations, and the generalized Mackey analysis
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston u.a.
Acad. Press
1988
|
| Series: | Pure and applied mathematics
126 |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII S., S. 747 - 1486 |
| ISBN: | 0122527224 |
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MARC
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| 245 | 1 | 0 | |a Representations of *-algebras, locally compact groups, and Banach *-algebraic bundles |n 2 |p Banach *-algebraic bundles, induced representations, and the generalized Mackey analysis |c J. M. G. Fell ; R. S. Doran |
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Record in the Search Index
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| adam_text | Contents
Introduction to Volume 2 (Chapters VIII to XII) 747
Chapter VIII. Banach Algebraic Bundles and Their
Representations 771
1. Multipliers of Algebras 773
2. Banach Algebraic Bundles 783
3. Banach * Algebraic Bundles 792
4. Semidirect Product Bundles and Central Extension Bundles 798
5. The Cross Sectional Algebra 803
6. Partial Cross Sectional Bundles 811
7. Transformation Bundles 818
8. Locally Convex Representations of Banach Algebraic
Bundles 823
9. * Representations of Banach * Algebraic Bundles and
Unitary Representations of Groups 827
10. Projective Representations of Groups 833
11. Integrable Locally Convex Representations 837
12. The Recovery of a Frechet Representation of 38 from its
Integrated Form 848
V
vi Contents
13. The Recovery of a Representation of Si from its Integrated
Form 852
14. The Existence of Irreducible * Representations of Banach
* Algebraic Bundles 860
15. The Extension of Representations to Multipliers;
Application to Semidirect Products and Partial Cross
Sectional Bundles 864
16. C* Algebraic Bundles; the Bundle C* Completion 871
17. Bundle Structures for C* Algebras; the Glimm Algebras 885
18. Transformation Bundles and Systems of Imprimitivity 889
19. Ergodic Measure Transformation Spaces and Certain
Irreducible Systems of Imprimitivity 901
20. Functionals of Positive Type on Banach * Algebraic Bundles 906
21. The Regional Topology of * Representations of Banach
? Algebraic Bundles 913
22. Exercises for Chapter VIII 925
Notes and Remarks 929
Chapter IX. Compact Groups 931
1. Preliminary Remarks on Function Spaces 932
2. The Peter Weyl Theorem 934
3. Finite Dimensional Representations of G 937
4. Orthogonality Relations 943
5. Characters and Central Functions 947
6. The Stone Weierstrass Theorem for Representations 951
7. ff Subspaces and Multiplicity for Locally Convex
Representations of G 954
8. Weak Fejer Summation 959
9. The Structure of the Regular Representation and the
Plancherel Formula 964
10. Induced Representations and the Frobenius Reciprocity
Theorem 967
11. The Representations of SU(2) 979
12. The Representations of SO(3) 985
13. Exercises for Chapter IX 988
Notes and Remarks 995
Contents vii
Chapter X. Abelian Groups and Commutative Banach * Algebraic
Bundles 999
1. The Character Group 1001
2. The Theorems of Stone, Bochner and Plancherel 1007
3. The Fourier Inversion Theorem, Regularity, and Pontryagin
Duality 1016
4. Commutative Banach * Algebraic Bundles 1024
5. Commutative C* Algebraic Bundles 1035
6. Exercises for Chapter X 1042
Notes and Remarks 1047
Chapter XL Induced Representations and the Imprimitivity
Theorem 1049
1. Operator Inner Products 1055
2. Duality for Operator Inner Products 1064
3. F bounded Endomorphisms and Modules; Completely
Positive Maps 1070
4. Rigged Modules and Abstractly Induced Representations 1078
5. General Properties of Abstractly Induced Representations 1088
6. Imprimitivity Bimodules and the Abstract Imprimitivity
Theorem 1095
7. Topological Versions of the Abstract Imprimitivity Theorem 1107
8. Positivity of Representations with Respect to a Banach
• Algebraic Bundle 1121
9. Induced Hilbert Bundles and Induced Representations of a
Banach * Algebraic Bundle 1131
10. Mackey s and Blattner s Formulations of Induced
Representations of Groups 1147
11. ^ Positive Representations and the C* Completion of 36 1155
