MATH 580 Functional Analysis (Formerly Applicable Analysis MATH 511): 3 hrs

Linear spaces, subspaces and linear span, examples of normed linear spaces, linear maps, null spaces, image spaces, invertibility, isomorphisms, normed linear spaces, product spaces, linear functionals, hahn-banach theorem, convergence and continuity, banach spaces,open mapping and closed graph theorems, inner product spaces, contraction mapping principle, orthogonal and complete orthonormal sets, hilbert spaces and linear operators. Prerequisite: MATH 511 or MATH 560