Introduces such topics as Banach spaces (Hahn-Banach theorem, open mapping theorem, etc.), operator theory (compact operators and integral equations, and spectral theorem for bounded self-adjoint operators), and Banach algebras (the Gelfand theory). See also MATH 8340. Prereqs., MATH 6310 and 6320. Undergraduates must have approval of the instructor. Prerequisites: Restricted to Graduate Students only.