A short course on spectral theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2002
|
| Schriftenreihe: | Graduate texts in mathematics
209 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | X, 135 S. |
| ISBN: | 0387953000 9781441929433 |
Internformat
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| 245 | 1 | 0 | |a A short course on spectral theory |c William Arveson |
| 264 | 1 | |a New York [u.a.] |b Springer |c 2002 | |
| 300 | |a X, 135 S. | ||
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| 490 | 1 | |a Graduate texts in mathematics |v 209 | |
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Datensatz im Suchindex
| _version_ | 1804128908077957120 |
|---|---|
| adam_text | Contents
Preface vii
Chapter 1. Spectral Theory and Banach Algebras 1
1.1. Origins of Spectral Theory 1
1.2. The Spectrum of an Operator 5
1.3. Banach Algebras: Examples 7
1.4. The Regular Representation 11
1.5. The General Linear Group of A 14
1.6. Spectrum of an Element of a Banach Algebra 16
1.7. Spectral Radius 18
1.8. Ideals and Quotients 21
1.9. Commutative Banach Algebras 25
1.10. Examples: C(X) and the Wiener Algebra 27
1.11. Spectral Permanence Theorem 31
1.12. Brief on the Analytic Functional Calculus 33
Chapter 2. Operators on Hilbert Space 39
2.1. Operators and Their C* Algebras 39
2.2. Commutative C* Algebras 46
2.3. Continuous Functions of Normal Operators 50
2.4. The Spectral Theorem and Diagonalization 52
2.5. Representations of Banach * Algebras 57
2.6. Borel Functions of Normal Operators 59
2.7. Spectral Measures 64
2.8. Compact Operators 68
2.9. Adjoining a Unit to a C* Algebra 75
2.10. Quotients of C* Algebras 78
Chapter 3. Asymptotics: Compact Perturbations and Fredholm
Theory 83
3.1. The Calkin Algebra 83
3.2. Riesz Theory of Compact Operators 86
3.3. Fredholm Operators 92
3.4. The Fredholm Index 95
Chapter 4. Methods and Applications 101
4.1. Maximal Abelian von Neumann Algebras 102
ix
x CONTENTS
4.2. Toeplitz Matrices and Toeplitz Operators 106
4.3. The Toeplitz C* Algebra 110
4.4. Index Theorem for Continuous Symbols 114
4.5. Some H2 Function Theory 118
4.6. Spectra of Toeplitz Operators with Continuous Symbol 120
4.7. States and the GNS Construction 122
4.8. Existence of States: The Gelfand Naimark Theorem 126
Bibliography 131
Index 133
|
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
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| discipline | Mathematik |
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| id | DE-604.BV014047667 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:56:43Z |
| institution | BVB |
| isbn | 0387953000 9781441929433 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009620139 |
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| physical | X, 135 S. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Springer |
| record_format | marc |
| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Arveson, William 1934- Verfasser (DE-588)128603577 aut A short course on spectral theory William Arveson New York [u.a.] Springer 2002 X, 135 S. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 209 Hier auch später erschienene, unveränderte Nachdrucke Spektraltheorie Spectral theory (Mathematics) Operatortheorie (DE-588)4075665-8 gnd rswk-swf Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Operatortheorie (DE-588)4075665-8 s Spektraltheorie (DE-588)4116561-5 s DE-604 Graduate texts in mathematics 209 (DE-604)BV000000067 209 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009620139&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Arveson, William 1934- A short course on spectral theory Graduate texts in mathematics Spektraltheorie Spectral theory (Mathematics) Operatortheorie (DE-588)4075665-8 gnd Spektraltheorie (DE-588)4116561-5 gnd |
| subject_GND | (DE-588)4075665-8 (DE-588)4116561-5 |
| title | A short course on spectral theory |
| title_auth | A short course on spectral theory |
| title_exact_search | A short course on spectral theory |
| title_full | A short course on spectral theory William Arveson |
| title_fullStr | A short course on spectral theory William Arveson |
| title_full_unstemmed | A short course on spectral theory William Arveson |
| title_short | A short course on spectral theory |
| title_sort | a short course on spectral theory |
| topic | Spektraltheorie Spectral theory (Mathematics) Operatortheorie (DE-588)4075665-8 gnd Spektraltheorie (DE-588)4116561-5 gnd |
| topic_facet | Spektraltheorie Spectral theory (Mathematics) Operatortheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009620139&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000067 |
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