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 ont)

K-theory (see [5, 6, 7, 28]), Quillen’s determinant line bundle over the space of Fredholm operators (see [46, 52]), and the work of Gowers [17] and Argyros{ Haydon [4] on Banach spaces on which every bounded linear operator is the

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  Analysis, Theory, Functional, Space, Functional analysis

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