A course in functional analysis
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| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer
2007
|
| Ausgabe: | 2. ed., [Nachdr.] |
| Schriftenreihe: | Graduate texts in mathematics
96 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
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| 245 | 1 | 0 | |a A course in functional analysis |c John B. Conway |
| 250 | |a 2. ed., [Nachdr.] | ||
| 264 | 1 | |a New York, NY |b Springer |c 2007 | |
| 300 | |a XVI, 399 S. |b graph. Darst. | ||
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| 490 | 1 | |a Graduate texts in mathematics |v 96 | |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0048 MAT 460f 2001 A 10975(2,2007) 0104 MAT 460f 2001 A 10975(2,2007) |
|---|---|
| DE-BY-TUM_katkey | 1627958 |
| DE-BY-TUM_location | LSB 01 |
| DE-BY-TUM_media_number | 040010227228 040010088036 |
| _version_ | 1820897413940903936 |
| adam_text | Contents
Preface
vii
Preface
to the Second Edition
xi
CHAPTER I
Hilbert Spaces
§1.
Elementary Properties and Examples
1
§2.
Orthogonality
7
§3.
The Riesz Representation Theorem
1
1
§4.
Orthonormal
Sets of Vectors and Bases
14
§5.
Isomorphic Hilbert Spaces and the Fourier Transform for the Circle
19
§6.
The Direct Sum of Hilbert Spaces
23
CHAPTER II
Operators on Hilbert Space
§1.
Elementary Properties and Examples
26
§2.
The Adjoint of an Operator
31
§3.
Projections and Idempotents; Invariant and Reducing Subspaces
36
§4.
Compact Operators
41
§5.*
The Diagonalization of Compact Self-Adjoint Operators
46
§6.*
An Application: Sturm-
Liou
ville
Systems
49
§7.*
The Spectral Theorem and Functional Calculus for Compact Normal
Operators
54
§8.·
Unitary Equivalence for Compact Normal Operators
60
CHAPTER III
Banach Spaces
§1.
Elementary Properties and Examples
63
§2.
Linear Operators on Normed Spaces
67
xiv
Contents
§3.
Finite Dimensional Normed Spaces
69
§4.
Quotients and Products of Normed Spaces
70
§5.
Linear Functionals
73
§6.
The Hahn-Banach Theorem
77
§7.
An Application: Banach Limits
82
§8.*
An Application: Runge s Theorem
83
§9.*
An Application: Ordered Vector Spaces
86
§10.
The Dual of a Quotient Space and a Subspace
88
§11.
Reflexive Spaces
89
§12.
The Open Mapping and Closed Graph Theorems
90
§13.
Complemented Subspaces of a Banach Space
93
§14.
The Principle of Uniform Boundedness
95
CHAPTER IV
Locally Convex Spaces
§1.
Elementary Properties and Examples
99
§2.
Metrizable and
Norma ble
Locally Convex Spaces
105
§3.
Some Geometric Consequences of the Hahn-Banach Theorem
108
§4.*
Some Examples of the Dual Space of a Locally Convex Space
114
§5.*
Inductive Limits and the Space of Distributions
116
CHAPTER V
Weak Topologies
§1.
Duality
124
§2.
The Dual of a Subspace and a Quotient Space
128
§3.
Alaoglu s Theorem
130
§4.
Reflexivity
Revisited
131
§5.
Separability and Metrizability
134
§6.·
An Application: The
Stone-Čech Compactification
137
§7.
The Krein-Milman Theorem
141
§8.
An Application: The Stone-
Weierstrass
Theorem
145
§9.·
The
Schauder
Fixed Point Theorem
149
§10.*
The Ryll-Nardzewski Fixed Point Theorem
151
§11.*
An Application:
Haar
Measure on a Compact Group
154
§12*
The Krein-Smulian Theorem
159
§13.»
Weak Compactness
163
CHAPTER VI
Linear Operators on a Banach Space
§1.
The Adjoint of a Linear Operator
166
§2*
The Banach-Stone Theorem
171
§3.
Compact Operators
173
§4.
Invariant Subspaces
178
§5.
Weakly Compact Operators
183
Contents Xv
CHAPTER
VII
Banach
Algebras and Spectral Theory for
Operators on a Banach Space
§1.
Elementary Properties and Examples
187
§2.
Ideals and Quotients
191
§3.
The Spectrum
195
§4.
The Riesz Functional Calculus
199
§5.
Dependence of the Spectrum on the Algebra
205
§6.
The Spectrum of a Linear Operator
208
§7.
