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FUNCTIONAL ANALYSIS - People

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.

functional analysis is the study of Banach spaces and bounded linear opera-tors between them, and this is the viewpoint taken in the present manuscript. This area of mathematics has both an intrinsic beauty, which we hope to convey to the reader, and a vast number of applications in many elds of mathematics.

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