0301712 Functional Analysis 3 Credit Hors.
Course Description :Hilbert spaces: the geometry of Hilbert space, the Riesz  representation theorem, orthonormal bases, isomorphic Hilbert  spaces, operators on Hilbert space: basic properties and examples, adjoints, projections, invariant and reducing  subspaces, positive operators and the polar decomposition, self-adjoint operators, normal operators,  isometric and unitary operators, the spectrum and the numerical range of an operator, operator inequalities, compact operators, Banach spaces: basic properties and examples, convex sets, subspaces and quotient spaces, linear functionals and the dual spaces, the Hahn-Banach theorem, the uniform boundedness principle, the open mapping theorem, and the closed graph theorem.
Department :Mathematics
Program :Masters In Mathematics
Course Level :Master
Course Outline :