Office Hours: MW:4pm-5:30pm, and by appointment.

734-764-6898, sijue@umich.edu

Office: 4064 East Hall.

Weekly Schedule:

Week 1: Linear spaces, linear functionals, the Hahn-Banach Theorem, The Geometric H-B Theorem, complex H-B Theorem, normed linear spaces. Chapter 1, 2.1 and 3 of Peter Lax.

Problems: Homework set 1 (Due Sept. 14)

Week 2: Normed linear space, Hilbert space, Chapter 5, 6, of Peter Lax.

Problems:

Week 3, 4: Hilbert space, Chapter 6 of Peter Lax.

Problems: Homework set 2 (Due Sept. 23)

Week 5: Radon-Nikodym Theorem, Dirichlet's problem, dual spaces, Chapter 7, 8 of Lax

Problems: Homework set 3 (Due Oct. 7)

Week 6: reflexive Banach spaces, dual of Lp, Baire Category Theorem, Open Mapping Theorem, Chap 8, 15 of Lax

Problems: Homework set 4 (Due Oct. 14)

Week 7: Closed graph Thm, Uniform boundedness principle, Banana-Steinhaus Thm, weak convergenece, Chap. 15, 10 of Lax

Problems: Homework set 5 (Due Oct. 21)

Week 8: weak convergence, weak* convergence, transpose, strong and weak convergence of operators Chap. 10, 15 of Lax

Problems: Homework set 6 (Due Oct. 28)

Week 9: Applications, Elementary spectral theory, Chap. 11, 17 of Lax

Problems: Homework set 7 (Due Nov. 4)

Week 10: Elementary spectral theory, examples, Chap. 17, 20 of Lax

Problems: Homework set 8 (Due Nov. 11)

Week 11, Compact operators, Fredholm Alternative Chap. 21 of Lax

Problems: Homework set 9 (Due Nov. 18)

Week 12: Fredholm Alternative, The Spectral Theory of compact operators, symmetric operators, Chap. 21, 28 of Lax

Problems: Homework set 10 (Due Dec. 2)

Week 13, 14: compact symmetric operators, Applications chap. 28, 22 of Lax

Syllabus