Professor David Blecher

Welcome to Functional analysis II (Math 7321)

Time and place : MWF 10-11 am in AH106 (NOTE CHANGE OF TIME AND PLACE)

Office Hours MW: 1-2:30pm (or by appointment--email or call 713-743-3451)

Email: dblecher@math.uh.edu

Final exam: Date to be announced.


Prerequisites: Functional analysis I (Math 7320 or some basic knowledge of Banach spaces, and Hilbert spaces) or consent of instructor. 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" and "A course in operator theory", Gerd Pedersen's "Analysis Now". Other books on advanced topics will be mentioned later when we encounter those topics.
Course description: I. Operator theory on Hilbert and Banach spaces II. Algebras and spectral theory. Commutative Banach algebras and the Gelfand transform. The characterization of commutative C*-algebras and the functional calculus for normal operators. The spectral theorem for normal operators. The Fourier transform for locally compact groups. III. Unbounded operators. IV. Special topics. A choice of: Von Neumann algebras, Fredholm theory, Fixed point theorems, Distributions, Nonselfadjoint operator algebras, Approved student requests.
Final grade is aproximately based on a total score of 300 points consisting of homework (100 points), a semester test (100 points), and a project/final exam (100 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.