Topological vector spaces:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton, [Florida], [u.a.]
CRC Press
2024
|
| Edition: | Second edition |
| Series: | Pure and applied mathematics
296 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | xvii, 610 Seiten |
| ISBN: | 9781584888666 9781032918105 |
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MARC
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| 245 | 1 | 0 | |a Topological vector spaces |c Lawrence Narici ; Edward Beckenstein |
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Record in the Search Index
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| adam_text |
Titel: Topological vector spaces
Autor: Narici, Lawrence
Jahr: 2011
Contents
Contents vii
Preface to This Edition xiii
Preface to First Edition xv
1 Background 1
1.1 TOPOLOGY. 1
1.1.1 Closure and Interior. 2
1.1.2 Filterbases and Nets. 2
1.1.3 Compactness. 5
1.2 VALUATION THEORY. 7
1.3 ALGEBRA. 8
1.4 LINEAR FUNCTIONALS. 9
1.5 HYPERPLANES. 11
1.6 MEASURE THEORY. 13
1.7 NORMED SPACES. 14
1.7.1 Inner Product Spaces . 17
2 Commutative Topological Groups 19
2.1 ELEMENTARY CONSIDERATIONS. 20
2.2 SEPARATION AND COMPACTNESS . 23
2.3 BASES AT 0 FOR GROUP TOPOLOGIES. 26
2.4 SUBGROUPS AND PRODUCTS . 28
2.5 QUOTIENTS. 30
2.6 S-TOPOLOGIES. 33
2.7 METRIZABILITY. 37
2.8 EXERCISES. 41
3 Completeness 47
3.1 COMPLETENESS. 48
3.2 FUNCTION GROUPS. 51
3.3 TOTAL BOUNDEDNESS. 53
3.3.1 Total Boundedness and Subbases. 54
VII
viii CONTENTS
3.3.2 Cauchy Boundedness. 54
3.4 COMPACTNESS. 55
3.5 UNIFORM CONTINUITY. 56
3.6 UNIFORMLY CONTINUOUS MAPS. 58
3.7 COMPLETION. 60
3.8 EXERCISES. 62
4 Topological Vector Spaces 67
4.1 ABSORBENT AND BALANCED SETS. 68
4.2 CONVEXITY?ALGEBRAIC . 71
4.3 BASIC PROPERTIES. 77
4.4 CONVEXITY?TOPOLOGICAL . 80
4.5 GENERATING VECTOR TOPOLOGIES. 83
4.6 A NON-LOCALLY CONVEX SPACE. 86
4.7 PRODUCTS AND QUOTIENTS. 88
4.8 METRIZABILITY AND COMPLETION. 91
4.9 TOPOLOGICAL COMPLEMENTS. 95
4.10 FINITE-DIMENSIONAL AND LOCALLY COMPACT SPACES 101
4.11 EXAMPLES .105
4.12 EXERCISES.107
5 Locally Convex Spaces and Seminorms 115
5.1 SEMINORMS.116
5.2 CONTINUITY OF SEMINORMS.117
5.3 GAUGES.119
5.4 SUBLINEAR FUNCTIONALS.120
5.5 SEMINORM TOPOLOGIES.121
5.6 METRIZABILITY OF LCS.123
5.7 CONTINUITY OF LINEAR MAPS.126
5.8 THE COMPACT-OPEN TOPOLOGY.128
5.9 THE POINT-OPEN TOPOLOGY.132
5.10 ASCOLPS THEOREM .133
5.11 PRODUCTS AND QUOTIENTS.136
5.12 ORDERED VECTOR SPACES.139
5.13 EXERCISES.149
6 Bounded Sets 155
6.1 BOUNDED SETS.156
6.2 METRIZABILITY.160
6.3 STABILITY OF BOUNDED SETS.161
6.4 CONTINUITY.163
6.5 WHEN LOCALLY BOUNDED IMPLIES CONTINUOUS . 165
6.6 LIOUVILLE'S THEOREM.166
6.7 BORNOLOGIES.167
6.8 EXERCISES.171
CONTENTS ix
7 Hahn-Banach Theorems 177
7.1 WHAT IS IT?.178
7.2 THE OBVIOUS SOLUTION.179
7.3 DOMINATED EXTENSIONS .179
7.4 CONSEQUENCES.184
7.4.1 The Dual of C[0,1] .186
7.5 THE MAZUR-ORLICZ THEOREM.187
7.6 MINIMAL SUBLINEAR FUNCTIONALS.189
7.7 GEOMETRIC FORM.191
7.8 SEPARATION OF CONVEX SETS.196
7.8.1 Smoothness.201
7.9 ORIGIN OF THE THEOREM.202
7.10 FUNCTIONAL PROBLEM SOLVED.206
7.11 THE AXIOM OF CHOICE.209
