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.

Syllabus and course policy

Lecture Notes:  Consolidated notes, Lecturenotes 1, Lecturenotes 2, Lecturenotes 3

Assignments: Assignment 0, Assignment 1, Assignment 2, Assignment 3, Assignment 4

Exams: Quiz-I, Quiz-II, Quiz-III, Quiz-IV