Algebras of linear transformations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2001
|
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 238 S. |
| ISBN: | 0387950621 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804128206154891264 |
|---|---|
| adam_text | Contents
Preface ix
1. Linear Algebra 1
1.1 Vector Spaces and Duality 1
1.2 Direct Sums and Quotients 8
1.3 Inner Product Spaces 11
1.4 The Spectral Theorem 20
1.5 Fields and Field Extensions 26
1.6 Existence of Bases for Infinite Dimensional Spaces 29
1.7 Notes 32
1.8 Exercises 33
2. Algebras 39
2.1 Algebraic Structures 39
2.2 Algebras with a Prescribed Basis 45
2.3 Algebras of Linear Transformations 49
2.4 Inversion and Spectra 56
2.5 Division Algebras and Other Simple Algebras 64
2.6 Notes 70
2.7 Exercises 70
3. Invariant Subspaces 77
3.1 The Invariant Subspace Lattice 77
3.2 Idempotents and Projections 81
3.3 Existence of Invariant Subspaces 87
3.4 Representations and Left Ideals 96
3.5 Functional Calculus and Polar Decomposition 103
3.6 Notes Ill
3.7 Exercises 112
4. Semisimple Algebras 117
4.1 Nilpotent Algebras and the Nil Radical 117
4.2 Structure of Semisimple Algebras 126
xiii
xiv CONTENTS
4.3 Structure of Simple Algebras 133
4.4 Isomorphism Classes of Semisimple Algebras 141
4.5 Notes 145
4.6 Exercises 146
5. Operator Algebras 151
5.1 Von Neumann Algebras 152
5.2 Real and Complex Involutive Algebras 159
5.3 Representation of Operator Algebras 167
5.4 Wedderburn Theorems for Operator Algebras 173
5.5 C* Algebras 178
5.5 Notes 186
5.7 Exercises 187
6. Tensor Products 193
6.1 Free Vector Spaces 193
6.2 Tensor Products of Vector Spaces 197
6.3 Tensor Products of Algebras 212
6.4 Tensor Products of Operator Algebras 222
6.5 Notes 227
6.6 Exercises 229
References 233
Index 235
|
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| author | Farenick, Douglas 1961- |
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| dewey-full | 512.24 |
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| dewey-ones | 512 - Algebra |
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| discipline | Mathematik |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:45:33Z |
| institution | BVB |
| isbn | 0387950621 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009156878 |
| oclc_num | 247106314 |
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| physical | XIV, 238 S. |
| publishDate | 2001 |
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| publishDateSort | 2001 |
| publisher | Springer |
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| series2 | Universitext |
| spelling | Farenick, Douglas 1961- Verfasser (DE-588)1119457823 aut Algebras of linear transformations Douglas R. Farenick New York [u.a.] Springer 2001 XIV, 238 S. txt rdacontent n rdamedia nc rdacarrier Universitext Lineare Transformation - Lineare Algebra - Assoziative Algebra Associative algebras Assoziative Algebra (DE-588)4293934-3 gnd rswk-swf Lineare Transformation (DE-588)4167712-2 gnd rswk-swf Assoziative Algebra (DE-588)4293934-3 s Lineare Transformation (DE-588)4167712-2 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009156878&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Farenick, Douglas 1961- Algebras of linear transformations Lineare Transformation - Lineare Algebra - Assoziative Algebra Associative algebras Assoziative Algebra (DE-588)4293934-3 gnd Lineare Transformation (DE-588)4167712-2 gnd |
| subject_GND | (DE-588)4293934-3 (DE-588)4167712-2 |
| title | Algebras of linear transformations |
| title_auth | Algebras of linear transformations |
| title_exact_search | Algebras of linear transformations |
| title_full | Algebras of linear transformations Douglas R. Farenick |
| title_fullStr | Algebras of linear transformations Douglas R. Farenick |
| title_full_unstemmed | Algebras of linear transformations Douglas R. Farenick |
| title_short | Algebras of linear transformations |
| title_sort | algebras of linear transformations |
| topic | Lineare Transformation - Lineare Algebra - Assoziative Algebra Associative algebras Assoziative Algebra (DE-588)4293934-3 gnd Lineare Transformation (DE-588)4167712-2 gnd |
| topic_facet | Lineare Transformation - Lineare Algebra - Assoziative Algebra Associative algebras Assoziative Algebra Lineare Transformation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009156878&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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