Instructor: Rowan Killip, 6935 Math Sciences Building.
Grading: There will be periodic homework, but no exams.
In the latter part of the course, we will follow
Methods of Mathematical Physics Vol. 1: Functional Analysis by M. Reed and B. Simon.
fairly closely. Other popular volumes on the subject are
Functional Analysis by P. Lax.
A Course in Functional Analysis by J. Conway
A proof of Fritz John's theorem can be found in Chapter 12 of
Topics in Banach Space Theory
by F. Albiac and N. Kalton.
For further discussion of (L1)* see
J. Schwartz, A note on the space $L_p^*$.
Proc. Amer. Math. Soc. 2 (1951), 270-275.
The original paper on Uniform Convexity is
J. Clarkson, Uniformly convex spaces. Trans. Amer. Math. Soc. 40 (1936), 396-414.
A simple proof of James' Theorem can be found in
R. C. James, Reflexivity and the sup of linear functionals. Israel J. Math. 13 (1972-3), 289--300.
For the sufficiency of Weyl's conditions (for prescribing singular values and eigenvalues) see
A. Horn, On the eigenvalues of a matrix with prescribed singular values. Proc. Amer. Math. Soc. 5 (1954), 4--7.
Homework: Problems
Notes: Compact operators