Course: MAT 476 3.0 Functional Analysis (Compulsory)
Course content:
Preliminaries, Normed spaces, Finite and infinite dimensional normed spaces, Equivalence of norms, l^p and function spaces, Convergence and Completeness, Riesz Lemma, Compactness in normed spaces, Banach Spaces, Bounded linear operators, Open mapping theorem and related results, Dual Spaces, Hahn Banach Theorem, Hilbert spaces, Operators on Hilbert spaces.
Recommended Readings:
- Rynne, B. & Youngson, M. A., Linear Functional Analysis, 2nd Springer (Undergraduate Mathematics Series), 2007
- Pedersen, G. K., Analysis Now, Springer (Graduate Texts in Mathematics), 2001
- Bollobas, B., Linear Analysis (An Introductory Course); 2nd Cambridge University Press, 1999
- Kreyszig, E., Introductory Functional Analysis with Applications 1st, Wiley, 1989
- Schechter, , Principles of Functional Analysis 2nd ed., American Mathematical Society (Graduate Studies in Mathematics), 2001