Topological vector spaces:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
1999
|
| Edition: | 2. ed. |
| Series: | Graduate texts in mathematics
3 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 330 - 338 |
| Physical Description: | XI, 346 S. |
| ISBN: | 0387987266 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804127415370252288 |
|---|---|
| adam_text | Table of Contents
Preface to the Second Edition v
Preface vi
Prerequisites
A. Sets and Order 1
B. General Topology 4
C. Linear Algebra 9
I. TOPOLOGICAL VECTOR SPACES
Introduction 12
1 Vector Space Topologies 12
2 Product Spaces, Subspaces, Direct Sums,
Quotient Spaces 19
3 Topological Vector Spaces of Finite Dimension 21
4 Linear Manifolds and Hyperplanes 24
5 Bounded Sets 25
6 Metrizability 28
7 Complexification 31
Exercises 33
II. LOCALLY CONVEX TOPOLOGICAL
VECTOR SPACES
Introduction 36
1 Convex Sets and Semi Norms 37
2 Normed and Normable Spaces 40
3 The Hahn Banach Theorem 45
viii
TABLE OF CONTENTS ix
4 Locally Convex Spaces 47
5 Projective Topologies 57
6 Inductive Topologies 54
7 Barreled Spaces 60
8 Bornological Spaces 61
9 Separation of Convex Sets 63
10 Compact Convex Sets 66
Exercises 68
III. LINEAR MAPPINGS
Introduction 73
1 Continuous Linear Maps and Topological
Homomorphisms 74
1 Banach s Homomorphism Theorem 76
3 Spaces of Linear Mappings 79
4 Equicontinuity. The Principle of Uniform Boundedness
and the Banach Steinhaus Theorem 82
5 Bilinear Mappings 87
6 Topological Tensor Products 92
7 Nuclear Mappings and Spaces 97
8 Examples of Nuclear Spaces 106
9 The Approximation Property. Compact Maps 108
Exercises 115
IV. DUALITY
Introduction 122
1 Dual Systems and Weak Topologies 123
2 Elementary Properties of Adjoint Maps 128
3 Locally Convex Topologies Consistent with a
Given Duality.The Mackey Arens Theorem 130
4 Duality of Projective and Inductive Topologies 133
5 Strong Dual of a Locally Convex Space. Bidual.
Reflexive Spaces 140
6 Dual Characterization of Completeness. Metrizable Spaces.
Theorems of Grothendieck, Banach Dieudonne, and
Krein Smulian 147
x TABLE OF CONTENTS
7 Adjoints of Closed Linear Mappings 155
8 The General Open Mapping and Closed Graph Theorems 161
9 Tensor Products and Nuclear Spaces 767
10 Nuclear Spaces and Absolute Summability 176
11 Weak Compactness. Theorems of Eberlein and Krein 185
Exercises 190
V. ORDER STRUCTURES
Introduction 203
1 Ordered Vector Spaces over the Real Field 204
2 Ordered Vector Spaces over the Complex Field 214
3 Duality of Convex Cones 215
4 Ordered Topological Vector Spaces 222
5 Positive Linear Forms and Mappings 225
6 The Order Topology 230
7 Topological Vector Lattices 234
8 Continuous Functions on a Compact Space. Theorems
of Stone Weierstrass and Kakutani 242
Exercises 250
VI. C AND r ALGEBRAS
Introduction 258
1 Preliminaries 259
2 C* Algebras.The Gelfand Theorem 260
3 Order Structure of a C* Algebra 267
4 Positive Linear Forms. Representations 270
5 Projections and Extreme Points 274
6 W* Algebras 277
7 Von Neumann Algebras. Kaplansky s Density Theorem 287
8 Projections and Types of W* Algebras 292
Exercises 299
Appendix. SPECTRAL PROPERTIES OF
POSITIVE OPERATORS
Introduction 306
1 Elementary Properties of the Resolvent 307
1 Pringsheim s Theorem and Its Consequences 309
TABLE OF CONTENTS xi
3 The Peripheral Point Spectrum 316
Index of Symbols 325
Bibliography 330
Index 339
|
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| dewey-full | 514.32 |
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| dewey-ones | 514 - Topology |
| dewey-raw | 514.32 |
| dewey-search | 514.32 |
| dewey-sort | 3514.32 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| isbn | 0387987266 |
| language | English |
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| physical | XI, 346 S. |
| publishDate | 1999 |
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| publisher | Springer |
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| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Schaefer, Helmut H. 1925-2005 Verfasser (DE-588)107361191 aut Topological vector spaces H. H. Schaefer with M. P. Wolff 2. ed. New York [u.a.] Springer 1999 XI, 346 S. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 3 Literaturverz. S. 330 - 338 Topologischer Vektorraum Linear topological spaces Topologischer Vektorraum (DE-588)4122383-4 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Topologischer Vektorraum (DE-588)4122383-4 s DE-604 Funktionalanalysis (DE-588)4018916-8 s 1\p DE-604 Wolff, Manfred 1939-2022 Verfasser (DE-588)121290506 aut Graduate texts in mathematics 3 (DE-604)BV000000067 3 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008668375&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Schaefer, Helmut H. 1925-2005 Wolff, Manfred 1939-2022 Topological vector spaces Graduate texts in mathematics Topologischer Vektorraum Linear topological spaces Topologischer Vektorraum (DE-588)4122383-4 gnd Funktionalanalysis (DE-588)4018916-8 gnd |
| subject_GND | (DE-588)4122383-4 (DE-588)4018916-8 |
| title | Topological vector spaces |
| title_auth | Topological vector spaces |
| title_exact_search | Topological vector spaces |
| title_full | Topological vector spaces H. H. Schaefer with M. P. Wolff |
| title_fullStr | Topological vector spaces H. H. Schaefer with M. P. Wolff |
| title_full_unstemmed | Topological vector spaces H. H. Schaefer with M. P. Wolff |
| title_short | Topological vector spaces |
| title_sort | topological vector spaces |
| topic | Topologischer Vektorraum Linear topological spaces Topologischer Vektorraum (DE-588)4122383-4 gnd Funktionalanalysis (DE-588)4018916-8 gnd |
| topic_facet | Topologischer Vektorraum Linear topological spaces Funktionalanalysis |
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| work_keys_str_mv | AT schaeferhelmuth topologicalvectorspaces AT wolffmanfred topologicalvectorspaces |