A course in commutative Banach algebras:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer
2009
|
| Schriftenreihe: | Graduate texts in mathematics
246 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 353 S. |
| ISBN: | 0387724753 9780387724751 |
Internformat
MARC
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| 245 | 1 | 0 | |a A course in commutative Banach algebras |c Eberhard Kaniuth |
| 264 | 1 | |a New York, NY |b Springer |c 2009 | |
| 300 | |a XII, 353 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Graduate texts in mathematics |v 246 | |
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Datensatz im Suchindex
| _version_ | 1804138326497689600 |
|---|---|
| adam_text | Contents
1 General Theory of Banach Algebras 1
1.1 Basic definitions and examples 1
1.2 The spectrum of a Banach algebra element 8
1.3 L1-algebras and Beurling algebras 18
1.4 Ideals and multiplier algebras 22
1.5 Tensor products of Banach algebras 30
1.6 Exercises 35
1.7 Notes and references 41
2 Gelfand Theory 43
2.1 Multiplicative linear functional 44
2.2 The Gelfand representation 52
2.3 Finitely generated commutative Banach algebras 60
2.4 Commutative C*-algebras 66
2.5 The uniform algebras P(X) and R(X) 73
2.6 The structure space of A(X) 84
2.7 The Gelfand representation of Lx (G) 89
2.8 Beurling algebras Ll(G,u;) 99
2.9 The Fourier algebra of a locally compact group 107
2.10 The algebra of almost periodic functions Ill
2.11 Structure spaces of tensor products 120
2.12 Exercises 125
2.13 Notes and references 135
3 Functional Calculus, Shilov Boundary, and Applications . .. 139
3.1 The holomorphic functional calculus 140
3.2 Some applications of the functional calculus 152
3.3 The Shilov boundary 158
3.4 Topological divisors of zero 169
3.5 Shilov s idempotent theorem and applications 178
3.6 Exercises 185
XII Contents
3.7 Notes and references 190
4 Regularity and Related Properties 193
4.1 The hull-kernel topology 194
4.2 Regular commutative Banach algebras 198
4.3 The greatest regular subalgebra 207
4.4 Regularity of Ll{G) 213
4.5 Spectral extension properties 222
4.6 The unique uniform norm property 229
4.7 Regularity of Beurling algebras 236
4.8 Exercises 245
4.9 Notes and references 251
5 Spectral Synthesis and Ideal Theory 253
5.1 Basic notions and local membership 254
5.2 Spectral sets and Ditkin sets 260
5.3 Ideals in C [0,1] 269
5.4 Spectral synthesis in the Mirkil algebra 278
5.5 Spectral sets and Ditkin sets for Ll(G) 288
5.6 Ideals with bounded approximate identities in £1(C?) 295
5.7 On spectral synthesis in protective tensor products 305
5.8 Exercises 310
5.9 Notes and references 316
A Appendix 319
A.I Topology 319
A.2 Functional analysis 321
A.3 Measure and integration 325
A.4 Haar measure and convolution on locally compact groups 327
A.5 The Pontryagin duality theorem 332
A.6 The coset ring of an Abelian group 336
References 343
Index 349
|
| adam_txt |
Contents
1 General Theory of Banach Algebras 1
1.1 Basic definitions and examples 1
1.2 The spectrum of a Banach algebra element 8
1.3 L1-algebras and Beurling algebras 18
1.4 Ideals and multiplier algebras 22
1.5 Tensor products of Banach algebras 30
1.6 Exercises 35
1.7 Notes and references 41
2 Gelfand Theory 43
2.1 Multiplicative linear functional 44
2.2 The Gelfand representation 52
2.3 Finitely generated commutative Banach algebras 60
2.4 Commutative C*-algebras 66
2.5 The uniform algebras P(X) and R(X) 73
2.6 The structure space of A(X) 84
2.7 The Gelfand representation of Lx (G) 89
2.8 Beurling algebras Ll(G,u;) 99
2.9 The Fourier algebra of a locally compact group 107
2.10 The algebra of almost periodic functions Ill
2.11 Structure spaces of tensor products 120
2.12 Exercises 125
2.13 Notes and references 135
3 Functional Calculus, Shilov Boundary, and Applications . . 139
3.1 The holomorphic functional calculus 140
3.2 Some applications of the functional calculus 152
3.3 The Shilov boundary 158
3.4 Topological divisors of zero 169
3.5 Shilov's idempotent theorem and applications 178
3.6 Exercises 185
XII Contents
3.7 Notes and references 190
4 Regularity and Related Properties 193
4.1 The hull-kernel topology 194
4.2 Regular commutative Banach algebras 198
4.3 The greatest regular subalgebra 207
4.4 Regularity of Ll{G) 213
4.5 Spectral extension properties 222
4.6 The unique uniform norm property 229
4.7 Regularity of Beurling algebras 236
4.8 Exercises 245
4.9 Notes and references 251
5 Spectral Synthesis and Ideal Theory 253
5.1 Basic notions and local membership 254
5.2 Spectral sets and Ditkin sets 260
5.3 Ideals in C"[0,1] 269
5.4 Spectral synthesis in the Mirkil algebra 278
5.5 Spectral sets and Ditkin sets for Ll(G) 288
5.6 Ideals with bounded approximate identities in £1(C?) 295
5.7 On spectral synthesis in protective tensor products 305
5.8 Exercises 310
5.9 Notes and references 316
A Appendix 319
A.I Topology 319
A.2 Functional analysis 321
A.3 Measure and integration 325
A.4 Haar measure and convolution on locally compact groups 327
A.5 The Pontryagin duality theorem 332
A.6 The coset ring of an Abelian group 336
References 343
Index 349 |
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| language | English |
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| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Kaniuth, Eberhard Verfasser aut A course in commutative Banach algebras Eberhard Kaniuth New York, NY Springer 2009 XII, 353 S. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 246 Banach-Algebra (DE-588)4193187-7 gnd rswk-swf Kommutative Algebra (DE-588)4164821-3 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Kommutative Algebra (DE-588)4164821-3 s Banach-Algebra (DE-588)4193187-7 s DE-604 Erscheint auch als Online-Ausgabe 978-0-387-72476-8 Graduate texts in mathematics 246 (DE-604)BV000000067 246 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016969503&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kaniuth, Eberhard A course in commutative Banach algebras Graduate texts in mathematics Banach-Algebra (DE-588)4193187-7 gnd Kommutative Algebra (DE-588)4164821-3 gnd |
| subject_GND | (DE-588)4193187-7 (DE-588)4164821-3 (DE-588)4123623-3 |
| title | A course in commutative Banach algebras |
| title_auth | A course in commutative Banach algebras |
| title_exact_search | A course in commutative Banach algebras |
| title_exact_search_txtP | A course in commutative Banach algebras |
| title_full | A course in commutative Banach algebras Eberhard Kaniuth |
| title_fullStr | A course in commutative Banach algebras Eberhard Kaniuth |
| title_full_unstemmed | A course in commutative Banach algebras Eberhard Kaniuth |
| title_short | A course in commutative Banach algebras |
| title_sort | a course in commutative banach algebras |
| topic | Banach-Algebra (DE-588)4193187-7 gnd Kommutative Algebra (DE-588)4164821-3 gnd |
| topic_facet | Banach-Algebra Kommutative Algebra Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016969503&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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