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May 22, 2026
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MATH 641 - Functional Analysis I3 Credit Hours
Hilbert spaces: orthonormal bases, orthogonal projections, duality, the spectral theorem for compact, self-adjoint operators. Banach spaces: the uniform boundedness, open mapping, closed graph, and Hahn-Banach theorems, adjoints, duality, weak and weak-* topologies. Additional topics in the theory of linear operators on Hilbert and Banach spaces as chosen by instructor.
Repeatability: May be repeated. Maximum 6 hours. Maximum 2 times.
(RE) Prerequisite(s): Math 545, Math 546, or Math 443
Recommended Background: Some knowledge in point set topology.
Registration Restriction(s): Minimum student level – graduate.
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