Introduction to Functional Analysis (MIT 18.102)
by Casey Rodriguez · MIT OpenCourseWare
Analysis on infinite-dimensional spaces: normed and Banach spaces, the Hahn-Banach theorem and duality, bounded operators, Lebesgue measure and Lp spaces, Hilbert spaces, compact and self-adjoint operators, and the spectral theorem. Includes 23 lecture videos, extensive lecture notes, problem sets and exams.
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Linear Operators in Hilbert Spaces
Graduate text (Springer GTM 68) on the theory of bounded and unbounded operators in Hilbert spaces, covering self-adjoint extensions, spectral theory, and perturbation theory, with applications to differential operators from quantum mechanics. Assumes measure theory and basic functional analysis.