The Spectral Theory of a Compact Operator
214
§8.
Abelian Banach Algebras
218
§9.*
The Group Algebra of a Locally Compact Abelian Group
223
CHAPTER
VIII
C*-Algebras
§1.
Elementary Properties and Examples
232
§2.
Abelian C*-Algebras and the Functional Calculus in C -Algebras
236
§3.
The Positive Elements in a C -Algebra
240
§4.·
Ideals and Quotients of C-Algebras
245
§5.*
Representations of C*-Algebras and the Gelfand-Naimark-Segal
Construction
248
CHAPTER IX
Normal Operators on Hubert Space
§1.
Spectral Measures and Representations of Abelian C -Algebras
255
§2.
The Spectral Theorem
262
§3.
Star-Cyclic Normal Operators
268
§4.
Some Applications of the Spectral Theorem
271
§5.
Topologies on
9ЦЖ)
274
§6.
Commuting Operators
276
§7.
Abelian
von
Neumann Algebras
281
§8.
The Functional Calculus for Normal Operators:
The Conclusion of the Saga
285
§9.
Invariant Subspaces for Normal Operators
290
§10.
Multiplicity Theory for Normal Operators:
A Complete Set of Unitary Invariants
293
CHAPTER X
Unbounded Operators
§1.
Basic Properties and Examples
303
§2.
Symmetric and Self-Adjoint Operators
308
§3.
The Cayley Transform
316
§4.
Unbounded Normal Operators and the Spectral Theorem
319
§5.
Stone s Theorem
327
§6.
The Fourier Transform and Differentiation
334
§7.
Moments
343
xvi
Contents
CHAPTER XI
Fredholm
Theory
§1.
The Spectrum Revisited
347
§2.
Fredholm
Operators
349
§3.
The
Fredholm
Index
352
§4.
The Essential Spectrum
358
§5.
The Components of if IF
362
§6.
A Finer Analysis of the Spectrum
363
APPENDIX A
Preliminaries
§1.
Linear Algebra
369
§2.
Topology
371
APENDIX B
The Dual of
Π{μ)
375
APPENDIX
С
The Dual of C0(X)
378
Bibliography
384
List of Symbols
391
Index
395
This book
«s an
introductory text in functional analysis, aimed at the
graduate student with a firm background in integration and measure
theory. Unlike many modem treatments, this book begins with the
particular and works its way to the more general, helping ttie stu¬
dent to develop an intuitive feel for the subject For example, the
author introduces the concept of a Banach space only after having
introduced HNbert spaces, and discussing their properties. The stu¬
dent
WH
also appreciate the large number of examples and exercises
which have been »eluded.
|
| any_adam_object | 1 |
| author | Conway, John B. 1939- |
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| discipline | Mathematik |
| edition | 2. ed., [Nachdr.] |
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| id | DE-604.BV023246258 |
| illustrated | Illustrated |
| indexdate | 2024-12-23T20:58:50Z |
| institution | BVB |
| isbn | 9780387972459 0387972455 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016431717 |
| oclc_num | 254457519 |
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| owner | DE-91G DE-BY-TUM DE-739 DE-706 DE-703 DE-188 |
| owner_facet | DE-91G DE-BY-TUM DE-739 DE-706 DE-703 DE-188 |
| physical | XVI, 399 S. graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Springer |
| record_format | marc |
| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spellingShingle | Conway, John B. 1939- A course in functional analysis Graduate texts in mathematics Funktionalanalysis Functional analysis Hilbert-Raum (DE-588)4159850-7 gnd Funktionalanalysis (DE-588)4018916-8 gnd Banach-Raum (DE-588)4004402-6 gnd |
| subject_GND | (DE-588)4159850-7 (DE-588)4018916-8 (DE-588)4004402-6 |
| title | A course in functional analysis |
| title_auth | A course in functional analysis |
| title_exact_search | A course in functional analysis |
| title_full | A course in functional analysis John B. Conway |
| title_fullStr | A course in functional analysis John B. Conway |
| title_full_unstemmed | A course in functional analysis John B. Conway |
| title_short | A course in functional analysis |
| title_sort | a course in functional analysis |
| topic | Funktionalanalysis Functional analysis Hilbert-Raum (DE-588)4159850-7 gnd Funktionalanalysis (DE-588)4018916-8 gnd Banach-Raum (DE-588)4004402-6 gnd |
| topic_facet | Funktionalanalysis Functional analysis Hilbert-Raum Banach-Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016431717&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016431717&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000067 |
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