MTL411: Functional Analysis

3 Credits (3-0-0)

Pre-requisites: MTL104 and MTL122

Overlaps with: MTL602

Review of some basic concepts in metric spaces and topological spaces; Normed linear spaces and Banach spaces, Examples of Banach spaces, Bounded linear operators and examples, Finite dimensional Banach spaces; Introduction of Lebesgue integration on real line, Fatou’s lemma, monotone convergence theorem, dominated convergence theorem, Lp spaces; Hahn Banach extension theorem, Hahn Banach separation theorem, Uniform boundedness principle, Open mapping theorem, Closed graph theorem; Characterization of dual of certain concrete Banach spaces; Schauder basis and separability, Reflexive Banach spaces, Best approximation in Banach spaces; Hilbert spaces and their geometry; Basic operator theory.