McGraw-Hill, 1991 - 424 páginas
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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addition applied Assume Banach algebra Banach space Borel bounded called Chapter closed 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 Fourier transform function f given gives Hence Hilbert space holds holomorphic ideal identity implies integral invertible Lemma lies linear functional locally mapping Math maximal means measure multiplication neighborhood norm normal Note obtain one-to-one open set operator polynomial positive PROOF properties Prove range result satisfies scalar self-adjoint separates sequence shows spectral subset subspace Theorem Suppose tion topological vector space topology unique unit