Topological vector spaces, Volume 1

This is a softcover reprint of the 1987 English translation of the second edition of Bourbaki's Espaces Vectoriels Topologiques. Much 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, reflecting decades of progress in the field. 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). It is equivalent to saying that E is a topological left K-module (GT, III, § 6.6).