Professor David Blecher

Welcome to Functional analysis I (Math 7320)

Time and place : MWF 10-11 am in SW102

Office Hours MWF: 1-2pm (or by appointment--email or call 713-743-3451)

Email: dblecher@math.uh.edu

Last date to drop with refund: Sept 12.

Final exam: Date to be announced.


Prerequisites: Graduate real variables (Math 6320-21) or equivalent, would be nice but not required. A little topology and metric spaces would be useful.
Text: Typed notes will be provided.
Recommended reading: J. B. Conway's "A course in Functional Analysis", Gerd Pedersen's "Analysis Now", and Megginson, "An introduction to Banach space theory".
Course description: Although we will be starting from scratch, if you wish to do some preliminary reading you could read the middle section in Royden's book on Real Analysis (on the Hahn Banach theorem, and so on). We will be starting with a little topology - so you might glance through any good basic book on topology to familiarize yourself with "compactness" , "locally compact", continuous functions between topological spaces, the basic theory of metric spaces. The reason I review some topology is to familiarize the students with the use of `nets' (=generalized sequences). We will mostly avoid measure theory, so don't be too concerned if you lack that background. The tests and exam will be based on the notes given in class, and on the homework. After each chapter we will schedule a problem solving workshop, based on the homework assigned for that chapter.
Final grade is aproximately based on a total score of 400 points consisting of homework (100 points), a semester test (100 points), and a final exam (200 points). The instructor may change this at his discretion.
This semester will be a leisurely and general presentation, starting from scratch, of the basic facts in Linear Analysis, Banach spaces, weak topologies, and a little spectral theory.
Please send me an email (or give me your email address) so that you can get the regular course emailings. Almost all course communication and instructions, assignments, keys etc. will be sent by email.