An introductory course in functional analysis:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY [u.a.]
Springer
2014
|
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 232 S. |
| ISBN: | 9781493919444 |
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Record in the Search Index
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Contents 1 Introduction. Exercises. 1 7 2 Classical Banach Spaces and Their Duals. 2.1 Sequence Spaces. 2.2 Function Spaces. 2.3 Completeness in Function Spaces. Exercises. 11 11 16 24 26 3 The Hahn-Banach Theorems. 3.1 The Axiom of Choice. 3.2 Sublinear Functionals and the Extension Theorem. 3.3 Banach Limits. 3.4 Haar Measure for Compact Abelian Groups. 3.5 Duals, Biduals, and More. 3.6 The Adjoint of an Operator . 3.7 New Banach Spaces From Old . 3.8 Duals of Quotients and Subspaces.
Exercises. 31 31 32 39 44 48 50 53 57 58 4 Consequences of Completeness. 4.1 The Baire Category Theorem. 4.2 Applications of Category. 4.3 The Open Mapping and Closed Graph Theorems. 4.4 Applications of the Open Mapping Theorem. Exercises. 61 61 64 71 77 81 5 Consequences of Convexity. 5.1 General Topology. 5.2 Topological Vector Spaces. 5.3 Some Metrizable Examples. 5.4 The Geometric Hahn-Banach Theorem. 83 83 86 88 93 XV
xvi Contents 5.5 Goldstine’s Theorem. 5.6 Mazur’s Theorem . 5.7 Extreme Points . 5.8 Milman’s Theorem. 5.9 Haar Measure on Compact Groups. 5.10 The Banach-Stone Theorem. Exercises. 106 108 Ill 116 118 121 124 6 129 6.1 Compact Operators. 129 6.2 A Rank-Nullity Theorem for Compact Operators. 141 Exercises. 148 7 Hilbert Space Theory. Compact Operators and Fredholm Theory. 7.1 Basics of Hilbert Spaces. 7.2 Operators on Hilbert Space . 7.3 Hilbert-Schmidt Operators. 7.4 Sturm-Liouville
Systems. Exercises. 8 Banach Algebras. 8.1 The Spectral Radius . 8.2 Commutative Algebras. 8.3 The Wiener Algebra . Exercises. 151 151 157 166 170 177 181 181 196 202 205 Appendix A Basics of Measure Theory. 207 Appendix В Results From Other Areas of Mathematics. 219 References. 225 Index. 227 |
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| author | Bowers, Adam Kalton, Nigel J. 1946-2010 |
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| dewey-full | 515.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| isbn | 9781493919444 |
| language | English |
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| spelling | Bowers, Adam Verfasser (DE-588)1064674348 aut An introductory course in functional analysis Adam Bowers ; Nigel J. Kalton New York, NY [u.a.] Springer 2014 XVI, 232 S. txt rdacontent n rdamedia nc rdacarrier Universitext Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Funktionalanalysis (DE-588)4018916-8 s DE-604 Kalton, Nigel J. 1946-2010 Verfasser (DE-588)172178754 aut Erscheint auch als Online-Ausgabe 978-1-4939-1945-1 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027698358&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bowers, Adam Kalton, Nigel J. 1946-2010 An introductory course in functional analysis Funktionalanalysis (DE-588)4018916-8 gnd |
| subject_GND | (DE-588)4018916-8 (DE-588)4151278-9 |
| title | An introductory course in functional analysis |
| title_auth | An introductory course in functional analysis |
| title_exact_search | An introductory course in functional analysis |
| title_full | An introductory course in functional analysis Adam Bowers ; Nigel J. Kalton |
| title_fullStr | An introductory course in functional analysis Adam Bowers ; Nigel J. Kalton |
| title_full_unstemmed | An introductory course in functional analysis Adam Bowers ; Nigel J. Kalton |
| title_short | An introductory course in functional analysis |
| title_sort | an introductory course in functional analysis |
| topic | Funktionalanalysis (DE-588)4018916-8 gnd |
| topic_facet | Funktionalanalysis Einführung |
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