Verfügbarkeit: An introductory course in functional analysis

An introductory course in functional analysis:

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Bibliographische Detailangaben
Beteiligte Personen:	Bowers, Adam (VerfasserIn), Kalton, Nigel J. 1946-2010 (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	New York, NY [u.a.] Springer 2014
Schriftenreihe:	Universitext
Schlagwörter:	Funktionalanalysis Einführung
Links:	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
Umfang:	XVI, 232 S.
ISBN:	9781493919444

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Datensatz im Suchindex

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adam_text	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
any_adam_object	1
author	Bowers, Adam Kalton, Nigel J. 1946-2010
author_GND	(DE-588)1064674348 (DE-588)172178754
author_facet	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
dewey-raw	515.7
dewey-search	515.7
dewey-sort	3515.7
dewey-tens	510 - Mathematics
discipline	Mathematik
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spellingShingle	Bowers, Adam Kalton, Nigel J. 1946-2010 An introductory course in functional analysis Funktionalanalysis (DE-588)4018916-8 gnd
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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
url	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
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