Functional AnalysisThis classic text is written for graduate courses in functional analysis. This text is used in modern investigations in analysis and applied mathematics. This new edition includes up-to-date presentations of topics as well as more examples and exercises. New topics include Kakutani's fixed point theorem, Lamonosov's invariant subspace theorem, and an ergodic theorem. This text is part of the Walter Rudin Student Series in Advanced Mathematics. |
Contents
Topological Vector Spaces | 3 |
Chapter 2 | 41 |
The closed graph theorem | 49 |
Copyright | |
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A₁ Assume Banach algebra Banach space bounded Cauchy sequence closed subspace closure commutative compact set compact subset compact support completes the proof complex contains continuous functions continuous linear functional converges convex hull convex set countable defined definition denote dense Exercise exists extreme point F-space finite follows Fourier transform Fréchet space function ƒ H₁ Hausdorff space Hence Hilbert space holomorphic functions hypothesis implies integral intersection invertible isometry L¹(R Lemma linear mapping locally convex space Math metric multi-index neighborhood nonempty normed space numbers one-to-one open mapping open set operator polynomial properties Prove satisfies Section seminorms separates points shows subspace t₁ Theorem Suppose topological vector space topology uniformly unit ball V₁ weak*-topology weakly x₁ y₁