Mathematics MA3422, Functional Analysis II
Notes
Some (not all) parts of the course notes will be in the form of a handout or will be available here. All will be in PDF format.
- Chapter 1, Hilbert Spaces
- Definition and examples. Orthonormal bases. Parallelogram Identity. Spaces of operators or functionals. Dual of a Hilbert space. Algebra of operators.
- Chapter 2, Main theorems on Banach spaces
- Direct sum of two normed spaces. Closed graph theorem. Uniform boundedness theorem. Zorn's lemma. Hahn-Banach Theorem. Definition of reflexivity.
- Chapter 3, Weak topologies and Tychonoff's theorem
- Locally convex topological vector spaces. Weak and weak*-topologies.