Functional AnalysisFunctional Analysis |
Contents
| 17 | |
Chapter 3 Linear Functionals | 37 |
Chapter 4 The Weak Topology | 55 |
Chapter 5 More about Weak Topologies | 75 |
Chapter 6 Applications to Analysis | 87 |
Chapter 7 The Theory of Distributions | 101 |
Solutions to Starred Problems in Chapters 14 | 145 |
Reflexive Banach Spaces | 159 |
| 161 | |
| 163 | |
Common terms and phrases
assume C*-function Cauchy sequence Cesaro means Chapter choose Clearly closure codimension compact operator compact set compact subset compact support contains converges to zero Corollary countable Definition denote dense distribution in Q dual space element equation equivalent Exercises family of seminorms finite dimensional fixed follows Fourier series Fourier transform functional f Hahn–Banach theorem Hausdorff Hence inequality Lemma let f let G linear functional linear map linear subspace locally convex space locally convex topology metric multi-index neighborhood of zero nonzero norm closed norm topology normed space null space positive integer positive number problem 1b Proof properties prove real linear functional real number real-valued recall reflexive Banach space satisfies scalar Schauder basis Section 4.1 seminorms sequence of points ſº space and let supp Suppose t-bounded tends to zero topological isomorphism unit ball vector space weak topology