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AuthorBourbaki, Nicolas. author
TitleTopological Vector Spaces [electronic resource] : Chapters 1-5 / by Nicolas Bourbaki
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 2003
Connect tohttp://dx.doi.org/10.1007/978-3-642-61715-7
Descript VII, 362 p. online resource

SUMMARY

This is a softcover reprint of the English translation of 1987 of the second edition of Bourbaki's Espaces Vectoriels Topologiques (1981). This ร{132}second editionร{156} 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)


CONTENT

I. โ{128}{148} Topological vector spaces over a valued division ring I. -- ยง 1. Topological vector spaces -- ยง 2. Linear varieties in a topological vector space -- ยง 3. Metrisable topological vector spaces -- Exercises of ยง 1 -- Exercises of ยง 2 -- Exercises of ยง 3 -- II. โ{128}{148} Convex sets and locally convex spaces II. -- ยง 1. Semi-norms -- ยง 2. Convex sets -- ยง 3. The Hahn-Banach Theorem (analytic form) -- ยง 4. Locally convex spaces -- ยง 5. Separation of convex sets -- ยง 6. Weak topologies -- ยง 7. Extremal points and extremal generators -- ยง 8. Complex locally convex spaces -- Exercises on ยง 2 -- Exercises on ยง 3 -- Exercises on ยง 4 -- Exercises on ยง 5 -- Exercises on ยง 6 -- Exercises on ยง 7 -- Exercises on ยง 8 -- III. โ{128}{148} Spaces of continuous linear mappings III. -- ยง 1. Bornology in a topological vector space -- ยง 2. Bornological spaces -- ยง 3. Spaces of continuous linear mappings -- ยง 4. The Banach-Steinhaus theorem -- ยง 5. Hypocontinuous bilinear mappings -- ยง 6. Borelโ{128}{153}s graph theorem -- Exercises on ยง 1 -- Exercises on ยง 2 -- Exercises on ยง 3 -- Exercises on ยง 4 -- Exercises on ยง 5 -- Exercises on ยง 6 -- IV. โ{128}{148} Duality in topological vector spaces IV. -- ยง 1. Duality -- ยง 2. Bidual. Reflexive spaces -- ยง 3. Dual of a Frรฉchet space -- ยง 4. Strict morphisms of Frรฉchet spaces -- ยง 5. Compactness criteria -- Appendix. โ{128}{148} Fixed points of groups of affine transformations -- Exercises on ยง 1 -- Exercises on ยง 2 -- Exercises on ยง 3 -- Exercises on ยง 4 -- Exercises on ยง 5 -- Exercises on Appendix -- Table I. โ{128}{148} Principal types of locally convex spaces -- Table II. โ{128}{148} Principal homologies on the dual of a locally convex space -- V. โ{128}{148} Hilbertian spaces (elementary theory) V. -- ยง 1. Prehilbertian spaces and hilbertian spaces -- ยง 2. Orthogonal families in a hilbertian space -- ยง 3. Tensor product of hilbertian spaces -- ยง 4. Some classes of operators in hilbertian spaces -- Exercises on ยง 1 -- Exercises on ยง 2 -- Exercises on ยง 3 -- Exercises on ยง 4 -- Historical notes -- Index of notation -- Index of terminology -- Summary of some important properties of Banach spaces


Mathematics Functional analysis Topology Mathematics Topology Functional Analysis



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