12. Elementary Properties of Induced Representations of Banach
? Algebraic Bundles 1160
13. Restrictions and Tensor Products of Induced Representations
of Banach * Algebraic Bundles 1173
14. The Imprimitivity Theorem for Banach * Algebraic Bundles 1179
15. A generalized Mackey Stone von Neumann Theorem 1198
16. Conjugation of Representations 1204
17. Non Involutory Induced Representations 1225
18. Exercises for Chapter XI 1234
Notes and Remarks 1240
viii Contents
Chapter XII. The Generalized Mackey Analysis 1243
1. The Mackey Normal Subgroup Analysis for Finite Groups 1246
2. The Mackey Analysis in the General Case; Step I 1264
3. The Mackey Analysis in the General Case; Step II 1273
4. The Mackey Analysis in the General Case; Step III 1284
5. The Mackey Analysis in the General Case; Final Results 1301
6. Saturated C* Algebraic Bundles with Unit Fibers of
Compact Type 1311
7. Saturated Bundles over Compact Groups 1327
8. Examples 1340
9. Further Examples 1356
10. Exercises for Chapter XII 1366
Notes and Remarks 1368
Bibliography 1373
Name Index 1451
Subject Index 1457
Index of Notation 1477
Topics in Volume 1
Chapter I. Preliminaries
Chapter II. Integration Theory and Banach Bundles
Chapter HI. Locally Compact Groups
Chapter IV. Algebraic Representation Theory
Chapter V. Locally Convex Representations and Banach Algebras
Chapter VI. C* Algebras and Their * Representations
Chapter VII. The Topology of the space of * Representations
|
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| indexdate | 2024-07-09T16:11:46Z |
| institution | BVB |
| isbn | 0122527224 |
| language | English |
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| physical | VIII S., S. 747 - 1486 |
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| publishDateSearch | 1988 |
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| spelling | Fell, J. M. G. 1923-2016 Verfasser (DE-588)124469167 aut Representations of *-algebras, locally compact groups, and Banach *-algebraic bundles 2 Banach *-algebraic bundles, induced representations, and the generalized Mackey analysis J. M. G. Fell ; R. S. Doran Boston u.a. Acad. Press 1988 VIII S., S. 747 - 1486 txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 126 Pure and applied mathematics ... Doran, Robert S. 1937- Verfasser (DE-588)135856574 aut (DE-604)BV003947714 2 Pure and applied mathematics 126 (DE-604)BV010177228 126 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002700416&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fell, J. M. G. 1923-2016 Doran, Robert S. 1937- Representations of *-algebras, locally compact groups, and Banach *-algebraic bundles Pure and applied mathematics |
| title | Representations of *-algebras, locally compact groups, and Banach *-algebraic bundles |
| title_auth | Representations of *-algebras, locally compact groups, and Banach *-algebraic bundles |
| title_exact_search | Representations of *-algebras, locally compact groups, and Banach *-algebraic bundles |
| title_full | Representations of *-algebras, locally compact groups, and Banach *-algebraic bundles 2 Banach *-algebraic bundles, induced representations, and the generalized Mackey analysis J. M. G. Fell ; R. S. Doran |
| title_fullStr | Representations of *-algebras, locally compact groups, and Banach *-algebraic bundles 2 Banach *-algebraic bundles, induced representations, and the generalized Mackey analysis J. M. G. Fell ; R. S. Doran |
| title_full_unstemmed | Representations of *-algebras, locally compact groups, and Banach *-algebraic bundles 2 Banach *-algebraic bundles, induced representations, and the generalized Mackey analysis J. M. G. Fell ; R. S. Doran |
| title_short | Representations of *-algebras, locally compact groups, and Banach *-algebraic bundles |
| title_sort | representations of algebras locally compact groups and banach algebraic bundles banach algebraic bundles induced representations and the generalized mackey analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002700416&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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