7.11.1 Avoiding the Axiom of Choice .210
7.12 NOTES ON THE HAHN-BANACH THEOREM.211
7.13 HELLY.214
7.14 EXERCISES.216
8 Duality 225
8.1 PAIRED SPACES.227
8.2 WEAK TOPOLOGIES.228
8.3 POLARS.232
8.4 ALAOGLU.235
8.5 POLAR TOPOLOGIES.241
8.6 EQUICONTINUITY.244
8.7 TOPOLOGIES OF PAIRS .247
8.8 PERMANENCE IN DUALITY.250
8.9 ORTHOGONALS .254
8.10 ADJOINTS.256
8.11 ADJOINTS AND CONTINUITY.258
8.12 SUBSPACES AND QUOTIENTS .260
8.13 OPENNESS OF LINEAR MAPS.264
8.14 LOCAL CONVEXITY AND HBEP.268
8.15 EXERCISES.269
9 Krein-Milman and Banach-Stone 275
9.1 MIDPOINTS AND SEGMENTS.276
9.2 EXTREME POINTS.278
9.3 FACES .283
9.4 KREIN-MILMAN THEOREMS.285
9.5 THE CHOQUET BOUNDARY.291
9.6 THE BANACH-STONE THEOREM .298
9.6.1 The Realcompactification.302
9.7 SEPARATTNG MAPS.303
x CONTENTS
9.7.1 Definitions and Examples.303
9.7.2 Support Map.305
9.7.3 Continuity of Weakly Separating Maps.309
9.7.4 Biseparating Maps.312
9.8 NON-ARCHIMEDEAN THEOREMS.320
9.9 BANACH-STONE VARIATIONS.326
9.9.1 Subspaces.326
9.9.2 Into Isometries.328
9.9.3 Vector-Valued Functions.329
9.9.4 Ordered Versions.333
9.10 EXERCISES.334
10 Vector-Valued Hahn?Banach Theorems 341
10.1 INJECTIVE SPACES.342
10.2 METRIC EXTENSION PROPERTY .345
10.3 INTERSECTION PROPERTIES.347
10.4 THE CENTER-RADIUS PROPERTY.350
10.5 METRIC EXTENSION = CRP.354
10.6 WEAK INTERSECTION PROPERTY.357
10.7 REPRESENTATION THEOREM.359
10.8 SUMMARY.365
10.8.1 Radial Descriptions .367
10.9 NOTES.368
10.10 EXERCISES.368
11 Barreled Spaces 371
11.1 THE SCOTTISH CAFE.372
11.2 5-TOPOLOGIES FOR L(X,Y).379
11.3 BARRELED SPACES.383
11.4 LOWER SEMICONTINUITY .385
11.5 RARE SETS.387
11.6 MEAGER, NONMEAGER AND BAIRE.389
11.7 THE BAIRE CATEGORY THEOREM.392
11.8 BAIRE TVS .394
11.8.1 Baire Variations.398
11.9 BANACH-STEINHAUS THEOREM.399
11.10 A DIVERGENT FOURIER SERIES.403
11.11 INFRABARRELED SPACES.405
11.12 PERMANENCE PROPERTIES.408
11.13 INCREASING SEQUENCES OF DISKS.413
11.14 EXERCISES.416
CONTENTS xi
12 Inductive Limits 425
12.1 STRICT INDUCTIVE LIMITS.426
12.2 INDUCTIVE LIMITS OF LCS.434
12.3 EXERCISES.435
13 Bornological Spaces 441
13.1 BANACH DISKS.441
13.2 BORNOLOGICAL SPACES .443
13.3 EXERCISES.451
14 Closed Graph Theorems 459
14.1 MAPS WITH CLOSED GRAPHS.460
14.2 CLOSED LINEAR MAPS.461
14.3 CLOSED GRAPH THEOREMS.464
14.4 OPEN MAPPING THEOREMS.466
14.5 APPLICATIONS.469
14.6 WEBBED SPACES .470
14.7 CLOSED GRAPH THEOREMS.473
14.8 LIMITS ON THE DOMAIN SPACE.476
14.9 OTHER CLOSED GRAPH THEOREMS.477
14.9.1 Webs without Convexity Conditions.479
14.10 EXERCISES.479
15 Reflexivity 485
15.1 REFLEXIVITY BASICS .487
15.2 REFLEXIVE SPACES.487
15.3 WEAK-STAR CLOSED SETS.491
15.4 EBERLEIN-SMULIAN THEOREM.496
15.5 REFLEXIVITY OF BANACH SPACES.501
15.6 NORM-ATTAINING FUNCTIONALS.503
15.7 PARTICULAR DUALS.505
15.8 SCHAUDER BASES.508
15.9 APPROXIMATION PROPERTIES .515
15.10 EXERCISES.516
16 Norm Convexities and Approximation 519
16.1 STRICT CONVEXITY.520
16.2 UNIFORM CONVEXITY.523
16.3 BEST APPROXIMATION.526
16.3.1 Best Approximation in C(T,F, || H^).534
16.4 UNIQUENESS OF HB EXTENSIONS.536
16.4.1 Dominated Extensions.536
