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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. Foundations1 Metric Spaces and Compact Sets2 Finite-Dimensional Banach Spaces17 The Dual Space25 Hilbert Spaces31 Banach Algebras35 The Baire Category Theorem40 Problems45 Chapter 2.

§5.3. Operators on Hilbert Spaces 222 §5.4. Functional Calculus for Self-Adjoint Operators 234 §5.5. Gelfand Spectrum and Normal Operators 246 §5.6. Spectral Measures 261 §5.7. Cyclic Vectors 281 §5.8. Problems 288 Chapter 6. Unbounded Operators 295 §6.1. Unbounded Operators on Banach Spaces 295 §6.2. The Dual of an Unbounded Operator ...

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