MA543: Functional Analysis (July-Nov 2020)
Functional analysis is roughly mixing linear structure
with the topological structure on some reasonable sets. As an effect, there
always occurred some inherent problems which require further mathematics
attention. In this course, we discuss some of the fundamental results arisen
while mixing the above two structures. Namely, Hahn-Banach theorem, uniform
boundedness principle, open mapping theorem, and closed graph theorem, spectral
theorem, etc. We apply these results to study the topology of dual spaces and
spectrum of the certain linear transformations.
Lecture Notes: Lecturenotes 1, Lecturenotes 2, Lecturenotes 3
Assignments: Assignment 0, Assignment 1, Assignment 2, Assignment 3, Assignment 4