Topological Vector Spaces: Chapters 1-5

by N. Bourbaki, H.G. Eggleston (Translator), S. Madan (Translator)

Overview

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).

Product Details

ISBN-13:	9783540423386
Publisher:	Springer Berlin Heidelberg
Publication date:	12/16/2002
Series:	Elements of Mathematics Series
Edition description:	1st ed. 1987. 2nd printing 2002
Pages:	362
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

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.