16.4.2 Norm-Preserving Extensions .538
16.4.3 HB-Subspaces.541
16.5 STONE-WEIERSTRASS THEOREM.544
xii CONTENTS
16.6 EXERCISES.549
Bibliography 555
Index 591 |
| any_adam_object | 1 |
| author | Narici, Lawrence 1941- Beckenstein, Edward 1940- |
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| discipline | Mathematik |
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| id | DE-604.BV036516578 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-14T15:00:59Z |
| institution | BVB |
| isbn | 9781584888666 9781032918105 |
| language | English |
| lccn | 2010007966 |
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| physical | xvii, 610 Seiten |
| publishDate | 2024 |
| publishDateSearch | 2024 |
| publishDateSort | 2024 |
| publisher | CRC Press |
| record_format | marc |
| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics A Chapman & Hall book |
| spelling | Narici, Lawrence 1941- (DE-588)121796361 aut Topological vector spaces Lawrence Narici ; Edward Beckenstein Second edition Boca Raton, [Florida], [u.a.] CRC Press 2024 xvii, 610 Seiten txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 296 A Chapman & Hall book Includes bibliographical references and index Linear topological spaces Hahn-Banach-Fortsetzungssatz (DE-588)4158765-0 gnd rswk-swf Topologischer Vektorraum (DE-588)4122383-4 gnd rswk-swf Banach-Stone-Theorem (DE-588)4660701-8 gnd rswk-swf Topologischer Vektorraum (DE-588)4122383-4 s Hahn-Banach-Fortsetzungssatz (DE-588)4158765-0 s Banach-Stone-Theorem (DE-588)4660701-8 s DE-604 Beckenstein, Edward 1940- (DE-588)12179637X aut Erscheint auch als Online-Ausgabe 978-0-429-14789-0 Pure and applied mathematics 296 (DE-604)BV000001885 296 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020438681&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Narici, Lawrence 1941- Beckenstein, Edward 1940- Topological vector spaces Pure and applied mathematics Linear topological spaces Hahn-Banach-Fortsetzungssatz (DE-588)4158765-0 gnd Topologischer Vektorraum (DE-588)4122383-4 gnd Banach-Stone-Theorem (DE-588)4660701-8 gnd |
| subject_GND | (DE-588)4158765-0 (DE-588)4122383-4 (DE-588)4660701-8 |
| title | Topological vector spaces |
| title_auth | Topological vector spaces |
| title_exact_search | Topological vector spaces |
| title_full | Topological vector spaces Lawrence Narici ; Edward Beckenstein |
| title_fullStr | Topological vector spaces Lawrence Narici ; Edward Beckenstein |
| title_full_unstemmed | Topological vector spaces Lawrence Narici ; Edward Beckenstein |
| title_short | Topological vector spaces |
| title_sort | topological vector spaces |
| topic | Linear topological spaces Hahn-Banach-Fortsetzungssatz (DE-588)4158765-0 gnd Topologischer Vektorraum (DE-588)4122383-4 gnd Banach-Stone-Theorem (DE-588)4660701-8 gnd |
| topic_facet | Linear topological spaces Hahn-Banach-Fortsetzungssatz Topologischer Vektorraum Banach-Stone-Theorem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020438681&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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