Functional Analysis I

4 credits

First course in graduate functional analysis. Locally convex spaces, weak topologies. Convexity and fixed point theorems. Banach algebras and C*-algebras. Operators on Hilbert spaces (bounded, unbounded, compact, normal). Spectral theory of operators, semigroups of operators. Fredholm theory. Prerequisites: MATH 240C. Students who have not completed MATH 240C may enroll with consent of instructor.