The Open Mapping and Closed Graph Theorems in Topological Vector Spaces:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Wiesbaden
Vieweg+Teubner Verlag
1965
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| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | THE main purpose of writing this monograph is to give a picture of the progress made in recent years in understanding three of the deepest results of Functional Analysis-namely, the open-mapping and closed graph theorems, and the so-called Krein-~mulian theorem. In order to facilitate the reading of this book, some of the important notions and well-known results about topological and vector spaces have been collected in Chapter 1. The proofs of these results are omitted for the reason that they are easily available in any standard book on topology and vector spaces e.g. Bourbaki [2], Keiley [18], or Köthe [22]. The results of Chapter 2 are supposed to be weil known for a study of topological vector spaces as weil. Most of the definitions and notations of Chapter 2 are taken from Bourbaki's books [3] and [4] with some trimming and pruning here and there. Keeping the purpose of this book in mind, the presentation of the material is effected to give a quick resume of the results and the ideas very commonly used in this field, sacrificing the generality of some theorems for which one may consult other books, e.g. [3], [4], and [22]. From Chapter 3 onward, a detailed study of the open-mapping and closed-graph theorems as weil as the Krein-~mulian theorem has been carried out. For the arrangement of the contents of Chapters 3 to 7, see the Historical Notes (Chapter 8) |
| Beschreibung: | 1 Online-Ressource (X, 108 p) |
| ISBN: | 9783322962102 9783322960771 |
| DOI: | 10.1007/978-3-322-96210-2 |
Internformat
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| 500 | |a THE main purpose of writing this monograph is to give a picture of the progress made in recent years in understanding three of the deepest results of Functional Analysis-namely, the open-mapping and closed graph theorems, and the so-called Krein-~mulian theorem. In order to facilitate the reading of this book, some of the important notions and well-known results about topological and vector spaces have been collected in Chapter 1. The proofs of these results are omitted for the reason that they are easily available in any standard book on topology and vector spaces e.g. Bourbaki [2], Keiley [18], or Köthe [22]. The results of Chapter 2 are supposed to be weil known for a study of topological vector spaces as weil. Most of the definitions and notations of Chapter 2 are taken from Bourbaki's books [3] and [4] with some trimming and pruning here and there. Keeping the purpose of this book in mind, the presentation of the material is effected to give a quick resume of the results and the ideas very commonly used in this field, sacrificing the generality of some theorems for which one may consult other books, e.g. [3], [4], and [22]. From Chapter 3 onward, a detailed study of the open-mapping and closed-graph theorems as weil as the Krein-~mulian theorem has been carried out. For the arrangement of the contents of Chapters 3 to 7, see the Historical Notes (Chapter 8) | ||
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Datensatz im Suchindex
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| indexdate | 2024-07-10T01:21:11Z |
| institution | BVB |
| isbn | 9783322962102 9783322960771 |
| language | English |
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| spelling | Husain, Taqdir Verfasser aut The Open Mapping and Closed Graph Theorems in Topological Vector Spaces by Taqdir Husain Wiesbaden Vieweg+Teubner Verlag 1965 1 Online-Ressource (X, 108 p) txt rdacontent c rdamedia cr rdacarrier THE main purpose of writing this monograph is to give a picture of the progress made in recent years in understanding three of the deepest results of Functional Analysis-namely, the open-mapping and closed graph theorems, and the so-called Krein-~mulian theorem. In order to facilitate the reading of this book, some of the important notions and well-known results about topological and vector spaces have been collected in Chapter 1. The proofs of these results are omitted for the reason that they are easily available in any standard book on topology and vector spaces e.g. Bourbaki [2], Keiley [18], or Köthe [22]. The results of Chapter 2 are supposed to be weil known for a study of topological vector spaces as weil. Most of the definitions and notations of Chapter 2 are taken from Bourbaki's books [3] and [4] with some trimming and pruning here and there. Keeping the purpose of this book in mind, the presentation of the material is effected to give a quick resume of the results and the ideas very commonly used in this field, sacrificing the generality of some theorems for which one may consult other books, e.g. [3], [4], and [22]. From Chapter 3 onward, a detailed study of the open-mapping and closed-graph theorems as weil as the Krein-~mulian theorem has been carried out. For the arrangement of the contents of Chapters 3 to 7, see the Historical Notes (Chapter 8) Mathematics Functional analysis Operator theory Topology Operator Theory Functional Analysis Mathematik Offene Abbildung (DE-588)4470619-4 gnd rswk-swf Topologischer Vektorraum (DE-588)4122383-4 gnd rswk-swf Satz vom abgeschlossenen Graphen (DE-588)4179178-2 gnd rswk-swf Topologischer Vektorraum (DE-588)4122383-4 s Offene Abbildung (DE-588)4470619-4 s 1\p DE-604 Satz vom abgeschlossenen Graphen (DE-588)4179178-2 s 2\p DE-604 https://doi.org/10.1007/978-3-322-96210-2 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Husain, Taqdir The Open Mapping and Closed Graph Theorems in Topological Vector Spaces Mathematics Functional analysis Operator theory Topology Operator Theory Functional Analysis Mathematik Offene Abbildung (DE-588)4470619-4 gnd Topologischer Vektorraum (DE-588)4122383-4 gnd Satz vom abgeschlossenen Graphen (DE-588)4179178-2 gnd |
| subject_GND | (DE-588)4470619-4 (DE-588)4122383-4 (DE-588)4179178-2 |
| title | The Open Mapping and Closed Graph Theorems in Topological Vector Spaces |
| title_auth | The Open Mapping and Closed Graph Theorems in Topological Vector Spaces |
| title_exact_search | The Open Mapping and Closed Graph Theorems in Topological Vector Spaces |
| title_full | The Open Mapping and Closed Graph Theorems in Topological Vector Spaces by Taqdir Husain |
| title_fullStr | The Open Mapping and Closed Graph Theorems in Topological Vector Spaces by Taqdir Husain |
| title_full_unstemmed | The Open Mapping and Closed Graph Theorems in Topological Vector Spaces by Taqdir Husain |
| title_short | The Open Mapping and Closed Graph Theorems in Topological Vector Spaces |
| title_sort | the open mapping and closed graph theorems in topological vector spaces |
| topic | Mathematics Functional analysis Operator theory Topology Operator Theory Functional Analysis Mathematik Offene Abbildung (DE-588)4470619-4 gnd Topologischer Vektorraum (DE-588)4122383-4 gnd Satz vom abgeschlossenen Graphen (DE-588)4179178-2 gnd |
| topic_facet | Mathematics Functional analysis Operator theory Topology Operator Theory Functional Analysis Mathematik Offene Abbildung Topologischer Vektorraum Satz vom abgeschlossenen Graphen |
| url | https://doi.org/10.1007/978-3-322-96210-2 |
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