Math 6473

Functional Analysis I

Fall 2013

Oklahoma brown tarantula (Ophonopelma hentzi). A few years back, the American Arachnological Society held its annual meeting at O.U., and a session was held in which the public was invited to see specimens of interesting spiders, and to bring in their own specimens for the experts to identify. On our way to the public session we saw one of these tarantulas crossing East Lindsey Street, and were able to pick it up and bring it in. The experts at the session told the audience that it was a male who had been wandering around looking for females, and that at this point in its life cycle probably only had a short time left to live --- so they encouraged us to take it back, afterwards, to where we found it, and let it continue its search. (Photo copyright 2008 by Charles Schurch Lewallen, taken from

Instructor: John Albert
Office: PHSC 1004
Office hours: Mondays and Fridays 12:30 to 1:30, Thursdays 9:30 to 10:30 (or by appointment)
Phone: 325-3782


  • Assignment 1 (due Friday Sept. 6)
  • Assignment 2 (due Friday Sept. 27)
  • Assignment 3 (due Friday Oct. 18)
  • Assignment 4: Exercises 5.3, 5.6, 5.8, 5.11, 5.12 from Prof. Remling's lecture notes.


  • Here is the theorem we were proving on what was supposed to be the next-to-last day of class, but turned out the be the last day of class.
  • Part one of Christian Remling's lecture notes on Functional Analysis. There is also a second part, whose chapters can be found here.
  • You can find a nice discussion proof of the Riesz Representation Theorem for the dual of C(K) in these lecture notes by Denis Labutin.
  • There is also an illuminating discussion in these notes on the Riesz-Markov representation theorem by William Arveson. In particular, he explains what happens when the underlying space is not compact, only locally compact.
  • Topics in Real and Functional Analysis, a text by Gerard Teschl.
  • The lecture notes Functional Analysis - Gently Done by Dr. I. F. Wilde give a nice introduction to the basics of functional analysis, with all the details written out clearly, and lots of illustrative examples. It does not cover Hilbert spaces, though. There are other notes on related material by Dr. Wilde at this page.
  • Prof. Efe A. Ok has written, or is writing, two interesting and useful introductory texts on real analysis and functional analysis, called "Real Analysis with Economic Applications" and "Probability with Economic Applications". They are well-written and entertaining, and go into the subjects in enough detail that even people familiar with the topics will likely find a lot that is new to them. (The book with "Real Analysis" in its title contains an introduction to functional analysis, and the book with "Probability" in its title contains an introduction to measure and integrals, usually covered in Real Analysis courses.) You can find chapters from these texts at
  • "This ain't no meager theorem", an article by Dylan Wilson on the many uses of the Baire category theorem.