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MARC 21

Topological Vector Spaces: Chapters 1–5
Tag	Description
020	$a9783642617157
082	$a514
099	$aOnline resource: Springer
100	$aBourbaki, Nicolas.
245	$aTopological Vector Spaces$h[EBook]$bChapters 1–5$cby Nicolas Bourbaki.
260	$aBerlin, Heidelberg$bSpringer$c2003.
300	$aVII, 362 pages$bonline resource.
336	$atext
338	$aonline resource
440	$aElements of Mathematics
505	$aI. — 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.
520	$aThis 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).
538	$aOnline access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
710	$aSpringerLink (Online service)
830	$aElements of Mathematics
856	$uhttp://dx.doi.org/10.1007/978-3-642-61715-7