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OverviewThis 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). Full Product DetailsAuthor: N. Bourbaki , H.G. Eggleston , S. MadanPublisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K Edition: 1st ed. 1987. 2nd printing 2002 Dimensions: Width: 15.50cm , Height: 1.90cm , Length: 23.50cm Weight: 0.675kg ISBN: 9783540423386ISBN 10: 3540423389 Pages: 362 Publication Date: 13 November 2002 Audience: College/higher education , Professional and scholarly , Undergraduate , Postgraduate, Research & Scholarly Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsI. — 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.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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