## 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 applied Assume B*-algebra Banach space Borel measure bounded Cauchy sequence Chapter closed subspace closure commutative Banach algebra compact set compact subset compact support completes the proof contains continuous function converges convex set countable definition denotes equation Exercise exists extreme point F-space finite follows formula Fourier transform Frechet space Gelfand transform Hahn-Banach theorem Hausdorff space Hence Hilbert space holds holomorphic functions hypothesis identity implies integral intersection invertible involution isometry isomorphism Lemma locally convex space Math metric multi-index multiplication neighborhood nonempty normed space null space numbers one-to-one open set operator in H polynomial proof of Theorem properties Prove satisfies Section self-adjoint seminorms shows spectral subalgebra Theorem Suppose topological vector space topology uniformly unique unit ball unitary weak*-topology weakly x e H y e H