Math 6483

Functional Analysis II

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 bugguide.net.)

Instructor: John Albert
Office: PHSC 1004
Office hours: Mondays and Wednesdays 2:30 to 3:30, Thursdays 10:30 to 11:30 (or by appointment)
Phone: 325-3782
E-mail: jalbert@ou.edu

Assignments

  • Assignment 1: Exercises 7.1, 7.2(c,d,e,f), 7.5(a), 7.6, 7.9, and 7.10 from Prof. Remling's lecture notes.
  • Assignment 2: Exercises 8.1, 8.5, 8.7, 8.9, 8.10 from Prof. Remling's lecture notes.
  • Assignment 3: Exercises 10.19 and 10.20 from Prof. Remling's lecture notes, also problem written on board in class.
  • Assignment 4: Exercises 6.1 and 6.3 from chapter 6 of "Functional Analysis, Sobolev Spaces, and Partial Differential Equations" by Brezis (see handout).

    Links

  • The book which Chun-Hsien mentioned in class as having a nice collection of examples in operator theory is ``Basic Operator Theory'' by Israel Gohberg and Seymour Goldberg.
  • The theorem we proved in class which states that the topology of a compact space K is determined by the algebraic structure of the space of continuous functions on K is known as the Banach-Stone theorem. The paper Variations on the Banach-Stone Theorem by M. Garrido and J. Jaramillo reviews this result and some of its generalizations.
  • Here is a nice discussion of the Gelfand-Naimark and Banach-Stone theorems on Math Stack Exchange.
  • Part one of Christian Remling's lecture notes on Functional Analysis. There is also a second part, whose chapters can be found here.