Prof. Richard Melrose
This is a undergraduate course. It will cover normed spaces, completeness, functionals, Hahn-Banach theorem, duality, operators; Lebesgue measure, measurable functions, integrability, completeness of L-p spaces; Hilbert space; compact, Hilbert-Schmidt and trace class operators; as well as spectral theorem.
Melrose, Richard. 18.102 Introduction to Functional Analysis, Spring 2009. (MIT OpenCourseWare: Massachusetts Institute of Technology), http://ocw.mit.edu/courses/mathematics/18-102-introduction-to-functional-analysis-spring-2009 (Accessed). License: Creative Commons BY-NC-SA