N. Bourbaki

Topological Vector Spaces (eBook, PDF)

Chapters 1-5
Übersetzer: Eggleston, H. G.; Madan, S.

• Format: PDF

Produktbeschreibung

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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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 362
• Erscheinungstermin: 1. Dezember 2013
• Englisch
• ISBN-13: 9783642617157
• Artikelnr.: 53393578

Inhaltsangabe

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.