McGraw-Hill, 1973 - 397 Seiten
This 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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Topological Vector Spaces
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addition applied Assume balanced ball Banach algebra Banach space base Borel bounded called Cauchy sequence Chapter closed subspace closure collection commutative compact complex conclusion Consequently consists constant contains continuous functions continuous linear converges corresponds countable defined definition denotes dense distribution element equicontinuous example Exercise exists extension extreme point fact finite follows formula Fourier given gives Hence holds holomorphic hypothesis identity implies integral intersection invertible Lemma lies linear functional locally convex Math maximal means measure metric multiplication neighborhood norm normal Note numbers obvious one-to-one open set operator origin polynomial positive PROOF properties Prove range respect satisfies scalar separates shows statement subset Theorem Suppose topological vector space topology transform uniformly union unique unit weak weakly