Functional Analysis (GATE MA) — GATE Mathematics (MA) Prep

Normed linear spaces, Bounded linear operators and compact linear operators, Banach spaces, Separability, Dual spaces, Hahn-Banach theorem, open mapping and closed graph theorems, principle of uniform boundedness; Inner-product spaces, Hilbert spaces, orthonormal bases, projection theorem, Riesz representation theorem, spectral theorem for compact self-adjoint operators.