N. Bourbaki: Topological Vector Spaces

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Cover: 9783540423386 | Topological Vector Spaces | Chapters 1¿5 | N. Bourbaki | Taschenbuch

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Sprache: Englisch

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Beschreibung

This is a softcover reprint of the English translation of 1987 of the second edition of Bourbaki's Espaces Vectoriels Topologiques (1981).
This [second edition] 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).

Inhaltsverzeichnis

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.- § 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.- Exercises on § 3.- Exercises on § 4.- Historical notes.- Index of notation.- Index of terminology.- Summary of some important propertiesof Banach spaces.