Normed linear spaces:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1973
|
| Edition: | 3. ed. |
| Series: | Ergebnisse der Mathematik und ihrer Grenzgebiete
21 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 211 S. |
Staff View
MARC
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| 245 | 1 | 0 | |a Normed linear spaces |c Mahlon M. Day |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1973 | |
| 300 | |a VIII, 211 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Ergebnisse der Mathematik und ihrer Grenzgebiete |v 21 | |
| 650 | 4 | |a Espaces linéaires normés | |
| 650 | 7 | |a Funktionalanalysis |2 swd | |
| 650 | 7 | |a Lineaire algebra |2 gtt | |
| 650 | 7 | |a Norm (Normung) |2 swd | |
| 650 | 7 | |a Normierter Raum |2 swd | |
| 650 | 7 | |a Vektorraum |2 swd | |
| 650 | 4 | |a Normed linear spaces | |
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Record in the Search Index
| _version_ | 1804136091004960768 |
|---|---|
| adam_text | Contents
Chapter I. Linear Spaces 1
§ 1. Linear Spaces and Linear Dependence 1
§ 2. Linear Functions and Conjugate Spaces 4
§ 3. The Hahn Banach Extension Theorem 9
§4. Linear Topological Spaces 12
§5. Conjugate Spaces 18
§ 6. Cones, Wedges, Order Relations 22
Chapter II. Normed Linear Spaces 27
§ 1. Elementary Definitions and Properties 27
§ 2. Examples of Normed Spaces; Constructions of New Spaces
from Old 32
§ 3. Category Proofs 38
§ 4. Geometry and Approximation 43
§5. Comparison of Topologies in a Normed Space 45
Chapter III. Completeness, Compactness, and Reflexivity .... 53
§ 1. Completeness in a Linear Topological Space 53
§ 2. Compactness 57
§ 3. Completely Continuous Linear Operators 65
§4. Reflexivity 69
§ 5. Weak Compactness and Structure in Normed Spaces ... 72
Chapter IV. Unconditional Convergence and Bases 78
§ 1. Series and Unconditional Convergence 78
§2. Tensor Products of Locally Convex Spaces 83
§ 3. Schauder Bases in Separable Spaces 87
§ 4. Unconditional Bases 95
Chapter V. Compact Convex Sets and Continuous Function Spaces 101
§ 1. Extreme Points of Compact Convex Sets 101
§ 2. Fixed point Theorems 106
VIII Contents
§3. Some Properties of Continuous Function Spaces 113
§ 4. Characterizations of Continuous Function Spaces among
Banach Spaces 116
Chapter VI. Norm and Order 126
§1. Vector Lattices and Normed Lattices 126
§2. Linear Sublattices of Continuous Function Spaces . . . . 131
§ 3. Monotone Projections and Extensions 135
§4. Special Properties of (AL) Spaces 137
Chapter VII. Metric Geometry in Normed Spaces . 142
§ 1. Isometry and the Linear Structure 142
§ 2. Rotundity and Smoothness 144
§3. Characterizations of Inner Product Spaces 151
§4. Isomorphisms to Improve the Norm 159
A. Rotundity, smoothness, and convex functions 159
B. Superreflexive spaces 168
Chapter VIII. Reader s Guide 175
Bibliography 184
Index of Citations . . . 197
Index of Symbols 201
Subject Index 205
|
| adam_txt |
Contents
Chapter I. Linear Spaces 1
§ 1. Linear Spaces and Linear Dependence 1
§ 2. Linear Functions and Conjugate Spaces 4
§ 3. The Hahn Banach Extension Theorem 9
§4. Linear Topological Spaces 12
§5. Conjugate Spaces 18
§ 6. Cones, Wedges, Order Relations 22
Chapter II. Normed Linear Spaces 27
§ 1. Elementary Definitions and Properties 27
§ 2. Examples of Normed Spaces; Constructions of New Spaces
from Old 32
§ 3. Category Proofs 38
§ 4. Geometry and Approximation 43
§5. Comparison of Topologies in a Normed Space 45
Chapter III. Completeness, Compactness, and Reflexivity . 53
§ 1. Completeness in a Linear Topological Space 53
§ 2. Compactness 57
§ 3. Completely Continuous Linear Operators 65
§4. Reflexivity 69
§ 5. Weak Compactness and Structure in Normed Spaces . 72
Chapter IV. Unconditional Convergence and Bases 78
§ 1. Series and Unconditional Convergence 78
§2. Tensor Products of Locally Convex Spaces 83
§ 3. Schauder Bases in Separable Spaces 87
§ 4. Unconditional Bases 95
Chapter V. Compact Convex Sets and Continuous Function Spaces 101
§ 1. Extreme Points of Compact Convex Sets 101
§ 2. Fixed point Theorems 106
VIII Contents
§3. Some Properties of Continuous Function Spaces 113
