Module code: G1029
15 credits in autumn teaching
Teaching method: Lecture
Assessment modes: Coursework, Unseen examination
In this module, you cover:
- Banach spaces, Banach fixed-point theorem, Baire's theorem
- bounded linear operators and on Banach spaces, continuous linear functionals, Banach-Steinhaus uniform boundedness principle
- open mapping and closed graph theorems, Hahn-Banach theorem
- Hilbert spaces, orthogonal expansions, Riesz representation theorem.
Module learning outcomes
- A successful student should:know the basic facts and the definitions about Hilbert and Banach spaces and their duals;
- be able to state and sketch the ideas of the proofs of the following basic theorems and principles: Baire, Banach-Steinhaus, Hahn- Banach, closed graph, open mapping; contraction mapping theorem.