Mathematics

Functional Analysis

Module code: G1029
Level 6
15 credits in autumn teaching
Teaching method: Lecture
Assessment modes: Unseen examination, Coursework

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.