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FUNCTIONAL ANALYSIS - ETH Z

FUNCTIONAL ANALYSISTheo B uhlerDietmar A. SalamonETH Z urichE-mail Subject 46-01 47-01 Key words and space, bounded linear operator, dualspace, dual operator, Arzel`a Ascoli, uniform boundedness, open mapping,closed graph, Hahn Banach, James space, weak and weak* topology,Banach Alaoglu, Banach Dieudonn e, Eberlein- Smulyan, Kre n Milman,ergodic theorem , closed image theorem , compact operator, Fredholmtheory, spectral theory, FUNCTIONAL calculus, Gelfand representation,spectral measure, unbounded operator, strongly continuous semigroup,infinitesimal generator, Hille Yosida Phillips, analytic book provides an introduction to the subject of Func-tional ANALYSIS for third year students of mathematics and physics witha basic knowledge of first year ANALYSIS and linear algebra as well as somecomplex ANALYSIS , point set topology, and measure and 1.

closes with a proof of the Baire category theorem. Chapter 2 is devoted to the three fundamental principles of functional analysis. They are the Uniform Boundedness Principle (a pointwise bounded family of bounded linear operators on a Banach space is bounded), the Open Mapping Theorem (a surjective bounded linear operator between Banach

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