Professor David Blecher
Welcome to Operator Theory (Math 6395)
Time and place : MWF 10-11 am in PGH 348
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: February 1. Last date to drop with W: April 3
Final exam: 11-2 Friday May 4.
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 Operator Theory", and "A course in Functional Analysis",
Gerd Pedersen's "Analysis Now",
and Arveson's "A short course in spectral theory".
Course description: An "operator" is a linear function between normed vector spaces (or between Hilbert spaces), usually continuous. Operator theory is a signicant part of many important areas of modern mathematics and mathematical physics. A subtitle for the course might be `Spectral Theory'. Spectral theory in some sense is the generalization to operators of the theory and applications of eigenvalues of matrices. This course covers the central themes of operator theory. We begin with Hilbert spaces, and the spectral theorem for compact operators. We continue discussing (in the setting of Banach spaces) compact operators, Fredholm operators and the Calkin algebra. We then turn to Gelfand's theory of commutative Banach algebras, and use this to develop the functional calculus and spectral theorem for normal operators. We also discuss Hilbert-Schmidt operators, the trace, index theory, and the Schatten classes. Finally we develop the very basics of the theory of C*-algebras and von Neumann algebras. If time permits we will study unbounded operators.
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.
Please send me an email (or give me your email address)
so that you can get the regular course emailings.
Homework assignment 1
Homework assignment 1 key
Assignments for later chapters are contained in the typed classnotes,
and keys will be emailed to all students.
The midterm Test will be in April, and will cover Chapters 1--3.
The Final Exam will be in May, and will cover Chapter 4 and parts
of Chapter 2.
Mock exam for midterm
Midterm test