MATH 7355 - Functional Analysis I

Credit Hours: (3)

Description Metric spaces, normed and Banach spaces, linear functionals, linear operators, examples of Banach spaces: Lebesgue spaces, spaces of continuous functions, sequence spaces, inner product and Hilbert spaces; form of functionals on Banach spaces, compactness in Banach spaces, Hahn-Banach Theorem, adjoint operators, Uniform Boundedness Theorem, Open Mapping Theorem, Closed Graph Theorem, Banach Fixed Point Theorem, applications to integral equations, Spectral Theorem for compact/bounded operators on Hilbert spaces and/or spectral measures. PREREQUISITE(S): MATH 7350 or instructor permission