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140122 ||| eng |
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|a 9783642617157
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| 100 |
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|a Bourbaki, N.
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| 245 |
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|a Topological Vector Spaces
|h Elektronische Ressource
|b Chapters 1–5
|c by N. Bourbaki
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| 250 |
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|a 1st ed. 2003
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| 260 |
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|a Berlin, Heidelberg
|b Springer Berlin Heidelberg
|c 2003, 2003
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| 300 |
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|a VII, 362 p
|b online resource
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|a I. — Topological vector spaces over a valued division ring I. -- § 1. Topological vector spaces -- § 2. Linear varieties in a topological vector space -- § 3. Metrisable topological vector spaces -- Exercises of § 1 -- Exercises of § 2 -- Exercises of § 3 -- II. — Convex sets and locally convex spaces II. -- § 1. Semi-norms -- § 2. Convex sets -- § 3. The Hahn-Banach Theorem (analytic form) -- § 4. Locally convex spaces -- § 5. Separation of convex sets -- § 6. Weak topologies -- § 7. Extremal points and extremal generators -- § 8. Complex locally convex spaces -- Exercises on § 2 -- Exercises on § 3 -- Exercises on § 4 -- Exercises on § 5 -- Exercises on § 6 -- Exercises on § 7 -- Exercises on § 8 -- III. — Spaces of continuous linear mappings III. -- § 1. Bornology in a topological vector space -- § 2. Bornological spaces -- § 3. Spaces of continuous linear mappings -- § 4. The Banach-Steinhaus theorem -- § 5. Hypocontinuous bilinear mappings --
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|a Exercises on § 3 -- Exercises on § 4 -- Historical notes -- Index of notation -- Index of terminology -- Summary of some important propertiesof Banach spaces
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|a § 6. Borel’s graph theorem -- Exercises on § 1 -- Exercises on § 2.-Exercises on § 3 -- Exercises on § 4 -- Exercises on § 5 -- Exercises on § 6 -- IV. — Duality in topological vector spaces IV. -- § 1. Duality -- § 2. Bidual. Reflexive spaces -- § 3. Dual of a Fréchet space -- § 4. Strict morphisms of Fréchet spaces -- § 5. Compactness criteria -- Appendix. — Fixed points of groups of affine transformations -- Exercises on § 1 -- Exercises on § 2 -- Exercises on § 3 -- Exercises on § 4 -- Exercises on § 5 -- Exercises on Appendix -- Table I. — Principal types of locally convex spaces -- Table II. — Principal homologies on the dual of a locally convex space -- V. — Hilbertian spaces (elementary theory) V. -- § 1. Prehilbertian spaces and hilbertian spaces -- § 2. Orthogonal families in a hilbertian space -- § 3. Tensor product of hilbertian spaces -- § 4. Some classes of operators in hilbertian spaces -- Exercises on § 1 -- Exercises on § 2 --
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| 653 |
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|a Functional analysis
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| 653 |
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|a Functional Analysis
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| 653 |
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|a Topology
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| 041 |
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|a eng
|2 ISO 639-2
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| 989 |
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|b SBA
|a Springer Book Archives -2004
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| 028 |
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|a 10.1007/978-3-642-61715-7
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| 856 |
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|u https://doi.org/10.1007/978-3-642-61715-7?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
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|a 514
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| 520 |
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|a This is a softcover reprint of the English translation of 1987 of the second edition of Bourbaki's Espaces Vectoriels Topologiques (1981). This Äsecond editionÜ is a brand new book and completely supersedes the original version of nearly 30 years ago. But a lot of the material has been rearranged, rewritten, or replaced by a more up-to-date exposition, and a good deal of new material has been incorporated in this book, all reflecting the progress made in the field during the last three decades. Table of Contents. Chapter I: Topological vector spaces over a valued field. Chapter II: Convex sets and locally convex spaces. Chapter III: Spaces of continuous linear mappings. Chapter IV: Duality in topological vector spaces. Chapter V: Hilbert spaces (elementary theory). Finally, there are the usual "historical note", bibliography, index of notation, index of terminology, and a list of some important properties of Banach spaces. (Based on Math Reviews, 1983)
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