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These are notes for the lecture course “Functional Analysis I” held by the second author at ETH Zurich in the fall semester 2015. Prerequisites are the first year courses on Analysis and Linear Algebra, and the second year courses on Complex Analysis, Topology, and Measure and Integration. The manuscript is addressed primarily to third year students of mathematics or physics, and the reader is assumed to be familiar with first year analysis and linear algebra, as well as complex analysis and the basics of point set topology and measure and integration. We also restrict the discussion to linear operators and say nothing about nonlinear functional analysis. Each of the seven chapters ends with a problem section, which we hope will give the interested reader the opportunity to deepen their understanding of the subject.
Foundations.
Principles of Functional Analysis.
The Weak and Weak* Topologies.
Fredholm Theory.
Spectral Theory.
Unbounded Operators.
Semigroups of Operators