§ 4. Characterizations of Continuous Function Spaces among
Banach Spaces 116
Chapter VI. Norm and Order 126
§1. Vector Lattices and Normed Lattices 126
§2. Linear Sublattices of Continuous Function Spaces . . . . 131
§ 3. Monotone Projections and Extensions 135
§4. Special Properties of (AL) Spaces 137
Chapter VII. Metric Geometry in Normed Spaces . 142
§ 1. Isometry and the Linear Structure 142
§ 2. Rotundity and Smoothness 144
§3. Characterizations of Inner Product Spaces 151
§4. Isomorphisms to Improve the Norm 159
A. Rotundity, smoothness, and convex functions 159
B. Superreflexive spaces 168
Chapter VIII. Reader's Guide 175
Bibliography 184
Index of Citations . . . 197
Index of Symbols 201
Subject Index 205 |
| any_adam_object | 1 |
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| author | Day, Mahlon Marsh 1913- |
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| ctrlnum | (OCoLC)1041468 (DE-599)BVBBV022117190 |
| dewey-full | 515/.73 |
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| dewey-ones | 515 - Analysis |
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| dewey-search | 515/.73 |
| dewey-sort | 3515 273 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 3. ed. |
| format | Book |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T16:16:02Z |
| indexdate | 2024-07-09T20:50:53Z |
| institution | BVB |
| language | English |
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| physical | VIII, 211 S. |
| publishDate | 1973 |
| publishDateSearch | 1973 |
| publishDateSort | 1973 |
| publisher | Springer |
| record_format | marc |
| series | Ergebnisse der Mathematik und ihrer Grenzgebiete |
| series2 | Ergebnisse der Mathematik und ihrer Grenzgebiete |
| spelling | Day, Mahlon Marsh 1913- Verfasser (DE-588)1070262749 aut Normed linear spaces Mahlon M. Day 3. ed. Berlin [u.a.] Springer 1973 VIII, 211 S. txt rdacontent n rdamedia nc rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete 21 Espaces linéaires normés Funktionalanalysis swd Lineaire algebra gtt Norm (Normung) swd Normierter Raum swd Vektorraum swd Normed linear spaces Vektorraum (DE-588)4130622-3 gnd rswk-swf Norm Normung (DE-588)4172022-2 gnd rswk-swf Normierter Raum (DE-588)4127735-1 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Normierter Raum (DE-588)4127735-1 s DE-604 Funktionalanalysis (DE-588)4018916-8 s Vektorraum (DE-588)4130622-3 s Norm Normung (DE-588)4172022-2 s 1\p DE-604 Ergebnisse der Mathematik und ihrer Grenzgebiete 21 (DE-604)BV005871160 21 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015332054&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 | Day, Mahlon Marsh 1913- Normed linear spaces Ergebnisse der Mathematik und ihrer Grenzgebiete Espaces linéaires normés Funktionalanalysis swd Lineaire algebra gtt Norm (Normung) swd Normierter Raum swd Vektorraum swd Normed linear spaces Vektorraum (DE-588)4130622-3 gnd Norm Normung (DE-588)4172022-2 gnd Normierter Raum (DE-588)4127735-1 gnd Funktionalanalysis (DE-588)4018916-8 gnd |
| subject_GND | (DE-588)4130622-3 (DE-588)4172022-2 (DE-588)4127735-1 (DE-588)4018916-8 |
| title | Normed linear spaces |
| title_auth | Normed linear spaces |
| title_exact_search | Normed linear spaces |
| title_exact_search_txtP | Normed linear spaces |
| title_full | Normed linear spaces Mahlon M. Day |
| title_fullStr | Normed linear spaces Mahlon M. Day |
| title_full_unstemmed | Normed linear spaces Mahlon M. Day |
| title_short | Normed linear spaces |
| title_sort | normed linear spaces |
| topic | Espaces linéaires normés Funktionalanalysis swd Lineaire algebra gtt Norm (Normung) swd Normierter Raum swd Vektorraum swd Normed linear spaces Vektorraum (DE-588)4130622-3 gnd Norm Normung (DE-588)4172022-2 gnd Normierter Raum (DE-588)4127735-1 gnd Funktionalanalysis (DE-588)4018916-8 gnd |
| topic_facet | Espaces linéaires normés Funktionalanalysis Lineaire algebra Norm (Normung) Normierter Raum Vektorraum Normed linear spaces Norm Normung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015332054&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV005871160 |
| work_keys_str_mv | AT daymahlonmarsh normedlinearspaces |