Functional Analysis is the study of spaces of functions and various structures on these spaces, in
particular norms. This subject has important applications to differential and integral equations in
mathematics, engineering and physics.
The syllabus will consist of the following: bounded linear
operators between Banach and Hilbert spaces; operator topologies; classical spectrum of an
operator; fine analysis of the spectrum; axiomatic spectral theory; isolated spectral sets; compact,
Kato, Fredholm and Browder operators; self-adjoint, normal and unitary operators on a Hilbert space;
C* and von Neumann algebras.
Subject objectives
After completing this subject, students will gain:
- familiarity with the theory of bounded linear operators
- an understanding of the spectral theory of operators
- recognition of familiar spaces in terms of their more formal properties
- exposure to applications in the solutions of linear equations in abstract spaces
- exposure to applications in physics
- the ability to pursue further studies in this and related areas