Topological Vector Spaces Chapters 1-5
Başlık:
Topological Vector Spaces Chapters 1-5
ISBN:
9783642617157
Personal Author:
Edition:
1st ed. 2003.
Yayın Bilgileri:
Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2003.
Fiziksel Tanımlama:
VII, 362 p. online resource.
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 properties of Banach spaces.
Abstract:
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).
Ek Kurum Yazarı:
Dil:
English