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Full Description
The present book grew out of several courses which I have taught at the University of Zurich and at the University of Maryland during the past seven years. It is primarily intended to be a systematic text on locally convex spaces at the level of a student who has some familiarity with general topology and basic measure theory. However, since much of the material is of fairly recent origin and partly appears here for the first time in a book, and also since some well-known material has been given a not so well-known treatment, I hope that this book might prove useful even to more advanced readers. And in addition I hope that the selection ofmaterial marks a sufficient set-offfrom the treatments in e.g. N. Bourbaki [4], [5], R.E. Edwards [1], K. Floret-J. Wloka [1], H.G.Garnir-M.De Wilde-J.Schmets [1], AGrothendieck [13], H.Heuser [1], J. Horvath [1], J. L. Kelley-I. Namioka et al. [1], G. Kothe [7], [10], A P. Robertson- W.Robertson [1], W.Rudin [2], H.H.Schaefer [1], F.Treves [l],A Wilansky [1]. A few sentences should be said about the organization of the book. It consists of 21 chapters which are grouped into three parts. Each chapter splits into several sections.
Chapters, sections, and the statements therein are enumerated in consecutive fashion.
Contents
I: Linear Topologies.- 1 Vector Spaces.- 2 Topological Vector Spaces.- 3 Completeness.- 4 Inductive Linear Topologies.- 5 Baire Tvs and Webbed Tvs.- 6 Locally r-Convex Tvs.- 7 Theorems of Hahn-Banach, Krein-Milman, and Riesz.- II: Duality Theory for Locally Convex Spaces.- 8 Basic Duality Theory.- 9 Continuous Convergence and Related Topologies.- 10 Local Convergence and Schwartz Spaces.- 11 Barrelledness and Reflexivity.- 12 Sequential Barrelledness.- 13 Bornological and Ultrabornological Spaces.- 14 On Topological Bases.- III Tensor Products and Nuclearity.- 15 The Projective Tensor Product.- 16 The Injective Tensor Product.- 17 Some Classes of Operators.- 18 The Approximation Property.- 19 Ideals of Operators in Banach Spaces.- 20 Components of Ideals on Particular Spaces.- 21 Nuclear Locally Convex Spaces.- List of Symbols.
