18.102 | Spring 2009 | Undergraduate

Introduction to Functional Analysis


Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session


Analysis I (18.100); Linear Algebra (18.06), Linear Algebra (18.700), or Algebra I (18.701)


The course will be in three approximately equal parts (so about 4 weeks each).

  1. Normed spaces and a brief treatment of integration
    • Norms, bounded linear operators, completeness
    • Step functions, covering lemma, Lebesgue integrable functions
    • Fatou’s lemma, dominated convergence, L1
  2. Hilbert space
    • Cauchy’s inequality, Bessel’s inequality, orthonormal bases
    • Convex sets, minimization, Riesz’ theorem, adjoints
    • Compact sets, weak convergence, Baire’s theorem, uniform boundeness
  3. Operators on Hilbert space
    • Finite rank and compact operators
    • Spectral theorem for compact self-adjoint operators
    • Fourier series, periodic functions
    • Dirichlet problem on the interval, completeness of eigenfunctions


Grades will be computed by two methods — the cumulative and the hope-springs-eternal method with the actual grade the greater of the two.

  • First method: Homework 30, Tests 30, Final 40
  • Second method is based purely on the final

Course Info

As Taught In
Spring 2009
Learning Resource Types
assignment_turned_in Problem Sets with Solutions
grading Exams
notes Lecture Notes