Baire category; Banach spaces and linear operators; Fundamental theorems: Open Mapping Theorem, Closed Range Theorem, Uniform Boundedness Principle, Hahn-Banach Theorem; Convexity; reflexive spaces; Spectral theory.
Learning objective
Lecture notes
M. Struwe: "Funktionalanalysis I" (lecture notes in German). There are also several excellent texts in English or in German.
