MTH-106.4 Functional Analysis
Normed Linear Spaces, Banach spaces, continuous linear functional, dual spaces.
Hahn-Banach theorem, applications of Baire Category Theorem: open mapping, closed graph and uniform boundedness theorems.
Weak, weak * topologies, Banach- Alaoglu Theorem, reflexivity.
Hilbert spaces, Reisz representation theorem, Adjoint, Hermitian, Normal, unitary operators, Compact operators. Spectral theorem for Compact Hermitian operators