## 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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### Contents

Topological Vector Spaces | 3 |

Completeness | 41 |

Convexity | 55 |

Copyright | |

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### Common terms and phrases

Amer applied Assume Banach space Borel measure Cauchy sequence closed subspace closure commutative Banach algebra compact set compact subset compact support complement completes the proof contains continuous functions continuous linear functional converges convex hull convex set countable definition denotes differential E(co entire function equation Exercise exists extreme points F-space finite follows formula Fourier transform Frechet space Gelfand transform Hausdorff space Hence Hilbert space holds holomorphic functions hypothesis identity implies integral intersection invertible involution isometry Lemma linear mapping locally convex space Math maximal ideal metric multi-index neighborhood nonempty normed space null space numbers one-to-one open mapping open set operator in H polynomial proof Let proof of Theorem properties Prove quotient satisfies Section self-adjoint seminorms separates points shows spectral Theorem Suppose topological vector space topology uniformly unique unit ball weak*-topology weakly x e H