Transcription of FUNCTIONAL ANALYSIS - ETH Z
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FUNCTIONAL ANALYSIS - ETH Z
FUNCTIONAL ANALYSISTheo B uhlerETH Z urichDietmar A. SalamonETH Z urich8 June 2017iiPrefaceThese are notes for the lecture course FUNCTIONAL ANALYSIS I held by thesecond author at ETH Z urich in the fall semester 2015. Prerequisites arethe first year courses onAnalysisandLinear Algebra, and the second yearcourses onComplex ANALYSIS ,Topology, andMeasure and material of Subsection on elementary Hilbert space theory, Sub-section on the Stone Weierstra Theorem, and the appendices on theLemma of Zorn and Tychonoff s Theorem has not been covered in the lec-tures. These topics were assumed to have been covered in previous lecturecourses. They are included here for completeness of the material of Subsection on the James space, Section on thefunctional calculus for bounded normal operators, Chapter 6 on unboundedlinear operators, Subsection on Banach space valuedLpfunctions, Sub-section on self-adjoint and unitary semigroups, and Section on an-alytic semigroups was not part of the lecture course (with the exception ofsome of the basic definitions in Chapter 6 that are relevant for infinitesimalgenerators of strongly continuous semigroups, namely, parts of Section onthe dual of an unbounded operator on a Banach space and Subsection the adjoint of an unbounded operator on a Hilbert space).
The material of Subsection 1.3.3 on elementary Hilbert space theory, Sub-section 5.4.2 on the Stone{Weierstraˇ Theorem, and the appendices on the ... quantum mechanics, probability theory, geo-metric group theory, dynamical systems, ergodic theory, and approximation theory, among many others. While we say little about speci c applications ...
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