Topological Vector Spaces I:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1983
|
| Schriftenreihe: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics
159 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | It is the author's aim to give a systematic account of the most important ideas, methods and results of the theory of topological vector spaces. After a rapid development during the last 15 years, this theory has now achieved a form which makes such an account seem both possible and desirable. This present first volume begins with the fundamental ideas of general topology. These are of crucial importance for the theory that follows, and so it seems necessary to give a concise account, giving complete proofs. This also has the advantage that the only preliminary knowledge required for reading this book is of classical analysis and set theory. In the second chapter, infinite dimensional linear algebra is considered in comparative detail. As a result, the concept of dual pair and linear topologies on vector spaces over arbitrary fields are introduced in a natural way. It appears to the author to be of interest to follow the theory of these linearly topologised spaces quite far, since this theory can be developed in a way which closely resembles the theory of locally convex spaces. It should however be stressed that this part of chapter two is not needed for the comprehension of the later chapters. Chapter three is concerned with real and complex topological vector spaces. The classical results of Banach's theory are given here, as are fundamental results about convex sets in infinite dimensional spaces |
| Beschreibung: | 1 Online-Ressource (XVI, 456 p) |
| ISBN: | 9783642649882 9783642649905 |
| DOI: | 10.1007/978-3-642-64988-2 |
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Datensatz im Suchindex
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| illustrated | Not Illustrated |
| indexdate | 2024-07-20T06:38:45Z |
| institution | BVB |
| isbn | 9783642649882 9783642649905 |
| language | English |
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| publishDate | 1983 |
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| series | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics |
| series2 | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics |
| spelling | Köthe, Gottfried Verfasser aut Topological Vector Spaces I by Gottfried Köthe Berlin, Heidelberg Springer Berlin Heidelberg 1983 1 Online-Ressource (XVI, 456 p) txt rdacontent c rdamedia cr rdacarrier Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics 159 It is the author's aim to give a systematic account of the most important ideas, methods and results of the theory of topological vector spaces. After a rapid development during the last 15 years, this theory has now achieved a form which makes such an account seem both possible and desirable. This present first volume begins with the fundamental ideas of general topology. These are of crucial importance for the theory that follows, and so it seems necessary to give a concise account, giving complete proofs. This also has the advantage that the only preliminary knowledge required for reading this book is of classical analysis and set theory. In the second chapter, infinite dimensional linear algebra is considered in comparative detail. As a result, the concept of dual pair and linear topologies on vector spaces over arbitrary fields are introduced in a natural way. It appears to the author to be of interest to follow the theory of these linearly topologised spaces quite far, since this theory can be developed in a way which closely resembles the theory of locally convex spaces. It should however be stressed that this part of chapter two is not needed for the comprehension of the later chapters. Chapter three is concerned with real and complex topological vector spaces. The classical results of Banach's theory are given here, as are fundamental results about convex sets in infinite dimensional spaces Mathematics Global analysis (Mathematics) Analysis Mathematik Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics 159 (DE-604)BV049758308 159 https://doi.org/10.1007/978-3-642-64988-2 Verlag Volltext |
| spellingShingle | Köthe, Gottfried Topological Vector Spaces I Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics Mathematics Global analysis (Mathematics) Analysis Mathematik |
| title | Topological Vector Spaces I |
| title_auth | Topological Vector Spaces I |
| title_exact_search | Topological Vector Spaces I |
| title_full | Topological Vector Spaces I by Gottfried Köthe |
| title_fullStr | Topological Vector Spaces I by Gottfried Köthe |
| title_full_unstemmed | Topological Vector Spaces I by Gottfried Köthe |
| title_short | Topological Vector Spaces I |
| title_sort | topological vector spaces i |
| topic | Mathematics Global analysis (Mathematics) Analysis Mathematik |
| topic_facet | Mathematics Global analysis (Mathematics) Analysis Mathematik |
| url | https://doi.org/10.1007/978-3-642-64988-2 |
| volume_link | (DE-604)BV049758308 |
| work_keys_str_mv | AT kothegottfried topologicalvectorspacesi |