Fundamentals of functional analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Dordrecht [u.a.]
Kluwer
1996
|
| Series: | Kluwer texts in the mathematical sciences
12 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Russ. übers. |
| Physical Description: | XIV, 276 S. |
| ISBN: | 0792338987 |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface to the English Translation ix
Preface to the First Russian Edition x
Preface to the Second Russian Edition xii
Chapter 1. An Excursion into Set Theory
1.1. Correspondences 1
1.2. Ordered Sets 3
1.3. Filters 6
Exercises 8
Chapter 2. Vector Spaces
2.1. Spaces and Subspaces 10
2.2. Linear Operators 12
2.3. Equations in Operators 15
Exercises 18
Chapter 3. Convex Analysis
3.1. Sets in Vector Spaces 20
3.2. Ordered Vector Spaces 22
3.3. Extension of Positive Functionals and Operators .. 25
3.4. Convex Functions and Sublinear Functionals 26
3.5. The Hahn Banach Theorem 29
3.6. The Krein Milman Theorem 31
3.7. The Balanced Hahn Banach Theorem 33
3.8. The Minkowski Functional and Separation 35
Exercises 39
Chapter 4. An Excursion into Metric Spaces
4.1. The Uniformity and Topology of a Metric Space .. 40
4.2. Continuity and Uniform Continuity 42
4.3. Semicontinuity 44
4.4. Compactness 46
4.5. Completeness 46
4.6. Compactness and Completeness 49
4.7. Baire Spaces 52
4.8. The Jordan Curve Theorem and Rough Drafts ... 54
Exercises 55
vi
Chapter 5. Multinormed and Banach Spaces
5.1. Seminorms and Multinorms 56
5.2. The Uniformity and Topology of a Multinormed
Space 60
5.3. Comparison Between Topologies 62
5.4. Metrizable and Normable Spaces 64
5.5. Banach Spaces 66
5.6. The Algebra of Bounded Operators 73
Exercises 79
Chapter 6. Hilbert Spaces
6.1. Hermitian Forms and Inner Products 80
6.2. Orthoprojections 84
6.3. A Hilbert Basis 87
6.4. The Adjoint of an Operator 90
6.5. Hermitian Operators 93
6.6. Compact Hermitian Operators 95
Exercises 99
Chapter 7. Principles of Banach Spaces
7.1. Banach s Fundamental Principle 100
7.2. Boundedness Principles 102
7.3. The Ideal Correspondence Principle 105
7.4. Open Mapping and Closed Graph Theorems 107
7.5. The Automatic Continuity Principle 112
7.6. Prime Principles 114
Exercises 118
Chapter 8. Operators in Banach Spaces
8.1. Holomorphic Functions and Contour Integrals .... 120
8.2. The Holomorphic Functional Calculus 126
8.3. The Approximation Property 132
8.4. The Riesz Schauder Theory 134
8.5. Fredholm Operators 137
Exercises 144
Chapter 9. An Excursion into General Topology
9.1. Pretopologies and Topologies 146
9.2. Continuity 148
9.3. Types of Topological Spaces 151
9.4. Compactness 155
9.5. Uniform and Multimetric Spaces 159
9.6. Covers, and Partitions of Unity 164
Exercises 168
vii
Chapter 10. Duality and Its Applications
10.1. Vector Topologies 169
10.2. Locally Convex Topologies 171
10.3. Duality Between Vector Spaces 173
10.4. Topologies Compatible with Duality 175
10.5. Polars 177
10.6. Weakly Compact Convex Sets 179
10.7. Reflexive Spaces 180
10.8. The Space C(Q, R) 181
10.9. Radon Measures 187
10.10. The Spaces 9(Q) and ® (ft) 194
10.11. The Fourier Transform of a Distribution 201
Exercises 211
Chapter 11. Banach Algebras
11.1. The Canonical Operator Representation 213
11.2. The Spectrum of an Element of an Algebra 215
11.3. The Holomorphic Functional Calculus in Algebras 216
11.4. Ideals of Commutative Algebras 218
11.5. Ideals of the Algebra C(Q, C) 219
11.6. The Gelfand Transform 220
11.7. The Spectrum of an Element of a C* Algebra 224
11.8. The Commutative Gelfand Naimark Theorem 226
11.9. Operator ^Representations of a C* Algebra 229
Exercises 234
References 237
Notation Index 255
Subject Index 259
|
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV010701555 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:57:26Z |
| institution | BVB |
| isbn | 0792338987 |
| language | English Russian |
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| physical | XIV, 276 S. |
| publishDate | 1996 |
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| publisher | Kluwer |
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| series | Kluwer texts in the mathematical sciences |
| series2 | Kluwer texts in the mathematical sciences |
| spelling | Kutateladze, Semen S. 1945- Verfasser (DE-588)123299268 aut Osnovy funkcional'nogo analiza Fundamentals of functional analysis by S. S. Kutateladze Dordrecht [u.a.] Kluwer 1996 XIV, 276 S. txt rdacontent n rdamedia nc rdacarrier Kluwer texts in the mathematical sciences 12 Aus dem Russ. übers. Functional analysis Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 s DE-604 Kluwer texts in the mathematical sciences 12 (DE-604)BV005450041 12 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007143096&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kutateladze, Semen S. 1945- Fundamentals of functional analysis Kluwer texts in the mathematical sciences Functional analysis Funktionalanalysis (DE-588)4018916-8 gnd |
| subject_GND | (DE-588)4018916-8 |
| title | Fundamentals of functional analysis |
| title_alt | Osnovy funkcional'nogo analiza |
| title_auth | Fundamentals of functional analysis |
| title_exact_search | Fundamentals of functional analysis |
| title_full | Fundamentals of functional analysis by S. S. Kutateladze |
| title_fullStr | Fundamentals of functional analysis by S. S. Kutateladze |
| title_full_unstemmed | Fundamentals of functional analysis by S. S. Kutateladze |
| title_short | Fundamentals of functional analysis |
| title_sort | fundamentals of functional analysis |
| topic | Functional analysis Funktionalanalysis (DE-588)4018916-8 gnd |
| topic_facet | Functional analysis Funktionalanalysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007143096&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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