Office Hours: Tu 5:30-6pm, Thur: 1-2:30pm, 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. Chapter 1, 2.1 and 3 of Peter Lax.

Week 2: The geometric H-B theorem, complex H-B theorem, metric spaces, normed linear space. Chapter 3, 5 of Peter Lax.

Problems: Homework set 1 (Due Sept. 22 )

Week 3: normed linear space, Inner product space Chapter 5, 6 of Peter Lax.

Problems: Homework set 2 (Due Sept. 29)

Week 4: Hilbert space, Bounded linear map, Chapter 6, Chapter 15.1 of Peter Lax.

Problems: Homework set 3 (Due Oct. 6)

Week 5: Duals of normed linear spaces, Chapter 8 of Peter Lax

Problems: Homework set 4 (Due Oct. 13)

Week 6: Dual of C[0,1], Radon-Nikodym theorem, Baire category theorem, open mapping theorem, Chapter 15 of Peter Lax

Problems: Homework set 5 (Due Oct. 20)

Week 7: weak convergence, weak * convergence, Chapter 10 of Peter Lax

Problems: Homework set 6 (Due Oct. 27)

Week 8: weak convergence, weak * convergence, and applications. Chapter 9.3, 10, 11.4, 15 of Peter Lax

Problems: Homework set 7 (Due Nov. 8)

Week 9: Banach algebra and their elementary spectral theory, Chapter 17 of Peter Lax

Problems: Homework set 8 (Due Nov. 17)

Week 10: Spectral theory, compact maps. Chapter 20 and Chapter 21 of Peter Lax

Problems: Homework set 9 (Due Nov. 29)

Week 11, 12: Spectral theory of compact maps, example of compact maps, Chapter 21 and Chapter 22 of Peter Lax

Problems: Homework set 10 (Due Dec. 8)

Week 13, 14: Compact self-adjoint, self-adjoint operators on Hilbert spaces. Chapter 28 and Chapter 31 of Peter Lax

Syllabus