## 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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addition applied Assume balanced ball Banach algebra Banach space base Borel bounded called Cauchy Chapter closed subspace closure collection commutative compact complex conclusion consequence consists constant contains converges convex corresponds defined definition denotes dense differential distribution element equation equicontinuous example Exercise exists extension fact finite follows formula function f given gives Hence holds holomorphic hypothesis ideal identity implies integral intersection invertible Lemma lies linear functional mapping Math maximal means measure metric multiplication neighborhood norm normal Note numbers obtain one-to-one open set operator origin polynomial positive PROOF properties Prove range result satisfies scalar self-adjoint separates sequence shows spectral statement subset Theorem Suppose theory tion topological vector space topology union unique unit