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. |
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Amer Assume B*-algebra Banach space Borel measure bounded Cauchy sequence Chapter closed subspace closure commutative Banach algebra compact subset compact support completes the proof contains continuous function continuous linear converges countable definition denotes equation Exercise exists extreme point F-space finite follows formula Fourier transform Fréchet space function ƒ G₁ Gelfand transform Hausdorff Hausdorff space Hence Hilbert space identity implies integral invertible involution isometry isomorphism Lebesgue Lemma linear functional locally convex Math maximal ideal metric multi-index multiplication neighborhood nonempty norm one-to-one open set operator in H polynomial proof of Theorem properties Prove satisfies scalar Section self-adjoint shows spectral subalgebra T₁ Theorem Suppose topological vector space topology unique unit ball unitary V₁ x₁ xe H