The main subjects of this course are complete normed vector spaces and bounded (continuous) linear operators. Highlights of the course include the following:

  * The open mapping theorem.
  * The closed graph theorem.
  * The Banach-Steinhaus theorem (the uniform boundedness principle).
  * The Hahn-Banach theorem.
  * Dual spaces.
  * Weak convergence.
  * The Banach-Alaoglu theorem.
  * The spectral theorem for bounded self-adjoint operators.
2010-02-04, hahamov