Course: MAT 476 3.0 Functional Analysis (Compulsory)
Course content:
Inequalities (Hlder, Minkowski and Cauchy-Schwarz), Metric Spaces, Linear Spaces, Definitions and Elementary Properties, Illustrations of Normed and Banach Spaces, Illustrations of Incomplete Spaces, Subspaces, Separable Spaces, Quotient Spaces, Completion of Normed Spaces , Inner Product Spaces, Bounded Linear Operators Definitions and elementary properties , Continuity and Boundedness of Linear Operators, Equivalent Norms, Finite Dimensional Normed Spaces and Compactness, Spaces of Bounded Linear Operators, Dual Space, Bounded Linear Functional Definitions and Elementary Properties , Different forms of Hahn-Banach Theorem, Uniform Bounded Principle , Weak Convergence, Open Mapping Theorem, Closed Graph Theorem.
Recommended Readings:
First Course in Functional Analysis by C. Goffman & G. Pedrick, Introduction To Functional Analysis by S.C. Bose, Linear Functional Analysis by Bryan Rynne and M.A. Youngson