Locally Convex Spaces [Paperback]

I: Linear Topologies.- 1 Vector Spaces.- 1.1 Generalities.- 1.2 Elementary Constructions.- 1.3 Linear Maps.- 1.4 Linear Independence.- 1.5 Linear Forms.- 1.6 Bilinear Maps and Tensor Products.- 1.7 Some Examples.- 2 Topological Vector Spaces.- 2.1 Generalities.- 2.2 Circled and Absorbent Sets.- 2.3 Bounded Sets. Continuous Linear Forms.- 2.4 Projective Topologies.- 2.5 A Universal Characterization of Products.- 2.6 Projective Limits.- 2.7 F-Seminorms.- 2.8 Metrizable Tvs.- 2.9 Projective Representation of Tvs.- 2.10 Linear Topologies on Function and Sequence Spaces.- 2.11 References.- 3 Completeness.- 3.1 Some General Concepts.- 3.2 Some Completeness Concepts.- 3.3 Completion of a Tvs.- 3.4 Extension of Uniformly Continuous Maps.- 3.5 Precompact Sets.- 3.6 Examples.- 3.7 References.- 4 Inductive Linear Topologies.- 4.1 Generalities.- 4.2 Quotients of Tvs.- 4.3 Direct Sums.- 4.4 Some Completeness Results.- 4.5 Inductive Limits.- 4.6 Strict Inductive Limits.- 4.7 References.- 5 Baire Tvs and Webbed Tvs.- 5.1 Baire Category.- 5.2 Webs in Tvs.- 5.3 Stability Properties of Webbed Tvs.- 5.4 The Closed Graph Theorem.- 5.5 Some Consequences.- 5.6 Strictly Webbed Tvs.- 5.7 Some Examples.- 5.8 References.- 6 Locally r-Convex Tvs.- 6.1 r-Convex Sets.- 6.2 r-Convex Sets in Tvs.- 6.3 Gauge Functionals and r-Seminorms.- 6.4 Continuity Properties of Gauge Functionals.- 6.5 Definition and Basic Properties of Lc,s.- 6.6 Some Permanence Properties of Lc,s.- 6.7 Bounded, Precompact, and Compact Sets.- 6.8 Locally Bounded Tvs.- 6.9 Linear Mappings Between r-Normable Tvs.- 6.10 Examples.- 6.11 References.- 7 Theorems of Hahn-Banach, Krein-Milman, and Riesz.- 7.1 Sublinear Functionals.- 7.2 Extension Theorem for Lcs.- 7.3 Separation Theorems.- 7.4 Extension Theorems for Normed Spaces.- 7.5 The Krein-Milman Theorem.- 7.6 The Riesz Representation Theorem.- 7.7 References.- II: Duality Theory for Locally Convex Spaces.- 8 Basic Duality Theory.- 8.1 Dual Pairings and Weak Topologies.- 8.2 Polƒ‰