Functional Analysis

3 Credits · Level: Graduate, Undergraduate

This is a PhD level course. Hilbert spaces, Banach spaces, convergence in topological vector spaces, dual spaces, Riesz representation theorem, Theorem of Hahn-Banach, open mapping theorem, closed graph theorem, principle of uniform boundedness, spectral theorem for (un)bounded operators, semigroups of linear operators, Fredholm operators, and Fredholm index.