A course in abstract analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
2012
|
| Schriftenreihe: | Graduate studies in mathematics
141 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 367 S. |
| ISBN: | 9780821890837 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804149488783196160 |
|---|---|
| adam_text | Titel: A course in abstract analysis
Autor: Conway, John B
Jahr: 2012
Contents
Preface
XI
Chapter 1. Setting the Stage 1
§1.1. Riemann-Stieltjes integrals 1
§1.2. Metrie Spaces redux 12
§1.3. Nor med Spaces 21
§1.4. Locally compact Spaces 29
§1.5. Linear functionals 37
Chapter 2. Elements of Measure Theory 41
§2.1. Positive linear functionals on C(X) 41
§2.2. The Radon measure space 42
§2.3. Measurable funetions 51
§2.4. Integration with respect to a measure 56
§2.5. Convergence theorems 71
§2.6. Signed measures 78
§2.7. 17-spaces 84
Chapter 3. A Hubert Space Interlude 93
§3.1. Introduction to Hubert space 93
§3.2. Orthogonality 98
§3.3. The Riesz Representation Theorem 103
Chapter 4. A Return to Measure Theory 107
§4.1. The Lebesgue-Radon-Nikodym Theorem 107
vn
viii Contents
§4.2. Complex functions and measures 114
§4.3. Linear functionals on C(X) 119
§4.4. Linear functionals on Co(X) 124
§4.5. Functions of bounded Variation 127
§4.6. Linear functionals on Z^-spaces 129
§4.7. Product measures 133
§4.8. Lebesgue measure on M.d 141
§4.9. Differentiation on Rd 144
§4.10. Absolutely continuous functions 151
§4.11. Convolution* 156
§4.12. The Fourier transform* 161
Chapter 5. Linear Transformations 171
§5.1. Basics 171
§5.2. Orthonormal basis 175
§5.3. Isomorphic Hubert spaces 179
§5.4. The adjoint 183
§5.5. The direct sum of Hubert spaces 190
§5.6. Compact linear transformations 195
§5.7. The Spectral Theorem 202
§5.8. Some applications of the Spectral Theorem* 205
§5.9. Unitary equivalence* 210
Chapter 6. Banach Spaces 213
§6.1. Finite-dimensional spaces 213
§6.2. Sums and quotients of normed spaces 216
§6.3. The Hahn-Banach Theorem 220
§6.4. Banach limits* 226
§6.5. The Open Mapping and Closed Graph Theorems 228
§6.6. Complemented subspaces* 232
§6.7. The Principle of Uniform Boundedness 234
Chapter 7. Locally Convex Spaces 237
§7.1. Basics of locally convex spaces 237
§7.2. Metrizable locally convex spaces* 243
§7.3. Geometrie consequences 244
Contents
ix
Chapter 8. Duality 251
§8.1. Basics of duality 251
§8.2. The dual of a quotient space and of a subspace 260
§8.3. Reflexive spaces 263
§8.4. The Krein-Milman Theorem 266
§8.5. The Stone-Weierstrass Theorem 270
Chapter 9. Operators on a Banach Space 277
§9.1. The adjoint 277
§9.2. Compact Operators 282
Chapter 10. Banach Algebras and Spectral Theory 287
§10.1. Elementary properties and examples 287
§10.2. Ideals and quotients 290
§10.3. Analytic functions 292
§10.4. The spectrum 297
§10.5. The spectrum of an Operator 302
§10.6. The spectrum of a compact Operator 310
§10.7. Abelian Banach algebras 314
Chapter 11. C*-Algebras 319
§11.1. Elementary properties and examples 319
§11.2. Abelian C*-algebras 323
§11.3. Positive elements in a C*-algebra 327
§11.4. A functional calculus for normal Operators 332
§11.5. The commutant of a normal Operator 342
§11.6. Multiplicity theory 345
Appendix 355
§A.l. Baire Category Theorem 355
§A.2. Nets 356
Bibliography 359
List of Symbols 361
Index 363
|
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| id | DE-604.BV040427443 |
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| indexdate | 2024-07-10T00:23:50Z |
| institution | BVB |
| isbn | 9780821890837 |
| language | English |
| lccn | 2012020947 |
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| series | Graduate studies in mathematics |
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| spelling | Conway, John B. 1939- Verfasser (DE-588)110699882 aut A course in abstract analysis John B. Conway Providence, RI American Math. Soc. 2012 XV, 367 S. txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 141 Measure theory Integration, Functional Functional analysis Measure and integration -- Instructional exposition (textbooks, tutorial papers, etc.) msc Functional analysis -- Instructional exposition (textbooks, tutorial papers, etc.) msc Banach-Raum (DE-588)4004402-6 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Maßtheorie (DE-588)4074626-4 gnd rswk-swf C-Stern-Algebra (DE-588)4136693-1 gnd rswk-swf Maßtheorie (DE-588)4074626-4 s Funktionalanalysis (DE-588)4018916-8 s Banach-Raum (DE-588)4004402-6 s C-Stern-Algebra (DE-588)4136693-1 s DE-604 Graduate studies in mathematics 141 (DE-604)BV009739289 141 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025280002&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Conway, John B. 1939- A course in abstract analysis Graduate studies in mathematics Measure theory Integration, Functional Functional analysis Measure and integration -- Instructional exposition (textbooks, tutorial papers, etc.) msc Functional analysis -- Instructional exposition (textbooks, tutorial papers, etc.) msc Banach-Raum (DE-588)4004402-6 gnd Funktionalanalysis (DE-588)4018916-8 gnd Maßtheorie (DE-588)4074626-4 gnd C-Stern-Algebra (DE-588)4136693-1 gnd |
| subject_GND | (DE-588)4004402-6 (DE-588)4018916-8 (DE-588)4074626-4 (DE-588)4136693-1 |
| title | A course in abstract analysis |
| title_auth | A course in abstract analysis |
| title_exact_search | A course in abstract analysis |
| title_full | A course in abstract analysis John B. Conway |
| title_fullStr | A course in abstract analysis John B. Conway |
| title_full_unstemmed | A course in abstract analysis John B. Conway |
| title_short | A course in abstract analysis |
| title_sort | a course in abstract analysis |
| topic | Measure theory Integration, Functional Functional analysis Measure and integration -- Instructional exposition (textbooks, tutorial papers, etc.) msc Functional analysis -- Instructional exposition (textbooks, tutorial papers, etc.) msc Banach-Raum (DE-588)4004402-6 gnd Funktionalanalysis (DE-588)4018916-8 gnd Maßtheorie (DE-588)4074626-4 gnd C-Stern-Algebra (DE-588)4136693-1 gnd |
| topic_facet | Measure theory Integration, Functional Functional analysis Measure and integration -- Instructional exposition (textbooks, tutorial papers, etc.) Functional analysis -- Instructional exposition (textbooks, tutorial papers, etc.) Banach-Raum Funktionalanalysis Maßtheorie C-Stern-Algebra |
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