. For the first part of the course I suggest you look at some of the following on-line notes to broaden your viewpoint!
Notes for the course
- I.F. Wilde's notes Only the first four chapters are really relevant for us and I will proceed a little more slowly.
- The coverage of WWL Chen's notes is a bit closer to what we will do
The first two chapters should help you to recall some of 18.100.
- Another useful set of notes are those by T.B. Ward Especially Chapters 1-5, but I will do a bit more on Lebesgue integration.
- For integration I will use a heavily modified version of (Jan) Mikusinski's approach which you can find in Debnaith and (Piotr) Mikusinski ``An introduction to Hilbert spaces with applications'' (Academic Press)
- A nice reference for Hilbert spaces is G.F. Simmons ``Introduction to Topology and Modern Analysis''
- You might like to look at P. Halmos' ``A Hilbert space problem book''
- A good over-all reference, a little more advanced than this course, is P.D. Lax's book ``Functional Analysis'' (Wiley-Interscience) -- a nice book to have.